Who is Judas, according to John? Part 1

This text was traditionally attributed to the author known variously as the “Apostle”, “St. John”, or “John the Evangelist”. It seems that after Pentecost he made his home on the West Coast of Asia Minor and his students compiled this work as well as those given under the name of John in the New Testament, the three Epistles of John and the book of Revelations.

It seems that these are among the latest of the works in the New Testament, and the Gospel of John has a well-known contrast from the other three who are known collectively as the “Synoptic Gospels”, either because they seem more similar or because they see things similarly to each other and thus differently from John. While there are a few details of the story that differ in John, none of these are very important in my view and we shall not focus on them in this work.

The basic background to this story comes out when we consider the recent history of this time. At this Beginning with the life of Jesus, there were differences between the three main factions that we find in the New Testament: “the Jews”, the Romans, and the Christians. Now of course during the life of Jesus, all or most Christians were Hebrew, and all Romans were non-Christian. However, by the time of the writing of the Gospel of John this was no longer the case; numerous Hebrews, Greeks, and Romans had accepted Christianity and the divide between Christians and what became known as “the Jews” became wider. In the works of John, we find that Jews and Christians are somewhat enemies. Now of course this has been the case since the earliest written works by Christians, the letters of Paul. Paul’s own backstory is itself part of this violent persecution, and the Gospel of John seeks to tell a story that dramatizes the relations between these three factions. I will comment on this story in the blocks of story given in my own New American Standard Bible.

Judas is an interesting character in this story, and it would be useful to write an entire book on him, especially since there are noncanonical and heretical “Gospels of Judas” that have recently been rediscovered. I will ignore these for the moment. My own interpretation begins with the idea that most of the narrative of this and other Gospels was written as a Christian supplement to the Jewish liturgical readings of the day. Both Jews and Christians (then as now) have a series of readings at various times during the year; for example at one time (the holiday of Shavuot, the Hebrews would celebrate the giving of the Law on Mt. Sinai, and the early Christians at that same time would supplement the reading of the Mt. Sianai story with the reading of the Beatitudes of the Gospel’s “Sermon on the Mount”. Likewise on passover the Jewish reading is of the original Passover story of the Tenth Plague of Egypt which killed the firstborn. According to my own view the first Christians would read this during that same holiday and supplement it with the Easter story as given in the Gospels, which took place at Passover and elaborated on it. Now Judas was one of the Twelve Apostles who were taught and led by Jesus. Since everything in the New Testament is in our view a recapitulation of something from the Old, it seems to me that this is God’s new version of the Twelve Sons of Israel (Jacob), each of whom were given a part in the Holy Land. The founding of Christianity is meant to be a recapitulation of this. While each Israelite could trace their own descent from one of the sons of Israel, each Christian could trace another sort of descent from one of the Twelve Apostles. A descent not “of the flesh” but one “of the spirit”.1 By this I refer to the idea that the Twelve went out into the world and preached the gospel and founded churches in nations as far away as India (for St. Thomas) and Russia (for St. Andrew). People of that time knew who brought the gospel to their area by what their parents and elders told them. Take for example the author of the Gospel of John, who would have been remembered as the person who brought the Gospel to the area of what we now call Turkey where the cities of Laodicea, Thyatira, Ephesus, et cetera. While we cannot be sure whether the New Testament works assigned to the authorship of John werr actually written by the same person, we can be sure that the authors of these works all traced their apostolic succession to this person and that they were from the general geopraochic region of those paces where John brought the Gospel: Western Asia Minor and the nearby islands such as Patmos. In many cases, the exact locations where the Twelve preached has been lost to us, but at that time people knew and even kept relics to make such claims more concrete and legitimate. So in this sense the Christians were descended not only from their earthly parents according to the flesh but also part of a line of descent form Jesus to the Apostles and to their disciples in succession.2

So we can see that the Twelve Apostles all represented the Twelve Tribes of Christianity, for whom the entire world was the “promised land”, which land of promise and its intended divine regime was referred to as the “Kingdom of Heaven”. Now Judas is unique among the Twelve in that he betrayed Jesus, not merely by denial in word as in the case of Peter’s denial that he knew or followed Jesus, but by Judas’ far more traitorous action of betraying Jesus to his enemies and bringing about his conviction, suffering, and execution.

Judas knew where Jesus would be at the right time, and leads the temple guards there to arrest him. The Gospels seem to imply that this is all part of Jesus’ plan to further God’s salvation history for all humankind, but still we are obviously meant to see this as a betrayal to his enemies and a very bad breach of faith on Judas’ part. There are in fact repeated episodes in this gospel that lead us to think very ill of Judas. For example, the Gospels all claim that he was punished in various ways, and that “it were better for him that he had never been born.”

So granted that Judas is one of the Twelve Disciples, which of the Twelve “Tribes-Nations-Churches” of Christianity does Judas represent? Unless we find that Judas founded a church somewhere where some bishop claimed apostolic authority from Judas, we a should see Judas as the “tribe” of those who rather than accepting and preaching the Gospel, were initially party to its promise, but who then rejected and fought against it. These people are the villains of John’s Gospel and they use their influence with the Romans to kill Jesus. 

This view is supported by the opening of the work where we read:

He [Jesus] came to his own, and those of His own did not receive Him. But as many as received Him, to them He gave the right to become children of God,, even to those who believe in His name, who were born, not of blood nor of the will of the flesh nor of the will of man, but of God. (John 1:11-13)

So the new covenant was extended as an invitation to everyone, but one group rejected him. In the present work I will claim that this was what I will call “tribe of Judas”, which usage is not found in the NT but which I will argue follows from the most obvious interpretation of John’s views. This “tribe” was then replaced by another Apostle who was not numbered among the original Twelve: St. Matthias (Acts 1:24-26).3
Curiously, there was another Apostle who as also not one of the Twelve but whose might well claim to be a more suitable replacement for Judas. I say this not to contradict Luke’s testimony in Acts but rather to point out that St. Paul was an inversion of Judas in the following ways:

  1. He was not one of the original, while Judas was.
  2. Judas was the treasurer of the Twelve, while Paul renounced payment in cash but only in room and board.
  3. Paul was a persecuter who then became an Apostle, while Judas was an Apostle who then betrayed Jesus to a violent death.
  4. Judas simply means “Jew”. Of the Apostles, Paul rejected his own Judaism more than any other easpecially in writings such as Romans ch. 6 and 7, where life as a Jew is contrasted with life as a Christian in the same way that life according to the flesh is to life in the spirit.

In the Hellenistic world twelve was considered an auspicious number of members for a group; for example cities formed a “dodecapolis” like the Ionian or Aeolian leagues for mutual defense and free trade.

So in this light we should read that Judas’ actions are to some extent allegorical for the habits and actions of a certain group of people who might be said to follow Judas in the same way that the Seven Churches of Asia follow John or that the churches founded by Paul follow him.4 So what is the nature of this tribe of Judas? Who are they and what do they do? This is what we shall deal with in our next blog post.

1 Note that in Romans ch. 7 and 8, this dualism of flesh vs. spirit maps onto that of Jewish Law vs. Christian “Law”, especially in ch 7:5-7, 14, and 25. All references to spirit vs, flesh in the following chapters should be seen in this light; not in the Platonic sense typical of Western philosophy but rather in terms of the primary conflicts in the Hellenistic Eastern Mediterranean at that time.

2For example, according to early Christian tradition John the Evangelist went to Western Turkey (where the Seven Churches of the Book of Revelations are), and he there preached the Gospels and made many converts. St. Polycarp (who became bishop of Smyrna) was among his disciples, and among his disciples in turn was St. Irenaeus, the author of Against the Heresies, which book has been dated to around A.D. 180, and is an important source of debates among various sects of competing “gospels” being propagated at that time.

3This St. Matthias is not mentioned again in the Bible, but early church authors record that he evangelized first in Cappadocia in Central Turkey and then was martyred in what was to become Armenia, although his mission was not successful and other saints get the credit for Christianizing the Armenians.

4This is not to say that “Paulism” is a separate religion or sect from that of John, only that they are two of the churches founded on the orders of Jesus just as the tribes of Judah and Mannaseh were two tribes with their own territory and descent. My treatment of this topic is only intended to point out the symbolism of the 12 tribes/apostles that would have been readily appraent to the original readers of the NT, which would then throw light on the curious character of Judas.

Announcing my podcast “The Aristotle Project”

My daughter Ada and I have recorded 25 episodes thus far (which episodes will be release between now and January 2021), will focus on the issues raised by Aristotle from a modern perspective. By “modern” we mean that we shall tackle the theoretical problems that arise from considering Aristotle’s thought with respect to modern science and the various religions, most especially Christianity. We shall also consider the practical of moral issues raised by being a practitioner of philosophy in the modern world.

Our first season covers Aristotle’s “Metaphysics” with special guest thinkers Heraclitus and Empedocles. The next season will cover the Ethics with special guest thinkers Seneca, St. Thomas Aquinas and perhaps others.

The podcast is already on Castbox, Apple podcast, Tune In, we hope very soon to be on Google Podcast.



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Plans for Podcast Series in the Works

Dear fans of the blog, I am now considering a podcast series might be called either

  • “Aristotle, Darwin, and Jesus walk into a bar…”
  • “The Prodigal Son” [for personally meaningful reasons]
  • ”The Three Wisdoms Project: Philosophy, Science, and Faith.”

Each of the “three wisdoms” is a competing candidate for the supreme form of knowledge which is alleged by various people to outrank other claims for the highest form of knowledge, each of whom is represented by

  • Aristotle (philosophy) – representing the possibility that we have access to a supreme source of wisdon apart from faith and natural science.
  • Darwin/Dawkins (natural science) – the idea that natural science is our highest form of wisomd that has not replaced philosophy and faith.
  • The Bible (faith) – the idea, common in most traditional cultures, that faith trumps the other two forms of reason.

The podcast episodes will fall under the following headings:

  1. The Philosophy of Aristotle
  2. Intermission – Empedocles the proto-evolutionist and failed messiah.
  3. Aristotle’s answer to Empedocles: the pre-Darwinian view of the cosmos.
  4. Darwin’s theory.
  5. Dawkin’s “Selfish Gene” theory.
  6. Aristotle’s Virtue ethics and politics.
  7. A Darwinian view of religion: the test case of the Bhagavad Gita.
  8. Faith and the Bible: a Darwinian interpretation.

The individual podcast episodes will probably be as follows:

I. The Philosopher – Aristotle

  1. What is knowledge and wisdom? Aristotle Metaphysics A.1,2
  2. Early naturalism and materialism – Aristotle Metaphysics A.3,4,8
  3. Early idealism – Aristotle Metaphysics A,5,6,9
  4. The Four Causes – Aristotle Metaphysics A.10, α.2
  5. The Wisdom Aristotle seeks is “first philosophy” – Aristotle Metaphysics B, Γ.1,2
  6. The “Three Laws of Thought” – Aristotle Metaphysics Γ.3-8
  7. The sacred science deals primarily with “Substance” – Aristotle Metaphysics Z.1-6
  8. Substance and essence – Aristotle Metaphysics Z.11-17
  9. Substance and definition – Aristotle Metaphysics H
  10. Potentiality and actuality – Aristotle Metaphysics Θ.

II. Intermission – Empedocles

  1. The Physics and Katharmoi.
  2. Empedocles’ theory of evolutionary cosmic cycles

III. Back to Aristotle

  1. Substance and metaphysical cosmology Aristotle Metaphysics Λ.1-5
  2. Aristotle’s God and Cosmic Order Aristotle Metaphysics Λ.6-10
  3. Aristotle’s De Anima.
  4. Practical good – Aristotle’s NE I
  5. Virtue – Aristotle’s NE II-V
  6. Moral and intellectual virtue – Aristotle’s NE VI
  7. Virtue and Pleasure Aristotle’s NE VII
  8. Friendship Aristotle’s NE VII-IX
  9. Pleasure and Eudaimonia (translated as ‘happiness’) Aristotle’s NE X.
  10. The nature of politics – Aristotle’s Politics I.
  11. The nature of the household or family – Aristotle’s Politics II.
  12. Utopian politics (e.g. Plato’s Republic) and the nature of political unity. – Aristotle’s Politics III.1-8.
  13. Existing states and lawgivers Aristotle’s Politics IV.9-12.
  14. More from Aristotle’s Politics ? I am tempted to go on, but there is just so much there…

IV. Charles Darwin

  1. Introduction” and “Variation under domestication” Darwin’s The Origin of Species.
  2. Variation under nature”– Darwin’s The Origin of Species.
  3. The struggle for existence” – Darwin’s The Origin of Species.
  4. Natural selection” – Darwin’s The Origin of Species.
  5. Conclusion” – Darwin’s The Origin of Species.
  6. Evidence for the descent of man” – Darwin’s The Descent of Man.
  7. Manner of development” – Darwin’s The Descent of Man.
  8. Comparison of mental powers” – Darwin’s The Descent of Man.
  9. Affinities and genealogy” – Darwin’s The Descent of Man.
  10. Summary and Conclusion – Darwin’s The Descent of Man.

V. Richard Dawkins

  1. Why are people?” – Richard Dawkins, The Selfish Gene.
  2. The Immortal Replicators – Richard Dawkins, The Selfish Gene.
  3. Immortal Coils” – Richard Dawkins, The Selfish Gene.
  4. The gene machine” – Richard Dawkins, The Selfish Gene.
  5. Aggression” – Richard Dawkins, The Selfish Gene.
  6. Genesmanship” – Richard Dawkins, The Selfish Gene.
  7. Family planning” – Richard Dawkins, The Selfish Gene.
  8. Battle of the generations” – Richard Dawkins, The Selfish Gene.
  9. Bettle of the sexes” – Richard Dawkins, The Selfish Gene.
  10. You scratch my back, I’ll scratch yours” – Richard Dawkins, The Selfish Gene.
  11. Memes: the new replicators” – Richard Dawkins, The Selfish Gene.
  12. Nice guys finish first” – Richard Dawkins, The Selfish Gene.
  13. The long reach of the gene” – Richard Dawkins, The Selfish Gene.
  14. Necker cubes and buffaloes” – Richard Dawkins, The Extended Phenotype.
  15. Host phenotypes of parasite genes” – Richard Dawkins, The Extended Phenotype.

VI. Intermission: The Dharma

  1. Bhagavad Gita

VII. The faith of the Bible

  1. God’s justice is not up for debate with humans: Job.
  2. God made humans for his own “glory” to “rule the earth” – Genesis.
  3. Righteousness within multicultural empires – Exodus.
  4. The acquisition of territory by the “hlessi – Joshua.
  5. The loss of territory and a call for a serious reconsideration of what must be done[a Prophet?]
  6. A radically new adaptive strategy is proposed Luke-Acts.
  7. Paul’s view of the strategy – [Ephesians and/or Hebrews]
  8. The origins of the current primary world conflict – John’s Gospel and Revelation

VIII. Recap and Conclusion

  1. The final episode?

Notes on Plato’s “Phaedo”


  1. Dramatis persona
    1. Phaedo of Elis (b. ~418/9)
      1. Student of Socrates
      2. founded the School of Elis
      3. aristocratic descent
      4. captured during war, sold as slave (as a “catamite”)
    2. Echecrates of Philus
      1. Student Eurytus of Tarentum and Philolaus)
      2. “last of the Pythagoreans”
      3. Philus was an ally of Sparta vs. Athens
    3. Antisthenes – student of Gorgias
    4. Critobolus of Alopece, son of Crito
    5. Appollodorus of Phaleron – “constant companion” of Socrates, “maniac”, flamboyant
    6. Hermogenes – Alopece, wealthy man
    7. Epigenes of Cephisia
    8. Aeschines – poor, dissolute, legal troubles w.r.t. debts, speaker, author of Socratic dialogues
    9. “Foreigners”
      1. Simmias of Thebes
      2. Cebes
      3. Phaedondes
      4. Euclides of Megara
      5. Terpsion of Megara
  2. Themes:
    1. Category identification (the soul, life, mind)
      1. Many dialogues, especially the early ones, have as their dominant theme the finding of what we call “definitions of common terms”, but which in Plato were called
    1. “what it is to be an ‘x'”
    2. “x itself”
    3. “the common character of all x”
    1. Philosophical way of life
    2. Dialectic
    3. Explanation of natural phenomena – life, sensation, movement, other changes in livin creatures.
  1. Introduction
    1. the fableof pleasure and pain (60c)
    2. The Socratic daimon’s last advice: “ “Socrates” it said “compose music and work at it.” …. philosophy is the greatest music” (61a)
    3. The soul, body and the gods
      1. Body as prison or fort (62b)
      2. Against suicide
      3. “It is gods who take care of us and that we human beings are one of the gods’ possessions.” (62b)
      4. The Afterlife:
        1. “firstly, the company of other gods, who are both wise and good”
        2. “secondly, the company of humans who have dies and who are better than the people here”
      5. “…the sole pursuit of those who correctly engage in philosophy is dying and being dead.” (64a)
    4. “For it is unreasonable that the wisest people shouldn’t resent leaving this ministration in which they are supervised by the best supervisors there are, namely gods. Because I take it such a person doesn’t think that he will take better care of himself after he has become free.” (62d)
  2. Philosophy and Death
    1. There is death (64c)
    2. Death is the separation of body and soul (64c).
    3. Pleasures vs. reason: food, drink, sex, clothes (64d)
    4. Lack of pleasure in body > death? (65a)
    5. Reasoning also seeks that which is separate from body? (65b-66a)
      1. “Just itself”, “…and a Beautiful and Good” (65d)
      2. .. which are not visible with the eyes (65d)
      3. but which are only visible with the mind (65e)
      4. And the affections of the body impede said mental vision? (66c)
      5. Virtue is such separation from the bodily affections. (67a)
    6. “Virtue” marginalia (67d)
    7. “Form” as ideal
    8. “nowhere but in Hades will he have a worthwhile encounter with it” (68b)
    9. courage, temperance (68c)
    10. “The reality is, I suspect, that temperance, justice, and courage are a kind of purification from everything like this and that wisdom itself is a kind of rite to purify us.” (69c)
    11. Concerns for possible mortality of the soul itself. (70a)
  3. Initial arguments for the immortality of the soul (70d-86)
    1. Argument from opposites or reciprocal processes of eternal recurrence (70d-73)
      1. If you want to consider this with regard to humans only, but in relation to all animals, and plants too. In short, everything that has a coming-to-be, let us see whether they all come to be in this way; the opposites from nowhere other than their opposites…” (70e)
      2. “being dead is the opposites of being alive” (71d)
    2. Argument based on the doctrine of recollection (73-78)
      1. “Suppose one set of things did not always balance the other by coming to be, going round in a circle, as it were, but instead the process of coming-to-be were a straight line from the one to its opposite only, and did not bend back again to the former or turn in its course. Do you realize that then everything in the end would have the same form, be in the same condition, and stop coming to be?” (72b)
      2. “also, according to that theory which you yourself habitually propound, that our learning is in fact nothing but recollection…” (72e)
      3. “I don;t quite remember at the moment.” (73a)
      4. “Equal itself” (74b)
      5. “For our present argument is no more about the Equal than about the Beautiful itself, the Good itself, the Just, the Pious, and, as I’ve been saying, about everything to which we attach this label, “what such and such is”…” (75d)
      6. [For other uses of the locution “what such and such is”..look at:]
        1. 65d-e
        2. 74d
        3. 75b
        4. 78d
        5. 92e
        6. Symposium 211c-d
        7. Republic
          • 490b
          • 507b
          • 532a-b
      7. Fears about the immortality of the soul:
        1. “For why shouldn’t it be that, on the one hand, the soul is born and constituted from somewhere else, and exists before it ever enters a human body, but that, on the other hand, when the soul has entered a body, and is being separated from it, it itself then dies and is destroyed?” (77b)
        2. “…when the soul leaves the body the wind blows it apart and dissipates it, especially when someone happens to die not in clam weather but in a strong wind.” (77e)
        3. “You must chant spells to him every day until you manage to chant it away.”
      8. “The Great Commission”: “Greece is a large place … and there are no doubt many good men in it. There are also many races of foreigners. All of these people you must comb in your search for such an enchanter, sparing neither money nor effort, as there’s nothing on which you’d be better off spending money. But you must yourselves work together as you search, because you may not easily find others more able to do this than you.” (78a)
    1. Argument involving these two arguments: souls as pre- and post- life existence.
      1. “What kind of thing is liable to undergo this – that is, to be dissipated?” (78b)
    2. Argument involving composite and incomposite objects [affinity argument] (78c-81)

















      1. The characterization of the form in future dialogues:
        1. Republic– “noeton” or “intelligible”
        2. Parmenides– “mono-eide” or “one idea”
        3. Sophist –
          • ever self-consistent
          • Khorismos(“separate”)
      2. “those who care about their own soul”
      3. “purifying rite that philosophy provides” (82d)
      4. “and philosophy observes the cleverness of the prison – that it works through desire, the best way to make the prisoner himself assist in his imprisonment.” (82e)
      5. “the god whose servants they are” (85a)
      6. “I myself am the swan’s fellow-slave and sacred to the same god” (85b)
  1. Objections (86-102)
    1. Epiphenomenalism (92-95c)
      1. Simmias’ Pythoagoreanism”
      2. Soul as harmony or attunement
      3. musical instrument analogy
        1. “…attunement, too, and a lyre and strings: that the attunement is something invisible, incorporeal, and utterly beautiful and divine in the tuned lyre, whereas the lyre itself and its strings are bodies, corporeal, composite and earthly and akin to the mortal.” (86a)
        2. “our soul is a blend and attunement of those every things, when they are blended properly and proportionately with one another.” (86c)
        3. “…a weaver who had dies in old age. One might argue that the human being has not perished but exists intact somewhere, providing as evidence the fact that the cloak that he himslef wove for his own use and wore is intact and has not perished.” (87b)
        4. “But let us suppose that, after granting this much, he refused to concede the further point that the soul does not suffer in its many births and at the end perish completely during one of those deaths, and that no one knows which death and which parting from the body make the soul perish.” (88b)
      4. Rebuttal 1: How can an assembly of material parts account for recollection? (92b-93)
        1. “For presumably you won’t allow yourself to say that an attunement existed, already composed, before those thing existed of which it was due to be composed.” (92b)
        2. “For the second has come to me with no proof but with a sort of plausibility and outward appeal, which is the basis on which most people believe it too.” (92d)
      5. Rebuttal 2: How can there be differences in moral worth among collections of material parts? (93-95)
        1. “In that case, an attunement is not the sort of thing to governits components, but rather to follow them.” (93a)
        2. “…is one soul in even the smallest degree this very thing, soul, more and to a greater extent than another, or less so and to an inferior extent?” (93b)
        3. “Of all the things in a human being, is there any other than soul that you would say is in command, and especially a wise soul? … Does soul do so by surrendering to the body’s affections or by actualy opposing them?” (94b)
        4. “Theban Harmonia” (95a) [wife of Cadmus, legendary founder of Thebes]
    2. Cebes’ reply (Mechanist naturalism) (95c-102)
      1. Based on Heraclitean theory of exchanges
      2. Analogy: weaver wearing out many coats or bodies as a covering.
      3. The soul viewed as psychic units of energy, which are variously allotted through the whole realm of souls.
      4. Requires the full treatment of the causes of generation and destruction; leads to the famous account of Socrattes’ intellectual development and critique of the Anaxagorean conception of nous. (96-102)
        1. Anaxagoras – “intelligence should be the cause of everything” (97c)
        2. Socrate’s intellectual quest:
          • Ionian physicists – combination of elements
          • Pythagoreans – numbers
          • Empedocles –
          • Anaxagoras – Mind
          • The Delphic Oracle – Wisdom, definitions, “common character”, “x-itself”, “ontos on
      5. dunamis” (98c) “method” or “function”
      6. “causes” (99b)
      7. cosmology (99b)
  2. The Theory of Forms (102-107d)
    1. Participation and Oppositional Forms (102-104)
      1. “In the same way, the small in us is never willing to come to be, or be, large, nor can any other opposite still be what it was and at the same time come to be, and be, its opposite, but it withe” (103a)
      2. “…not only does the Form iteslf merit its own name for all time, but there is also something else that merits it, which is not the same as the Form, but which, whenever it exists, always has the feature of that Form.” (103e)
    2. Concluding section on dialectic and the soul as an animating principle. Difference between accidental and essential predication. (104-105c)
      1. “For if you were to ask me what I is that, when it comes to be present in anything’s body, makes the thing hot, I will not give that safe, ignorant answer – namely that it is hotness – but, thanks to what we now say, a more ingenious one: that it is fire.” (105c)
    3. Formal argument for immortality from the premise that the soul is a principle of life – the Form of Life.
    4. “…and as for God, I suppose, and the Form of Life itself, and any other immortal thing there may be, it would be agreed by everyone that they may never perish.” (106d)
  3. The Myth of the Underworld.
    1. “Now there are many wondrous regions of the earth, and the earth itself is neither of the nature nor of the size it is believed to be by those who usually talk about it, as I have been convinced by someone.” (108c)
    2. “…if the earth is round and in the middle of the heaven, it has no need of air or of any other such necessity to stop it falling” (109a)
    3. “the earth is extremely large” (109b)
    4. “aether” (109c)
    5. “Now we are unaware that we dwell in the earth’s hollows, and we suppose that we dwell up on the earth’s surface…” (109c)
    6. “…true heaven, the genuine light and the vertiable earth.” (110b)
    7. “For if it’s also appropriate to tell a myth, it’s worth hearing, Simmias, what the things on the surface of the earth under the heaven are really like.” (110b)
    8. “One of the chasms in the earth is in fact the largest in a number of ways, but in particular because it is bored right through the whole earth.” (112a)
    9. “Tartarus” (112b)

Taran, Leonardo. “Plato, Phaedo, 62 A.” The American Journal of Philology, vol. 87, no. 3, 1966, pp. 326–336. JSTOR,www.jstor.org/stable/292854.

Deborah Kamen. “The Manumission of Socrates: A Rereading of Plato’s Phaedo.” Classical Antiquity, vol. 32, no. 1, 2013, pp. 78–100. JSTOR,www.jstor.org/stable/10.1525/ca.2013.32.1.78.

Rundin, John S. “Gods and Corporations: Fifth-Century B.C.E. Athena and the Economic Utility of Extraordinary Agents.” Method & Theory in the Study of Religion, vol. 19, no. 3/4, 2007, pp. 323–331. JSTOR, http://www.jstor.org/stable/23551850.

The “Elements” of Musical Composition.

A neo-Aristotelean ontology of musical works.

By Adam Voight.


The current work defines an Aristotelean approach to the ontology of musical works and other related abstracta. The theory would satisfy multiple conditions: 1) It would provide a workable theory of abstract artifacts. 2) It would be consistent with modern scientific naturalism (broadly defined), and 3) It is at least a possible reading of what Aristotle has to say as well as what he should say if he were to answer the questions concerning the coming-to-be of musical compositions.

Table of Contents

I.1. Introduction

A surprisingly hot subfield of analytic philosophy in the past generation has been aesthetics. Of late, one of the more active topics has been the ontology of music, especially the problem of the individuation of musical works. Thus far, no one approach to defining the being of musical works seems to ‘save the phenomena’ to the satisfaction of those involved. A perusal of the ideas on offer is daunting, but thus far there is no distinctly Aristotelean perspective available.1 Two extreme positions include “Musical Platonism”2 and “musical fictionalism”.3 The former claims that musical works are eternal ideas and the latter claims that “music” does not really refer. Aristotle’s general approach was intended to chart a middle path between two similar extremes – Platonism and materialism, and so we might benefit from something similar tailored to today.4 However, in order to make a proposal, I have questioned one thesis that is often taken to be essential to Aristoteleanism: that unlike matter, forms are unchangeable. In my view, we should explore the possibility for an Aristotelean conception of changes of forms and thus essences. If this could be done, it is likely that such a view would be superior to those who ignore essences on the one hand and those who deny their changeability on the other.

My goal being to define a hylomorphic theory of said “abstract artifacts”, I must first defend the claim that there are abstract “elements” or “matter” from which abstract artifacts are made. It is the latter more limited goal with which the current work shall attempt.

I.2 The Ontological Strangeness of Musical Works

Musical works (songs, symphonies, concertos, etc.) are ontologically unique for many reasons:

1) They are abstracta , which ‘are’ in a radically different way from concreta. I will assume that Platonic Ideas are “abstract” in the modern sense assumed here.5

2) They are created. While numbers are not generally thought to be created or invented, it seems much more intuitive to say that composers create their works in some way, while numbers are simply “discovered”. Perhaps transfinite numbers or imaginary numbers might be “invented”, but in general the natural numbers are often though of as “discovered”. Of course, Musical Platonists have differed on this point Kivy (1987) famously claims that they are eternal.

3) They are arbitrary or contingent. – Likewise, abstract artifacts are in most cases far more contingent that the numbers. While there is no room for creativity in the integers, it seem that there is a lot about musical works that is radically contingent or arbitrary. For example, Beethoven could have transposed the Ninth Symphony up a whole step and it would still be the Ninth Symphony, whereas it seems that numbers are pretty much unchangeable. People may debate whether zero, negative numbers, irrational numbers etc. are invented, but they seem much less contingent than musical works.

4) Another difference is that musical works are “perishable”, but not in the same way as an apple or table. Musical works are “lost” when we can no longer know or learn how to perform them and this is something that applies to many other classes of abstract products from biological species to poems or inventions.

In order to handle these difficulties, we shall treat music as a part of Aristotle’s “physics”; a goal-oriented behavior of an organism that takes place in space and time and which is causally efficacious.

II. The Idea of “Musical Physics”

Metaphysics and physics both have as part of their mission the description and explanation of change. Things are not created ex nihilo but from existing matter. In many cases, this matter must be made, as when bricks must be made first for a house, or plants must be grown first for animal’s food. If there were poesis of abstract products, such as a prose, poetic or musical compositions, it would also operate on existing matter. It is typical that this matter would be different matter from concrete products. All products would have their own forms specific to the matter that they are, just as bricks have their own matter and form, and the houses made from brick their own matter and form. For musical composition, this matter is not made of material but rather abstract elements. I will not make too much about the details of how we construe abstractions; perhaps it would have been better to call them “virtual elements”. Here we shall focus on the material cause of music, a.k.a. the classical “Elements of Harmony”. But first we shall have a close look at what “elements” are in Aristotle’s philosophy in the broader non-musical sense.

II. The General Sense of “Elements” in Aristotle

II.A. “Elements” vs. “Matter”

In Aristotle there are two words with similar meaning that might well refer to the “that-from-which” of abstracta: “elements” [stoicheia] and ”matter” [hyle]. I am using the term “elements” rather than “matter” for the following reasons:

  1. It is a term with slightly wider meaning. In other words, all “matter” are “elements”, but not vice versa. For example, the while the “matter” of geometry is space or alternatively, the genus of space, the elements of geometry include in addition to space itself, points, lines, shapes, axioms, theorems et cetera. ‘Elements’ has a much wider applicability.
  2. Intelligible matter” is only mentioned three times in all of Aristotle’s corpus, whereas “elements” is much better explained at length in many different contexts.
  3. Intelligible matter is only ever related to arithmetic and geometry, while “elements” are mentioned with respect to grammar, logic, and many other sciences.
  4. Elements”, has its own entry in Aristotle’s glossary (Book Delta, see below.), while “matter” does not.

For these reasons, I will use the term “elements”, except where said elements are spoken of as a material cause.

II.B. “Elements” defined.

Book V of the Metaphysics consists in a series of definitions of Aristotle’s philosophical terms, including and section three is as follows:

“ ‘Element’ [Greek stoicheion] means (1)[6] the primary component immanent in a thing, and indivisible in kind into other kinds; For example, grammar- the elements of speech are the parts of which speech consists and into which it is ultimately divided, while they are no longer divided into other forms of speech different in kind from them. If they are divided, their parts are of the same kind, as a part of water is water (while a part of the syllable is not a syllable).” “Those who speak of the elements of bodies mean the things into which bodies are ultimately divided, while they are no longer divided into other things differing in kind; and whether the things of this sort are one or more, they call these elements.” “The so-called elements of geometrical proofs, and in general the elements of demonstrations, have a similar character; for the primary demonstrations, each of which is implied in many demonstrations, are called elements of demonstrations; and the primary syllogisms, which have three terms and proceed by means of one middle, are of this nature. (1014a26 – b5)7 

Notice that we have examples of elements from three separate sciences: grammar, nature, and logic. Of these three, it seems that the one most similar to music is that of speech, for the following reasons: 1)The elements are neither wholly physical nor exclusively intelligible. For grammar, the elements something like letters, syllables, and words, with letters being the elements of syllables, which are in turn the elements of words. For logic, the elements are terms, operators, and quantifiers which are the elements of propositions. 2) For both grammar and logic, the elements are made into utterances in much the same way that musical elements are made into musical works. 3) For all three sciences, they deal with objects which are abstract or universal by virtue of the “one above many” argument. In logic, it is possible to give the same argument on different occasions. For grammar, one may also make the same utterance on various occasions, and in music, one may perform the same musical work on various occasions. And in all of these sciences, one cannot say, argue, or perform the same thing with out the thing said/argued/performed first coming to exist in the first place. For these and other reasons, we can see that the works of Aristotle are filled with the exact sorts of “elements” of which we speak here. But that is not all; he often refers to specifically musical elements in many contexts.

III. Musical Elements in Aristotle.

III. A. Musical “Units” In the Metaphysics.

The concept of a distinctly and explicitly musical element is common in the Aristotelean corpus. In the following passage from Metaphysics V, he is defining “one” or “unity”.

The essence of what is one is to be some kind of beginning of number; for the first measure is the beginning, since that by which we first know each class is the first measure of the class; the one, then, it the beginning of the knowable regarding each class. But the one is not the same in all classes. For here it is the quarter-tone, and there it is the vowel of the consonant; and there is another unit of weight and another of movement. But everywhere the one is indivisible either in quantity or in kind.” (1016b18-24)


Units” here are the most fundamental parts or elements, in that letters make up words just as dieses (meaning a smallest interval in music) make up melodies.

We have said previously… that ‘one’ has several meanings…..In music the measure is the diesis, since it is the smallest, and in speech it is the letter … but the measure is not always numerically one. Sometimes there are several, as for instance there are two dieses – not those given by the ear, but those found in ratios – and several articulate sounds that we use for measuring [in phonetics].” (Metaphysics X.1 1053a12-17)

Here we see a musical element compared with others in grammar and units of measurement for weight alongside various physical elements. The elements of each fields are the fundamental units of which those beings are composed. Again, the same comparison is made for letters in grammar and the smallest musical interval. Elements or fundamental units are different in nature for different fields of study. Some fields of study elements that are substances, but others do not, including music.

III. B. Music and other Elements in De Sensu.

In the physical treatises, Aristotle considers the elements of music to be analogous to those of other sciences of sensibles. In the following passage, he treats them in conjunction with color. His discussion assumes an analysis where notes are the elements of chords in (analogically) the same way that black and white pixels can combine into a gray field:

We must now speak of the other colours, reviewing the number of ways in which it is possible for them to arise. It is possible, first, that the white and the black are laid side by side in such a way that while each of them is invisible because of its smallness, the combination of the two becomes visible. This cannot appear as either white or as black, but since it must necessarily have some colour, and can have neither of those, it must be something mixed, a different kind of colour. In this way then, it is possible to accept that there are more colors than just white and black, and that they are many in ratio: for they may lie side by side in the ratio of three to two or that of three to four or in other relations of numbers. (Some may be in no ratio whatsoever, but in some incommensurable relation of excess and deficiency.) Thus they may be in the same condition as concords [symphoniai]: the colors that depend on well ratioed numbers, like concords in their domain, are taken to be the pleasantest of colors (purple and red and a few others of that kind – few for the same reason that concords are few), while those that are not in numbers are the other colours.8 (439b19-440a4)

Aristotle is here anticipating some very modern ideas: primary colors which combine in order to produce secondary colors as well as what we now call “pixels” (the smallest visible unit of visibility). His hypothesis is that the underlying mechanism behind concords and color-wheel aesthetics are based on an underlying unity of principle, which was taken up by Johannes Itten in modern color theory. This is far ahead of his time, since the analogy between them is based on wave-phenomena – one of sound, the other of light. In De Anima, he expands this to taste:

If a concord is a sound, and if a sound and the hearing of it are in a way one, while a concord is a ratio, then the hearing must necessarily be a ratio. For this reason either element in excess – either the high or the low – destroys the hearing : similarly in flavors such excess destroys the taste, in colours what is exceedingly bright or shadowy destroys the sight, and in smelling the same applies to a powerful smell, whether sweet or biter, since the perception is a ratio. That is why, while things are pleasant when they are brought pure and unmixed into the ratio (things such as the high-pitched or the sweet or the salty: for they are pleasant in such circumstances) nevertheless what is mixed, concord, is more pleasant than the high or the low. The perception is a ratio, and things in excess dissolve or destroy it.” (426a27-b7)

So clearly Aristotle’s work is filled with “elements” of many sorts, not all of which are substances in the strict sense. Grammar and music treat of relations among substances: animals and air are substances, but they are not the per se focus of music theory, rather these substances are only “musical” insofar as they contribute to the composition and performance of musical works. The principles of music are not those of a substance per se, but rather emerge from the interactions of many substances, in much the same way as the principles of grammar and strategy. In the next section, we shall treat in detail the process of such emergence of analogous (nonsubstantial) per se objects from the relations among substances.

IV. Elemental “Genealogies” for Houses and Music.

On the view defended here, a neo-Aristotelean theory of music will start with some kind(s) of concrete substance and tell how some quantity, relation, affection, etc. thereof relates to the science in question. The following is a simple but modern description of how the phenomenon of music comes from the relations, qualities or affectations among substances. To clarify this process in true Stagirite fashion, we shall use the analogy with house building.

IV. A. The Genealogy of the Elements of Houses.

House building is a “science”, and its per se object is the production of houses. Pace Plato, the knowledge of a house-builder will include the Form of the House, but following Aristotle, it must also include the matter of the house (wood, stone, bricks), the efficient causes (the different workers and tools available) and the final causes. It is not enough to know the overall purpose of a house (“to live in”), but also the lower-level purposes such as “create a level foundation”, and “make sure the walls are square”. A house builder will not only know the form of level and square, but also why houses need to be level and square in the first place.

Houses are not substances in the strict sense and exist by convention. Their “forms” are not natural but emerge from the skillful interaction of humans and nature. The Form of the House cannot be found in a dictionary or even in a building code, but can only be in the mind of a qualified architect. This is the main difference between a productive science and a theoretical science in Aristotle: a theoretical science knows about a substance such as an atom, a cell or a plant, while a productive science knows about something which is not a substance but whose essence is primarily in the mind of the maker. The principles of housebuilding include axioms that are not the essence of a substance and might not be deduced therefrom. For instance “always make all floors and walls level, plumb, and square” cannot be deduced from the essence of any substance, neither from the essence of the house’s matter, nor from the definition of “house”. While the definitions of “level”, “plumb”, and “square” refer to abstract geometry, the presence of these terms in the definition of the essence of “house” is not rigorously demonstrated but rather emerges from the interaction of builders with material over many generations. This being the case, in place of a demonstration, we need a causal story which I will call a “genealogy”. Such a genealogy will be implicit in the principles and causes of all sciences whose per se objects are not “substances” in the strict sense. The genealogy of the principles and elements of housebuilding are as such:

  1. Substances – First we have atoms, molecules, energy and living things.
  2. Other categories. – Some living things need “shelter” from other things.
  3. Some materials have been found useful to “construct” said shelter.
  4. There are a lot of useful rules to follow that make building such shelter more effective, including some with arithmetic and geometry. Contra Pythagoras, such elements are not being used qua geometrical but are used qua useful for a specific purpose.
  5. Once construction is finished, then living things can “live in” the shelter.

Contra Plato, the builder’s tekne cannot be deduced a priori but are rather learned by those who cooperate to build houses and discuss the pros and cons of different ways of building. So with this in mind, let us look at a similar genealogy for the science of music.


IV. B. The Genealogy of the Elements of Music.

As with house-building, so with music, we need to start from some set of commonly-accepted sumbstances and construct our nonsubstantial elements therefrom.

  1. Substances – First we have atoms, molecules, and living things.
  2. Other categories. – The energy imparts motion to the atoms and molecules.
  3. Some forms of this motion are made or perceived as “sound” by some living things.
  4. Sound is used by living creatures for the following purposes: sensation (mere hearing), communication, or music.
  5. There are a lot of useful rules for making musical sound, including many that involve some arithmetic. Contra Pythagoras and kata Aristoxenus, such rules are not being used qua geometrical but rather qua musical.

According to this framework, music is a science somewhat like phonetics, house building, computer science, or military strategy. In all of these fields, there is a physical substrate or set of elements which can take on various forms imposed on it by rational agents for various purposes. Thus while “music” has no Aristotelean substance as its per se focus, it can define its focus as a certain set of activities that assume a certain physical substrate, principles, purposes, and rational agency of those involved. With that in mind, let us give a full catalogue of the elements of music, from the most fundamental to the most final:

  1. Atoms9
  2. Molecules
  3. Sound
  4. Musical Sound – sound made of notes, intervals, and rhythm.
  5. Melody – Musical sounds in a dynamic sequence.
  6. Harmony – Melodies arranged simultaneously.
  7. Works – Songs, Concertos, Operas, Musicals, etc.
  8. Performances – Social events.
  9. Culture (Ethos) of a People.
  10. The Final Final Cause – There may be some higher telos for music than contributing to the life of a people who have a certain culture.


IV. C. Proximate and Ultimate Elements of Music.

Art and sciences take matter from some more fundamental art: the house builder takes his material and tools from the makers of tools and bricks. Music is similar in this respect. Notice that many of the above elements are not part of music per se:

  1. Elements 1-3 pertain to physics.
  2. Elements 4-10 pertain “music theory” in the widest sense, which might study the ultimate basis for the smallest intervals and scales.
  3. Elements 4-8 are the proper study of musical artists.
  4. Element 9 is in political philosophy.
  5. Element 10 is theology.

The distinctively musical elements (4-8) in this “scala musica” are not substances, but derived by cognitions concerning substances “in a certain respect” – those relations which are musically relevant. For music to be a science, we must know:

  1. What are the per se phenomena that are the focus of music. – Musical sound.
  2. What it is about the focus that makes it music. – The sound exhibiting proportions and patterns of a certain type.
  3. How the elements are defined. – The elements are those most useful for defining said proportions and patterns that define music.
  4. Other causes: formal causes, final causes, etc.

Something like this will be the the most simple version of our theory: There are various substances, including atoms, molecules and living things. The atoms and molecules collect in “atmospheres”; layers of gas surrounding some planets. Atmospheres transmit sound, which animals find useful for hearing events in their environment. Some animals also use sound for “music”, whose purpose is unclear, and it may have multiple uses. However it seems clear that communication is a large part of it, because we find that musical sound has been split into distinguishable elements rather similar to the elements of codes or languages.

This last line is where we come to the fundamental principles of music: in other words, we begin to find the ultimate causes and principles that underly the distinction between normal sound and music. Music exhibits its distinctive character by having all pitches and beats limited to one of a few selected our of many. So the fundamental elements of music are both melodic and rhythmic, but in the following, I shall focus on melodic units or elements, which are intervals. But why is this the case? Because of communication – each unit (pitch or note) must be distinguished from the others so that patterns are easier to recognize.10 This is the origin of the “diesis” or smallest interval. In Greek music, it was a quarter tone, but later on it was dropped and the diesis was made the semitone, perhaps due to the increasing importance of harmony over melody in Western music. In almost all Greek music, harmonies were sung in unison. With the later increase in polyphony, however, quarter tones perhaps seemed too cluttered. Since complex polyphony provided a great many more possibilities than single melodies, Western composers dropped the quarter-tone.

The “whole tone” is another intervallic element derived from the space between the two concords of the fourth and fifth. In both ancient Greek and modern Western scales, we find that the middle of each octave is taken up with the whole step that divides the fourth from the fifth degrees. Below the fourth and above the fifth, we always find a mix of whole tones and smaller intervals depending on the tonality needed for the occasion. Dieses could in theory be defined in many ways, but in order to be more compatible with the structure defined by the concords, it should be some whole number fraction of a major fourth. In modern Western music, we have five semitones below the fourth degree which can be broken up into either the major scale (whole, whole, semitone) or the minor scale (whole, semitone, whole). If you were to try to divide the fourth into three equal units, they would be slightly larger than the whole tone and not so much larger that they would be readily distinguishable nor mathematically proportionate with the other intervals. The three whole tone interval falls directly between the two concords and is the most discordant interval, rarely used for most serious music, but in blues and other blues-influenced styles it is prominent. However, the harmonic structure of such music has been simplified to the extent that it is not too cluttered. If Bach were to try a fugue on the theme containing a tritone, it would not work, but some popular music can get away with it.

This is what we might expect to find as the essence of musical elements – a mix of nature and convention, not so different from grammar and logic. In none of these sciences are the elements substances in the strict sense, but instead they define their elements based on a mix of natural and pragmatic considerations. Once we have the fundamental melodic elements defined as the octave, concords, semitone and whole tone we can add them together to make melodies, which melodies must then obey the rules of “dynamics”. These rules are generalizations of what sorts of rising or falling series of notes or chords “make melodic sense”. Said melodies must at the very least must seem like a unified entity and be complex enought to hold interest but not be too complex to exhibit perceivable order..

In order to accomplish this, composers will follow certain principles:

  1. Define a “motif” or “theme” by the compostition of lower level elements such as notes and rhythyms.
  2. Repeat the motif.– the motif can be used over and over again in the same way that many of the same type of brick are needed to make a house.
  3. The motif undergoes “development”, “variation”, “restatement” – the elements of the motif are slightly re-arranged into a related motif or variation.
  4. Then “resolution”, other dynamic patterns … and so on and so forth.

Thus we have various sets of principles that are not reducible to those of lower levels but which build on them to further the same purpose. Thus far, I have only given a superficial look at the physics of musical poetics or composition; next we shall explore the deeper metaphysics and philosophy of science involved.

V. Music and Ontology.

V. A. Music and Substance.

Music was a prominent topic in classical Greek metaphysics starting from the Pythagorean school, which influenced Plato and Aristotle’s ideas concerning music as mathematical science. Even as late as Aristotle Metaphysics Books I and VII. After that Aristotle’s student Aristoxenus continued the same trend to be even more empirical than the Stagirite, and our views are very much in this latter vein.

V.A.1. Pythagoreanism – Numerical Substance.

On my Aristotelean reading, Pythagorean “substance” is ultimately numerical, so Pythagorean substances are non-sensible ideal beings. My interpretation of them here is based solely on the assumption that their numbers are ideal or abstract beings, their placement “in” those things of which they are the substance notwithstanding. Sensible beings may not seem numerical at first glance, however according to our reading of Pythagoreanism the substance of these beings must be numerical in some way. One way this could be seen is where there is some unlimited substrate, which substrate then takes form through numerical proportionality. On this reading, music is seen to be an example of a sensible phenomena whose essence / substance has been shown to be mathematical ratios that underly rhythms and melody. So while music is not substance per se, it is shown to be more substantial than many other things whose mathematical essence is less clear and which are therefore less beautiful. On this view, the closer to the numerical substance a phenomenon is, the more beautiful it will be. On this view music is far more substantial than other sensible beings, and contrary to our position, it would be one of the substantial sciences, as it was under Platonically-inclined thinkers.

Since Pythagorean metaphysics makes the substance of beings numerical, Pythagorean science should be somewhat “numerological”. In Pythagoreanism, it is of the essence of planets that there are a certain number of them. Which number it is is up for debate, but most numerological astronomers counted seven. The fact that there were seven planets was taken to be a clue to their essence, and their research consisted in looking for other sets of sevens, such as the seven “metals of antiquity”, days of the week, and the number of notes in the diatonic scale. On this view, the discovery of Uranus would throw the “numerological” astronomy into crisis, because through the change of number there would be a corresponding change of planetary essence. However, for either modern or Aristotelean science the number of planets is not essential to the nature of planets. On both of these views, planets are natural concreta whose number is accidental to their nature. Other planets in other solar systems may be fewer than in ours and they will still be essentially the same as our own.

V.A.2. Aristotle: Music as Mathematical Science.

Aristotlean substances are natural concreta that are not mere aggregates but are a separate “this”: in modern terms (which for conveniences’ sake I will use in this work), the following are what he would call Aristotelean substances: atoms, molecules, cells, organs, organisms, planets, and stars. (Whether the inclusion of atoms in this list undermines my entire approach is something best left for a separate work.11)

Aristotle differs from Pythagoras in claiming that numbers are not themselves substance; instead, numbers are properties of concrete physical substances. Thus, because the of the nature of reality, there happen to be planets (for example); the fact that there are a certain number of planets is not really essential to their nature. Pythagoreans, on the contrary, tend to think that the number of planets is essential to their planetary natures, whether these are the number of planets counted, their number in order from the center of the solar system outward, or their periods of revolution. For Pythagoreans, these quantities are the very essence of substance of what the planets are.12 Aristotle is having none of this; for him, there are material beings of such and such type who move in a certain way based on their physical nature, and the number of these beings is accidental. As a result, the number of planets is of no more consequence for astronomy than the number of continents is for geology; in other words, the discovery of a new one (changing its number) does not change its substantial essence.

However, Aristotle has taken up the conception common to his idealistic predecessors that mathematical sciences are more scientific than their non-mathematical counterparts. Some empirical sciences, such as music or astronomy are essentially mathematical while other branches of ‘physics’ are not. Strangely enough, this would include the field of study that we call “modern physics”. In Posterior Analytics, he makes this assumption without any argument:

…[i]t is the task of those who use perception to know the fact that, and that of the mathematical scientists to know the reason why: for the latter possess the demonstrations of the causes, and often do not know the fact that, just as people who study the universal often do not know some of the particular instances because they have not observed them. (78b34 – 79a6)

It is difficult to see how this could be under the more naturalistic approach of Aristotle, where mathematical entities are not substance, nor essence, but rather the mere definition of the essence. In the following, we see where he went wrong with this approach. Through the examples of astronomy and music he seeks to show how mathematical sciences can define the essence of sensibles.

…in all these examples it is clear the nature of the thing and the reason of the fact are identical: the question ‘What is an eclipse?’ and its answer ‘The privation of the moon’s light by the imposition of the earth’ are identical with the question ‘What is the reason of the eclipse?’ or ‘Why does the moon suffer eclipse?’ and the reply ‘Because of the failure of the light through the earth’s shutting it out’. Again, for ‘What is a concord? A commensurate ratio of a high and a low note’, we may substitute ‘What reason makes a high and low note concordant? Their relation according to commensurate numerical ratio.’ ‘Are the high and low note concordant?’ is equivalent to ‘Is their ration commensurate?’; and when we find that it is commensurate, we ask ‘What then, is their ratio?’ (90a15-24)

In the former example, we see that clearly geometrical analysis is essential to predicting and explaining eclipses; however this should not be taken too far: the assumption that Euclidean geometry is axiomatic for physics has recently been disproven and discarded under relativity. However, Euclid will suffice for the solar system’s orbital dynamics as known to Aristotle and Newton. In a sense, modern physics’ recourse to non-Euclidean geometry undermines Aristotle’s argument. Admittedly it is still geometry with different axioms, but there are so many different ways to do non-Euclidean geometry. How does one choose how many spatial dimensions and what topology to use? This can only be derived from the study of cosmology. Thus rather than geometry ruling over astronomy as under the ancien regime, modern astronomy uses whichever version of geometry suits its purpose. Of course, Euclid is still interesting form most mid-scale phenomena, but it no longer exerts the sort of absolute authority we find in ancient science. In my view, this same dethroning of the exact sciences over the empirical in modern astronomy is implied in Aristoxenus’ criticism of dogmatically mathematical music theories.

V.A.3. The Aristoxenian Paradigm Shift in Music Theory.

Aristoxenus (fl. 335 BC), a student of Aristotle, wrote the first major work of music theory, the “Elements of Harmony”. While a student of Pythagoreanism in his native Italy, he converted to Aristoteleanism and eventually created a theory of music that was even less Pythagorean and more ‘physical’ than his teacher’s. Aristoxenus was more faithful to the naturalistic spirit of Aristotle and disregarded the above-criticized assumption that music is an essentially mathematical substance. Because he pursued a science of music theory and because his innovation required a change in how music itself was defined, I call it a “paradigm shift”.

While Aristotle still saw mathematical ratios as being radically essential to music, Aristoxenus’ claim that mathematics was less essential than a species of aesthetic sensation. Thus the essence of music is not Pythagorean substance nor sound qua mathematically rationalized, but rather sound qua sensibly proportioned, by which we mean that which appears properly proportioned rather than that which conforms most exactly to mathematical proportions. In Aristotle’s view, concords just are numerical ratios and nothing else besides. (90a30) But with Aristoxenus, concords have a curious relation with numerical ratios without being identical, almost like the relation between the astronomical solar calendar and paper calendars. Just as there needs to be days added onto leap years to keep our yearly tally of days in line with the revolutions of the earth, so also do we need to adjust the arithmetical proportions of pure Pythagorean temperment to keep it in line with our musical perceptions.

Through hearing we assess the magnitudes of intervals, and through reason we apprehend their functions. … While it is usual in dealing with geometrical diagrams to say ‘let this be straight line’, we must not be satisfied with similar remarks in relation to intervals. The geometer makes no use of the faculty of perception; he does not train his eyesight to assess the straight or the circular or anything else of that kind either well or badly: it is rather the carpenter, the wood turner, and some of the other crafts that concern themselves with this. But for the student of music accuracy of perception stands just about first in order of importance, since if he perceives badly it is impossible for him to give a good account of the things which he does not perceive at all.” (Barker 150)

This means that contra Aristotle, musical proportion is not a species of mathematical proportion. However since we are retaining an Aristotelean conception of science, we have to say that musical proportion is not a species of arithmetical proportion and is defined separately.

Likewise, as befits the author of the “Elements of Harmony”, Aristoxenus also believes in elements that are essentially musical, but which are analogous to other sorts of virtual or abstract elements:

… the order which relates the melodic and unmelodic is similar to that concerned with the combination of letters in speech: for from a given set of letters a syllable is not generated in just any way, but in some ways and not others.” (Barker 153)

He also adheres to a rigorous distinction between arithmetic and musical elements. On the one hand “… we accept that from a purely abstract point of view there is no least interval.”(Barker 160), but on the other

The claim that there is no least interval by which we divide ad infinitum in melody is one that commands assent: there is some greatest number of parts into which melody divides each of the intervals.” (Barker 160)

What prevents a contradiction with the one before is the qualification “in melody”; once we assume that we are speaking of musical intervals and not mere differences in merely physical frequencies, which is what he is taking about “from a purely abstract view.”

Furthermore, there is also found in Aristoxenus the view that musical composition is the placing the musical elements in a certain arrangement:

However, there is a major hurdle in this conception of music; how to explain the presence of numerical ratio in pre-rational sensation without recourse to an abstract conception of substance or subordination of music to mathematics. In my view, this is done by giving an account something like that given above for the ultimate basis for whole tones, semitones, and how they are pieced together to make scales.

The last part of the science is that concerned with melodic composition itself. Since many forms of melody, of all sorts, come into existence in notes which are themselves the same and unchanging, it is clear that this variety depends on the use to which the notes are put: and this is what we call melodic composition.” (Barker 155)

Here we find that the Musician also has our own conception of Universal Hylomorphism: the idea that there are changes where units of matter are arranged into a form without themselves undergoing any change. Just as bronze is not changed by being made a sphere, so also are notes not changes by being composed into a song. The fact that said “matter” is neither wood nor molecule does not change the fact that songs are made from notes in the way a sphere is made from bronze.

V.B.1 Science, Music, and Substance in Aristotle.

Under the idealistic systems of Plato and Pythagoras, one of the main arguments that substance is the “argument from the sciences”. On this view, the sciences of the ideal were the most rigorous and certain and thus the most suitable per se objects are ideal beings. If substance is prior in definition, knowledge and time, (as in Aristotle 1028a30) then the idealists argue that ideal objects are “substance” in the strict sense. This is an objection which Aristotle went to great pains to answer, devoting not only significant portions of books I and VII but all of books XIII and XIV to this and related problems. In the following, I will try to explain a plausible Aristotelean way to rebut the argument from the sciences, which, if successful would undermine Aristotle and boost Plato.

V.B.2. Aristotle’s ‘substance’.

Aristotle uses many of the same words for various related or “analogous” senses. The most famous is “’Being’ is said in many senses.”. As a result, many other substances have analogous senses of the various “be” verbs. Key to the argument of Book Zeta, there is a distinction between two senses of “substance” which we shall discuss on the way to our presnet conclusion. For the sake of distinguishing them in this chapter, we will call them “substance1” and “substance2”. For Aristotle, the following are true:

  1. A substance1 is a compound of matter and form.
  2. Substance2 is the form of a substance1.
  3. The essence of a substance1 is a substance2. (2 and 3 are equivalent statements.)
  4. A substance1 is anything that has substance2.
  5. Conversely, substance2 belongs most properly to substance1..
  6. Substance2 cannot exist separately.
  7. Only substance1 can exist separately.
  8. When substance2 is spoken of as if it were separate from substance1, it is being spoken of “abstractly”.
  9. A substance1 cannot be artificial since artificial beings do not have substance2 in the full and proper sense.13 (The formal cause belongs to it only extrinsically, and the efficient and final causes even less so.)

Such are the basic assumptions concerning substance in what follows.

V.B.3. The distinction between Substantial and Analogous sciences.

It is substance1, the concrete substance1, that is most real. The latter formal substance2 is the content of science, while substance1 is the object of science (in our modern sense of “objective”). I say an object of science, because sciences do not only learn the form of the substance, but the other causes as well, a fact which further tells against the idealist “argument from the sciences”.14 But what I call a “substantial science” does have a substance as its per se object, but these substances are concrete, and the science studies the form as form of the concrete: examples of this include chemistry (the study of atoms and molecules), biology, botany, zoology, medicine, astronomy, geology.

These sciences deal with substances, meaning that members of a particular genus are individuated into concrete units which cannot be divided into smaller units of the same kind. So if you divide an atom, you do not get another atom, but rather an other type of substance. When you divide a molecule, you do not get molecules, but rather atoms. When you divide a cell, you do not get another cell, but rather parts of a cell which cannot come to be nor survive separately. When you divide an organ such as a heart, you do not get another heart, but rather tissue, a mere aggregate of cells of a certain type. Organisms, planets, and stars also exhibit a similar unity, and the fundamental principles of the science include the following the study of atoms and molecules as substances.

  1. The form of the genus – what all atoms share qua atoms.
  2. The elements of matter of the genus – protons, neutron, electrons, etc.
  3. The formal causes of the substance. For atoms, this includes
    • Genus – the essential form shared by all atoms as well as
    • Differentia – the various ways that atoms differ based on the different arrangements of the elements of the genus.
  1. Fourth, other causes as applicable, including efficient and final causes.

A conception of atoms as a certain kind of substance might provide the fundamental principles of a natural science that studies atoms. Today we would call such a science “physics” or “chemistry”, which, for the sake of convenience, would include as well the study of molecules. However, given that our current topic music concerns how matter reacts to certain sorts of sonic energy, we can call this science “physics”. It is exemplary for how a science can be defined by its primary concern with a particular type of substance. In addition, biology is defined by its concern with another type of substance, the organism, which forms its natural ‘unit’ in the same way that atoms and molecules do for our sense of “physics”. The fact that molecules are a different kind of substance only means that its inclusion in the same science is only due to their ontic proximity or pragmatic concerns. It is not so different from how biologists not only study complete organisms, but also their organs and cells. Whether some biologists find it better to specialize in cells of organs is contingent on the usefulness of such a strategy w.r.t. epistemology or application rather than ontology.

So now that we have a preliminary conception of substantial sciences, we also need to see how an analogical science, even those of logic and arithmetic, can find their rigour without having a per se focus on a primary substance.

V.B.4 Analogical Sciences in Book Lambda.

The idealist can respond to the above by pointing out that on Aristotle’s view, the most rigorous sciences paradoxically have the least substantial objects. If mathematics and geometry are not sciences of substance, then what is? Aristotle gives many examples of rigorous sciences that do not focus on per se substances – arithmetic, logic, grammar, and music among others. How would such a science work if it did not have a substantial per se object? The answer may be found in the following passage:

The causes and the principles of different things are in a sense different, but in a sense, if one speaks universally and analogically, they are the same for all. For one might raise the question whether the principles and elements are different or the same for substances and for relative terms, and similarly in the case of each of the categories. But it would be paradoxical if they were the same for all. For then from the same elements will proceed relative terms and substances. (1070a31ff)

Elders (1972) reads this and other nearby related passages as referring solely to Aristotle’s criticism of Platonism where different substances are not univocal in the senses of their categories.15 In that reading, each of the “different things” in line 31 are the different substances whose various categories and predicates are analogically but not univocally “the same” as they are for other classes of substance. In other words, the “different things” refers to different members of the category “substance” – for instance stars, organisms, and atoms. But there are two reasons why we might not limit the reading of “different things” to the category of substance, and they include the following:

  1. In these passages, it seems that the primary difference being discussed is between substance and other categories:
    • different or the same for substances and for relative terms” (1070a34-35)
    • for then from the same elements will proceed relative terms and substances” (1070a37-b01)
    • [T]here is nothing common to and distinct from substance and the other categories….” (1070b01)
    • Substance is not an element in relative terms, nor is any of these an element in substance.” (1070b02-3)
    • None of the elements, then, will be neither a substance or a relative term; but it must be one or the other.”(1070b7-9)
  1. There is independent reason to think that for many sciences, we are forced to speak of non-substances as being “substantial” in a derivative or loose sense. It is these sciences that we speak of here as being “analogical” (as in 1070a31), and the independent grounds for this assumption will be the primary topic of this chapter.

There are two ways that one might argue for such a reading: first, one might claim that this is what Aristotle meant in his texts, or secondly, Aristotle must argue something like this in order to claim that rigorous sciences can have per se objects which are not substance in the strict sense. In the following, I shall pursue the latter thesis, that something like this is needed for a science of music, not to mention logic, grammar, rhetoric, strategy, geometry, arithmetic, and many others. So from this point, I shall argue under this assumption, that the science of “music” grants its objects with a what I shall call “virtual substantiality”, and as such they are the sort of thing that are composed of ‘virtual elements’ or ‘abstract elements’.

On this view, Aristotle could answer the idealists thusly: the rigour of the exact sciences comes not from the substantiality of their per se objects, but rather the fact that they limit their investigation to some dependent category which has well-defined objects. On this view, math investigates substances but not qua substance but rather qua quantifiable being. This places math in a secondary class of sciences that do not deal with a substance as their per se object, but only treat substance qua some other category. If Aristotle is to answer the idealist’s challenge, each accepted science must have some account that defines how it relates to substances in the full concrete sense. So for math, he claims that it deals with substances, if at all, solely in the category of quantity and that this limitation of focus is what gives it its rigour. Other sciences limit themselves in other ways and other categories: logic deals with propositions insofar as they are true or false, grammar deals with sound insofar as it is articulate and meaningful, and music deals with sound insofar as it forms the ‘essence’ of musical works. While there former exact sciences are simply the sciences of the category of quantity, the others are the sciences of something is by nature in the overlap of the ta phusika and the ta pragmata: grammar, for example is the science of articulate sound, meaning that it looks at a particular physical phenomenon – sound, but sound only insofar as it is used by animals for language. Military science, for example, looks at men, horses, weather and terrain – but only insofar as these elements are related to the need for armed groups to control territory. Musical theory also has a similar account that it must give for how it treats sound- sound in so far as it relates to the need for certain living creatures to make sound that is musically structured.


VI. An Possible Objection from Final Causes.

In performance, and existing form is applied to existing matter. In composition, a form is created from abstract elements. Only once this form is created can it then go on to be the form of a musical performance. Thus we have a explanation of a change that occurs. However, there is more than matter and form iin Aristotle’s physics, there is also the final cause. It seems that the analogy between performance and composition might break down down due to the lack of an existing form as final cause. Since there is no form as final cause, how can the change happen? The performer knows what they are after in a performance; how does the composer know?

My initial view, which will be postponed for a future work, is that composition is more akin in this respect to praxis than to tekne. While the content of the science of composition has a lot of overlap with the tekne of performance, in terms of teleology. In this respect they are similar to the relations between military praxis and military science. Praxis is that form of goal-oriented behavior which has no clearly defined form as its telos. If we say that that the goal of praxis is the “Form of the Good”, this is in a much looser sense than with the form of a house. It is highly unlikely that the Good has a form in the same sense as other concreta. When the composer composes, they are seeking to implement a certain specific way of being “good” in a way that we find in other goal-oriented processes that create forms rather than instantiate them:

  1. Praxis – Political action which seeks to maximize the Good.
  2. Invention – Technical action which seems to create a form in matter that can acheive a goal.
  3. Rhetoric – Technical action which seeks to maximize the persuasiveness of speech.
  4. Poetic composition – Technical action which seeks to create a form of poetic speech that is poetically Good.
  5. Musical composition – Technical action which seeks to create a form of musical sound that is musically Good.
  6. Legislation – Political action that seeks to define laws of such a form as to achieve the Good for a people.

In all of these sciences, poesis is at the service of a Good rather than a Form. In each the Form is the product rather than the telos as it is with productive arts or nature. In virtual poesis, the form is created by the maker according to the process given above.


VII. Conclusion.

In contemporary ontology of musical works, there are extreme views who we have been influenced by and we hope that we have saved the relevant phenomena using an Aristotelean “middle path”.

To the fictionalists who deny that compositions are real16 we say that there are many ways of saying “real”, and each differs by virtue of the essence of what is spoken of. For nonsubstances like musical works, we have a conventional or derivative sort of “reality”, but it is its own reality nonetheless, a reality suited to the being of music. Our above “genealogy” of musical elements details the difference between the substantiality of material elements and living things and analogous reality of musical elements of works.

To the Platonists who say that musical works are substances, we claim that such a view is subject to the same objections given by Aristotle so long ago, chief among them being the following: 1) The objection from lack of causality. “Above all, one might discuss the question what on earth the Forms contribute to sensible things, either to those that are eternal or to those that come into being and cease to be.” (991a7-8) How do eternal forms cause composers to reveal them to us in the Plato’s Cave? What is the relationship between the two? We might be satisfied with leaving it open for future inquiry if only there were not a superior option in Aristotle’s immanent forms. 2) The point that no universal is a substance, given that universals are predicated of concreta (1038b15) and cannot exist apart from them.

This is not to say that neither of these views is lacking in value, but we hope that something like our view will seem plausible both for the issue of artificial abstracta but natural ones as well, including biological essences and natural languages. In our view each of these beings has virtual elements specific to the sorts of beings they are: genes17, phonemes, memes or others as needed to save the phenomena in those domains.

End notes

  1. The one who seemed me as the most Aristotelean among them, Nicolas Wolterstorff (1980) is called a sort of a “Platonic (eternal) norm-kind/norm types” in Killin (2018.) 272
  2. Peter Kivy and Julian Dodds are the most respected such “Platonists” of whom neither actually ever cites Plato, something they share with mathematical Platonists since Frege. The best introduction is Kivy (1987) and Ostertag (2012) In the present work, I will refer to “Platonism” with respect to musical works to refer to Kivy’s position in the above-cited piece.

  3.  Killin (2018).

  4.  I admit that we have modern theories that explain music in terms of set theory, qualia, and others which are not part of classical metaphysics and which do not clearly resemble anything that he dealt with. However, the factors adduced in favor of these more recent approaches may be even more amenable to an Aristotelean analysis.

  5.  Rosen 2018

  6.  In the first line, the “(1)” means that these are the primary meanings of ‘element’, the next section (“2”) (not quoted here) begins “people also transfer the word ‘element’ from this meaning and apply it to” another secondary meaning. But the following are the primary meanings of ‘element’.

  7.  All Aristotle quotes, unless otherwise specified, are from McKeon (1941).

  8.  Barker (1990) Page 47.

  9.  Aristotle’s relationship with the atomism of his time is contentious. However, I will simply assume that atoms qualify as Aristotelean substances on the following basis: They are the smallest unit of material bodies which is a “this” and not merely an aggregate of such-and-such. I think that this topic deserves its own full treatment in another piece, but here I shall assume that modern atoms and molecules are substances.

  10.  This is rather similar to how languages separate certain sounds to make “letters” while other sounds are not excepted because they would muddy up the code. For example, letters are often dropped from languages, especially when phonemes from other languages are introduced. For example, when the Francophile Normans conquered England, that introduced a great many new sounds into Old English which led to the elimination of the Scandinavian “ð”, which is midway between a “d” and a “th” or “t”. With the more crowded list of elements to choose from, the Scandinavian “ð” just muddied things up.

  11. I do this to simplify my exposition, to make this work more readable and relevant for non-Aristoteleans. I am thereby choosing to make my thesis primarily a “neo-Aristotelean” theory as opposed to an interpretation of Aristotle’s work. However, my goal is an argument that resembles something he might support if he were alive today.
  12.  The fact that none of these numbers works out to exact ratios could, in a Pythagorean research program, be either explained away or be the goal of future work. For example, the desire to square the numerical messiness of the heavens with the beauty of whole numbers was a major impetus behind Mesoamerican astronomy, and the Pythagoreans could undertake such a project of their own. One might also claim that this mathematical inelegance is empirical “noise” as opposed to the pure signal of the mathematical “music of the spheres”.
  13. Note that the demotion of products of skill from substantiality is especially crucial in the anti-Platonism the motivates the theory of abstract artifacts. Any further treatment of substance will be given when we treat of natural abstract or virtual products, such as biological essences and perhaps natural languages.
  14.  Physics II.2 194a21- 27
  15.  Elders (1972) pg. 114ff.
  16.  Killin 2018
  17.  For biological essences, the distinction of composition and performance is exactly analogous to that of phylogeny and ontogeny, with phylogeny being the manipulation of genes through the efficacy of natural selection.



Barker, Andrew, ed. 1990. Greek Musical Writings Volume 2: Harmonic and Acoustic Theory. Cambridge UP.

Elders, Leo. Aristotle’s Theology. 1972. Van Gorcum and Co. N.V., Assen, The Netherlands.

Killin, Anton, 2018. “Fictionalism about musical works.” Canadian Journal of Philosophy. Vol. 48, No. 2, 266-291.

Kivy, Peter, 1987 “Platonism in Music: Another Kind of Defense.” American Philosophical Quarterly Vol. 24, Number 3, July 1987.

McKeon, Richard, ed. 1941 The Basic Works of Aristotle. Random House. New York.

Ostertag, Gary. 2012. “Critical Study: Julian Dodd. ‘Works of Music: An Essay in Ontology.’” Nous. 46:2 (2012) 355-374.

Rosen, Gideon, “Abstract Objects”, The Stanford Encyclopedia of Philosophy (Fall 2018 Edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/archives/fall2018/entries/abstract- objects/>.

Witt, Charlotte. 1989. Substance and Essence in Aristotle. Ithaca and London. Cornell U.P.

Wolterstorff, Nicolas. 1980. Works and Worlds of Art. Clarendon Press, Oxford UK.












































Barker, Andrew, ed. 1990. Greek Musical Writings Volume 2: Harmonic and Acoustic Theory. Cambridge UP.

Elders, Leo. Aristotle’s Theology. 1972. Van Gorcum and Co. N.V., Assen, The Netherlands.

Killin, Anton, 2018. “Fictionalism about musical works.” Canadian Journal of Philosophy. Vol. 48, No. 2, 266-291.

Kivy, Peter, 1987 “Platonism in Music: Another Kind of Defense.” American Philosophical Quarterly Vol. 24, Number 3, July 1987.

McKeon, Richard, ed. 1941 The Basic Works of Aristotle. Random House. New York.

Ostertag, Gary. 2012. “Critical Study: Julian Dodd. ‘Works of Music: An Essay in Ontology.’” Nous. 46:2 (2012) 355-374.

Rosen, Gideon, “Abstract Objects”, The Stanford Encyclopedia of Philosophy (Fall 2018 Edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/archives/fall2018/entries/abstract- objects/>.

Witt, Charlotte. 1989. Substance and Essence in Aristotle. Ithaca and London. Cornell U.P.

Wolterstorff, Nicolas. 1980. Works and Worlds of Art. Clarendon Press, Oxford UK.

1The one who seemed me as the most Aristotelean among them, Nicolas Wolterstorff (1980) is called a sort of a “Platonic (eternal) norm-kind/norm types” in Killin (2018.) 272

2Peter Kivy and Julian Dodds are the most respected such “Platonists” of whom neither actually ever cites Plato, something they share with mathematical Platonists since Frege. The best introduction is Kivy (1987) and Ostertag (2012) In the present work, I will refer to “Platonism” with respect to musical works to refer to Kivy’s position in the above-cited piece.

3Killin (2018).

4 I admit that we have modern theories that explain music in terms of set theory, qualia, and others which are not part of classical metaphysics and which do not clearly resemble anything that he dealt with. However, the factors adduced in favor of these more recent approaches may be even more amenable to an Aristotelean analysis.

5 (Rosen 2018)

6 In the first line, the “(1)” means that these are the primary meanings of ‘element’, the next section (“2”) (not quoted here) begins “people also transfer the word ‘element’ from this meaning and apply it to” another secondary meaning. But the following are the primary meanings of ‘element’.

7All Aristotle quotes, unless otherwise specified, are from McKeon (1941).

8Barker (1990) Page 47.

9Aristotle’s relationship with the atomism of his time is contentious. However, I will simply assume that atoms qualify as Aristotelean substances on the following basis: They are the smallest unit of material bodies which is a “this” and not merely an aggregate of such-and-such. I think that this topic deserves its own full treatment in another piece, but here I shall assume that atoms and molecules are substances.

10This is rather similar to how languages separate certain sounds to make “letters” while other sounds are not excepted because they would muddy up the code. For example, letters are often dropped from languages, especially when phonemes from other languages are introduced. For example, when the Francophile Normans conquered England, that introduced a great many new sounds into Old English which led to the elimination of the Scandinavian “ð”, which is midway between a “d” and a “th” or “t”. With the more crowded list of elements to choose from, the Scandinavian “ð” just muddied things up.

11. I do this to simplify my exposition, to make this work more readable and relevant for non-Aristoteleans. I am thereby choosing to make my thesis primarily a “neo-Aristotelean” theory as opposed to an interpretation of Aristotle’s work. However, my goal is an argument that resembles something he might support if he were alive today.

  • 12 The fact that none of these numbers works out to exact ratios could, in a Pythagorean research program, be either explained away or be the goal of future work. For example, the desire to square the numerical messiness of the heavens with the beauty of whole numbers was a major impetus behind Mesoamerican astronomy, and the Pythagoreans could undertake such a project of their own. One might also claim that this mathematical inelegance is empirical “noise” as opposed to the pure signal of the mathematical “music of the spheres”.

13 Note that the demotion of products of skill from substantiality is especially crucial in the anti-Platonism the motivates the theory of abstract artifacts. Any further treatment of substance will be given when we treat of natural abstract or virtual products, such as biological essences and perhaps natural languages.

14Physics II.2 194a21- 27

15 Elders (1972) pg. 114ff.

16Killin 2018

17 For biological essences, the distinction of composition and performance is exactly analogous to that of phylogeny and ontogeny, with phylogeny being the manipulation of genes through the efficacy of natural selection.

Notes on Aristotle’s “Metaphysics” Book IV


IV.1 The Supreme Science of Ontology

Q: What is metaphysics or “first philosophy” about?

A: This science investigates “beingquabeing”. What does that mean?

  • The word “qua” means “as” in Latin.
  • For example,
    • The science of biology investigates living things qua living;insofar as they are alive.
    • Physics studies beings qua physical – insofar as they are matter and energy.
    • Chemistry studies beings insofar as they are made of atoms and molecules.

Now you can study a living creature as such, or you can ignore its biological traits and focus on its character as a merely physical being, for example, its mass and energy. If you study it qua chemical being, you are also ignoring its distinctivelybiological traits and focusing on its atoms and molecules and the chemical reactions inside of it. You could also study a living creature, such as a raven,qualiterarybeing; for example its symbolism when used in Poe’s poem “The Raven”. Every science has a certain type or character of things that it focuses on. For each of these sciences, the essence of what they study is assumed as part of a “scientific paradigm”. Living things, numbers, and poemsare alltypesof beings. However, the science of numbers can be used to study anything quaquantifiablebeing; in so far as it has quantity or magnitude. Likewise, the study of poetry can study anything qua poetic being, in so far as it relates to whatever it is that poetry does.

So biology studies anything in so far as it relates to living beings, and it studies living beings qualiving beings, insofar as they are alive and in no other respect, unless that respect is interesting from a biological perspective. For example, the fact that Samson killed a lion in the Bible is not interesting to a biologist because of its theological import, but only in so far as it gives witness of the former range of this creature and perhaps shows that it has been slowly going extinct for thousands of years. Since species, range, fitness and extinction are distinctly and essentially biological traits they are part of the science of life qualife. But the fact that the Lord was with Sampson on that day is not biological per se.

So biology can study anything, but only insofar as it relates to life. A planet and its orbit are only of interest insofar to biology as it relates to the life that may live on that planet. Words, logic and mathematics are only of interest insofar as they relate to life or are done by life; for example, “How does logical reasoningcontribute to a species’ fitness?” In this case we are not worried about logic qualogic, but only qualiving, as an adaptive behavior.

So what does it mean to study “being quabeing”? This is what the rest of the BookIV is about.

IV.2 “Substance” and the Different Senses of ‘Being’

Q: What are the sorts of “being”?

A: Just as a biologist would want to do in their study of living things qua living, the ontologist will study being qua being. Biologists will start by compiling various lists concerning their subject:

  1. Things that they believe are done onlyby living creatures. For example, metabolism, reproduction, movement, sensation, death, et cetera.
  2. Things that pertain to allliving things.
  3. The next higher genus of things of which the living are a species. For example, living things are a subset (species) of physical or chemical beings.
  4. The next lower species of things of which the living are a superset(what Aristotle called “genus”): for example, the largestspecies/subgroup of living things are the “domains”:archaebacteria, eubacteria, and eukaryotes.

These are all the foundational questions for the science of living things qua living things.

Now in respect of questions one and two, we can say very little except that every being can be said to ‘be’insomeway. For example, the word “nothing” refers to nothing…or does it? I mean it has a meaning, and we know whatis meant when it is said. So in a sense it does refer to something, just not a normalsort of “thing”. In fact this “thing” not even a thing in the normal sense of the word, and most people would agree that it is pretty much nothing. I mean if I make up a fake word and do not assign a meaning to it, then that word refers to nothing. However, the word “nothing”doeshave a meaning because it refers to nothing. This paradox is called “Plato’s Beard”, and as Quine said, it is tough enough to dull “Ockahm’s Razor”, and is a proper subject for ontology, the study of being quabeing. The referents of a fake word and the word “nothing” are not the same sort of nothing at all, but rather different sorts, and even though we use the same word to refer to them, nobody would confuse them. After the study of ontology, you will be even less confused rather than more. Or at least this is what you will expect IF ontology is a real science. If it is a real science, then it must have a specific thing that is its per seobject, in the same way that organisms are the per se object of biology and propositions are of logic and numbers are for math.

What about question three? Well, one of the special things about ontology is that there is no wider super set or “genus” of which being is a subset or “species”. Being includes everything, even nothingis a being in a sense (not so much the word “nothing”, but the referent of that word).

And here we come to question four, where the real action is. If “Being” is a genus, then what are the widest species of that genus? Now you will really have to think hard, because there are so many types of beings, but for this you need to list the highesttypes. When I listed the highest “species” of living things, I had to list some pretty exotic taxa: forget about moths, starfish and humans, we had to go to the very top of the tree of life: archaebacteria, eubacteria, and eukaryotes. What are those? Well just as it takes some knowledge of biology to even know what these creatures are, it takes a bit of work to even understand what the highest kinds of “being” are. Those are the “categories”.

Q:What is the primarysort of “being”?

A: By “primary” we mean the most substantial and essential sense of “being” that ontology focuses on. To see what is meant by this, let us return to the example of biology above. We said that biology focuses on living things, by which we mean organisms. It also studies soil, mountains, the weather, entire planets and solar systems, etc.So any of these things can be “biological”, but our use of this word has a different meaning than when we call an organism “biological”. For biologists only study planets insofar as they might have organisms living on them. They only study soil or the weather insofar as they are relate to organisms. They only study game theory or chaos theory insofar as they relate to organisms. This is ultimately the same as with Aristotle’s example of “healthy”; “healthy people” are “healthy” in a different sense from “healthy food” or “healthy activities” or “healthy lifestyles”. Just as organisms are the primary object of biology, “healthy people” are the primary object of medicine. All the sciences also have focus on some sort of thing which is their primary object; math has numbers, music has music, chemistry has atoms, geology has the Earth, astronomy has stars, linguistics has language, psychology has the mind, et cetera. So if ontology is actually a science, then it too must have a primary object which is the primary sense of “being”, and the other senses of “being” will be seen as secondary to it.

In this chapter, he introduces the word “substance” in this context refers to the primary focus of a thisscience. Later on in Aristotle’s work, this word will acquire a different meaning based on its use in ontology. But since we do not yetknow what the primary sense of “being” is, he is not using it to refer to the primary focus of any science. Health, numbers, articulate sounds, melodies, and logical arguments, (for example) are not really substances in the full sense that we shall learn about later on, but since each of these sorts of beings are the focus of their own science (medicine, math, grammar, music, and logic), they are substances in thatsense which he uses here. Other sciences study beings which are substances in the fullsense: physics, chemistry, biology, astronomy, and metaphysics all study “substances” in the full sense, which we shall learn about later.

The study of substance and its relation to other more superficial categories will be completed in Book VII (Zeta), where he shows why substances must have form (they must have matter) but cannot be mere forms without matter.

IV.3 The First Axiom


In addition to its “substance” (whatever that might be) there are also proper to each science some axioms which define the essence of how one ought to think about that substance. In the case of ontology, are these axioms part of it or do they instead belong to logic or some other science?

These axioms are true of all beings, not merely physical beings or ideal beings. Do they apply to all beings qua being or only as objects of speech or thought? If the former, then perhaps they are part of the study of ontology, if the latter, then they belong to logic.

Aristotle claims that the supreme axioms are assumed by logic. You cannot even begin to study logic without assuming them. No natural scientist, not mathematician nor geometer ever doubts or tries to prove them, since they are assumed by all. Only in ontology or “firstphilosophy” can we even raise the question of what the First Principles or Axioms are that apply to all beings qua being.

The axioms of ontology are those which:

  1. Are assumed by any other study, even logic.
  2. Are more certain than the axioms of any other subject.
  3. Are more general than other axioms.



The “First Axiom” is this: “The same attribute cannot belong and not belong to the same subject and in the same respect.” (1005b20)

This axiom is assumed by any belief, statements, reasoning, or thought about anything at all of any sort, be they numbers, atoms, fictional characters, colors, Gods, et certera. Even if you say that you doubt it, and even if you actually doubt it, it is still impossible to actually think or believe opposite things at the same time according to Aristotle.


Why the First Axiom cannot and does not need to be proven.

That this axiom is first among all possible axioms can be seen from the fact that if one were to try an prove it, one first needs to assume it. Is is already proven or not? It’s either one of the other right? Why can’t it be BOTH? Oh yeah, the First Axiom tells us it can’t be both. For anything that is A, it has to not be not-A. You cannot begin to “prove” anything at all unless you already assume the First Axiom. Not only does proof depend on the First Axiom, even statments depend on the First Axiom to have meaning. If I say that “x is blue”, does this necesssarily mean it is false that “x is not blue”? If it does not, then what is the point of saying “x is blue” in the first place? If not, are you really “saying” anything? If not, you are just making noises without any propositional meaning. So in a sense, the First Axiom is simply a definition of what it means to engage in a certain form of communication, where meaning is encoded in symbols grouped into “propositions” with “truth value”. Many other facts follow from this truth, such as the following:

  1. Each proposition is not necessarily a full sentence, and each sentence may express multiple propositions.
  2. There are others sorts of speech acts that are non-propostional, such as questions, exclamations and emotive noises or calls.
  3. As for propositions that may have some truth value, they must each be either true or not and can never be both.
  4. If their meaning is ambiguous, then of course they may be neither, but in that case they are not really a ‘proposition’ in the full sense of the word.

First philosophy must imply many things like the above in explaining the meaning of the First Axiom, and we could go on forever saying new things like this. However, the important thing to see here is that all of this follows from the First Axiom, which cannot be proven and need not be proven, since all proof assumes the First Axiom before it can even begin.

After this, you might be ready to read Metaphysics Book VII.

Common themes in the Bible and Homer.

I am a big fan of classic literature, the older the better. It is very beneficial to have a deep knowledge of the Bible and other scriptures. I have no special expertise in comparative mythology, but it has occurred to me that this might interest my readers. The similarities are shared by many other great scriptures and epics in the world, but here I will focus on just the Bible and the two Homeric epics. I could do a lot more if I had read the epics of “Gilgamesh”, since this mythos is ancestral to both the Bible and Homer. However, even without this, it is shocking just how many similarities there are between them, even when at first glance they might seem different.

Old Testament/ Illiad:

  1. In both, we have a group of tribes/city-states who share a common language, descent and religion.
    1. The Twelve Tribes
    2. The Greeks.
  2. The gods demand that the leader sacrifices a child.
    1. Abraham and Isaac.
    2. Agamemnon and Iphigenia.
  3. They both form a military coalition at the behest of a leader.
    1. Moses
    2. Agamemnon
  4. Because of divine affairs, there is a conflict.
    1. God’s promise to Abraham, Isaac and Jacob.
    2. The Judgement of Paris.
  5. Which cause them to invade another country and kill everyone there.
    1. Canaan – even the women, children and livestock are not spared.
    2. Troy – they kill the entire royal family, and only a few people escape.
  1. In both Homer and the Bible, the war lasted 10 years.
  2. The antagonists lived in a large city, whose walls were vast and seemingly impregnable.
    1. Troy’s walls.
    2. The walls of Jericho.


  1. During the siege of the city, the protagonists:
    1. Raid nearby towns.
      1. Ai (Joshua 6)
      2. Towns near Troy
    2. And they contact spies within the city whose treason leads to victory.
      1. Rahab the prostitute. (Joshua 2)
      2. The Trojan traitors. – Antenor and Sinon.
        NOTE: Sinon is not mentioned in Homer, but is in Virgil’s “Aeneid”. But keep in mind that most of the full story of the Trojan War (including the Judgement of Paris, the sacrifice of Iphigenia, and the Trojan Horse) is not included in Homer at all. We rely on other works to fill in the details.
        ALSO NOTE: Both of these people are included among the traitors in Dante’s Inferno. For some reason, Rahab the Harlot is remembered rather kindly by being an ancestor of Jesus in the Gospel’s genealogies. But the fact that she is a whore in itself preserves the idea that treason is wrong in itself, even when it benefit’s the “good guys”.


  1. During the war, they have rather difficult relations with God(s), which lead to divine punishments.
    1. The lapses into idolatry and various violations of the Law.
    2. Improper sacrifice to Artemis, refusal to release the daughter of the priest of Apollo, stealing Apollo’s cattle.
  2. There are lots of rebellions among the protagonist’s coalition that questions their authority.
    1. The grumblings of the children of Israel.
    2. The complaints of Achilles against Agamemnon, and his refusal to fight.
  3. In the end, the protagonists win and slaughter the antagonists completely.
    1. The children of Israel occupied the land of Canaan and lived there for many years.
    2. In the story of the Trojan War, the Greeks went back home, although in Homer’s time and after ward, the coasts of Asia Minor were occupied by Greek colonies who replaced the original Anatolian or Celtic inhabitants. The Greeks occupied Asia Minor for nearly 1000 years until the Ottoman Turks forced them out in 1923.

Odyssey/ New Testament

  1. The protagonists, though victorious in the short run, do not see their cause last very long due to the vagaries of the inscrutable divine will.
    1. The Israelites lose their independence to the Persians, Greeks and Romans.
    2. Odysseus fails to return home and suffers more than any other man:
      1. Whoever you know that bear the heaviest burden of suffering, I might compare myself to them in sorrow. Yes, and the tale of all the troubles that by the gods’ will I have endured, would be longer.” (Book VII 182-239)
      2. My queen, it would be difficult to recount the story of my sufferings from start to end, since the gods in heaven have inflicted so many on me.” (Book VII 240-297)
  2. They keep alive the memory of their promised homeland and sovereignty.
    1. The israelites have the prophecy of their long-awaited Messiah.
    2. The Ithakans still hope for the return of Odysseus.
  3. In the end, the hero comes back into his promised Kingdom to prepare the way for its liberation.
    1. The Messiah came to his people, who had kept alive his prophecy for so long.
    2. Odysseus returned in disguise, finding that his people still revered his memory, and cherished the possibility that he might return, even though it seemed that this was mererly wishful thinking.
  4. He comes as the most debased member of society, whom the current rulers cruelly abused and threaten to destroy his dynasty forever.
    1. The tyrants mistreat him and drive him out of their presence.
      1. The Pharisses and Saducees reject Jesus’ teaching and anointing. He is “the stone that the buiders refused, which shall become the main cornerstone”.
      2. The suitors abuse the disguised Odysseus, who to them is merely a beggar dressed in rags.
    2. Others, such as the rightful heirs and his faithful servants, treat him well despite his apparent low station.
      1. The believers and disciples have faith that Jesus is the Messiah.
      2. Telemachos and Eumaios both accept the Odysseus in disguise. This is one of the most touching scenes in world literature, where the heir to the throne treats this old bum in rags with the such manners as would befit an old friend of the family. You know that no father could be more proud of their child that was Odysseus.
  5. The Messiah reveals his true nature and mission to a faithful inner circle.
    1. Jesus has his own plan to Sacrifice for the people’s redemption.
    2. Odysseus reveals to Telemakos his plan to lure the suitors to their deaths.
  6. They then lure the arrogant tyrants into the final battle and defeat them.
    1. The Powers of This World think that crucifiction will finish this upstart pretender forever.
    2. The Suitors think that through this archery contest they can finally win the throne of Ithaka.
  7. Then they bring justice back to the kingdom and the dynasty is restored.
    1. Well, apparently there is some doubt as to whether Jesus actually won, but in any case Christians still think he did.
    2. Odysseus slaughters the suitors and restores his rightful dynasty.

You should also recognize many other tales in this pattern: the Niebelungenlied / Volsungs Saga, King Arthur, Robin Hood, the Mahabharata, Lord of the Rings, et cetera.

The Metaphysics of ‘Natural Goodness’, Pt. III

This is part of a series where we outline a way that we might base some sort of Aristotelean philosophy on modern science, especially biology. In this post, we look at modern biology a la “Selfish Gene” for some conception of the “Summum Bonum” or “Supreme Good”.

Modern views on life’s “top-level function”.

Modern biology has an ambiguous relationship with teleology. One famous quip (whose source I cannot recall) says that “evolutionary biology believes in teleology during the week but not on Sundays.” I take this to mean that teleology is necessary in everyday biological work, but in biological theoryteleology seems out of place. Why is this so? For these reasons:

  1. Biology supervenes on physics.
  2. Physics lacks teleology.
  3. Darwinian theory is utterly a-teleological.

In the following, I hope to show that even though points 1) and 2) are correct, point 3) does not follow.1Even if we did assume all three points, biologists are forced to admit that something like “purpose” is part of their field. The very concept of “adaptation” implies being adapted for some sort of purpose, and this sense of purpose clearly supervenes on physics. Julian Huxley and Niko Tinbergen both listed “function” as one of the major questions answerable by evolutionary science, in addition to phylogenetic, ontogenetic, and mechanistic questions. (Hladaky andHavlíček1998) But when theoretical biologists thematize the teleology inherent (as I believe) in their field of study, they do so in a way that betrays how weird Darwinian teleology truly is. Take for example the opening of “The Selfish Gene”:

This book should be read almost as though it were science fiction. It is designed to appeal to the imagination. But it is not science fiction: it is science. Cliche or not, ‘stranger than fiction’ expresses exactly how I feel about the truth. We are survival machines—robot vehicles blindly programmed to preserve the selfish molecules known as genes. This is a truth which still fills me with astonishment. Though I have known it for years, I never seem to get fully used to it. One of my hopes is that I may have some success in astonishing others. (Dawkins pp. vii)

Notice how in this statement, he states what natural living thingsqualiving are for, according to evolutionary theory. Later on Dawkins characterizes his ‘Selfish Gene’ thesisagainst a background of competing evolutionary teleologies:

The trouble with these [other]books is that their authors got it totally and utterly wrong. They got it wrong because they misunderstood how evolution works. They made the erroneous assumption that the important thing in evolution is the good of the species (or the group) rather than the good of the individual (or the gene).(Dawkins pp. 2)

The “Selfish Gene” theory is a teleological theory that prescribes what we should expect to find in the structure and behavior of living creatures:

If we were told that a man had lived a long and prosperous life in the world of Chicago gangsters, we would be entitled to make some guesses as to the sort of man he was. We might expect that he would have qualities such as toughness, a quick trigger finger, and the ability to attract loyal friends. These would not be infallible deductions, but you can make some inferences about a man’s character if you know something about the conditions in which he has survived and prospered. The argument of this book is that we, and all other animals, are machines created by our genes. Like successful Chicago gangsters, our genes have survived, in some cases for millions of years, in a highly competitive world. This entitles us to expect certain qualities in our genes. I shall argue that a predominant quality to be expected in a successful gene is ruthless selfishness. This gene selfishness will usually give rise to selfishness in individual behaviour. However, as we shall see, there are special circumstances in which a gene can achieve its own selfish goals best by fostering a limited form of altruism at the level of individual animals. ‘Special’ and ‘limited’ are important words in the last sentence. Much as we might wish to believe otherwise, universal love and the welfare of the species as a whole are concepts that simply do not make evolutionary sense. (Dawkins pp. 2)

So we can clearly see that the entire Selfish Gene theory is about natural teleology. Clearly we have come a long way from Athens to Oxford, butteleologicalconcepts arestill just as essential for Darwin as they are for Aristotle.

Conclusion: Ethics As Physics

Now we are in a position to ask some rather weird questions about morality. For example, what is the purpose of morality? There are two trends to be noticed in most modern authors: one is that morality is an inherent good; I am now thinking of Kant’s statement ‘There is nothing in heaven or earth that is good in itself except a good will.’ (Citation?)Others think that morality is some instrumental good; most consequentialism or contractualism would say that moral behavior serves to maximize the payoff of the felicific calculus. In the light of our previous discussion, we are not in a position to develop a new approach to this, that of biology. We shall strive to place ourselves in the epistemic position of some alien anthropologists who step off their flying saucer and observe various behaviors of the species Homo sapiens. How would they explain moral behavior within the limits of science alone? This is not an idle question; every day biologists in the field are faced with unexplained behaviors of a wide variety of organisms. An instructive example is a recent decade-long effort to explain the reproductive behavior of a certain slime-mold. This slime mold is a ‘colonial’ organism; meaning that while it does exhibit extensive cooperation, it is made up of separate cells with their own genotypes.


Among the many implications of this view are the following:

Morality is for a purpose, this purpose is the purpose for which we are alive, it is natural, morality is not a “by product” of the structure of our brains which evolved for some other purpose:

It may be objected that if some aspects of our capacity to reason conferred an evolutionary advantage, while other aspects were disadvantageous in that respect (perhaps because they lead us to act more altruistically that we would otherwise have done), then those other aspects would have been selected against and would have disappeared. … It appears to be the case, however, that we have retained capacities to reason that do not confer any evolutionary advantage and may even be disadvantageous. How can that be? A plausible explanation of the existence of these capacities is that the ability to reason comes as a package that could not be economically divided by evolutionary pressures. Either we have a capacity to reason that includes the capacity to do advance phyics and mathematics and grasp objective moral truths, or we would have a much more limited capacity to reason that lacks not only these abilities but other that confer an overriding evolutionary advantage. If reason is a unity of this kind, having the package would have been more conducive to survival than not having it. (de Lazari and Singer pp. 17)







Aristotle, & McKeon, R. (1941). The basic works of Aristotle.NY:Random House.

Boulter, Stephen. Metaphysics from a biological point of view. Palgrave Macmillan, 2013.

Dawkins, Richard. Theselfish gene. Oxford Univ Press, 2016.

De Cruz, Helen. Innate ideas as a naturalistic source of of mathematical knowledge; towards a Darwinian approach to mathematics. (PhD. dissertation) Brussel: Vrije Universiteit Brussel, 2007

De Lazari-Radek, Singer, P. “The objectivity of ethics and the unity of practical reason.” Ethicsvol. 123, no. 1 (October 2012), pp. 9-21.

Feser, Edward. “From Aristotle to John Searle and Back Again: Formal Causes, Teleology, and Computation in Nature.” Nova et vetera, vol. 14, no. 2, 2016, pp. 459–494., doi:10.1353/nov.2016.0039.

Haidt, Jonathan. Therighteousmind:whygoodpeoplearedivided by politics and religion.New York: Pantheon Books, 2012.

Hladky,V., Havlíček, J. “Was Tinbergen an Aristotelean? Comparison Of Tinbergen’s Four Whys And Aristotle’s Four Causes” Human Ethology Bulletinvol. 28, no 4, 2013: pp. 3-11

Hull, David L. and Michael Ruse, (eds.), 1998, The Philosophy of Biology, Oxford: Clarendon Press.

Lowe, Ernest Jonathan. The possibility of metaphysics: substance, identity, and time. Clarendon Press, 2004.

O’Rourke, F. “Aristotle and the Metaphysics of Evolution” The Review of Metaphysics vol. 56, September 2004, pp. 3-59.

1. In short, I will argue that adaptive purpose is an emergent quality of physics, and thus does not derive its telosfrom physics in the same way we find in Aristotle. So long as adaptive functions can be implemented in known physical interactions, then we have all we need for our concept of ‘purpose’, which we hope to show is substantially the same as the of Aristotle.


The Metaphysics of ‘Natural Goodness’, pt. II

This is part of a series where we outline a way that we might base some sort of Aristotelian value theory on evolutionary naturalism. In the previous post, we introduced

  1. A theory of how modern evolutionary biology fits into Aristototelean ideas about natural science ,especially formal causes.
  2. In this view, ethical theory falls under natural science thusly:
    1. It is the study of the principles and causes of the behavior certain living creatures.
    2. Moral behavior is behavior of a natural being, taking place in space and time
    3. It takes as its starting point the final causes of said behavior, which final causes are also one of the ‘Four Causes’, and are thus part of natural science.
  3. In modern biological terms forms or “essence” taken to be to creature’s genome. The “form” of the creature is the telos of the developmental process
  4. To accommodate evolution, we need to define ‘shallow’ and ‘deep’ versions of each of the first three causes.
  5. The ‘form’ is also the product of an evolutionary process.

In the following, we look at the material and efficient causes of natural beings, which in our view include moral beings such as humans.

Efficient Causes
In the original works of Aristotle, the male gamete was not the efficient and formal cause for sexually-reproducing beings was said to be, and the female was said to be the material cause.(Citation?)However, in light of modern science, we have to say that the female is themore properly efficient cause. She absorbs the matter and her body processes cause her food to take the form of a human. In addition, for modern science the formal cause is both male and femaleAsbefore, this sense of“form” is not merely the form as outward aspect but more essentially the deeper substantial form. The female takes the essence (or as I say it “deepform”)of her mate and mixes itwith her own to create the new form of the offspring. Here is where we run into an issue that many people consider Aristotle’s great shortcoming: the idea that Aristotelanforms are not subject to change. For my own part, I assume that he must have noticed the sense in whichforms were created in sexual reproduction. Every child isclearly seen to share in the forms of bothparents,because it might have the mother’s eyes and the father’s face.In spite of this mixture of form, the childonly has oneform.So even to the pre-modern mind itought to beclear that the form of the child has been created by combiningelements from other forms. HereI follow a view where individuation of organisms is not merely by matter but by individual essences. (See Witt 1996pp. 175ff) Whether or not you accept this as Aristotle’s intent in his extant works, it is clear that something like this is needed for the modern philosopher,not merely for the present case of sexual reproduction but even more so for many cases of intellectual products, such as literature, architectural design, graphic design, mechanical design, computer programming, and others.Individuals clearly have their own forms in both the shallow and deep senses: the outward aspect of an individual can be recognized just as surely as that of a species like a cardinal. Similarly, the deeper essence of a species and an individual both propagate their distinctive outward aspects and behavior through time, whether it be down the generations for a species or over a single lifetime for an individual. Individual essences are also needed to make sense of cloning and other artificial forms of precise emulation. So whether or not individual essences are part of the originalAristotelian metaphysics I will use them here.
The shallow and deep efficient causes exactly correspond to the shallow and deep senses of matter, so the definitions are the same except for italicizing the agent rather than matter. After this short return to formal causes, we can see that even in the phenomena available to Aristotle, we have strong reasons to see that while Aristotle’s analysis is still very much at home, even in thecommon-sense view of sexual reproduction we can see‘deep agency’ working with genes as ‘intelligible matter.
To sum up, we have two separate levels of efficient causality in biology:

  1. Shallow form – The female reproductive systemtakes matter from food and applies the form to it that results from combining elements from her own genes and those of her mate.
  2. Deep form – Natural selection manipulatesthe genome(the elementsor matterof inheritance)to create the formof the biological species. Note that the “agency” of selection forms the DNA, but DNA quagenetic material rather than quaorganic molecule.

NOTE: while I spoke of meiosisabove as being an efficient cause in mixing the formal elements (genes) from both parents, I left it out of the above summary for the reason that sexual reproduction is itself the result of natural selection. It is a paradigmatic case of the ‘evolution of evolvability’, where deep agency is built into the essence of the organism rather than left to ‘agencyofnatural selection.

Final Cause

The final causes of modern Aristotelian biology are also in the shallow and deep senses, but the shallow sense is twofold.

Final Cause as “Shallow ontogeny”

First, there is the sense in which ontogentic development is a goal-oriented behaviorwhere an organismcomes to be because of its own essence, as when a seed grows into an adult tree or an egg grows into a bird. In Aristotle’s Greek this was called ‘phusis’.

Final cause as “shallow adaptation”

Anothersortof goal-orientation in nature concerns the “fitness” of adaptations. Adaptation is essentiallyusefulness inavoiding extinction. The theory of evolution’s main task is to explainhow much more suitable the shallow form of an organism is than what might have occurred by chance. Notice that “chance” here isAristotle’s sense: something which is “for” something, but which does not have atelosas its originating cause. Now as much as you might have heard that “final causes” are notpart of modern biology; butnothing is more common than for a biologist to ask the question “What is xfor?” where “x” is some physical structureor behavior of some living creature. Consider the redness characteristic of malecardinals; what is it for? Biologists say that it is for the purpose of competing for mates, and Darwin’s theory explains how this is the case. Nothing would be more ridiculous thanto say that biology can have nothing to say about the purpose of plumage color in male birds, and that this should be the province of Platonism, natural theology, or revealed religion. If there is to be a science of living creatures, then purpose must be part of it. Why do cardinals lay eggs? To reproduce; and if one asks why they lay eggs, then we must say that reproduction is the purpose. Why do they have wings?We know that not only does the red plumage have a purpose, but we also know quabiologist that red plumage is actualfor-the-sake-ofsome purpose, and that this purpose is in the purview of natural science.
Clearly,there was no idea of desire in the mind of someone who made the cardinal; I am not saying that. If there were, cardinals would be artificial products. But as it is they are natural products, meaning that the form of the cardinal pre-exists only in the bodiesof actual cardinals. In my view, the whole point of naturalteleology quanaturalis that there is no pre-conception in the mind of some maker at all.The normativity and final causality of Aristotle’s god does not follow from conscious conceptions of purpose such as we find in our subjective experience, but rather in the role God or other prime mover (if any)plays in natural science. I feel that there is in fact a substantive conception of final cause in modern natural science, and that this conception has normative implications for moral theory, before we deal with that, we need look at the role of ‘Final Cause’ in both ancient and modern biology. In doing so, we hope to clear up any doubts you may have about teleology and modern science.

The Deep Telos a.k.a. the “FinalFinal Cause”

As with Aristotle’s other Four Causes the shallow and deep versions work on different levels; shallow forms the individual, while the deep forms the species-essenceitself quaintelligible matter. So while while clearly the species form provides the telosof development, and this species form follows adaptive function, there must be some higher final cause which determines why adaptive function is as it is; where does the “adaptive” get its essential normativity? There must be a “FinalFinal Cause” which explains all other subsidiary functions served by biological adaptations in nature: wings, legs, cell membranes, enzymes, gall bladders, mating rituals, dentition, are all adaptations that serve various lesser functions. However, there must be some highest function served by the various lower-level traits that we notice. What is it? First let us see what Aristotle says on the subject and compare his answer with the modern biologist.

Aristotle on the Final Cause of Life

The telos of life as such in Aristotle’s biology.

Of the psychic power above numerated some kinds of living things, as we have said, possess all, some less than all, others one only. Those we have mentioned are the nutritive, the appetitive, the sensory, the locomotive, and the power of thinking. Plants have none but the first, the nutritive, while another order of living things has this plus the sensory. (DeAnima II.2 414a30)

Among the many things done by living creatures, those which we call “essential” are reproduction and and nutrition, which I take to be pretty much the same as what we nowadays call “metabolism”. So far so good, Aristotle is in agreement with modern science thus far. How does he fare if we dig a little deeper?

It follows that first of all we must treat of nutrition and reproduction. For the nutritive soul is found along with all the others and is the most primitive and widely distributed power of soul, being indeed that one in virtue of which all are said to have life. The acts in which it manifests itself are reproduction and the use of food – reproduction I say, because any living thing that has reached its normal development and which is unmutilated, and whose mode of generation is not spontaneous, the most natural act is the production of another like itself, an animal producing an animal, a plant a plant, in order that, as far as its nature allows, it may partake in the eternal and divine. That is the goal towards which all things strive, and for the sake of which they do whatsoever their nature renders possible. (De AnimaII.2 415a25)

Here we find the introduction of distinctively Platonic influences; the Form of the organism is that by which:

  1. It is created.
  2. It is kept in being, i.e. it avoids death and decay.
  3. It is an individual “this’.
  4. It is “this such”, something of a species.
  5. It partakes of the “eternal” and “divine”, which supernatural reality is the final cause of all that comes-to-be.

Ross summarizes thusly: “Reproduction for has Aristotle this special interest, that the perpetuation of the type is for him the clearest evidence of the purposiveness of nature.” (pp. 125-67) Aristotle’s entire conception of purpose, the core concept of his ethics, politics, and astronomy, is primarily derived from biology.

‘[W]henever there is plainly some final end, to which a motion [not mere motion of matter, but here he refers to ontogeny] tends should nothing stand in the way, we always say that such a final end is the aim of the motion; and from this is evident that there must be a something or other really existing, corresponding to what we call by the name of Nature. For a given germ does not give rise to any chance living being, nor spring from any chance one; but each germ springs from a definite parent and gives rise to a definite progeny. And thus it is the germ that is the ruling influence and fabricator of offspring. For it is these by nature, the offspring being at any rate that which id nature will spring from it. At the same time the offspring is anterior to the germ; for germ and perfected progeny are related as the developmental process and the result. Anterior, however, to both germ and product is the organism from which the germ was derived, For every germ implies two organisms, the parent and the progeny. For germ or seed is both the seed of the organism from which it came, of the horse, for instance, from which it was derived, and the seed of the organism that will eventually arise from it…’ (De Partibus AnimaliumI.1 641b23-29)

This is where the critique of Platonic Forms really comes into play; for natural beings, the substance of the organism is physically interior to the organism and not in Plato’s Ideal realm. In the case of natural organisms, the essence is three causes at once:

  1. Formal cause – The essence is an arrangement of material elements, a form of matter.
  2. Efficient cause – this arrangement is such that it can reproduce; arrange other matter into another individual with the same essence
  3. Final cause – The entire purpose of having creatures of such a form is to reproduce, thus participating in the “eternal”.

We have now given a brief summary of one possible view of final causes in Aristotle’s biology. I am not an Aristotle expert by any means, but this is at least a possible interpretation, Furthermore, it has the virtue of being the possible interpretation that makes Aristotle the most interesting to the modern naturalist.

Aristotle, & McKeon, R. (1941). The basic works of Aristotle.NY:Random House.
Boulter, Stephen. Metaphysics from a biological point of view. Palgrave Macmillan, 2013.
Dawkins, Richard. Theselfish gene. Oxford Univ Press, 2016.
De Lazari-Radek, Singer, P. “The objectivity of ethics and the unity of practical reason.” Ethicsvol. 123, no. 1 (October 2012), pp. 9-21.
Hladky,V., Havlíček, J. “Was Tinbergen an Aristotelean? Comparison Of Tinbergen’s Four Whys And Aristotle’s Four Causes” Human Ethology Bulletinvol. 28, no 4, 2013: pp. 3-11
Lowe, Ernest Jonathan. The possibility of metaphysics: substance, identity, and time. Clarendon Press, 2004.
O’Rourke, F. “Aristotle and the Metaphysics of Evolution” The Review of Metaphysics vol. 56, September 2004, pp. 3-59.

1. In short, I will argue that adaptive purpose is an emergent quality of physics, and thus does not derive its telosfrom physics in the same way we find in Aristotle. So long as adaptive functions can be implemented in known physical interactions, then we have all we need for our concept of ‘purpose’, which we hope to show is substantially the same as the of Aristotle.

The “Bhagavad Gita”, an Evolutionary Interpretation, Pt. III


Many chapters of the Gita begin with a question from Arjuna, for this one it is this:

“Why do you want me to engage in this ghastly warfare, if you think that intelligence is better than fruitive work?” (III.1)

Before we proceed, let us point out that this question is relevant to a major debate in Aristotleean ethics: whether the good (Greek “eudaimonia”) is intellectualistic or comprehensive. The former view takes its cue from the fact that in various places Aristotle claims that the only truly inherently good activity is the contemplation of the Divine: metaphysics, theology, fundamental physical laws, et cetera. The comprehensive view of the good live takes its cue from the fact that in other places (e.g. Nicomachean EthicsI.1), he implies the contrary, that political science is the highest science, or that virtuous action is inherently good. According to the intellectualistic view, these latter activities would only be instrumentally good, This same dilemma is exactly what we see here between Krishna and Arjuna: while Krishna is arguing for a comprehensive view of the good where fulfilling caste duties are inherently good, even in the case of the slaughter of one’s friends and peers who happen to have been on the other side. In Indian, the trend towards an intellectualistic view of the Good is at least as strong as among the Greeks, so what Krishna is arguing here is not self-evident. The options available to him could include be the following:

  1. Pacifism – Yhe war was wrong, and he should lay down his weapons.
  2. Instrumentalism – The war is only just in the sense that we cannot get around them, and being willing to fight wars actually prevents wars by deterring invasions from the wicked.
  3. War as Bad Karma – Being is any other caste than the Brahmin is due to bad karma, therefore the war is penance for past misdeeds rather than some postive occasion for virtuous action.
  4. Tragedy – As in Greek Tragedy, Arjuna’s dilemma need not be resolvable; there might be conflicting duties that each make absolute demands. Therefore it might be the case that he has no available choice that does not incur bad karma.
  5. Holy War – The Kurukshetra War and perhaps many other wars are an inherently good occasions for virtuous action.

Krishna claims that there is one supreme Good for all humanity, but that different people realize it in different ways (III.3-4). This is a primary principle of “Raja Yoga” – that yoga is different in different types of people while still retaining a universal essence common to all.

Working With Nature

Physical determinism? Sort of.

So far we are on Socratic turf, but in the next verse, we enter the realm of distinctively Indian thought:

Everyone is forced to act helplessly according to the qualities he has acquired from the modes of material nature; therefore no one can refrain from doing something, not even for a moment. (III.5)

The meaning of this verse refers to the “Three Gunas” (or Three Modes of Material Nature). The “Gunas” are kind of like Yin and Yang or the elements of Western thoughtt (fire, water, air, earth, spirit). They are concepts of traditional physical science just as the former are the principles and causes of Traditional Chinese Medicine and the medical theory Hippocrates and Galen, the three Gunas are also used in “ayurveda”, traditional Indian medicine. So it seems that Krishna is accepting that human action comes from the workings of material elements. Clearly, his concept of ‘material’ and ‘natural’ are different from the modern, but in a sense this is not far from modern naturalistic arguments rejective freewill. Here his argument is related to the Buddhist idea of “No-Soul” or “No-Self” (Sanskrit “Anatman”, Pali ‘annatta’). Whereas traditional Indian thought ascribed all awareness and action to an inner “Self”, not only in the individual, but in the world as a whole, Buddhism rejects such an idea, saying that human action is the result of the workings of natural elements, and that nothing in the world could possibly have a True Self. In fact, according to Buddhism, the very concept of a True Self is a form of ignorance; to be happy we should just accept that we are acting out of nature and karma. In ascribing all human action to the Three Gunas, Krishna is granting some validity to this disctinctively Buddhist dogma, in spite of its anti-Vedic implications for Buddhists. Like Buddha, Krishna is claiming that we should just accept that our actions are the results of physical events in order to have true knowledge and happiness. But unlike Buddha, Krishna accepts the Atman, so his reaction to phyiscal determinism is different. While Buddhist doctrine is rather intellectualistic, based on meditation on one’s own Un-Selfhood, Krishna has a more practical recommendation: do one’s work as a sacrifice to the Self.

…if a sincere persons tries to control the active senses by the mind and begins karma-yoga without attachment, he is by far superior. Perform your prescribed duty, for doing so is better than not working. One cannot even maintain one’s physical body without work. Work as a sacrifice for Vishnu has to be performed, otherwise work causes bondage in this material world. Therefore … perform your prescribed duties for his satisfaction, and in that way you will always remain free from bondage. (III.9)

The Purpose of Life

So on this view, all work is purposeful in two senses:

  1. First, it has its mundane purpose as a productive or instrumental activity.
  2. It is a sacrifice to the Divine.

Once again, Krishna is trying to expand or sublimate the meaning of ‘sacrifice’ (Skt. ‘yajna’), by including normal work, warfare, meditation, prayer, and study. In my very un-expert view, he is getting around Buddha’s metaphysical rejection of Atman (which we will not deal with here now), by reclaiming Atman as a teleological principle. This means that we could have an Atmanin a way that does not conflict with the physical causation of our actions and mental workings. Without completely rejecting the concept of substantial soul-dualism, he seems to define our self in ways that are fundamentally about teleology. There are various ways he approaches this:

  1. Purpose as “For the sake of which” – The service if the Atman is in some way the reason for the coming-to-be of living things as such. Thus, the service of the Atman is our originating purpose, in the sense that transport is the originating purpose of a vehicle.
  2. Purpose as “for the benefit of which” – in addition to the above, we also speak of purpose as for the benefits of some living recipient. There are two sorts of recipient spoken of in th Gita:
    1. Humanhappinessdepends on serving the Atman; thus humans benefit from doing their duty.
    2. The “Supreme Enjoyer” – Later on, Krishna will argue that all purpose-oriented behavior in the cosmos (human and natural) is actually for the benefit ofthe Supreme Atman.

This last point is rather unique to the Gita; in Aristotle, for example, action and natural changeis not for the benefit ofGod, but merely for the sake ofGod. He claimed that the life-cycle of living creatures, for example, was for the sake of participating in the eternal, and that such a life-cycle’s progress was also for the benefit of the individual organisms, but Atistotle would not say that living processes were somehow for the benefit of God.I do not believe that Krishnais claiming that God is made happy or avoids pain in the same way as a human, but that God is already the ultimate enjoyer of all the productive activities of all living things. This is rather weird thing to say; it makes sense to say that we ought to imagine ourselves pleasing God or avoiding His wrath, but not that God issubjectof all goal oriented behavior rather than the mere object.

Dharmaas the Love of Life.

In the next few verses, Krishna elaborates on this as follows:

  1. First he discusses the traditional Vedic practice of animal sacrifice; its benefits both in terms of prosperity and morality. In this traditional concept, sacrifice is for the devas, who are polytheistic mythical gods.(II.10-14)
  2. Then Krishna claims that sacrifices and all Vedic practices ultimately come from and are for the benefit of Brahman, the monotheistic God or Self. (II.15-16)
  3. Thus, it is possible and ultimately better for one to serve the Atman directly by working out of “Self-Realization”. (II.17-19)
  4. There is a moral system based on this which is a ‘virtue theory’, where we strive to become like great moral heroes and saints.(II.20-21, 23)
  5. Why is such a moral life of virtue necessary? There are two answers to this:
    1. Intellectualist– A life of virtue is needful to calm the mind and facilitate Samadhi, as in Buddha and Patanjali.
    2. Comprehensive – The continuation of life is not a meremeans but agood thing in its own right.

In this work, I shall argue the latter based on verses like the following:

‘If I did not preform the prescribed duties, all these worlds would be put to ruination, and I would thereby destroy the peace of all living beings.’ (III.24)

Based on verses like these and other factors, I read the Gita as a program for an actual way of life that will last for ever, not for a few mystics or priests who drop out of society and life and look down on workers and warriors. While mystics have their place in this society, all people have a valid role to play, all of society serves the Good,and all of a proper society is itself Good.