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.

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