NOTE: These are my notes from an earlier presentation to Ottawa Cognitive Science Meetup.
Who cares about semantics?
- Linguistics needs another neutral language that makes clear logical and semantic connections or distinctions of Natural Language.
- Philosophy- Frege, Russell, Moore, et al used logical notation as a “semantic microscope” to analyze the claims of science, ethics, etc.
- Psychology takes semantic theories as material for making psycholinguistic hypotheses.
- Artificial Intelligence, contra the ”the Chinese Room”, needs to understand the meaning of natural language in order to process it.
Socrates- Discovered the very idea of semantics, that is=t could be interesting to worry about the meaning of such terms as “good”, “virtue”, “piety”, etc.
Plato- Proposed the theory of “Ideas” (eidoi, sing. eidos).
Aristotle- Created the study of formal logic.
Modern semantic theory began with German mathematician and philosopher Gottlob Frege (1848-1925), who founded the movement “analytic philosophy”, which defines philosophical research in much of the English-speaking world, Austria and Finland.
Frege began his research trying to axiomatize mathematics; i.e., derive math from logic. He failed, but his failure is one of the most instructive failures of all time, since cognitive and computer science are based on his efforts.
His first discovery is the distinction between sense and reference. “Reference” is the set of objects intended by a statement, and “sense” is how the reference is intended. For example, one can refer to the planet Venus in three ways, “Venus”, “the Morning Star”, or “The Evening Star”. In other words, all three of these terms has the same reference; they mean the same object. However, they have different senses in that they determine their object in three different ways.
- Venus = Venus
- Venus = Morning Star
- Venus = Evening Star
- Evening Star = Morning Star
He devised his system of logical notation as a “semantic microscope.” Rather than replacing natural language, logical notation lays bare language at the micro level. His notation is horrible to decode, so others have revised it using his ideas as a starting point.
- éxù Û “the semantic value of x”
- {x} Û ”the set of x”
- [“Churchhill smoked.”] Û [ áChurchillñ Î {smokers}]
- é”smoked”ùÛ{individuals who smoked}Û{Groucho Marx, Cmd. Che, Chucrchill, Sherlock Holmes, etc.}
- éABù is true for any sentence “AB” (if A is a NP and B is an intransitive VP) iff [ éAùÎ{B}].
Predicate logic.
Natural language suffers from quantifier ambiguity.
Ø negation
” universal -“for any____ ”
$ existential – “there is at least one___“
® implication- “if A then B”
“Beer is not available everywhere.”
Ø(“x) {xL®(ØxB)}
$x(xL+ØxB)
“Somebody voted for every candidate.”
$x”y(yC®xVy)
“y(yC®$x(xVy))
Temporal logic.
“Chuchhill smoked.” Is true now, but it was not always true,, e.g., before he started smoking. Similarly, “Orangutans eat.” is true, even though it is in the present tense and the orangutans are all asleep.
Modal logic.
“Churchill was PM during WW2.” is true, although it is not necessarily true, since Churchill might not have been PM at all. Since the word “is” are used for both contingent and necessary statements, modal logic has been created that make these distinctions explicit.
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