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Ideas for 'The Evolution of Logic', 'Philosophy of Language' and 'Deflating Existential Consequence'

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11 ideas

5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
7755 Singular terms refer, using proper names, definite descriptions, singular personal pronouns, demonstratives, etc. [Lycan]
     Full Idea: The paradigmatic referring devices are singular terms, denoting particular items. In English these include proper names, definite descriptions, singular personal pronouns, demonstrative pronouns, and a few others.
     From: William Lycan (Philosophy of Language [2000], Ch. 1)
     A reaction: This list provides the agenda for twentieth century philosophy of language, since this is the point where language is supposed to hook onto the world.
5. Theory of Logic / F. Referring in Logic / 1. Naming / e. Empty names
12446 Names function the same way, even if there is no object [Azzouni]
     Full Idea: Names function the same way (semantically and grammatically) regardless of whether or not there's an object that they refer to.
     From: Jody Azzouni (Deflating Existential Consequence [2004], Ch.3 n55)
     A reaction: I take this to be a fairly clear rebuttal of the 'Fido'-Fido view of names (that the meaning of the name IS the dog), which never seems to quite go away. A name is a peg on which description may be hung, seems a good slogan to me.
5. Theory of Logic / G. Quantification / 3. Objectual Quantification
13506 The universal quantifier can't really mean 'all', because there is no universal set [Hart,WD]
     Full Idea: All the main set theories deny that there is a set of which everything is a member. No interpretation has a domain with everything in it. So the universal quantifier never gets to mean everything all at once; 'all' does not mean all.
     From: William D. Hart (The Evolution of Logic [2010], 4)
     A reaction: Could you have an 'uncompleted' universal set, in the spirit of uncompleted infinities? In ordinary English we can talk about 'absolutely everything' - we just can't define a set of everything. Must we 'define' our domain?
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
13512 Modern model theory begins with the proof of Los's Conjecture in 1962 [Hart,WD]
     Full Idea: The beginning of modern model theory was when Morley proved Los's Conjecture in 1962 - that a complete theory in a countable language categorical in one uncountable cardinal is categorical in all.
     From: William D. Hart (The Evolution of Logic [2010], 9)
13505 Model theory studies how set theory can model sets of sentences [Hart,WD]
     Full Idea: Modern model theory investigates which set theoretic structures are models for which collections of sentences.
     From: William D. Hart (The Evolution of Logic [2010], 4)
     A reaction: So first you must choose your set theory (see Idea 13497). Then you presumably look at how to formalise sentences, and then look at the really tricky ones, many of which will involve various degrees of infinity.
13511 Model theory is mostly confined to first-order theories [Hart,WD]
     Full Idea: There is no developed methematics of models for second-order theories, so for the most part, model theory is about models for first-order theories.
     From: William D. Hart (The Evolution of Logic [2010], 9)
13513 Models are ways the world might be from a first-order point of view [Hart,WD]
     Full Idea: Models are ways the world might be from a first-order point of view.
     From: William D. Hart (The Evolution of Logic [2010], 9)
5. Theory of Logic / K. Features of Logics / 6. Compactness
13496 First-order logic is 'compact': consequences of a set are consequences of a finite subset [Hart,WD]
     Full Idea: First-order logic is 'compact', which means that any logical consequence of a set (finite or infinite) of first-order sentences is a logical consequence of a finite subset of those sentences.
     From: William D. Hart (The Evolution of Logic [2010], 3)
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / c. Berry's paradox
13484 Berry's Paradox: we succeed in referring to a number, with a term which says we can't do that [Hart,WD]
     Full Idea: Berry's Paradox: by the least number principle 'the least number denoted by no description of fewer than 79 letters' exists, but we just referred to it using a description of 77 letters.
     From: William D. Hart (The Evolution of Logic [2010], 3)
     A reaction: I struggle with this. If I refer to 'an object to which no human being could possibly refer', have I just referred to something? Graham Priest likes this sort of idea.
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / c. Burali-Forti's paradox
13482 The Burali-Forti paradox is a crisis for Cantor's ordinals [Hart,WD]
     Full Idea: The Burali-Forti Paradox was a crisis for Cantor's theory of ordinal numbers.
     From: William D. Hart (The Evolution of Logic [2010], 3)
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
13507 The machinery used to solve the Liar can be rejigged to produce a new Liar [Hart,WD]
     Full Idea: In effect, the machinery introduced to solve the liar can always be rejigged to yield another version the liar.
     From: William D. Hart (The Evolution of Logic [2010], 4)
     A reaction: [He cites Hans Herzberger 1980-81] The machinery is Tarski's device of only talking about sentences of a language by using a 'metalanguage'.