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Ideas for 'fragments/reports', 'The Evolution of Logic' and 'works'

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15 ideas

5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
9179 Frege frequently expressed a contempt for language [Frege, by Dummett]
     Full Idea: Frege frequently expressed a contempt for language.
     From: report of Gottlob Frege (works [1890], p.228) by Michael Dummett - Frege's Distinction of Sense and Reference p.228
     A reaction: This strikes me as exactly the right attitude for a logician to have. Russell seems to have agreed. Attitudes to vagueness are the test case. Over-ambitious modern logicians dream of dealing with vagueness. Forget it. Stick to your last.
5. Theory of Logic / C. Ontology of Logic / 2. Platonism in Logic
13473 Frege thinks there is an independent logical order of the truths, which we must try to discover [Frege, by Hart,WD]
     Full Idea: Frege thinks there is a single right deductive order of the truths. This is not an epistemic order, but a logical order, and it is our job to arrange our beliefs in this order if we can make it out.
     From: report of Gottlob Frege (works [1890]) by William D. Hart - The Evolution of Logic 2
     A reaction: Frege's dream rests on the belief that there exists a huge set of logical truths. Pluralism, conventionalism, constructivism etc. about logic would challenge this dream. I think the defence of Frege must rest on Russellian rooting of logic in nature.
5. Theory of Logic / E. Structures of Logic / 7. Predicates in Logic
6076 For Frege, predicates are names of functions that map objects onto the True and False [Frege, by McGinn]
     Full Idea: For Frege, a predicate does not refer to the objects of which it is true, but to the function that maps these objects onto the True and False; ..a predicate is a name for this function.
     From: report of Gottlob Frege (works [1890]) by Colin McGinn - Logical Properties Ch.3
     A reaction: McGinn says this is close to the intuitive sense of a property. Perhaps 'predicates are what make objects the things they are?'
3319 Frege gives a functional account of predication so that we can dispense with predicates [Frege, by Benardete,JA]
     Full Idea: The whole point of Frege's functional account of predication lies in its allowing us to dispense with all properties across the board.
     From: report of Gottlob Frege (works [1890]) by José A. Benardete - Metaphysics: the logical approach Ch.9
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
9871 Frege always, and fatally, neglected the domain of quantification [Dummett on Frege]
     Full Idea: Frege persistently neglected the question of the domain of quantification, which proved in the end to be fatal.
     From: comment on Gottlob Frege (works [1890]) by Michael Dummett - Frege philosophy of mathematics Ch.16
     A reaction: The 'fatality' refers to Russell's paradox, and the fact that not all concepts have extensions. Common sense now says that this is catastrophic. A domain of quantification is a topic of conversation, which is basic to all language. Cf. Idea 9874.
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 / I. Semantics of Logic / 3. Logical Truth
16884 Basic truths of logic are not proved, but seen as true when they are understood [Frege, by Burge]
     Full Idea: In Frege's view axioms are basic truth, and basic truths do not need proof. Basic truths can be (justifiably) recognised as true by understanding their content.
     From: report of Gottlob Frege (works [1890]) by Tyler Burge - Frege on Knowing the Foundations 1
     A reaction: This is the underpinning of the rationalism in Frege's philosophy.
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
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)
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)
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'.