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All the ideas for 'Letters to Edward Stillingfleet', 'works' and 'On the Nature of Truth and Falsehood'

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10 ideas

3. Truth / A. Truth Problems / 2. Defining Truth
In everyday language, truth seems indefinable, inconsistent, and illogical [Tarski]
     Full Idea: In everyday language it seems impossible to define the notion of truth or even to use this notion in a consistent manner and in agreement with the laws of logic.
     From: Alfred Tarski (works [1936]), quoted by Feferman / Feferman - Alfred Tarski: life and logic Int III
     A reaction: [1935] See Logic|Theory of Logic|Semantics of Logic for Tarski's approach to truth.
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
For Russell, both propositions and facts are arrangements of objects, so obviously they correspond [Horwich on Russell]
     Full Idea: Given Russell's notion of a proposition, as an arrangement of objects and properties, it is hard to see how there could be any difference at all between such a proposition and the fact corresponding to it, since they each involve the same arrangement.
     From: comment on Bertrand Russell (On the Nature of Truth and Falsehood [1910]) by Paul Horwich - Truth (2nd edn) Ch.7.35
     A reaction: This seems a little unfair, given that Russell (in 1912) uses the notion now referred to as 'congruence', so that the correspondence is not in the objects and properties, but in how they are 'ordered', which may differ between proposition and fact.
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
Tarski thought axiomatic truth was too contingent, and in danger of inconsistencies [Tarski, by Davidson]
     Full Idea: Tarski preferred an explicit definition of truth to axioms. He says axioms have a rather accidental character, only a definition can guarantee the continued consistency of the system, and it keeps truth in harmony with physical science and physicalism.
     From: report of Alfred Tarski (works [1936]) by Donald Davidson - Truth and Predication 2 n2
     A reaction: Davidson's summary, gleaned from various sources in Tarski. A big challenge for modern axiom systems is to avoid inconsistency, which is extremely hard to do (given that set theory is not sure of having achieved it).
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
There is no clear boundary between the logical and the non-logical [Tarski]
     Full Idea: No objective grounds are known to me which permit us to draw a sharp boundary between the two groups of terms, the logical and the non-logical.
     From: Alfred Tarski (works [1936]), quoted by Alan Musgrave - Logicism Revisited §3
     A reaction: Musgrave is pointing out that this is bad news if you want to 'reduce' something like arithmetic to logic. 'Logic' is a vague object.
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
Logical consequence: true premises give true conclusions under all interpretations [Tarski, by Hodges,W]
     Full Idea: Tarski's definition of logical consequence (1936) is that in a fully interpreted formal language an argument is valid iff under any allowed interpretation of its nonlogical symbols, if the premises are true then so is the conclusion.
     From: report of Alfred Tarski (works [1936]) by Wilfrid Hodges - Model Theory 3
     A reaction: The idea that you can only make these claims 'under an interpretation' seems to have had a huge influence on later philosophical thinking.
Logical consequence is when in any model in which the premises are true, the conclusion is true [Tarski, by Beall/Restall]
     Full Idea: Tarski's 1936 definition of logical consequence is that in any model in which the premises are true, the conclusion is true too (so that no model can make the conclusion false).
     From: report of Alfred Tarski (works [1936]) by JC Beall / G Restall - Logical Consequence 3
     A reaction: So the general idea is that a logical consequence is distinguished by being unstoppable. Sounds good. But then we have monotonic and non-monotonic logics, which (I'm guessing) embody different notions of consequence.
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Tarski improved Hilbert's geometry axioms, and without set-theory [Tarski, by Feferman/Feferman]
     Full Idea: Tarski found an elegant new axiom system for Euclidean geometry that improved Hilbert's earlier version - and he formulated it without the use of set-theoretical notions.
     From: report of Alfred Tarski (works [1936]) by Feferman / Feferman - Alfred Tarski: life and logic Ch.9
9. Objects / D. Essence of Objects / 3. Individual Essences
Every individual thing which exists has an essence, which is its internal constitution [Locke]
     Full Idea: I take essences to be in everything that internal constitution or frame for the modification of substance, which God in his wisdom gives to every particular creature, when he gives it a being; and such essences I grant there are in all things that exist.
     From: John Locke (Letters to Edward Stillingfleet [1695], Letter 1), quoted by Simon Blackburn - Quasi-Realism no Fictionalism
     A reaction: This is the clearest statement I have found of Locke's commitment to essences, for all his doubts about whether we can know such things. Alexander says (ch.13) Locke was reacting against scholastic essence, as pertaining to species.
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
If it is knowledge, it is certain; if it isn't certain, it isn't knowledge [Locke]
     Full Idea: What reaches to knowledge, I think may be called certainty; and what comes short of certainty, I think cannot be knowledge.
     From: John Locke (Letters to Edward Stillingfleet [1695], Letter 2), quoted by Simon Blackburn - Quasi-Realism no Fictionalism
     A reaction: I much prefer that fallibilist approach offered by the pragmatists. Knowledge is well-supported belief which seems (and is agreed) to be true, but there is a small shadow of doubt hanging over all of it.
19. Language / D. Propositions / 6. Propositions Critique
In 1906, Russell decided that propositions did not, after all, exist [Russell, by Monk]
     Full Idea: With a characteristic readiness to abandon views that he had previously considered definitively correct, Russell declared in 1906 that there were, after all, no such 'things' as propositions. It is judgements that are true or false.
     From: report of Bertrand Russell (On the Nature of Truth and Falsehood [1910]) by Ray Monk - Bertrand Russell: Spirit of Solitude Ch.6
     A reaction: Written 1906. Russell developed a 'multiple relation theory of judgement'. But if a judgement is an assessment of truth or falsehood, what is it that is being assessed?