8 ideas
10153 | 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. |
19141 | 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). |
10048 | 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. |
10694 | 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. |
10479 | 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. |
10157 | 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 |
7844 | The Golden Rule is accepted everywhere, and gives a fixed target for morality [Voltaire] |
Full Idea: Pascal asks where we can find a fixed point in morality. The answer is in that single maxim accepted by all nations: "Do not do to others what you would not like to have done to you". | |
From: Francois-Marie Voltaire (Philosophical Letters from England [1733], 25) | |
A reaction: Should I only offer to my guests foods which I myself like? If I don't mind a bit of pain, is it all right to inflict it? It is a sensible rule, but not precise enough for philosophy. |
7482 | Resurrection developed in Judaism as a response to martyrdoms, in about 160 BCE [Anon (Dan), by Watson] |
Full Idea: The idea of resurrection in Judaism seems to have first developed around 160 BCE, during the time of religious martyrdom, and as a response to it (the martyrs were surely not dying forever?). It is first mentioned in the book of Daniel. | |
From: report of Anon (Dan) (27: Book of Daniel [c.165 BCE], Ch.7) by Peter Watson - Ideas | |
A reaction: Idea 7473 suggests that Zoroaster beat them to it by 800 years. |