Ideas from 'works' by Alfred Tarski [1936], by Theme Structure

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3. Truth / A. Truth Problems / 2. Defining Truth
In everyday language, truth seems indefinable, inconsistent, and illogical
                        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 / G. Axiomatic Truth / 1. Axiomatic Truth
Tarski thought axiomatic truth was too contingent, and in danger of inconsistencies
                        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
                        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 is when in any model in which the premises are true, the conclusion is true
                        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.
Logical consequence: true premises give true conclusions under all interpretations
                        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.
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Tarski improved Hilbert's geometry axioms, and without set-theory
                        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