10 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. |
| 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. |
| 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. |
| 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 |
| 6356 | Maybe a reliable justification must come from a process working with its 'proper function' [Plantinga, by Pollock/Cruz] |
| Full Idea: A modified version of reliabilism proposes that a belief is justified in case it is the product of a process that is working according to its 'proper function' in the environment for which it is appropriate. | |
| From: report of Alvin Plantinga (Warrant and Proper Function [1993]) by J Pollock / J Cruz - Contemporary theories of Knowledge (2nd) §1.5.4 | |
| A reaction: Something might infallibly indicate something without that being its proper function (e.g. 'Red sky at night/ Shepherds' delight'). An inaccurate clock is fulfilling its proper function (telling the time), but not very well. |
| 21386 | We should accept as explanations all the plausible ways in which something could come about [Epicurus] |
| Full Idea: The phases of the Moon could happen in all the ways [at least four] which the phenomena in our experience suggest for the explanation of this kind of thing - as long as one is not so enamoured of unique explanations as to groundlessly reject the others. | |
| From: Epicurus (Letter to Pythocles [c.292 BCE], 94) | |
| A reaction: Very interesting, for IBE. While you want to embrace the 'best', it is irrational to reject all of the other candidates, simply because you want a single explanation, if there are no good grounds for the rejection. |
| 14051 | A cosmos is a collection of stars and an earth, with some sort of boundary, movement and shape [Epicurus] |
| Full Idea: A cosmos is a circumscribed portion of the heavens containing stars and an earth; it is separated from the unlimited, with a boundary which is rare or dense; it is revolving or stationary; it is round or triangular, or some shape. All these are possible. | |
| From: Epicurus (Letter to Pythocles [c.292 BCE], 88) | |
| A reaction: Notice that there seem to exist the 'heavens' which extend beyond the cosmos. See Idea 14036, saying that there are many other cosmoi in the heavens. |
| 1828 | God does not intervene in heavenly movements, but is beyond all action and perfectly happy [Epicurus] |
| Full Idea: Let us beware of making the Deity interpose in heavenly movements, for that being we ought to suppose exempt from all occupation and perfectly happy. | |
| From: Epicurus (Letter to Pythocles [c.292 BCE]), quoted by Diogenes Laertius - Lives of Eminent Philosophers 10.25 |