10 ideas
| 23295 | Truth cannot be reduced to anything simpler [Davidson] |
| Full Idea: We cannot hope to underpin the concept of truth with something more transparent or easier to grasp. | |
| From: Donald Davidson (The Folly of Trying to Define Truth [1999], p.21) | |
| A reaction: I suppose precise accounts of correspondence or coherence are offered as replacements for truth, but neither of those ever seem to be possible. I agree with accepting truth as a primitive. |
| 23298 | Neither Aristotle nor Tarski introduce the facts needed for a correspondence theory [Davidson] |
| Full Idea: Neither Aristotle's formula nor Tarski's truth definitions are sympathetic to the correspondence theory, because they don't introduce entities like facts or states of affairs for sentences to correspond. | |
| From: Donald Davidson (The Folly of Trying to Define Truth [1999], p.25) | |
| A reaction: This seems convincing, although it is often claimed that both theories offer a sort of correspondence. |
| 23297 | The language to define truth needs a finite vocabulary, to make the definition finite [Davidson] |
| Full Idea: If the definition of the truth predicate is to be finite (Tarski insisted on this), the definition must take advantage of the fact that sentences, though potentially infinite in number, are constructed from a finite vocabulary. | |
| From: Donald Davidson (The Folly of Trying to Define Truth [1999], p.23) | |
| A reaction: Not sure whether this is in the object language or the meta-language, though I guess the former. |
| 23296 | We can elucidate indefinable truth, but showing its relation to other concepts [Davidson] |
| Full Idea: We can still say revealing things about truth, by relating it to other concepts like belief, desire, cause and action. | |
| From: Donald Davidson (The Folly of Trying to Define Truth [1999], p.21) | |
| A reaction: The trickiest concept to link it to is meaning. I think Davidson's view points to the Axiomatic account of truth, which flourished soon after Davidson wrote this. We can give rules for the correct use of 'true'. |
| 17879 | Axiomatising set theory makes it all relative [Skolem] |
| Full Idea: Axiomatising set theory leads to a relativity of set-theoretic notions, and this relativity is inseparably bound up with every thoroughgoing axiomatisation. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.296) |
| 17878 | If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem] |
| Full Idea: Löwenheim's theorem reads as follows: If a first-order proposition is satisfied in any domain at all, it is already satisfied in a denumerably infinite domain. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.293) |
| 17880 | Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem] |
| Full Idea: The initial foundations should be immediately clear, natural and not open to question. This is satisfied by the notion of integer and by inductive inference, by it is not satisfied by the axioms of Zermelo, or anything else of that kind. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.299) | |
| A reaction: This is a plea (endorsed by Almog) that the integers themselves should be taken as primitive and foundational. I would say that the idea of successor is more primitive than the integers. |
| 17881 | Mathematician want performable operations, not propositions about objects [Skolem] |
| Full Idea: Most mathematicians want mathematics to deal, ultimately, with performable computing operations, and not to consist of formal propositions about objects called this or that. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.300) |
| 23294 | It is common to doubt truth when discussing it, but totally accept it when discussing knowledge [Davidson] |
| Full Idea: You are following Plato's lead if you worry about the concept of truth when it is the focus of your attention, but you pretend you understand it when trying to cope with knowledge (or belief, memory, perception etc.). | |
| From: Donald Davidson (The Folly of Trying to Define Truth [1999], p.20) | |
| A reaction: Nice to find someone pointing out this absurdity. He says Hume does the same with doubts about the external world, which he ignores when discussing other minds. Belief is holding true; only truths are actually remembered…. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |