8 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'. |
| 12427 | All of mathematics is properties of the whole numbers [Kronecker] |
| Full Idea: All the results of significant mathematical research must ultimately be expressible in the simple forms of properties of whole numbers. | |
| From: Leopold Kronecker (works [1885], Vol 3/274), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 09.5 | |
| A reaction: I've always liked Kronecker's line, but I'm beginning to realise that his use of the word 'number' is simply out-of-date. Natural numbers have a special status, but not sufficient to support this claim. |
| 10091 | God made the integers, all the rest is the work of man [Kronecker] |
| Full Idea: God made the integers, all the rest is the work of man. | |
| From: Leopold Kronecker (works [1885]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Intro | |
| A reaction: This famous remark was first quoted in Kronecker's obituary. A response to Dedekind, it seems. See Idea 10090. Did he really mean that negative numbers were the work of God? We took a long time to spot them. |
| 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…. |
| 1590 | The just man does not harm his enemies, but benefits everyone [Plato] |
| Full Idea: First, Socrates, you told me justice is harming your enemies and helping your friends. But later it seemed that the just man, since everything he does is for someone's benefit, never harms anyone. | |
| From: Plato (Clitophon [c.372 BCE], 410b) | |
| A reaction: Socrates certainly didn't subscribe to the first view, which is the traditional consensus in Greek culture. In general Socrates agreed with the views later promoted by Jesus. |