12 ideas
| 18470 | Maybe truth-making is an unanalysable primitive, but we can specify principles for it [Smith,B] |
| Full Idea: The signs are that truth-making is not analysable in terms of anything more primitive, but we need to be able to say more than just that. So we ought to consider it as specified by principles of truth-making. | |
| From: Barry Smith (Truth-maker Realism: response to Gregory [2000], p.20), quoted by Fraser MacBride - Truthmakers 1.5 | |
| A reaction: This is the axiomatic approach to such problems - treat the target concept as an undefinable, unanalysable primitive, and then give rules for its connections. Maybe all metaphysics should work like that, with a small bunch of primitives. |
| 18469 | God might necessitate that something happen, but He is not the truth-maker for it [Smith,B] |
| Full Idea: Suppose that God wills that John kiss Mary now. God's willing thereby necessitates the truth of 'John is kissing Mary'. But God's act is not a truth-maker for this judgement. | |
| From: Barry Smith (Truth-maker Realism [1999], p.6), quoted by Fraser MacBride - Truthmakers 1.2 | |
| A reaction: The point is that truth-making relates to the fact that it happened, not what necessitated it to happen. But Armstrong might reply that his truth-maker 'necessitation' primitive is not the kind of necessitation found in worldly relations. |
| 11022 | Gentzen introduced a natural deduction calculus (NK) in 1934 [Gentzen, by Read] |
| Full Idea: Gentzen introduced a natural deduction calculus (NK) in 1934. | |
| From: report of Gerhard Gentzen (works [1938]) by Stephen Read - Thinking About Logic Ch.8 |
| 11065 | The inferential role of a logical constant constitutes its meaning [Gentzen, by Hanna] |
| Full Idea: Gentzen argued that the inferential role of a logical constant constitutes its meaning. | |
| From: report of Gerhard Gentzen (works [1938]) by Robert Hanna - Rationality and Logic 5.3 | |
| A reaction: Possibly inspired by Wittgenstein's theory of meaning as use? This idea was the target of Prior's famous connective 'tonk', which has the role of implying anything you like, proving sentences which are not logical consequences. |
| 11023 | The logical connectives are 'defined' by their introduction rules [Gentzen] |
| Full Idea: The introduction rules represent, as it were, the 'definitions' of the symbols concerned, and the elimination rules are no more, in the final analysis, than the consequences of these definitions. | |
| From: Gerhard Gentzen (works [1938]), quoted by Stephen Read - Thinking About Logic Ch.8 | |
| A reaction: If an introduction-rule (or a truth table) were taken as fixed and beyond dispute, then it would have the status of a definition, since there would be nothing else to appeal to. So is there anything else to appeal to here? |
| 11213 | Each logical symbol has an 'introduction' rule to define it, and hence an 'elimination' rule [Gentzen] |
| Full Idea: To every logical symbol there belongs precisely one inference figure which 'introduces' the symbol ..and one which 'eliminates' it. The introductions represent the 'definitions' of the symbols concerned, and eliminations are consequences of these. | |
| From: Gerhard Gentzen (works [1938], II.5.13), quoted by Ian Rumfitt - "Yes" and "No" III | |
| A reaction: [1935 paper] This passage is famous, in laying down the basics of natural deduction systems of logic (ones using only rules, and avoiding axioms). Rumfitt questions whether Gentzen's account gives the sense of the connectives. |
| 13832 | Natural deduction shows the heart of reasoning (and sequent calculus is just a tool) [Gentzen, by Hacking] |
| Full Idea: Gentzen thought that his natural deduction gets at the heart of logical reasoning, and used the sequent calculus only as a convenient tool for proving his chief results. | |
| From: report of Gerhard Gentzen (Investigations into Logical Deduction [1935]) by Ian Hacking - What is Logic? §05 |
| 10067 | Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Gentzen, by Musgrave] |
| Full Idea: Gentzen proved the consistency of arithmetic from assumptions which transcend arithmetic. | |
| From: report of Gerhard Gentzen (works [1938]) by Alan Musgrave - Logicism Revisited §5 | |
| A reaction: This does not contradict Gödel's famous result, but reinforces it. The interesting question is what assumptions Gentzen felt he had to make. |
| 16062 | A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow] |
| Full Idea: It seems unavoidable that the facts about logically necessary relations between levels of facts are themselves logically distinct further facts, irreducible to the microphysical facts. | |
| From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], C) | |
| A reaction: I'm beginning to think that rejecting every theory of reality that is proposed by carefully exposing some infinite regress hidden in it is a rather lazy way to do philosophy. Almost as bad as rejecting anything if it can't be defined. |
| 16061 | If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow] |
| Full Idea: Logical supervenience, restricted to individuals, seems to imply strong reduction. It is said that where the B-facts logically supervene on the A-facts, the B-facts simply re-describe what the A-facts describe, and the B-facts come along 'for free'. | |
| From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], C) | |
| A reaction: This seems to be taking 'logically' to mean 'analytically'. Presumably an entailment is logically supervenient on its premisses, and may therefore be very revealing, even if some people think such things are analytic. |
| 16060 | Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow] |
| Full Idea: The root intuition behind nonreductive materialism is that reality is composed of ontologically distinct layers or levels. …The upper levels depend on the physical without reducing to it. | |
| From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], B) | |
| A reaction: A nice clear statement of a view which I take to be false. This relationship is the sort of thing that drives people fishing for an account of it to use the word 'supervenience', which just says two things seem to hang out together. Fluffy materialism. |
| 16064 | The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow] |
| Full Idea: Jessica Wilson (1999) says what makes physicalist accounts different from emergentism etc. is that each individual causal power associated with a supervenient property is numerically identical with a causal power associated with its base property. | |
| From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], n 11) | |
| A reaction: Hence the key thought in so-called (serious, rather than self-evident) 'emergentism' is so-called 'downward causation', which I take to be an idle daydream. |