21 ideas
| 13838 | A decent modern definition should always imply a semantics [Hacking] |
| Full Idea: Today we expect that anything worth calling a definition should imply a semantics. | |
| From: Ian Hacking (What is Logic? [1979], §10) | |
| A reaction: He compares this with Gentzen 1935, who was attempting purely syntactic definitions of the logical connectives. |
| 4742 | Correspondence may be one-many or many one, as when either p or q make 'p or q' true [Armstrong] |
| Full Idea: In Armstrong's version of the correspondence theory, the truth-making relation is not one-one, but one-many or many-one. Thus 'p or q' has two truth makers, p and q. | |
| From: David M. Armstrong (A World of States of Affairs [1997], p.129), quoted by Pascal Engel - Truth Ch.1 | |
| A reaction: Interesting. Armstrong deals in universals. He also cites many swans as truth-makers for 'there is a least one black swan'. Not correspondence as we know it, Jim. |
| 13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking] |
| Full Idea: 'Dilution' (or 'Thinning') provides an essential contrast between deductive and inductive reasoning; for the introduction of new premises may spoil an inductive inference. | |
| From: Ian Hacking (What is Logic? [1979], §06.2) | |
| A reaction: That is, inductive logic (if there is such a thing) is clearly non-monotonic, whereas classical inductive logic is monotonic. |
| 13834 | Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking] |
| Full Idea: If A |- B and B |- C, then A |- C. This generalises to: If Γ|-A,Θ and Γ,A |- Θ, then Γ |- Θ. Gentzen called this 'cut'. It is the transitivity of a deduction. | |
| From: Ian Hacking (What is Logic? [1979], §06.3) | |
| A reaction: I read the generalisation as 'If A can be either a premise or a conclusion, you can bypass it'. The first version is just transitivity (which by-passes the middle step). |
| 13835 | Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking] |
| Full Idea: Only the cut rule can have a conclusion that is less complex than its premises. Hence when cut is not used, a derivation is quite literally constructive, building up from components. Any theorem obtained by cut can be obtained without it. | |
| From: Ian Hacking (What is Logic? [1979], §08) |
| 13845 | The various logics are abstractions made from terms like 'if...then' in English [Hacking] |
| Full Idea: I don't believe English is by nature classical or intuitionistic etc. These are abstractions made by logicians. Logicians attend to numerous different objects that might be served by 'If...then', like material conditional, strict or relevant implication. | |
| From: Ian Hacking (What is Logic? [1979], §15) | |
| A reaction: The idea that they are 'abstractions' is close to my heart. Abstractions from what? Surely 'if...then' has a standard character when employed in normal conversation? |
| 13840 | First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking] |
| Full Idea: First-order logic is the strongest complete compact theory with a Löwenheim-Skolem theorem. | |
| From: Ian Hacking (What is Logic? [1979], §13) |
| 13844 | A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking] |
| Full Idea: Henkin proved that there is no first-order treatment of branching quantifiers, which do not seem to involve any idea that is fundamentally different from ordinary quantification. | |
| From: Ian Hacking (What is Logic? [1979], §13) | |
| A reaction: See Hacking for an example of branching quantifiers. Hacking is impressed by this as a real limitation of the first-order logic which he generally favours. |
| 13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
| Full Idea: Second-order logic has no chance of a completeness theorem unless one ventures into intensional entities and possible worlds. | |
| From: Ian Hacking (What is Logic? [1979], §13) |
| 13837 | With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking] |
| Full Idea: My doctrine is that the peculiarity of the logical constants resides precisely in that given a certain pure notion of truth and consequence, all the desirable semantic properties of the constants are determined by their syntactic properties. | |
| From: Ian Hacking (What is Logic? [1979], §09) | |
| A reaction: He opposes this to Peacocke 1976, who claims that the logical connectives are essentially semantic in character, concerned with the preservation of truth. |
| 13839 | Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking] |
| Full Idea: For some purposes the variables of first-order logic can be regarded as prepositions and place-holders that could in principle be dispensed with, say by a system of arrows indicating what places fall in the scope of which quantifier. | |
| From: Ian Hacking (What is Logic? [1979], §11) | |
| A reaction: I tend to think of variables as either pronouns, or as definite descriptions, or as temporary names, but not as prepositions. Must address this new idea... |
| 13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
| Full Idea: A Löwenheim-Skolem theorem holds for anything which, on my delineation, is a logic. | |
| From: Ian Hacking (What is Logic? [1979], §13) | |
| A reaction: I take this to be an unusually conservative view. Shapiro is the chap who can give you an alternative view of these things, or Boolos. |
| 9497 | Without modality, Armstrong falls back on fictionalism to support counterfactual laws [Bird on Armstrong] |
| Full Idea: Armstrong has difficulty explaining how laws entail regularities. There is no real modality in the basic components of the world, but he wants to support counterfactuals. His official position is a kind of fictionalism. | |
| From: comment on David M. Armstrong (A World of States of Affairs [1997], 49-51) by Alexander Bird - Nature's Metaphysics 4.4.4 | |
| A reaction: Armstrong seems to be up against the basic problems that laws won't explain anything if they are merely regularities (assuming they are not decrees of a supernatural force). |
| 15550 | Properties are contingently existing beings with multiple locations in space and time [Armstrong, by Lewis] |
| Full Idea: Armstrong has a distinctive conception of (fundamental) properties as contingently existing beings with multiple locations in space and time. | |
| From: report of David M. Armstrong (A World of States of Affairs [1997]) by David Lewis - A world of truthmakers? p.220 | |
| A reaction: Armstrong tries to get a naturalistically founded platonism (which he claims is Aristotelian), but the idea that one thing can be multiply located strikes me as daft (especially if the number of its locations increases or decreases). |
| 4743 | The truth-maker for a truth must necessitate that truth [Armstrong] |
| Full Idea: The truth-maker for a truth must necessitate that truth. | |
| From: David M. Armstrong (A World of States of Affairs [1997], p.115), quoted by Pascal Engel - Truth Ch.1 | |
| A reaction: Armstrong's 'truth-make principle'. It seems to be a necessity which is neither natural nor analytic, making it metaphysically necessary. Or is it part of the definition of truth? |
| 12432 | Explanation of necessity must rest on something necessary or something contingent [Hale] |
| Full Idea: The dilemma is that to give the ultimate source of any necessity, we must either appeal to something which could not have been otherwise (i.e. is itself necessary), or advert to something which could have been otherwise (i.e. is itself merely contingent). | |
| From: Bob Hale (The Source of Necessity [2002], p.301) | |
| A reaction: [Hale is summarising Blackburn's view, and going on to disagree with it] Hale looks for a third way, but Blackburn seems to face us with quite a plausible dilemma. |
| 12434 | Why is this necessary, and what is necessity in general; why is this necessary truth true, and why necessary? [Hale] |
| Full Idea: We must distinguish between explaining particular necessities and explaining necessity in general; and we ought to distinguish between explaining, in regard to any necessary truth, why it is true, and explaining why it is necessary. | |
| From: Bob Hale (The Source of Necessity [2002], p.308) | |
| A reaction: Useful. The pluralist view I associate with Fine says we can explain types of necessity, but not necessity in general. If we seek truthmakers, there is a special case of what adds the necessity to the truth. |
| 12435 | The explanation of a necessity can be by a truth (which may only happen to be a necessary truth) [Hale] |
| Full Idea: My claim is that there are non-transitive explanations of necessities, where what explains is indeed necessary, but what explains the necessity of the explanandum is not the explanation's necessity, but its truth simpliciter. | |
| From: Bob Hale (The Source of Necessity [2002], p.311) | |
| A reaction: The big idea is to avoid a regress of necessities. The actual truths he proposes are essentialist. An interesting proposal. It might depend on how one views essences (as giving identity, or causal power) |
| 12433 | If necessity rests on linguistic conventions, those are contingent, so there is no necessity [Hale] |
| Full Idea: If the alleged necessity, e,g, 2+2=4, really does depend upon a convention governing the use of the words in which we state it, and the existence of that convention is merely a contingent matter, then it can't after all be necessary. | |
| From: Bob Hale (The Source of Necessity [2002], p.302) | |
| A reaction: [Hale is citing Blackburn for this claim] Hale suggests replies, by keeping truth and meaning separate, and involving laws of logic. Blackburn clearly has a good point. |
| 12436 | Concept-identities explain how we know necessities, not why they are necessary [Hale] |
| Full Idea: It seems to me that identity-relations among concepts have more to do with explaining how we know that vixens are female foxes etc., than with explaining why it is necessary, and, more generally, with explaining why some necessities are knowable a priori. | |
| From: Bob Hale (The Source of Necessity [2002], P.313) | |
| A reaction: Hale rejects the conceptual and conventional accounts of necessity, in favour of the essentialist view. This strikes me as a good suggestion of Hale's, since I agree with him about the essentialism. |
| 4798 | In recent writings, Armstrong makes a direct identification of necessitation with causation [Armstrong, by Psillos] |
| Full Idea: In recent writings, Armstrong makes a direct identification of necessitation with causation. | |
| From: report of David M. Armstrong (A World of States of Affairs [1997]) by Stathis Psillos - Causation and Explanation §6.3.3 | |
| A reaction: Obviously logical necessity is not causal, but as a proposal for simplifying accounts of necessity in nature, this is wonderfully simple and appealing. Is his proposal an elevation of causation, or a degradation of necessity? |