17 ideas
| 15545 | Armstrong's analysis seeks truthmakers rather than definitions [Lewis] |
| Full Idea: I suggest that Armstrong has an unfamiliar notion of analysis, as not primarily a quest for definitions, but as a quest for truth-makers. | |
| From: David Lewis (Armstrong on combinatorial possibility [1992], 'The demand') | |
| A reaction: This is not a dichotomy, I think, but a shift of emphasis. A definition will probably refer to truthmakers; a decent account of truthmakers would approximate a definition. |
| 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. |
| 15546 | Predications aren't true because of what exists, but of how it exists [Lewis] |
| Full Idea: Predications seem, for the most part, to be true not because of whether things are, but because of how things are. | |
| From: David Lewis (Armstrong on combinatorial possibility [1992], 'The demand') | |
| A reaction: This simple point shows that you get into a tangle if you insist that truthmakers just consist of what exists. Lewis says Armstrong offers states of affairs as truthmakers for predications. |
| 15548 | Say 'truth is supervenient on being', but construe 'being' broadly [Lewis] |
| Full Idea: I want to say that 'truth is supervenient on being', but as an Ostrich about universals I want to construe 'being' broadly. | |
| From: David Lewis (Armstrong on combinatorial possibility [1992], 'Truth') | |
| A reaction: [His slogan is borrowed from Bigelow 1988:132-,158-9] This seems much more promising that the more precise and restricted notion of truthmakers, as resting on the existence of particular things. Presentism is the big test case. |
| 14399 | Presentism says only the present exists, so there is nothing for tensed truths to supervene on [Lewis] |
| Full Idea: Presentism says that although there is nothing outside the present, yet there are past-tensed and future-tensed truths that do not supervene on the present, and hence do not supervene on being. | |
| From: David Lewis (Armstrong on combinatorial possibility [1992], p.207) | |
| A reaction: Since I rather like both presentism and truth supervening on being, this observation comes as rather a devastating blow. I thought philosophy would be quite easy, but it's turning out to be rather tricky. Could tensed truths supervene on the present? |
| 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. |
| 15543 | How do things combine to make states of affairs? Constituents can repeat, and fail to combine [Lewis] |
| Full Idea: To me it is mysterious how a state of affairs is made out of its particular and universal constituents. Different states of affairs may have the very same constituents, and the existence of constituents by no means entails the existence of the states. | |
| From: David Lewis (Armstrong on combinatorial possibility [1992], 'What is there') | |
| A reaction: He is rejecting the structure of states of affairs as wholes made of parts. But then mereology was never going to explain the structure of the world. |
| 16668 | Modes of things exist in some way, without being full-blown substances [Gassendi] |
| Full Idea: Modes are not nothing but something more than mere nothing; they are therefore 'res' of some kind, not substantial of course, but at least modal. | |
| From: Pierre Gassendi (Disquisitions [1644], II.3.4), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 260 | |
| A reaction: This is the great modern atomist talking pure scholastic metaphysics. He's been reading Suárez. Gassendi seems to accept more than one type of existence. |