25 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. |
| 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) |
| 7548 | Classes, grouped by a convenient property, are logical constructions [Russell] |
| Full Idea: Classes or series of particulars, collected together on account of some property which makes it convenient to be able to speak of them as wholes, are what I call logical constructions or symbolic fictions. | |
| From: Bertrand Russell (The Ultimate Constituents of Matter [1915], p.125) | |
| A reaction: When does a construction become 'logical' instead of arbitrary? What is it about a property that makes it 'convenient'? At this point Russell seems to have built his ontology on classes, and the edifice was crumbling, thanks to Wittgenstein. |
| 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. |
| 5500 | Biologists see many organic levels, 'abstract' if seen from below, 'structural' if seen from above [Lycan] |
| Full Idea: Biologists don't split living things into a 'structural' level and an 'abstract' level; ..rather, they are organised at many levels, each level 'abstract' with respect to those beneath it, but 'structural' as it realises those levels above it. | |
| From: William Lycan (Introduction - Ontology [1999], p.9) | |
| A reaction: This is a very helpful distinction. Compare Idea 4601. It seems to fit well with the 'homuncular' picture of a hierarchical mind, and explains why there are so many levels of description available for mental life. |
| 7545 | Visible things are physical and external, but only exist when viewed [Russell] |
| Full Idea: I believe that common sense is right in regarding what we see as physical and (in one of several possible senses) outside the mind, but is probably wrong in supposing that it continues to exist when we are no longer looking at it. | |
| From: Bertrand Russell (The Ultimate Constituents of Matter [1915], p.123) | |
| A reaction: This remark (in 1915) is a bit startling from a philosopher well known for his robustly realist stance. Just one of his phases! It seems very counterintuitive - that objects really exist externally, but only when viewed. Schrödinger's Cat? |
| 5494 | 'Lightning is electric discharge' and 'Phosphorus is Venus' are synthetic a posteriori identities [Lycan] |
| Full Idea: There is such a thing as synthetic and a posteriori identity that is nonetheless genuine identity, as in lightning being electrical discharge, and the Morning Star being Venus. | |
| From: William Lycan (Introduction - Ontology [1999], p.5) | |
| A reaction: It is important to note that although these identities are synthetic a posteriori, that doesn't make them contingent. The early identity theorists like Smart seemed to think that it did. Kripke must be right that they are necessary identities. |
| 7549 | If my body literally lost its mind, the object seen when I see a flash would still exist [Russell] |
| Full Idea: My meaning may be made plainer by saying that if my body could remain in exactly the same state in which it is, though my mind had ceased to exist, precisely that object which I now see when I see a flash would exist, though I should not see it. | |
| From: Bertrand Russell (The Ultimate Constituents of Matter [1915], p.126) | |
| A reaction: Zombies, 70 years before Robert Kirk! Sense-data are physical. It is interesting to see a philosopher as committed to empiricism, anti-spiritualism and the priority of science as this, still presenting an essentially dualist picture of perception. |
| 7553 | Sense-data are purely physical [Russell] |
| Full Idea: Sense-data are purely physical, and all that is mental in connection with them is our awareness of them. | |
| From: Bertrand Russell (The Ultimate Constituents of Matter [1915], p.138) | |
| A reaction: Once this account of sense-data becomes fully clear, it also becomes apparent what a dualist theory it is. The mind is a cinema, I am the audience, and sense-data are the screen. There has to be a big logical gap between viewer and screen. |
| 7546 | A man is a succession of momentary men, bound by continuity and causation [Russell] |
| Full Idea: The real man, I believe, however the police may swear to his identity, is really a series of momentary men, each different one from the other, and bound together, not by a numerical identity, but by continuity and certain instrinsic causal laws. | |
| From: Bertrand Russell (The Ultimate Constituents of Matter [1915], p.124) | |
| A reaction: This seems to be in the tradition of Locke and Parfit, and also follows the temporal-slices idea of physical objects. Personally I take a more physical view of things, and think the police are probably more reliable than Bertrand Russell. |
| 5496 | Functionalism has three linked levels: physical, functional, and mental [Lycan] |
| Full Idea: Functionalism has three distinct levels of description: a neurophysiological description, a functional description (relative to a program which the brain is realising), and it may have a further mental description. | |
| From: William Lycan (Introduction - Ontology [1999], p.6) | |
| A reaction: I have always thought that the 'levels of description' idea was very helpful in describing the mind/brain. I feel certain that we are dealing with a single thing, so this is the only way we can account for the diverse ways in which we discuss it. |
| 5499 | A mental state is a functional realisation of a brain state when it serves the purpose of the organism [Lycan] |
| Full Idea: Some theorists have said that the one-to-one correspondence between the organism and parts of its 'program' is too liberal, and suggest that the state and its functional role are seen teleologically, as functioning 'for' the organism. | |
| From: William Lycan (Introduction - Ontology [1999], p.9) | |
| A reaction: This seems an inevitable development, once the notion of a 'function' is considered. It has to be fitted into some sort of Aristotelian teleological picture, even if the functions are seen subjectively (by what?). Purpose is usually seen as evolutionary. |
| 7550 | We could probably, in principle, infer minds from brains, and brains from minds [Russell] |
| Full Idea: It seems not improbable that if we had sufficient knowledge we could infer the state of a man's mind from the state of his brain, or the state of his brain from the state of his mind. | |
| From: Bertrand Russell (The Ultimate Constituents of Matter [1915], p.131) | |
| A reaction: This strikes me as being a very good summary of the claim that mind is reducible to brain, which is the essence of physicalism. Had he been born a little later, Russell would have taken a harder line with physicalism. |
| 5501 | People are trying to explain biological teleology in naturalistic causal terms [Lycan] |
| Full Idea: There is now a small but vigorous industry whose purpose is to explicate biological teleology in naturalistic terms, typically in terms of causes. | |
| From: William Lycan (Introduction - Ontology [1999], p.10) | |
| A reaction: This looks like a good strategy. In some sense, it seems clear that the moon has no purpose, but an eyeball has one. Via evolution, one would expect to reduce this to causation. Purposes are real (not subjective), but they are reducible. |
| 7551 | Matter is a logical construction [Russell] |
| Full Idea: We must regard matter as a logical construction. | |
| From: Bertrand Russell (The Ultimate Constituents of Matter [1915], p.132) | |
| A reaction: A logical construction is a fancy way of saying a best explanation (but with Ockham's Razor hanging over it). A key component missing from Russell's account is that we can directly experience matter, because we are made of it. |
| 7547 | Matter requires a division into time-corpuscles as well as space-corpuscles [Russell] |
| Full Idea: A true theory of matter requires a division of things into time-corpuscles as well as space-corpuscles. | |
| From: Bertrand Russell (The Ultimate Constituents of Matter [1915], p.125) | |
| A reaction: The division of matter in space seems decidable by physicists, but the division in time seems a bit arbitrary (unless it is quanta of time?). Russell focuses on observable qualities, but are there also intrinsic qualities? |
| 7552 | Six dimensions are needed for a particular, three within its own space, and three to locate that space [Russell] |
| Full Idea: The world of particulars is a six-dimensional space, where six co-ordinates will be required to assign the position of any particular, three to assign its position in its own space, and three to assign the position of its space among the other spaces. | |
| From: Bertrand Russell (The Ultimate Constituents of Matter [1915], p.134) | |
| A reaction: Not a proposal that has caught on. One might connect the idea with the notion of 'frames of reference' in Einstein's Special Theory. Inside a frame of reference, three co-ordinates are needed; but where is the frame of reference? |