17 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) |
| 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. |
| 21315 | A tree remains the same in the popular sense, but not in the strict philosophical sense [Butler] |
| Full Idea: When a man swears to the same tree having stood for fifty years in the same place, he means ...not that the tree has been all that time the same in the strict philosophical sense of the word. ...In a loose and popular sense they are said to be the same. | |
| From: Joseph Butler (Analogy of Religion [1736], App.1) | |
| A reaction: A helpful distinction which we should hang on. Of course, by the standards of modern physics, nothing is strictly the same from one Planck time to the next. All is flux. So we either drop the word 'same' (for objects) or relax a bit. |
| 17503 | Theories can never represent accurately, because their components are abstract [Cartwright,N, by Portides] |
| Full Idea: Cartwright objects that the claim that theories represent what happens in actual situations is to overlook that the concepts used in them (such as 'force functions' and 'Hamiltonians') are abstract. | |
| From: report of Nancy Cartwright (The Dappled World [1999]) by Demetris Portides - Models 'Current' | |
| A reaction: I'm not convinced by this. The term 'abstract' is too loose. In a sense most words are abstract because they are universals. If I say 'that's a cat', that is a very accurate remark, despite the generality of 'cat'. |
| 21317 | Despite consciousness fluctuating, we are aware that it belongs to one person [Butler] |
| Full Idea: Though the successive consciousnesses which we have of our own existence are not the same, yet they are consciousnesses of one and the same thing or object; of the same person, self, or living agent. | |
| From: Joseph Butler (Analogy of Religion [1736], App.1) | |
| A reaction: Butler's arguments seems to be that he appears to be the same person, so he is the same person. He is explicitly disagreeing with Locke. |
| 21313 | If consciousness of events makes our identity, then if we have forgotten them we didn't exist then [Butler] |
| Full Idea: Though consciousness of what is past does ascertain our personal identity to ourselves, yet to say that it makes personal identity, or is necessary to our being the same persons is to say a person has not existed a single moment but what he can remember. | |
| From: Joseph Butler (Analogy of Religion [1736], App.1) | |
| A reaction: An over-cautious scepticism has crept in about the reliability of bodily identity. Now we can have photographs and CCTV to prove that we experienced events we have forgotten. Butler is right. |
| 21314 | Consciousness presupposes personal identity, so it cannot constitute it [Butler] |
| Full Idea: One would think it really self-evident that consciousness of personal identity presupposes, and therefore cannot constitute, personal identity, any more than knowledge can presuppose truth, which it presupposes. | |
| From: Joseph Butler (Analogy of Religion [1736], App.1) | |
| A reaction: It rather begs the question to dogmatically assert that mere consciousness presupposes a self, especially after Hume's criticisms. That consciousness implies a subject to experience needs arguing for. Is it the best explanation? |
| 21318 | If the self changes, we have no responsibilities, and no interest in past or future [Butler] |
| Full Idea: If personality is a transient thing ...then it follows that it is a fallacy to charge ourselves with any thing we did, or to imagine our present selves interested in any thing which befell us yesterday, or what will befall us tomorrow. | |
| From: Joseph Butler (Analogy of Religion [1736], App.1) | |
| A reaction: We seem to care about the past and future of our children, without actually being our children. Can't my future self be my descendant, a close one, instead of me? |