20 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) |
| 8358 | There are no rules for the exact logic of ordinary language, because that doesn't exist [Strawson,P] |
| Full Idea: Neither Aristotelian nor Russellian rules give the exact logic of any expression of ordinary language; for ordinary language has no exact logic. | |
| From: Peter F. Strawson (On Referring [1950], §5) | |
| A reaction: This seems to imply that it is impossible to find precise logical forms, because of the pragmatic element in language, but I don't see why. Even more extreme modern pragmatics (where meaning is shifted) doesn't rule out precise underlying propositions. |
| 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... |
| 6413 | 'The present King of France is bald' presupposes existence, rather than stating it [Strawson,P, by Grayling] |
| Full Idea: Strawson argues that in saying 'the present King of France is bald' one is not stating that a present King of France exists, but presupposing or assuming that it does. | |
| From: report of Peter F. Strawson (On Referring [1950]) by A.C. Grayling - Russell Ch.2 | |
| A reaction: We have the notion of a leading question, such as 'when did you stop beating your wife?' But is a presupposition not simply an implied claim, as Russell said it was? |
| 8354 | Russell asks when 'The King of France is wise' would be a true assertion [Strawson,P] |
| Full Idea: The way in which Russell arrived at his analysis was by asking himself what would be the circumstances in which we would say that anyone who uttered the sentence 'The King of France is wise' had made a true assertion. | |
| From: Peter F. Strawson (On Referring [1950], §1) | |
| A reaction: This seems to connect Russell's theory of definite descriptions with the truth conditions theory of meaning which is associated (initially) with Frege. Truth will require some reference to what actually exists. |
| 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. |
| 8356 | The meaning of an expression or sentence is general directions for its use, to refer or to assert [Strawson,P] |
| Full Idea: To give the meaning of an expression is to give general directions for its use to refer to or mention particular objects or persons; in like manner, sentences are for use to make true or false assertions. | |
| From: Peter F. Strawson (On Referring [1950], §2) | |
| A reaction: The influence of Wittgenstein? I don't like it. The general idea that you can say what something is by giving directions for its use is what I think of as the Functional Fallacy: confusing the role of x with its inherent nature. Shirt as goalpost. |
| 10430 | Reference is mainly a social phenomenon [Strawson,P, by Sainsbury] |
| Full Idea: Strawson's early work gave a new direction to the study of reference by stressing that it is a social phenomenon. | |
| From: report of Peter F. Strawson (On Referring [1950]) by Mark Sainsbury - The Essence of Reference 18.2 | |
| A reaction: The question is whether speakers refer, or sentences, or expressions, or propositions. The modern consensus seems to be that some parts of language are inherently referring, but speakers combine such tools with context. Sounds right. |
| 10448 | If an expression can refer to anything, it may still instrinsically refer, but relative to a context [Bach on Strawson,P] |
| Full Idea: Strawson claimed that virtually any expression that can be used to refer to one thing in one context can be used to refer to something else in another context. Maybe expressions still refer, but only relative to a context. | |
| From: comment on Peter F. Strawson (On Referring [1950]) by Kent Bach - What Does It Take to Refer? 22.2 | |
| A reaction: If there is complete freedom, then Bach's criticism doesn't sound plausible. If something is semantically referential, that should impose pretty tight restrictions on speakers. Why distinguish names as intrinsically referential, and descriptions as not? |
| 8355 | Expressions don't refer; people use expressions to refer [Strawson,P] |
| Full Idea: 'Mentioning', or 'referring', is not something an expression does; it is something that someone can use an expression to do. | |
| From: Peter F. Strawson (On Referring [1950], §2) | |
| A reaction: That can't be whole story, because I might make a mistake when referring, so that I used the expression to refer to x, but unfortunately the words themselves referred to y. The power of language exceeds the intentions of speakers. |
| 8357 | If an utterance fails to refer then it is a pseudo-use, though a speaker may think they assert something [Strawson,P] |
| Full Idea: If an utterance is not talking about anything, then the speaker's use is not a genuine one, but a spurious or pseudo-use; he is not making either a true or a false assertion, though he may think he is. | |
| From: Peter F. Strawson (On Referring [1950], §2) | |
| A reaction: This is Strawson's verdict on 'The present King of France is bald'. His view puts speculative statements in no man's land. What do we make of 'Elvis lives' or 'phlogiston explains fire'? |
| 21058 | Enlightenment requires the free use of reason in the public realm [Kant] |
| Full Idea: The public use of man's reason must always be free, and it alone can bring about enlightenment among men; the private use of reason may quite often be very narrowly restricted (…in a particular civil post or office). | |
| From: Immanuel Kant (Answer to 'What is Enlightenment?' [1784], p.55) | |
| A reaction: The private aspect seems to be the common restriction on speech by employees of the state. Does free speech have only instrumental value? Is the life of virtue possible without it? |