18 ideas
| 6859 | Analytic philosophy has much higher standards of thinking than continental philosophy [Williamson] |
| Full Idea: Certain advances in philosophical standards have been made within analytic philosophy, and there would be a serious loss of integrity involved in abandoning them in the way required to participate in current continental philosophy. | |
| From: Timothy Williamson (Interview with Baggini and Stangroom [2001], p.151) | |
| A reaction: The reply might be to concede the point, but say that the precision and rigour achieved are precisely what debar analytical philosophy from thinking about the really interesting problems. One might as well switch to maths and have done with it. |
| 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) |
| 6862 | Fuzzy logic uses a continuum of truth, but it implies contradictions [Williamson] |
| Full Idea: Fuzzy logic is based on a continuum of degrees of truth, but it is committed to the idea that it is half-true that one identical twin is tall and the other twin is not, even though they are the same height. | |
| From: Timothy Williamson (Interview with Baggini and Stangroom [2001], p.154) | |
| A reaction: Maybe to be shocked by a contradiction is missing the point of fuzzy logic? Half full is the same as half empty. The logic does not say the twins are different, because it is half-true that they are both tall, and half-true that they both aren't. |
| 6858 | Formal logic struck me as exactly the language I wanted to think in [Williamson] |
| Full Idea: As soon as I started learning formal logic, that struck me as exactly the language that I wanted to think in. | |
| From: Timothy Williamson (Interview with Baggini and Stangroom [2001]) | |
| A reaction: It takes all sorts… It is interesting that formal logic might be seen as having the capacity to live up to such an aspiration. I don't think the dream of an ideal formal language is dead, though it will never encompass all of reality. Poetic truth. |
| 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. |
| 6863 | Close to conceptual boundaries judgement is too unreliable to give knowledge [Williamson] |
| Full Idea: If one is very close to a conceptual boundary, then one's judgement will be too unreliable to constitute knowledge, and therefore one will be ignorant. | |
| From: Timothy Williamson (Interview with Baggini and Stangroom [2001], p.156) | |
| A reaction: This is the epistemological rather than ontological interpretation of vagueness. It sounds very persuasive, but I am reluctant to accept that reality is full of very precise boundaries which we cannot quite discriminate. |
| 6861 | What sort of logic is needed for vague concepts, and what sort of concept of truth? [Williamson] |
| Full Idea: The problem of vagueness is the problem of what logic is correct for vague concepts, and correspondingly what notions of truth and falsity are applicable to vague statements (does one need a continuum of degrees of truth, for example?). | |
| From: Timothy Williamson (Interview with Baggini and Stangroom [2001], p.153) | |
| A reaction: This certainly makes vagueness sound like one of the most interesting problems in all of philosophy, though also one of the most difficult. Williamson's solution is that we may be vague, but the world isn't. |
| 6860 | How can one discriminate yellow from red, but not the colours in between? [Williamson] |
| Full Idea: If one takes a spectrum of colours from yellow to red, it might be that given a series of colour samples along that spectrum, each sample is indiscriminable by the naked eye from the next one, though samples at either end are blatantly different. | |
| From: Timothy Williamson (Interview with Baggini and Stangroom [2001], p.151) | |
| A reaction: This seems like a nice variant of the Sorites paradox (Idea 6008). One could demonstrate it with just three samples, where A and C seemed different from each other, but other comparisons didn't. |
| 22454 | We tolerate inconsistency in ethics but not in other beliefs (which reflect an independent order) [Williams,B, by Foot] |
| Full Idea: Williams argued that we can tolerate inconsistency in moral principles though not in assertions, and that this is explained by the fact that it is the concern of the latter but not of the former to reflect an 'independent order of things'. | |
| From: report of Bernard Williams (Consistency and realism (with 1972 note) [1966]) by Philippa Foot - Moral Realism and Moral Dilemma p.37 | |
| A reaction: Put like this, Williams seems to beg the question, which is whether there is an independent moral order to things. There seems to be an easy answer, which is that we are only intolerant of inconsistency when we are confident about it. |