19 ideas
| 21960 | Ordinary language is the beginning of philosophy, but there is much more to it [Austin,JL] |
| Full Idea: Ordinary language is not the last word: in principle it can everywhere be supplemented and improved upon and superseded. Only remember, it is the first word. | |
| From: J.L. Austin (A Plea for Excuses [1956], p.185), quoted by A.W. Moore - The Evolution of Modern Metaphysics Intro | |
| A reaction: To claim anything more would be absurd. The point is that this remark comes from the high priest of ordinary language philosophy. |
| 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. |
| 16066 | Additional or removal of any part changes a thing, so people are never the same person [Epicharmus] |
| Full Idea: If you add or take away a pebble, the same number does not remain. If you add to a length or cut off from it, the former measure does not remain. So human beings grow or waste away. Both you and I were, and shall be, other men. | |
| From: Epicharmus (comedies (frags) [c.470 BCE], B02), quoted by Diogenes Laertius - Lives of Eminent Philosophers 03.12 | |
| A reaction: [The original is in dialogue form from a play. The context is a joke about not paying a debt.] Note the early date for this metaphysical puzzle. My new favourite reply is Chrysippus's Idea 16059; identity actually requires change. |
| 436 | A dog seems handsome to another a dog, and even a pig to another pig [Epicharmus] |
| Full Idea: Dog seems very handsome to dog, and ox to ox, and donkey very handsome to donkey, and even pig to pig. | |
| From: Epicharmus (comedies (frags) [c.470 BCE], B05), quoted by (who?) - where? |
| 442 | Pleasures are like pirates - if you are caught they drown you in a sea of pleasures [Epicharmus] |
| Full Idea: Pleasures for mortals are like impious pirates, for the man who is caught by pleasures is immediately drowned in a sea of them. | |
| From: Epicharmus (comedies (frags) [c.470 BCE], B44), quoted by (who?) - where? | |
| A reaction: Not all slopes are slippery. Plenty of people hold themselves to strict rules about alcohol or gambling. People have occasional treats. |
| 440 | Hands wash hands; give that you may get [Epicharmus] |
| Full Idea: The hand washes the hand; give something and you may get something. | |
| From: Epicharmus (comedies (frags) [c.470 BCE], B30), quoted by (who?) - where? |
| 441 | Against a villain, villainy is not a useless weapon [Epicharmus] |
| Full Idea: Against a villain, villainy is not a useless weapon. | |
| From: Epicharmus (comedies (frags) [c.470 BCE], B32), quoted by (who?) - where? |
| 439 | God knows everything, and nothing is impossible for him [Epicharmus] |
| Full Idea: Nothing escapes the divine, this you must realise. God himself is our overseer, and nothing is impossible for him. | |
| From: Epicharmus (comedies (frags) [c.470 BCE], B23), quoted by (who?) - where? |
| 443 | Human logos is an aspect of divine logos, and is sufficient for successful living [Epicharmus] |
| Full Idea: Man has calculation, but there is also the divine logos. But human logos is sprung from the divine logos, and it brings to each man his means of life, and his maintenance. | |
| From: Epicharmus (comedies (frags) [c.470 BCE], B57), quoted by (who?) - where? |