19 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. |
| 14895 | 'Superficial' contingency: false in some world; 'Deep' contingency: no obvious verification [Evans, by Macià/Garcia-Carpentiro] |
| Full Idea: Evans says intuitively a sentence is 'superficially' contingent if the function from worlds to truth values assigns F to some world; it is 'deeply' contingent if understanding it does not guarantee that there is a verifying state of affairs. | |
| From: report of Gareth Evans (Reference and Contingency [1979]) by Macià/Garcia-Carpentiro - Introduction to 'Two-Dimensional Semantics' 2 | |
| A reaction: This distinction is used by Davies and Humberstone (1980) to construct an early version of 2-D semantics (see under Language|Semantics). The point is that part comes from understanding it, and another part from assigning truth values. |
| 11881 | Rigid designators can be meaningful even if empty [Evans, by Mackie,P] |
| Full Idea: Evans argues that there can be rigid designators that are meaningful even if empty. | |
| From: report of Gareth Evans (Reference and Contingency [1979]) by Penelope Mackie - How Things Might Have Been 1.8 |
| 2851 | Emotivists find it hard to analyse assertions of moral principles, rather than actual judgements [Brink] |
| Full Idea: It is hard for the emotivist to give an analysis of the occurrence of moral ideas in unasserted contexts, such as "IF he did wrong, then he should be punished". | |
| From: David O. Brink (Emotivism [1995], p.224) | |
| A reaction: This is the 'Frege-Geach Problem'. |
| 2850 | How can emotivists explain someone who recognises morality but is indifferent to it? [Brink] |
| Full Idea: It is not clear how the emotivist can accommodate the amoralist - one who recognises moral requirements but is indifferent to them. | |
| From: David O. Brink (Emotivism [1995], p.224) | |
| A reaction: Nietzsche recognised current morals, but was indifferent to them. It is hard to imagine, though, an amoralist who lacked all the feelings which imply morality. |
| 2848 | Two people might agree in their emotional moral attitude while disagreeing in their judgement [Brink] |
| Full Idea: Critics of emotivism claim that moral agreement need not track agreement in attitude; moralists with the same attitude can disagree in their views, and they can hold the same view while disagreeing in attitude. | |
| From: David O. Brink (Emotivism [1995], p.224) | |
| A reaction: Thus two racists can disagree about how racists should behave. Sounds like a good criticism. |
| 2853 | Emotivists claim to explain moral motivation by basing morality on non-cognitive attitudes [Brink] |
| Full Idea: By stressing the intimate connection between moral judgements and the agent's non-cognitive attitudes, emotivists claim to capture the motivational properties of moral judgement. | |
| From: David O. Brink (Emotivism [1995], p.223) | |
| A reaction: The same claim is made by contractarians, who start from our universal self-interest. Emotivists also nicely capture the motivation properties of immoral judgements. |
| 2852 | Emotivists tend to favour a redundancy theory of truth, making moral judgement meaningless [Brink] |
| Full Idea: If you want to recognise the truth of some moral judgements, perhaps to make room for the possibility of moral mistakes, then one may not be satisfied with the emotivists' tendency to appeal to the redundancy theory of truth. | |
| From: David O. Brink (Emotivism [1995], p.224) | |
| A reaction: Probably thinking of Simon Blackburn. People who adopt a redundancy view of truth for semantics are left floundering when discussing what is true in the rest of philosophy. |
| 2849 | Emotivism implies relativism about moral meanings, but critics say disagreements are about moral reference [Brink] |
| Full Idea: Emotivism suggests that different feelings lead to different individual meanings for moral terms, but critics say that meanings are the same, and disagreement is about the extension (range of reference) of the terms. | |
| From: David O. Brink (Emotivism [1995], p.224) | |
| A reaction: It's hard to see how 'ought to p' could have quite different meanings for an emotivist and (say) a theistic moralist. 'Ought' is an obvious and simple word. Good criticism. |