21 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. |
| 8249 | Class membership is not transitive, unlike being part of a part of the whole [Lesniewski, by George/Van Evra] |
| Full Idea: Lesniewski distinguished the part-whole relationship from class membership. Membership is not transitive: if s is an element of t, and t of u, then s is not an element of u, whereas a part of a part is a part of the whole. | |
| From: report of Stanislaw Lesniewski (works [1916]) by George / Van Evra - The Rise of Modern Logic 7 | |
| A reaction: If I am a member of a sports club, and my club is a member of the league, I am not thereby a member of the league (so clubs are classes, not wholes). This distinction is clearly fairly crucial in ontology. |
| 23418 | Liberal state legitimacy is based on a belief in justice, not in some conception of the good life [Kymlicka] |
| Full Idea: For liberals the basis of state legitimacy is a shared sense of justice, not a shared conception of the good. | |
| From: Will Kymlicka (Community [1993], 'legitimacy') | |
| A reaction: For a liberal state to work, the citizens have to roughly believe in the core values of liberalism, which are primarily freedom and equality (and hence justice). |
| 23414 | Liberals say state intervention in culture restricts people's autonomy [Kymlicka] |
| Full Idea: According to liberal theory, a state which intervenes in the cultural market place to encourage any particular way of life restricts people's autonomy. | |
| From: Will Kymlicka (Community [1993], 'social') | |
| A reaction: The communitarian idea is that the state should intervene, in order to foster the best aspects of communal culture. The dangers are obvious, and can be seen in any totalitarian state. A gentle hand on the tiller, perhaps? Increase the options? |
| 23410 | Modern liberals see a community as simply a society which respects freedom and equality [Kymlicka] |
| Full Idea: Most contemporary liberal philosophers have little to say about the ideal of community. …It is often seen as derivative of liberty and equality - a society lives up to the ideal of community if its members are treated as free and equal persons. | |
| From: Will Kymlicka (Community [1993], 'Intro') | |
| A reaction: He cites Rawls as an example. This is the central idea which was attacked by modern communitarians. A collection of scattered self-seeking isolated individuals doesn't seem to amount to a healthy communal life. Maybe community needs further rights? |
| 23409 | Community can focus on class or citizenship or ethnicity or culture [Kymlicka] |
| Full Idea: In recent centuries the ideal of community has taken many forms, from class solidarity or shared citizenship to a common ethnic descent or cultural identity. | |
| From: Will Kymlicka (Community [1993], 'Intro') | |
| A reaction: Language and religion are not explicitly mentioned, but must be implied. Supporting a major sports team is also worth mentioning. |
| 23419 | Communitarianism struggles with excluded marginalised groups [Kymlicka] |
| Full Idea: The problem of the exclusion of historically marginalised groups is endemic to the communitarian project. | |
| From: Will Kymlicka (Community [1993], 'legitimacy') | |
| A reaction: Put simply, old-fashioned styles of community are probably impossible in large modern states, some with rather arbitrary borders. |
| 23413 | Feminism has shown that social roles are far from fixed (as communitarians tend to see them) [Kymlicka] |
| Full Idea: Communitarians say that some of our social roles must be regarded as fixed when planning our lives, …but the women's movement has shown how deeply entrenched social roles can be questioned and rejected. | |
| From: Will Kymlicka (Community [1993], 'Embedded') | |
| A reaction: True, but parents walking out on young children also shows that. The ideal must be some sort of balance. |
| 23415 | Participation aids the quest for the good life, but why should that be a state activity? [Kymlicka] |
| Full Idea: Communitarians rarely distinguish between collective activities and political activities. Shared participation aids intelligent decisions about the good life, but why should that be organised through the state, rather than by free individuals? | |
| From: Will Kymlicka (Community [1993], 'need') | |
| A reaction: Kylicka points out later that local groups can be very unintelligent or prejudiced. Modern media have changed that picture, because participation can be with geographically remote people. |
| 23411 | Communitarians see justice as primarily a community matter, rather than a principle [Kymlicka] |
| Full Idea: Communitarians believe either that community replaces the need for principles of justice, or that the community is either the source of such principles or should play a greater role in deciding their content. | |
| From: Will Kymlicka (Community [1993], 'Intro') | |
| A reaction: [compressed] The idea that a racist or chauvinist or puritanical or insular community should decide justice for all its members sounds horrible. It drives you to liberal individualism, just thinking about it. |
| 23412 | Justice resolves conflicts, but may also provoke them [Kymlicka] |
| Full Idea: Justice can help mediate conflicts, but it also tends to creat conflicts, and to decrease the natural expression of sociability. | |
| From: Will Kymlicka (Community [1993], 'limits') | |
| A reaction: [He is discussing Michael Sandel on liberalism] Family life might not go well if all of its members continually demanded justice for themselves as individuals. Maybe our concept of justice is too individualistic? Do we need a sense of 'group' justice? |