16 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. |
| 20991 | People prepare our dinner from their own self-interest, not from humanity [Smith,A] |
| Full Idea: It is not from the benevolence of the butcher, the brewer, or the baker that we expect our dinner, but from their regard to their own interest. We address ourselves, not to their humanity but to their self-love. | |
| From: Adam Smith (The Wealth of Nations [1776], p.26-7), quoted by Amartya Sen - The Idea of Justice 08 'Narrowing' | |
| A reaction: Sen passionately pleads that this not be taken out of context. It is about the motivation for the relationship of exchange, and not about morality in general, which also includes trust etc. The subsequent lines in Smith show this. |
| 21991 | The middle class gain freedom through property, but workers can only free all of humanity [Marx, by Singer] |
| Full Idea: Where the middle class can win freedom for themselves on the basis of rights to property - thus excluding others from their freedom - the working class have nothing but their title as human beings. They only liberate themselves by liberating humanity. | |
| From: report of Karl Marx (Contrib to Critique of Hegel's Phil of Right [1844]) by Peter Singer - Marx 4 | |
| A reaction: Individual workers might gain freedom via education, marriage, or entrepreneurship, or by opting for total simplicity of life, but in general Marx seems to be right about this. But we must ask what sort of 'freedom' is needed. |
| 21990 | Theory is as much a part of a revolution as material force is [Marx] |
| Full Idea: Material force must be overthrown by material force. But theory also becomes a material force once it has gripped the masses. | |
| From: Karl Marx (Contrib to Critique of Hegel's Phil of Right [1844], Intro p.69), quoted by Peter Singer - Marx 4 | |
| A reaction: A huge problem, I think, is that every theory (even conservatism) has to be simplified in a democracy if it is to grip the imagination of the majority. My current hatred is labels in political philosophy. They give us a cartoon view of the world. |
| 20680 | Selfish profit-seeking increases collective wealth, so greed is good, and egoism is altruism [Smith,A, by Harari] |
| Full Idea: Smith's claim that the selfish human urge to increase private profits is the basis for collective wealth is one of the most revolutionary ideas in human history. …Greed is good …and egoism is altruism. | |
| From: report of Adam Smith (The Wealth of Nations [1776]) by Yuval Noah Harari - Sapiens: brief history of humankind 16 'Growing' | |
| A reaction: The central confrontation of political philosophy still seems to be Adam Smith v Karl Marx. Why can't there be altruistic non-greedy profit-seeking? Not 'I want profits' but 'we want profits'. Altruistic capitalists aim to create jobs. |
| 7128 | Religion is the opium of the people, and real happiness requires its abolition [Marx] |
| Full Idea: Religion is the opium of the people. The abolition of religion as the illusory happiness of the people is required for their real happiness. | |
| From: Karl Marx (Contrib to Critique of Hegel's Phil of Right [1844], Intro) | |
| A reaction: Not being religious myself, I have some sympathy with this ringing clarion-call. However, while opium satisfies an artificial and superficial need, religion certainly seems to speak to something deeper and more central in people. |