23 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. |
| 1394 | Can the mental elements of a 'bundle' exist on their own? [Carruthers] |
| Full Idea: If the mind is merely a bundle of states and events, it must be logically possible for the various elements of the bundle to exist on their own. | |
| From: Peter Carruthers (Introducing Persons [1986], 2.iii (A)) | |
| A reaction: Depends how literally you take the bundle metaphor, and how much you are worried about 'logical' possibility (which only seems to mean imaginable). The answers to these questions do not have to be all-or-nothing. |
| 1395 | Why would a thought be a member of one bundle rather than another? [Carruthers] |
| Full Idea: What makes it true that a particular thought or experience is a member of one bundle rather than another? | |
| From: Peter Carruthers (Introducing Persons [1986], 2.iii (B)) | |
| A reaction: I'm not sure if you can answer this nice question without mentioning values. The mental events in are in my bundle because they matter to me (because they are related to my body, for which I am responsible). Compare picking my possessions out of a pile. |
| 1396 | We identify persons before identifying conscious states [Carruthers] |
| Full Idea: We can have no conception of the particularity of conscious states prior to, and independently of, a conception of a particularity of persons. | |
| From: Peter Carruthers (Introducing Persons [1986], 2.iii (C)) | |
| A reaction: agrees with Butler |
| 23429 | The environment needs localised politics, with its care for the land [Dobson] |
| Full Idea: More localised politics helps to generate the disposition of care for the land which is a core feature of environmental politics. | |
| From: Andrew Dobson (Environmental Politics: very short intro [2016], 4) | |
| A reaction: I currently live in a time when localised politics is hugely devalued, because centralisation and privatisation are cheaper. It seems obvious that many human needs require a commitment to a particular locality. |
| 23424 | An ideology judges things now, and offers an ideal, with a strategy for reaching it [Dobson] |
| Full Idea: An ideology generally has three components: a judgement (usually critical) of how things are, a picture of the ideology's ideal society, and a strategy for progressing towards the ideal. | |
| From: Andrew Dobson (Environmental Politics: very short intro [2016], 2) | |
| A reaction: Conservatives tend to think we are already living in the ideal, and they reject most ideologies for being 'idealistic' (which presumably means delusional). I'm a fan of ideals, but combined with cool judgement. |
| 23426 | Ecologism is often non-liberal, by claiming to know other people's best interests [Dobson] |
| Full Idea: Liberals say that their preferences are their interests, and resist the idea that anyone could know their interests better than they can. …To this degree, ecologism might be regarded as 'non-liberal'. | |
| From: Andrew Dobson (Environmental Politics: very short intro [2016], 2) | |
| A reaction: There are lots of other cases where liberal citizens may not realise their best interests, such as in the control of traffic, or of drugs. |
| 23427 | Socialism can be productive and centralised, or less productive and decentralised [Dobson] |
| Full Idea: Marx and his heirs promote a productivist socialism, but utopian socialists such as William Morris offer a less productivist and more decentralised form of socialism. | |
| From: Andrew Dobson (Environmental Politics: very short intro [2016], 2) | |
| A reaction: Modern history teaches us to be very cautious about the centralised version. Presumably you could be decentralised but still value production highly, even if it is a bit less efficient. |
| 23428 | Difference feminists say women differ fundamentally from men [Dobson] |
| Full Idea: Difference feminists argue that men and women are fundamentally different. | |
| From: Andrew Dobson (Environmental Politics: very short intro [2016], 2) | |
| A reaction: You can be significantly different without being 'fundamentally' different. Personally I don't see a huge difference, even though history may have greatly exaggerated and dramatised what differences there are. |
| 23422 | For the environment, affluence and technology matter as much as population size [Dobson] |
| Full Idea: Although bare population figures are important for environmental impact, the level of affluence and the technology are also crucial factors. | |
| From: Andrew Dobson (Environmental Politics: very short intro [2016], 2) | |
| A reaction: It is worth noting that the technology can also have a good impact, though affluence is nearly always bad. |
| 23425 | Ecologism says growth must be reduced, and efficiency is not enough [Dobson] |
| Full Idea: A central belief of the ideology of ecologism is that aggregate growth must be reduced, and that this is very unlikely to be achieved by efficiency gains alone. | |
| From: Andrew Dobson (Environmental Politics: very short intro [2016], 2) | |
| A reaction: He argues that efficiency gains invariably lead to increased production. Trickle down economics needs huge growth to deliver a good life for the poorest sector. Ecologism has to be fairly egalitarian about wealth. |
| 23430 | A million years is a proper unit of political time [Dobson] |
| Full Idea: We must acknowledge that a million years is a proper unit of political time. | |
| From: Andrew Dobson (Environmental Politics: very short intro [2016], 5) | |
| A reaction: [He cites Colin Tudge] Such thinking is almost impossible, but owners of large aristocratic estates seem to have thought in centuries, because they were confident of continuity. The more we identify with all of humanity, the more this is possible. |
| 23423 | We currently value the present fourteen times more highly than the future [Dobson] |
| Full Idea: At current rates we seem to value present concerns as fourteen times more valuable than future concerns. | |
| From: Andrew Dobson (Environmental Politics: very short intro [2016], 2) | |
| A reaction: A sobering figure, which sounds about right. This directly influences how much we spend on future concerns. One thought is that future generations may be much more affluent than us! |