22 ideas
| 13737 | The empiricist says that metaphysics is meaningless, rather than false [Schlick] |
| Full Idea: The empiricist does not say to the metaphysician 'what you say is false', but 'what you say asserts nothing at all!' He does not contradict him, but says 'I don't understand you'. | |
| From: Moritz Schlick (Positivism and Realism [1934], p.107), quoted by Jonathan Schaffer - On What Grounds What 1.1 | |
| A reaction: I take metaphysics to be meaningful, but at such a high level of abstraction that it is easy to drift into vague nonsense, and incredibly hard to assess what is meant, and whether it is correct. The truths of metaphysics are not recursive. |
| 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. |
| 13941 | Are the truth-bearers sentences, utterances, ideas, beliefs, judgements, propositions or statements? [Cartwright,R] |
| Full Idea: What is it that is susceptible of truth or falsity? The answers suggested constitute a bewildering variety: sentences, utterances, ideas, beliefs, judgments, propositions, statements. | |
| From: Richard Cartwright (Propositions [1962], 01) | |
| A reaction: Carwright's answer is 'statements', which seem to be the same as propositions. |
| 13942 | Logicians take sentences to be truth-bearers for rigour, rather than for philosophical reasons [Cartwright,R] |
| Full Idea: The current fashion among logicians of taking sentences to be the bearers of truth and falsity indicates less an agreement on philosophical theory than a desire for rigor and smoothness in calculative practice. | |
| From: Richard Cartwright (Propositions [1962], 01) | |
| A reaction: A remark close to my heart. Propositions are rejected first because language offers hope of answers, then because they seem metaphysically odd, and finally because you can't pin them down rigorously. But the blighters won't lie down and die. |
| 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. |
| 13945 | A token isn't a unique occurrence, as the case of a word or a number shows [Cartwright,R] |
| Full Idea: We cannot take a token of a word to be an occurrence of it. Suppose there is exactly one occurrence of the word 'etherized' in the whole of English poetry? Exactly one 'token'? This sort of occurrence is like the occurrence of a number in a sequence. | |
| From: Richard Cartwright (Propositions [1962], Add 2) | |
| A reaction: This remark is in an addendum to his paper, criticising his own lax use of the idea of 'token' in the actual paper. The example nicely shows that the type/token distinction isn't neat and tidy - though I consider it very useful. |
| 13948 | For any statement, there is no one meaning which any sentence asserting it must have [Cartwright,R] |
| Full Idea: It does have to be acknowledged, I think, that every statement whatever is such that there is no one meaning which any sentence used to assert it must have. | |
| From: Richard Cartwright (Propositions [1962], 11) | |
| A reaction: This feels to me like a Gricean move - that what we are really interested in is communicating one mental state to another mental state, and there are all sorts of tools that can do that one job. |
| 13950 | People don't assert the meaning of the words they utter [Cartwright,R] |
| Full Idea: No one ever asserts the meaning of the words he utters. | |
| From: Richard Cartwright (Propositions [1962], 12) | |
| A reaction: Cartwright is using this point to drive a wedge between sentence meaning and the assertion made by the utterance. Hence he defends propositions. Presumably people utilise word-meanings, rather than asserting them. Meanings (not words) are tools. |
| 13944 | We can pull apart assertion from utterance, and the action, the event and the subject-matter for each [Cartwright,R] |
| Full Idea: We need to distinguish 1) what is asserted, 2) that assertion, 3) asserting something, 4) what is predicated, 5) what is uttered, 6) that utterance, 7) uttering something, 8) the utterance token, and 9) the meaning. | |
| From: Richard Cartwright (Propositions [1962], 05-06) | |
| A reaction: [summary of his overall analysis in the paper] It is amazingly hard to offer a critical assessment of this sort of analysis, but it gives you a foot in the door for thinking about the issues with increasing clarity. |
| 13947 | 'It's raining' makes a different assertion on different occasions, but its meaning remains the same [Cartwright,R] |
| Full Idea: A person who utters 'It's raining' one day does not normally make the same statement as one who utters it the next. But these variations are not accompanied by corresponding changes of meaning. The words 'It's raining' retain the same meaning throughout. | |
| From: Richard Cartwright (Propositions [1962], 10) | |
| A reaction: This is important, because it shows that a proposition is not just the mental shadow behind a sentence, or a mental shadow awaiting a sentence. Unlike a sentence, a proposition can (and possibly must) include its own context. Very interesting! |
| 13943 | We can attribute 'true' and 'false' to whatever it was that was said [Cartwright,R] |
| Full Idea: We do sometimes say of something to which we have referred that it is true (or false). Are we not ordinarily doing just this when we utter such sentences as 'That's true' and 'What he said was false'? | |
| From: Richard Cartwright (Propositions [1962], 03) | |
| A reaction: This supports propositions, but doesn't clinch the matter. One could interpret this phenomenon as always being (implicitly) the reference of one sentence to another. However, I remember what he said, but I can't remember how he said it. |
| 13946 | To assert that p, it is neither necessary nor sufficient to utter some particular words [Cartwright,R] |
| Full Idea: In order to assert that p it is not necessary to utter exactly those words. ...Clearly, also, in order to assert that p, it is not sufficient to utter the words that were actually uttered. | |
| From: Richard Cartwright (Propositions [1962], 07) | |
| A reaction: I take the first point to be completely obvious (you can assert one thing with various wordings), and the second seems right after a little thought (the words could be vague, ambiguous, inaccurate, contextual) |
| 13951 | Assertions, unlike sentence meanings, can be accurate, probable, exaggerated, false.... [Cartwright,R] |
| Full Idea: Whereas what is asserted can be said to be accurate, exaggerated, unfounded, overdrawn, probable, improbable, plausible, true, or false, none of these can be said of the meaning of a sentence. | |
| From: Richard Cartwright (Propositions [1962], 12) | |
| A reaction: That fairly firmly kicks into touch the idea that the assertion is the same as the meaning of the sentence. |