19 ideas
| 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. |
| 10688 | 'Equivocation' is when terms do not mean the same thing in premises and conclusion [Beall/Restall] |
| Full Idea: 'Equivocation' is when the terms do not mean the same thing in the premises and in the conclusion. | |
| From: JC Beall / G Restall (Logical Consequence [2005], Intro) |
| 10690 | Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought [Beall/Restall] |
| Full Idea: Logic is purely formal either when it is invariant under permutation of object (Tarski), or when it has totally abstracted away from all contents, or it is the constitutive norms for thought. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 2) | |
| A reaction: [compressed] The third account sounds rather woolly, and the second one sounds like a tricky operation, but the first one sounds clear and decisive, so I vote for Tarski. |
| 10691 | Logical consequence needs either proofs, or absence of counterexamples [Beall/Restall] |
| Full Idea: Technical work on logical consequence has either focused on proofs, where validity is the existence of a proof of the conclusions from the premises, or on models, which focus on the absence of counterexamples. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 3) |
| 10695 | Logical consequence is either necessary truth preservation, or preservation based on interpretation [Beall/Restall] |
| Full Idea: Two different views of logical consequence are necessary truth-preservation (based on modelling possible worlds; favoured by Realists), or truth-preservation based on the meanings of the logical vocabulary (differing in various models; for Anti-Realists). | |
| From: JC Beall / G Restall (Logical Consequence [2005], 2) | |
| A reaction: Thus Dummett prefers the second view, because the law of excluded middle is optional. My instincts are with the first one. |
| 10689 | A step is a 'material consequence' if we need contents as well as form [Beall/Restall] |
| Full Idea: A logical step is a 'material consequence' and not a formal one, if we need the contents as well as the structure or form. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 2) |
| 10696 | A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises [Beall/Restall] |
| Full Idea: If a conclusion follows from an empty collection of premises, it is true by logic alone, and is a 'logical truth' (sometimes a 'tautology'), or, in the proof-centred approach, 'theorems'. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 4) | |
| A reaction: These truths are written as following from the empty set Φ. They are just implications derived from the axioms and the rules. |
| 10693 | Models are mathematical structures which interpret the non-logical primitives [Beall/Restall] |
| Full Idea: Models are abstract mathematical structures that provide possible interpretations for each of the non-logical primitives in a formal language. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 3) |
| 10692 | Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall] |
| Full Idea: There are many proof-systems, the main being Hilbert proofs (with simple rules and complex axioms), or natural deduction systems (with few axioms and many rules, and the rules constitute the meaning of the connectives). | |
| From: JC Beall / G Restall (Logical Consequence [2005], 3) |
| 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. |
| 7535 | If all beliefs are propositional, then belief and judgement are the same thing [Monk] |
| Full Idea: Whether the words 'belief' and 'judgement' mean the same thing is a moot point. Traditionally, a judgement is the assent of mind to a proposition. If one thinks that all beliefs are propositional, then beliefs and judgements are the same thing. | |
| From: Ray Monk (Bertrand Russell: Spirit of Solitude [1996], Ch.19 n6) | |
| A reaction: If I think I have put a bit too much toothpaste on my brush, that strikes me as a non-propositional judgement, even though it could be spelled out as a proposition. But it also strikes me as a belief. |
| 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. |