display all the ideas for this combination of philosophers
14 ideas
| 14780 | Only study logic if you think your own reasoning is deficient [Peirce] |
| Full Idea: It is foolish to study logic unless one is persuaded that one's own reasonings are more or less bad. | |
| From: Charles Sanders Peirce (Criterion of Validity in Reasoning [1903], II) |
| 19296 | If second-order variables range over sets, those are just objects; properties and relations aren't sets [Hale] |
| Full Idea: Contrary to what Quine supposes, it is neither necessary nor desirable to interpret bound higher-order variables as ranging over sets. Sets are a species of object. They should range over entities of a completely different type: properties and relations. | |
| From: Bob Hale (Necessary Beings [2013], 08.2) | |
| A reaction: This helpfully clarifies something which was confusing me. If sets are objects, then 'second-order' logic just seems to be the same as first-order logic (rather than being 'set theory in disguise'). I quantify over properties, but deny their existence! |
| 19237 | Deduction is true when the premises facts necessarily make the conclusion fact true [Peirce] |
| Full Idea: The question of whether a deductive argument is true or not is simply the question whether or not the facts stated in the premises could be true in any sort of universe no matter what be true without the fact stated in the conclusion being true likewise. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], III) | |
| A reaction: A remarkably modern account, fitting the normal modern view of semantic consequence, and expressing the necessity in the validity in terms of something close to possible worlds. |
| 19256 | Our research always hopes that reality embodies the logic we are employing [Peirce] |
| Full Idea: Every attempt to understand anything at least hopes that the very objects of study themselves are subject to a logic more or less identical with that which we employ. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], VIII) | |
| A reaction: The idea that external objects might be subject to a logic has become very unfashionable since Frege, but I love the idea. I'm inclined to think that we derive our logic from the world, so I'm a bit more confident that Peirce. |
| 21493 | Pure mathematics deals only with hypotheses, of which the reality does not matter [Peirce] |
| Full Idea: The pure mathematician deals exclusively with hypotheses. Whether or not there is any corresponding real thing, he does not care. | |
| From: Charles Sanders Peirce (works [1892], CP5.567), quoted by Albert Atkin - Peirce 3 'separation' | |
| A reaction: [Dated 1902] Maybe we should identify a huge branch of human learning as Hyptheticals. Professor of Hypotheticals at Cambridge University. The trouble is it would have to include computer games. So why does maths matter more than games? |
| 14783 | Logic, unlike mathematics, is not hypothetical; it asserts categorical ends from hypothetical means [Peirce] |
| Full Idea: Mathematics is purely hypothetical: it produces nothing but conditional propositions. Logic, on the contrary, is categorical in its assertions. True, it is a normative science, and not a mere discovery of what really is. It discovers ends from means. | |
| From: Charles Sanders Peirce (The Nature of Mathematics [1898], II) |
| 19289 | Maybe conventionalism applies to meaning, but not to the truth of propositions expressed [Hale] |
| Full Idea: An old objection to conventionalism claims that it confuses sentences with propositions, confusing what makes sentences mean what they do with what makes them (as propositions) true. | |
| From: Bob Hale (Necessary Beings [2013], 05.2) | |
| A reaction: The conventions would presumably apply to the sentences, but not to the propositions. Since I think that focusing on propositions solves a lot of misunderstandings in modern philosophy, I like the sound of this. |
| 19102 | Bivalence is a regulative assumption of enquiry - not a law of logic [Peirce, by Misak] |
| Full Idea: Peirce takes bivalence not to be a law of logic, but a regulative assumption of enquiry. | |
| From: report of Charles Sanders Peirce (works [1892]) by Cheryl Misak - Pragmatism and Deflationism 2 n10 | |
| A reaction: I like this. For most enquiries it's either true or not true, it's either there or it's not there. When you aren't faced with these simple dichotomies (in history, or quantum mechanics) you can relax, and allow truth value gaps etc. |
| 19238 | The logic of relatives relies on objects built of any relations (rather than on classes) [Peirce] |
| Full Idea: In the place of the class ...the logic of relatives considers the system, which is composed of objects brought together by any kind of relations whatsoever. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], III) | |
| A reaction: Peirce's logic of relations might support the purely structural view of reality defended by Ladyman and Ross. Modern logic standardly expresses its semantics in terms of set theory. Peirce pioneered relations in logic. |
| 10316 | We should decide whether singular terms are genuine by their usage [Hale] |
| Full Idea: The criteria for a genuine singular term should pick out not the singular terms themselves but their uses, since they may be genuine in one context and not another. | |
| From: Bob Hale (Abstract Objects [1987], Ch.2.II) | |
| A reaction: [rephrased] This will certainly meet problems with vagueness (e.g. as the reference of a singular term is gradually clarified). |
| 10312 | Often the same singular term does not ensure reliable inference [Hale] |
| Full Idea: In 'the whale is increasingly scarce' and 'the whale is much improved today' (our pet whale), we cannot infer that there is something that is much improved and increasingly scarce, so this singular term fails Dummett's criterion based on inference. | |
| From: Bob Hale (Abstract Objects [1987], Ch.2) | |
| A reaction: [much rephrased] This is not just a problem for a few cunningly selected examples. With contortions almost any singular term can be undermined in this way. Singular terms are simply not a useful guide to the existence of abstracta. |
| 10313 | Plenty of clear examples have singular terms with no ontological commitment [Hale] |
| Full Idea: Some examples where a definite singular noun phrase is not 'genuine' (giving ontological commitment): 'left us in the lurch'; 'for my mother's sake'; 'given the sack'; 'in the nick of time', 'the whereabouts of the PM', 'the identity of the murderer'. | |
| From: Bob Hale (Abstract Objects [1987], Ch.2.II) | |
| A reaction: These are not just freakish examples. If I 'go on a journey', that doesn't involve extra entities called 'journeys', just because the meaning is clearer and a more commonplace part of the language. |
| 10322 | If singular terms can't be language-neutral, then we face a relativity about their objects [Hale] |
| Full Idea: If we lack any general, language-neutral characterization of singular terms, must not a parallel linguistic relativity infect the objects which are to be thought of as their non-linguistic correlates? | |
| From: Bob Hale (Abstract Objects [1987], Ch.2.III) | |
| A reaction: Hale thinks he can answer this, but I would have thought that this problem dooms the linguistic approach from the start. There needs to be more imagination about how very different a language could be, while still qualifying as a language. |
| 19298 | Unlike axiom proofs, natural deduction proofs needn't focus on logical truths and theorems [Hale] |
| Full Idea: In contrast with axiomatic systems, in natural deductions systems of logic neither the premises nor the conclusions of steps in a derivation need themselves be logical truths or theorems of logic. | |
| From: Bob Hale (Necessary Beings [2013], 09.2 n7) | |
| A reaction: Not sure I get that. It can't be that everything in an axiomatic proof has to be a logical truth. How would you prove anything about the world that way? I'm obviously missing something. |