16 ideas
| 12204 | The logic of metaphysical necessity is S5 [Rumfitt] |
| Full Idea: It is a widely accepted thesis that the logic of metaphysical necessity is S5. | |
| From: Ian Rumfitt (Logical Necessity [2010], §5) | |
| A reaction: Rumfitt goes on to defend this standard view (against Dummett's defence of S4). The point, I take it, is that one can only assert that something is 'true in all possible worlds' only when the worlds are all accessible to one another. |
| 13655 | The Löwenheim-Skolem theorems show that whether all sets are constructible is indeterminate [Putnam, by Shapiro] |
| Full Idea: Putnam claims that the Löwenheim-Skolem theorems indicate that there is no 'fact of the matter' whether all sets are constructible. | |
| From: report of Hilary Putnam (Models and Reality [1977]) by Stewart Shapiro - Foundations without Foundationalism | |
| A reaction: [He refers to the 4th and 5th pages of Putnam's article] Shapiro offers (p.109) a critique of Putnam's proposal. |
| 9915 | V = L just says all sets are constructible [Putnam] |
| Full Idea: V = L just says all sets are constructible. L is the class of all constructible sets, and V is the universe of all sets. | |
| From: Hilary Putnam (Models and Reality [1977], p.425) |
| 12195 | Soundness in argument varies with context, and may be achieved very informally indeed [Rumfitt] |
| Full Idea: Our ordinary standards for deeming arguments to be sound vary greatly from context to context. Even the package tourist's syllogism ('It's Tuesday, so this is Belgium') may meet the operative standards for soundness. | |
| From: Ian Rumfitt (Logical Necessity [2010], Intro) | |
| A reaction: No doubt one could spell out the preconceptions of package tourist reasoning, and arrive at the logical form of the implication which is being offered. |
| 12199 | There is a modal element in consequence, in assessing reasoning from suppositions [Rumfitt] |
| Full Idea: There is a modal element in consequence, in its applicability to assessing reasoning from suppositions. | |
| From: Ian Rumfitt (Logical Necessity [2010], §2) |
| 12201 | We reject deductions by bad consequence, so logical consequence can't be deduction [Rumfitt] |
| Full Idea: A rule is to be rejected if it enables us to deduce from some premisses a purported conclusion that does not follow from them in the broad sense. The idea that deductions answer to consequence is incomprehensible if consequence consists in deducibility. | |
| From: Ian Rumfitt (Logical Necessity [2010], §2) |
| 12194 | Contradictions include 'This is red and not coloured', as well as the formal 'B and not-B' [Rumfitt] |
| Full Idea: Overt contradictions include formal contradictions of form 'B and not B', but I also take them to include 'This is red all over and green all over' and 'This is red and not coloured'. | |
| From: Ian Rumfitt (Logical Necessity [2010], Intro) |
| 12198 | Geometrical axioms in logic are nowadays replaced by inference rules (which imply the logical truths) [Rumfitt] |
| Full Idea: The geometrical style of formalization of logic is now little more than a quaint anachronism, largely because it fails to show logical truths for what they are: simply by-products of rules of inference that are applicable to suppositions. | |
| From: Ian Rumfitt (Logical Necessity [2010], §1) | |
| A reaction: This is the rejection of Russell-style axiom systems in favour of Gentzen-style natural deduction systems (starting from rules). Rumfitt quotes Dummett in support. |
| 9913 | The Löwenheim-Skolem Theorem is close to an antinomy in philosophy of language [Putnam] |
| Full Idea: The Löwenheim-Skolem Theorem says that a satisfiable first-order theory (in a countable language) has a countable model. ..I argue that this is not a logical antinomy, but close to one in philosophy of language. | |
| From: Hilary Putnam (Models and Reality [1977], p.421) | |
| A reaction: See the rest of this paper for where he takes us on this. |
| 9914 | It is unfashionable, but most mathematical intuitions come from nature [Putnam] |
| Full Idea: Experience with nature is undoubtedly the source of our most basic 'mathematical intuitions', even if it is unfashionable to say so. | |
| From: Hilary Putnam (Models and Reality [1977], p.424) | |
| A reaction: Correct. I find it quite bewildering how Frege has managed to so discredit all empirical and psychological approaches to mathematics that it has become a heresy to say such things. |
| 14532 | A distinctive type of necessity is found in logical consequence [Rumfitt, by Hale/Hoffmann,A] |
| Full Idea: Rumfitt argues that there is a distinctive notion of necessity implicated in the notion of logical consequence. | |
| From: report of Ian Rumfitt (Logical Necessity [2010]) by Bob Hale/ Aviv Hoffmann - Introduction to 'Modality' 2 |
| 12193 | Logical necessity is when 'necessarily A' implies 'not-A is contradictory' [Rumfitt] |
| Full Idea: By the notion of 'logical necessity' I mean that there is a sense of 'necessary' for which 'It is necessary that A' implies and is implied by 'It is logically contradictory that not A'. ...From this, logical necessity is implicated in logical consequence. | |
| From: Ian Rumfitt (Logical Necessity [2010], Intro) | |
| A reaction: Rumfitt expresses a commitment to classical logic at this point. We will need to be quite sure what we mean by 'contradiction', which will need a clear notion of 'truth'.... |
| 12200 | A logically necessary statement need not be a priori, as it could be unknowable [Rumfitt] |
| Full Idea: There is no reason to suppose that any statement that is logically necessary (in the present sense) is knowable a priori. ..If a statement is logically necessary, its negation will yield a contradiction, but that does not imply that someone could know it. | |
| From: Ian Rumfitt (Logical Necessity [2010], §2) | |
| A reaction: This remark is aimed at Dorothy Edgington, who holds the opposite view. Rumfitt largely defends McFetridge's view (q.v.). |
| 12202 | Narrow non-modal logical necessity may be metaphysical, but real logical necessity is not [Rumfitt] |
| Full Idea: While Fine suggests defining a narrow notion of logical necessity in terms of metaphysical necessity by 'restriction' (to logical truths that can be defined in non-modal terms), this seems unpromising for broad logical necessity, which is modal. | |
| From: Ian Rumfitt (Logical Necessity [2010], §2) | |
| A reaction: [compressed] He cites Kit Fine 2002. Rumfitt glosses the non-modal definitions as purely formal. The metaphysics lurks somewhere in the proof. |
| 12203 | If a world is a fully determinate way things could have been, can anyone consider such a thing? [Rumfitt] |
| Full Idea: A world is usually taken to be a fully determinate way that things could have been; but then one might seriously wonder whether anyone is capable of 'considering' such a thing at all. | |
| From: Ian Rumfitt (Logical Necessity [2010], §4) | |
| A reaction: This has always worried me. If I say 'maybe my coat is in the car', I would hate to think that I had to be contemplating some entire possible world (including all the implications of my coat not being on the hat stand). |
| 14080 | Are causal descriptions part of the causal theory of reference, or are they just metasemantic? [Kaplan, by Schaffer,J] |
| Full Idea: Kaplan notes that the causal theory of reference can be understood in two quite different ways, as part of the semantics (involving descriptions of causal processes), or as metasemantics, explaining why a term has the referent it does. | |
| From: report of David Kaplan (Dthat [1970]) by Jonathan Schaffer - Deflationary Metaontology of Thomasson 1 | |
| A reaction: [Kaplan 'Afterthought' 1989] The theory tends to be labelled as 'direct' rather than as 'causal' these days, but causal chains are still at the heart of the story (even if more diffused socially). Nice question. Kaplan takes the meta- version as orthodox. |