display all the ideas for this combination of texts
11 ideas
| 16333 | The underestimated costs of giving up classical logic are found in mathematical reasoning [Halbach] |
| Full Idea: The costs of giving up classical logic are easily underestimated, …the price being paid in terms of mathematical reasoning. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 16.2) | |
| A reaction: No one cares much about such costs, until you say they are 'mathematical'. Presumably this is a message to Graham Priest and his pals. |
| 16310 | A theory is some formulae and all of their consequences [Halbach] |
| Full Idea: A theory is a set of formulae closed under first-order logical consequence. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 5.1) |
| 7760 | Russell only uses descriptions attributively, and Strawson only referentially [Donnellan, by Lycan] |
| Full Idea: Donnellan objects that Russell's theory of definite descriptions overlooks the referential use (Russell writes as if all descriptions are used attributively), and that Strawson assumes they are all used referentially, to draw attention to things. | |
| From: report of Keith Donnellan (Reference and Definite Descriptions [1966]) by William Lycan - Philosophy of Language Ch.1 | |
| A reaction: This seems like a nice little success for analytical philosophy - clarifying a horrible mess by making a simple distinction that leaves everyone happy. |
| 5811 | A definite description can have a non-referential use [Donnellan] |
| Full Idea: A definite description may also be used non-referentially, even as it occurs in one and the same sentence. | |
| From: Keith Donnellan (Reference and Definite Descriptions [1966], §I) | |
| A reaction: Donnellan says we have to know about the particular occasion on which the description is used, as in itself it will not achieve reference. "Will the last person out switch off the lights" achieves its reference at the end of each day. |
| 5812 | Definite descriptions are 'attributive' if they say something about x, and 'referential' if they pick x out [Donnellan] |
| Full Idea: A speaker who uses a definite description 'attributively' in an assertion states something about whoever or whatever is the so-and-so; a speaker who uses it 'referentially' enables his audience to pick out whom or what he is talking about. | |
| From: Keith Donnellan (Reference and Definite Descriptions [1966], §III) | |
| A reaction: "Smith's murderer is insane" exemplifies the first use before he is caught, and the second use afterwards. The gist is that reference is not a purely linguistic activity, but is closer to pointing at something. This seems right. |
| 5814 | 'The x is F' only presumes that x exists; it does not actually entail the existence [Donnellan] |
| Full Idea: For Russell there is a logical entailment: 'the x is F' entails 'there exists one and only one x'. Whether or not this is true of the attributive use of definite descriptions, it does not seem true of the referential use. The existence is a presumption. | |
| From: Keith Donnellan (Reference and Definite Descriptions [1966], §VI) | |
| A reaction: Can we say 'x does not exist, but x is F'? Strictly, that sounds to me more like a contradiction than a surprising rejection of a presumption. However, 'Father Xmas does not exist, but he has a red coat'. |
| 16342 | You cannot just say all of Peano arithmetic is true, as 'true' isn't part of the system [Halbach] |
| Full Idea: One cannot just accept that all the theorems of Peano arithmetic are true when one accepts Peano arithmetic as the notion of truth is not available in the language of arithmetic. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 22.1) | |
| A reaction: This is given as the reason why Kreisel and Levy (1968) introduced 'reflection principles', which allow you to assert whatever has been proved (with no mention of truth). (I think. The waters are closing over my head). |
| 16341 | Normally we only endorse a theory if we believe it to be sound [Halbach] |
| Full Idea: If one endorses a theory, so one might argue, one should also take it to be sound. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 22.1) |
| 16344 | Soundness must involve truth; the soundness of PA certainly needs it [Halbach] |
| Full Idea: Soundness seems to be a notion essentially involving truth. At least I do not know how to fully express the soundness of Peano arithmetic without invoking a truth predicate. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 22.1) | |
| A reaction: I suppose you could use some alternative locution such as 'assertible' or 'cuddly'. Intuitionists seem a bit vague about the truth end of things. |
| 16347 | Many new paradoxes may await us when we study interactions between frameworks [Halbach] |
| Full Idea: Paradoxes that arise from interaction of predicates such as truth, necessity, knowledge, future and past truths have receive little attention. There may be many unknown paradoxes lurking when we develop frameworks with these intensional notions. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 24.2) | |
| A reaction: Nice. This is a wonderful pointer to new research in the analytic tradition, in which formal problems will gradually iron out our metaphysical framework. |
| 16336 | The liar paradox applies truth to a negated truth (but the conditional will serve equally) [Halbach] |
| Full Idea: An essential feature of the liar paradox is the application of the truth predicate to a sentence with a negated occurrence of the truth predicate, though the negation can be avoided by using the conditional. | |
| From: Volker Halbach (Axiomatic Theories of Truth [2011], 19.3) |