13 ideas
| 10825 | The notion of truth is to help us make use of the utterances of others [Field,H] |
| Full Idea: I suspect that the original purpose of the notion of truth was to aid us in utilizing the utterances of others in drawing conclusions about the world,...so we must attend to its social role, and that being in a position to assert something is what counts. | |
| From: Hartry Field (Tarski's Theory of Truth [1972], §5) | |
| A reaction: [Last bit compressed] This sounds excellent. Deflationary and redundancy views are based on a highly individualistic view of utterances and truth, but we need to be much more contextual and pragmatic if we are to get the right story. |
| 10820 | In the early 1930s many philosophers thought truth was not scientific [Field,H] |
| Full Idea: In the early 1930s many philosophers believed that the notion of truth could not be incorporated into a scientific conception of the world. | |
| From: Hartry Field (Tarski's Theory of Truth [1972], §3) | |
| A reaction: This leads on to an account of why Tarski's formal version was so important, and Field emphasises Tarski's physicalist metaphysic. |
| 13499 | Tarski reduced truth to reference or denotation [Field,H, by Hart,WD] |
| Full Idea: Tarski can be viewed as having reduced truth to reference or denotation. | |
| From: report of Hartry Field (Tarski's Theory of Truth [1972]) by William D. Hart - The Evolution of Logic 4 |
| 10818 | Tarski really explained truth in terms of denoting, predicating and satisfied functions [Field,H] |
| Full Idea: A proper account of Tarski's truth definition explains truth in terms of three other semantic notions: what it is for a name to denote something, and for a predicate to apply to something, and for a function symbol to be fulfilled by a pair of things. | |
| From: Hartry Field (Tarski's Theory of Truth [1972]) | |
| A reaction: This is Field's 'T1' version, which is meant to spell out what was really going on in Tarski's account. |
| 10817 | Tarski just reduced truth to some other undefined semantic notions [Field,H] |
| Full Idea: It is normally claimed that Tarski defined truth using no undefined semantic terms, but I argue that he reduced the notion of truth to certain other semantic notions, but did not in any way explicate these other notions. | |
| From: Hartry Field (Tarski's Theory of Truth [1972], §0) |
| 10819 | Tarski gives us the account of truth needed to build a group of true sentences in a model [Field,H] |
| Full Idea: Model theory must choose the denotations of the primitives so that all of a group of sentences come out true, so we need a theory of how the truth value of a sentence depends on the denotation of its primitive nonlogical parts, which Tarski gives us. | |
| From: Hartry Field (Tarski's Theory of Truth [1972], §1) |
| 10827 | Model theory is unusual in restricting the range of the quantifiers [Field,H] |
| Full Idea: In model theory we are interested in allowing a slightly unusual semantics for quantifiers: we are willing to allow that the quantifier not range over everything. | |
| From: Hartry Field (Tarski's Theory of Truth [1972], n 5) |
| 18253 | I wish to go straight from cardinals to reals (as ratios), leaving out the rationals [Frege] |
| Full Idea: You need a double transition, from cardinal numbes (Anzahlen) to the rational numbers, and from the latter to the real numbers generally. I wish to go straight from the cardinal numbers to the real numbers as ratios of quantities. | |
| From: Gottlob Frege (Letters to Russell [1902], 1903.05.21), quoted by Michael Dummett - Frege philosophy of mathematics 21 'Frege's' | |
| A reaction: Note that Frege's real numbers are not quantities, but ratios of quantities. In this way the same real number can refer to lengths, masses, intensities etc. |
| 18166 | The loss of my Rule V seems to make foundations for arithmetic impossible [Frege] |
| Full Idea: With the loss of my Rule V, not only the foundations of arithmetic, but also the sole possible foundations of arithmetic, seem to vanish. | |
| From: Gottlob Frege (Letters to Russell [1902], 1902.06.22) | |
| A reaction: Obviously he was stressed, but did he really mean that there could be no foundation for arithmetic, suggesting that the subject might vanish into thin air? |
| 18269 | Logical objects are extensions of concepts, or ranges of values of functions [Frege] |
| Full Idea: How are we to conceive of logical objects? My only answer is, we conceive of them as extensions of concepts or, more generally, as ranges of values of functions ...what other way is there? | |
| From: Gottlob Frege (Letters to Russell [1902], 1902.07.28), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 7 epigr | |
| A reaction: This is the clearest statement I have found of what Frege means by an 'object'. But an extension is a collection of things, so an object is a group treated as a unity, which is generally how we understand a 'set'. Hence Quine's ontology. |
| 4871 | A thing is free if it acts only by the necessity of its own nature [Spinoza] |
| Full Idea: I say that a thing is free, which exists and acts solely by the necessity of its own nature. | |
| From: Baruch de Spinoza (Letter to G.H. Schaller [1674], 1674.10) | |
| A reaction: Of course, this isn't 'freedom' at all, but it seems to exactly right as an account of so-called freedom. In the case of a human being the 'necessity of our own nature' is character, and virtue and vice are the expressions of the necessities of character. |
| 10826 | 'Valence' and 'gene' had to be reduced to show their compatibility with physicalism [Field,H] |
| Full Idea: 'Valence' and 'gene' were perfectly clear long before anyone succeeded in reducing them, but it was their reducibility and not their clarity before reduction that showed them to be compatible with physicalism. | |
| From: Hartry Field (Tarski's Theory of Truth [1972], §5) |
| 7615 | Field says reference is a causal physical relation between mental states and objects [Field,H, by Putnam] |
| Full Idea: In Field's view reference is a 'physicalistic relation', i.e. a complex causal relation between words or mental representations and objects or sets of objects; it is up to physical science to discover what that physicalistic relation is. | |
| From: report of Hartry Field (Tarski's Theory of Truth [1972]) by Hilary Putnam - Reason, Truth and History Ch.2 | |
| A reaction: I wouldn't hold your breath while the scientists do their job. If physicalism is right then Field is right, but physics seems no more appropriate for giving a theory of reference than it does for giving a theory of music. |