16 ideas
| 10528 | Definitions concern how we should speak, not how things are [Fine,K] |
| Full Idea: Our concern in giving a definition is not to say how things are by to say how we wish to speak | |
| From: Kit Fine (Precis of 'Limits of Abstraction' [2005], p.310) | |
| A reaction: This sounds like an acceptable piece of wisdom which arises out of analytical and linguistic philosophy. It puts a damper on the Socratic dream of using definition of reveal the nature of reality. |
| 18369 | There are at least fourteen candidates for truth-bearers [Kirkham] |
| Full Idea: Among the candidates [for truthbearers] are beliefs, propositions, judgments, assertions, statements, theories, remarks, ideas, acts of thought, utterances, sentence tokens, sentence types, sentences (unspecified), and speech acts. | |
| From: Richard L. Kirkham (Theories of Truth: a Critical Introduction [1992], 2.3) | |
| A reaction: I vote for propositions, but only in the sense of the thoughts underlying language, not the Russellian things which are supposed to exist independently from thinkers. |
| 19319 | If one sequence satisfies a sentence, they all do [Kirkham] |
| Full Idea: If one sequence satisfies a sentence, they all do. ...Thus it matters not whether we define truth as satisfaction by some sequence or as satisfaction by all sequences. | |
| From: Richard L. Kirkham (Theories of Truth: a Critical Introduction [1992], 5.4) | |
| A reaction: So if the striker scores a goal, the team has scored a goal. |
| 19318 | A 'sequence' of objects is an order set of them [Kirkham] |
| Full Idea: A 'sequence' of objects is like a set of objects, except that, unlike a set, the order of the objects is important when dealing with sequences. ...An infinite sequence satisfies 'x2 is purple' if and only if the second member of the sequence is purple. | |
| From: Richard L. Kirkham (Theories of Truth: a Critical Introduction [1992], 5.4) | |
| A reaction: This explains why Tarski needed set theory in his metalanguage. |
| 19320 | If we define truth by listing the satisfactions, the supply of predicates must be finite [Kirkham] |
| Full Idea: Because the definition of satisfaction must have a separate clause for each predicate, Tarski's method only works for languages with a finite number of predicates, ...but natural languages have an infinite number of predicates. | |
| From: Richard L. Kirkham (Theories of Truth: a Critical Introduction [1992], 5.5) | |
| A reaction: He suggest predicates containing natural numbers, as examples of infinite predicates. Davidson tried to extend the theory to natural languages, by (I think) applying it to adverbs, which could generate the infinite predicates. Maths has finite predicates. |
| 19315 | In quantified language the components of complex sentences may not be sentences [Kirkham] |
| Full Idea: In a quantified language it is possible to build new sentences by combining two expressions neither of which is itself a sentence. | |
| From: Richard L. Kirkham (Theories of Truth: a Critical Introduction [1992], 5.4) | |
| A reaction: In propositional logic the components are other sentences, so the truth value can be given by their separate truth-values, through truth tables. Kirkham is explaining the task which Tarski faced. Truth-values are not just compositional. |
| 21566 | 'Propositional functions' are ambiguous until the variable is given a value [Russell] |
| Full Idea: By a 'propositional function' I mean something which contains a variable x, and expresses a proposition as soon as a value is assigned to x. That is to say, it differs from a proposition solely by the fact that it is ambiguous. | |
| From: Bertrand Russell (The Theory of Logical Types [1910], p.216) | |
| A reaction: This is Frege's notion of a 'concept', as an assertion of a predicate which still lacks a subject. |
| 19317 | An open sentence is satisfied if the object possess that property [Kirkham] |
| Full Idea: An object satisfies an open sentence if and only if it possesses the property expressed by the predicate of the open sentence. | |
| From: Richard L. Kirkham (Theories of Truth: a Critical Introduction [1992], 5.4) | |
| A reaction: This applies to atomic sentence, of the form Fx or Fa (that is, some variable is F, or some object is F). So strictly, only the world can decide whether some open sentence is satisfied. And it all depends on things called 'properties'. |
| 21567 | 'All judgements made by Epimenedes are true' needs the judgements to be of the same type [Russell] |
| Full Idea: Such a proposition as 'all the judgements made by Epimenedes are true' will only be prima facie capable of truth if all his judgements are of the same order. | |
| From: Bertrand Russell (The Theory of Logical Types [1910], p.227) | |
| A reaction: This is an attempt to use his theory of types to solve the Liar. Tarski's invocation of a meta-language is clearly in the same territory. |
| 10529 | If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K] |
| Full Idea: Neo-Fregeans have thought that Hume's Principle, and the like, might be definitive of number and therefore not subject to the usual epistemological worries over its truth. | |
| From: Kit Fine (Precis of 'Limits of Abstraction' [2005], p.310) | |
| A reaction: This seems to be the underlying dream of logicism - that arithmetic is actually brought into existence by definitions, rather than by truths derived from elsewhere. But we must be able to count physical objects, as well as just counting numbers. |
| 10530 | Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K] |
| Full Idea: The fundamental difficulty facing the neo-Fregean is to either adopt the predicative reading of Hume's Principle, defining numbers, but inadequate, or the impredicative reading, which is adequate, but not really a definition. | |
| From: Kit Fine (Precis of 'Limits of Abstraction' [2005], p.312) | |
| A reaction: I'm not sure I understand this, but the general drift is the difficulty of building a system which has been brought into existence just by definition. |
| 23457 | Type theory cannot identify features across levels (because such predicates break the rules) [Morris,M on Russell] |
| Full Idea: Russell's theory of types meant that features common to different levels of the hierarchy became uncapturable (since any attempt to capture them would involve a predicate which disobeyed the hierarchy restrictions). | |
| From: comment on Bertrand Russell (The Theory of Logical Types [1910]) by Michael Morris - Guidebook to Wittgenstein's Tractatus 2H | |
| A reaction: I'm not clear whether this is the main reason why type theory was abandoned. Ramsey was an important critic. |
| 21556 | Classes are defined by propositional functions, and functions are typed, with an axiom of reducibility [Russell, by Lackey] |
| Full Idea: In Russell's mature 1910 theory of types classes are defined in terms of propositional functions, and functions themselves are regimented by a ramified theory of types mitigated by the axiom of reducibility. | |
| From: report of Bertrand Russell (The Theory of Logical Types [1910]) by Douglas Lackey - Intros to Russell's 'Essays in Analysis' p.133 |
| 21568 | A one-variable function is only 'predicative' if it is one order above its arguments [Russell] |
| Full Idea: We will define a function of one variable as 'predicative' when it is of the next order above that of its arguments, i.e. of the lowest order compatible with its having an argument. | |
| From: Bertrand Russell (The Theory of Logical Types [1910], p.237) | |
| A reaction: 'Predicative' just means it produces a set. This is Russell's strict restriction on which functions are predicative. |
| 19322 | Why can there not be disjunctive, conditional and negative facts? [Kirkham] |
| Full Idea: It has been said that there are no disjunctive facts, conditional facts, or negative facts. ...but it is not at all clear why there cannot be facts of this sort. | |
| From: Richard L. Kirkham (Theories of Truth: a Critical Introduction [1992], 5.6) | |
| A reaction: I love these sorts of facts, and offer them as a naturalistic basis for logic. You probably need the world to have modal features, but I have those in the form of powers and dispositions. |
| 10527 | An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K] |
| Full Idea: If an abstraction principle is going to be acceptable, then it should not 'inflate', i.e. it should not result in there being more abstracts than there are objects. By this mark Hume's Principle will be acceptable, but Frege's Law V will not. | |
| From: Kit Fine (Precis of 'Limits of Abstraction' [2005], p.307) | |
| A reaction: I take this to be motivated by my own intuition that abstract concepts had better be rooted in the world, or they are not worth the paper they are written on. The underlying idea this sort of abstraction is that it is 'shared' between objects. |