64 ideas
15357 | Philosophy is the most general intellectual discipline [Horsten] |
Full Idea: Philosophy is the most general intellectual discipline. | |
From: Leon Horsten (The Tarskian Turn [2011], 05.1) | |
A reaction: Very simple, but exactly how I see the subject. It is continuous with the sciences, and tries to give an account of nature, but operating at an extreme level of generality. It must respect the findings of science, but offer bold interpretations. |
6806 | Do not multiply entities beyond necessity [William of Ockham] |
Full Idea: Do not multiply entities beyond necessity. | |
From: William of Ockham (works [1335]) | |
A reaction: This is the classic statement of Ockham's Razor, though it is not found in his printed works. It appears to be mainly aimed at Plato's Theory of Forms. It is taken to refer to types of entities, not numbers. One seraph is as bad as a hundred. |
15352 | A definition should allow the defined term to be eliminated [Horsten] |
Full Idea: A definition allows a defined term to be eliminated in every context in which it appears. | |
From: Leon Horsten (The Tarskian Turn [2011], 04.2) | |
A reaction: To do that, a definition had better be incredibly comprehensive, so that no nice nuance of the original term is thrown out. |
15323 | Truth is a property, because the truth predicate has an extension [Horsten] |
Full Idea: I take truth to be a property because the truth predicate has an extension - the collection of all true sentences - and this collection does not (unlike the 'extension' of 'exists') consist of everything, or even of all sentences. | |
From: Leon Horsten (The Tarskian Turn [2011], 01.1) | |
A reaction: He concedes that it may be an 'uninteresting' property. My problem is always that I am unconvinced that truth is tied to sentences. I can make perfect sense of animal thoughts being right or wrong. Extension of mental propositions? |
15324 | Semantic theories of truth seek models; axiomatic (syntactic) theories seek logical principles [Horsten] |
Full Idea: There are semantical theories of truth, concerned with models for languages containing the truth predicate, and axiomatic (or syntactic) theories, interested in basic logical principles governing the concept of truth. | |
From: Leon Horsten (The Tarskian Turn [2011], 01.1) | |
A reaction: This is the map of contemporary debates, which seem now to have given up talking about 'correspondence', 'coherence' etc. |
15374 | Truth has no 'nature', but we should try to describe its behaviour in inferences [Horsten] |
Full Idea: We should not aim at describing the nature of truth because there is no such thing. Rather, we should aim at describing the inferential behaviour of truth. | |
From: Leon Horsten (The Tarskian Turn [2011], 10.2.3) |
15348 | Propositions have sentence-like structures, so it matters little which bears the truth [Horsten] |
Full Idea: It makes little difference, at least in extensional contexts, whether the truth bearers are propositions or sentences (or assertions). Even if the bearers are propositions rather than sentences, propositions are structured rather like sentences. | |
From: Leon Horsten (The Tarskian Turn [2011], 02.4) | |
A reaction: The 'extensional' context means you are only talking about the things that are referred to, and not about the way this is expressed. I prefer propositions, but this is an interesting point. |
15333 | Modern correspondence is said to be with the facts, not with true propositions [Horsten] |
Full Idea: Modern correspondence theorists no longer take things to correspond to true propositions; they consider facts to be the truthmakers of propositions. | |
From: Leon Horsten (The Tarskian Turn [2011], 02.1) | |
A reaction: If we then define facts as the way certain things are, independently from our thinking about it, at least we seem to be avoiding circularity. Not much point in correspondence accounts if you are not a robust realist (like me). [14,000th idea, 23/4/12!] |
15337 | The correspondence 'theory' is too vague - about both 'correspondence' and 'facts' [Horsten] |
Full Idea: The principle difficulty of the correspondence theory of truth is its vagueness. It is too vague to be called a theory until more information is given about what is meant by the terms 'correspondence' and 'fact'. Facts can involve a heavy ontology. | |
From: Leon Horsten (The Tarskian Turn [2011], 02.1) | |
A reaction: I see nothing here to make me give up my commitment to the correspondence view of truth, though it sounds as if I will have to give up the word 'theory' in that context. Truth is so obviously about thought fitting reality that there is nothing to discuss. |
15334 | The coherence theory allows multiple coherent wholes, which could contradict one another [Horsten] |
Full Idea: The coherence theory seems too liberal. It seems there can be more than one systematic whole which, while being internally coherent, contradict each other, and thus cannot all be true. Coherence is a necessary but not sufficient condition for truth. | |
From: Leon Horsten (The Tarskian Turn [2011], 02.1) | |
A reaction: This is a modern post-Tarski axiomatic truth theorist making very short work indeed of the coherence theory of truth. I take Horsten to be correct. |
15336 | The pragmatic theory of truth is relative; useful for group A can be useless for group B [Horsten] |
Full Idea: The pragmatic theory is unsatisfactory because usefulness is a relative notion. One theory can be useful to group A while being thoroughly impractical for group B. This would make the theory both truth and false. | |
From: Leon Horsten (The Tarskian Turn [2011], 02.1) | |
A reaction: This objection, along with the obvious fact that certain falsehoods can be very useful, would seem to rule pragmatism out as a theory of truth. It is, in fact, an abandonment of truth. |
15340 | Tarski Bi-conditional: if you'll assert φ you'll assert φ-is-true - and also vice versa [Horsten] |
Full Idea: The axiom schema 'Sentence "phi;" is true iff φ' is the (unrestricted) Tarski-Biconditional, and is motivated by the thought that if you are willing to assume or outright assert that φ, you will assert that φ is true - and also vice versa. | |
From: Leon Horsten (The Tarskian Turn [2011], 02.2) | |
A reaction: Very helpful! Most people are just bewildered by the Tarski bi-conditional ('"Snow is white"...), but this formulation nicely shows its minimal character while showing that it really does say something. It says what truths and truth-claims commit you to. |
15354 | Tarski's hierarchy lacks uniform truth, and depends on contingent factors [Horsten] |
Full Idea: According to the Tarskian hierarchical conception, truth is not a uniform notion. ...Also Kripke has emphasised that the level of a token of the truth predicate can depend on contingent factors, such as what else has been said by a speaker. | |
From: Leon Horsten (The Tarskian Turn [2011], 04.5) |
15345 | Semantic theories have a regress problem in describing truth in the languages for the models [Horsten] |
Full Idea: Semantic theories give a class of models with a truth predicate, ...but Tarski taught us that this needs a more encompassing framework than its language...so how is the semantics of the framework expressed? The model route has a regress. | |
From: Leon Horsten (The Tarskian Turn [2011], 02.3) | |
A reaction: [compressed] So this regress problem, of endless theories of truth going up the hierarchy, is Horsten's main reason for opting for axiomatic theories, which he then tries to strengthen, so that they are not quite so deflated. |
15373 | Axiomatic approaches avoid limiting definitions to avoid the truth predicate, and limited sizes of models [Horsten] |
Full Idea: An adequate definition of truth can only be given for the fragment of our language that does not contain the truth predicate. A model can never encompass the whole of the domain of discourse of our language. The axiomatic approach avoids these problems. | |
From: Leon Horsten (The Tarskian Turn [2011], 10.1) |
15332 | 'Reflexive' truth theories allow iterations (it is T that it is T that p) [Horsten] |
Full Idea: A theory of truth is 'reflexive' if it allows us to prove truth-iterations ("It is true that it is true that so-and-so"). | |
From: Leon Horsten (The Tarskian Turn [2011], 01.4) |
15350 | The Naïve Theory takes the bi-conditionals as axioms, but it is inconsistent, and allows the Liar [Horsten] |
Full Idea: The Naïve Theory of Truth collects all the Tarski bi-conditionals of a language and takes them as axioms. But no consistent theory extending Peano arithmetic can prove all of them. It is inconsistent, and even formalises the liar paradox. | |
From: Leon Horsten (The Tarskian Turn [2011], 03.5.2) | |
A reaction: [compressed] This looks to me like the account of truth that Davidson was working with, since he just seemed to be compiling bi-conditionals for tricky cases. (Wrong! He championed the Compositional Theory, Horsten p.71) |
15351 | Axiomatic theories take truth as primitive, and propose some laws of truth as axioms [Horsten] |
Full Idea: In the axiomatic approach we take the truth predicate to express an irreducible, primitive notion. The meaning of the truth predicate is partially explicated by proposing certain laws of truth as basic principles, as axioms. | |
From: Leon Horsten (The Tarskian Turn [2011], 04.2) | |
A reaction: Judging by Horsten's book, this is a rather fruitful line of enquiry, but it still seems like a bit of a defeat to take truth as 'primitive'. Presumably you could add some vague notion of correspondence as the background picture. |
15367 | By adding truth to Peano Arithmetic we increase its power, so truth has mathematical content! [Horsten] |
Full Idea: It is surprising that just by adding to Peano Arithmetic principles concerning the notion of truth, we increase the mathematical strength of PA. So, contrary to expectations, the 'philosophical' notion of truth has real mathematical content. | |
From: Leon Horsten (The Tarskian Turn [2011], 06.4) | |
A reaction: Horsten invites us to be really boggled by this. All of this is in the Compositional Theory TC. It enables a proof of the consistency of arithmetic (but still won't escape Gödel's Second). |
15346 | Axiomatic approaches to truth avoid the regress problem of semantic theories [Horsten] |
Full Idea: The axiomatic approach to truth does not suffer from the regress problem. | |
From: Leon Horsten (The Tarskian Turn [2011], 02.3) | |
A reaction: See Idea 15345 for the regress problem. The difficulty then seems to be that axiomatic approaches lack expressive power, so the hunt is on for a set of axioms which will do a decent job. Fun work, if you can cope with it. |
15371 | An axiomatic theory needs to be of maximal strength, while being natural and sound [Horsten] |
Full Idea: The challenge is to find the arithmetically strongest axiomatical truth theory that is both natural and truth-theoretically sound. | |
From: Leon Horsten (The Tarskian Turn [2011], 07.7) |
15361 | A good theory of truth must be compositional (as well as deriving biconditionals) [Horsten] |
Full Idea: Deriving many Tarski-biconditionals is not a sufficient condition for being a good theory of truth. A good theory of truth must in addition do justice to the compositional nature of truth. | |
From: Leon Horsten (The Tarskian Turn [2011], 06.1) |
15330 | Friedman-Sheard theory keeps classical logic and aims for maximum strength [Horsten] |
Full Idea: The Friedman-Sheard theory of truth holds onto classical logic and tries to construct a theory that is as strong as possible. | |
From: Leon Horsten (The Tarskian Turn [2011], 01.4) |
15331 | Kripke-Feferman has truth gaps, instead of classical logic, and aims for maximum strength [Horsten] |
Full Idea: If we abandon classical logic in favour of truth-value gaps and try to strengthen the theory, this leads to the Kripke-Feferman theory of truth, and variants of it. | |
From: Leon Horsten (The Tarskian Turn [2011], 01.4) |
15356 | Deflationism concerns the nature and role of truth, but not its laws [Horsten] |
Full Idea: Deflationism is not a theory of the laws of truth. It is a view on the nature and role of the concept of truth. | |
From: Leon Horsten (The Tarskian Turn [2011], 05 Intro) |
15325 | Inferential deflationism says truth has no essence because no unrestricted logic governs the concept [Horsten] |
Full Idea: According to 'inferential deflationism', truth is a concept without a nature or an essence. This is betrayed by the fact that there are no unrestricted logical laws that govern the concept of truth. | |
From: Leon Horsten (The Tarskian Turn [2011], 01.1) |
15358 | Deflationism says truth isn't a topic on its own - it just concerns what is true [Horsten] |
Full Idea: Deflationism says the theory of truth does not have a substantial domain of its own. The domain of the theory of truth consists of the bearers of truth. | |
From: Leon Horsten (The Tarskian Turn [2011], 05.1) | |
A reaction: The immediate thought is that truth also concerns falsehoods, which would be inexplicable without it. If physics just concerns the physical, does that mean that physics lacks its own 'domain'? Generalising about the truths is a topic. |
15359 | Deflation: instead of asserting a sentence, we can treat it as an object with the truth-property [Horsten] |
Full Idea: The Deflationary view just says that instead of asserting a sentence, we can turn the sentence into an object and assert that this object has the property of truth. | |
From: Leon Horsten (The Tarskian Turn [2011], 05.2.2) | |
A reaction: That seems to leave a big question hanging, which concerns the nature of the property that is being attributed to this object. Quine 1970:10-13 says it is just a 'device'. Surely you can rest content with that as an account of truth? |
15344 | Deflationism skips definitions and models, and offers just accounts of basic laws of truth [Horsten] |
Full Idea: Contemporary deflationism about truth does not attempt to define truth, and does not rely on models containing the truth predicate. Instead they are interpretations of axiomatic theories of truth, containing only basic laws of truth. | |
From: Leon Horsten (The Tarskian Turn [2011], 02.3) |
15368 | This deflationary account says truth has a role in generality, and in inference [Horsten] |
Full Idea: On the conception of deflationism developed in this book, the prime positive role of the truth predicate is to serve as a device for expressing generalities, and an inferential tool. | |
From: Leon Horsten (The Tarskian Turn [2011], 07.5) |
18806 | Frege thought traditional categories had psychological and linguistic impurities [Frege, by Rumfitt] |
Full Idea: Frege rejected the traditional categories as importing psychological and linguistic impurities into logic. | |
From: report of Gottlob Frege (Function and Concept [1891]) by Ian Rumfitt - The Boundary Stones of Thought 1.2 | |
A reaction: Resisting such impurities is the main motivation for making logic entirely symbolic, but it doesn't follow that the traditional categories have to be dropped. |
15329 | Nonclassical may accept T/F but deny applicability, or it may deny just T or F as well [Horsten] |
Full Idea: Some nonclassical logic stays close to classical, assuming two mutually exclusive truth values T and F, but some sentences fail to have one. Others have further truth values such as 'half truth', or dialethists allow some T and F at the same time. | |
From: Leon Horsten (The Tarskian Turn [2011], 01.2) | |
A reaction: I take that to say that the first lot accept bivalence but reject excluded middle (allowing 'truth value gaps'), while the second lot reject both. Bivalence gives the values available, and excluded middle says what has them. |
15326 | Doubt is thrown on classical logic by the way it so easily produces the liar paradox [Horsten] |
Full Idea: Aside from logic, so little is needed to generate the liar paradox that one wonders whether the laws of classical logic are unrestrictedly valid after all. (Many theories of truth have therefore been formulated in nonclassical logic.) | |
From: Leon Horsten (The Tarskian Turn [2011], 01.2) | |
A reaction: Kripke uses Strong Kleene logic for his theory. The implication is that debates discussed by Horsten actually have the status of classical logic at stake, as well as the nature of truth. |
15341 | Deduction Theorem: ψ only derivable from φ iff φ→ψ are axioms [Horsten] |
Full Idea: The Deduction Theorem says ψ is derivable in classical predicate logic from ψ iff the sentence φ→ψ is a theorem of classical logic. Hence inferring φ to ψ is truth-preserving iff the axiom scheme φ→ψ is provable. | |
From: Leon Horsten (The Tarskian Turn [2011], 02.2) | |
A reaction: Horsten offers this to show that the Tarski bi-conditionals can themselves be justified, and not just the rule of inference involved. Apparently you can only derive something if you first announce that you have the ability to derive it. Odd. |
8490 | First-level functions have objects as arguments; second-level functions take functions as arguments [Frege] |
Full Idea: Just as functions are fundamentally different from objects, so also functions whose arguments are and must be functions are fundamentally different from functions whose arguments are objects. The latter are first-level, the former second-level, functions. | |
From: Gottlob Frege (Function and Concept [1891], p.38) | |
A reaction: In 1884 he called it 'second-order'. This is the standard distinction between first- and second-order logic. The first quantifies over objects, the second over intensional entities such as properties and propositions. |
8492 | Relations are functions with two arguments [Frege] |
Full Idea: Functions of one argument are concepts; functions of two arguments are relations. | |
From: Gottlob Frege (Function and Concept [1891], p.39) | |
A reaction: Nowadays we would say 'two or more'. Another interesting move in the aim of analytic philosophy to reduce the puzzling features of the world to mathematical logic. There is, of course, rather more to some relations than being two-argument functions. |
15328 | A theory is 'non-conservative' if it facilitates new mathematical proofs [Horsten] |
Full Idea: A theory is 'non-conservative' if it allows us to prove mathematical facts that go beyond what the background mathematical theory can prove on its own. | |
From: Leon Horsten (The Tarskian Turn [2011], 01.4) | |
A reaction: This is an instance of the relationship with mathematics being used as the test case for explorations of logic. It is a standard research method, because it is so precise, but should not be mistaken for the last word about a theory. |
15349 | It is easier to imagine truth-value gaps (for the Liar, say) than for truth-value gluts (both T and F) [Horsten] |
Full Idea: It is easier to imagine what it is like for a sentence to lack a truth value than what it is like for a sentence to be both truth and false. So I am grudgingly willing to entertain the possibility that certain sentences (like the Liar) lack a truth value. | |
From: Leon Horsten (The Tarskian Turn [2011], 02.5) | |
A reaction: Fans of truth value gluts are dialethists like Graham Priest. I'm with Horsten on this one. But in what way can a sentence be meaningful if it lacks a truth-value? He mentions unfulfilled presuppositions and indicative conditionals as gappy. |
15366 | Satisfaction is a primitive notion, and very liable to semantical paradoxes [Horsten] |
Full Idea: Satisfaction is a more primitive notion than truth, and it is even more susceptible to semantical paradoxes than the truth predicate. | |
From: Leon Horsten (The Tarskian Turn [2011], 06.3) | |
A reaction: The Liar is the best known paradox here. Tarski bases his account of truth on this primitive notion, so Horsten is pointing out the difficulties. |
15353 | The first incompleteness theorem means that consistency does not entail soundness [Horsten] |
Full Idea: It is a lesson of the first incompleteness theorem that consistency does not entail soundness. If we add the negation of the gödel sentence for PA as an extra axiom to PA, the result is consistent. This negation is false, so the theory is unsound. | |
From: Leon Horsten (The Tarskian Turn [2011], 04.3) |
15355 | Strengthened Liar: 'this sentence is not true in any context' - in no context can this be evaluated [Horsten] |
Full Idea: The Strengthened Liar sentence says 'this sentence is not true in any context'. It is not hard to figure out that there is no context in which the sentence can be coherently evaluated. | |
From: Leon Horsten (The Tarskian Turn [2011], 04.6) |
15364 | English expressions are denumerably infinite, but reals are nondenumerable, so many are unnameable [Horsten] |
Full Idea: The number of English expressions is denumerably infinite. But Cantor's theorem can be used to show that there are nondenumerably many real numbers. So not every real number has a (simple or complex name in English). | |
From: Leon Horsten (The Tarskian Turn [2011], 06.3) | |
A reaction: This really bothers me. Are we supposed to be committed to the existence of entities which are beyond our powers of naming? How precise must naming be? If I say 'pick a random real number', might that potentially name all of them? |
15360 | ZFC showed that the concept of set is mathematical, not logical, because of its existence claims [Horsten] |
Full Idea: One of the strengths of ZFC is that it shows that the concept of set is a mathematical concept. Many originally took it to be a logical concept. But ZFC makes mind-boggling existence claims, which should not follow if it was a logical concept. | |
From: Leon Horsten (The Tarskian Turn [2011], 05.2.3) | |
A reaction: This suggests that set theory is not just a way of expressing mathematics (see Benacerraf 1965), but that some aspect of mathematics has been revealed by it - maybe even its essential nature. |
15369 | Set theory is substantial over first-order arithmetic, because it enables new proofs [Horsten] |
Full Idea: The nonconservativeness of set theory over first-order arithmetic has done much to establish set theory as a substantial theory indeed. | |
From: Leon Horsten (The Tarskian Turn [2011], 07.5) | |
A reaction: Horsten goes on to point out the price paid, which is the whole new ontology which has to be added to the arithmetic. Who cares? It's all fictions anyway! |
8487 | Arithmetic is a development of logic, so arithmetical symbolism must expand into logical symbolism [Frege] |
Full Idea: I am of the opinion that arithmetic is a further development of logic, which leads to the requirement that the symbolic language of arithmetic must be expanded into a logical symbolism. | |
From: Gottlob Frege (Function and Concept [1891], p.30) | |
A reaction: This may the the one key idea at the heart of modern analytic philosophy (even though logicism may be a total mistake!). Logic and arithmetical foundations become the master of ontology, instead of the servant. The jury is out on the whole enterprise. |
15370 | Predicativism says mathematical definitions must not include the thing being defined [Horsten] |
Full Idea: Predicativism has it that a mathematical object (such as a set of numbers) cannot be defined by quantifying over a collection that includes that same mathematical object. To do so would be a violation of the vicious circle principle. | |
From: Leon Horsten (The Tarskian Turn [2011], 07.7) | |
A reaction: In other words, when you define an object you are obliged to predicate something new, and not just recycle the stuff you already have. |
18899 | Frege takes the existence of horses to be part of their concept [Frege, by Sommers] |
Full Idea: Frege regarded the existence of horses as a property of the concept 'horse'. | |
From: report of Gottlob Frege (Function and Concept [1891]) by Fred Sommers - Intellectual Autobiography 'Realism' |
15338 | We may believe in atomic facts, but surely not complex disjunctive ones? [Horsten] |
Full Idea: While positive and perhaps even negative atomic facts may be unproblematic, it seems excessive to commit oneself to the existence of logically complex facts such as disjunctive facts. | |
From: Leon Horsten (The Tarskian Turn [2011], 02.1) | |
A reaction: Presumably it is hard to deny that very complex statements involving massive disjunctions can be true or false. But why does commitment to real facts have to involve a huge ontology? The ontology is just the ingredients of the fact, isn't it? |
15363 | In the supervaluationist account, disjunctions are not determined by their disjuncts [Horsten] |
Full Idea: If 'Britain is large' and 'Italy is large' lack truth values, then so must 'Britain or Italy is large' - so on the supervaluationist account the truth value of a disjunction is not determined by the truth values of its disjuncts. | |
From: Leon Horsten (The Tarskian Turn [2011], 06.2) | |
A reaction: Compare Idea 15362 to get the full picture here. |
15362 | If 'Italy is large' lacks truth, so must 'Italy is not large'; but classical logic says it's large or it isn't [Horsten] |
Full Idea: If 'Italy is a large country' lacks a truth value, then so too, presumably, does 'Italy is not a large country'. But 'Italy is or is not a large country' is true, on the supervaluationist account, because it is a truth of classical propositional logic. | |
From: Leon Horsten (The Tarskian Turn [2011], 06.2) | |
A reaction: See also Idea 15363. He cites Fine 1975. |
4028 | Frege allows either too few properties (as extensions) or too many (as predicates) [Mellor/Oliver on Frege] |
Full Idea: Frege's theory of properties (which he calls 'concepts') yields too few properties, by identifying coextensive properties, and also too many, by letting every predicate express a property. | |
From: comment on Gottlob Frege (Function and Concept [1891]) by DH Mellor / A Oliver - Introduction to 'Properties' §2 | |
A reaction: Seems right; one extension may have two properties (have heart/kidneys), two predicates might express the same property. 'Cutting nature at the joints' covers properties as well as objects. |
22132 | Species and genera are individual concepts which naturally signify many individuals [William of Ockham] |
Full Idea: In his mature nominalism, species and genera are identified with certain mental qualities called concepts or intentions of the mind. Ontologically they are individuals too, like everthing else, ...but they naturally signify many different individuals. | |
From: William of Ockham (works [1335]), quoted by Claude Panaccio - William of Ockham p.1056 | |
A reaction: 'Naturally' is the key word, because the concepts are not fictions, but natural responses to encountering individuals in the world. I am an Ockhamist. |
8489 | The concept 'object' is too simple for analysis; unlike a function, it is an expression with no empty place [Frege] |
Full Idea: I regard a regular definition of 'object' as impossible, since it is too simple to admit of logical analysis. Briefly: an object is anything that is not a function, so that an expression for it does not contain any empty place. | |
From: Gottlob Frege (Function and Concept [1891], p.32) | |
A reaction: Here is the core of the programme for deriving our ontology from our logic and language, followed through by Russell and Quine. Once we extend objects beyond the physical, it becomes incredibly hard to individuate them. |
15372 | Some claim that indicative conditionals are believed by people, even though they are not actually held true [Horsten] |
Full Idea: In the debate about doxastic attitudes towards indicative conditional sentences, one finds philosophers who claim that conditionals can be believed even though they have no truth value (and thus are not true). | |
From: Leon Horsten (The Tarskian Turn [2011], 09.3) |
9947 | Concepts are the ontological counterparts of predicative expressions [Frege, by George/Velleman] |
Full Idea: Concepts, for Frege, are the ontological counterparts of predicative expressions. | |
From: report of Gottlob Frege (Function and Concept [1891]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
A reaction: That sounds awfully like what many philosophers call 'universals'. Frege, as a platonist (at least about numbers), I would take to be in sympathy with that. At least we can say that concepts seem to be properties. |
10319 | An assertion about the concept 'horse' must indirectly speak of an object [Frege, by Hale] |
Full Idea: Frege had a notorious difficulty over the concept 'horse', when he suggests that if we wish to assert something about a concept, we are obliged to proceed indirectly by speaking of an object that represents it. | |
From: report of Gottlob Frege (Function and Concept [1891], Ch.2.II) by Bob Hale - Abstract Objects | |
A reaction: This sounds like the thin end of a wedge. The great champion of objects is forced to accept them here as a façon de parler, when elsewhere they have ontological status. |
8488 | A concept is a function whose value is always a truth-value [Frege] |
Full Idea: A concept in logic is closely connected with what we call a function. Indeed, we may say at once: a concept is a function whose value is always a truth-value. ..I give the name 'function' to what is meant by the 'unsaturated' part. | |
From: Gottlob Frege (Function and Concept [1891], p.30) | |
A reaction: So a function becomes a concept when the variable takes a value. Problems arise when the value is vague, or the truth-value is indeterminable. |
9948 | Unlike objects, concepts are inherently incomplete [Frege, by George/Velleman] |
Full Idea: For Frege, concepts differ from objects in being inherently incomplete in nature. | |
From: report of Gottlob Frege (Function and Concept [1891]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
A reaction: This is because they are 'unsaturated', needing a quantified variable to complete the sentence. This could be a pointer towards Quine's view of properties, as simply an intrinsic feature of predication about objects, with no separate identity. |
4972 | I may regard a thought about Phosphorus as true, and the same thought about Hesperus as false [Frege] |
Full Idea: From sameness of meaning there does not follow sameness of thought expressed. A fact about the Morning Star may express something different from a fact about the Evening Star, as someone may regard one as true and the other false. | |
From: Gottlob Frege (Function and Concept [1891], p.14) | |
A reaction: This all gets clearer if we distinguish internalist and externalist theories of content. Why take sides on this? Why not just ask 'what is in the speaker's head?', 'what does the sentence mean in the community?', and 'what is the corresponding situation?' |
15347 | A theory of syntax can be based on Peano arithmetic, thanks to the translation by Gödel coding [Horsten] |
Full Idea: A notion of formal provability can be articulated in Peano arithmetic. ..This is surprisingly 'linguistic' rather than mathematical, but the key is in the Gödel coding. ..Hence we use Peano arithmetic as a theory of syntax. | |
From: Leon Horsten (The Tarskian Turn [2011], 02.4) | |
A reaction: This is the explanation of why issues in formal semantics end up being studied in systems based on formal arithmetic. And I had thought it was just because they were geeks who dream in numbers, and can't speak language properly... |
19381 | The past has ceased to exist, and the future does not yet exist, so time does not exist [William of Ockham] |
Full Idea: Time is composed of non-entities, because it is composed of the past which does not exist now, although it did exist, and of the future, which does not yet exist; therefore time does not exist. | |
From: William of Ockham (works [1335], 6:496), quoted by Richard T.W. Arthur - Leibniz 7 'Nominalist' | |
A reaction: I've a lot of sympathy with this! I favour Presentism, so the past is gone and the future is yet to arrive. But we have no coherent concept of a present moment of any duration to contain reality. We are just completely bogglificated by it all. |
8010 | William of Ockham is the main spokesman for God's commands being the source of morality [William of Ockham] |
Full Idea: The most notable philosopher who makes God's commandment the basis of goodness, rather than God's goodness a reason for obeying him, is William of Occam. | |
From: William of Ockham (works [1335]), quoted by Alasdair MacIntyre - A Short History of Ethics Ch.9 | |
A reaction: Either view has problems. Why choose God to obey? Obey anyone who is powerful? But how do you decide that God is good? How do we know the nature of God's commands, or the nature of God's goodness? Etc. |
8491 | The Ontological Argument fallaciously treats existence as a first-level concept [Frege] |
Full Idea: The ontological proof of God's existence suffers from the fallacy of treating existence as a first-level concept. | |
From: Gottlob Frege (Function and Concept [1891], p.38 n) | |
A reaction: [See Idea 8490 for first- and second-order functions] This is usually summarised as the idea that existence is a quantifier rather than a predicate. |
16679 | Even an angel must have some location [William of Ockham, by Pasnau] |
Full Idea: Ockham dismisses the possibility of non-location out of hand, remarking that even an angel has some location. | |
From: report of William of Ockham (works [1335]) by Robert Pasnau - Metaphysical Themes 1274-1671 14.4 |