19 ideas
| 15647 | Truth definitions don't produce a good theory, because they go beyond your current language [Halbach] |
| Full Idea: It is far from clear that a definition of truth can lead to a philosophically satisfactory theory of truth. Tarski's theorem on the undefinability of the truth predicate needs resources beyond those of the language for which it is being defined. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1) | |
| A reaction: The idea is that you need a 'metalanguage' for the definition. If I say 'p' is a true sentence in language 'L', I am not making that observation from within language L. The dream is a theory confined to the object language. |
| 15649 | In semantic theories of truth, the predicate is in an object-language, and the definition in a metalanguage [Halbach] |
| Full Idea: In semantic theories of truth (Tarski or Kripke), a truth predicate is defined for an object-language. This definition is carried out in a metalanguage, which is typically taken to include set theory or another strong theory or expressive language. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1) | |
| A reaction: Presumably the metalanguage includes set theory because that connects it with mathematics, and enables it to be formally rigorous. Tarski showed, in his undefinability theorem, that the meta-language must have increased resources. |
| 15655 | Should axiomatic truth be 'conservative' - not proving anything apart from implications of the axioms? [Halbach] |
| Full Idea: If truth is not explanatory, truth axioms should not allow proof of new theorems not involving the truth predicate. It is hence said that axiomatic truth should be 'conservative' - not implying further sentences beyond what the axioms can prove. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1.3) | |
| A reaction: [compressed] |
| 15654 | If truth is defined it can be eliminated, whereas axiomatic truth has various commitments [Halbach] |
| Full Idea: If truth can be explicitly defined, it can be eliminated, whereas an axiomatized notion of truth may bring all kinds of commitments. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1.3) | |
| A reaction: The general principle that anything which can be defined can be eliminated (in an abstract theory, presumably, not in nature!) raises interesting questions about how many true theories there are which are all equivalent to one another. |
| 15648 | Instead of a truth definition, add a primitive truth predicate, and axioms for how it works [Halbach] |
| Full Idea: The axiomatic approach does not presuppose that truth can be defined. Instead, a formal language is expanded by a new primitive predicate of truth, and axioms for that predicate are then laid down. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1) | |
| A reaction: Idea 15647 explains why Halbach thinks the definition route is no good. |
| 15650 | Axiomatic theories of truth need a weak logical framework, and not a strong metatheory [Halbach] |
| Full Idea: Axiomatic theories of truth can be presented within very weak logical frameworks which require very few resources, and avoid the need for a strong metalanguage and metatheory. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1) |
| 15656 | Deflationists say truth merely serves to express infinite conjunctions [Halbach] |
| Full Idea: According to many deflationists, truth serves merely the purpose of expressing infinite conjunctions. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1.3) | |
| A reaction: That is, it asserts sentences that are too numerous to express individually. It also seems, on a deflationist view, to serve for anaphoric reference to sentences, such as 'what she just said is true'. |
| 15657 | To prove the consistency of set theory, we must go beyond set theory [Halbach] |
| Full Idea: The consistency of set theory cannot be established without assumptions transcending set theory. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 2.1) |
| 15652 | We can use truth instead of ontologically loaded second-order comprehension assumptions about properties [Halbach] |
| Full Idea: The reduction of 2nd-order theories (of properties or sets) to axiomatic theories of truth may be conceived as a form of reductive nominalism, replacing existence assumptions (for comprehension axioms) by ontologically innocent truth assumptions. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1.1) | |
| A reaction: I like this very much, as weeding properties out of logic (without weeding them out of the world). So-called properties in logic are too abundant, so there is a misfit with their role in science. |
| 15651 | Instead of saying x has a property, we can say a formula is true of x - as long as we have 'true' [Halbach] |
| Full Idea: Quantification over (certain) properties can be mimicked in a language with a truth predicate by quantifying over formulas. Instead of saying that Tom has the property of being a poor philosopher, we can say 'x is a poor philosopher' is true of Tom. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1.1) | |
| A reaction: I love this, and think it is very important. He talks of 'mimicking' properties, but I see it as philosophers mistakenly attributing properties, when actually what they were doing is asserting truths involving certain predicates. |
| 1635 | Mathematics reduces to set theory (which is a bit vague and unobvious), but not to logic proper [Quine] |
| Full Idea: Mathematics reduces only to set theory, and not to logic proper… but set theory cannot claim the same firmness and obviousness as logic. | |
| From: Willard Quine (Epistemology Naturalized [1968], p.69-70) |
| 7627 | You can't reduce epistemology to psychology, because that presupposes epistemology [Maund on Quine] |
| Full Idea: There is something seriously misguided about Quine's project of reducing epistemology to psychology, since psychology, like any of the natural sciences, presupposes an epistemology. | |
| From: comment on Willard Quine (Epistemology Naturalized [1968]) by Barry Maund - Perception Ch.1 | |
| A reaction: I wonder if epistemology presupposes psychology? Belief, for example, is a category of folk psychology, which could be challenged. There is a quiet battle going on between philosophy and science. |
| 8871 | We should abandon a search for justification or foundations, and focus on how knowledge is acquired [Quine, by Davidson] |
| Full Idea: Quine is suggesting that philosophy should abandon the attempt to provide a foundation for knowledge, or otherwise justify it, and should instead give an account of how knowledge is acquired. | |
| From: report of Willard Quine (Epistemology Naturalized [1968]) by Donald Davidson - Epistemology Externalized p.193 | |
| A reaction: If you are going to explain how 'knowledge' is acquired, you'd better know what knowledge is. My suspicion is that Quine would be quite happy (in the pragmatist tradition) to just focus on belief, and forget about knowledge entirely. |
| 8826 | If we abandon justification and normativity in epistemology, we must also abandon knowledge [Kim on Quine] |
| Full Idea: Quine asks us to set aside the entire framework of justification-centered epistemology, ..and repudiate normativity. ..But then knowledge itself drops out of epistemology, for our concept of knowledge is inseparably tied to that of justification. | |
| From: comment on Willard Quine (Epistemology Naturalized [1968]) by Jaegwon Kim - What is 'naturalized epistemology'? p.305 | |
| A reaction: Presumably this would not bother Quine, who wants to hand so-called 'epistemology' over to the psychologists. A psychological account of belief seems plausible. Presumably false beliefs could only be pragmatically characterised. |
| 8827 | Without normativity, naturalized epistemology isn't even about beliefs [Kim on Quine] |
| Full Idea: If normativity is wholly excluded from naturalized epistemology it cannot even be thought of as being about beliefs. | |
| From: comment on Willard Quine (Epistemology Naturalized [1968]) by Jaegwon Kim - What is 'naturalized epistemology'? p.306 | |
| A reaction: And if it doesn't refer to beliefs, it certainly doesn't refer to knowledge. One might try to subsume normativity under evolutionary pragmatic 'drives', or something. Quine's project would then become wildly speculative, and hence boring. |
| 8899 | Epistemology is a part of psychology, studying how our theories relate to our evidence [Quine] |
| Full Idea: Epistemology falls into place as a chapter of psychology, and hence of natural science. ..We study meagre input and torrential output, to see how evidence relates to theory, and in what ways one's theory of nature transcends any available evidence. | |
| From: Willard Quine (Epistemology Naturalized [1968], p.83) | |
| A reaction: It depends what you are interested in. If you just want to know what makes humans tick, then Quine is your man, but if you want to know things in general, and want to know how to get it right, then the normative side of epistemology is unavoidable. |
| 8638 | Thomae's idea of abstract from peculiarities gives a general concept, and leaves the peculiarities [Frege on Thomae] |
| Full Idea: When Thomae says "abstract from the peculiarities of the individual members of a set of items", or "disregard those characteristics which serve to distinguish them", we get a general concept under which they fall. The things keep their characteristics. | |
| From: comment on C.J. Thomae (works [1869], §34) by Gottlob Frege - Grundlagen der Arithmetik (Foundations) §34 | |
| A reaction: Interesting. You don't have to leave out their distinctive fur in order to count cats. But you have to focus on some aspect of them, because they aren't 'three meats'. |
| 8898 | Inculcations of meanings of words rests ultimately on sensory evidence [Quine] |
| Full Idea: All inculcation of meanings of words must rest ultimately on sensory evidence. | |
| From: Willard Quine (Epistemology Naturalized [1968], p.75) | |
| A reaction: This betrays Quine's behaviourist tendencies, and rules out introspection, definitions and inferences. Quine's conclusion is fairly total scepticism about meaning, but that is not surprising, given his external and meaningless starting point. |
| 8900 | In observation sentences, we could substitute community acceptance for analyticity [Quine] |
| Full Idea: Perhaps the controversial notion of analyticity can be dispensed with, in our definition of observation sentences, in favour of the straightforward attitude of community-wide acceptance. | |
| From: Willard Quine (Epistemology Naturalized [1968], p.86) | |
| A reaction: That might be a reasonable account of 'bachelors'. If the whole community accepts 'God exists', does that make it analytic? If a whole (small!) community claims to actually observe a ghost or a flying saucer, is that then analytic? |