24 ideas
| 9376 | A sentence may simultaneously define a term, and also assert a fact [Boghossian] |
| Full Idea: It doesn't follow from the fact that a given sentence is being used to implicitly define one of its ingredient terms, that it is not a factual statement. 'This stick is a meter long at t' may define an ingredient terms and express something factual. | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], §III) | |
| A reaction: This looks like a rather good point, but it is tied in with a difficulty about definition, which is deciding which sentences are using a term, and which ones are defining it. If I say 'this stick in Paris is a meter long', I'm not defining it. |
| 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. |
| 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) |
| 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. |
| 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. |
| 9375 | Conventionalism agrees with realists that logic has truth values, but not over the source [Boghossian] |
| Full Idea: Conventualism is a factualist view: it presupposes that sentences of logic have truth values. It differs from a realist view in its conception of the source of those truth values, not on their existence. I call the denial of truths Non-Factualism. | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], §III) | |
| A reaction: It barely seems to count as truth is we say 'p is true because we say so'. It is a truth about an agreement, not a truth about logic. Driving on the left isn't a truth about which side of the road is best. |
| 8714 | Fictionalists say 2+2=4 is true in the way that 'Oliver Twist lived in London' is true [Field,H] |
| Full Idea: The fictionalist can say that the sense in which '2+2=4' is true is pretty much the same as the sense in which 'Oliver Twist lived in London' is true. They are true 'according to a well-known story', or 'according to standard mathematics'. | |
| From: Hartry Field (Realism, Mathematics and Modality [1989], 1.1.1), quoted by Michèle Friend - Introducing the Philosophy of Mathematics 6.3 | |
| A reaction: The roots of this idea are in Carnap. Fictionalism strikes me as brilliant, but poisonous in large doses. Novels can aspire to artistic truth, or to documentary truth. We invent a fiction, and nudge it slowly towards reality. |
| 9369 | 'Snow is white or it isn't' is just true, not made true by stipulation [Boghossian] |
| Full Idea: Isn't it overwhelmingly obvious that 'Either snow is white or it isn't' was true before anyone stipulated a meaning for it, and that it would have been true even if no one had thought about it, or chosen it to be expressed by one of our sentences? | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], §I) | |
| A reaction: Boghossian would have to believe in propositions (unexpressed truths) to hold this - which he does. I take the notion of truth to only have relevance when there are minds around. Otherwise the so-called 'truths' are just the facts. |
| 9367 | The a priori is explained as analytic to avoid a dubious faculty of intuition [Boghossian] |
| Full Idea: The central impetus behind the analytic explanation of the a priori is a desire to explain the possibility of a priori knowledge without having to postulate a special evidence-gathering faculty of intuition. | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], §I) | |
| A reaction: I don't see at all why one has to postulate a 'faculty' in order to talk about intuition. I take an intuition to be an apprehension of a probable truth, combined with an inability to articulate how the conclusion was arrived at. |
| 9373 | That logic is a priori because it is analytic resulted from explaining the meaning of logical constants [Boghossian] |
| Full Idea: The analytic theory of the apriority of logic arose indirectly, as a by-product of the attempt to explain in what a grasp of the meaning of the logical constants consists. | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], §III) | |
| A reaction: Preumably he is referring to Wittgenstein's anguish over the meaning of the word 'not' in his World War I notebooks. He first defined the constants by truth tables, then asserted that they were purely conventional - so logic is conventional. |
| 9380 | We can't hold a sentence true without evidence if we can't agree which sentence is definitive of it [Boghossian] |
| Full Idea: If there is no sentence I must hold true if it is to mean what it does, then there is no basis on which to argue that I am entitled to hold it true without evidence. | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], §III) | |
| A reaction: He is exploring Quine's view. Truth by convention depends on agreeing which part of the usage of a term constitutes its defining sentence(s), and that may be rather tricky. Boghossian says this slides into the 'dreaded indeterminacy of meaning'. |
| 9384 | We may have strong a priori beliefs which we pragmatically drop from our best theory [Boghossian] |
| Full Idea: It is consistent with a belief's being a priori in the strong sense that we should have pragmatic reasons for dropping it from our best overall theory. | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], n 6) | |
| A reaction: Does 'dropping it' from the theory mean just ignoring it, or actually denying it? C.I. Lewis is the ancestor of this view. Could it be our 'best' theory, while conflicting with beliefs that were strongly a priori? Pragmatism can embrace falsehoods. |
| 9374 | If we learn geometry by intuition, how could this faculty have misled us for so long? [Boghossian] |
| Full Idea: If we learn geometrical truths by intuition, how could this faculty have misled us for so long? | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], §III) | |
| A reaction: This refers to the development of non-Euclidean geometries, though the main misleading concerns parallels, which involves infinity. Boghossian cites 'distance' as a concept the Euclideans had misunderstood. Why shouldn't intuitions be wrong? |
| 9378 | If meaning depends on conceptual role, what properties are needed to do the job? [Boghossian] |
| Full Idea: Conceptual Role Semantics must explain what properties an inference or sentence involving a logical constant must have, if that inference or sentence is to be constitutive of its meaning. | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], §III) | |
| A reaction: This is my perennial request that if something is to be defined by its function (or role), we must try to explain what properties it has that make its function possible, and those properties will be the more basic explanation. |
| 9377 | 'Conceptual role semantics' says terms have meaning from sentences and/or inferences [Boghossian] |
| Full Idea: 'Conceptual role semantics' says the logical constants mean what they do by virtue of figuring in certain inferences and/or sentences involving them and not others, ..so some inferences and sentences are constitutive of an expression's meaning. | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], §III) | |
| A reaction: If the meaning of the terms derives from the sentences in which they figure, that seems to be meaning-as-use. The view that it depends on the inferences seems very different, and is a more interesting but more risky claim. |
| 9372 | Could expressions have meaning, without two expressions possibly meaning the same? [Boghossian] |
| Full Idea: Could there be a fact of the matter about what each expression means, but no fact of the matter about whether they mean the same? | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], §II) | |
| A reaction: He is discussing Quine's attack on synonymy, and his scepticism about meaning. Boghossian and I believe in propositions, so we have no trouble with two statements having the same meaning. Denial of propositions breeds trouble. |
| 17721 | There are no truths in virtue of meaning, but there is knowability in virtue of understanding [Boghossian, by Jenkins] |
| Full Idea: Boghossian distinguishes metaphysical analyticity (truth purely in virtue of meaning, debunked by Quine, he says) from epistemic analyticity (knowability purely in virtue of understanding - a notion in good standing). | |
| From: report of Paul Boghossian (Analyticity Reconsidered [1996]) by Carrie Jenkins - Grounding Concepts 2.4 | |
| A reaction: [compressed] This fits with Jenkins's claim that we have a priori knowledge just through understanding and relating our concepts. She, however, rejects that idea that a priori is analytic. |
| 9368 | Epistemological analyticity: grasp of meaning is justification; metaphysical: truth depends on meaning [Boghossian] |
| Full Idea: The epistemological notion of analyticity: a statement is 'true by virtue of meaning' provided that grasp of its meaning alone suffices for justified belief in its truth; the metaphysical reading is that it owes its truth to its meaning, not to facts. | |
| From: Paul Boghossian (Analyticity Reconsidered [1996], §I) | |
| A reaction: Kripke thinks it is neither, but is a purely semantic notion. How could grasp of meaning alone be a good justification if it wasn't meaning which was the sole cause of the statement's truth? I'm not convinced by his distinction. |