20 ideas
| 18274 | Analysis complicates a statement, but only as far as the complexity of its meaning [Wittgenstein] |
| Full Idea: Analysis makes the statement more complicated than it was; but it cannot and ought not to make it more complicated than its meaning (Bedeutung) was to begin with. When the statement is as complex as its meaning, then it is completely analysed. | |
| From: Ludwig Wittgenstein (Notebooks 1914-1916 [1915], 46e) | |
| A reaction: But how do you assess how complex the 'Bedeutung' was before you started? |
| 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) |
| 16908 | We can dispense with self-evidence, if language itself prevents logical mistakes [Jeshion on Wittgenstein] |
| Full Idea: The 'self-evidence' of which Russell talks so much can only be dispensed with in logic if language itself prevents any logical mistake. | |
| From: comment on Ludwig Wittgenstein (Notebooks 1914-1916 [1915], 4) by Robin Jeshion - Frege's Notion of Self-Evidence 4 | |
| A reaction: Jeshion presents this as a key idea, turning against Frege, and is the real source of the 'linguistic turn' in philosophy. If self-evidence is abandoned, then language itself is the guide to truth, so study language. I think I prefer Frege. See Quine? |
| 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. |
| 18276 | A statement's logical form derives entirely from its constituents [Wittgenstein] |
| Full Idea: The logical form of the statement must already be given in the forms of its constituents. | |
| From: Ludwig Wittgenstein (Notebooks 1914-1916 [1915], 23e) | |
| A reaction: This would evidently require each constituent to have a 'logical form'. It is hard to see what that could beyond its part of speech. Do two common nouns have the same logical form? |
| 6563 | 'And' and 'not' are non-referring terms, which do not represent anything [Wittgenstein, by Fogelin] |
| Full Idea: Wittgenstein's 'fundamental idea' is that the 'and' and 'not' which guarantee the truth of "not p and not-p" are meaningful, but do not get their meaning by representing or standing for or referring to some kind of entity; they are non-referring terms. | |
| From: report of Ludwig Wittgenstein (Notebooks 1914-1916 [1915], §37) by Robert Fogelin - Walking the Tightrope of Reason Ch.1 | |
| A reaction: Wittgenstein then defines the terms using truth tables, to show what they do, rather than what they stand for. This seems to me to be a candidate for the single most important idea in the history of the philosophy of logic. |
| 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. |
| 23472 | The sense of propositions relies on the world's basic logical structure [Wittgenstein] |
| Full Idea: In order for a proposition to be CAPABLE of making sense, the world must already have the logical structure it has. The logic of the world is prior to all truth and falsehood. | |
| From: Ludwig Wittgenstein (Notebooks 1914-1916 [1915], p.14c) | |
| A reaction: It seems that in Tractatus it is propositions about facts which are true or false, but prior to the facts are substance and the objects, and it is there that we find the logical structure of the world. I see this view as modern stoicism. |
| 23500 | My main problem is the order of the world, and whether it is knowable a priori [Wittgenstein] |
| Full Idea: The great problem around which everything turns that I write is: is there an order in the world a priori, and if so what does it consist in? | |
| From: Ludwig Wittgenstein (Notebooks 1914-1916 [1915], 15.06.01) | |
| A reaction: Morris identifies this as a 'Kantian question'. I trace it back to stoicism. This question has never bothered me. It just seems weird to think that you can infer reality from the examination of your own thinking. Perhaps I should take it more seriously? |
| 22323 | The philosophical I is the metaphysical subject, the limit - not a part of the world [Wittgenstein] |
| Full Idea: The philosophical I is not the man, not the human body, or the human soul of wh9ch psychology treats, but the metaphysical subject, the limit - not a part of the world. | |
| From: Ludwig Wittgenstein (Notebooks 1914-1916 [1915], 1916. 2 Sep), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 58 Intro | |
| A reaction: This is to treat the self as a phenomenon of thought, rather than of a human being. So if a machine could think, would it hence necessarily have a metaphysical self? |
| 23481 | Propositions assemble a world experimentally, like the model of a road accident [Wittgenstein] |
| Full Idea: In the proposition a world is as it were put together experimentally. (As when in the law court in Paris a motor-car accident is represented by means of dolls, etc). | |
| From: Ludwig Wittgenstein (Notebooks 1914-1916 [1915], 14.09.29) | |
| A reaction: [see Tractatus 4.031] This is the first appearance of LW's picture (or model) theory of meaning. It may well be the best theory of meaning anyone has come up with, since meaning being out in the world strikes me as absurd. |
| 18006 | Chomsky's 'interpretative semantics' says syntax comes first, and is then interpreted [Chomsky, by Magidor] |
| Full Idea: Chomsky and his followers (whose position was labelled 'interpretative semantics') claimed that a sentence is first assigned a syntactic structure by an autonomous syntactic module, and this structure is then provided as input for semantic interpretation. | |
| From: report of Noam Chomsky (Aspects of the Theory of Syntax [1965]) by Ofra Magidor - Category Mistakes 1.3 | |
| A reaction: This certainly doesn't fit the experience of introspecting speech, but then I suppose good pianists focus entirely on the music, and overlook the finger movements which have obvious priority. But I don't know the syntax of the sentence when I begin it. |
| 4678 | Absolute prohibitions are the essence of ethics, and suicide is the most obvious example [Wittgenstein] |
| Full Idea: If suicide is allowed, then everything is allowed. If anything is not allowed, then suicide is not allowed. This throws a light on the nature of ethics, for suicide is, so to speak, the elementary sin. | |
| From: Ludwig Wittgenstein (Notebooks 1914-1916 [1915], end), quoted by Jonathan Glover - Causing Death and Saving Lives §13 | |
| A reaction: This reveals the religious streak in Wittgenstein. I am reluctant to judge suicide, but this seems wrong. Should a 'jumper' worry if they land on someone else and kill them? Of course they should. |