display all the ideas for this combination of texts
27 ideas
16330 | Truth-value 'gluts' allow two truth values together; 'gaps' give a partial conception of truth [Halbach] |
Full Idea: Truth-value 'gluts' correspond to a so-called dialethic conception of truth; excluding gluts and admitting only 'gaps' leads to a conception of what is usually called 'partial' truth. | |
From: Volker Halbach (Axiomatic Theories of Truth [2011], 15.2) | |
A reaction: Talk of 'gaps' and 'gluts' seem to be the neatest way of categorising views of truth. I want a theory with no gaps or gluts. |
16339 | Truth axioms prove objects exist, so truth doesn't seem to be a logical notion [Halbach] |
Full Idea: Two typed disquotation sentences, truth axioms of TB, suffice for proving that there at least two objects. Hence truth is not a logical notion if one expects logical notions to be ontologically neutral. | |
From: Volker Halbach (Axiomatic Theories of Truth [2011], 21.2) |
16324 | Any definition of truth requires a metalanguage [Halbach] |
Full Idea: It is plain that the distinction between object and metalanguage is required for the definability of truth. | |
From: Volker Halbach (Axiomatic Theories of Truth [2011], 11) | |
A reaction: Halbach's axiomatic approach has given up on definability, and therefore it can seek to abandon the metalanguage and examine 'type-free' theories. |
16293 | Traditional definitions of truth often make it more obscure, rather than less [Halbach] |
Full Idea: A common complaint against traditional definitional theories of truth is that it is far from clear that the definiens is not more in need of clarification than the definiendum (that is, the notion of truth). | |
From: Volker Halbach (Axiomatic Theories of Truth [2011], 1) | |
A reaction: He refers to concepts like 'correspondence', 'facts', 'coherence' or 'utility', which are said to be trickier to understand than 'true'. I suspect that philosophers like Halbach confuse 'clear' with 'precise'. Coherence is quite clear, but imprecise. |
16301 | If people have big doubts about truth, a definition might give it more credibility [Halbach] |
Full Idea: If one were wondering whether truth should be considered a legitimate notion at all, a definition might be useful in dispersing doubts about its legitimacy. | |
From: Volker Halbach (Axiomatic Theories of Truth [2011], 3) | |
A reaction: Halbach is proposing to skip definitions, and try to give rules for using 'true' instead, but he doesn't rule out definitions. A definition of 'knowledge' or 'virtue' or 'democracy' might equally give those credibility. |
16297 | Semantic theories avoid Tarski's Theorem by sticking to a sublanguage [Halbach] |
Full Idea: In semantic theories (e.g.Tarski's or Kripke's), a definition evades Tarski's Theorem by restricting the possible instances in the schema T[φ]↔φ to sentences of a proper sublanguage of the language formulating the equivalences. | |
From: Volker Halbach (Axiomatic Theories of Truth [2011], 1) | |
A reaction: The schema says if it's true it's affirmable, and if it's affirmable it's true. The Liar Paradox is a key reason for imposing this restriction. |
16337 | Disquotational truth theories are short of deductive power [Halbach] |
Full Idea: The problem of restricted deductive power has haunted disquotational theories of truth (…because they can't prove generalisations). | |
From: Volker Halbach (Axiomatic Theories of Truth [2011], 19.5) |
16294 | Axiomatic truth doesn't presuppose a truth-definition, though it could admit it at a later stage [Halbach] |
Full Idea: Choosing an axiomatic approach to truth might well be compatible with the view that truth is definable; the definability of truth is just not presupposed at the outset. | |
From: Volker Halbach (Axiomatic Theories of Truth [2011], 1) | |
A reaction: Is it possible that a successful axiomatisation is a successful definition? |
16326 | The main semantic theories of truth are Kripke's theory, and revisions semantics [Halbach] |
Full Idea: Revision semantics is arguably the main competitor of Kripke's theory of truth among semantic truth theories. …In the former one may hope through revision to arrive at better and better models, ..sorting out unsuitable extensions of the truth predicate. | |
From: Volker Halbach (Axiomatic Theories of Truth [2011], 14) | |
A reaction: Halbach notes later that Kripke's theory (believe it or not) is considerably simpler than revision semantics. |
16299 | Gödel numbering means a theory of truth can use Peano Arithmetic as its base theory [Halbach] |
Full Idea: Often syntactic objects are identified with their numerical codes. …Expressions of a countable formal language can be coded in the natural numbers. This allows a theory of truth to use Peano Arithmetic (with its results) as a base theory. | |
From: Volker Halbach (Axiomatic Theories of Truth [2011], 2) | |
A reaction: The numbering system is the famous device invented by Gödel for his great proof of incompleteness. This idea is a key to understanding modern analytic philosophy. It is the bridge which means philosophical theories can be treated mathematically. |
16340 | Truth axioms need a base theory, because that is where truth issues arise [Halbach] |
Full Idea: Considering the truth axioms in the absence of a base theory is not very sensible because characteristically truth theoretic reasoning arises from the interplay of the truth axioms with the base theory. | |
From: Volker Halbach (Axiomatic Theories of Truth [2011], 21.2) | |
A reaction: The base theory usually seems to be either Peano arithmetic or set theory. We might say that introverted thought (e.g. in infants) has little use for truth; it is when you think about the world that truth becomes a worry. |
16305 | We know a complete axiomatisation of truth is not feasible [Halbach] |
Full Idea: In the light of incompleteness phenomena, one should not expect a categorical axiomatisation of truth to be feasible, but this should not keep one from studying axiomatic theories of truth (or of arithmetic). | |
From: Volker Halbach (Axiomatic Theories of Truth [2011], 3) | |
A reaction: This, of course, is because of Gödel's famous results. It is important to be aware in this field that there cannot be a dream of a final theory, so we are just seeing what can be learned about truth. |
16311 | To axiomatise Tarski's truth definition, we need a binary predicate for his 'satisfaction' [Halbach] |
Full Idea: If the clauses of Tarski's definition of truth are turned into axioms (as Davidson proposed) then a primitive binary predicate symbol for satisfaction is needed, as Tarski defined truth in terms of satisfaction. Standard language has a unary predicate. | |
From: Volker Halbach (Axiomatic Theories of Truth [2011], 5.2) |
16318 | Compositional Truth CT has the truth of a sentence depending of the semantic values of its constituents [Halbach] |
Full Idea: In the typed Compositional Truth theory CT, it is compositional because the truth of a sentence depends on the semantic values of the constituents of that sentence. | |
From: Volker Halbach (Axiomatic Theories of Truth [2011], 8) | |
A reaction: [axioms on p. 65 of Halbach] |
16322 | CT proves PA consistent, which PA can't do on its own, so CT is not conservative over PA [Halbach] |
Full Idea: Compositional Truth CT proves the consistency of Peano arithmetic, which is not provable in Peano arithmetic by Gödel's second incompleteness theorem. Hence the theory CT is not conservative over Peano arithmetic. | |
From: Volker Halbach (Axiomatic Theories of Truth [2011], 8.6) |
16313 | A theory is 'conservative' if it adds no new theorems to its base theory [Halbach, by PG] |
Full Idea: A truth theory is 'conservative' if the addition of the truth predicate does not add any new theorems to the base theory. | |
From: report of Volker Halbach (Axiomatic Theories of Truth [2011], 6 Df 6.6) by PG - Db (ideas) | |
A reaction: Halbach presents the definition more formally, and this is my attempt at getting it into plain English. Halbach uses Peano Arithmetic as his base theory, but set theory is also sometimes used. |
16315 | The Tarski Biconditional theory TB is Peano Arithmetic, plus truth, plus all Tarski bi-conditionals [Halbach] |
Full Idea: The truth theory TB (Tarski Biconditional) is all the axioms of Peano Arithmetic, including all instances of the induction schema with the truth predicate, plus all the sentences of the form T[φ] ↔ φ. | |
From: Volker Halbach (Axiomatic Theories of Truth [2011], 7) | |
A reaction: The biconditional formula is the famous 'snow is white' iff snow is white. The truth of the named sentence is equivalent to asserting the sentence. This is a typed theory of truth, and it is conservative over PA. |
16314 | Theories of truth are 'typed' (truth can't apply to sentences containing 'true'), or 'type-free' [Halbach] |
Full Idea: I sort theories of truth into the large families of 'typed' and 'type-free'. Roughly, typed theories prohibit a truth predicate's application to sentences with occurrences of that predicate, and one cannot prove the truth of sentences containing 'true'. | |
From: Volker Halbach (Axiomatic Theories of Truth [2011], II Intro) | |
A reaction: The problem sentence the typed theories are terrified of is the Liar Sentence. Typing produces a hierarchy of languages, referring down to the languages below them. |
16327 | Friedman-Sheard is type-free Compositional Truth, with two inference rules for truth [Halbach] |
Full Idea: The Friedman-Sheard truth system FS is based on compositional theory CT. The axioms of FS are obtained by relaxing the type restriction on the CT-axioms, and adding rules inferring sentences from their truth, and vice versa. | |
From: Volker Halbach (Axiomatic Theories of Truth [2011], 15) | |
A reaction: The rules are called NEC and CONEC by Halbach. The system FSN is FS without the two rules. |
16329 | Kripke-Feferman theory KF axiomatises Kripke fixed-points, with Strong Kleene logic with gluts [Halbach] |
Full Idea: The Kripke-Feferman theory KF is an axiomatisation of the fixed points of an operator, that is, of a Kripkean fixed-point semantics with the Strong Kleene evaluation schema with truth-value gluts. | |
From: Volker Halbach (Axiomatic Theories of Truth [2011], 15.1) |
16331 | The KF is much stronger deductively than FS, which relies on classical truth [Halbach] |
Full Idea: The Kripke-Feferman theory is relatively deductively very strong. In particular, it is much stronger than its competitor FS, which is based on a completely classical notion of truth. | |
From: Volker Halbach (Axiomatic Theories of Truth [2011], 15.3) |
16332 | The KF theory is useful, but it is not a theory containing its own truth predicate [Halbach] |
Full Idea: KF is useful for explicating Peano arithmetic, but it certainly does not come to close to being a theory that contains its own truth predicate. | |
From: Volker Halbach (Axiomatic Theories of Truth [2011], 16) | |
A reaction: Since it is a type-free theory, its main philosophical aspiration was to contain its own truth predicate, so that is bad news (for philosophers). |
16338 | Deflationism says truth is a disquotation device to express generalisations, adding no new knowledge [Halbach] |
Full Idea: There are two doctrines at the core of deflationism. The first says truth is a device of disquotation used to express generalisations, and the second says truth is a thin notion that contributes nothing to our knowledge of the world | |
From: Volker Halbach (Axiomatic Theories of Truth [2011], 21) |
16319 | Compositional Truth CT proves generalisations, so is preferred in discussions of deflationism [Halbach] |
Full Idea: Compositional Truth CT and its variants has desirable generalisations among its logical consequences, so they seem to have ousted purely disquotational theories such as TB in the discussion on deflationism. | |
From: Volker Halbach (Axiomatic Theories of Truth [2011], 8) |
16316 | Deflationists say truth is just for expressing infinite conjunctions or generalisations [Halbach] |
Full Idea: Deflationists do not hold that truth is completely dispensable. They claim that truth serves the purpose of expressing infinite conjunctions or generalisations. | |
From: Volker Halbach (Axiomatic Theories of Truth [2011], 7) | |
A reaction: It is also of obvious value as a shorthand in ordinary conversation, but rigorous accounts can paraphrase that out. 'What he said is true'. 'Pick out the true sentences from p,q,r and s' seems to mean 'affirm some of them'. What does 'affirm' mean? |
16317 | The main problem for deflationists is they can express generalisations, but not prove them [Halbach] |
Full Idea: The main criticism that deflationist theories based on the disquotation sentences or similar axioms have to meet was raised by Tarski: the disquotation sentences do not allow one to prove generalisations. | |
From: Volker Halbach (Axiomatic Theories of Truth [2011], 7) |
16320 | Some say deflationism is axioms which are conservative over the base theory [Halbach] |
Full Idea: Some authors have tried to understand the deflationist claim that truth is not a substantial notion as the claim that a satisfactory axiomatisation of truth should be conservative over the base theory. | |
From: Volker Halbach (Axiomatic Theories of Truth [2011], 8) |