16 ideas
| 19125 | If we define truth, we can eliminate it [Halbach/Leigh] |
| Full Idea: If truth can be explicitly defined, it can be eliminated. | |
| From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.3) | |
| A reaction: That we could just say p corresponds to the facts, or p coheres with our accepted beliefs, or p is the aim of our enquiries, and never mention the word 'true'. Definition is a strategy for reduction or elimination. |
| 19128 | If a language cannot name all objects, then satisfaction must be used, instead of unary truth [Halbach/Leigh] |
| Full Idea: If axioms are formulated for a language (such as set theory) that lacks names for all objects, then they require the use of a satisfaction relation rather than a unary truth predicate. | |
| From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 3.3) | |
| A reaction: I take it this is an important idea for understanding why Tarski developed his account of truth based on satisfaction. |
| 19120 | Semantic theories need a powerful metalanguage, typically including set theory [Halbach/Leigh] |
| Full Idea: Semantic approaches to truth usually necessitate the use of a metalanguage that is more powerful than the object-language for which it provides a semantics. It is usually taken to include set theory. | |
| From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1) | |
| A reaction: This is a motivation for developing an axiomatic account of truth, that moves it into the object language. |
| 19127 | The T-sentences are deductively weak, and also not deductively conservative [Halbach/Leigh] |
| Full Idea: Although the theory is materially adequate, Tarski thought that the T-sentences are deductively too weak. …Also it seems that the T-sentences are not conservative, because they prove in PA that 0=0 and ¬0=0 are different, so at least two objects exist. | |
| From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 3.2) | |
| A reaction: They are weak because they can't prove completeness. This idea give two reasons for looking for a better theory of truth. |
| 19124 | A natural theory of truth plays the role of reflection principles, establishing arithmetic's soundness [Halbach/Leigh] |
| Full Idea: If a natural theory of truth is added to Peano Arithmetic, it is not necessary to add explicity global reflection principles to assert soundness, as the truth theory proves them. Truth theories thus prove soundess, and allows its expression. | |
| From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.2) | |
| A reaction: This seems like a big attraction of axiomatic theories of truth for students of metamathematics. |
| 19126 | If deflationary truth is not explanatory, truth axioms should be 'conservative', proving nothing new [Halbach/Leigh] |
| Full Idea: If truth does not have any explanatory force, as some deflationists claim, the axioms of truth should not allow us to prove any new theorems that do not involve the truth predicate. That is, a deflationary axiomatisation of truth should be 'conservative'. | |
| From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.3) | |
| A reaction: So does truth have 'explanatory force'? These guys are interested in explaining theorems of arithmetic, but I'm more interested in real life. People do daft things because they have daft beliefs. Logic should be neutral, but truth has values? |
| 19129 | The FS axioms use classical logical, but are not fully consistent [Halbach/Leigh] |
| Full Idea: It is a virtue of the Friedman-Sheard axiomatisation that it is thoroughly classical in its logic. Its drawback is that it is ω-inconsistent. That is, it proves &exists;x¬φ(x), but proves also φ(0), φ(1), φ(2), … | |
| From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 4.3) | |
| A reaction: It seems the theory is complete (and presumably sound), yet not fully consistent. FS also proves the finite levels of Tarski's hierarchy, but not the transfinite levels. |
| 19130 | KF is formulated in classical logic, but describes non-classical truth, which allows truth-value gluts [Halbach/Leigh] |
| Full Idea: KF is formulated in classical logic, but describes a non-classical notion of truth. It allow truth-value gluts, making some sentences (such as the Liar) both true and not-true. Some authors add an axiom ruling out such gluts. | |
| From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 4.4) | |
| A reaction: [summary, which I hope is correct! Stanford is not wholly clear] |
| 19121 | We can reduce properties to true formulas [Halbach/Leigh] |
| Full Idea: One might say that 'x is a poor philosopher' is true of Tom instead of saying that Tom has the property of being a poor philosopher. We quantify over formulas instead of over definable properties, and thus reduce properties to truth. | |
| From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.1) | |
| A reaction: [compressed] This stuff is difficult (because the axioms are complex and hard to compare), but I am excited (yes!) about this idea. Their point is that you need a truth predicate within the object language for this, which disquotational truth forbids. |
| 19122 | Nominalists can reduce theories of properties or sets to harmless axiomatic truth theories [Halbach/Leigh] |
| Full Idea: The reduction of second-order theories (of properties or sets) to axiomatic theories of truth is a form of reductive nominalism, replacing existence assumptions (e.g. comprehension axioms) by innocuous assumptions about the truth predicate. | |
| From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.1) | |
| A reaction: I'm currently thinking that axiomatic theories of truth are the most exciting development in contemporary philosophy. See Halbach and Horsten. |
| 16065 | Constitution is identity (being in the same place), or it isn't (having different possibilities) [Wasserman] |
| Full Idea: Some insist that constitution is identity, on the grounds that distinct material objects cannot occupy the same place at the same time. Others argue that constitution is not identity, since the statue and its material differ in important respects. | |
| From: Ryan Wasserman (Material Constitution [2009], Intro) | |
| A reaction: The 'important respects' seem to concern possibilities rather than actualities, which is suspicious. It is misleading to think we are dealing with two things and their relation here. Objects must have constitutions; constitutions make objects. |
| 16067 | Constitution is not identity, because it is an asymmetric dependence relation [Wasserman] |
| Full Idea: For those for whom 'constitution is not identity' (the 'constitution view'), constitution is said to be an asymmetric relation, and also a dependence relation (unlike identity). | |
| From: Ryan Wasserman (Material Constitution [2009], 2) | |
| A reaction: It seems obvious that constitution is not identity, because there is more to a thing's identity than its mere constitution. But this idea makes it sound as if constitution has nothing to do with identity (chalk and cheese), and that can't be right. |
| 16069 | There are three main objections to seeing constitution as different from identity [Wasserman] |
| Full Idea: The three most common objections to the constitution view are the Impenetrability Objection (two things in one place?), the Extensionality Objection (mereology says wholes are just their parts), and the Grounding Objection (their ground is the same). | |
| From: Ryan Wasserman (Material Constitution [2009], 2) | |
| A reaction: [summary] He adds a fourth, that if two things can be in one place, why stop at two? [Among defenders of the Constitution View he lists Baker, Fine, Forbes, Koslicki, Kripke, Lowe, Oderberg, N.Salmon, Shoemaker, Simons and Yablo.] |
| 16068 | The weight of a wall is not the weight of its parts, since that would involve double-counting [Wasserman] |
| Full Idea: We do not calculate the weight of something by summing the weights of all its parts - weigh bricks and the molecules of a wall and you will get the wrong result, since you have weighed some parts more than once. | |
| From: Ryan Wasserman (Material Constitution [2009], 2) | |
| A reaction: In fact the complete inventory of the parts of a thing is irrelevant to almost anything we would like to know about the thing. The parts must be counted at some 'level' of division into parts. An element can belong to many different sets. |
| 16074 | Relative identity may reject transitivity, but that suggests that it isn't about 'identity' [Wasserman] |
| Full Idea: If the relative identity theorist denies transitivity (to deal with the Ship of Theseus, for example), this would make us suspect that relativised identity relations are not identity relations, since transitivity seems central to identity. | |
| From: Ryan Wasserman (Material Constitution [2009], 6) | |
| A reaction: The problem here, I think, focuses on the meaning of the word 'same'. One change of plank leaves you with the same ship, but that is not transitive. If 'identical' is too pure to give the meaning of 'the same' it's not much use in discussing the world. |
| 3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
| Full Idea: Anaxarchus said that he was not even sure that he knew nothing. | |
| From: report of Anaxarchus (fragments/reports [c.340 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.10.1 |