25 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] |
| 9406 | A class is natural when everybody can spot further members of it [Quinton] |
| Full Idea: To say that a class is natural is to say that when some of its members are shown to people they pick out others without hesitation and in agreement. | |
| From: Anthony Quinton (The Nature of Things [1973], 9 'Nat') | |
| A reaction: He concedes a number of problems with his view, but I admire his attempt to at least begin to distinguish the natural (real!) classes from the ersatz ones. A mention of causal powers would greatly improve his story. |
| 15730 | Extreme nominalists say all classification is arbitrary convention [Quinton] |
| Full Idea: Pure, extreme nominalism sees all classification as the product of arbitrary convention. | |
| From: Anthony Quinton (The Nature of Things [1973], 9 'Nat') | |
| A reaction: I'm not sure what the word 'arbitrary' is doing there. Nominalists are not daft, and if they can classify any way they like, they are not likely to choose an 'arbitrary' system. Pragmatism tells the right story here. |
| 15728 | The naturalness of a class depends as much on the observers as on the objects [Quinton] |
| Full Idea: The naturalness of a class depends as essentially on the nature of the observers who classify as it does on the nature of the objects that they classify. ...It depends on our perceptual apparatus, and on our relatively mutable needs and interests. | |
| From: Anthony Quinton (The Nature of Things [1973], 9 'Nat') | |
| A reaction: This seems to translate 'natural' as 'natural for us', which is not much use to scientists, who spend quite a lot of effort combating folk wisdom. Do desirable sports cars constitute a natural class? |
| 9407 | Properties imply natural classes which can be picked out by everybody [Quinton] |
| Full Idea: To say there are properties is to say there are natural classes, classes introduction to some of whose members enables people to pick out others without hesitation and in agreement. | |
| From: Anthony Quinton (The Nature of Things [1973], 9 'Nat') | |
| A reaction: Aristotle would like this approach, but it doesn't find many friends among modern logician/philosophers. We should go on to ask why people agree on these things. Causal powers will then come into it. |
| 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. |
| 15729 | Uninstantiated properties must be defined using the instantiated ones [Quinton] |
| Full Idea: Properties that have no concrete instances must be defined in terms of those that have. | |
| From: Anthony Quinton (The Nature of Things [1973], 9 'Nat') | |
| A reaction: I wonder what the dodo used to smell like? |
| 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. |
| 8520 | An individual is a union of a group of qualities and a position [Quinton, by Campbell,K] |
| Full Idea: Quinton proposes that an individual is a union of a group of qualities and a position. | |
| From: report of Anthony Quinton (The Nature of Things [1973], Pt I) by Keith Campbell - The Metaphysic of Abstract Particulars §5 | |
| A reaction: This seems the obvious defence of a bundle account of objects against the charge that indiscernibles would have to be identical. It introduces, however, 'positions' into the ontology, but maybe that price must be paid. Materialism needs space. |
| 5901 | Is 'productive of happiness' the definition of 'right', or the cause of it? [Ross on Bentham] |
| Full Idea: Bentham has not made up his mind whether he thinks that 'right' means 'productive of the general happiness', or that being productive of the general happiness is what makes acts right (and he would have thought the difference unimportant). | |
| From: comment on Jeremy Bentham (Intro to Principles of Morals and Legislation [1789]) by W. David Ross - The Right and the Good §I | |
| A reaction: The issue is whether rightness exists as a concept separate from happiness. I take it Bentham would vote for the first reading, as he has no interest in what is right, apart from increasing happiness. |
| 5934 | Of Bentham's 'dimensions' of pleasure, only intensity and duration matter [Ross on Bentham] |
| Full Idea: Most of Bentham's 'dimensions' of pleasure refer to further pleasures, or are irrelevant to the pleasure; we are left with intensity and duration as the characteristics on which depend the value of a pleasure qua pleasure, and there is nothing to add. | |
| From: comment on Jeremy Bentham (Intro to Principles of Morals and Legislation [1789]) by W. David Ross - The Right and the Good §VI | |
| A reaction: I agree. When Bentham produces his list he seems to be trying to add a bogus enrichment to what is really a rather crude and basic notion of the aim of life. Your simple hedonist appears to only desire high intensity and long duration. |
| 3777 | Pleasure and pain control all human desires and duties [Bentham] |
| Full Idea: Nature has placed mankind under the governance of two sovereign masters, pain and pleasure. It is for them alone to point out what we ought to do, as well as to determine what we shall do. | |
| From: Jeremy Bentham (Intro to Principles of Morals and Legislation [1789], I.1) | |
| A reaction: Ridiculous. Both halves are false. We pursue things for other reasons, and to deny this makes his idea a tautology. Deep ecology has nothing to do with human pleasure or pain. |
| 3554 | Bentham thinks happiness is feeling good, but why use morality to achieve that? [Annas on Bentham] |
| Full Idea: It is easy to fall into Bentham's mindless assumption that happiness must be a specific state of feeling good about something, but it is mysterious why anyone would think morality a good strategy for achieving this. | |
| From: comment on Jeremy Bentham (Intro to Principles of Morals and Legislation [1789]) by Julia Annas - The Morality of Happiness 2.7 |
| 3781 | The value of pleasures and pains is their force [Bentham] |
| Full Idea: It behoves the legislator to understand the force of pleasures and pains, which is their value. | |
| From: Jeremy Bentham (Intro to Principles of Morals and Legislation [1789], IV.1) |
| 3778 | The community's interest is a sum of individual interests [Bentham] |
| Full Idea: The interest of the community is the sum of the interests of the several members who compose it. | |
| From: Jeremy Bentham (Intro to Principles of Morals and Legislation [1789], I.4) |
| 20280 | Large mature animals are more rational than babies. But all that really matters is - can they suffer? [Bentham] |
| Full Idea: A full-grown horse or dog is beyond comparison a more rational animal than an infant of a day, or even a month, old. But suppose they be otherwise, what would it avail? The question is not, Can they reason? nor Can they talk? but, Can they suffer? | |
| From: Jeremy Bentham (Intro to Principles of Morals and Legislation [1789], XVIII 1 n), quoted by Peter Singer - Practical Ethics 03 | |
| A reaction: This is certainly an inspiring, and even shocking question, which never seems to have been so directly asked before in the entire history of European thought. Awesome. |
| 3779 | Unnatural, when it means anything, means infrequent [Bentham] |
| Full Idea: Unnatural, when it means anything, means unfrequent. | |
| From: Jeremy Bentham (Intro to Principles of Morals and Legislation [1789], II.14 n8.9) |
| 3780 | We must judge a thing morally to know if it conforms to God's will [Bentham] |
| Full Idea: It is necessary to know first whether a thing is right in order to know from thence whether it be conformable to the will of God. | |
| From: Jeremy Bentham (Intro to Principles of Morals and Legislation [1789], II.18) |