32 ideas
4697 | There has been a distinct 'Social Turn' in recent philosophy, like the earlier 'Linguistic Turn' [O'Grady] |
Full Idea: The Social Turn is as defining a characteristic of contemporary philosophy as the Linguistic Turn has been of the earlier twentieth century period. | |
From: Paul O'Grady (Relativism [2002], Ch.1) | |
A reaction: A helpful observation. It ties in with externalism about concepts (Twin Earth), impossibility of Private Language, and externalism about knowledge. |
4731 | Good reasoning will avoid contradiction, enhance coherence, not ignore evidence, and maximise evidence [O'Grady] |
Full Idea: The four basic principles of rationality are 1) avoid contradiction, 2) enhance coherence, 3) avoid ignoring evidence, and 4) maximise evidence. | |
From: Paul O'Grady (Relativism [2002], Ch.5) | |
A reaction: I like this, and can't think of any additions. 'Coherence' is the vaguest of the conditions. Maximising evidence is still the driving force of science, even if it does sound quaintly positivist. |
4735 | Just as maps must simplify their subject matter, so thought has to be reductionist about reality [O'Grady] |
Full Idea: A map that is identical in all respects with that which is mapped is just useless. So reductionism is not just a good thing - it is essential to thought. | |
From: Paul O'Grady (Relativism [2002], Ch.6) | |
A reaction: A useful warning, when thinking about truth. It is folly to want your thoughts to exactly correspond to reality. I want to understand the world, but not if it requires being the world. |
4703 | The epistemic theory of truth presents it as 'that which is licensed by our best theory of reality' [O'Grady] |
Full Idea: The epistemic theory of truth presents it as 'that which is licensed by our best theory of reality'. | |
From: Paul O'Grady (Relativism [2002], Ch.2) | |
A reaction: Dangerous nonsense. This leaves truth shifting as our theories change, it leads to different truths in different cultures, and no palpable falsehood in ignorant cultures. Don't give it house-room. |
4701 | To say a relative truth is inexpressible in other frameworks is 'weak', while saying it is false is 'strong' [O'Grady] |
Full Idea: Weak alethic relativism holds that while a statement may be true in one framework, it is inexpressible in another. Strong alethic relativism is where a sentence is true relative to one framework, but false relative to another. | |
From: Paul O'Grady (Relativism [2002], Ch.2) | |
A reaction: The weak version will be Kuhn's 'incommensurability' of scientific theories, while the strong version will be full Protagorean relativism, saying all beliefs are true. |
4705 | Logical relativism appears if we allow more than one legitimate logical system [O'Grady] |
Full Idea: Logical relativism emerges if one defends the existence of two or more rival systems that one may legitimately choose between, or move back and forth between. | |
From: Paul O'Grady (Relativism [2002], Ch.2) | |
A reaction: All my instincts rebel against this possibility. All of Aristotle's and Kant's philosophy would be rendered meaningless. Obviously you can create artificial logics (like games), but I believe there is a truth logic. (Pathetic, isn't it?) |
4700 | A third value for truth might be "indeterminate", or a point on a scale between 'true' and 'false' [O'Grady] |
Full Idea: Suggestions for a third value for truth are "indeterminate", or a scale running from "true", through "mostly true", "mainly true", "half true", "mainly false", "mostly false", to "false", or maybe even "0.56 true". | |
From: Paul O'Grady (Relativism [2002], Ch.2) | |
A reaction: Anything on a sliding scale sounds wrong, as it seems to be paracitic on an underlying fixed idea of 'true'. "Indeterminate", though, seems just right for the truth of predictions ('sea-fight tomorrow'). |
4704 | Wittgenstein reduced Russell's five primitive logical symbols to a mere one [O'Grady] |
Full Idea: While Russell and Whitehead used five primitive logical symbols in their system, Wittgenstein suggested in his 'Tractatus' that this be reduced to one. | |
From: Paul O'Grady (Relativism [2002], Ch.2) | |
A reaction: This certainly captures why Russell was so impressed by him. In retrospect what looked like progress presumably now looks like the beginning of the collapse of the enterprise. |
13489 | Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD] |
Full Idea: Von Neumann's decision was to start with the ordinals and to treat cardinals as a special sort of ordinal. | |
From: report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by William D. Hart - The Evolution of Logic 3 | |
A reaction: [see Hart 73-74 for an explication of this] |
12336 | A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou] |
Full Idea: In Von Neumann's definition an ordinal is a transitive set in which all of the elements are transitive. | |
From: report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Alain Badiou - Briefings on Existence 11 |
18179 | For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy] |
Full Idea: For Von Neumann the successor of n is n U {n} (rather than Zermelo's successor, which is {n}). | |
From: report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Penelope Maddy - Naturalism in Mathematics I.2 n8 |
18180 | Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann] |
Full Idea: Von Neumann's version of the natural numbers is in fact preferred because it carries over directly to the transfinite ordinals. | |
From: comment on John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Penelope Maddy - Naturalism in Mathematics I.2 n9 |
15925 | Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine] |
Full Idea: Each Von Neumann ordinal number is the set of its predecessors. ...He had shown how to introduce ordinal numbers as sets, making it possible to use them without leaving the domain of sets. | |
From: report of John von Neumann (On the Introduction of Transfinite Numbers [1923]) by Shaughan Lavine - Understanding the Infinite V.3 |
8698 | Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend] |
Full Idea: The modal structuralist thinks of mathematical structures as possibilities. The application of mathematics is just the realisation that a possible structure is actualised. As structures are possibilities, realist ontological problems are avoided. | |
From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Michèle Friend - Introducing the Philosophy of Mathematics 4.3 | |
A reaction: Friend criticises this and rejects it, but it is appealing. Mathematics should aim to be applicable to any possible world, and not just the actual one. However, does the actual world 'actualise a mathematical structure'? |
9557 | Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara] |
Full Idea: Hellman represents statements of pure mathematics as elliptical for modal conditionals of a certain sort. | |
From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Charles Chihara - A Structural Account of Mathematics 5.3 | |
A reaction: It's a pity there is such difficulty in understanding conditionals (see Graham Priest on the subject). I intuit a grain of truth in this, though I take maths to reflect the structure of the actual world (with possibilities being part of that world). |
10263 | Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman] |
Full Idea: The usual way to show that a sentence is possible is to show that it has a model, but for Hellman presumably a sentence is possible if it might have a model (or if, possibly, it has a model). It is not clear what this move brings us. | |
From: comment on Geoffrey Hellman (Mathematics without Numbers [1989]) by Stewart Shapiro - Philosophy of Mathematics 7.3 | |
A reaction: I can't assess this, but presumably the possibility of the model must be demonstrated in some way. Aren't all models merely possible, because they are based on axioms, which seem to be no more than possibilities? |
4711 | Anti-realists say our theories (such as wave-particle duality) give reality incompatible properties [O'Grady] |
Full Idea: The anti-realist says we have theories about the world that are incompatible with each other, and irreducible to each other. They often cite wave-particle duality, which postulate incompatible properties to reality. | |
From: Paul O'Grady (Relativism [2002], Ch.3) | |
A reaction: Most physicists, of course, hate this duality, precisely because they can't conceive how the two properties could be real. I say realism comes first, and the theories must try to accommodate that assumption. |
4698 | What counts as a fact partly depends on the availability of human concepts to describe them [O'Grady] |
Full Idea: What counts as a fact partly depends on human input, such as the availability of concepts to describe such facts. | |
From: Paul O'Grady (Relativism [2002], Ch.1) | |
A reaction: The point must be taken. I am happy to generalise about 'The Facts', meaning 'whatever is the case', but the individuation of specific facts is bound to hit the current problem. |
4715 | We may say that objects have intrinsic identity conditions, but still allow multiple accounts of them [O'Grady] |
Full Idea: Those defending the claim that objects exist with identity conditions not imposed by us, do not have to say that there is just one account of those objects possible. | |
From: Paul O'Grady (Relativism [2002], Ch.3) | |
A reaction: This seems right, but the test question is whether the mind of God contains a single unified theory/account. Are multiple accounts the result of human inadequacy? Yes, I surmise. |
4719 | Maybe developments in logic and geometry have shown that the a priori may be relative [O'Grady] |
Full Idea: A weaker form of relativism holds that developments in logic, in maths and in geometry have shown how a relativised notion of the a priori is possible. | |
From: Paul O'Grady (Relativism [2002], Ch.4) | |
A reaction: This is non-Euclidean geometry, and multiple formalisations of logic. Personally I don't believe it. You can expand these subjects, and pursue whimsical speculations, but I have faith in their stable natural core. Neo-Platonism. |
4720 | Sense-data are only safe from scepticism if they are primitive and unconceptualised [O'Grady] |
Full Idea: The reason sense-data were immune from doubt was because they were so primitive; they were unstructured and below the level of conceptualisation. Once they were given structure and conceptualised, they were no longer safe from sceptical challenge. | |
From: Paul O'Grady (Relativism [2002], Ch.4) | |
A reaction: The question of whether sense-data are conceptualised doesn't have to be all-or-nothing. As concepts creep in, so does scepticism, but so what? Sensible philosophers live with scepticism, like a mad aunt in the attic. |
4722 | Modern epistemology centres on debates about foundations, and about external justification [O'Grady] |
Full Idea: The two dichotomies which set the agenda in contemporary epistemology are the foundationalist-coherentist debate, and the internalist-externalist debate. | |
From: Paul O'Grady (Relativism [2002], Ch.4) | |
A reaction: Helpful. Roughly, foundationalists are often externalists (if they are empiricists), and coherentists are often internalists (esp. if they are rationalists). An eccentric combination would make a good PhD. |
4724 | Internalists say the reasons for belief must be available to the subject, and externalists deny this [O'Grady] |
Full Idea: Internalism about justification says that the reasons one has for a belief must be in some sense available to the knowing subject, ..while externalism holds that it is possible for a person to have a justified belief without having access to the reason. | |
From: Paul O'Grady (Relativism [2002], Ch.4) | |
A reaction: It strikes me that internalists are talking about the believer being justified, and externalists talk about the belief being justified. I'm with the internalists. If this means cats don't know much, so much the worse for cats. |
4723 | Coherence involves support from explanation and evidence, and also probability and confirmation [O'Grady] |
Full Idea: Coherentist justification is more than absence of contradictions, and will involve issues like explanatory support and evidential support, and perhaps issues about probability and confirmation too. | |
From: Paul O'Grady (Relativism [2002], Ch.4) | |
A reaction: Something like this is obviously essential. Is the notion of 'relevance' also needed (e.g. to avoid the raven paradox of induction)? Coherence of justification will combine with correspondence for truth. |
4709 | Ontological relativists are anti-realists, who deny that our theories carve nature at the joints [O'Grady] |
Full Idea: Ontological relativists are anti-realists in the strong sense; they hold as meaningless the view that our theories carve nature at the joints. | |
From: Paul O'Grady (Relativism [2002], Ch.3) | |
A reaction: This pinpoints my disagreement with such relativism, as it seems obvious to me that nature has 'joints', and that we would agree with any sensible alien about lots of things. |
4725 | Contextualism says that knowledge is relative to its context; 'empty' depends on your interests [O'Grady] |
Full Idea: Contextualist about knowledge say that "to know" means different things in different context. For example, a warehouse may be empty for a furniture owner, but not for a bacteriologist or a physicist. | |
From: Paul O'Grady (Relativism [2002], Ch.4) | |
A reaction: There is obviously some truth in this, but we might say that 'empty' is a secondary quality, or that 'empty for furniture' is not relative. We needn't accept relativism here. |
4732 | One may understand a realm of ideas, but be unable to judge their rationality or truth [O'Grady] |
Full Idea: It is possible to conceive of one understanding the meaning of a realm of ideas, but holding that one cannot judge as to the truth or rationality of the claims made in it. | |
From: Paul O'Grady (Relativism [2002], Ch.5) | |
A reaction: I think Davidson gives good grounds for challenging this, by doubt whether one 'conceptual scheme' can know another without grasping its rationality and truth-conditions. |
4710 | Verificationism was attacked by the deniers of the analytic-synthetic distinction, needed for 'facts' [O'Grady] |
Full Idea: Verificationism came under attack from empiricists who were friendly to the banishment of traditional metaphysics, but unfriendly to the analytic-synthetic distinction, on which the idea of a 'factual statement' depended. | |
From: Paul O'Grady (Relativism [2002], Ch.3) | |
A reaction: I don't accept this move because I don't consider the 'facts' to be language-dependent. They are pre-linguistic, they outrun that capacity of our language, and they are available to animals. |
4717 | If we abandon the analytic-synthetic distinction, scepticism about meaning may be inevitable [O'Grady] |
Full Idea: There may be no way to avoid scepticism about meaning if you abandon the analytic-synthetic distinction in the way Quine does. | |
From: Paul O'Grady (Relativism [2002], Ch.3) | |
A reaction: My suspicion was always that Quine's proposal began the slippery road to hell. It appears to be pragmatists who are most drawn to Quine's idea. The proposal that all my analytic propositions could be treated as synthetic totally baffles me. |
4706 | Early Quine says all beliefs could be otherwise, but later he said we would assume mistranslation [O'Grady] |
Full Idea: In his earlier work, Quine defended the view that no belief (including logic) is in principle unrevisable, but in his later work (1970) he took the conservative view that we would always impute mistranslation rather than deviancy. | |
From: Paul O'Grady (Relativism [2002], Ch.2) | |
A reaction: I take it he was influenced by Davidson's 'principle of charity'. He says that if someone asserts 'p and not-p', we would assume a misunderstanding of 'and' or 'not'. |
4734 | Cryptographers can recognise that something is a language, without translating it [O'Grady] |
Full Idea: It makes sense to think that one could recognise that something is a language without necessarily being able to translate it; cryptographers do this all the time. | |
From: Paul O'Grady (Relativism [2002], Ch.5) | |
A reaction: Maybe, but cryptographers usually have a lot of context to work with. If we met extraterrestrials if might not be so clear. One can only spot patterns, and crystals have those. |
4727 | The chief problem for fideists is other fideists who hold contrary ideas [O'Grady] |
Full Idea: The chief problem for fideists is other fideists who hold contrary ideas. | |
From: Paul O'Grady (Relativism [2002], Ch.4) | |
A reaction: The other problem is trying to find grounds for sticking to the object of one's faith, rather than changing from time to time. |