24 ideas
| 19079 | For idealists reality is like a collection of beliefs, so truths and truthmakers are not distinct [Young,JO] |
| Full Idea: Idealists do not believe that there is an ontological distinction between beliefs and what makes beliefs true. From their perspective, reality is something like a collection of beliefs. | |
| From: James O. Young (The Coherence Theory of Truth [2013], §2.1) | |
| A reaction: This doesn't seem to me to wholly reject truthmakers, since beliefs can still be truthmakers for one another. This is something like Davidson's view, that only beliefs can justify other beliefs. |
| 19076 | Coherence theories differ over the coherence relation, and over the set of proposition with which to cohere [Young,JO] |
| Full Idea: Coherence theories of truth differ on their accounts of the coherence relation, and on their accounts of the set (or sets) of propositions with which true propositions occur (the 'specified set'). | |
| From: James O. Young (The Coherence Theory of Truth [2013], §1) | |
| A reaction: Coherence is clearly more than consistency or mutual entailment, and I like to invoke explanation. The set has to be large, or the theory is absurd (as two absurdities can 'cohere'). So very large, or very very large, or maximally large? |
| 19077 | Two propositions could be consistent with your set, but inconsistent with one another [Young,JO] |
| Full Idea: It is unsatisfactory for the coherence relation to be consistency, because two propositions could be consistent with a 'specified set', and yet be inconsistent with each other. That would imply they are both true, which is impossible. | |
| From: James O. Young (The Coherence Theory of Truth [2013], §1) | |
| A reaction: I'm not convinced by this. You first accept P because it is consistent with the set; then Q turns up, which is consistent with everything in the set except P. So you have to choose between them, and might eject P. Your set was too small. |
| 19078 | Coherence with actual beliefs, or our best beliefs, or ultimate ideal beliefs? [Young,JO] |
| Full Idea: One extreme for the specified set is the largest consistent set of propositions currently believed by actual people. A moderate position makes it the limit of people's enquiries. The other extreme is what would be believed by an omniscient being. | |
| From: James O. Young (The Coherence Theory of Truth [2013], §1) | |
| A reaction: One not considered is the set of propositions believed by each individual person. Thoroughgoing relativists might well embrace that one. Peirce and Putnam liked the moderate one. I'm taken with the last one, since truth is an ideal, not a phenomenon. |
| 19084 | Coherent truth is not with an arbitrary set of beliefs, but with a set which people actually do believe [Young,JO] |
| Full Idea: It must be remembered that coherentists do not believe that the truth of a proposition consists in coherence with an arbitrarily chosen set of propositions; the coherence is with a set of beliefs, or a set of propositions held to be true. | |
| From: James O. Young (The Coherence Theory of Truth [2013], §3.1) | |
| A reaction: This is a very good response to critics who cite bizarre sets of beliefs which happen to have internal coherence. You have to ask why they are not actually believed, and the answer must be that the coherence is not extensive enough. |
| 19083 | How do you identify the best coherence set; and aren't there truths which don't cohere? [Young,JO] |
| Full Idea: The two main objections to the coherence theory of truth are that there is no way to identify the 'specified set' of propositions without contradiction, ...and that some propositions are true which cohere with no set of beliefs. | |
| From: James O. Young (The Coherence Theory of Truth [2013], §3.1/2) | |
| A reaction: The point of the first is that you need a prior knowledge of truth to say which of two sets is the better one. The second one is thinking of long-lost tiny details from the past, which seem to be true without evidence. A huge set might beat the first one. |
| 19075 | Deflationary theories reject analysis of truth in terms of truth-conditions [Young,JO] |
| Full Idea: Unlike deflationary theories, the coherence and correspondence theories both hold that truth is a property of propositions that can be analyzed in terms of the sorts of truth-conditions propositions have, and the relation propositions stand in to them. | |
| From: James O. Young (The Coherence Theory of Truth [2013], Intro) | |
| A reaction: This is presumably because deflationary theories reject the external relations of a proposition as a feature of its truth. This evidently leaves them in need of a theory of meaning, which may be fairly minimal. Horwich would be an example. |
| 10702 | Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter] |
| Full Idea: Set theory has three roles: as a means of taming the infinite, as a supplier of the subject-matter of mathematics, and as a source of its modes of reasoning. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], Intro 1) | |
| A reaction: These all seem to be connected with mathematics, but there is also ontological interest in set theory. Potter emphasises that his second role does not entail a commitment to sets 'being' numbers. |
| 10713 | Usually the only reason given for accepting the empty set is convenience [Potter] |
| Full Idea: It is rare to find any direct reason given for believing that the empty set exists, except for variants of Dedekind's argument from convenience. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 04.3) |
| 13044 | Infinity: There is at least one limit level [Potter] |
| Full Idea: Axiom of Infinity: There is at least one limit level. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 04.9) | |
| A reaction: A 'limit ordinal' is one which has successors, but no predecessors. The axiom just says there is at least one infinity. |
| 10708 | Nowadays we derive our conception of collections from the dependence between them [Potter] |
| Full Idea: It is only quite recently that the idea has emerged of deriving our conception of collections from a relation of dependence between them. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.2) | |
| A reaction: This is the 'iterative' view of sets, which he traces back to Gödel's 'What is Cantor's Continuum Problem?' |
| 13546 | The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter] |
| Full Idea: We group under the heading 'limitation of size' those principles which classify properties as collectivizing or not according to how many objects there are with the property. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 13.5) | |
| A reaction: The idea was floated by Cantor, toyed with by Russell (1906), and advocated by von Neumann. The thought is simply that paradoxes start to appear when sets become enormous. |
| 10707 | Mereology elides the distinction between the cards in a pack and the suits [Potter] |
| Full Idea: Mereology tends to elide the distinction between the cards in a pack and the suits. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 02.1) | |
| A reaction: The example is a favourite of Frege's. Potter is giving a reason why mathematicians opted for set theory. I'm not clear, though, why a pack cannot have either 4 parts or 52 parts. Parts can 'fall under a concept' (such as 'legs'). I'm puzzled. |
| 10704 | We can formalize second-order formation rules, but not inference rules [Potter] |
| Full Idea: In second-order logic only the formation rules are completely formalizable, not the inference rules. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 01.2) | |
| A reaction: He cites Gödel's First Incompleteness theorem for this. |
| 10703 | Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter] |
| Full Idea: A 'supposition' axiomatic theory is as concerned with truth as a 'realist' one (with undefined terms), but the truths are conditional. Satisfying the axioms is satisfying the theorem. This is if-thenism, or implicationism, or eliminative structuralism. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 01.1) | |
| A reaction: Aha! I had failed to make the connection between if-thenism and eliminative structuralism (of which I am rather fond). I think I am an if-thenist (not about all truth, but about provable truth). |
| 10712 | If set theory didn't found mathematics, it is still needed to count infinite sets [Potter] |
| Full Idea: Even if set theory's role as a foundation for mathematics turned out to be wholly illusory, it would earn its keep through the calculus it provides for counting infinite sets. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.8) |
| 17882 | It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter] |
| Full Idea: It is a remarkable fact that all the arithmetical properties of the natural numbers can be derived from such a small number of assumptions (as the Peano Axioms). | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 05.2) | |
| A reaction: If one were to defend essentialism about arithmetic, this would be grist to their mill. I'm just saying. |
| 13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
| Full Idea: A set is called a 'relation' if every element of it is an ordered pair. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 04.7) | |
| A reaction: This is the modern extensional view of relations. For 'to the left of', you just list all the things that are to the left, with the things they are to the left of. But just listing the ordered pairs won't necessarily reveal how they are related. |
| 13042 | If dependence is well-founded, with no infinite backward chains, this implies substances [Potter] |
| Full Idea: The argument that the relation of dependence is well-founded ...is a version of the classical arguments for substance. ..Any conceptual scheme which genuinely represents a world cannot contain infinite backward chains of meaning. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.3) | |
| A reaction: Thus the iterative conception of set may imply a notion of substance, and Barwise's radical attempt to ditch the Axiom of Foundation (Idea 13039) was a radical attempt to get rid of 'substances'. Potter cites Wittgenstein as a fan of substances here. |
| 13041 | Collections have fixed members, but fusions can be carved in innumerable ways [Potter] |
| Full Idea: A collection has a determinate number of members, whereas a fusion may be carved up into parts in various equally valid (although perhaps not equally interesting) ways. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 02.1) | |
| A reaction: This seems to sum up both the attraction and the weakness of mereology. If you doubt the natural identity of so-called 'objects', then maybe classical mereology is the way to go. |
| 10709 | Priority is a modality, arising from collections and members [Potter] |
| Full Idea: We must conclude that priority is a modality distinct from that of time or necessity, a modality arising in some way out of the manner in which a collection is constituted from its members. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.3) | |
| A reaction: He is referring to the 'iterative' view of sets, and cites Aristotle 'Metaphysics' 1019a1-4 as background. |
| 19074 | Are truth-condtions other propositions (coherence) or features of the world (correspondence)? [Young,JO] |
| Full Idea: For the coherence theory of truth, the truth conditions of propositions consist in other propositions. The correspondence theory, in contrast, states that the truth conditions of propositions are ... objective features of the world. | |
| From: James O. Young (The Coherence Theory of Truth [2013], Intro) | |
| A reaction: It is obviously rather important for your truth-conditions theory of meaning that you are clear about your theory of truth. A correspondence theory is evidently taken for granted, even in possible worlds versions. |
| 19082 | Coherence truth suggests truth-condtions are assertion-conditions, which need knowledge of justification [Young,JO] |
| Full Idea: Coherence theorists can argue that the truth conditions of a proposition are those under which speakers tend to assert it, ...and that speakers can only make a practice of asserting a proposition under conditions they can recognise as justifying it. | |
| From: James O. Young (The Coherence Theory of Truth [2013], §2.2) | |
| A reaction: [compressed] This sounds rather verificationist, and hence wrong, since if you then asserted anything for which you didn't know the justification, that would remove its truth, and thus make it meaningless. |
| 20329 | A work of art is an artifact created for the artworld [Dickie] |
| Full Idea: A work of art is an artifact of a kind created to be presented to an artworld public. | |
| From: George Dickie (The New Institutional Theory of Art [1983], p.53) | |
| A reaction: This is the culminating definition in his paper, deriving originally from Danto, and an improvement of his earlier more complex definition. Since this definition amounts to 'this is art if I say it is art', it doesn't seem to reveal much. |