13 ideas
16252 | Metaphysics uses empty words, or just produces pseudo-statements [Carnap] |
Full Idea: Since metaphysics doesn't want to assert analytic propositions, nor fall within the domain of physical science, it is compelled to employ words for which no criteria of application are specified, ..or else combine meaningful words..into pseudo-statements. | |
From: Rudolph Carnap (Elimination of Metaphysics by Analysis of Language [1959]), quoted by Tim Maudlin - The Metaphysics within Physics 2.4 | |
A reaction: A classic summary of the logical positivist rejection of metaphysics. I incline to treat metaphysics as within the domain of science, but at a level of generality so high that practising scientists become bewildered and give up. |
12223 | It is a fallacy to explain the obscure with the even more obscure [Hale/Wright] |
Full Idea: The fallacy of 'ad obscurum per obscurius' is to explain the obscure by appeal to what is more obscure. | |
From: B Hale / C Wright (The Metaontology of Abstraction [2009], §3) | |
A reaction: Not strictly a fallacy, so much as an example of inadequate explanation, along with circularity and infinite regresses. |
15943 | Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann] |
Full Idea: Von Neumann's Limitation of Size axiom is not self-evident, and he himself admitted that it seemed too strong. | |
From: comment on John von Neumann (An Axiomatization of Set Theory [1925]) by Shaughan Lavine - Understanding the Infinite VII.1 |
12230 | Singular terms refer if they make certain atomic statements true [Hale/Wright] |
Full Idea: Anyone should agree that a justification for regarding a singular term as having objectual reference is provided just as soon as one has justification for regarding as true certain atomic statements in which it functions as a singular term. | |
From: B Hale / C Wright (The Metaontology of Abstraction [2009], §9) | |
A reaction: The meat of this idea is hidden in the word 'certain'. See Idea 10314 for Hale's explanation. Without that, the proposal strikes me as absurd. |
13672 | All the axioms for mathematics presuppose set theory [Neumann] |
Full Idea: There is no axiom system for mathematics, geometry, and so forth that does not presuppose set theory. | |
From: John von Neumann (An Axiomatization of Set Theory [1925]), quoted by Stewart Shapiro - Foundations without Foundationalism 8.2 | |
A reaction: Von Neumann was doubting whether set theory could have axioms, and hence the whole project is doomed, and we face relativism about such things. His ally was Skolem in this. |
12225 | Neo-Fregeanism might be better with truth-makers, rather than quantifier commitment [Hale/Wright] |
Full Idea: A third way has been offered to 'make sense' of neo-Fregeanism: we should reject Quine's well-known criterion of ontological commitment in favour of one based on 'truth-maker theory'. | |
From: B Hale / C Wright (The Metaontology of Abstraction [2009], §4 n19) | |
A reaction: [The cite Ross Cameron for this] They reject this proposal, on the grounds that truth-maker theory is not sufficient to fix the grounding truth-conditions of statements. |
12224 | Are neo-Fregeans 'maximalists' - that everything which can exist does exist? [Hale/Wright] |
Full Idea: It is claimed that neo-Fregeans are committed to 'maximalism' - that whatever can exist does. | |
From: B Hale / C Wright (The Metaontology of Abstraction [2009], §4) | |
A reaction: [The cite Eklund] They observe that maximalism denies contingent non-existence (of the £20 note I haven't got). There seems to be the related problem of 'hyperinflation', that if abstract objects are generated logically, the process is unstoppable. |
12226 | The identity of Pegasus with Pegasus may be true, despite the non-existence [Hale/Wright] |
Full Idea: Identity is sometimes read so that 'Pegasus is Pegasus' expresses a truth, the non-existence of any winged horse notwithstanding. | |
From: B Hale / C Wright (The Metaontology of Abstraction [2009], §5) | |
A reaction: This would give you ontological commitment to truth, without commitment to existence. It undercuts the use of identity statements as the basis of existence claims, which was Frege's strategy. |
12229 | Maybe we have abundant properties for semantics, and sparse properties for ontology [Hale/Wright] |
Full Idea: There is a compatibilist view which says that it is for the abundant properties to play the role of 'bedeutungen' in semantic theory, and the sparse ones to address certain metaphysical concerns. | |
From: B Hale / C Wright (The Metaontology of Abstraction [2009], §9) | |
A reaction: Only a philosopher could live with the word 'property' having utterly different extensions in different areas of discourse. They similarly bifurcate words like 'object' and 'exist'. Call properties 'quasi-properties' and I might join in. |
18443 | A successful predicate guarantees the existence of a property - the way of being it expresses [Hale/Wright] |
Full Idea: The good standing of a predicate is already trivially sufficient to ensure the existence of an associated property, a (perhaps complex) way of being which the predicate serves to express. | |
From: B Hale / C Wright (The Metaontology of Abstraction [2009], §9) | |
A reaction: 'Way of being' is interesting. Is 'being near Trafalgar Sq' a way of being? I take properties to be 'features', which seems to give a clearer way of demarcating them. They say they are talking about 'abundant' (rather than 'sparse') properties. |
12227 | Abstractionism needs existential commitment and uniform truth-conditions [Hale/Wright] |
Full Idea: Abstractionism needs a face-value, existentially committed reading of the terms occurring on the left-hand sides together with sameness of truth-conditions across the biconditional. | |
From: B Hale / C Wright (The Metaontology of Abstraction [2009], §5) | |
A reaction: They employ 'abstractionism' to mean their logical Fregean strategy for defining abstractions, not to mean the older psychological account. Thus the truth-conditions for being 'parallel' and for having the 'same direction' must be consistent. |
12228 | Equivalence abstraction refers to objects otherwise beyond our grasp [Hale/Wright] |
Full Idea: Abstraction principles purport to introduce fundamental means of reference to a range of objects, to which there is accordingly no presumption that we have any prior or independent means of reference. | |
From: B Hale / C Wright (The Metaontology of Abstraction [2009], §8) | |
A reaction: There's the rub! They make it sound like a virtue, that we open up yet another heaven of abstract toys to play with. As fictions, they are indeed exciting new fun. As platonic discoveries they strike me as Cloud-Cuckoo Land. |
12231 | Reference needs truth as well as sense [Hale/Wright] |
Full Idea: It takes, over and above the possession of sense, the truth of relevant contexts to ensure reference. | |
From: B Hale / C Wright (The Metaontology of Abstraction [2009], §9) | |
A reaction: Reference purely through sense was discredited by Kripke. The present idea challenges Kripke's baptismal realist approach. How do you 'baptise' an abstract object? But isn't reference needed prior to the establishment of truth? |