19 ideas
13734 | Modern Quinean metaphysics is about what exists, but Aristotelian metaphysics asks about grounding [Schaffer,J] |
Full Idea: On the now dominant Quinean view, metaphysics is about what there is (such as properties, meanings and numbers). I will argue for the revival of a more traditional Aristotelian view, on which metaphysics is about what grounds what. | |
From: Jonathan Schaffer (On What Grounds What [2009], Intro) | |
A reaction: I find that an enormously helpful distinction, and support the Aristotelian view. Schaffer's general line is that what exists is fairly uncontroversial and dull, but the interesting truths about the world emerge when we grasp its structure. |
13751 | If you tore the metaphysics out of philosophy, the whole enterprise would collapse [Schaffer,J] |
Full Idea: Traditional metaphysics is so tightly woven into the fabric of philosophy that it cannot be torn out without the whole tapestry unravelling. | |
From: Jonathan Schaffer (On What Grounds What [2009], 2.3) | |
A reaction: I often wonder why the opponents of metaphysics still continue to do philosophy. I don't see how you address questions of ethics, or philosophy of mathematics (etc) without coming up against highly general and abstract over-questions. |
13743 | We should not multiply basic entities, but we can have as many derivative entities as we like [Schaffer,J] |
Full Idea: Occam's Razor should only be understood to concern substances: do not multiply basic entities without necessity. There is no problem with the multiplication of derivative entities - they are an 'ontological free lunch'. | |
From: Jonathan Schaffer (On What Grounds What [2009], 2.1) | |
A reaction: The phrase 'ontological free lunch' comes from Armstrong. This is probably what Occam meant. A few extra specks of dust, or even a few more numbers (thank you, Cantor!) don't seem to challenge the principle. |
10185 | Set theory is the standard background for modern mathematics [Burgess] |
Full Idea: In present-day mathematics, it is set theory that serves as the background theory in which other branches of mathematics are developed. | |
From: John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], §1) | |
A reaction: [He cites Bourbaki as an authority for this] See Benacerraf for a famous difficulty here, when you actually try to derive an ontology from the mathematicians' working practices. |
10184 | Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure [Burgess] |
Full Idea: On the structuralist interpretation, theorems of analysis concerning the real numbers R are about all complete ordered fields. So R, which appears to be the name of a specific structure, is taken to be a variable ranging over structures. | |
From: John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], §1) | |
A reaction: Since I am beginning to think that nearly all linguistic expressions should be understood as variables, I find this very appealing, even if Burgess hates it. Terms slide and drift, and are vague, between variable and determinate reference. |
10189 | There is no one relation for the real number 2, as relations differ in different models [Burgess] |
Full Idea: One might meet the 'Van Inwagen Problem' by saying that the intrinsic properties of the object playing the role of 2 will differ from one model to another, so that no statement about the intrinsic properties of 'the' real numbers will make sense. | |
From: John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], §5) | |
A reaction: There seems to be a potential confusion among opponents of structuralism between relations at the level of actual mathematical operations, and generalisations about relations, which are captured in the word 'patterns'. Call them 'meta-relations'? |
10186 | If set theory is used to define 'structure', we can't define set theory structurally [Burgess] |
Full Idea: It is to set theory that one turns for the very definition of 'structure', ...and this creates a problem of circularity if we try to impose a structuralist interpretation on set theory. | |
From: John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], §1) | |
A reaction: This seems like a nice difficulty, especially if, like Shapiro, you wade in and try to give a formal account of structures and patterns. Resnik is more circumspect and vague. |
10187 | Abstract algebra concerns relations between models, not common features of all the models [Burgess] |
Full Idea: Abstract algebra, such as group theory, is not concerned with the features common to all models of the axioms, but rather with the relationships among different models of those axioms (especially homomorphic relation functions). | |
From: John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], §1) | |
A reaction: It doesn't seem to follow that structuralism can't be about the relations (or patterns) found when abstracting away and overviewing all the models. One can study family relations, or one can study kinship in general. |
10188 | How can mathematical relations be either internal, or external, or intrinsic? [Burgess] |
Full Idea: The 'Van Inwagen Problem' for structuralism is of explaining how a mathematical relation (such as set membership, or the ratios of an ellipse) can fit into one of the three scholastics types of relations: are they internal, external, or intrinsic? | |
From: John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], §5) | |
A reaction: The difficulty is that mathematical objects seem to need intrinsic properties to get any of these three versions off the ground (which was Russell's complaint against structures). |
13741 | If 'there are red roses' implies 'there are roses', then 'there are prime numbers' implies 'there are numbers' [Schaffer,J] |
Full Idea: We can automatically infer 'there are roses' from 'there are red roses' (with no shift in the meaning of 'roses'). Likewise one can automatically infer 'there are numbers' from 'there are prime numbers'. | |
From: Jonathan Schaffer (On What Grounds What [2009], 2.1) | |
A reaction: He similarly observes that the atheist's 'God is a fictional character' implies 'there are fictional characters'. Schaffer is not committing to a strong platonism with his claim - merely that the existence of numbers is hardly worth disputing. |
13748 | Grounding is unanalysable and primitive, and is the basic structuring concept in metaphysics [Schaffer,J] |
Full Idea: Grounding should be taken as primitive, as per the neo-Aristotelian approach. Grounding is an unanalyzable but needed notion - it is the primitive structuring conception of metaphysics. | |
From: Jonathan Schaffer (On What Grounds What [2009], 2.2) | |
A reaction: [he cites K.Fine 1991] I find that this simple claim clarifies the discussions of Kit Fine, where you are not always quite sure what the game is. I agree fully with it. It makes metaphysics interesting, where cataloguing entities is boring. |
13747 | Supervenience is just modal correlation [Schaffer,J] |
Full Idea: Supervenience is mere modal correlation. | |
From: Jonathan Schaffer (On What Grounds What [2009], 2.2) |
13744 | The cosmos is the only fundamental entity, from which all else exists by abstraction [Schaffer,J] |
Full Idea: My preferred view is that there is only one fundamental entity - the whole concrete cosmos - from which all else exists by abstraction. | |
From: Jonathan Schaffer (On What Grounds What [2009], 2.1) | |
A reaction: This looks to me like weak anti-realism - that there are no natural 'joints' in nature - but I don't think Schaffer intends that. I take the joints to be fundamentals, which necessitates that the cosmos has parts. His 'abstraction' is clearly a process. |
13739 | Maybe categories are just the different ways that things depend on basic substances [Schaffer,J] |
Full Idea: Maybe the categories are determined by the different grounding relations, ..so that categories just are the ways things depend on substances. ...Categories are places in the dependence ordering. | |
From: Jonathan Schaffer (On What Grounds What [2009], 1.3) |
13742 | There exist heaps with no integral unity, so we should accept arbitrary composites in the same way [Schaffer,J] |
Full Idea: I am happy to accept universal composition, on the grounds that there are heaps, piles etc with no integral unity, and that arbitrary composites are no less unified than heaps. | |
From: Jonathan Schaffer (On What Grounds What [2009], 2.1 n11) | |
A reaction: The metaphysical focus is then placed on what constitutes 'integral unity', which is precisely the question which most interested Aristotle. Clearly if there is nothing more to an entity than its components, scattering them isn't destruction. |
13752 | The notion of 'grounding' can explain integrated wholes in a way that mere aggregates can't [Schaffer,J] |
Full Idea: The notion of grounding my capture a crucial mereological distinction (missing from classical mereology) between an integrated whole with genuine unity, and a mere aggregate. x is an integrated whole if it grounds its proper parts. | |
From: Jonathan Schaffer (On What Grounds What [2009], 3.1) | |
A reaction: That gives a nice theoretical notion, but if you remove each of the proper parts, does x remain? Is it a bare particular? I take it that it will have to be an abstract principle, the one Aristotle was aiming at with his notion of 'form'. Schaffer agrees. |
13749 | Belief in impossible worlds may require dialetheism [Schaffer,J] |
Full Idea: One motivation for dialetheism is the view that there are impossible worlds. | |
From: Jonathan Schaffer (On What Grounds What [2009], 2.3) |
13740 | 'Moorean certainties' are more credible than any sceptical argument [Schaffer,J] |
Full Idea: A 'Moorean certainty' is when something is more credible than any philosopher's argument to the contrary. | |
From: Jonathan Schaffer (On What Grounds What [2009], 2.1) | |
A reaction: The reference is to G.E. Moore's famous claim that the existence of his hand is more certain than standard sceptical arguments. It sounds empiricist, but they might be parallel rational truths, of basic logic or arithmetic. |
21929 | Derrida focuses on ambiguity, but talks of 'dissemination', not traditional multiple meanings [Derrida] |
Full Idea: Derrida affirms something like an 'ambiguity of meaning'. But he explicitly contrasts the word he uses to characterize the phenomenon at issue, what he calls 'dissemination', with the traditional concept of 'polysemia' - multiple meanings. | |
From: Jacques Derrida (Of Grammatology [1967]), quoted by Simon Glendinning - Derrida: A Very Short Introduction 2 'After' | |
A reaction: The point, I presume, is that there is vagueness and elision to the meanings, rather than a list of options, such as bank/bank. Context (sense-making paths) is crucial for Derrida. Can the analytic apparatus for the logic of vagueness be brought to bear? |