20 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. |
14249 | Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley] |
Full Idea: Boolos's conception of plural logic is as a reinterpretation of second-order logic. | |
From: report of George Boolos (On Second-Order Logic [1975]) by Oliver,A/Smiley,T - What are Sets and What are they For? n5 | |
A reaction: Oliver and Smiley don't accept this view, and champion plural reference differently (as, I think, some kind of metalinguistic device?). |
10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
Full Idea: The metatheory of second-order logic is hopelessly set-theoretic, and the notion of second-order validity possesses many if not all of the epistemic debilities of the notion of set-theoretic truth. | |
From: George Boolos (On Second-Order Logic [1975], p.45) | |
A reaction: Epistemic problems arise when a logic is incomplete, because some of the so-called truths cannot be proved, and hence may be unreachable. This idea indicates Boolos's motivation for developing a theory of plural quantification. |
10829 | A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos] |
Full Idea: One may be of the opinion that no sentence ought to be considered as a truth of logic if, no matter how it is interpreted, it asserts that there are sets of certain sorts. | |
From: George Boolos (On Second-Order Logic [1975], p.44) | |
A reaction: My intuition is that in no way should any proper logic assert the existence of anything at all. Presumably interpretations can assert the existence of numbers or sets, but we should be able to identify something which is 'pure' logic. Natural deduction? |
10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
Full Idea: One may say that '∀x x=x' means 'everything is identical to itself', but one must realise that one's answer has a determinate sense only if the reference (range) of 'everything' is fixed. | |
From: George Boolos (On Second-Order Logic [1975], p.46) | |
A reaction: This is the problem now discussed in the recent book 'Absolute Generality', of whether one can quantify without specifying a fixed or limited domain. |
10834 | Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos] |
Full Idea: A weak completeness theorem shows that a sentence is provable whenever it is valid; a strong theorem, that a sentence is provable from a set of sentences whenever it is a logical consequence of the set. | |
From: George Boolos (On Second-Order Logic [1975], p.52) | |
A reaction: So the weak version says |- φ → |= φ, and the strong versions says Γ |- φ → Γ |= φ. Presumably it is stronger if it can specify the source of the inference. |
13841 | Why should compactness be definitive of logic? [Boolos, by Hacking] |
Full Idea: Boolos asks why on earth compactness, whatever its virtues, should be definitive of logic itself. | |
From: report of George Boolos (On Second-Order Logic [1975]) by Ian Hacking - What is Logic? §13 |
10833 | Many concepts can only be expressed by second-order logic [Boolos] |
Full Idea: The notions of infinity and countability can be characterized by second-order sentences, though not by first-order sentences (as compactness and Skolem-Löwenheim theorems show), .. as well as well-ordering, progression, ancestral and identity. | |
From: George Boolos (On Second-Order Logic [1975], p.48) |
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. |
16557 | Salmon's mechanisms are processes and interactions, involving marks, or conserved quantities [Salmon, by Machamer/Darden/Craver] |
Full Idea: For Salmon mechanisms are composed of processes and interactions. The interactions are identified in terms of transmitted marks and statistical relations, or (more recently) exchanges of conserved quantities. | |
From: report of Wesley Salmon (Causality and Explanation [1998], 3.1) by Machamer,P/Darden,L/Craver,C - Thinking About Mechanisms 3.1 | |
A reaction: They say that Salmon has too little to say about the activities that constitute a mechanism. A 'mark' doesn't sound too promising, but I quite like the exchange of conserved quantities, which gets into the guts of what is going on. |