39 ideas
| 15053 | If metaphysics can't be settled, it hardly matters whether it makes sense [Fine,K] |
| Full Idea: If there is no way of settling metaphysical questions, then who cares whether or not they make sense? | |
| From: Kit Fine (The Question of Realism [2001], 4 n20) | |
| A reaction: This footnote is aimed at logical positivists, who seemed to worry about whether metaphysics made sense, and also dismissed its prospects even if it did make sense. |
| 15054 | 'Quietist' says abandon metaphysics because answers are unattainable (as in Kant's noumenon) [Fine,K] |
| Full Idea: The 'quietist' view of metaphysics says that realist metaphysics should be abandoned, not because its questions cannot be framed, but because their answers cannot be found. The real world of metaphysics is akin to Kant's noumenal world. | |
| From: Kit Fine (The Question of Realism [2001], 4) | |
| A reaction: [He cites Blackburn, Dworkin, A.Fine, and Putnam-1987 as quietists] Fine aims to clarify the concepts of factuality and of ground, in order to show that metaphysics is possible. |
| 9570 | In Field's Platonist view, set theory is false because it asserts existence for non-existent things [Field,H, by Chihara] |
| Full Idea: Field commits himself to a Platonic view of mathematics. The theorems of set theory are held to imply or presuppose the existence of things that don't in fact exist. That is why he believes that these theorems are false. | |
| From: report of Hartry Field (Science without Numbers [1980]) by Charles Chihara - A Structural Account of Mathematics 11.1 | |
| A reaction: I am sympathetic to Field, but this sounds wrong. A response that looks appealing is that maths is hypothetical ('if-thenism') - the truth is in the logical consequences, not in the ontological presuppositions. |
| 10260 | Logical consequence is defined by the impossibility of P and ¬q [Field,H, by Shapiro] |
| Full Idea: Field defines logical consequence by taking the notion of 'logical possibility' as primitive. Hence q is a consequence of P if the conjunction of the items in P with the negation of q is not possible. | |
| From: report of Hartry Field (Science without Numbers [1980]) by Stewart Shapiro - Philosophy of Mathematics 7.2 | |
| A reaction: The question would then be whether it is plausible to take logical possibility as primitive. Presumably only intuition could support it. But then intuition will equally support natural and metaphysical possibilities. |
| 8958 | In Field's version of science, space-time points replace real numbers [Field,H, by Szabó] |
| Full Idea: Field's nominalist version of science develops a version of Newtonian gravitational theory, where no quantifiers range over mathematical entities, and space-time points and regions play the role of surrogates for real numbers. | |
| From: report of Hartry Field (Science without Numbers [1980]) by Zoltán Gendler Szabó - Nominalism 5.1 | |
| A reaction: This seems to be a very artificial contrivance, but Field has launched a programme for rewriting science so that numbers can be omitted. All of this is Field's rebellion against the Indispensability Argument for mathematics. I sympathise. |
| 18221 | 'Metric' axioms uses functions, points and numbers; 'synthetic' axioms give facts about space [Field,H] |
| Full Idea: There are two approaches to axiomatising geometry. The 'metric' approach uses a function which maps a pair of points into the real numbers. The 'synthetic' approach is that of Euclid and Hilbert, which does without real numbers and functions. | |
| From: Hartry Field (Science without Numbers [1980], 5) |
| 8757 | The Indispensability Argument is the only serious ground for the existence of mathematical entities [Field,H] |
| Full Idea: There is one and only one serious argument for the existence of mathematical entities, and that is the Indispensability Argument of Putnam and Quine. | |
| From: Hartry Field (Science without Numbers [1980], p.5), quoted by Stewart Shapiro - Thinking About Mathematics 9.1 | |
| A reaction: Personally I don't believe (and nor does Field) that this gives a good enough reason to believe in such things. Quine (who likes 'desert landscapes' in ontology) ends up believing that sets are real because of his argument. Not for me. |
| 18212 | Nominalists try to only refer to physical objects, or language, or mental constructions [Field,H] |
| Full Idea: The most popular approach of nominalistically inclined philosophers is to try to reinterpret mathematics, so that its terms and quantifiers only make reference to, say, physical objects, or linguistic expressions, or mental constructions. | |
| From: Hartry Field (Science without Numbers [1980], Prelim) | |
| A reaction: I am keen on naturalism and empiricism, but only referring to physical objects is a non-starter. I think I favour constructions, derived from the experience of patterns, and abstracted, idealised and generalised. Field says application is the problem. |
| 10261 | The application of mathematics only needs its possibility, not its truth [Field,H, by Shapiro] |
| Full Idea: Field argues that to account for the applicability of mathematics, we need to assume little more than the possibility of the mathematics, not its truth. | |
| From: report of Hartry Field (Science without Numbers [1980]) by Stewart Shapiro - Philosophy of Mathematics 7.2 | |
| A reaction: Very persuasive. We can apply chess to real military situations, provided that chess isn't self-contradictory (or even naturally impossible?). |
| 18218 | Hilbert explains geometry, by non-numerical facts about space [Field,H] |
| Full Idea: Facts about geometric laws receive satisfying explanations, by the intrinsic facts about physical space, i.e. those laid down without reference to numbers in Hilbert's axioms. | |
| From: Hartry Field (Science without Numbers [1980], 3) | |
| A reaction: Hilbert's axioms mention points, betweenness, segment-congruence and angle-congruence (Field 25-26). Field cites arithmetic and geometry (as well as Newtonian mechanics) as not being dependent on number. |
| 9623 | Field needs a semantical notion of second-order consequence, and that needs sets [Brown,JR on Field,H] |
| Full Idea: Field needs the notion of logical consequence in second-order logic, but (since this is not recursively axiomatizable) this is a semantical notion, which involves the idea of 'true in all models', a set-theoretic idea if there ever was one. | |
| From: comment on Hartry Field (Science without Numbers [1980], Ch.4) by James Robert Brown - Philosophy of Mathematics | |
| A reaction: Brown here summarises a group of critics. Field was arguing for modern nominalism, that actual numbers could (in principle) be written out of the story, as useful fictions. Popper's attempt to dump induction seemed to need induction. |
| 18215 | It seems impossible to explain the idea that the conclusion is contained in the premises [Field,H] |
| Full Idea: No clear explanation of the idea that the conclusion was 'implicitly contained in' the premises was ever given, and I do not believe that any clear explanation is possible. | |
| From: Hartry Field (Science without Numbers [1980], 1) |
| 18210 | Why regard standard mathematics as truths, rather than as interesting fictions? [Field,H] |
| Full Idea: Why regard the axioms of standard mathematics as truths, rather than as fictions that for a variety of reasons mathematicians have become interested in? | |
| From: Hartry Field (Science without Numbers [1980], p.viii) |
| 18214 | Mathematics is only empirical as regards which theory is useful [Field,H] |
| Full Idea: Mathematics is in a sense empirical, but only in the rather Pickwickian sense that is an empirical question as to which mathematical theory is useful. | |
| From: Hartry Field (Science without Numbers [1980], 1) | |
| A reaction: Field wants mathematics to be fictions, and not to be truths. But can he give an account of 'useful' that does not imply truth? Only in a rather dubiously pragmatist way. A novel is not useful. |
| 18216 | Abstractions can form useful counterparts to concrete statements [Field,H] |
| Full Idea: Abstract entities are useful because we can use them to formulate abstract counterparts of concrete statements. | |
| From: Hartry Field (Science without Numbers [1980], 3) | |
| A reaction: He defends the abstract statements as short cuts. If the concrete statements were 'true', then it seems likely that the abstract counterparts will also be true, which is not what fictionalism claims. |
| 15007 | If you make 'grounding' fundamental, you have to mention some non-fundamental notions [Sider on Fine,K] |
| Full Idea: My main objection to Fine's notion of grounding as fundamental is that it violates 'purity' - that fundamental truths should involve only fundamental notions. | |
| From: comment on Kit Fine (The Question of Realism [2001]) by Theodore Sider - Writing the Book of the World 08.2 | |
| A reaction: [p.106 of Sider for 'purity'] The point here is that to define a grounding relation you have to mention the 'higher' levels of the relationship (as in a 'city' being grounded in physical stuff), which doesn't seem fundamental enough. |
| 15006 | Something is grounded when it holds, and is explained, and necessitated by something else [Fine,K, by Sider] |
| Full Idea: When p 'grounds' q then q holds in virtue of p's holding; q's holding is nothing beyond p's holding; the truth of p explains the truth of q in a particularly tight sense (explanation of q by p in this sense requires that p necessitates q). | |
| From: report of Kit Fine (The Question of Realism [2001], 15-16) by Theodore Sider - Writing the Book of the World 08.1 | |
| A reaction: This proposal has become a hot topic in current metaphysics, as attempts are made to employ 'grounding' in various logical, epistemological and ontological contexts. I'm a fan - it is at the heart of metaphysics as structure of reality. |
| 15055 | Grounding relations are best expressed as relations between sentences [Fine,K] |
| Full Idea: I recommend that a statement of ground be cast in the following 'canonical' form: Its being the case that S consists in nothing more than its being the case that T, U... (where S, T, U... are particular sentences). | |
| From: Kit Fine (The Question of Realism [2001], 5) | |
| A reaction: The point here is that grounding is to be undestood in terms of sentences (and 'its being the case that...'), rather than in terms of objects, properties or relations. Fine thus makes grounding a human activity, rather than a natural activity. |
| 15050 | Reduction might be producing a sentence which gets closer to the logical form [Fine,K] |
| Full Idea: One line of reduction is logical analysis. To say one sentence reduces to another is to say that they express the same proposition (or fact), but the grammatical form of the second is closer to the logical form than the grammatical form of the first. | |
| From: Kit Fine (The Question of Realism [2001], 3) | |
| A reaction: Fine objects that S-and-T reduces to S and T, which is two propositions. He also objects that this approach misses the de re ingredient in reduction (that it is about the things themselves, not the sentences). It also overemphasises logical form. |
| 15051 | Reduction might be semantic, where a reduced sentence is understood through its reduction [Fine,K] |
| Full Idea: A second line of reduction is semantic, and holds in virtue of the meaning of the sentences. It should then be possible to acquire an understanding of the reduced sentence on the basis of understanding the sentences to which it reduces. | |
| From: Kit Fine (The Question of Realism [2001], 3) | |
| A reaction: Fine says this avoids the first objection to the grammatical approach (see Reaction to Idea 15050), but still can't handle the de re aspect of reduction. Fine also doubts whether this understanding qualifies as 'reduction'. |
| 15052 | Reduction is modal, if the reductions necessarily entail the truth of the target sentence [Fine,K] |
| Full Idea: The third, more recent, approach to reduction is a modal matter. A class of propositions will reduce to - or supervene upon - another if, necessarily, any truth from the one is entailed by truths from the other. | |
| From: Kit Fine (The Question of Realism [2001], 3) | |
| A reaction: [He cites Armstrong, Chalmers and Jackson for this approach] Fine notes that some people reject supervenience as a sort of reduction. He objects that this reduction doesn't necessarily lead to something more basic. |
| 15056 | The notion of reduction (unlike that of 'ground') implies the unreality of what is reduced [Fine,K] |
| Full Idea: The notion of ground should be distinguished from the strict notion of reduction. A statement of reduction implies the unreality of what is reduced, but a statement of ground does not. | |
| From: Kit Fine (The Question of Realism [2001], 5) | |
| A reaction: That seems like a bit of a caricature of reduction. If you see a grey cloud and it reduces to a swarm of mosquitoes, you do not say that the cloud was 'unreal'. Fine is setting up a stall for 'ground' in the metaphysical market. We all seek structure. |
| 15047 | What is real can only be settled in terms of 'ground' [Fine,K] |
| Full Idea: Questions of what is real are to be settled upon the basis of considerations of ground. | |
| From: Kit Fine (The Question of Realism [2001], Intro) | |
| A reaction: This looks like being one of Fine's most important ideas, which is shifting the whole basis of contemporary metaphysics. Only Parmenides and Heidegger thought Being was the target. Aristotle aims at identity. What grounds what is a third alternative. |
| 15046 | Reality is a primitive metaphysical concept, which cannot be understood in other terms [Fine,K] |
| Full Idea: I conclude that there is a primitive metaphysical concept of reality, one that cannot be understood in fundamentally different terms. | |
| From: Kit Fine (The Question of Realism [2001], Intro) | |
| A reaction: Fine offers arguments to support his claim, but it seems hard to disagree with. The only alternative I can see is to understand reality in terms of our experiences, and this is the road to metaphysical hell. |
| 15048 | In metaphysics, reality is regarded as either 'factual', or as 'fundamental' [Fine,K] |
| Full Idea: The first main approach says metaphysical reality is to be identified with what is 'objective' or 'factual'. ...According to the second conception, metaphysical reality is to be identified with what is 'irreducible' or 'fundamental'. | |
| From: Kit Fine (The Question of Realism [2001], 1) | |
| A reaction: Fine is defending the 'fundamental' approach, via the 'grounding' relation. The whole structure, though, seems to be reality. In particular, a complete story must include the relations which facilitate more than mere fundamentals. |
| 15060 | Why should what is explanatorily basic be therefore more real? [Fine,K] |
| Full Idea: We may grant that some things are explanatorily more basic than others, but why should that make them more real? | |
| From: Kit Fine (The Question of Realism [2001], 8) | |
| A reaction: This is the question asked by the 'quietist'. Fine's answer is that our whole conception of Reality, with its intrinsic structure, is what lies at the basis, and this is primitive. |
| 18211 | You can reduce ontological commitment by expanding the logic [Field,H] |
| Full Idea: One can often reduce one's ontological commitments by expanding one's logic. | |
| From: Hartry Field (Science without Numbers [1980], p.ix) | |
| A reaction: I don't actually understand this idea, but that's never stopped me before. Clearly, this sounds like an extremely interesting thought, and hence I should aspire to understand it. So I do aspire to understand it. First, how do you 'expand' a logic? |
| 8959 | Field presumes properties can be eliminated from science [Field,H, by Szabó] |
| Full Idea: Field regards the eliminability of apparent reference to properties from the language of science as a foregone result. | |
| From: report of Hartry Field (Science without Numbers [1980]) by Zoltán Gendler Szabó - Nominalism 5.1 n50 | |
| A reaction: Field is a nominalist who also denies the existence of mathematics as part of science. He has a taste for ontological 'desert landscapes'. I have no idea what a property really is, so I think he is on to something. |
| 18213 | Abstract objects are only applicable to the world if they are impure, and connect to the physical [Field,H] |
| Full Idea: To be able to apply any postulated abstract entities to the physical world, we need impure abstact entities, e.g. functions that map physical objects into pure abstract objects. | |
| From: Hartry Field (Science without Numbers [1980], 1) | |
| A reaction: I am a fan of 'impure metaphysics', and this pinpoints my reason very nicely. |
| 15061 | Although colour depends on us, we can describe the world that way if it picks out fundamentals [Fine,K] |
| Full Idea: As long as colour terms pick out fundamental physical properties, I would be willing to countenance their use in the description of Reality in itself, ..even if they are based on a peculiar form of sensory awareness. | |
| From: Kit Fine (The Question of Realism [2001], 8) | |
| A reaction: This seems to explain why metaphysicians are so fond of using colour as their example of a property, when it seems rather subjective. There seem to be good reasons for rejecting Fine's view. |
| 18222 | Beneath every extrinsic explanation there is an intrinsic explanation [Field,H] |
| Full Idea: A plausible methodological principle is that underlying every good extrinsic explanation there is an intrinsic explanation. | |
| From: Hartry Field (Science without Numbers [1980], 5) | |
| A reaction: I'm thinking that Hartry Field is an Aristotelian essentialist, though I bet he would never admit it. |
| 15059 | Grounding is an explanation of truth, and needs all the virtues of good explanations [Fine,K] |
| Full Idea: The main sources of evidence for judgments of ground are intuitive and explanatory. The relationship of ground is a form of explanation, ..explaining what makes a proposition true, which needs simplicity, breadth, coherence, non-circularity and strength. | |
| From: Kit Fine (The Question of Realism [2001], 7) | |
| A reaction: My thought is that not only must grounding explain, and therefore be a good explanation, but that the needs of explanation drive our decisions about what are the grounds. It is a bit indeterminate which is tail and which is dog. |
| 15057 | Ultimate explanations are in 'grounds', which account for other truths, which hold in virtue of the grounding [Fine,K] |
| Full Idea: We take ground to be an explanatory relation: if the truth that P is grounded in other truths, then they account for its truth; P's being the case holds in virtue of the other truths' being the case. ...It is the ultimate form of explanation. | |
| From: Kit Fine (The Question of Realism [2001], 5) | |
| A reaction: To be 'ultimate' that which grounds would have to be something which thwarted all further explanation. Popper, for example, got quite angry at the suggestion that we should put a block on further investigation in this way. |
| 9917 | 'Abstract' is unclear, but numbers, functions and sets are clearly abstract [Field,H] |
| Full Idea: The term 'abstract entities' may not be entirely clear, but one thing that does seem clear is that such alleged entities as numbers, functions and sets are abstract. | |
| From: Hartry Field (Science without Numbers [1980], p.1), quoted by JP Burgess / G Rosen - A Subject with No Object I.A.1.a | |
| A reaction: Field firmly denies the existence of such things. Sets don't seem a great problem, if the set is a herd of elephants, but the null and singleton sets show up the difficulties. |
| 15058 | A proposition ingredient is 'essential' if changing it would change the truth-value [Fine,K] |
| Full Idea: A proposition essentially contains a given constituent if its replacement by some other constituent induces a shift in truth value. Thus Socrates is essential to the proposition that Socrates is a philosopher, but not to Socrates is self-identical. | |
| From: Kit Fine (The Question of Realism [2001], 6) | |
| A reaction: In this view the replacement of 'is' by 'isn't' would make 'is' (or affirmation) part of the essence of most propositions. This is about linguistic essence, rather than real essence. It has the potential to be trivial. Replace 'slightly' by 'fairly'? |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |
| 18223 | In theories of fields, space-time points or regions are causal agents [Field,H] |
| Full Idea: According to theories that take the notion of a field seriously, space-time points or regions are fully-fledge causal agents. | |
| From: Hartry Field (Science without Numbers [1980], n 23) |
| 18220 | Both philosophy and physics now make substantivalism more attractive [Field,H] |
| Full Idea: In general, it seems to me that recent developments in both philosophy and physics have made substantivalism a much more attractive position than it once was. | |
| From: Hartry Field (Science without Numbers [1980], 4) | |
| A reaction: I'm intrigued as to what philosophical developments are involved in this. The arrival of fields is the development in physics. |
| 18219 | Relational space is problematic if you take the idea of a field seriously [Field,H] |
| Full Idea: The problem of the relational view of space is especially acute in the context of physical theories that take the notion of a field seriously, e.g. classical electromagnetic theory. | |
| From: Hartry Field (Science without Numbers [1980], 4) | |
| A reaction: In the Leibniz-Clarke debate I sided with the Newtonian Clarke (defending absolute space), and it looks like modern science agrees with me. Nothing exists purely as relations. |