42 ideas
| 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) |
| 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. |
| 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. |
| 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) |
| 22427 | To explain object qualities, primary qualities must be more than mere sources of experience [McGinn] |
| Full Idea: In order that we have available an explanation of the qualities of objects we need to be able to conceive primary qualities as consisting in something other than powers to produce experiences. | |
| From: Colin McGinn (Subjective View: sec qualities and indexicals [1983], 6 n 52) | |
| A reaction: I suppose if the qualities are nothing more than the source of the experiences, that is Kant's noumenon. Nothing more could be said. The seems to be a requirement for tacit inference here. We infer the interior of the tomato. |
| 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. |
| 22413 | Being red simply consists in looking red [McGinn] |
| Full Idea: What we should claim is that being red consists in looking red. | |
| From: Colin McGinn (Subjective View: sec qualities and indexicals [1983], 2) | |
| A reaction: A very nice simple account. There is more to being square than looking square (which may not even guarantee that it is square). That's the primary/secondary distinction in a nut shell. But red things don't look red in the dark. Sufficient, not necessary. |
| 22415 | Relativity means differing secondary perceptions are not real disagreements [McGinn] |
| Full Idea: Relativity permits differences in the perceived secondary qualities not to imply genuine disagreement, whereas perceived differences of primary qualities imply that at least one perceiver is in error. | |
| From: Colin McGinn (Subjective View: sec qualities and indexicals [1983], 2) | |
| A reaction: An example of 'relativity' is colour blindness. Sounds good, but what of one perceiver seeing a square as square, and another seeing it obliquely as a parallelogram? The squareness then seems more like a theory than a perception. |
| 22416 | Phenomenalism is correct for secondary qualities, so scepticism is there impossible [McGinn] |
| Full Idea: We might say that scepticism is ruled out for secondary qualities because (roughly) phenomenalism is correct for them; but phenomenalism is not similarly correct for primary qualities, and scepticism cannot get a foothold. | |
| From: Colin McGinn (Subjective View: sec qualities and indexicals [1983], 2) | |
| A reaction: An odd idea, if phenomenalism says that reality consists entirely of phenomena. I should think phenomenalism is a commitment to the absence of primary qualities. |
| 22422 | Maybe all possible sense experience must involve both secondary and primary qualities [McGinn] |
| Full Idea: The inseparability thesis about perception says that for any actual and possible sense the content of experiences delivered by that sense must be both of secondary qualities and of primary qualities. | |
| From: Colin McGinn (Subjective View: sec qualities and indexicals [1983], 6) | |
| A reaction: That would mean that all possible experience must have a mode of presentation, and also must be 'of' something independent of experience. So a yellow after-image would not count as an 'experience'? |
| 22428 | You understood being red if you know the experience involved; not so with thngs being square [McGinn] |
| Full Idea: To grasp what it is to be red is to know the kind of sensory experience red things produce; ...but it is not true that to grasp what it is to be square one needs to know what kinds of sensory experience square things produce. | |
| From: Colin McGinn (Subjective View: sec qualities and indexicals [1983], 8) | |
| A reaction: Are any experiences involved in the understanding of squareness? We don't know squareness by a priori intuition (do we?). To grasp squareness if may be necessary to have a variety of experiences of it. Or to grasp that it is primary. |
| 22414 | You don't need to know how a square thing looks or feels to understand squareness [McGinn] |
| Full Idea: To grasp what it is for something to be square it is not constitutively necessary to know how square things look or feel, since what it is to be square does not involve any such relation to experience. | |
| From: Colin McGinn (Subjective View: sec qualities and indexicals [1983], 2) | |
| A reaction: You could even describe squareness verbally, unlike redness. It seems crucial that almost any sense (such as bat echoes) can communicate primary qualities, but secondary qualities are tied to a sense, and wouldn't exist without it. |
| 22423 | Touch doesn't provide direct experience of primary qualities, because touch feels temperature [McGinn] |
| Full Idea: Bennett's claim that touch provides experience of primary qualities without experience of any secondary qualities strikes me as false, because tactile experience includes felt temperature, which is a dispositional secondary quality. | |
| From: Colin McGinn (Subjective View: sec qualities and indexicals [1983], 6) | |
| A reaction: [J.Bennett 1971 pp. 90-4] Fair point. What about shape and texture? We experience forces, but the shape is assembled in imagination rather than in experience. So do we meet primary qualities directly in forces, such as acceleration? No secondary quality? |
| 22426 | We can perceive objectively, because primary qualities are not mind-created [McGinn] |
| Full Idea: I hold that experience succeeds in representing the world objectively, since primary quality perceptual content is not contributed by the mind. | |
| From: Colin McGinn (Subjective View: sec qualities and indexicals [1983], 6) | |
| A reaction: My new example of a direct perception of a primary quality is acceleration in a lift. What would we say to one passenger who denied feeling the acceleration? It took an effort to see that mind contributes to secondary qualities (so make more effort?). |
| 22412 | Lockean secondary qualities (unlike primaries) produce particular sensory experiences [McGinn] |
| Full Idea: In the Lockean tradition, secondary qualities are defined as those whose instantiation in an object consists in a power or disposition of the object to produce sensory experiences in perceivers of a certain phenomenological character. | |
| From: Colin McGinn (Subjective View: sec qualities and indexicals [1983], 2) | |
| A reaction: Primary qualities are said to lack such dispositions. Not sure about these definitions. Primaries offer no experiences? With these definitions, comparing them would be a category mistake. I take it primaries reflect reality and secondaries do not. |
| 22421 | Could there be a mind which lacked secondary quality perception? [McGinn] |
| Full Idea: Can we form a conception of a type of mind whose representations are free of secondary quality perceptions? | |
| From: Colin McGinn (Subjective View: sec qualities and indexicals [1983], 6) | |
| A reaction: Nice question. Minds must have experiences, and there has to be a 'way' or 'mode' for those experiences. A mind which directly grasped the primary quality of sphericity would seem to be visionary rather than sensual or experiential. |
| 22424 | Secondary qualities contain information; their variety would be superfluous otherwise [McGinn] |
| Full Idea: Surely we learn something about an object when we discover its secondary qualities? ...If secondary quality experience were informationally inert, its variety would be something of a puzzle. Why not employ the same medium for all primary informaton? | |
| From: Colin McGinn (Subjective View: sec qualities and indexicals [1983], 6) | |
| A reaction: This is important. We can't just focus on the primary qualities, and ignore the secondary. But diverse colours draw attention to information, which can then be translated into neutral data, as in spectroscopic analysis. Locke agrees with this. |
| 22425 | The utility theory says secondary qualities give information useful to human beings [McGinn] |
| Full Idea: Secondary quality perception, according to the utility theory, gives information about the relation between the perceptual object and the perceiver's needs and interests. | |
| From: Colin McGinn (Subjective View: sec qualities and indexicals [1983], 6) | |
| A reaction: Almost the only example I can think of is whether fruit is ripe or rotten. ...Also 'bad' smells. We recognise aggressive animal noises, but that is not the same as dangerous (e.g. rustling snake). Divine design is behind this theory, I think. |
| 7629 | We see objects 'directly' by representing them [McGinn] |
| Full Idea: My view is that we see objects 'directly' by representing them in visual experience. | |
| From: Colin McGinn (Subjective View: sec qualities and indexicals [1983], Ch.8 n1) | |
| A reaction: [Quoted by Maund] This rejects both inference in perception and sense-data, while retaining the notion of representation. It is a view which has gained a lot of support. But how can it be direct if it represents? Photographs can't do that. |
| 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. |
| 22420 | The indexical perspective is subjective, incorrigible and constant [McGinn] |
| Full Idea: I attribute three properties to the indexical perspective: it is subjective, incorrigible, and constant. | |
| From: Colin McGinn (Subjective View: sec qualities and indexicals [1983], 5) | |
| A reaction: That is as good an idea as any for summarising the view (associated with John Perry) that the indexical perspective is an indispensable feature of reality. For a good attack on this, which I favour, see Cappelen and Dever. |
| 18410 | Indexical thought is in relation to my self-consciousness [McGinn] |
| Full Idea: Very roughly, we can say that to think of something indexically is to think of it in relation to me, as I am presented to myself in self-consciousness. | |
| From: Colin McGinn (Subjective View: sec qualities and indexicals [1983], 2) | |
| A reaction: So it is characterised relationally, which doesn't mean it has a distinctive intrinsic character. If I'm lost, and I overhear someone say 'Peter is in Hazlemere', I get the same relational information (in a different mode) without the indexicality. |
| 22417 | Indexicals do not figure in theories of physics, because they are not explanatory causes [McGinn] |
| Full Idea: Indexicals are like secondary qualities in not figuring in causal explanations of the interactions of objects: physics omits them not because they are relative and egocentric, but because they do not constitute explanatory predicates of a causal theory. | |
| From: Colin McGinn (Subjective View: sec qualities and indexicals [1983], 2) | |
| A reaction: They are outside explanatory physics, but not outside explanation. The object moved because a force acted on it; or the object moved because I wanted it moved. |
| 18402 | Indexical concepts are indispensable, as we need them for the power to act [McGinn] |
| Full Idea: The present suggestion is that indexical concepts are ineliminable because without them agency would be impossible: when I imagine myself divested of indexical thoughts employing only centreless mental representations, I am deprived of the power to act. | |
| From: Colin McGinn (Subjective View: sec qualities and indexicals [1983], 6) | |
| A reaction: A nice clear statement of the view developed by Perry and Lewis. I agree with Cappelen and Dever that it is entirely wrong, and that indexical thought is entirely eliminable, and nothing special. |
| 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. |
| 22418 | I can know indexical truths a priori, unlike their non-indexical paraphrases [McGinn] |
| Full Idea: I know the truth of the sentence 'I am here now' a priori, but I do not know a priori 'McGinn is in London on 15th Nov 1981'. | |
| From: Colin McGinn (Subjective View: sec qualities and indexicals [1983], 3) | |
| A reaction: I'm not convinced that I can grasp the concepts of 'here' and 'now' (i.e. space and time) by purely a priori means. But he certainly shows that you can't glibly dismiss indexicals by paraphrasing them in that way. |
| 11945 | In addition to laws, God must also create appropriate natures for things [Leibniz] |
| Full Idea: It isn't sufficient to say that God has made a general law, for in addition to the decree there has also to be a natural way of carrying it out. It is necessary, that is, that what happens should be explicable in terms of the God-given nature of things. | |
| From: Gottfried Leibniz (Letter to the Editor about Bayle [1698], p.205) | |
| A reaction: Thus Leibniz is an ancestor of scientific essentialism, but he was too frightened to take the next step, which is to see that once God has endowed the natures, he doesn't need to wield his laws as well. The natures will do the whole job. |
| 19348 | All that is real in motion is the force or power which produces change [Leibniz] |
| Full Idea: As for motion, what is real in it is force or power; that is to say, what there is in the present state which carries with it a change in the future. The rest is only phenomena and relations. | |
| From: Gottfried Leibniz (Letter to the Editor about Bayle [1698], §13) | |
| A reaction: This presumably contradicts Newton's concept of inertia, which allows constant motion without force. I always like a reference to powers. What is 'kinetic energy' in this context? |
| 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. |