32 ideas
| 12036 | Xenophanes began the concern with knowledge [Annas] |
| Full Idea: Xenophanes begins a long concern with knowledge and its grounds. | |
| From: Julia Annas (Ancient Philosophy: very short introduction [2000], Intro) | |
| A reaction: Having that on his cv ought to make Xenophanes more famous than he is. |
| 12046 | Plato was the first philosopher who was concerned to systematize his ideas [Annas] |
| Full Idea: In the ancient world Plato was seen as a pivotal figure, the first philosopher who was concerned to systematize his ideas. | |
| From: Julia Annas (Ancient Philosophy: very short introduction [2000], Ch.6) |
| 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) |
| 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. |
| 7720 | Two things can only resemble one another in some respect, and that may reintroduce a universal [Lowe] |
| Full Idea: A problem for resemblance nominalism is that in saying that two particulars 'resemble' one another, it is necessary to specify in what respect they do so (e.g. colour, shape, size), and this threatens to reintroduce what appears to be talk of universals. | |
| From: E.J. Lowe (Locke on Human Understanding [1995], Ch.7) | |
| A reaction: We see resemblance between faces instantly, long before we can specify the 'respects' of the resemblance. This supports the Humean hard-wired view of resemblance, rather than some appeal to Platonic universals. |
| 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. |
| 7712 | On substances, Leibniz emphasises unity, Spinoza independence, Locke relations to qualities [Lowe] |
| Full Idea: Later philosophers emphasised different strands of Aristotle's concept of substances: Leibniz (in his theory of monads) emphasised their unity; Spinoza emphasised their ontological independence; Locke emphasised their role in relation to qualities. | |
| From: E.J. Lowe (Locke on Human Understanding [1995], Ch.4) | |
| A reaction: Note that this Aristotelian idea had not been jettisoned in the late seventeenth century, unlike other Aristotelianisms. I think it is only with the success of atomism in chemistry that the idea of substance is forced to recede. |
| 7710 | Perception is a mode of belief-acquisition, and does not involve sensation [Lowe] |
| Full Idea: According to one school of thought, perception is simply a mode of belief-acquisition,and there is no reason to suppose that any element of sensation is literally involved in perception. | |
| From: E.J. Lowe (Locke on Human Understanding [1995], Ch.3) | |
| A reaction: Blindsight would be an obvious supporting case for this view. I think this point is crucial in understanding what is wrong with Jackson's 'knowledge argument' (involving Mary, see Idea 7377). Sensation gives knowledge, so it can't be knowledge. |
| 7711 | Science requires a causal theory - perception of an object must be an experience caused by the object [Lowe] |
| Full Idea: Only a causal theory of perception will respect the facts of physiology and physics ...meaning a theory which maintains that for a subject to perceive a physical object the subject should enjoy some appropriate perceptual experience caused by the object. | |
| From: E.J. Lowe (Locke on Human Understanding [1995], Ch.3) | |
| A reaction: If I hallucinate an object, then presumably I am not allowed to say that I 'perceive' it, but that seems to make the causal theory an idle tautology. If we are in virtual reality then there aren't any objects. |
| 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. |
| 7714 | Personal identity is a problem across time (diachronic) and at an instant (synchronic) [Lowe] |
| Full Idea: There is the question of the identity of a person over or across time ('diachronic' personal identity), and there is also the question of what makes for personal identity at a time ('synchronic' personal identity). | |
| From: E.J. Lowe (Locke on Human Understanding [1995], Ch.5) | |
| A reaction: This seems to me to be the first and most important distinction in the philosophy of personal identity, and they regularly get run together. Locke, for example, has an account of synchronic identity, which is often ignored. It applies to objects too. |
| 7715 | Mentalese isn't a language, because it isn't conventional, or a means of public communication [Lowe] |
| Full Idea: 'Mentalese' would be neither conventional nor a means of public communication so that even to call it a language is seriously misleading. | |
| From: E.J. Lowe (Locke on Human Understanding [1995], Ch.7) | |
| A reaction: It is, however, supposed to contain symbolic representations which are then used as tokens for computation, so it seems close to a language, if (for example) symbolic logic or mathematics were accepted as languages. But who understands it? |
| 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. |
| 7722 | If meaning is mental pictures, explain "the cat (or dog!) is NOT on the mat" [Lowe] |
| Full Idea: If meaning is a private mental picture, what does 'the cat is NOT on the mat' mean, and how does it differ from 'the dog is not on the mat?'. | |
| From: E.J. Lowe (Locke on Human Understanding [1995], Ch.7) | |
| A reaction: Not insurmountable. We picture an empty mat, combined with a cat (or whatever) located somewhere else. A mental 'picture' of something shouldn't be contrued as a single image in a neat black frame. |
| 12037 | Euripides's Medea is a key case of reason versus the passions [Annas] |
| Full Idea: Euripides's Medea has remained a key case for discussion of reason and the passions. | |
| From: Julia Annas (Ancient Philosophy: very short introduction [2000], Ch.1) |
| 12040 | Virtue is a kind of understanding of moral value [Annas] |
| Full Idea: There is a widespread view in ancient ethics that virtue is a kind of understanding of moral value. | |
| From: Julia Annas (Ancient Philosophy: very short introduction [2000], Ch.3) | |
| A reaction: In Aristotle's case, this coincides with his apparent view that 'understanding' is the aim of all areas of human thought. See Idea 12038. |
| 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. |