32 ideas
| 15585 | Later Heidegger sees philosophy as more like poetry than like science [Heidegger, by Polt] |
| Full Idea: In his later work Heidegger came to view philosophy as closer to poetry than to science. | |
| From: report of Martin Heidegger (The Origin of the Work of Art [1935], p.178) by Richard Polt - Heidegger: an introduction 5 'Signs' |
| 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. |
| 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. |
| 5806 | Belief is the power of metarepresentation [Dretske] |
| Full Idea: Belief is the power of metarepresentation. | |
| From: Fred Dretske (Naturalizing the Mind [1997], §2.3) | |
| A reaction: Hm. I have always defined belief as 'commitment to truth', and this definition leaves out both parts. Where is the commitment? If hope is another metarepresentation, how does it differ from belief? I imagine things, not believing them to be true. |
| 5801 | A mouse hearing a piano played does not believe it, because it lacks concepts and understanding [Dretske] |
| Full Idea: A mouse can see and hear a piano being played, but believing is something else; it requires the concept of a piano, and understanding. Mice who hear pianos being played do not believe pianos are being played. | |
| From: Fred Dretske (Naturalizing the Mind [1997], §1.3) | |
| A reaction: Are we to say that when a mouse hears a piano it has no beliefs at all? Might not a belief involve images, so that a mouse calls up appropriate images from previous experiences, which are in a grey area on the edge of belief? |
| 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. |
| 5802 | Representations are in the head, but their content is not, as stories don't exist in their books [Dretske] |
| Full Idea: Representations are in the head, but their content is not; in this sense, the mind isn't in the head any more than stories (i.e. story contents) are in books. | |
| From: Fred Dretske (Naturalizing the Mind [1997], §1.6) | |
| A reaction: This is the final consequence of Putnam's idea that meanings ain't in the head. Intentionality is an extraordinary bridge between the brain and the external world. The ontology of stories, and musical compositions, is one philosophy's deepest problems. |
| 5809 | Some activities are performed better without consciousness of them [Dretske] |
| Full Idea: Some tasks (playing the piano, speaking foreign languages, playing fast sports) are best performed when the agent is largely unconscious of the details. | |
| From: Fred Dretske (Naturalizing the Mind [1997], Ch.4 n16) | |
| A reaction: A significant point, but it supports the evolutionary view, which is that what matters is success, and consciousness will switch on or off, whichever promotes the activity best. |
| 5808 | Qualia are just the properties objects are represented as having [Dretske] |
| Full Idea: The Representational Thesis of mind identifies the qualities of experience - qualia - with the properties objects are represented as having. | |
| From: Fred Dretske (Naturalizing the Mind [1997], §3.2) | |
| A reaction: This seems to challenge the distinction between primary and secondary qualities, of which I am very fond. Is 'looks beautiful' a property of an object? Is the feeling of anger a property of an object? Qualia are properties of brains? |
| 5803 | In a representational theory of mind, introspection is displaced perception [Dretske] |
| Full Idea: On a representational theory of the mind, introspection becomes an instance of displaced perception - knowledge of internal (mental) facts via an awareness of external (physical) objects. | |
| From: Fred Dretske (Naturalizing the Mind [1997], §2) | |
| A reaction: This sounds close to a behaviourist (e.g. Ryle) account of introspection, via observing one's own behaviour. The word 'displaced' is an easy one, concealing a multitude of questions. |
| 5807 | Introspection is the same as the experience one is introspecting [Dretske] |
| Full Idea: Introspection has no phenomenology or, if it does, it always has the same phenomenology as the experience one is introspecting. | |
| From: Fred Dretske (Naturalizing the Mind [1997], §2.4) | |
| A reaction: There is a difference between looking at a tree, and being aware of yourself looking at a tree. You can be faintly depressed, and then become aware that you are faintly depressed. He is nearly right. |
| 5805 | Introspection does not involve looking inwards [Dretske] |
| Full Idea: The 'problem' of introspection evaporates once one understands that it is not a process in which one looks inward. | |
| From: Fred Dretske (Naturalizing the Mind [1997], §2) | |
| A reaction: I take it that when we introspect we look at the contents of thoughts, which are representations of the external world, on the whole. But surely only the connections of those contents with memories can be seen inwardly? |
| 5804 | A representational theory of the mind is an externalist theory of the mind [Dretske] |
| Full Idea: A representational theory of the mind is an externalist theory of the mind. | |
| From: Fred Dretske (Naturalizing the Mind [1997], §2) | |
| A reaction: Presumably brain events bring the world into the mind, so the world must be mentioned in explaining the mind. Maybe 'externalism' sounds grand, but is stating the boringly obvious. Explanations of mind need no mention of external particulars. |
| 5800 | All mental facts are representation, which consists of informational functions [Dretske] |
| Full Idea: My thesis is that all mental facts are representational facts, and that all representational facts are facts about informational functions. | |
| From: Fred Dretske (Naturalizing the Mind [1997], Prol) | |
| A reaction: The first half of the thesis seems a bit difficult to disagree with, but that a fact is 'represented' may not be the essence of that fact. The biggest mystery is the content, not its representation. And everything is 'information' about everything else. |
| 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. |
| 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. |