36 ideas
| 4901 | Truth has to be correspondence to facts, and a match between relations of ideas and relations in the world [Perry] |
| Full Idea: I think knowledge and truth are a matter of correspondence to facts, despite all the energy spent showing the naïveté of this view. The connections of our ideas in our heads correspond to relations in the outside world. | |
| From: John Perry (Knowledge, Possibility and Consciousness [2001], §8.1) | |
| A reaction: Yes. Modern books offer the difficulties of defining 'correspondence', and finding an independent account of 'facts', as conclusive objections, but I say a brain is a truth machine, and it had better be useful. Indefinability doesn't nullify concepts. |
| 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. |
| 4885 | Identity is a very weak relation, which doesn't require interdefinability, or shared properties [Perry] |
| Full Idea: The truth of "a=b" doesn't require much of 'a' and 'b' other than that there is a single thing to which they both refer. They needn't be interdefinable, or have supervenient properties. In this sense, identity is a very weak relation. | |
| From: John Perry (Knowledge, Possibility and Consciousness [2001], §1.2) | |
| A reaction: Interesting. This is seeing the epistemological aspects of identity. Ontologically, identity must invoke Leibniz's Law, and is the ultimately powerful 'relation'. A given student, and the cause of a crop circle, may APPEAR to be quite different. |
| 4899 | Possible worlds thinking has clarified the logic of modality, but is problematic in epistemology [Perry] |
| Full Idea: Using possible worlds to model truth-conditions of statements has led to considerable clarity about the logic of modality. Attempts to use the system for epistemic purposes, however, have been plagued by problems. | |
| From: John Perry (Knowledge, Possibility and Consciousness [2001], §8.1) | |
| A reaction: Presumably what lurks behind this is a distinction between what is logically or naturally possible, and what appears to be possible from the perspective of a conscious mind. Is there a possible world in which I can fly? |
| 4898 | Possible worlds are indices for a language, or concrete realities, or abstract possibilities [Perry] |
| Full Idea: Possible worlds can be thought of as indices for models of the language in question, or as concrete realities (David Lewis), or as abstract ways the world might be (Robert Stalnaker), or in various other ways. | |
| From: John Perry (Knowledge, Possibility and Consciousness [2001], §8.1) | |
| A reaction: I strongly favour the Stalnaker route here. Reducing great metaphysics to mere language I find abhorrent, and I suspect that Lewis was trapped by his commitment to strong empiricism. We must embrace abstractions into our ontology. |
| 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. |
| 4887 | We try to cause other things to occur by causing mental events to occur [Perry] |
| Full Idea: We try to cause other things to occur by causing mental events to occur. | |
| From: John Perry (Knowledge, Possibility and Consciousness [2001], §2.4) | |
| A reaction: A small and obvious, but important, point. Mental causation isn't just thoughts leading to physical happenings. Here Perry means that events can be designed to cause thoughts, such as a threatening letter. Not much room for epiphenomenalism here. |
| 4884 | Brain states must be in my head, and yet the pain seems to be in my hand [Perry] |
| Full Idea: The brain state will involve certain parts of the brain, whereas my feeling of pain seems to be located in my hand insofar as it has a bodily location. | |
| From: John Perry (Knowledge, Possibility and Consciousness [2001], §1.2) | |
| A reaction: This seems important to me. The brain is a ventriloquist. Perry implies that pain is quasi-disembodied, but it isn't, it is just experienced as IN the hand. Perhaps it is in the hand? Cutting the nerves loses contact with the pain. |
| 4888 | It seems plausible that many animals have experiences without knowing about them [Perry] |
| Full Idea: It seems quite plausible to me that many animals have experiences without knowing about them. | |
| From: John Perry (Knowledge, Possibility and Consciousness [2001], §3.1) | |
| A reaction: I agree, which makes us acknowledge levels of consciousness, which probably applies to human experience as well. The simplest idea is to distinguish between experiences which involve concepts, and those which don't. Animals sometimes appear surprised. |
| 16002 | The self is a combination of pairs of attributes: freedom/necessity, infinite/finite, temporal/eternal [Kierkegaard] |
| Full Idea: A human being is essentially spirit, but what is spirit? Spirit is to be a self. But what is the Self? In short, it is a synthesis of the infinite and the finite, of the temporal and the eternal, of freedom and necessity. | |
| From: Søren Kierkegaard (Sickness unto Death [1849], p.59) | |
| A reaction: The dense language of his first paragraph was to poke fun at fashionable Hegelian writing. The book gets very lucid afterwards! [SY] |
| 4891 | If epiphenomenalism just says mental events are effects but not causes, it is consistent with physicalism [Perry] |
| Full Idea: Epiphenomenalism is usually considered to be a form of dualism, but if we define it as the doctrine that conscious events are effects but not causes, it appears to be consistent with physicalism. | |
| From: John Perry (Knowledge, Possibility and Consciousness [2001], §4.2) | |
| A reaction: Interesting. The theory was invented to put mind outside physics, and make the closure of physics possible. However, being capable of causing things seems to be a necessary condition for physical objects. An effect in one domain is a cause in another. |
| 4900 | Prior to Kripke, the mind-brain identity theory usually claimed that the identity was contingent [Perry] |
| Full Idea: Advocates of the mind-body identity theory typically claimed that identity between particular mental states and brain states was contingent, until Kripke argued persuasively that identity is always necessary. | |
| From: John Perry (Knowledge, Possibility and Consciousness [2001], §8.1) | |
| A reaction: Kripke wanted to argue against the identity theory, but what he seems to have done is reformulate it into a much more powerful version (involving necessary identity). |
| 4892 | If physicalists stick with identity (not supervenience), Martian pain will not be like ours [Perry] |
| Full Idea: The physicalist should not retreat to causal supervenience but should stick with identity. This means we will have to accept that a Martian and I (when in pain) are not in the same phenomenal state. | |
| From: John Perry (Knowledge, Possibility and Consciousness [2001], §4.3) | |
| A reaction: We naturally presume that frogs feel pain as we do, but many different phenomenal states could lead to the same behavioural end. Only an unpleasant feeling is required. A foul smell would do. Frogs could function with inverted qualia, too. |
| 4889 | Although we may classify ideas by content, we individuate them differently, as their content can change [Perry] |
| Full Idea: Although we classify ideas by content for many purposes, we do not individuate them by content. The content of an idea can change. | |
| From: John Perry (Knowledge, Possibility and Consciousness [2001], §3.2) | |
| A reaction: As the compiler of this database, I find this very appealing. The mind works exactly like a database. I have a 'file' (Perry's word) marked "London", the content of which undergoes continual change. I am a database management system. |
| 4896 | The intension of an expression is a function from possible worlds to an appropriate extension [Perry] |
| Full Idea: In possible-worlds semantics, expressions have intensions, which are functions from possible worlds to appropriate extensions (names to individuals, n-place predicates to n-tuples, and sentences to truth values, built from parts). | |
| From: John Perry (Knowledge, Possibility and Consciousness [2001], §8.1) | |
| A reaction: Interesting. Perry distinguishes 'referential' (or 'subject matter') content, which is prior to the link to extensions - a link which creates 'reflexive' content. He is keen that they should not become confused. True knowledge is 'situated'. |
| 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. |
| 4897 | A proposition is a set of possible worlds for which its intension delivers truth [Perry] |
| Full Idea: The proposition expressed by a sentence can be thought of as a set of possible worlds, the worlds for which its intension delivers truth. | |
| From: John Perry (Knowledge, Possibility and Consciousness [2001], §8.1) | |
| A reaction: It has always struck me as important to hang on to the concept of a 'proposition' (over and above sentences). This idea gives a metaphysics for the concept, and the 'language of thought' offers appropriate brain structures. A neat picture. |
| 4890 | A sharp analytic/synthetic line can rarely be drawn, but some concepts are central to thought [Perry] |
| Full Idea: Although there is seldom a sharp analytic/synthetic distinction to be drawn in the case of our concepts, there are clearly things that are more and less central. | |
| From: John Perry (Knowledge, Possibility and Consciousness [2001], §3.2) | |
| A reaction: Most Americans seem enslaved to Quine on this one, so it is nice to see the obvious being stated for once. Human thought is an organic offshoot of the natural world. To think it is all arbitrary and changeable is human arrogance. |
| 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. |