43 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) |
| 21982 | I only wish I had such eyes as to see Nobody! It's as much as I can do to see real people. [Carroll,L] |
| Full Idea: "I see nobody on the road," said Alice. - "I only wish I had such eyes," the King remarked. ..."To be able to see Nobody! ...Why, it's as much as I can do to see real people." | |
| From: Lewis Carroll (C.Dodgson) (Through the Looking Glass [1886], p.189), quoted by A.W. Moore - The Evolution of Modern Metaphysics 07.7 | |
| A reaction: [Moore quotes this, inevitably, in a chapter on Hegel] This may be a better candidate for the birth of philosophy of language than Frege's Groundwork. |
| 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. |
| 4938 | Prior to language, concepts are universals created by self-mapping of brain activity [Edelman/Tononi] |
| Full Idea: Before language is present, concepts depend on the brain's ability to construct 'universals' through higher-order mapping of the activity of the brain's own perceptual and motor maps. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch.15) | |
| A reaction: It should be of great interest to philosophers that one can begin to give a neuro-physiological account of universals. A physical system can be ordered as a database, and universals are the higher branches of a tree-structure of information. |
| 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. |
| 4934 | Cultures have a common core of colour naming, based on three axes of colour pairs [Edelman/Tononi] |
| Full Idea: We seem to have a set of colour axes (red-green, blue-yellow, and light-dark). Color naming in different cultures tend to have universal categories based on these axes, with a few derived or composite categories (e.g. orange, purple, pink, brown, grey). | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch.13) | |
| A reaction: This confirms my view of all supposed relativism: that there are degrees of cultural and individual relativism possible, but it is daft to think this goes all the way down, as nature has 'joints', and our minds are part of nature. |
| 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. |
| 4924 | A conscious human being rapidly reunifies its mind after any damage to the brain [Edelman/Tononi] |
| Full Idea: It seems that after a massive stroke or surgical resection, a conscious human being is rapidly "resynthesised" or reunified within the limits of a solipsistic universe that, to outside appearances, is warped and restricted. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch. 3) | |
| A reaction: Note that there are two types of 'unity of mind'. This comment refers to the unity of seeing oneself as a single person, rather than the smooth unbroken quality of conscious experience. I presume that there is no point in a mind without the first unity. |
| 4932 | A conscious state endures for about 100 milliseconds, known as the 'specious present' [Edelman/Tononi] |
| Full Idea: The 'specious present' (William James), a rough estimate of the duration of a single conscious state, is of the order of 100 milliseconds, meaning that conscious states can change very rapidly. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch.12) | |
| A reaction: A vital feature of our subjective experience of time. I wonder what the figure is for a fly? It suggests that conscious experience really is like a movie film, composed of tiny independent 'frames' of very short duration. |
| 4931 | Consciousness is a process (of neural interactions), not a location, thing, property, connectivity, or activity [Edelman/Tononi] |
| Full Idea: Consciousness is neither a thing, nor a simple property. ..The conscious 'dynamic core' of the brain is a process, not a thing or a place, and is defined in terms of neural interactions, not in terms of neural locations, connectivity or activity. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch.12) | |
| A reaction: This must be of great interest to philosophers. Edelman is adamant that it is not any specific neurons. The nice question is: what would it be like to have your brain slowed down? Presumably we would experience steps in the process. Is he a functionalist? |
| 4923 | The three essentials of conscious experience are privateness, unity and informativeness [Edelman/Tononi] |
| Full Idea: The fundamental aspects of conscious experience that are common to all its phenomenological manifestations are: privateness, unity, and informativeness. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch. 3) | |
| A reaction: Interesting, coming from neuroscientists. The list strikes me as rather passive. It is no use having good radar if you can't make decisions. Privacy and unity are overrated. Who gets 'informed'? Personal identity must be basic. |
| 4941 | Consciousness can create new axioms, but computers can't do that [Edelman/Tononi] |
| Full Idea: Conscious human thought can create new axioms, which a computer cannot do. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch.17) | |
| A reaction: A nice challenge for the artificial intelligence community! I don't understand their confidence in making this assertion. Nothing in Gödel's Theorem seems to prevent the reassignment of axioms, and Quine implies that it is an easy and trivial game. |
| 4930 | Consciousness arises from high speed interactions between clusters of neurons [Edelman/Tononi] |
| Full Idea: Our hypothesis is that the activity of a group of neurons can contribute directly to conscious experience if it is part of a functional cluster, characterized by strong interactions among a set of neuronal groups over a period of hundreds of milliseconds. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch.12) | |
| A reaction: This is their 'dynamic core' hypothesis. It doesn't get at the Hard Questions about consciousness, but this is a Nobel prize winner hot on the trail of the location of the action. It gives support to functionalism, because the neurons vary. |
| 4929 | Dreams and imagery show the brain can generate awareness and meaning without input [Edelman/Tononi] |
| Full Idea: Dreaming and imagery are striking phenomenological demonstrations that the adult brain can spontaneously and intrinsically produce consciousness and meaning without any direct input from the periphery. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch.11) | |
| A reaction: This offers some support for Searle's claim that brain's produce 'intrinsic' (rather than 'derived') intentionality. Of course, one can have a Humean impressions/ideas theory about how the raw material got there. We SEE meaning in our experiences. |
| 4940 | Physicists see information as a measure of order, but for biologists it is symbolic exchange between animals [Edelman/Tononi] |
| Full Idea: Physicists may define information as a measure of order in a far-from-equilibrium state, but it is best seen as a biological concept which emerged in evolution with animals that were capable of mutual symbolic exchange. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch.17) | |
| A reaction: The physicists' definition seems to open the road to the possibility of non-conscious intentionality (Dennett), where the biological view seems to require consciousness of symbolic meanings (Searle). Tree-rings contain potential information? |
| 4935 | The sensation of red is a point in neural space created by dimensions of neuronal activity [Edelman/Tononi] |
| Full Idea: The pure sensation of red is a particular neural state identified by a point within the N-dimensional neural space defined by the integrated activity of all the group of neurons that constitute the dynamic core. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch.13) | |
| A reaction: This hardly answers the Hard Question (why experience it? why that experience?), but it is interesting to see a neuroscientist fishing for an account of qualia. He says three types of neuron firing generate the dimensions of the 'space'. |
| 4936 | The self is founded on bodily awareness centred in the brain stem [Edelman/Tononi] |
| Full Idea: Structures in the brain stem map the state of the body and its relation to the environment, on the basis of signals with proprioceptive, kinesthetic, somatosensory and autonomic components. We may call these the dimensions of the proto-self. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch.13) | |
| A reaction: It seems to me that there is no free will, but moral responsibility depends on the existence of a Self, and philosophers had better fight for it (are you listening, Hume?). Fortunately neuroscientists seem to endorse it fairly unanimously. |
| 4939 | A sense of self begins either internally, or externally through language and society [Edelman/Tononi] |
| Full Idea: Two extreme views on the development of the self are 'internalist' and 'externalist'. The first starts with a baby's subjective experience, and increasing differentiation as self-consciousness develops. The externalist view requires language and society. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch.15) | |
| A reaction: Edelman rightly warns against this simple dichotomy, but if I have to vote, it is for internalism. I take a sense of self as basic to any mind, even a slug's. What is a mind for, if not to look after the creature? Self makes sensation into mind. |
| 4925 | Brains can initiate free actions before the person is aware of their own decision [Edelman/Tononi] |
| Full Idea: Libet concluded that the cerebral initiation of a spontaneous, freely voluntary act can begin unconsciously, that is, before there is any recallable awareness that a decision to act has already been initiated cerebrally. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch. 6) | |
| A reaction: We should accept this result. 'Free will' was always a bogus metaphysical concept (invented, I think, because God had to be above natural laws). A person is the source of responsibility, and is the controller of the brain, but not entirely conscious. |
| 4933 | Consciousness is a process, not a thing, as it maintains unity as its composition changes [Edelman/Tononi] |
| Full Idea: The conscious 'dynamic core' of the brain can maintain its unity over time even if its composition may be constantly changing, which is the signature of a process as opposed to a thing. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch.12) | |
| A reaction: This is the functionalists' claim that the mind is 'multiply realisable', since different neurons can maintain the same process. 'Process' strikes me as a much better word than 'function'. These theories capture passive mental life better than active. |
| 4928 | Brain complexity balances segregation and integration, like a good team of specialists [Edelman/Tononi] |
| Full Idea: A theoretical analysis of complexity suggests that neuronal complexity strikes an optimum balance between segregation and integration, which fits the view of the brain as a collection of specialists who talk to each other a lot. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch.11) | |
| A reaction: This is a theoretical point, but comes from a leading neuroscientist, and seems to endorse Fodor's modularity proposal. For a philosopher, one of the issues here is how to reconcile the segregation with the Cartesian unity and personal identity of a mind. |
| 4927 | Information-processing views of the brain assume the existence of 'information', and dubious brain codes [Edelman/Tononi] |
| Full Idea: So-called information-processing views of the brain have been criticized because they typically assume the existence in the world of previously defined information, and often assume the existence of precise neural codes for which there is no evidence. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch.11) | |
| A reaction: Fodor is the target here. Searle is keen that 'intrinsic intentionality' is required to see something as 'information'. It is hard to see how anything acquires significance as it flows through a mechanical process. |
| 4922 | Consciousness involves interaction with persons and the world, as well as brain functions [Edelman/Tononi] |
| Full Idea: We emphatically do not identify consciousness in its full range as arising solely in the brain, since we believe that higher brain functions require interactions both with the world and with other persons. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Pref) | |
| A reaction: Would you gradually lose higher brain functions if you lived entirely alone? Intriguingly, this sounds like a neuroscientist asserting the necessity for broad content in order to understand the brain. |
| 5793 | Concepts and generalisations result from brain 'global mapping' by 'reentry' [Edelman/Tononi, by Searle] |
| Full Idea: When you get maps all over the brain signalling to each other by reentry you have what Edelman calls 'global mapping', and this allows the system not only to have perceptual categories and generalisation, but also to coordinate perception and action. | |
| From: report of G Edelman / G Tononi (Consciousness: matter becomes imagination [2000]) by John Searle - The Mystery of Consciousness Ch.3 | |
| A reaction: This is the nearest we have got to a proper scientific account of thought (as opposed to untested speculation about Turing machines). Something like this account must be right. A concept is a sustained process, not a static item. |
| 4926 | Concepts arise when the brain maps its own activities [Edelman/Tononi] |
| Full Idea: We propose that concepts arise from the mapping by the brain itself of the activity of the brain's own areas and regions. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch. 9) | |
| A reaction: Yes. One should add that the brain appears to be physically constructed with the logic of a filing system, which would mean that our concepts were labels for files within the system. Nature generates some of the files, and thinking creates the others. |
| 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. |
| 4937 | Systems that generate a sense of value are basic to the primitive brain [Edelman/Tononi] |
| Full Idea: Early and central in the development of the brain are the dimensions provided by value systems indicating salience for the entire organism. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch.13) | |
| A reaction: This doesn't quite meet Hume's challenge to find values in the whole of nature, but it matches Charles Taylor's claim that for humans values are knowable a priori. Conditional values can be facts of the whole of nature. "If there is life, x has value..". |
| 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. |