28 ideas
| 12456 | I aim to establish certainty for mathematical methods [Hilbert] |
| Full Idea: The goal of my theory is to establish once and for all the certitude of mathematical methods. | |
| From: David Hilbert (On the Infinite [1925], p.184) | |
| A reaction: This is the clearest statement of the famous Hilbert Programme, which is said to have been brought to an abrupt end by Gödel's Incompleteness Theorems. |
| 12461 | We believe all mathematical problems are solvable [Hilbert] |
| Full Idea: The thesis that every mathematical problem is solvable - we are all convinced that it really is so. | |
| From: David Hilbert (On the Infinite [1925], p.200) | |
| A reaction: This will include, for example, Goldbach's Conjecture (every even is the sum of two primes), which is utterly simple but with no proof anywhere in sight. |
| 9633 | No one shall drive us out of the paradise the Cantor has created for us [Hilbert] |
| Full Idea: No one shall drive us out of the paradise the Cantor has created for us. | |
| From: David Hilbert (On the Infinite [1925], p.191), quoted by James Robert Brown - Philosophy of Mathematics | |
| A reaction: This is Hilbert's famous refusal to accept any account of mathematics, such as Kant's, which excludes actual infinities. Cantor had laid out a whole glorious hierarchy of different infinities. |
| 12460 | We extend finite statements with ideal ones, in order to preserve our logic [Hilbert] |
| Full Idea: To preserve the simple formal rules of ordinary Aristotelian logic, we must supplement the finitary statements with ideal statements. | |
| From: David Hilbert (On the Infinite [1925], p.195) | |
| A reaction: I find very appealing the picture of mathematics as rooted in the physical world, and then gradually extended by a series of 'idealisations', which should perhaps be thought of as fictions. |
| 12462 | Only the finite can bring certainty to the infinite [Hilbert] |
| Full Idea: Operating with the infinite can be made certain only by the finitary. | |
| From: David Hilbert (On the Infinite [1925], p.201) | |
| A reaction: See 'Compactness' for one aspect of this claim. I think Hilbert was fighting a rearguard action, and his idea now has few followers. |
| 12455 | The idea of an infinite totality is an illusion [Hilbert] |
| Full Idea: Just as in the limit processes of the infinitesimal calculus, the infinitely large and small proved to be a mere figure of speech, so too we must realise that the infinite in the sense of an infinite totality, used in deductive methods, is an illusion. | |
| From: David Hilbert (On the Infinite [1925], p.184) | |
| A reaction: This is a very authoritative rearguard action. I no longer think the dispute matters much, it being just a dispute over a proposed new meaning for the word 'number'. |
| 12457 | There is no continuum in reality to realise the infinitely small [Hilbert] |
| Full Idea: A homogeneous continuum which admits of the sort of divisibility needed to realise the infinitely small is nowhere to be found in reality. | |
| From: David Hilbert (On the Infinite [1925], p.186) | |
| A reaction: He makes this remark as a response to Planck's new quantum theory (the year before the big works of Heisenberg and Schrödinger). Personally I don't see why infinities should depend on the physical world, since they are imaginary. |
| 12459 | The subject matter of mathematics is immediate and clear concrete symbols [Hilbert] |
| Full Idea: The subject matter of mathematics is the concrete symbols themselves whose structure is immediately clear and recognisable. | |
| From: David Hilbert (On the Infinite [1925], p.192) | |
| A reaction: I don't think many people will agree with Hilbert here. Does he mean token-symbols or type-symbols? You can do maths in your head, or with different symbols. If type-symbols, you have to explain what a type is. |
| 18112 | Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert] |
| Full Idea: We can conceive mathematics to be a stock of two kinds of formulas: first, those to which the meaningful communications of finitary statements correspond; and secondly, other formulas which signify nothing and which are ideal structures of our theory. | |
| From: David Hilbert (On the Infinite [1925], p.196), quoted by David Bostock - Philosophy of Mathematics 6.1 |
| 1350 | Continuity is needed for existence, otherwise we would say a thing existed after it ceased to exist [Reid] |
| Full Idea: Identity supposes an uninterrupted continuance of existence….Otherwise we must suppose a being to exist after it has ceased to exist, and to have existed before it was produced, which are manifest contradictions. | |
| From: Thomas Reid (Essays on Intellectual Powers 3: Memory [1785], III.Ch 4) | |
| A reaction: I take the point to be that if something is supposed to survive a gap in its existence, that must imply that it somehow exists during the gap. If a light flashes on and off, is it really a new entity each time? |
| 21322 | We treat slowly changing things as identical for the sake of economy in language [Reid] |
| Full Idea: All bodies, as they consist of innumerable parts, are subject to continual changes of their substance. When such changes are gradual, because language could not afford a different name for each state, it retains the same name and is considered the same. | |
| From: Thomas Reid (Essays on Intellectual Powers 3: Memory [1785], III.Ch 4) | |
| A reaction: This is hard to deny. We could hardly rename a child each morning. Simlarly, we can't have a unique name for each leaf on a tree. Economy of language explains a huge amount in philosophy. |
| 21320 | Identity is familiar to common sense, but very hard to define [Reid] |
| Full Idea: Every man of common sense has a clear and distinct notion of identity. If you ask for a definition of identity, I confess I can give none. It is too simple a notion. | |
| From: Thomas Reid (Essays on Intellectual Powers 3: Memory [1785], III.Ch 4) | |
| A reaction: 'Identical' seems to be a two-place predicate, but the only strict way two things can be identical is if there is actually just one thing. In which case just drop the word 'identity' (instead of defining it), and say there is just one thing here. |
| 1367 | Identity can only be affirmed of things which have a continued existence [Reid] |
| Full Idea: Identity can only be affirmed of things which have a continued existence. | |
| From: Thomas Reid (Essays on Intellectual Powers 3: Memory [1785], III.Ch 6) | |
| A reaction: This doesn't mean that Reid thinks there is nothing more to the identity than their similitude. But he, like Hume, denies that there is personal identity at any given instant. Reid is better at criticism than at formulating his own theory. |
| 9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
| Full Idea: The goal of my theory is to establish once and for all the certitude of mathematical methods. | |
| From: David Hilbert (On the Infinite [1925], p.184), quoted by James Robert Brown - Philosophy of Mathematics Ch.5 | |
| A reaction: This dream is famous for being shattered by Gödel's Incompleteness Theorem a mere six years later. Neverless there seem to be more limited certainties which are accepted in mathematics. The certainty of the whole of arithmetic is beyond us. |
| 23643 | We all trust our distinct memories (but not our distinct imaginings) [Reid] |
| Full Idea: Every man feels he must believe what he distinctly remembers, though he can give no other reason for his belief, but that he remembers the thing distinctly; whereas, when he merely distinctly imagines a thing, he has no belief in it upon that account. | |
| From: Thomas Reid (Essays on Intellectual Powers 3: Memory [1785], 1) | |
| A reaction: The word 'distinct' is doing some heavy work here. I fear that believing the memory is the only criterion we have for calling it distinct. As a boy I was persuaded to change my testimony about a car accident, and I realised I was not distinct about it. |
| 23644 | Without memory we could have no concept of duration [Reid] |
| Full Idea: It is impossible to show how we could acquire a notion of duration if we had no memory. | |
| From: Thomas Reid (Essays on Intellectual Powers 3: Memory [1785], 1) | |
| A reaction: We would probably not have a notion of duration if we possessed a memory, but nothing ever changed. Maybe in Shoemaker's frozen worlds they retain memories, but nothing happens? |
| 1356 | A person is a unity, and doesn't come in degrees [Reid] |
| Full Idea: The identity of a person is a perfect identity: wherever it is real, it admits of no degrees; and it is impossible that a person should be in part the same, and in part different; because a person is a 'monad', and is not divisible into parts. | |
| From: Thomas Reid (Essays on Intellectual Powers 3: Memory [1785], III.Ch 4) | |
| A reaction: I don't accept this, because I don't accept the metaphysics needed to underpin it. To watch a person with Alzheimer's disease fade out of existence before they die seems sufficient counter-evidence. I believe in personal identity, but it isn't 'perfect'. |
| 1359 | Personal identity is the basis of all rights, obligations and responsibility [Reid] |
| Full Idea: Identity, when applied to persons, has no ambiguity, and admits of no degrees. It is the foundation of all rights and obligations, and of all accountableness. | |
| From: Thomas Reid (Essays on Intellectual Powers 3: Memory [1785], III.Ch 4) | |
| A reaction: This seems to me to be one of the key mistakes in all of philosophy - thinking that items must always be all-or-nothing. If a person deteriorates through Alzheimer's, there seem to be obvious degrees of personhood. Responsibility comes in degrees, too. |
| 21319 | I can hardly care about rational consequence if it wasn't me conceiving the antecedent [Reid] |
| Full Idea: The conviction of personal identity is indispensably necessary to all exercise of reason. Reasoning is made up of successive parts. Without the conviction that the antecedent have been seen by me, I could have no reason to proceed to the consequent. | |
| From: Thomas Reid (Essays on Intellectual Powers 3: Memory [1785], III.Ch 4) | |
| A reaction: Society needs philosophers precisely to point such things out. It isn't conclusive, but populist waffle about the self not existing undermines the very concept of a 'train of thought', which everybody is signed up to. Trains of thought can take years. |
| 21323 | The identity of a thief is only known by similarity, but memory gives certainty in our own case [Reid] |
| Full Idea: A man challenges a thief in possession of his horse only on similarity. The testimony of witnesses to the identity of a person is commonly grounded on no other evidence. ...Evidence of our own identity is grounded in memory, and gives undoubted certainty. | |
| From: Thomas Reid (Essays on Intellectual Powers 3: Memory [1785], III.Ch 4) | |
| A reaction: With other people the best we can hope for is type-identity, hoping that each individual being is a unique type, but with otherselves we are always confident of establishing token identity. Could I have been someone different yesterday, without realising? |
| 21321 | Memory reveals my past identity - but so does testimony of other witnesses [Reid] |
| Full Idea: Although memory gives the most irresistible evidence of my being the identical person that did such a thing, I may have other good evidence of things which befell me. I know who bare me and suckled me, but I do not remember those events. | |
| From: Thomas Reid (Essays on Intellectual Powers 3: Memory [1785], III.Ch 4) | |
| A reaction: A splendidly accurate and simple observation. Reid's criticisms of Locke are greatly superior to those of Butler. We now have vast collections of photographs showing our past identities. |
| 21324 | If consciousness is transferable 20 persons can be 1; forgetting implies 1 can be 20 [Reid] |
| Full Idea: If the same consciousness can be transferred from one intelligent being to another, then two or twenty beings may be the same person. If he may lose the consciousness of actions done by him, one intelligent being may be two or twenty different persons. | |
| From: Thomas Reid (Essays on Intellectual Powers 3: Memory [1785], III.Ch 6) | |
| A reaction: Reid says Locke was aware of these two implications of his theory of personal identity (based on consciousness). The first example is me replicated like software. The second is if I forget that I turned the light off, then who did turn the light off? |
| 21325 | Boy same as young man, young man same as old man, old man not boy, if forgotten! [Reid] |
| Full Idea: Suppose a brave officer, flogged as a boy for robbing an orchard, to have captured a standard in his first campaign, and become a general in advanced life. [If the general forgets the flogging] he is and at the same time is not the same as the boy. | |
| From: Thomas Reid (Essays on Intellectual Powers 3: Memory [1785], III.Ch 6) | |
| A reaction: The point is that strict identity has to be transitive, and if the general forgets his boyhood that breaks the transitivity. If identity is less strict there is no problem. The general may only have memories related to some part of his boyhood. |
| 21327 | If a stolen horse is identified by similitude, its identity is not therefore merely similitude [Reid] |
| Full Idea: When a stolen horse is claimed, the only evidence that this is the same horse is similitude. But would it not be ridiculous from this to infer that the identity of a horse consists in similitude only? | |
| From: Thomas Reid (Essays on Intellectual Powers 3: Memory [1785], III.Ch 6) | |
| A reaction: Actually that is exactly Hume's view of the matter (Idea 21292). For a strict empiricist there is nothing else be close resemblance over time. I prefer Reid's account to Hume's. - but then I am not a 'strict' empiricist. |
| 1366 | If consciousness is personal identity, it is continually changing [Reid] |
| Full Idea: Is it not strange that the identity of a person should consist in a thing (consciousness) which is continually changing? | |
| From: Thomas Reid (Essays on Intellectual Powers 3: Memory [1785], III.Ch 6) | |
| A reaction: This is the panicky slippery slope view of Locke, that sees his doctrine as the first step to the destruction of religion. The fact is, though, that parts of my consciousness changes continually, but other parts stay the same for years on end. |
| 1352 | Thoughts change continually, but the self doesn't [Reid] |
| Full Idea: My thoughts, and actions, and feelings, change every moment: they have no continued, but a successive, existence: but that self, or I, to which they belong, is permanent. | |
| From: Thomas Reid (Essays on Intellectual Powers 3: Memory [1785], III.Ch 4) | |
| A reaction: The word 'permanent' may be excessive, but one could hardly say there is nothing more to personal identity than the contents of consciousnes, given how much and how quickly those continually fluctuate. |
| 7861 | Libet says the processes initiated in the cortex can still be consciously changed [Libet, by Papineau] |
| Full Idea: Libet himself points out that the conscious decisions still have the power to 'endorse' or 'cancel', so to speak, the processes initiated by the earlier cortical activity: no action will result if the action's execution is consciously countermanded. | |
| From: report of Benjamin Libet (Unconscious Cerebral Initiative [1985]) by David Papineau - Thinking about Consciousness 1.4 | |
| A reaction: This is why Libet's findings do not imply 'epiphenomenalism'. It seems that part of a decisive action is non-conscious, undermining the all-or-nothing view of consciousness. Searle tries to smuggle in free will at this point (Idea 3817). |
| 6660 | Libet found conscious choice 0.2 secs before movement, well after unconscious 'readiness potential' [Libet, by Lowe] |
| Full Idea: Libet found that a subject's conscious choice to move was about a fifth of a second before movement, and thus later than the onset of the brain's so-called 'readiness potential', which seems to imply that unconscious processes initiates action. | |
| From: report of Benjamin Libet (Unconscious Cerebral Initiative [1985]) by E.J. Lowe - Introduction to the Philosophy of Mind Ch.9 | |
| A reaction: Of great interest to philosophers! It seems to make conscious choices epiphenomenal. The key move, I think, is to give up the idea of consciousness as being all-or-nothing. My actions are still initiated by 'me', but 'me' shades off into unconsciousness. |