20 ideas
| 5331 | You can't infer that because you have a hidden birth-mark, everybody else does [Ayer] |
| Full Idea: My knowing that I had a hidden birth-mark would not entitle me to infer with any great degree of confidence that the same was true of everybody else. | |
| From: A.J. Ayer (The Central Questions of Philosophy [1973], §VI.E) | |
| A reaction: This is the notorious 'induction from a single case' which was used by Mill to prove that other minds exist. It is a very nice illustration of the weakness of arguments from analogy. Probably analogy on its own is useless, but is a key part of induction. |
| 17963 | The facts of geometry, arithmetic or statics order themselves into theories [Hilbert] |
| Full Idea: The facts of geometry order themselves into a geometry, the facts of arithmetic into a theory of numbers, the facts of statics, electrodynamics into a theory of statics, electrodynamics, or the facts of the physics of gases into a theory of gases. | |
| From: David Hilbert (Axiomatic Thought [1918], [03]) | |
| A reaction: This is the confident (I would say 'essentialist') view of axioms, which received a bit of a setback with Gödel's Theorems. I certainly agree that the world proposes an order to us - we don't just randomly invent one that suits us. |
| 17966 | Axioms must reveal their dependence (or not), and must be consistent [Hilbert] |
| Full Idea: If a theory is to serve its purpose of orienting and ordering, it must first give us an overview of the independence and dependence of its propositions, and second give a guarantee of the consistency of all of the propositions. | |
| From: David Hilbert (Axiomatic Thought [1918], [09]) | |
| A reaction: Gödel's Second theorem showed that the theory can never prove its own consistency, which made the second Hilbert requirement more difficult. It is generally assumed that each of the axioms must be independent of the others. |
| 17967 | To decide some questions, we must study the essence of mathematical proof itself [Hilbert] |
| Full Idea: It is necessary to study the essence of mathematical proof itself if one wishes to answer such questions as the one about decidability in a finite number of operations. | |
| From: David Hilbert (Axiomatic Thought [1918], [53]) |
| 17965 | The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert] |
| Full Idea: The linearity of the equation of the plane and of the orthogonal transformation of point-coordinates is completely adequate to produce the whole broad science of spatial Euclidean geometry purely by means of analysis. | |
| From: David Hilbert (Axiomatic Thought [1918], [05]) | |
| A reaction: This remark comes from the man who succeeded in producing modern axioms for geometry (in 1897), so he knows what he is talking about. We should not be wholly pessimistic about Hilbert's ambitious projects. He had to dig deeper than this idea... |
| 17964 | Number theory just needs calculation laws and rules for integers [Hilbert] |
| Full Idea: The laws of calculation and the rules of integers suffice for the construction of number theory. | |
| From: David Hilbert (Axiomatic Thought [1918], [05]) | |
| A reaction: This is the confident Hilbert view that the whole system can be fully spelled out. Gödel made this optimism more difficult. |
| 2611 | It is currently held that quantifying over something implies belief in its existence [Ayer] |
| Full Idea: It is currently held that we are committed to a belief in the existence of anything over which we quantify. | |
| From: A.J. Ayer (The Central Questions of Philosophy [1973], IX.C) |
| 16520 | We see properties necessary for a kind (in the definition), but not for an individual [Ayer] |
| Full Idea: We can significantly ask what properties it is necessary for something to possess in order to be a thing of such and such a kind, since that asks what properties enter into the definition of the kind. But there is no such definition of the individual. | |
| From: A.J. Ayer (The Central Questions of Philosophy [1973], 9.A.5) | |
| A reaction: [Quoted, not surprisingly, by Wiggins] Illuminating. If essence is just about necessary properties, I begin to see why the sortal might be favoured. I take it to concern explanatory mechanisms, and hence the individual. |
| 2613 | The theory of other minds has no rival [Ayer] |
| Full Idea: The theory that other people besides oneself have mental states is one that has no serious rival. | |
| From: A.J. Ayer (The Central Questions of Philosophy [1973], §VI.E) | |
| A reaction: See 3463, where Searle says there is no such thing as our "theory" about other minds. In a science fiction situation (see 'Blade Runner'), this unrivalled theory could quickly unravel. It could even be a fact that you are the only humanoid with a mind. |
| 5328 | Originally I combined a mentalistic view of introspection with a behaviouristic view of other minds [Ayer] |
| Full Idea: In 1936 I combined a mentalistic analysis of the propositions in which one attributes experiences to oneself with a behaviouristic analysis of the propositions in which one attributes experiences to others. | |
| From: A.J. Ayer (The Central Questions of Philosophy [1973], §VI.D) | |
| A reaction: He then criticises his view for inconsistency. Ryle preferred a behaviouristic account of introspection, but Ayer calls this 'ridiculous'. Ayer hunts for a compromise, but then settles for the right answer, which makes mentalism the 'best explanation'. |
| 5330 | Physicalism undercuts the other mind problem, by equating experience with 'public' brain events [Ayer] |
| Full Idea: The acceptance of physicalism undercuts the other minds problem by equating experiences with events in the brain, which are publicly observable. | |
| From: A.J. Ayer (The Central Questions of Philosophy [1973], §VI.E) | |
| A reaction: It strikes me that if we could actually observe the operations of one another's brains, a great many of the problems of philosophy would never have appeared in the first place. Imagine a transparent skull and brain, with coloured waves moving through it. |
| 5326 | Qualia must be united by a subject, because they lead to concepts and judgements [Ayer] |
| Full Idea: The ground for thinking that qualia are only experiences because they relate to a unifying subject is that they have to be identified, by being brought under concepts, and giving rise to judgements which usually go beyond them. | |
| From: A.J. Ayer (The Central Questions of Philosophy [1973], §VI.B) | |
| A reaction: Thus one of Hume's greatest fans gives the clearest objection to Hume. It strikes me as a very powerful objection, better than anything Carruthers offers (1394,1395,1396). The conceptual element is very hard to disentangle from the qualia. |
| 5325 | Is something an 'experience' because it relates to other experiences, or because it relates to a subject? [Ayer] |
| Full Idea: Is the character of being an item of experience one that can accrue to a quale through its relation to other qualia, or must it consist in a relation to a subject, which is conscious of these elements and distinct from them? | |
| From: A.J. Ayer (The Central Questions of Philosophy [1973], §VI.B) | |
| A reaction: When nicely put like this, it is hard to see how qualia could be experiences just because they relate to one another. It begs the question of what is causing the relationship. There seems to be a Cogito-like assumption of a thinker. |
| 5324 | Bodily identity and memory work together to establish personal identity [Ayer] |
| Full Idea: In general the two criteria of memory and bodily identity work together. | |
| From: A.J. Ayer (The Central Questions of Philosophy [1973], §VI.B) | |
| A reaction: This seems better than any simplistic one-criterion approach. In life we use different criteria for our own identity, as when dreaming, or waking with a hangover, or wondering if we are dead after an accident. |
| 5322 | Self-consciousness is not basic, because experiences are not instrinsically marked with ownership [Ayer] |
| Full Idea: Self-consciousness is not a primitive datum, or in other words the observer's experiences are not intrinsically marked as his own. | |
| From: A.J. Ayer (The Central Questions of Philosophy [1973], §VI.A) | |
| A reaction: This is a very Humean, ruthlessly empiricist view of the matter. Plenty of philosophers (existentialists, or Charles Taylor) would say that our experiences have our interests or values built into them. Why are they experiences, and not just events? |
| 5327 | Temporal gaps in the consciousness of a spirit could not be bridged by memories [Ayer] |
| Full Idea: If there were temporal gaps in the consciousness of disembodied spirits, the occurrences of memory-experiences would not be sufficient to bridge them. | |
| From: A.J. Ayer (The Central Questions of Philosophy [1973], §VI.C) | |
| A reaction: Ayer is very sympathetic to the idea that the body is a key ingredient in personal identity. Without a body, there would be no criteria at all for the continuity of a spirit which lost consciousness for a while, since consciousness is all it is. |
| 5329 | Why shouldn't we say brain depends on mind? Better explanation! [Ayer] |
| Full Idea: If mind and brain exactly correspond we have as good ground for saying the brain depends on the mind as the other way round; if predominance is given to the brain, the reason is that it fits into a wider explanatory system. | |
| From: A.J. Ayer (The Central Questions of Philosophy [1973], §VI.D) | |
| A reaction: A small but significant point. If an 'identity' theory is to be developed, then this step in the argument has to be justified. It is tempting here to move to the eliminativist view, because we no longer have to worry about a 'direction of priority'. |
| 2610 | Talk of propositions is just shorthand for talking about equivalent sentences [Ayer] |
| Full Idea: Our talk of propositions should not be regarded as anything more than a concise way of talking about equivalent sentences. | |
| From: A.J. Ayer (The Central Questions of Philosophy [1973], IX.C) | |
| A reaction: Wrong, though I can see why he says it. We struggle to express difficult propositions by offering several similar (but not equivalent) sentences. What is the criterion for deciding his 'equivalence'? |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
| 17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |
| Full Idea: By pushing ahead to ever deeper layers of axioms ...we also win ever-deeper insights into the essence of scientific thought itself, and become ever more conscious of the unity of our knowledge. | |
| From: David Hilbert (Axiomatic Thought [1918], [56]) | |
| A reaction: This is the less fashionable idea that scientific essentialism can also be applicable in the mathematic sciences, centring on the project of axiomatisation for logic, arithmetic, sets etc. |