25 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. |
10001 | An adjective contributes semantically to a noun phrase [Hofweber] |
Full Idea: The semantic value of a determiner (an adjective) is a function from semantic values to nouns to semantic values of full noun phrases. | |
From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §3.1) | |
A reaction: This kind of states the obvious (assuming one has a compositional view of sentences), but his point is that you can't just eliminate adjectival uses of numbers by analysing them away, as if they didn't do anything. |
10007 | Quantifiers for domains and for inference come apart if there are no entities [Hofweber] |
Full Idea: Quantifiers have two functions in communication - to range over a domain of entities, and to have an inferential role (e.g. F(t)→'something is F'). In ordinary language these two come apart for singular terms not standing for any entities. | |
From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §6.3) | |
A reaction: This simple observations seems to me to be wonderfully illuminating of a whole raft of problems, the sort which logicians get steamed up about, and ordinary speakers don't. Context is the key to 90% of philosophical difficulties (?). See Idea 10008. |
10002 | '2 + 2 = 4' can be read as either singular or plural [Hofweber] |
Full Idea: There are two ways to read to read '2 + 2 = 4', as singular ('two and two is four'), and as plural ('two and two are four'). | |
From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §4.1) | |
A reaction: Hofweber doesn't notice that this phenomenon occurs elsewhere in English. 'The team is playing well', or 'the team are splitting up'; it simply depends whether you are holding the group in though as an entity, or as individuals. Important for numbers. |
9998 | What is the relation of number words as singular-terms, adjectives/determiners, and symbols? [Hofweber] |
Full Idea: There are three different uses of the number words: the singular-term use (as in 'the number of moons of Jupiter is four'), the adjectival (or determiner) use (as in 'Jupiter has four moons'), and the symbolic use (as in '4'). How are they related? | |
From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §1) | |
A reaction: A classic philosophy of language approach to the problem - try to give the truth-conditions for all three types. The main problem is that the first one implies that numbers are objects, whereas the others do not. Why did Frege give priority to the first? |
10003 | Why is arithmetic hard to learn, but then becomes easy? [Hofweber] |
Full Idea: Why is arithmetic so hard to learn, and why does it seem so easy to us now? For example, subtracting 789 from 26,789. | |
From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §4.2) | |
A reaction: His answer that we find thinking about objects very easy, but as children we have to learn with difficulty the conversion of the determiner/adjectival number words, so that we come to think of them as objects. |
10008 | Arithmetic is not about a domain of entities, as the quantifiers are purely inferential [Hofweber] |
Full Idea: I argue for an internalist conception of arithmetic. Arithmetic is not about a domain of entities, not even quantified entities. Quantifiers over natural numbers occur in their inferential-role reading in which they merely generalize over the instances. | |
From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §6.3) | |
A reaction: Hofweber offers the hope that modern semantics can disentangle the confusions in platonist arithmetic. Very interesting. The fear is that after digging into the semantics for twenty years, you find the same old problems re-emerging at a lower level. |
10005 | Arithmetic doesn’t simply depend on objects, since it is true of fictional objects [Hofweber] |
Full Idea: That 'two dogs are more than one' is clearly true, but its truth doesn't depend on the existence of dogs, as is seen if we consider 'two unicorns are more than one', which is true even though there are no unicorns. | |
From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §6.2) | |
A reaction: This is an objection to crude empirical accounts of arithmetic, but the idea would be that there is a generalisation drawn from objects (dogs will do nicely), which then apply to any entities. If unicorns are entities, it will be true of them. |
10000 | We might eliminate adjectival numbers by analysing them into blocks of quantifiers [Hofweber] |
Full Idea: Determiner uses of number words may disappear on analysis. This is inspired by Russell's elimination of the word 'the'. The number becomes blocks of first-order quantifiers at the level of semantic representation. | |
From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §2) | |
A reaction: [compressed] The proposal comes from platonists, who argue that numbers cannot be analysed away if they are objects. Hofweber says the analogy with Russell is wrong, as 'the' can't occur in different syntactic positions, the way number words can. |
10006 | First-order logic captures the inferential relations of numbers, but not the semantics [Hofweber] |
Full Idea: Representing arithmetic formally we do not primarily care about semantic features of number words. We are interested in capturing the inferential relations of arithmetical statements to one another, which can be done elegantly in first-order logic. | |
From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §6.3) | |
A reaction: This begins to pinpoint the difference between the approach of logicists like Frege, and those who are interested in the psychology of numbers, and the empirical roots of numbers in the process of counting. |
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. |
10004 | Our minds are at their best when reasoning about objects [Hofweber] |
Full Idea: Our minds mainly reason about objects. Most cognitive problems we are faced with deal with particular objects, whether they are people or material things. Reasoning about them is what our minds are good at. | |
From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §4.3) | |
A reaction: Hofweber is suggesting this as an explanation of why we continually reify various concepts, especially numbers. Very plausible. It works for qualities of character, and explains our tendency to talk about universals as objects ('redness'). |
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'? |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |