32 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. |
| 10017 | Truth in a model is more tractable than the general notion of truth [Hodes] |
| Full Idea: Truth in a model is interesting because it provides a transparent and mathematically tractable model - in the 'ordinary' rather than formal sense of the term 'model' - of the less tractable notion of truth. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.131) | |
| A reaction: This is an important warning to those who wish to build their entire account of truth on Tarski's rigorously formal account of the term. Personally I think we should start by deciding whether 'true' can refer to the mental state of a dog. I say it can. |
| 10018 | Truth is quite different in interpreted set theory and in the skeleton of its language [Hodes] |
| Full Idea: There is an enormous difference between the truth of sentences in the interpreted language of set theory and truth in some model for the disinterpreted skeleton of that language. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.132) | |
| A reaction: This is a warning to me, because I thought truth and semantics only entered theories at the stage of 'interpretation'. I must go back and get the hang of 'skeletal' truth, which sounds rather charming. [He refers to set theory, not to logic.] |
| 10015 | Higher-order logic may be unintelligible, but it isn't set theory [Hodes] |
| Full Idea: Brand higher-order logic as unintelligible if you will, but don't conflate it with set theory. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.131) | |
| A reaction: [he gives Boolos 1975 as a further reference] This is simply a corrective, because the conflation of second-order logic with set theory is an idea floating around in the literature. |
| 10011 | Identity is a level one relation with a second-order definition [Hodes] |
| Full Idea: Identity should he considered a logical notion only because it is the tip of a second-order iceberg - a level 1 relation with a pure second-order definition. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984]) |
| 10016 | When an 'interpretation' creates a model based on truth, this doesn't include Fregean 'sense' [Hodes] |
| Full Idea: A model is created when a language is 'interpreted', by assigning non-logical terms to objects in a set, according to a 'true-in' relation, but we must bear in mind that this 'interpretation' does not associate anything like Fregean senses with terms. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.131) | |
| A reaction: This seems like a key point (also made by Hofweber) that formal accounts of numbers, as required by logic, will not give an adequate account of the semantics of number-terms in natural languages. |
| 10027 | Mathematics is higher-order modal logic [Hodes] |
| Full Idea: I take the view that (agreeing with Aristotle) mathematics only requires the notion of a potential infinity, ...and that mathematics is higher-order modal logic. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984]) | |
| A reaction: Modern 'modal' accounts of mathematics I take to be heirs of 'if-thenism', which seems to have been Russell's development of Frege's original logicism. I'm beginning to think it is right. But what is the subject-matter of arithmetic? |
| 10026 | Arithmetic must allow for the possibility of only a finite total of objects [Hodes] |
| Full Idea: Arithmetic should be able to face boldly the dreadful chance that in the actual world there are only finitely many objects. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.148) | |
| A reaction: This seems to be a basic requirement for any account of arithmetic, but it was famously a difficulty for early logicism, evaded by making the existence of an infinity of objects into an axiom of the system. |
| 10021 | It is claimed that numbers are objects which essentially represent cardinality quantifiers [Hodes] |
| Full Idea: The mathematical object-theorist says a number is an object that represents a cardinality quantifier, with the representation relation as the entire essence of the nature of such objects as cardinal numbers like 4. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984]) | |
| A reaction: [compressed] This a classic case of a theory beginning to look dubious once you spell it our precisely. The obvious thought is to make do with the numerical quantifiers, and dispense with the objects. Do other quantifiers need objects to support them? |
| 10022 | Numerical terms can't really stand for quantifiers, because that would make them first-level [Hodes] |
| Full Idea: The dogmatic Frege is more right than wrong in denying that numerical terms can stand for numerical quantifiers, for there cannot be a language in which object-quantifiers and objects are simultaneously viewed as level zero. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.142) | |
| A reaction: Subtle. We see why Frege goes on to say that numbers are level zero (i.e. they are objects). We are free, it seems, to rewrite sentences containing number terms to suit whatever logical form appeals. Numbers are just quantifiers? |
| 21110 | An understanding of the most basic physics should explain all of the subject's mysteries [Krauss] |
| Full Idea: Once we understood the fundamental laws that govern forces of nature at its smallest scales, all of these current mysteries would be revealed as natural consequences of these laws. | |
| From: Lawrence M. Krauss (A Universe from Nothing [2012], 08) | |
| A reaction: This expresses the reductionist view within physics itself. Krauss says the discovery that empty space itself contains energy has led to a revision of this view (because that is not part of the forces and particles studied in basic physics). |
| 21105 | In 1676 it was discovered that water is teeming with life [Krauss] |
| Full Idea: Van Leeuwenhoek first stared at a drop of seemingly empty water with a microscope in 1676 and discovered in was teeming with life. | |
| From: Lawrence M. Krauss (A Universe from Nothing [2012], 04) | |
| A reaction: I am convinced that this had a huge influence on Leibniz's concept of monads. He immediately became convinced that it was some sort of life all the way down. He would be have been disappointed by the subsequent chemical reduction of life. |
| 10023 | Talk of mirror images is 'encoded fictions' about real facts [Hodes] |
| Full Idea: Talk about mirror images is a sort of fictional discourse. Statements 'about' such fictions are not made true or false by our whims; rather they 'encode' facts about the things reflected in mirrors. | |
| From: Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.146) | |
| A reaction: Hodes's proposal for how we should view abstract objects (c.f. Frege and Dummett on 'the equator'). The facts involved are concrete, but Hodes is offering 'encoding fictionalism' as a linguistic account of such abstractions. He applies it to numbers. |
| 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'? |
| 21109 | Space itself can expand (and separate its contents) at faster than light speeds [Krauss] |
| Full Idea: Special Relativity says nothing can travel 'through space' faster than the speed of light. But space itself can do whatever the heck it wants, at least in general relativity. And it can carry distant objects apart from one another at superluminal speeds | |
| From: Lawrence M. Krauss (A Universe from Nothing [2012], 06) | |
| A reaction: Another of my misunderstandings corrected. I assumed that the event horizon (limit of observability) was defined by the stuff retreating at (max) light speed. But beyond that it retreats even faster! What about the photons in space? |
| 21104 | General Relativity: the density of energy and matter determines curvature and gravity [Krauss] |
| Full Idea: The left-hand side of the general relativity equations descrbe the curvature of the universe, and the strength of gravitational forces acting on matter and radiation. The right-hand sides reflect the total density of all kinds of energy and matter. | |
| From: Lawrence M. Krauss (A Universe from Nothing [2012], 04) | |
| A reaction: I had assumed that the equations just described the geometry. In fact the matter determines the nature of the universe in which it exists. Presumably only things with mass get a vote. |
| 21107 | Uncertainty says that energy can be very high over very short time periods [Krauss] |
| Full Idea: The Heisenberg Uncertainty Principle says that the uncertainty in the measured energy of a system is inversely proportional to the length of time over which you observe it. (This allow near infinite energy over very short times). | |
| From: Lawrence M. Krauss (A Universe from Nothing [2012], 04) | |
| A reaction: Apparently this brief energy is 'borrowed', and must be quickly repaid. |
| 21106 | Most of the mass of a proton is the energy in virtual particles (rather than the quarks) [Krauss] |
| Full Idea: The quarks provide very little of the total mass of a proton, and the fields created by the virtual particles contribute most of the energy that goes into the proton's rest energy and, hence, its mass. | |
| From: Lawrence M. Krauss (A Universe from Nothing [2012], 04) | |
| A reaction: He gives an artist's impression of the interior of a proton, which looks like a ship's engine room. |
| 21112 | Empty space contains a continual flux of brief virtual particles [Krauss] |
| Full Idea: Empty space is complicated. It is a boiling brew of virtual particles that pop in and out of existence in a time so short we cannot see them directly. | |
| From: Lawrence M. Krauss (A Universe from Nothing [2012], 10) | |
| A reaction: Apparently the interior of a proton is also like this. This fact gives a foot in the door for explanations of how the Big Bang got started, from these virtual particles. And yet surely space itself only arrives with the Big Bang? |
| 21108 | The universe is precisely 13.72 billion years old [Krauss] |
| Full Idea: We now know the age of the universe to four significant figures. It is 13.72 billion years old! | |
| From: Lawrence M. Krauss (A Universe from Nothing [2012], 05) | |
| A reaction: It amazes me how many people, especially in philosophy, would be reluctant to accept that this is a know fact. I'm not accepting its certainty, but an assertion like this from a leading figure is good enough for me, and it should be for you. |
| 21111 | It seems likely that cosmic inflation is eternal, and this would make a multiverse inevitable [Krauss] |
| Full Idea: A multiverse is inevitable if inflation is eternal, and eternal inflation is by far the most likely possibility in most, if not all, inflationary scenarios. | |
| From: Lawrence M. Krauss (A Universe from Nothing [2012], 08) |