50 ideas
| 10702 | Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter] |
| Full Idea: Set theory has three roles: as a means of taming the infinite, as a supplier of the subject-matter of mathematics, and as a source of its modes of reasoning. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], Intro 1) | |
| A reaction: These all seem to be connected with mathematics, but there is also ontological interest in set theory. Potter emphasises that his second role does not entail a commitment to sets 'being' numbers. |
| 10713 | Usually the only reason given for accepting the empty set is convenience [Potter] |
| Full Idea: It is rare to find any direct reason given for believing that the empty set exists, except for variants of Dedekind's argument from convenience. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 04.3) |
| 13044 | Infinity: There is at least one limit level [Potter] |
| Full Idea: Axiom of Infinity: There is at least one limit level. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 04.9) | |
| A reaction: A 'limit ordinal' is one which has successors, but no predecessors. The axiom just says there is at least one infinity. |
| 10708 | Nowadays we derive our conception of collections from the dependence between them [Potter] |
| Full Idea: It is only quite recently that the idea has emerged of deriving our conception of collections from a relation of dependence between them. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.2) | |
| A reaction: This is the 'iterative' view of sets, which he traces back to Gödel's 'What is Cantor's Continuum Problem?' |
| 13546 | The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter] |
| Full Idea: We group under the heading 'limitation of size' those principles which classify properties as collectivizing or not according to how many objects there are with the property. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 13.5) | |
| A reaction: The idea was floated by Cantor, toyed with by Russell (1906), and advocated by von Neumann. The thought is simply that paradoxes start to appear when sets become enormous. |
| 10707 | Mereology elides the distinction between the cards in a pack and the suits [Potter] |
| Full Idea: Mereology tends to elide the distinction between the cards in a pack and the suits. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 02.1) | |
| A reaction: The example is a favourite of Frege's. Potter is giving a reason why mathematicians opted for set theory. I'm not clear, though, why a pack cannot have either 4 parts or 52 parts. Parts can 'fall under a concept' (such as 'legs'). I'm puzzled. |
| 10704 | We can formalize second-order formation rules, but not inference rules [Potter] |
| Full Idea: In second-order logic only the formation rules are completely formalizable, not the inference rules. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 01.2) | |
| A reaction: He cites Gödel's First Incompleteness theorem for this. |
| 10703 | Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter] |
| Full Idea: A 'supposition' axiomatic theory is as concerned with truth as a 'realist' one (with undefined terms), but the truths are conditional. Satisfying the axioms is satisfying the theorem. This is if-thenism, or implicationism, or eliminative structuralism. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 01.1) | |
| A reaction: Aha! I had failed to make the connection between if-thenism and eliminative structuralism (of which I am rather fond). I think I am an if-thenist (not about all truth, but about provable truth). |
| 10712 | If set theory didn't found mathematics, it is still needed to count infinite sets [Potter] |
| Full Idea: Even if set theory's role as a foundation for mathematics turned out to be wholly illusory, it would earn its keep through the calculus it provides for counting infinite sets. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.8) |
| 17882 | It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter] |
| Full Idea: It is a remarkable fact that all the arithmetical properties of the natural numbers can be derived from such a small number of assumptions (as the Peano Axioms). | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 05.2) | |
| A reaction: If one were to defend essentialism about arithmetic, this would be grist to their mill. I'm just saying. |
| 3942 | I do not believe in the existence of anything, if I see no reason to believe it [Berkeley] |
| Full Idea: It is to me a sufficient reason not to believe the existence of anything, if I see no reason for believing it. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], II p.205) | |
| A reaction: This may just be a reasonable application of Ockham's Razor, but I fear that Berkeley painted himself into corner by demanding too many 'reasons' for everything. |
| 3952 | I know that nothing inconsistent can exist [Berkeley] |
| Full Idea: I know that nothing inconsistent can exist. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], III p.224) | |
| A reaction: Fine, but the problem is to assess with confidence what is inconsistent. Human imagination seems to be the test for existence. But what else can we do? |
| 13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
| Full Idea: A set is called a 'relation' if every element of it is an ordered pair. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 04.7) | |
| A reaction: This is the modern extensional view of relations. For 'to the left of', you just list all the things that are to the left, with the things they are to the left of. But just listing the ordered pairs won't necessarily reveal how they are related. |
| 13042 | If dependence is well-founded, with no infinite backward chains, this implies substances [Potter] |
| Full Idea: The argument that the relation of dependence is well-founded ...is a version of the classical arguments for substance. ..Any conceptual scheme which genuinely represents a world cannot contain infinite backward chains of meaning. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.3) | |
| A reaction: Thus the iterative conception of set may imply a notion of substance, and Barwise's radical attempt to ditch the Axiom of Foundation (Idea 13039) was a radical attempt to get rid of 'substances'. Potter cites Wittgenstein as a fan of substances here. |
| 3959 | There is no other substance, in a strict sense, than spirit [Berkeley] |
| Full Idea: There is no other substance, in a strict sense, than spirit. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], III p.257) | |
| A reaction: A nice clear statement of idealism. Why is he so confident of making this assertion. Note the addition, though, of 'in a strict' sense. He is presenting an epistemological claim as if it was an ontological one. |
| 13041 | Collections have fixed members, but fusions can be carved in innumerable ways [Potter] |
| Full Idea: A collection has a determinate number of members, whereas a fusion may be carved up into parts in various equally valid (although perhaps not equally interesting) ways. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 02.1) | |
| A reaction: This seems to sum up both the attraction and the weakness of mereology. If you doubt the natural identity of so-called 'objects', then maybe classical mereology is the way to go. |
| 10709 | Priority is a modality, arising from collections and members [Potter] |
| Full Idea: We must conclude that priority is a modality distinct from that of time or necessity, a modality arising in some way out of the manner in which a collection is constituted from its members. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.3) | |
| A reaction: He is referring to the 'iterative' view of sets, and cites Aristotle 'Metaphysics' 1019a1-4 as background. |
| 3946 | A thing is shown to be impossible if a contradiction is demonstrated within its definition [Berkeley] |
| Full Idea: A thing is shown to be impossible when a repugnancy is demonstrated between the ideas comprehended in its definition. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], II p.214) | |
| A reaction: The problem is always that imagination is needed to see the 'repugnancy', and that is relative and limited. |
| 3958 | Since our ideas vary when the real things are said to be unchanged, they cannot be true copies [Berkeley] |
| Full Idea: As our ideas are perpetually varied, without any change in the supposed real things, it necessarily follows that they cannot all be true copies of them. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], III p.239) | |
| A reaction: This seems a good objection to any direct or naďve realist view. Colours get darker as the sun goes down, and objects become blurred as they recede into the distance. |
| 3943 | If existence is perceived directly, by which sense; if indirectly, how is it inferred from direct perception? [Berkeley] |
| Full Idea: Either you perceive the being of matter immediately, or mediately; if immediately, pray inform me by which of the senses you perceive it; if mediately, let me know by what reasonings it is inferred from those things which you perceive immediately. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], II p.208) | |
| A reaction: A problem for strong empiricists, and he is right that existence can't be directly perceived, but it seems a good explanation (for which some reason can be shown), and supports a more rationalist view. |
| 3931 | Sensible objects are just sets of sensible qualities [Berkeley] |
| Full Idea: Sensible things are nothing else but so many sensible qualities. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], I p.154) | |
| A reaction: As it stands this is phenomenalism, but Berkeley eventually votes for idealism. He should acknowledge possible sensations which aren't actually experienced. |
| 5192 | Berkeley did not deny material things; he merely said they must be defined through sensations [Berkeley, by Ayer] |
| Full Idea: Berkeley did not (as we are commonly told) deny the reality of material things. ..What Berkeley discovered was that material things must be defined in terms of sense-contents. | |
| From: report of George Berkeley (Three Dialogues of Hylas and Philonous [1713]) by A.J. Ayer - Language,Truth and Logic Ch.2 | |
| A reaction: This seems to be a rather debatable attempt to claim that Berkeley was a phenomenalist (like Ayer), rather than an idealist. Try ideas 3942, 3944, 3945, 3957, 3959 in this database. |
| 5174 | Berkeley needed a phenomenalist account of the self, as well as of material things [Ayer on Berkeley] |
| Full Idea: The considerations which make it necessary, as Berkeley saw, to give a phenomenalist account of material things, make it necessary also, as Berkeley did not see, to give a phenomenalist account of the self. | |
| From: comment on George Berkeley (Three Dialogues of Hylas and Philonous [1713]) by A.J. Ayer - Language,Truth and Logic Ch.7 | |
| A reaction: Phenomenalism involves 'possible' experiences as well as actual ones. That could add up to quite a rich and stable account of the self, as opposed to Hume's notorious introspection, which only saw an actual shifting 'bundle' of experience. |
| 1103 | 'To be is to be perceived' is a simple confusion of experience with its objects [Russell on Berkeley] |
| Full Idea: Berkeley thinks 'to be is to be perceived', and only God provides continuity. He has simply confused the experience of perception with the thing being perceived. Ideas have content. | |
| From: comment on George Berkeley (Three Dialogues of Hylas and Philonous [1713]) by Bertrand Russell - Problems of Philosophy |
| 6403 | For Berkelely, reality is ideas and a community of minds, including God's [Berkeley, by Grayling] |
| Full Idea: Berkeley's thesis is that reality ultimately consists of a community of minds and their ideas; one of the minds (God) is infinite, and causes most of the ideas. | |
| From: report of George Berkeley (Three Dialogues of Hylas and Philonous [1713]) by A.C. Grayling - Russell Ch.2 | |
| A reaction: I think Russell nicely pinpoints what is wrong with Berekely, which is that he confuses ideas with their contents. If I think about my garden, the garden is real (probably), which is the content, and they idea is just a way of thinking. |
| 3936 | Time is measured by the succession of ideas in our minds [Berkeley] |
| Full Idea: Time is measured by the succession of ideas in our minds. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], I p.172) | |
| A reaction: But we distinguish between subjective time (which flies when you are having fun), and objective time, judged from observation of clocks and nature. |
| 3930 | There is no such thing as 'material substance' [Berkeley] |
| Full Idea: That there is no such thing as what philosophers call 'material substance', I am seriously persuaded. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], I p.150) | |
| A reaction: I'm sorry, but I can't do with this. It confuses epistemology with ontology. Ontology is a matter of judgement; epistemology is the evidence on which we base it. We know sensations; personally I judge that there are material substances. What about you? |
| 3939 | I conceive a tree in my mind, but I cannot prove that its existence can be conceived outside a mind [Berkeley] |
| Full Idea: I may conceive in my own thoughts the idea of a tree, but that is all. And this is far from proving that I can conceive it existing out of the minds of all spirits. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], I p.184) | |
| A reaction: If Berkeley has based a world view on this point, then his mistake is to require a 'proof'. Aristotle explained why you can't prove everything (not to mention Gödel). |
| 3945 | There is nothing in nature which needs the concept of matter to explain it [Berkeley] |
| Full Idea: I challenge you to show me that thing in nature which needs matter to explain or account for it. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], II p.212) | |
| A reaction: I disagree. Physics is a good theory for explaining why we have perceptions. Failing that there is not even a glimmer of an explanation of our experiences. |
| 3947 | Perceptions are ideas, and ideas exist in the mind, so objects only exist in the mind [Berkeley] |
| Full Idea: Wood, fire, water, flesh, iron, are things that I know, and only known because I perceive them by my senses; these are immediately perceived, and so are ideas; ideas cannot exist without the mind; their existence consists therefore in being perceived. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], III p.220) | |
| A reaction: This makes no distinction between an idea and its content. Berkeley fails to grasp the weird concept of intentionality. Trees aren't in my head, just because I think about them! |
| 3933 | Primary qualities (such as shape, solidity, mass) are held to really exist, unlike secondary qualities [Berkeley] |
| Full Idea: Sensible qualities are by philosophers divided into primary and secondary; the former are extension, figure, solidity, gravity, motion and rest, which exist really in bodies. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], I p.169) | |
| A reaction: A crucial distinction, which anti-realists such as Berkeley end up denying. I think it is a good distinction, and philosophers should fight to preserve it. |
| 3934 | A mite would see its own foot as large, though we would see it as tiny [Berkeley] |
| Full Idea: A mite must be supposed to see his own foot as a body of some considerable dimension, though they appear to you scarcely discernible. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], I p.170) | |
| A reaction: Berkeley is confused. Hot is secondary, but temperature is primary. Bigness is secondary, size primay. Midgets and tall people don't disagree over the size of a table. |
| 3935 | The apparent size of an object varies with its distance away, so that can't be a property of the object [Berkeley] |
| Full Idea: As we approach to or recede from an object, the visible extension varies, being at one distance ten or a hundred times greater than at another; doth it not follow that it is not really inherent in the object? | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], I p.171) | |
| A reaction: Berkeley is confused, because he is too literally empirical. Qualities are not self-evidently primary or secondary, but are judged so after comparisons (e.g. with testimony, or with the other senses). |
| 3937 | 'Solidity' is either not a sensible quality at all, or it is clearly relative to our senses [Berkeley] |
| Full Idea: By 'solidity' either you do not mean any sensible quality, and so it is beside our enquiry; or if you do, it must be hardness or resistance, which are plainly relative to our senses. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], I p.173) | |
| A reaction: Berkeley fails to recognise that a quality can have primary and secondary aspects (hot/high temperature). He is right that primary qualities are not directly perceived. They are judgements. |
| 3940 | Distance is not directly perceived by sight [Berkeley] |
| Full Idea: Distance is not properly and immediately perceived by sight. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], I p.186) | |
| A reaction: Interestingly, if secondary qualities are not strictly perceptions of the object, and primary qualities are not directly perceived, then we don't seem to perceive anything at all. Perhaps we should drop the concept of 'perception'? |
| 3957 | Immediate objects of perception, which some treat as appearances, I treat as the real things themselves [Berkeley] |
| Full Idea: Those immediate objects of perception, which, according to you, are only appearances of things, I take to be the real things themselves. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], III p.237) | |
| A reaction: If that is a judgement, which it seems to be, it is a strange one. Realists offer a much better explanation of perceptions. |
| 3953 | Real things and imaginary or dreamed things differ because the latter are much fainter [Berkeley] |
| Full Idea: The difference between real things, and chimeras formed by the imagination, or the visions of a dream, is that the latter are faint and indistinct. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], III p.225) | |
| A reaction: In Hume this becomes 'impressions' and 'ideas'. It does raise the question of WHY some ideas are not as faint as others. |
| 3938 | Geometry is originally perceived by senses, and so is not purely intellectual [Berkeley] |
| Full Idea: Figures and extension, being originally perceived by sense, do not belong to pure intellect. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], I p.176) | |
| A reaction: Is the square root of 169 less 'pure' in my mind if I learn it from laying out bricks instead of by thinking about numbers? Confusion of how you learn with what you learn? |
| 3944 | It is possible that we could perceive everything as we do now, but nothing actually existed. [Berkeley] |
| Full Idea: We might perceive all things just as we do now, though there was no matter in the world. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], II p.209) | |
| A reaction: An old Greek argument. Now we have an explanation of experience, but we wouldn't if nothing existed. Which doesn't prove that anything exists. Is some explanation always preferable to none? Cf. religion. |
| 3932 | A hot hand and a cold hand will have different experiences in the same tepid water [Berkeley] |
| Full Idea: Suppose now one of your hands hot, and the other cold, and that they are both at once put into the same vessel of water, in an intermediate state; will not the water seem cold to one hand, and warm to the other? | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], I p.158) | |
| A reaction: A nice clear example of how some relativism must be acknowledged. It feels hot, but what is its temperature in degrees C? |
| 3948 | Experience tells me that other minds exist independently from my own [Berkeley] |
| Full Idea: It is plain that other minds have an existence exterior to my mind, since I find them by experience to be independent of it. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], III p.220) | |
| A reaction: This is a surprising claim from Berkeley. If trees only exist through their experience in my mind, why don't other minds exist in the same way? |
| 3941 | How can that which is unthinking be a cause of thought? [Berkeley] |
| Full Idea: How can that which is unthinking be a cause of thought? | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], II p.203) | |
| A reaction: Presumably, though, he thinks that thought can cause 'that which is unthinking' to move'. He likes one half of the interaction problem (which supports dualism), but avoids the other half. |
| 5374 | Berkeley probably used 'idea' to mean both the act of apprehension and the thing apprehended [Russell on Berkeley] |
| Full Idea: Berkeley seems to have confused the colour of the thing apprehended with the act of apprehension; probably either of these would have been called an 'idea' be Berkeley. | |
| From: comment on George Berkeley (Three Dialogues of Hylas and Philonous [1713]) by Bertrand Russell - Problems of Philosophy | |
| A reaction: If we are saying that Berkeley's error was entirely verbal, there is a chicken-and-egg problem. He was an idealist, so he wouldn't have thought that there were two separate concepts behind the word 'idea'. Russell merely asserts that there are. |
| 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? |
| 3954 | Immorality is not in the action, but in the deviation of the will from moral law [Berkeley] |
| Full Idea: Sin or moral turpitude doth not consist in the outward physical action or motion, but in the internal deviation of the will from the laws of reason and religion. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], III p.227) | |
| A reaction: A Kantian view (that the only good thing is a good will). It is a very empiricist (and anti-Greek) view to deny that actions have any intrinsic value. |
| 3950 | There must be a God, because all sensible things must be perceived by him [Berkeley] |
| Full Idea: I immediately and necessarily conclude the being of a God, because all sensible things must be perceived by him. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], II p.198) | |
| A reaction: Daft. This contradicts Berkeley's whole empiricist position, that existence depends on known experience. Who knows whether God is thinking about trees? |
| 3951 | There must be a God, because I and my ideas are not independent [Berkeley] |
| Full Idea: From the dependency I find in myself and my ideas, I do by an act of reason necessarily infer the existence of a God. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], III p.222) | |
| A reaction: No. Hume answered this, by showing how big abstract ideas are built up from experience. This is a future bishop's wish-fulfilment. |
| 3949 | It has been proved that creation is the workmanship of God, from its beauty and usefulness [Berkeley] |
| Full Idea: Divines and philosophers have proved beyond all controversy, from the beauty and usefulness of the several parts of creation, that it was the workmanship of God. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], II p.198) | |
| A reaction: Not convincing. Beauty is probably a sublimation of sexual desire (or an echo of the human mind in the external world, in music), and utility is relative to homo sapiens, I presume. |
| 3956 | People are responsible because they have limited power, though this ultimately derives from God [Berkeley] |
| Full Idea: Thinking rational beings, in the production of motions, have the use of limited powers, ultimately derived from God, but immediately under the direction of their own wills, which is sufficient to entitle them to all the guilt of their own actions. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], III p.228) | |
| A reaction: An episcopal evasion. A classic attempt to have cake and eat it. Either God is in charge or he isn't. |
| 3955 | If sin is not just physical, we don't consider God the origin of sin because he causes physical events [Berkeley] |
| Full Idea: If sin doth not consist of purely physical actions, the making God a cause of all such actions, is not making him the author of sin. | |
| From: George Berkeley (Three Dialogues of Hylas and Philonous [1713], III p.227) | |
| A reaction: An equivocation. If responsibility resides in consciousness, God is presumably conscious, and we can judge the events he causes. |