32 ideas
| 9967 | 'Impure' sets have a concrete member, while 'pure' (abstract) sets do not [Jubien] |
| Full Idea: Any set with a concrete member is 'impure'. 'Pure' sets are those that are not impure, and are paradigm cases of abstract entities, such as the sort of sets apparently dealt with in Zermelo-Fraenkel (ZF) set theory. | |
| From: Michael Jubien (Ontology and Mathematical Truth [1977], p.116) | |
| A reaction: [I am unclear whether Jubien is introducing this distinction] This seems crucial in accounts of mathematics. On the one had arithmetic can be built from Millian pebbles, giving impure sets, while logicists build it from pure sets. |
| 9968 | A model is 'fundamental' if it contains only concrete entities [Jubien] |
| Full Idea: A first-order model can be viewed as a kind of ordered set, and if the domain of the model contains only concrete entities then it is a 'fundamental' model. | |
| From: Michael Jubien (Ontology and Mathematical Truth [1977], p.117) | |
| A reaction: An important idea. Fundamental models are where the world of logic connects with the physical world. Any account of relationship between fundamental models and more abstract ones tells us how thought links to world. |
| 9965 | There couldn't just be one number, such as 17 [Jubien] |
| Full Idea: It makes no sense to suppose there might be just one natural number, say seventeen. | |
| From: Michael Jubien (Ontology and Mathematical Truth [1977], p.113) | |
| A reaction: Hm. Not convinced. If numbers are essentially patterns, we might only have the number 'twelve', because we had built our religion around anything which exhibited that form (in any of its various arrangements). Nice point, though. |
| 9966 | The subject-matter of (pure) mathematics is abstract structure [Jubien] |
| Full Idea: The subject-matter of (pure) mathematics is abstract structure per se. | |
| From: Michael Jubien (Ontology and Mathematical Truth [1977], p.115) | |
| A reaction: This is the Structuralist idea beginning to take shape after Benacerraf's launching of it. Note that Jubien gets there by his rejection of platonism, whereas some structuralist have given a platonist interpretation of structure. |
| 9963 | If we all intuited mathematical objects, platonism would be agreed [Jubien] |
| Full Idea: If the intuition of mathematical objects were general, there would be no real debate over platonism. | |
| From: Michael Jubien (Ontology and Mathematical Truth [1977], p.111) | |
| A reaction: It is particularly perplexing when Gödel says that his perception of them is just like sight or smell, since I have no such perception. How do you individuate very large numbers, or irrational numbers, apart from writing down numerals? |
| 9962 | How can pure abstract entities give models to serve as interpretations? [Jubien] |
| Full Idea: I am unable to see how the mere existence of pure abstract entities enables us to concoct appropriate models to serve as interpretations. | |
| From: Michael Jubien (Ontology and Mathematical Truth [1977], p.111) | |
| A reaction: Nice question. It is always assumed that once we have platonic realm, that everything else follows. Even if we are able to grasp the objects, despite their causal inertness, we still have to discern innumerable relations between them. |
| 9964 | Since mathematical objects are essentially relational, they can't be picked out on their own [Jubien] |
| Full Idea: The essential properties of mathematical entities seem to be relational, ...so we make no progress unless we can pick out some mathematical entities wihout presupposing other entities already picked out. | |
| From: Michael Jubien (Ontology and Mathematical Truth [1977], p.112) | |
| A reaction: [compressed] Jubien is a good critic of platonism. He has identified the problem with Frege's metaphor of a 'borehole', where we discover delightful new properties of numbers simply by reaching them. |
| 16588 | I prefer a lack of form to mean non-existence, than to think of some quasi-existence [Augustine] |
| Full Idea: I sooner judged that what lacks all form does not exist, than thought of as something in between form and nothing, neither formed nor nothing, unformed and next to nothing. | |
| From: Augustine (Confessions [c.398], XII.6), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 03.1 | |
| A reaction: Scholastics were struck by the contrast between this remark, and the remark of Averroes (Idea 16587) that prime matter was halfway existence. Their two great authorities disagreed! This sort of thing stimulated the revival of metaphysics. |
| 22979 | Three main questions seem to be whether a thing is, what it is, and what sort it is [Augustine] |
| Full Idea: I am told that I can ask three sorts of questions - whether a thing is, what it is, and what sort it is. | |
| From: Augustine (Confessions [c.398], X.10) | |
| A reaction: This seems to be a very Aristotelian approach. I am pleased to see that what it is and what sort it is are not conflated. The first one must be its individual essence, and the second its generic essence. |
| 9969 | The empty set is the purest abstract object [Jubien] |
| Full Idea: The empty set is the pure abstract object par excellence. | |
| From: Michael Jubien (Ontology and Mathematical Truth [1977], p.118 n8) | |
| A reaction: So a really good PhD on the empty set could crack the whole nature of reality. Get to work, whoever you are! |
| 22977 | I can distinguish different smells even when I am not experiencing them [Augustine] |
| Full Idea: I can distinguish the scent of lilies from that of violets, even though there is no scent at all in my nostrils. | |
| From: Augustine (Confessions [c.398], X.08) | |
| A reaction: Augustine has a nice introspective account of how we experience memory, and identifies lots of puzzling features. I know I can identify the smell of vinegar, but I can't bring it to mind, the way I can the appearance of roses. |
| 22982 | Why does joy in my mind make me happy, but joy in my memory doesn't? [Augustine] |
| Full Idea: How can it be that my mind can be happy because of the joy that is in it, and yet my memory is not sad by reason of the sadness that is in it? | |
| From: Augustine (Confessions [c.398], X.14) | |
| A reaction: This seems to contradict his thought in Idea 22981, that memory and mind are the same. Recall seems to be a part of consciousness which is not fully wired up to the rest of the mind. |
| 22981 | Mind and memory are the same, as shown in 'bear it in mind' or 'it slipped from mind' [Augustine] |
| Full Idea: The mind and the memory are one and the same. We even call the memory the mind, for when we tell a person to remember something, we tell them to 'bear this in mind', and when we forget something 'it slipped out of my mind'. | |
| From: Augustine (Confessions [c.398], X.14) | |
| A reaction: This idea has become familiar in modern neuroscience, I think, presumably because we do not find distinct types of neurons for consciousness and for memory. |
| 22980 | Memory contains innumerable principles of maths, as well as past sense experiences [Augustine] |
| Full Idea: The memory contains the innumerable principles and laws of numbers and dimensions. None of these can have been conveyed to me by the bodily senses. | |
| From: Augustine (Confessions [c.398], X.12) | |
| A reaction: Even if you have a fairly empirical view of the sources of mathematics (a view with which I sympathise), it must by admitted that our endless extrapolations from the sources also reside in memory. So we remember thoughts as well as experiences. |
| 22983 | We would avoid remembering sorrow or fear if that triggered the emotions afresh [Augustine] |
| Full Idea: If we had to experience sorrow or fear every time that we mentioned these emotions, no one would be willing to speak of them. | |
| From: Augustine (Confessions [c.398], X.14) | |
| A reaction: Remembering the death of a loved one can trigger fresh grief, but remembering their dangerous illness from which they recovered no longer contains the feeling of fear. |
| 8406 | Not all explanations are causal, but if a thing can be explained at all, it can be explained causally [Sanford] |
| Full Idea: Although not all explanations are causal, anything which can be explained in any way can be explained causally. | |
| From: David H. Sanford (Causation [1995], p.79) | |
| A reaction: A nice bold claim with which I am in sympathy, but he would have a struggle proving it. Does this imply that causal explanations are basic, or in some way superior? Note that functional explanations would thus have underlying causal explanations. |
| 22978 | Memory is so vast that I cannot recognise it as part of my mind [Augustine] |
| Full Idea: The memory is a vast immeasurable sanctuary. It is part of my nature, but I cannot understand all that I am. Hence the mind is too narrow to contain itself entirely. Is the other part outside of itself, and not within it? How then can it be a part? | |
| From: Augustine (Confessions [c.398], X.08) | |
| A reaction: He seems to understand the mind as entirely consisting of consciousness. Nevertheless, this seems to be the first inklings of the modern externalist view of the mind. |
| 22984 | Without memory I could not even speak of myself [Augustine] |
| Full Idea: I do not understand the power of memory that is in myself, although without it I could not even speak of myself. | |
| From: Augustine (Confessions [c.398], X.16) | |
| A reaction: Even if the self is not identical with memory, this idea seems to establish that memory is an essential aspect of the self. This point is neglected by those who see the self as an entity (the 'soul pearl') which persists through all experience. |
| 5982 | If the future does not exist, how can prophets see it? [Augustine] |
| Full Idea: How do prophets see the future, if there is not a future to be seen? | |
| From: Augustine (Confessions [c.398], XI.17) | |
| A reaction: The answer, I suspect, is that prophets can't see the future. The prospect that the future already exists would seem to saboutage human freedom and responsibility, and point to Calvinist predestination, and even fatalism. |
| 22976 | Memories are preserved separately, according to category [Augustine] |
| Full Idea: In memory everything is preserved separately, according to its category. | |
| From: Augustine (Confessions [c.398], X.08) | |
| A reaction: This strikes me as the first seeds of the idea that the mind functions by means of mental files. Our memories of cats are 'close to' or 'linked to' our memories of dogs. |
| 22985 | Everyone wants happiness [Augustine] |
| Full Idea: Surely happiness is what everyone wants, so much so that there can be none who do not want it? | |
| From: Augustine (Confessions [c.398], X.20) | |
| A reaction: His concept of happiness is, of course, religious. Occasionally you meet habitual grumblers about life who give the impression that they are only happy when they are discontented. So happiness is achieving desires, not feeling good? |
| 8407 | A totality of conditions necessary for an occurrence is usually held to be jointly sufficient for it [Sanford] |
| Full Idea: A totality of conditions necessary for an occurrence is jointly sufficient for it. This is a widely held but controversial view, and it is not a logical truth. | |
| From: David H. Sanford (Causation [1995], p.82) | |
| A reaction: This wouldn't work for an impossible occurrence. What are the necessary conditions to produce a large planet made of uranium? One of them would have to be a naturally impossible necessity. |
| 5984 | Maybe time is an extension of the mind [Augustine] |
| Full Idea: I begin to wonder whether time is an extension of the mind itself. | |
| From: Augustine (Confessions [c.398], XI.26) | |
| A reaction: The observation that the mind creates a 'specious present' (spreading experience out over a short fraction of second) reinforces this. Personally I like David Marshall's proposal that consciousness is entirely memory, which would deny this idea. |
| 22888 | To be aware of time it can only exist in the mind, as memory or anticipation [Augustine, by Bardon] |
| Full Idea: Augustine answers that for us to be aware of time it must exist only in the mind, …and the difference between past and future is just the difference between memory and anticipation. | |
| From: report of Augustine (Confessions [c.398]) by Adrian Bardon - Brief History of the Philosophy of Time 1 'Augustine's' | |
| A reaction: This is an extreme idealist view. Are we to say that the past consists only of what can be remembered, and the future only of what is anticipated? Absurd anti-realism, in my view. Where do his concepts come from, asks Le Poidevin. |
| 5980 | How can ten days ahead be a short time, if it doesn't exist? [Augustine] |
| Full Idea: A short time ago or a short time ahead we might put at ten days, but how can anything which does not exist be either long or short? | |
| From: Augustine (Confessions [c.398], XI.15) | |
| A reaction: A nice question, which gets at the paradoxical nature of time very nicely. How can it be long, but non-existent? We could break the paradox by concluding '..and therefore time does exist', even though we can't see how. |
| 5979 | If the past is no longer, and the future is not yet, how can they exist? [Augustine] |
| Full Idea: Of the three divisions of time, how can two, the past and the future, be, when the past no longer is, and the future is not yet? | |
| From: Augustine (Confessions [c.398], XI.14) | |
| A reaction: This is the oldest bewilderment about time, which naturally leads us to the thought that time cannot actually 'exist'. The remark implies that at least 'now' is safe, but that also succumbs to paradox pretty quickly. |
| 5981 | The whole of the current year is not present, so how can it exist? [Augustine] |
| Full Idea: We cannot say that the whole of the current year is present, and if the whole of it is not present, the year is not present. | |
| From: Augustine (Confessions [c.398], XI.15) | |
| A reaction: Another nice way of presenting the paradox of time. We are in a particular year, so it has to be real. |
| 5978 | I know what time is, until someone asks me to explain it [Augustine] |
| Full Idea: I know well enough what time is, provided that nobody asks me; but if I am asked what it is and try to explain, I am baffled. | |
| From: Augustine (Confessions [c.398], XI.14) | |
| A reaction: A justly famous remark, even though it adds nothing to our knowledge of time. This sort of thought pushes us towards accepting many things as axiomatic, such as time, space, identity, persons, mind. |
| 5983 | I disagree with the idea that time is nothing but cosmic movement [Augustine] |
| Full Idea: I once heard a learned man say that time is nothing but the movement of the sun and the moon and the stars, but I do not agree. | |
| From: Augustine (Confessions [c.398], XI.22) | |
| A reaction: It is tempting to say that you either take time or movement as axiomatic, and describe one in terms of the other, but you are stuck unable to give the initial statement of the axiom without mentioning the second property you were saving for later. |
| 5977 | Heaven and earth must be created, because they are subject to change [Augustine] |
| Full Idea: The fact that heaven and earth are there proclaims that they were created, for they are subject to change and variation; ..the meaning of change and variation is that something is there which was not there before. | |
| From: Augustine (Confessions [c.398], XI.04) | |
| A reaction: It seems possible that the underlying matter is eternal (as in various conservation laws, such as that of energy), and that all change is in the form rather than the substance. |
| 22887 | If God existed before creation, why would a perfect being desire to change things? [Augustine, by Bardon] |
| Full Idea: If nothing existed by God before creation, then what could have happened to, or within, God that led God to decide to create the universe at that particular moment? Why would an eternal or perfect being want or need to change? | |
| From: report of Augustine (Confessions [c.398]) by Adrian Bardon - Brief History of the Philosophy of Time 1 'Augustine's' | |
| A reaction: I suppose you could reply that change is superior to stasis, but then why did God delay the creation? |
| 5976 | If God is outside time in eternity, can He hear prayers? [Augustine] |
| Full Idea: O Lord, since you are outside time in eternity, are you unaware of the things that I tell you? | |
| From: Augustine (Confessions [c.398], XI.01) | |
| A reaction: This strikes me as the single most difficult and most elusive question about the nature of a supreme divine being. If the being is trapped in time, as we are, it is greatly diminished, and if it is outside, it is hard to see how it could be a participant. |