33 ideas
| 10882 | Predicative definitions only refer to entities outside the defined collection [Horsten] |
| Full Idea: Definitions are called 'predicative', and are considered sound, if they only refer to entities which exist independently from the defined collection. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §2.4) |
| 9161 | Maybe reasonableness requires circular justifications - that is one coherentist view [Field,H] |
| Full Idea: It is not out of the question to hold that without circular justifications there is no reasonableness at all. That is the view of a certain kind of coherence theorist. | |
| From: Hartry Field (Apriority as an Evaluative Notion [2000], 2) | |
| A reaction: This nicely captures a gut feeling I have had for a long time. Being now thoroughly converted to coherentism, I am drawn to the idea - like a moth to a flame. But how do we distinguish cuddly circularity from its cruel and vicious cousin? |
| 10884 | A theory is 'categorical' if it has just one model up to isomorphism [Horsten] |
| Full Idea: If a theory has, up to isomorphism, exactly one model, then it is said to be 'categorical'. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §5.2) |
| 10885 | Computer proofs don't provide explanations [Horsten] |
| Full Idea: Mathematicians are uncomfortable with computerised proofs because a 'good' proof should do more than convince us that a certain statement is true. It should also explain why the statement in question holds. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §5.3) |
| 10881 | The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten] |
| Full Idea: The notion of an ordinal number is a set-theoretic, and hence non-arithmetical, concept. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §2.3) |
| 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. |
| 9160 | Lots of propositions are default reasonable, but the a priori ones are empirically indefeasible [Field,H] |
| Full Idea: Propositions such as 'People usually tell the truth' seem to count as default reasonable, but it is odd to count them as a priori. Empirical indefeasibility seems the obvious way to distinguish those default reasonable propositions that are a priori. | |
| From: Hartry Field (Apriority as an Evaluative Notion [2000], 1) | |
| A reaction: Sounds reasonable, but it would mean that all the uniformities of nature would then count as a priori. 'Every physical object exerts gravity' probably has no counterexamples, but doesn't seem a priori (even if it is necessary). See Idea 9164. |
| 9164 | We treat basic rules as if they were indefeasible and a priori, with no interest in counter-evidence [Field,H] |
| Full Idea: I argue not that our most basic rules are a priori or empirically indefeasible, but that we treat them as empirically defeasible and indeed a priori; we don't regard anything as evidence against them. | |
| From: Hartry Field (Apriority as an Evaluative Notion [2000], 4) | |
| A reaction: This is the fictionalist view of a priori knowledge (and of most other things, such as mathematics). I can't agree. Most people treat heaps of a posteriori truths (like the sun rising) as a priori. 'Mass involves energy' is indefeasible a posteriori. |
| 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. |
| 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. |
| 9165 | Reliability only makes a rule reasonable if we place a value on the truth produced by reliable processes [Field,H] |
| Full Idea: Reliability is not a 'factual property'; in calling a rule reasonable we are evaluating it, and all that makes sense to ask about is what we value. We place a high value on the reliability of our inductive and perceptual rules that lead to truth. | |
| From: Hartry Field (Apriority as an Evaluative Notion [2000], 5) | |
| A reaction: This doesn't seem to be a contradiction of reliabilism, since truth is a pretty widespread epistemological value. If you do value truth, then eyes are pretty reliable organs for attaining it. Reliabilism is still wrong, but not for this reason. |
| 9162 | Believing nothing, or only logical truths, is very reliable, but we want a lot more than that [Field,H] |
| Full Idea: Reliability is not all we want in an inductive rule. Completely reliable methods are available, such as believing nothing, or only believing logical truths. But we don't value them, but value less reliable methods with other characteristics. | |
| From: Hartry Field (Apriority as an Evaluative Notion [2000], 3) | |
| A reaction: I would take this excellent point to be an advertisement for inference to the best explanation, which requires not only reliable inputs of information, but also a presiding rational judge to assess the mass of evidence. |
| 9166 | People vary in their epistemological standards, and none of them is 'correct' [Field,H] |
| Full Idea: We should concede that different people have slightly different basic epistemological standards. ..I doubt that any clear sense could be given to the notion of 'correctness' here. | |
| From: Hartry Field (Apriority as an Evaluative Notion [2000], 5) | |
| A reaction: I think this is dead right. There is a real relativism about knowledge, which exists at the level of justification, rather than of truth. The scientific revolution just consisted of making the standards tougher, and that seems to have been a good idea. |
| 9163 | If we only use induction to assess induction, it is empirically indefeasible, and hence a priori [Field,H] |
| Full Idea: If some inductive rule is basic for us, in the sense that we never assess it using any rules other than itself, then it must be one that we treat as empirically indefeasible (hence as fully a priori, given that it will surely have default status). | |
| From: Hartry Field (Apriority as an Evaluative Notion [2000], 4) | |
| A reaction: This follows on from Field's account of a priori knowledge. See Ideas 9160 and 9164. I think of induction as simply learning from experience, but if experience goes mad I will cease to trust it. (A rationalist view). |
| 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? |
| 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. |