12 ideas
| 17697 | The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert] |
| Full Idea: The standpoint of pure experience seems to me to be refuted by the objection that the existence, possible or actual, of an arbitrarily large number can never be derived through experience, that is, through experiment. | |
| From: David Hilbert (On the Foundations of Logic and Arithmetic [1904], p.130) | |
| A reaction: Alternatively, empiricism refutes infinite numbers! No modern mathematician will accept that, but you wonder in what sense the proposed entities qualify as 'numbers'. |
| 17698 | Logic already contains some arithmetic, so the two must be developed together [Hilbert] |
| Full Idea: In the traditional exposition of the laws of logic certain fundamental arithmetic notions are already used, for example in the notion of set, and to some extent also of number. Thus we turn in a circle, and a partly simultaneous development is required. | |
| From: David Hilbert (On the Foundations of Logic and Arithmetic [1904], p.131) | |
| A reaction: If the Axiom of Infinity is meant, it may be possible to purge the arithmetic from the logic. Then the challenge to derive arithmetic from it becomes rather tougher. |
| 22167 | Our images of bodies are not produced by the bodies, but by our own minds [Augustine, by Aquinas] |
| Full Idea: Augustine says bodies don't form images in our spirit; our spirit does that itself with amazing quickness. ...So the appearances under which mind knows things aren't drawn from the things themselves. | |
| From: report of Augustine (works [c.415]) by Thomas Aquinas - Quodlibeta 8.2.1 | |
| A reaction: This is Augustine's theory of 'illumination' - that God creates experience within us. His theory was soon discarded by the early scholastics. |
| 22117 | Our minds grasp reality by direct illumination (rather than abstraction from experience) [Augustine, by Matthews] |
| Full Idea: Instead of supposing that what we know can be abstracted from sensible particulars that instantiate such knowledge, Augustine insists that our mind is so constituted as to see 'intelligible realities' directly by inner illumination. | |
| From: report of Augustine (works [c.415]) by Gareth B. Matthews - Augustine p.74 | |
| A reaction: His 'theory of illumination'. This seems to be a sort of super-rationalism. This doesn't make clear the role of sensations. Surely he doesn't thing that we just bypass them? |
| 22118 | Augustine created the modern concept of the will [Augustine, by Matthews] |
| Full Idea: The modern concept of the will is often said to originate with Augustine. | |
| From: report of Augustine (works [c.415]) by Gareth B. Matthews - Augustine p.74 | |
| A reaction: I'm beginning to think that this is the source of the trouble. How can a thing be intrinsically free? Surely freedom is always a contextual concept? |
| 4348 | Love, and do what you will [Augustine] |
| Full Idea: Love, and do what you will. | |
| From: Augustine (works [c.415]) | |
| A reaction: This sounds libertarian, but Augustine had a stern concept of what love required. It nicely captures one of the essential ideas of virtue ethics. |
| 7821 | Pagans produced three hundred definitions of the highest good [Augustine, by Grayling] |
| Full Idea: Augustine claimed that the pagan schools between them had produced nearly three hundred different definitions of the highest good. | |
| From: report of Augustine (works [c.415]) by A.C. Grayling - What is Good? Ch.5 | |
| A reaction: I would expect the right definition to be in there somewhere, but no doubt Augustine's definition made it 301. Perhaps the biggest problem of human life is that (as with the Kennedy assassination) proliferating stories obscure the true story. |
| 22119 | Augustine said (unusually) that 'ought' does not imply 'can' [Augustine, by Matthews] |
| Full Idea: Augustine insisted that 'ought' does not, in any straightforward way, imply 'can' - which distinguishes him from most modern ethicists. | |
| From: report of Augustine (works [c.415]) by Gareth B. Matthews - Augustine p.74 | |
| A reaction: Not unreasonable. I ought to help my ailing friend who lives abroad, but I haven't the time or money to do it. We can experience impossibilities as duties. Impossibilities are just excuses. Augustine is opposing the Pelagian heresy. |
| 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. |
| 22116 | Augustine identified Donatism, Pelagianism and Manicheism as the main heresies [Augustine, by Matthews] |
| Full Idea: Augustine did the most to define Christian heresy. The three most prominent were Donatism, Pelagianism (that humans are perfectible), and Manicheism (that good and evil are equally basic metaphysical realities). | |
| From: report of Augustine (works [c.415]) by Gareth B. Matthews - Augustine p.73 | |
| A reaction: Manicheans had presumably been studying Empedocles. (I suppose it's too late to identify Christianity as a heresy?). |
| 19338 | Augustine said evil does not really exist, and evil is a limitation in goodness [Augustine, by Perkins] |
| Full Idea: Augustine solution to the problem of evil was to say that, strictly speaking, evil does not exist. Human beings are not part evil and part good, but rather just a limited amount of goodness. | |
| From: report of Augustine (works [c.415]) by Franklin Perkins - Leibniz: Guide for the Perplexed 2.III | |
| A reaction: Augustine was rebelling against Manicheanism, which he espoused when young, which proposed a good and an evil force. An apathetic slob seems devoid of goodness, but is not evil. It takes extra effort to perform active evil. |