8 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. |
9295 | Not only substances have attributes; events, actions, states and qualities can have them [Teichmann] |
Full Idea: It is not true that only substances have attributes; events, actions, states and qualities can all be characterized. | |
From: Jenny Teichmann (The Mind and the Soul [1974], Ch.2) | |
A reaction: This is why it is so important to distinguish the actual properties in nature from those that can be fancifully hypothesized by a linguistic being. Is there any limit to the possible number of levels of meta-properties? |
9293 | Body-spirit interaction ought to result in losses and increases of energy in the material world [Teichmann] |
Full Idea: Since the interaction of bodies themselves involves energy-flow, it looks as if interaction between body and spirit ought to result in losses and increases of energy in the material world. | |
From: Jenny Teichmann (The Mind and the Soul [1974], Ch.2) | |
A reaction: A nice statement of an important argument. It forces the dualist to go the whole way, asserting that not only is the mind immaterial, but that it can be active without energy, and cover its traces in the physical world. Doesn't look good. |
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. |
9292 | The Soul has no particular capacity (in the way thinking belongs to the mind) [Teichmann] |
Full Idea: On the whole, the Soul has no capacities which belong to it pre-eminently in the way that thinking 'belongs' to the mind. | |
From: Jenny Teichmann (The Mind and the Soul [1974], Ch.1) | |
A reaction: There are no phenomena which have to be saved by postulating a soul. It lacks a function within a human being, but it has a crucial function within a large theological picture. |
9294 | No individuating marks distinguish between Souls [Teichmann] |
Full Idea: There are no individuating marks which could serve to differentiate one Soul from another. | |
From: Jenny Teichmann (The Mind and the Soul [1974], Ch.2) | |
A reaction: Presumably they could have at least much identity as two different electrons (if they are in space-time?). It is hard to see why anyone would be interested in their 'own' immortality, if loss of all individuality was a condition. |