8 ideas
| 17809 | Gödel showed that the syntactic approach to the infinite is of limited value [Kreisel] |
| Full Idea: Usually Gödel's incompleteness theorems are taken as showing a limitation on the syntactic approach to an understanding of the concept of infinity. | |
| From: Georg Kreisel (Hilbert's Programme [1958], 05) |
| 17810 | The study of mathematical foundations needs new non-mathematical concepts [Kreisel] |
| Full Idea: It is necessary to use non-mathematical concepts, i.e. concepts lacking the precision which permit mathematical manipulation, for a significant approach to foundations. We currently have no concepts of this kind which we can take seriously. | |
| From: Georg Kreisel (Hilbert's Programme [1958], 06) | |
| A reaction: Music to the ears of any philosopher of mathematics, because it means they are not yet out of a job. |
| 4894 | I say Mary does not have new knowledge, but knows an old fact in a new way [Perry on Jackson] |
| Full Idea: I say Mary knows an old fact in a new way, but I do not find a new bit of knowledge and a new fact. | |
| From: comment on Frank Jackson (What Mary Didn't Know [1986]) by John Perry - Knowledge, Possibility and Consciousness §7.3 | |
| A reaction: This seems roughly the right way to attack Jackson's 'knowledge argument', by asking exactly what he means by 'knowledge'. It is hard to see how 'qualia' can be both the means of acquiring knowledge, and the thing itself. |
| 4895 | Is it unfair that physicalist knowledge can be written down, but dualist knowledge can't be [Perry on Jackson] |
| Full Idea: Jackson seems to imply that it isn't fair that all physicalist knowledge can be written down, but not all dualist knowledge can be. | |
| From: comment on Frank Jackson (What Mary Didn't Know [1986]) by John Perry - Knowledge, Possibility and Consciousness §7.5 | |
| A reaction: This pinpoints a problem for the 'Mary' example - that Mary's new sight of colour is claimed as 'knowledge', and yet the whole point is that it cannot be expressed in propositions (which seems to leave it as 'procedural' or 'acquaintance' knowledge). |
| 4886 | Mary knows all the physical facts of seeing red, but experiencing it is new knowledge [Jackson] |
| Full Idea: Mary knows all the physical facts. ..It seems, however, that Mary does not know all there is to know. For when she is let out of the black and white room .. she will learn what it is like to see something red. | |
| From: Frank Jackson (What Mary Didn't Know [1986], §1.4) | |
| A reaction: Jackson is begging the question. A new physical event occurs when the red wavelength stimulates Mary's visual cortex for the first time. For an empiricist raw experience creates knowledge, so it can't BE knowledge. Does Mary acquire a new concept? |
| 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. |
| 17811 | The natural conception of points ducks the problem of naming or constructing each point [Kreisel] |
| Full Idea: In analysis, the most natural conception of a point ignores the matter of naming the point, i.e. how the real number is represented or by what constructions the point is reached from given points. | |
| From: Georg Kreisel (Hilbert's Programme [1958], 13) | |
| A reaction: This problem has bothered me. There are formal ways of constructing real numbers, but they don't seem to result in a name for each one. |
| 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. |