5 ideas
17750 | The first clear proof of the consistency of the first order predicate logic was in 1928 [Hilbert/Ackermann, by Walicki] |
Full Idea: The first clear proof of the consistency of the first order predicate logic is found in the 1928 book of Hilbert and Ackermann. | |
From: report of Hilbert,D/Ackermann,W (Principles of Theoretical Logic [1928]) by Michal Walicki - Introduction to Mathematical Logic History E.2.1 |
19043 | Bivalence applies not just to sentences, but that general terms are true or false of each object [Quine] |
Full Idea: It is in the spirit of bivalence not just to treat each closed sentence as true or false; as Frege stressed, each general term must be definitely true or false of each object, specificiable or not. | |
From: Willard Quine (What Price Bivalence? [1981], p.36) | |
A reaction: But note that this is only the 'spirit' of the thing. If you had (as I do) doubts about whether predicates actually refer to genuine 'properties', you may want to stick to the whole sentence view, and not be so fine-grained. |
19042 | Terms learned by ostension tend to be vague, because that must be quick and unrefined [Quine] |
Full Idea: A term is apt to be vague if it is to be learned by ostension, since its applicability must admit of being judged on the spot and so cannot hinge of fine distinctions laboriously drawn. | |
From: Willard Quine (What Price Bivalence? [1981], p.32) | |
A reaction: [Quine cites C. Wright for this] Presumably precision can steadily increased by repeated ostension. After the first 'dog' it's pretty vague; after hundreds of them we are pretty clear about it. Long observation of borderline 'clouds' could do the same. |
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. |