6 ideas
5042 | For every event it is possible for an omniscient being to give a reason for its occurrence [Leibniz] |
Full Idea: Nothing ever takes place without its being possible for one who knew everything to give some reason why it should have happened rather than not. | |
From: Gottfried Leibniz (Letter on Freedom [1689], p.112) | |
A reaction: Presumably there will be GOOD reason why genocide occurs. Note that there is a reason for every 'event'. Is there a reason for every truth? Presumably not, or there would have to be reasons for self-evident truths. |
17807 | To study formal systems, look at the whole thing, and not just how it is constructed in steps [Curry] |
Full Idea: In the study of formal systems we do not confine ourselves to the derivation of elementary propositions step by step. Rather we take the system, defined by its primitive frame, as datum, and then study it by any means at our command. | |
From: Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'The formalist') | |
A reaction: This is what may potentially lead to an essentialist view of such things. Focusing on bricks gives formalism, focusing on buildings gives essentialism. |
17806 | It is untenable that mathematics is general physical truths, because it needs infinity [Curry] |
Full Idea: According to realism, mathematical propositions express the most general properties of our physical environment. This is the primitive view of mathematics, yet on account of the essential role played by infinity in mathematics, it is untenable today. | |
From: Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'The problem') | |
A reaction: I resist this view, because Curry's view seems to imply a mad metaphysics. Hilbert resisted the role of the infinite in essential mathematics. If the physical world includes its possibilities, that might do the job. Hellman on structuralism? |
17808 | Saying mathematics is logic is merely replacing one undefined term by another [Curry] |
Full Idea: To say that mathematics is logic is merely to replace one undefined term by another. | |
From: Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'Mathematics') |
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. |