Class Times: 6.30 pm Mondays 7, 14, 21 28 Feb and 7, 14 Mar
Zoom link |online-only | same link for all six classes
Dial-in back-up in case of internet disruptions: 03 7018 2005 | Meeting ID: 875 8655 4482 Passcode: 210861
Access to texts
All readings from ‘The Last Days of Socrates’ which includes the dialogues Euthyphro, Apology and Phaedo.
- Buy the recommended Penguin translation
- Download Loeb Classical Library Greek/English edition (PDF)
- Online, we recommend David Horan’s translation (Euthyphro, Apology and Phaedo) which can be printed in PDF.
Catch-up class videos
Definition of two (logical)
After hundreds of pages of symbolic deductions from non-intuitive (‘dogmatic’) principles, Principia Mathematica arrives at a definition [of the cardinal number 2], which Russell later translated as follows:
The cardinal number 2 consists of the class of all couples. These couples are defined as follows: there is some concept or other, which we will call p, such that, if A and B, which are not identical, are both members of p, and there are no other members, then p is a couple.Recalled in Russell Remembered by Rupert Crawshay-Williams [p. 7]. Not until page 86 of Volume III of Principia Mathematica is the “occasionally useful” equation, 1 + 1 = 2, established as a logical proposition.
Note that here two is defined through reference to particulars—to the class of all couples—and thus a mystical ground is apparently avoided. In contrast, the intuitive account of two gives two-in-itself, as entirely formal in the Platonic sense, which is to say, it is entirely mystical. Every instance of twoness is only an example, or expression, of the formal concept of two. The form of two has no particular name, expression or exemplar. It is invisible and nameless, yet knowable and immediate to the mind. It cannot be proven but only perceived more or less clearly. I can show you twoness. I can define it only by showing you how it fits in with other aspects of the arithmetic system. But that is all. This then is one very ordinary way that mathematical reasoning is found to be mystical. [Enthusiastic Mathematics, p. 75]
Platonic Myths and Buddhism
This week, discussion came around to the myths of the afterlife and reincarnation found in Plato and their striking similarity to Buddhist myths. For those interested in a possible historical influence from west to east, see this post which focuses on ancient Gandhara. For those interested in the influence on Christian myths, our course Platonism and Christianity might be of interest, as also the lecture Lullabies for the Dying.