191 



which the upper note is too flat or too sharp gives two beats per 

 second. 



In an appendix, Mr. De Morgan gives some tables of beats, repeats 

 some theorems on temperament from the Penny Cyclopaedia, and 

 recommends and argues in favour of tuning being performed by a 

 whole octave of tuning forks, adjusted by beats to the system em- 

 ployed. 



November 23, 1857. 



A paper was read by Professor Thompson, " On the Sophista of 

 Plato." 



In this paper the genuineness of the Sophista was defended, and 

 some of its philosophical bearings pointed out. In answer to the 

 doubts expressed by the Master of Trinity in a previous communi- 

 cation, it was shown that the Sophista, as well as the Politicus, 

 which is a continuation of it, are repeatedly referred to in the works 

 of Aristotle. In particular, Arist. Metaph. v. ii. 93 was appealed to 

 as evidence that Aristotle had not only read the dialogue called 

 Sophista, but believed it to have been written by his master. 



The Dialogue was analysed, and shown to be a critique of the 

 negative or Eristic systems of logic, derived from the Eleatics, which 

 were taught by Euclides and Antisthenes, the founders of the Socratic 

 sects of the Megarics and Cynics respectively. Many allusions, 

 personal and otherwise, to Antisthenes were pointed out, as existing 

 both in this dialogue and in the Thecetetus, of which it is a professed 

 continuation. The Thecetetus was regarded as a critique of the 

 contemporary psychology, and the Sophista as a confutation of the 

 prevailing schemes of logic ; and both were shown to contain exem- 

 plifications of the twin processes of Induction or Collection, and 

 Division or Classification, which constitute, according to Plato in the 

 Phadrus, p. 265 E., the science or art of Dialectic. 



It was also argued, in opposition to Schleiermacher, that the 

 Materialistic doctrines confuted in Sophista, p. 246, represent those 

 of Antisthenes, rather than the atomic theory of Democritus, or the 

 empirical system of Aristippus. 



The analysis of the simple Proposition (Soph. p. 262) was shown, 

 by the testimony of Plutarch and others, to be Platonic, and the 

 imperfect Idealists refuted in p. 276 were identified with the Megarics, 

 and distinguished from the Platonists. 



Passages were also quoted from the Politicus, showing the dis- 

 ciplinary and educational uses to which the method of Division was 

 made subservient in the teaching of the Academy ; and this teaching 

 was further illustrated by a quotation of considerable length from 

 a Comic Poet ap. Athen. lib. ii. 



* Incidentally, Porphyry and Abelard were appealed to in evidence 

 that Plato's Method of Division was known to the Neo-Platonists and 

 the Schoolmen, and recognized by them as characteristic of his 

 Dialectic. 



