the Republic. [Hamilton LECT. V. LOGIC. 62] Law of Excluded Middle: The law of Excluded Middle between two contradictories remounts, as I have said, also to Plato, though the Second Alcibiades, the dialogue in which it is most clearly expressed, must be admitted to be spurious. It is also in the fragments of Pseudo-Archytas, to be found in Stobæus. [Hamilton LECT. V. LOGIC. 65] Hamilton further observes that "It is explicitly and emphatically enounced by Aristotle in many passages both of his Metaphysics (l. iii. (iv.) c.7.) and of his Analytics, both Prior (l. i. c. 2) and Posterior (1. i. c. 4). In the first of these, he says: "It is impossible that there should exist any medium between contradictory opposites, but it is necessary either to affirm or to deny everything of everything." [Hamilton LECT. V. LOGIC. 65] "Law of Identity. [Hamilton also calls this "The principle of all logical affirmation and definition"] Antonius Andreas: The law of Identity, I stated, was not explicated as a coordinate principle till a comparatively recent period. The earliest author in whom I have found this done, is Antonius Andreas, a scholar of Scotus, who flourished at the end of the thirteenth and beginning of the fourteenth century. The schoolman, in the fourth book of his Commentary of Aristotle's Metaphysics – a commentary which is full of the most ingenious and original views, – not only asserts to the law of Identity a coordinate dignity with the law of Contradiction, but, against Aristotle, he maintains that the principle of Identity, and not the principle of Contradiction, is the one absolutely first. The formula in which Andreas expressed it was Ens est ens. Subsequently to this author, the question concerning the relative priority of the two laws of Identity and of Contradiction became one much agitated in the schools; though there were also found some who asserted to the law of Excluded Middle this supreme rank." [From Hamilton LECT. V. LOGIC. 65–66] Three traditional laws: identity, non-contradiction, excluded middle The following states the three traditional "laws" in the words of Bertrand Russell (1912): The law of identity The law of identity: 'Whatever is, is.' For all a: a = a. Regarding this law, Aristotle wrote: More than two millennia later, George Boole alluded to the very same principle as did Aristotle when Boole made the following observation with respect to the nature of