to be the case with the law of continuity, these two laws involve matters which, in contemporary terms, are subject to much debate and analysis (respectively on determinism and extensionality). Leibniz's principles were particularly influential in German thought. In France, the Port-Royal Logic was less swayed by them. Hegel quarrelled with the identity of indiscernibles in his Science of Logic (1812–1816). Schopenhauer Four laws "The primary laws of thought, or the conditions of the thinkable, are four: – 1. The law of identity [A is A]. 2. The law of contradiction. 3. The law of exclusion; or excluded middle. 4. The law of sufficient reason." (Thomas Hughes, The Ideal Theory of Berkeley and the Real World, Part II, Section XV, Footnote, p. 38) Arthur Schopenhauer discussed the laws of thought and tried to demonstrate that they are the basis of reason. He listed them in the following way in his On the Fourfold Root of the Principle of Sufficient Reason, §33: A subject is equal to the sum of its predicates, or a = a. No predicate can be simultaneously attributed and denied to a subject, or a ≠ ~a. Of every two contradictorily opposite predicates one must belong to every subject. Truth is the reference of a judgment to something outside it as its sufficient reason or ground. Also: To show that they are the foundation of reason, he gave the following explanation: Schopenhauer's four laws can be schematically presented in the following manner: A is A. A is not not-A. X is either A or not-A. If A then B (A implies B). Two laws Later, in 1844, Schopenhauer claimed that the four laws of thought could be reduced to two. In the ninth chapter of the second volume of The World as Will and Representation, he wrote: Boole (1854): From his "laws of the mind" Boole derives Aristotle's "Law of contradiction" The title of George Boole's 1854 treatise on logic, An Investigation on the Laws of Thought, indicates an alternate path. The laws are now incorporated into an algebraic representation of his "laws of the mind", honed over the years into modern Boolean algebra. Rationale: How the "laws of the mind" are to be distinguished Boole begins his chapter I "Nature and design of this Work" with a discussion of what characteristic distinguishes, generally, "laws of the mind" from "laws of nature": "The general laws of Nature