Another midnight reading/studying (with glass of fine scotch whiskey), still partaking of George Boole's 1854 book An Investigation of the Laws of Thought as part of a list of books in preparation for my current book project on the singular human right to consent or dissent on all matters. Thus, intriguingly fascinating...
"That axiom of metaphysicians which is termed the principle of contradiction, and which affirms that it is impossible for any being to possess a quality, and at the same time not to possess it, is a consequence of the fundamental law of thought, whose expression is x2 = x. Let us write this equation in the form x − x2 = 0, whence we have x (1 − x) = 0; both these transformations being justified by the axiomatic laws of combination and transposition."
George Boole (1815-1864, mathematician/philosopher/logician)
Boole clarified the context prior by defining the number "1" to equal "Universe" or "Everything" while the number "0" to equal "Nothing" or "Impossible". In so doing, he algebraically represented the logical law of contradiction (2nd law below), or as Jevons described thus defined best in his 1870 book Elementary Lessons in Logic: Deductive and Inductive...
"These laws describe the very simplest truths, in which all people must agree, and which at the same time apply to all notions which we can conceive. It is impossible to think correctly and avoid evident self-contradiction unless we observe what are called the Three Primary Laws of Thought, which may be stated as follows:
1. The Law of Identity. Whatever is, is.
2. The Law of Contradiction. Nothing can both be and not be.
3. The Law of Excluded Middle. Everything must either be or not be.
Though these laws when thus stated may seem absurdly obvious...I have found that students are seldom able to see at first their full meaning and importance."
William Stanley Jevons (1835-1882, economist/logician)
Come let us Reason. Peace is always a Choice.
Study, Ponder, Labor, till last Breath.
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