nature and application of logic
Propositions are contrary if they cannot both be true (though they both may be false). Propositions are contradictory when the truth of one implies the falsity of the other, and conversely. Two properties are contraries if their intersection is null and their union is a whole. A merism is a rhetorical combination of two contrary […]
I’ve written before about Laws of Form (the calculus of indications); see here and here. In the beginning is an undifferentiated state, an unmarked space. The first distinction is the first differentiation, the advent of a mark, a cross, a form. The unmarked state is the urgrund of the form, its origin and basis. The
George Boole is known for introducing a logical calculus for propositions in the mid-19th century. Although others before him such as Leibniz worked on logical calculi, Boole developed the first systematic one. Later C. S. Peirce and Gottlob Frege developed calculi that took into account the difference between universal and existential propositions. Since then many
George Boole wrote on “the laws of thought,” now known as Boolean Algebra, and started the discipline known as Symbolic Logic. A different George, George Spencer Brown, wrote on “the laws of form,” which presented an arithmetic system underlying logic. Below are two symbolic logics equivalent to Boolean algebra that resemble ordinary arithmetic in some
Another paper that should get wider exposure: “The Classical Model of Science: a millennia-old model of scientific rationality” by Willem R. de Jong and Arianna Betti. Synthese (2010) 174:185-203. Excerpts: Throughout more than two millennia philosophers adhered massively to ideal standards of scientific rationality going back ultimately to Aristotle’s Analytica posteriora. These standards got progressively
John P. McCaskey has done a lot of research (including a PhD dissertation) on the meaning of induction since ancient times. He keeps some of his material online at http://www.johnmccaskey.com/. A good summary is Induction Without the Uniformity Principle. McCaskey traced the origin of the principle of the uniformity of nature (PUN) to Richard Whately
Two propositions are contrary if they cannot both be simultaneously true but it is possible for both to be simultaneously false. For example, the proposition that “every man is just” is contrary to the proposition that “no man is just,” since both propositions may be false if some men are just. Two propositions are contradictory if both cannot
In the beginning God created the heavens and the earth. The merism “the heavens and and the earth” indicates the totality of what God created. It also indicates the first distinction, which is between the heavens and the earth. The subsequent focus on the earth indicates that the earth is the marked state (cf. post
This is a follow-up to the introductory post on Laws of Form here. There are two kinds of negation: contraries and contradictories, and Laws of Form (LoF) represents both types. Furthermore both types apply to terms and propositions. Contraries are two complete opposites; the negation of one is the other. The poles of a magnet
The remarkable book Laws of Form by George Spencer-Brown was published in 1969 and is almost forgotten today. The best expositors have been William Bricken with his boundary mathematics, Louis Kauffman with his knot theory, and Francisco Varela with his work on self-reference. Otherwise it has become something of an underground classic but otherwise forgotten.
