nature and application of logic
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. …
The real scientific method is the inductive method invented by Socrates and elaborated by Aristotle, Bacon, and Whewell. It is different from the hypothetico-deductive method invented by JS Mill in the 19th century which is passed off as the method of modern science. Consider Francis Bacon. He called immature concepts “notions”. Induction starts with notions …
We have some knowledge but it is not complete knowledge, not even arguably near complete. So what should we do about the areas where knowledge is lacking? We should certainly continue to investigate. But what do we say in the mean time? What can we justify saying about the unknown side of partial knowledge? There …
Motivating Example According to the Gospels, there was an inscription above Christ on the cross which said (in English translation): Matthew (27.37): “This is Jesus, the King of the Jews. ” (ABD) Mark (15.27): “The King of the Jews.” (D) Luke (23.38): “This is the King of the Jews.” (AD) John (19.19): “Jesus of Nazareth, …
