Augustus De Morgan and the Logic of Relations by Daniel D. Merrill

By Daniel D. Merrill

The heart years of the 19th century observed the most important advance­ ments within the historical past of contemporary common sense: George Boole's algebraic deal with­ ment of common sense and Augustus De Morgan's formula of the common sense of kinfolk. the previous episode has been studied broadly; the latter, hardly ever in any respect. it is a pity, for the main significant characteristic of contemporary good judgment might be its skill to deal with relational inferences. De Morgan used to be the 1st individual to see an intensive common sense of relatives, and the aim of this publication is to check this test intimately. Augustus De Morgan (1806-1871) used to be a British mathematician and philosopher who was once Professor of arithmetic on the college of London (now, college collage) from 1828 to 1866. A prolific yet no longer hugely unique mathematician, De Morgan dedicated a lot of his energies to the really assorted box of good judgment. In his Formal good judgment (1847) and a chain of papers "On the Syllogism" (1846-1862), he tried with nice ingenuity to reformulate and expand the tradi­ tional syllogism and to systematize modes of reasoning that lie outdoor its obstacles. leader between those is the common sense of kin. De Mor­ gan's curiosity in kinfolk culminated in his vital memoir, "On the Syllogism: IV and at the good judgment of Relations," learn in 1860.

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Is the standard first figure AAA of the syllogism which, however, is stated in a somewhat unusual way. De Morgan supposes that we are given three figures, a circle, a triangle, and a square, and we wish to assert propositions concerning which of them are contained in which of the others. 7) All the 0 is in the 6.. All the 0 is in the O. All the 0 is in the 6.. " This would make it appear that we have yet another relation whose transitivity is taken as a primitive rule. 8) All the B is in the A.

Furthermore, one may well wonder just how an assertion is being made in saying, "If Mary is at work then John is at home," since neither "is" carries assertive force, and there is no other sign of assertion in the usual form. " We seem headed for a Procrustean bed, especially when this standard form is taken to contain something much more specific as well. " When the "ultimate" form of "every living man respires" is "every living man is one of the things which respire," the verb "respires" has become "is one of the things which respire"; and what is really asserted is that "every living man is identical with one of the things which respire"(FL, 9).

His claim is not one of unlimited generality, though, because it uses the notion of comparison, of noting similarities and differences between two items and some other "middle" item. The point may be put by saying that a wider generalization would involve somehow relating two terms by means of a third term, but that De Morgan limits this to relations involving similarity or difference. We may conclude that De Morgan's characterization of inference is not inherently syllogistic, and that it only becomes so when a very specific mode of propositional analysis is introduced.

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