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- W246130529 abstract "In the 1880 paper, Peirce struggled to work out the sense in which universal and existential quantification was dual via negation, in an attempt to bring the Aristotelian syllogisms within the introduced system of implicative logic. The quantified variables introduced, were not explicit, nor were a good properly scoped substitute available. In this paper, Peirce not only reworks some of the material of previous research, but also shows evidence of his originality as a mathematician and logician. A lattice-theoretic treatment of Boolean algebra has been introduced that appears to be the first of such approach. A system of implicative propositional logic that anticipates the main features of modern systems of “natural deduction” by a rule converting deductions (illations) into implications (there called inclusions) have also been developed. This appears to have been completely original with him. Peirce's 1880 paper is long and complex. It can be seen in latter equations in this paper that the notation for quantification has been used over individuals. Still, he can be given no credit for understanding quantifier logic at this time, because he did nothing with it. After all, sums and products over indices occur all over mathematics in infinite series and products; the challenge is the alternation of quantifiers. This chapter first gives a summary, with commentary, of its important points; then the chapter discusses in detail, some of the ideas that it develops." @default.
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- W246130529 date "1983-12-01" @default.
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- W246130529 title "Writings of Charles S. Peirce. A Chronological Edition. Vol. I. 1857–1866" @default.
- W246130529 doi "https://doi.org/10.1016/0378-2166(83)90097-8" @default.
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