[CG] Re: Peirce's 1885 “Algebra of Logic”

Peirce's 1885 “Algebra of Logic” • Selection 2.3 • https://inquiryintoinquiry.com/2024/03/26/peirces-1885-algebra-of-logic-sel… ❝On the Algebra of Logic❞ ❝A Contribution to the Philosophy of Notation❞ ❝§1. Three Kinds Of Signs❞ (cont.) ❝With these two kinds of signs alone any proposition can be expressed; but it cannot be reasoned upon, for reasoning consists in the observation that where certain relations subsist certain others are found, and it accordingly requires the exhibition of the relations reasoned with in an icon. ❝It has long been a puzzle how it could be that, on the one hand, mathematics is purely deductive in its nature, and draws its conclusions apodictically, while on the other hand, it presents as rich and apparently unending a series of surprising discoveries as any observational science. ❝Various have been the attempts to solve the paradox by breaking down one or other of these assertions, but without success. The truth, however, appears to be that all deductive reasoning, even simple syllogism, involves an element of observation; namely, deduction consists in constructing an icon or diagram the relations of whose parts shall present a complete analogy with those of the parts of the object of reasoning, of experimenting upon this image in the imagination, and of observing the result so as to discover unnoticed and hidden relations among the parts.❞ (3.363). Regards. Jon cc: https://www.academia.edu/community/LpepBY cc: https://mathstodon.xyz/@Inquiry/112156450035935700