Post : Mathematical Demonstration & the Doctrine of Individuals : 1
http://inquiryintoinquiry.com/2015/02/22/mathematical-demonstration-the-doctrine-of-individuals-1/
Posted : February 22, 2015 at 11:40 am
Selection from C.S. Peirce, “Logic Of Relatives” (1870), CP 3.45–149
<blockquote>
92. Demonstration of the sort called mathematical is founded on suppositions of particular cases. The geometrician
draws a figure; the algebraist assumes a letter to signify a single quantity fulfilling the required conditions. But
while the mathematician supposes an individual case, his hypothesis is yet perfectly general, because he considers no
characters of the individual case but those which must belong to every such case. The advantage of his procedure lies
in the fact that the logical laws of individual terms are simpler than those which relate to general terms, because
individuals are either identical or mutually exclusive, and cannot intersect or be subordinated to one another as
classes can. Mathematical demonstration is not, therefore, more restricted to matters of intuition than any other kind
of reasoning. Indeed, logical algebra conclusively proves that mathematics extends over the whole realm of formal
logic; and any theory of cognition which cannot be adjusted to this fact must be abandoned. We may reap all the
advantages which the mathematician is supposed to derive from intuition by simply making general suppositions of
individual cases.
</blockquote>
References
• Peirce, C.S. (1870), “Description of a Notation for the Logic of Relatives,
Resulting from an Amplification of the Conceptions of Boole's Calculus of
Logic”,
''Memoirs of the American Academy of Arts and Sciences'' 9, 317–378, 26
January 1870.
Reprinted, ''Collected Papers'' 3.45–149, ''Chronological Edition'' 2,
359–429.
Online
(1) ( http://www.jstor.org/stable/25058006 )
(2) ( https://archive.org/details/jstor-25058006 )
(3) ( http://books.google.com/books?id=fFnWmf5oLaoC ) .
• Peirce, C.S., ''Collected Papers of Charles Sanders Peirce'',
vols. 1–6, Charles Hartshorne and Paul Weiss (eds.),
vols. 7–8, Arthur W. Burks (ed.), Harvard University Press,
Cambridge, MA, 1931–1935, 1958.
• Peirce, C.S., ''Writings of Charles S. Peirce : A Chronological Edition'',
Peirce Edition Project (eds.), Indiana University Press,
Bloomington and Indianoplis, IN, 1981–.
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