Dissertation Abstract
Peircean Imagination: The Role Of
Mathematical Reasoning
In C. S. Pierce's Philosophy Of
Religion
by
Kathleen Ann Hull
Degree: PH.D.
Year: 1996
Pages: 00216
Institution:
Advisor: Robert Corrington
Source: DAI, 57, no. 04A, (1996): 1653
The primary focus of this project is Peirce's
theory of mathematical reasoning and its application to his philosophy of
religion, after 1890. The central thesis is that Peirce carries Kant's critique
of pure reason to its next logical step by incorporating a role for a
non-empirical, inner "experience" into mathematics. Necessary
reasoning is thus grounded in human experience, carefully understood. The key
to Peirce's contribution is his phenomenological examination of mathematical
proof, in light of his three categories of reality. Imaginative reasoning with diagrams
is found to be intimately tied with Peirce's metaphysics: we
"experience" our mathematical diagrams not only cognitively, but
sensuously, in virtue of their iconicity (Firstness) and percussivity
(Secondness). Mathematical reasoning with diagrams is found, by Peirce, to be
essentially creative; and it is the backbone of his view of how we reason
toward a belief in God in his "Neglected Argument for the Reality of
God."
Our
starting point for discussion is the claim that Peirce makes an important
distinction between mathematics and logic. In contrast to the philosophical
"tradition" stemming from Frege, Russell, et.al.,
we find that Peircean mathematics is a pre-logical reasoning practice which
does not require a theoretical foundation in logic. Peirce's view of
mathematical reasoning emerges, we suggest, from Kant's First Critique where
the mathematician is said to make an intuitive, not discursive, use of reason
by means of the construction of concepts. This method becomes a model for
reasoning with diagrams, in which the thinker is not reduced to reasoning upon
a rule or definition, but may create new concepts and ideas based on inner
observations.
Musement
in Peirce's N. A. is read as an exploration of how we reason about God through
reasoning about infinite sets, by applying Cantorian set theory to Peirce's
three categories. A direct perception of God is understood as the experience of
creatively reasoning with diagrams about the interrelations of the three
categories.
Peirce
is situated in the history of the philosophy of mathematics, in relation to
Plato, Aristotle, Lully, Leibniz, Descartes, Kant, Mill and key
twentieth-century thinkers. We discuss his rejection of mechanistic views of
reasoning, including Babbage's reasoning machine.
SUBJECT(S)
Descriptor:
PHILOSOPHY
RELIGION, PHILOSOPHY OF THEOLOGY
Accession No:
AAG9629112
Provider:
OCLC
Database:
Dissertations