Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Intuitionistic Logic As Epistemic Logic

Intuitionistic Logic As Epistemic Logic 8 JAAKKO HINTIKKA But what are the intentions of the founding fathers of intuitionism? An example can illustrate the situation. A crucial experiment is presen- ted to us by the most important single bone of contention in the early controversies between intuitionists and their opponents. This paradigm problem concerns the status of the axiom of choice. This axiom was firmly rejected by Brouwer and it was mooted in the controversies between the French intuitionists and their opponents (cf. Moore 1982, 92–103; 135–137; 311–320). For the purposes of this paper, we can consider the second-order form of the axiom schema for this axiom: (1) .8x/.9y/STx;yU .9f/.8x/STx;f.x/U The antecedent of (1), that is, (2) .8x/.9y/STx;yU is true according to our “intuitive” presystematic ideas if and only if for each value of x thereisa value of y, dependent on x, which makes the matrix STx;yU true. Such verifying individuals are sometimes known as “witness individuals”. If f is a function that expresses the dependence of witness individual y on x,then f satisfies (3) .8x/STx;f .x/U But this means that (1) always is true according to our “intuitions” if (2) is. The function f selects one member of each classfy V STx;yUg and http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Synthese Springer Journals

Intuitionistic Logic As Epistemic Logic

Hintikka, Jaakko
Synthese , Volume 127 (2) – Oct 3, 2004
Download PDF
14 pages

Loading next page...
 
/lp/springer-journals/intuitionistic-logic-as-epistemic-logic-2cJUxamwD9

References (14)

Publisher
Springer Journals
Copyright
Copyright © 2001 by Kluwer Academic Publishers
Subject
Philosophy; Philosophy of Science; Epistemology; Logic; Philosophy of Language; Metaphysics
ISSN
0039-7857
eISSN
1573-0964
DOI
10.1023/A:1010357829038
Publisher site
See Article on Publisher Site

Abstract

8 JAAKKO HINTIKKA But what are the intentions of the founding fathers of intuitionism? An example can illustrate the situation. A crucial experiment is presen- ted to us by the most important single bone of contention in the early controversies between intuitionists and their opponents. This paradigm problem concerns the status of the axiom of choice. This axiom was firmly rejected by Brouwer and it was mooted in the controversies between the French intuitionists and their opponents (cf. Moore 1982, 92–103; 135–137; 311–320). For the purposes of this paper, we can consider the second-order form of the axiom schema for this axiom: (1) .8x/.9y/STx;yU .9f/.8x/STx;f.x/U The antecedent of (1), that is, (2) .8x/.9y/STx;yU is true according to our “intuitive” presystematic ideas if and only if for each value of x thereisa value of y, dependent on x, which makes the matrix STx;yU true. Such verifying individuals are sometimes known as “witness individuals”. If f is a function that expresses the dependence of witness individual y on x,then f satisfies (3) .8x/STx;f .x/U But this means that (1) always is true according to our “intuitions” if (2) is. The function f selects one member of each classfy V STx;yUg and

Journal

Synthese – Springer Journals

Published: Oct 3, 2004

There are no references for this article.