TY - JOUR
AU1 - Hintikka, Jaakko
AB - 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 
TI - Intuitionistic Logic As Epistemic Logic
JF - Synthese
DO - 10.1023/A:1010357829038
DA - 2004-10-03
UR - https://www.deepdyve.com/lp/springer-journals/intuitionistic-logic-as-epistemic-logic-2cJUxamwD9
SP - 7
EP - 19
VL - 127
IS - 2
DP - DeepDyve
ER -