The first part of this paper recalls contributions of general philosophical interest which have been made by foundational research, and lists some specific contributions of this sort made by constructivist foundations; in particular, to the history of ideas, and to the correction of wide-spread convictions. The second part goes into the heuristic value of developing constructivist foundations systematically, and into the conflict between the (naive) requirement of (i) solving a problem by means of constructive operations, and the additional (sophisticated) requirement of establishing (i) by a constructive proof. The third part contains some new results on constructive propositional logic (also of interest to specialists in the subject), which illustrate pedagogic uses of constructivist foundations; in particular, for understanding phenomena in advanced model-theoretic socalled classical logic, in connection with functional and deductive completeness, or with extending the domain of definition of familiar operations.
[1]
Carl G. Jockusch,et al.
Ramsey's theorem and recursion theory
,
1972,
Journal of Symbolic Logic.
[2]
H. Keisler.
Logic with the quantifier “there exist uncountably many”
,
1970
.
[3]
A. S. Troelstra.
On a second order propositional operator in intuitionistic logic
,
1981
.
[4]
H. Keisler,et al.
Handbook of mathematical logic
,
1977
.
[5]
J. Paris.
A Mathematical Incompleteness in Peano Arithmetic
,
1977
.
[6]
Olgierd Wojtasiewicz,et al.
Elements of mathematical logic
,
1964
.
[7]
A. Troelstra.
Choice sequences : a chapter of intuitionistic mathematics
,
1977
.
[8]
D. Gabbay.
On some new intuitionistic propositional connectives. I
,
1977
.
[9]
Jeffery I. Zucker,et al.
The adequacy problem for inferential logic
,
1978,
J. Philos. Log..
[10]
Dean P. McCullough.
Logical Connectives for Intuitionistic Propositional Logic
,
1971,
J. Symb. Log..
[11]
Horst Luckhardt.
Über das Markov-Prinzip II
,
1977,
Arch. Math. Log..