ANDRZEJ MOSTOWSKI AND PHILOSOPHY OF MATHEMATICS
Jan Wolenski (Jagiellonian University, Kraków, Poland)

The Polish attitude to metamathematics, shared by most Polish logicians was 
(and is) guided by two principles: (a) all commonly accepted mathematical 
methods should be applied in metamathematical investigations; 
(b) metamathematical research cannot be limited by any a priori accepted 
philosophical standpoint. On the other hand, mathematics has own genuine 
philosophical problems, which should not be neglected by mathematicians. 
In particular, although metamathematical results do not solve philosophical 
controversies about mathematics, yet the former illuminate the latter. 
Tarski was an extreme example of this practice. He used all admissible 
mathematical methods in his logical works, in particular, infinitary ones, 
usually associated with Platonism in the philosophy of mathematics. On the 
other hand, Tarski had explicit sympathies to empiricism, nominalism, reism 
and finitism (he even called himself "a tortured nominalism"). In general, 
Mostowski inherited his general philosophical attitude from Tarski. He was 
very sensitive to philosophical problems in mathematics and considered them 
as important. Although Mostowski stressed that there is no hope in achieving 
the solution of such questions, he yet insisted that should be illuminated 
by mathematical treatment of them. He freely used infinitary methods and 
strongly insisted that no formal work should be limited by philosophical 
assumptions. On the other hand, he had some sympathy to constructivism 
and related views.