Logic and the foundations of mathematics in early logical empiricism

2021 ◽  
pp. 139-147
Author(s):  
Erich H. Reck
Hypatia ◽  
2004 ◽  
Vol 19 (1) ◽  
pp. 48-72 ◽  
Author(s):  
Kathleen Okruhlik
Keyword(s):  

Author(s):  
Michael Ernst

In the foundations of mathematics there has been an ongoing debate about whether categorical foundations can replace set-theoretical foundations. The primary goal of this chapter is to provide a condensed summary of that debate. It addresses the two primary points of contention: technical adequacy and autonomy. Finally, it calls attention to a neglected feature of the debate, the claim that categorical foundations are more natural and readily useable, and how deeper investigation of that claim could prove fruitful for our understanding of mathematical thinking and mathematical practice.


2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Thomas Mormann

Abstract The main thesis of this paper is that Pap’s The Functional A Priori in Physical Theory and Cassirer’s Determinism and Indeterminism in Modern Physics may be conceived as two kindred accounts of a late Neo-Kantian philosophy of science. They elucidate and clarify each other mutually by elaborating conceptual possibilities and pointing out affinities of neo-Kantian ideas with other currents of 20th century’s philosophy of science, namely, pragmatism, conventionalism, and logical empiricism. Taking into account these facts, it seems not too far fetched to conjecture that under more favorable circumstances Pap could have served as a mediator between the “analytic” and “continental” tradition thereby overcoming the dogmatic dualism of these two philosophical currents that has characterized philosophy in the second half the 20th century.


Synthese ◽  
2021 ◽  
Author(s):  
Ansgar Seide

AbstractIn this paper, I take a closer look at Hans Reichenbach’s relation to metaphysics and work out some interesting parallels between his account and that of the proponents of inductive metaphysics, a tradition that emerged in the mid- and late 19th century and the early 20th century in Germany. It is in particular Hans Reichenbach’s conception of the relation between the natural sciences and metaphysics, as displayed in his treatment of the question of the existence of the external world, that shows some very interesting similarities with inductive metaphysics. By a comparison with the position of the inductive metaphysician Erich Becher and his handling of the problem of realism, I work out the parallels between Reichenbach’s program and inductive metaphysics. I come to the conclusion that while there are certainly some respects in which Reichenbach’s logical empiricism is closer to the positions of the representatives of the Vienna Circle, it turns out that with regard to his views on metaphysics there is a greater affinity with the program of inductive metaphysics.


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