intuitionism

When it comes to the relation of modern mathematics and philosophy, most people tend to think of the three major schools of thought—i.e. logicism, formalism, and intuitionism—that emerged as profound researches on the foundations and nature of mathematics in the beginning of the 20th century and have shaped the dominant discourse of an autonomous discipline of analytic philosophy, generally known under the rubric of “philosophy of mathematics” since then. What has been completely disregarded by these philosophical attitudes, these foundational researches which seek to provide pure mathematics with a philosophically plausible justification by founding it on firm logico-philosophical bases, is that the genuine self-foundation of pure mathematics had been done before, namely during the 19th century, when it was developing into an entirely new and independent discipline as a concomitant of the continuous dissociation of mathematics from the physical world. This self-foundation of the 19th-century pure mathematics, however, was more akin to the German-idealist interpretations of Kant’s transcendental philosophy, than the post-factum, retrospective 20th-century researches on the foundations of mathematics. This article aims to demonstrate this neglected historical fact via delving into the philosophical inclinations of the three major founders of the 19th-century pure mathematics, Riemann, Dedekind and Cantor. Consequently, pure mathematics, with respect to its idealist origins, proves to be a formalization and idealization of certain activities specific to a self-conscious transcendental subjectivity.

Farabi, as a philosopher who presented the Aristotelian tradition in the Islamic world in a distinctive way, combining it with Neoplatonism and Platonism, also retained a large part of Aristotelian epistemology in his own cognitive system. Just as Aristotle, according to modern epistemological interpretations, is largely considered an evidentialist, so is Farabi. Evidentialism means that the only acceptable criterion for adopting beliefs is valid rational or empirical reasons appropriate to that belief. However, in Iran, many, especially some admirers of the Illuminationist  and Mulla Sadra's traditions, attempt to somehow discover a kind of intuitionism or at least evidence against evidentialism in Farabi. This judgment contradicts the view of some major specialists in Islamic philosophy, such as Dimitri Gutas. This issue is very important because the shift in Islamic epistemology from evidentialism to other directions played a very significant role in changing the nature of this philosophy. Accordingly, in this article, we will attempt to show based on which evidence Farabi is an evidentialist, and how he is largely indebted to Aristotle in this evidentialism, and we will also examine the evidence against Farabi's evidentialism. Given that the term "evidentialism" is an expression from contemporary Western epistemology, we will look at Farabi's philosophy from the perspective of this branch of philosophy. In this article, we will primarily view the matter from the perspective of Western specialists in Islamic philosophy, as their language is close to the language of contemporary epistemology. Our research method is descriptive and analytical, and comparative where appropriate. The findings of this research indicate that Farabi is largely an evidentialist, but a moderate one. This finding is very important in relation to determining the place and role of Farabi's epistemology in Islamic philosophy, as well as the later introduction of intuitionism into Islamic philosophy.