The problem of a priori justification in contemporary philosophies of logic, mathematics and knowledge

It's usually been thought that epistemic justification has an a priori character in logic and mathematics, which are traditionally regarded as formal sciences. In this study, the question of the extent to which this idea can be defended today is evaluated by taking into consideration the approaches from the contemporary philosophy of logic, mathematics and knowledge. In other words, this study reveals the contemporary dialectic about the problem of the source of epistemic justification in logic and in mathematics, and outlines and critically examines it. On this basis, in this study it is primarily argued that the contemporary dialectic of the problem develops around three approaches that have succeeded in creating thought schools or traditions. The first one is the analytic approach, which suggests that in logic and mathematics a priori justification is possible, but a priori knowledge is not possible. The second one is the moderate rationalist approach, which suggests that both a priori justification and a priori knowledge are possible. The third one is the naturalist approach, which suggests that neither a priori justification nor a priori knowledge is possible. In this study, these three approaches are examined together with their basic arguments in three separate sections, and the dialogue between these approaches is revealed, and at the end of each chapter, the approaches examined are evaluated together with the criticism directed towards these approaches. At the end of the study, it is argued that the debates around these three main approaches, and therefore the contemporary dialectic about the problem, were unfortunately rooted around the modal status attributed to the logical and mathematical judgements, and in this way, the basic arguments about the problem were established primarily by considering this subject. On the other hand, epistemological inquiries are meaningful only when they are focused on actual or concrete problems. Today, the most fervent debate in philosophy of logic concerns how a choice can be made between standard logic and deviant logics (eg, intuitive logic, para-consistent logic, etc.). The most heated debates in the philosophy of mathematics ultimately address what kind of system (or theory) should be placed on the base of mathematics and how a choice may be made between applied mathematics tendency and pure mathematics tendency in the selection of this system. On this basis, in the conclusion section of this work, these three basic contemporary approaches are re-evaluated by taking these actual and concrete problems into account. As a result of this evaluation, it is argued that the analytic approach offers a moderate way between pure mathematics tendency and applied mathematics tendency, which is closer to empiricist standpoint; that moderate rationalism offers a mathematical (and logical) methodology which, on the one hand, remains in pure mathematics while on the other hand does not give up its claim of truth and reality; and that naturalist approach offers a methodology in which mathematics and logic become applied areas by leaving the pure mathematics tendency behind. Keywords: A Priori, A Priori Justification, A Priori Knowledge, Philosophy of Logic, Philosophy of Mathematics, Epistemology