Murat Kelikli

This paper reconstructs a “logic of the future” for indeterministic settings by separating three semantic roles that are often conflated when future-tense truth is identified with probability. First, we introduce an external bivalent semantics in which truth is evaluated along branching histories and settlement is defined relative to admissible continuations. Second, we distinguish an internal probabilistic layer: a measure over admissible histories representing objective chance or assertibility rather than truth. Third, and most importantly, we add a minimal record–determination layer, expressed by the operators $$\boldsymbol {\mathsf Rec}$$ and $$\boldsymbol {\mathsf Det}$$, which explains when classical reasoning is locally licensed within an otherwise open and indeterministic future. We show that under $$\boldsymbol {\mathsf Rec}+\boldsymbol {\mathsf Det}$$ classical inference is recovered exactly at those points where records determine outcomes, without entailing global determinism. The main technical results, including the Domino Lemma and the Record-to-Outcome Theorem, formalize the idea that once a fact is recorded and dynamically linked to a future outcome, that outcome becomes settled for purposes of truth-evaluation and reasoning. The framework is semantic and interpretation-neutral: rather than adjudicating between quantum interpretations, it provides a principled semantic criterion for when classical reasoning is locally licensed within an indeterministic setting. In this way it preserves Aristotle’s anti-fatalist insight from De Interpretatione 9, retains Sudbery’s probabilistic machinery for quantum chance, and provides a principled criterion for the local return of classical logic.

Mathematics embodies a complex universe of abstract concepts in human thought. However, the ontology of mathematical objects requires a deep analysis in order to understand not only the physical world, but also beyond the abstract world. This paper considers the fundamental qualities of mathematical objects and how we can use Aristotle's theory of substance to understand these entities. Aristotle's account of mathematical objects may be incomplete, but by using his understanding of substance, I aim to present my own assessment in the most favourable light to Aristotle. Rather than being a direct assessment of Aristotle, this paper aims to explain my view as the most favourable possible.

In ancient philosophy, Logic was seen as the instrument and method of philosophy. However, sometimes detailed and profound discussions have been made about the demonstrativeness of philosophical sciences. Most philosophers have accepted that the mathematical sciences were especially demonstrative and likewise, most of the natural sciences are demonstrative for them. But can metaphysics be demonstrative or not? This is one of the fundamental issues around which the great debates were made in Islamic philosophy. While these issues are known to specialists in this field, we can hardly find studies and research that deal with this issue to a sufficient degree and precise discussions in our day, I mean the issue of demonstrativeness of art of demonstration, art of dialectic, art of sophistry, art of rhetoric and art of poetry. It is clear that the peripatetic philosophers did not write a separate book or treatise on the issue of the demonstrativeness of the logical arts, but we can claim that they believed that all these arts were demonstrative and that they were extracted/abstracted using the art of demonstration. We can come across important phrases and statements that prove this claim between the lines of the books that these philosophers wrote in the science of logic. And while Aristotle is the founder of the science of logic, then how is it to be understood that there are practical particular examples and some easy rules of these arts? According to their texts, we can say that they believed that the actual performance of these arts by their actors in materials by particular and practical actions differs from extracting their universal rules by abstracting them from their materials through theoretical and analytical research. For example, the poems of the great poets; Homer and al-Mutanabbi, are particular works in the matter of the art of poetry performed by poets. The books written by Aristotle and Ibn Rushd in the art of poetry contain universal rules extracted abstractly from the materials of their particular poems. As for understanding the demonstrativeness of the remaining four arts, it is easier, but how should we understand the demonstrativeness of the art of demonstration itself? It seems that the peripatetic logicians also distinguished between applying demonstrative inferences to significant materials and extracting the universal rules of the art of demonstration from these materials. These five logical arts are not particular and practical things, but they are philosophical, demonstrative, and analytical studies for the peripatetic logicians in Islam. In this paper, we will try to draw attention to the issue of the demonstrativeness of the five arts and to open a new discussion about it based on some important sentences and phrases expressed by al-Fārābī, Ibn Zur‘a, Ibn Sīnā, Ibn Bājja and Ibn Rushd between the lines in their books, which they wrote in the field of logic and within different and multiple contexts.

Although there are many questions to be asked about philosophy of mathematics, the fundamental questions to be asked will be questions about what the mathematical object is in view of being and what the mathematical reasoning is in view of knowledge. It is clear that other problems will develop in parallel within the framework of the answers to these questions. For this rea­ son, when we approach Aristotle's philosophy of mathematics over these two basic problems, we come up with the concept of abstraction. In our work, I will try to explain the mathematical abstraction that Aristotle has developed to understand mathematical philosophy.

Redictio ad absurdum is an important part of Aristotle’s syllogistic. It is connected with direct proof and they are complementary methods. All moods of Aristotle are provable by direct methods and redictio ad absurdum. In this paper, I have studied on the bases and principles of redictio ad absurdum, I showed how to prove by redictio ad absurdum, and how to prove Aristotle by redictio ad absurdum. By redictio ad absurdum, all forms of Aristotle’s method proved in the first figure can be reduced to the perfect forms.

There are a lot of studies on Ahmed Cevdet Paşa who has been considered as statesman, politician, jurist, historian, sociologist and educationalist. At the same time Ahmet Cevdet Paşa’s studies on logic are critically important when we deal with the last period of the Ottoman Empire. His book which is called Miyar-ı Sedad had both influenced the development of instruction of logic education in madrasahs and created a turning point in the studies on modern logic. For this reason we have discussed his opinions about logic and science in this study and we have also tried to show that how his opinions on these issues affecected the instruction and the other fields.