Mathematical Platonism in Roger Penrose

Are mathematical objects independent “beings” from physical objects? How can we define the “existence” of the symmetry groups, Laplace operators or semi-symmetrical hyperbolic functions called “mathematical objects”? Does the condition of existence for mathematical objects lie outside the world, or could it be defined within this world? Is it possible to go beyond this world, to that of ideas? Seen from the perspective of these questions, the problem of the reality of mathematical objects has been a topic of many debates throughout the history of thought. Plato responded to this problem with the concept of the world of ideas. His approach is also in line with many predictions made during the history of mathematics. One of the fundamental debates within the philosophy of mathematics, the question of the existence of mathematical objects has been discussed from different perspectives, including those of Frege, Hilbert, Brouwer, Russell, Turing, Gödel, and finally that of Roger Penrose, who is one of the prominent theoretical physicists of recent history. A significant figure within the current literature, Penrose establishes a connection between mathematics and the field of an “other being,” which has led to the fact that his approach has been called “mathematical Platonism.” This is a philosophical view that argues that mathematical objects exist independently of time, space and the human mind that thinks of them. For this reason, according to this view, mathematical objects such as sets, numbers and mathematical operators etc., exist as objects-in-themselves. For mathematics takes part in an existential domain that is located away from the sheer perception of the human being underlying the universe. Therefore, for Penrose talking about “mathematical objects” is essentially equivalent to a judgement on “physical objects.”

In Search of an Authentic Answer to an Immemorial Question: Is It Possible to Describe (Conclusively) Reality Through Language?

The problem of knowledge and description of reality in language is among the most significant problems of epistemology in general, and philosophy of science in particular. This article discusses the question of whether it is possible to accurately depict reality through language via an examination of the studies of Şakir Kocabaş, who made a rigorous and profound analysis on engineering, applied sciences, logic, artificial intelligence, and philosophy of science. For both understanding and truly solving the problems encountered within philosophy-science, Kocabaş first pointed out the necessity of Grammatical Distinctions of the Statements. He argued that reality, being unable to be described accurately and consistently up to today within both the Western tradition and Islamic thought of the post-translation movement, might be described accurately only by means of a powerful and true conceptual framework. To accomplish this task, he attempted to investigate the concepts in the Qur’an, which he regarded as the unique source of powerful and true language. This article critically examines the scientific approach that Kocabaş tried to develop and his overall judgments on both Western and Islamic traditions. It classifies and analyzes Kocabaş’s project in three steps: his warnings about grammatical distinctions are characterized as obligatory, his efforts to reconcile physics and reality as possible, and finally his inquiry into science relying upon the concepts of the Qur’an as impossible.

The Constituent Effect of Practice on the Modern Science: Solidarity between Homo Faber and Homo Economicus

Main views on the emergence of Modern Science as a revolution in history of thought entail the assumption that its epistemological foundations were unique to the West and reached its maturity after the industrial revolution in terms of determining the common needs of the society. This article argues, in the context of the background of the development of natural philosophy, that daily practices and mechanical arts played a crucial role in rivalry among the social classes for building an ontological security. The problem of the emblematic view of the outside world offered an opportunity for the experimental science and mechanical arts to be the only way of producing knowledge suitable to facts. The continuity of this situation was ensured by the solidarity of the bourgeoisie and artisans as social classes in their survival struggle ending with high level of influence in the society. This process resulted in the controllable and verifiable order of knowledge, causing the transformation of the mindset towards the emergence of the contemporary tekhne.

An Anthropology of the Laboratory Life: Bruno Latour’s Science Studies and their Metaphysical Consequences

Although critiques of positivism in social science literature have overturned the privileged position of science, contemporary techno-science has been penetrating all aspects of our lives. All life areas including production of everyday gadgets to political decision making processes has been determined by science and technology. Some of the most important contributions to understanding the nature of today’s technoscience come from the sociology of science. This article examines, focusing on Bruno Latour’s studies on laboratories, the formation of actor-network theory as a new approach to social sciences, rising from the consequences of laboratory studies developed by the literature of sociology of science, and metaphysical consequences of this theory. In the first section, I try to display the background, in which Latour and Woolgar’s book Laboratory Life is situated, by giving the brief summary of history of the development of sociology of science. Then I panoramically describe the dense discussions in the sociology of science during the 1970s. Thus, I show how Latour differentiates himself from the Edinbugh School’s sociology of scientific knowledge and the Mertonian and Kuhnian sociology of science, thus offering a new approach to the subject. In the second section I review Woolgar and Latour’s laboratory studies in the context of the sociology of science literature. Here I also explain Latour’s findings on the nature of the modern science by means of a discussion on his observations in a neurobiology laboratory. I examine how Latour sees all laboratory practices as an inscription system, how he frames scientific production as a grammatical operation and how he depicts scientists as craftsmen in pursuit of credit. Then I explain his generalized symmetry approach and his critiques on the modern nature-culture dichotomy. Finally, by addressing the philosophical implication of these works, I discuss the significance of the actor-network theory’s realist-constructivist and object-oriented metaphysics and its position within the contemporary philosophical milieu. I thus examine how Latour has developed a post-phenomenological relational approach by deactivating such notions as consciousness, the self, subject, the human and so on. My main argument is that Latour’s anthropological investigation on the social dimension of science has eventually turned into a systematic philosophy and a sociological methodology. I propose that the Latourian object-oriented, constructivist and realist ontology offers new possibilities to conceiving a new mode of subjectivity beyond the notions of the subject or the human.

Technology and Meditation

This article discusses, from a Heideggerian perspective, technology as a fundamental question of our age and consequently the technological understanding of being. Technology has become an eminently autonomous phenomenon in our age, entering between man and being, and imposing its understanding of being on him. Because of this problematic understanding, man forgets his essential relation to being and the very meaning of his existence on earth. The calculative and/or representative thinking constitutes the basis of technological understanding. Heidegger proposes as an antidote to it the meditative manner of thinking. According to him, the essence of thinking is but meditation. The fact that man is a “thinking being” signifies that he is a “being that meditates”. Meditation leads us to serenity/calmness (Gelassenheit), and then to the truth of being. In the framework of meditative thinking and serenity, Heidegger speaks of two significant attitudes as remedy to technology and technological understanding: “indifference toward things” and “openness to mystery”. Man who lives meditatively and serenely knows saying “both yes and no” to technology and maintaining an appropriate relationship to technological devices. Thus, this man, whose relationship to being remains always lively, knows how to serenely and meaningfully reside on earth. The second element of the meditative thinking in Heidegger is, as mentioned, “openness to mystery”. We can experience both elements in our technological world. Once we remain open to mystery, it becomes possible to go beyond the narrow horizons of the calculative and/or representative imagination. We can therefore keep what remains (or should remain) as mysterious away from the reductive light of science, and develop a respect for the enigma of mystery. Thus, we can open up a space for the immeasurable, the indefinable, and unfathomable, in a word, for mystery, in our world that science or the technical reason has demystified; this way we can give its surprise-character back to being, which measurement, calculation, design and objectification have imagined as dissolved/dissolvable. This makes it possible to be vigilant against the reductive attitude of the technical-scientific reason, which consumes everything that it re-presents (vor-stellen), by turning it into an “object of knowledge” and translating it into its own terms. Consequently, man who holds “indifference toward things” and “openness to mystery” can develop an appropriate way of living by saying “both yes and no” to technology, and find an opportunity for a calm residence on earth.

Can We Talk About A Tradition of Logic in Turkey? A Thematic and Bıbliographical Investigation

This article discusses the question of whether we can talk about a tradition of logic in Turkey within the context of a thematic bibliography. Because it is assumed that we can only talk about such a tradition with a bibliographical overview of directly related works. This study not only focuses on logic itself as a discipline but also examines it in terms of its function as a ground for all philosophical and scholarly activities. The bibliography entails the works on both logic specifically and on related areas, including the doctoral and master’s theses, as well as articles, books and conference proceedings, done in Turkey between 1928, when the “Alphabet Revolution” took place, and 2014. An original aspect of the study is its thematic focus. The reason for this is that we aim to determine the range of studies on logic based on different themes, thus also pointing out the issues that have been neglected, thereby helping those who want to study in this field to do a more detailed exploration. Finally, we aim to determine the main problems faced in the study of logic in Turkey. The most important challenge in this context is the fact that the many studies have been done with a strictly academic orientation in the form of studies on specific topics, which may have led them to neglect a concern for developing a sound conception of the history of logic. As a result of extremely specialization, they are extorted from their authentic historical perspective. A result of such an overspecialization has been the treatment of the concepts and problems of logic as if they are separate from the specific context of the history of philosophy, from which it has sprung. The best evidence for this problem is that we see very few works on the philosophy of logic (meta-logic). In additon to these, we also make a number of recommendations for future research in order to help re-construct our conception of logic in Turkey. One of them is the establishment of some instutions specifically focusing on the study of logic, including a “Logic Studies Center”, a “Logic Specialization Library”, and a “Journal of Logic Studies.” We believe that these institutions may play a major role in the formation of a tradition of logic in Turkey. The article also entails, in addition to the specific works on logic, studies on the philosophy of science and of language, and epistemology. The rationale behind this is the idea that logic studies cannot be complete without interaction with these neighboring disciplines.


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