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.
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