The authors explicate Aquinas's conception of mathematics. They show that in his work the Aristotelian conception is prevalent, according to which this discipline is—together with physics and metaphysics—a theoretical science, whose subject is the study of real quantity and its necessary properties. But, alongside this dominant and prevalent conception, Aquinas's work contains a number of indications that cast doubt. These sparse and rather marginal reflections lead the authors to conclude that Aquinas's texts contain a "constructivist" conception of mathematics in rudimentary (...) form. According to this approach, mathematics is not a theoretical science examining real quantity but, rather, a special kind of "art" by means of which mathematical objects are "created." From a constructivist point of view the authors then attempt to formulate a conception of mathematics that would accord with the basic Aristotelian assumptions of Aquinas's thought. (shrink)

We deal with the concept of man and woman, as well as with the problem of their equality, in the two great ancient thinkers Plato and Aristotle. The discussion of Plato leads to the conclusion that there is no substantial difference between man and woman. We find Plato’s view close or similar to today’s widely held doctrine of “unisexism”. Aristotle on the other hand believes that there are important differences between man and woman and we find in his texts two (...) approaches to the problem. In his first view the sex difference is due to the lesser perfection of woman, according to the second view both sexes are equally perfect, nevertheless each in its own way. Both conceptions have their supporters in contemporary thought (so-called theories of „polarism“ and „compatibilism“). From a systematic point of view we suggest that Aristotle´s second approach should be further developed as it is most in accord with our Christian worldview. (shrink)

The author shows that, after some considerations about the nature of speech, we can take two substantially different paths. Wittgenstein’s early philosophy is the paradigm of the first path, his later the paradigm of the second. According the author, the difference between these two conceptions is that in the late Wittgenstein, as opposed to his early conception, rejects the search for, and the clarification of, the essence of our language.

Discussion on Two Remarks on Ondřej Švec’s Note regarding Philosophy of History.

The author shows that Aquinas’s treatise on the Trinity can be viewed in two ways. According to the first, now prevailing opinion, the thoughts of the Angelic Doctor are too speculative and in essence they harm our personal relationship with God. He aims to show that the main source of inspiration for this approach are those currents in modern and contemporary philosophy according to which any metaphysics is impossible. Adherents of the other view do not reject metaphysics, and so they (...) are also sympathetic towards Aquinas’s connecting speculation with the Trinity doctrine. They see a great advantage in this connexion, as it allows us to understand more deeply the mysteries of faith and so to demonstrate the uniqueness of the Christian message. The author aims to show that both approaches are justified and one should not be sacrificed for the other. He believes that a philosophical framework allowing the old and the new Trinitarian theologies to coexist is provided by Wittgenstein’s conception of speech games. (shrink)

This paper is a Czech translation and critical interpretation of 'Dialog s Pünjerem' by G. Frege.

Responsione nostra disputationem cum L. Novák prosequimur, qui tractationem nostram, cui titulus “Různá pojetí matematiky u vybraných autorů od antiky po raný novověk”, impugnavit. Impugnatio a L. Novák sub titulo “Tomáš Akvinský instrumentalistou v matematice?” conscripta ansam praebuit nobis ad nonnulla, quae dixeramus, non solum clarius, sed etiam latius ac profundius explananda. Qua in re inprimis ad hoc attendimus, quomodo S. Thomas mathematicam, scientiasque medias necnon philosophiam intellexerit. Adhuc in nostra sententia sistimus, duplicem scil. ac valde diversam interpretationem harum disciplinarum (...) proponi posse. Quamquam multi textus testantur, S. Thomam mathematicam scientiasque medias realistice intellexisse, inveniuntur tamen apud eum dicta nonnulla, quae interpretationi favent instrumentalisticae. Hanc duplicem interpretationem prae oculis ponere multum iuvat, nostro iudicio, ad subsequentem intellectualem historiam, praecipue modernae aetatis, adaequate intelligendam.In our contribution we continue our discussion with L. Novák, who criticised our paper “Různá pojetí matematiky u vybraných autorů od antiky po raný novověk.” Novák’s critique titled “Tomáš Akvinský instrumentalistou v matematice?” served as an incentive for us not only to clarify certain points, but also to deepen our original exposition. We focused on Aquinas’s understanding of mathematics, the middle sciences and philosophy. We still insist that two substantially different interpretations of these disciplines are possible. On the one hand, there is much evidence for Aquinas’s realistic approach to mathematics and the middle sciences. On the other hand, ideas can also be found in Aquinas’s texts supporting an instrumentalist reading. In our opinion, it is important to point out these two approaches to the mathematical sciences in order to adequately understand the subsequent evolution of the history of ideas, especially in the modern period. (shrink)

Petr Dvořák hájí ve své knize Kauzalita činitele libertariánské pojetí svobody lidské vůle. Vůli považuje za duševní schopnost člověka a její svobodu spatřuje v možnosti její sebedeterminace. Tuto tezi autor tohoto příspěvku kritizuje. Dokazuje, že sebedeterminující schopnost je contradictio in terminis. Libertariánsky pojatá svobodná vůle je možná jen, pokud není schopností. Takovou vůlí je pouze vůle Boží (za předpokladu, že Bůh existuje). Autor připojuje historické upozornění, že autorem omylu zaměňujícího lidskou vůli s Boží je renezanční teolog Ludvík Molina, že k (...) jeho stoupencům náležel i René Descartes. (shrink)

In this article I consider two aspects of Moore’s philosophical method which lead to the turn to natural language. These are his interest in the meaning (not the truth) of problematic philosophical theses and his interest in common sense philosophy. However, Moore himself did not completely achieve the linguistic turn: he merely prepared the way for it. In the conclusions I show that Moore’s themes were developed by N. Malcom. The deeper sense of my paper is to show that the (...) linguistic turn as begun by Moore does not conflict with the spirit of the Aristotelian tradition. (shrink)

Mathematics in the 19th century underwent explosive development. The discussion among philosophers was motivated by new results which conflicted with Kant’s very influential conception. One of the most important areas which lead to the meeting of philosophy and mathematics was a rigorous account of the infinitesimal calculus. In his article the author shows that considerations of this type found in Bolzano and Frege are important not only for the overcoming of the Kantian conception, but as for what we today call (...) the linguistic turn. (shrink)

Ocherk 1. Voprosy ontologii -- Ocherk 2. Voprosy ėtiki i ėstetiki -- Ocherk 3. Voprosy gnoseologii i aksiologii.

According to formalism, a mathematician is not concerned with mysterious metaphysical entities but with mathematical symbols. As a result, mathematical entities become simply sensible signs. However, the price that has to be paid for this move seems to be too high, for mathematics, at present considered to be the queen of sciences, turns out to be a to a contentless game. That is why it seems absurd to regard numbers and all mathematical entities as mere symbols. The aim of our (...) paper is to show the reasons that have led some philosophers and mathematicians to adopt the view that mathematical terms in the proper sense refer to nothing and mathematical propositions have no real content. At the same time we want to explain how formalism helped to overcome the traditional concept of science. (shrink)