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)

The article shows the positions philosophers held to the relationship between a priori judgments and those judgments which are valid necessarily. Enlightenment philosophers of the 18th and 19th century, who, though often in different ways, opposed the concept of metaphysics and scholastic necessity , play the leading role. At the beginning of the 20th century analytic philosophy was born. Its first leaders inherited from their predecessors an antipathy to metaphysics, and so they had no desire to return again to the (...) traditional concept of necessity . Their logic and the new characterization of the a priori paved the way for the linguistic turn. Some of their followers in the second half of the 20th century realized that the concept needed to be returned to its original meaning . This is not a mere repetition of the Aristotelian-scholastic conception, but a new addition that rethinks the relationship between the notions of a priori and necessity. (shrink)

Throughout the greater part of the twentieth century, both in the analytic and continental traditions, metaphysics was deemed to be passé. The last few decades, however, have witnessed a remarkable growth of interest among analytic philosophers in various traditional metaphysical topics, such as modality, truth, causality, etc. which resulted in the emergence of various forms of analytic metaphysics. The new forms of metaphysics differ from its traditional forms mostly in their methodology and in the range of proposed solutions to particular (...) problems. Besides these and other differences, however, there are also many similarities and there are even some who intentionally develop traditional metaphysical themes using the contemporary analytical methods. All these developments call for detailed exploration, which is the general goal of the present publication Metaphysics: Aristotelian, Scholastic, Analytic. The publication is the fruit of the conference which took place in Prague in 2010 and which had for its aim to bring together those willing to explore relations between the traditional and contemporary concerns, both from among the leading analytic philosophers working in metaphysics and the historians of philosophy devoted to the study of the metaphysical tradition. The specific focus of the conference was a re-examination of topics such as categories, metaphysical structure, substance and accident, existence, modalities, and predication. (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.

The paper deals with the ontological status of number. The authors are convinced that it is useful to discuss the concept of number within the framework of the Aristotelian division of being into substance and accident. Number can thus be taken as ens in se or ens in alio. Aristotle and Thomas Aquinas believed that number is an accident and their concept is explained in the first part of the paper. In the second part it is shown that the Aristotelian (...) concept is not correct. However, if number is not an accident then it seems that it must be identified with a Platonic entity. In the third part the authors reject this Platonic conclusion that Frege seems to have defended. In the final part, a possible solution is shown: From the logical point of view number is an object but from the ontological point of view it is an entity that depends on linguistic structure. (shrink)

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)

When Aristotle deals with specific kinds of motion, he surprisingly asserts that there is no movement according to a relation. This assertion is, on the one hand, well justifiable, but, on the other hand, it is at variance with the naturalistic spirit of peripatetic philosophy. In this paper I would like to propose a solution to this dilemma. Such an achievement, however, has an implication which may be difficult to accept: viz. the necessity to quite radically transform the traditional categorial (...) scheme. (shrink)

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)

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)

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)

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)

The main purpose of this paper is to contest the Aristotelian notion that the objects of metaphysics, mathematics and physics are all abstract, which is the reason why these disciplines constitute a homogeneous class. For a reflection on the way how objects are introduced into scientific discourse leads to the conclusion that some of these objects (especially the mathematical ones) are fictions of reason an that their nature is defined purely by their mutual relationships. From this it follows that, far (...) from being theoretical sciences, the respective disciplines are justifiedly classified as arts. (shrink)

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)