The sum of all objects of a science, the objects’ features and their mutual relations compose the reality described by that sense. The reality described by mathematics consists of objects such as sets, functions, algebraic structures, etc. Generally speaking, the use of terms reality and existence, in relation to describing various objects’ characteristics, usually implies an employment of physical and perceptible attributes. This is not the case in mathematics. Its reality and the existence of its objects, leaving aside its application, (...) are completely virtual and yet clearly organized. This organization can be recognized in the creation of axioms or in the arrival at new theorems and definitions. It results either from a formalization of an intuitive idea or from a combinatorics that has not been guided by intuition. In all four possible cases—therefore, also in the two in which there is no intuitive “lead”, we can plausibly talk about a discovery of mathematical facts and thus support the Platonist view. (shrink)

This discussion note points to some verbal imprecisions in the formulation of the Enhanced Indispensability Argument. The examination of the plausibility of alternative interpretations reveals that the argument’s minor premise should be understood as a particular, not a universal, statement. Interpretations of the major premise and the conclusion oscillate between de re and de dicto readings. The attempt to find an appropriate interpretation for the EIA leads to undesirable results. If assumed to be valid and sound, the argument warrants the (...) rationality of the belief in an unusual variant of Platonism. On the other hand, if taken as it stands, the argument is either invalid or is unsound or does not support the mathematical Platonism. Thus, the EIA in its present form cannot serve as a useful device for the Platonist. (shrink)

Platonists in mathematics endeavour to prove the truthfulness of the proposal about the existence of mathematical objects. However, there have not been many explicit proofs of this proposal. One of the explicit ones is doubtlessly Baker’s Enhanced Indispensability Argument, formulated as a sort of modal syllogism. We aim at showing that the purpose of its creation – the defence of Platonist viewpoint – was not accomplished. Namely, the second premise of the Argument was imprecisely formulated, which gave space for various (...) interpretations of the EIA. Moreover, it is not easy to perceive which of the more precise formulations of the above-mentioned premise would be acceptable. For all these reasons, it is disputable whether the EIA can be used to defend Platonist outlook. At the beginning of this century, Baker has shown that the so-called Quine-Putnam Indispensability Argument can not provide “full” platonism - a guarantee of the existence of all mathematical objects. It turns out, however, that the EIA has a similar disadvantage. (shrink)

Causal theory of knowledge has been used by some theoreticians who, dealing with the philosophy of mathematics, touched the subject of mathematical knowledge. Some of them discuss the necessity of the causal condition for justification, which creates the grounds for renewing the old conflict between empiricists and rationalists. Emphasizing the condition of causality as necessary for justifiability, causal theory has provided stimulus for the contemporary empiricists to venture on the so far unquestioned cognitive foundations of mathematics. However, in what sense (...) can we speak about the justifiability as causality when it comes to mathematical knowledge? Can we justify the mathematical statement 2+2=4 by means of causality-perceptibility? Do we need perceptibility, a visual image of apples and marbles we add up in our first mathematics lesson, in order to know that statement? Does the same go with the statement that any two points can be joined by a straight line, and that the sum of angles in any triangle is the angle the measure of which equals the sum of the measures of the two right angles? Even though the major part of this article offers a review of the attitudes of various authors who endeavor to discuss the application of the causal theory to the problem of understanding of mathematical knowledge, it advocates the idea that knowledge expressed in a mathematical statement is acquired and transmitted by evidence. Evidence is by itself a guarantee of truth. It convinces us of the accuracy of mathematical truths. Proving, we find out. The greatest part of what we know is based on evidence of the previous knowledge . Due to the previous knowledge, we can say that knowledge in mathematics is in itself different from the knowledge in empirical sciences, i.e. it does not require causal relation that is considered necessary condition of knowing in those sciences.Uzročna teorija znanja iskorištena je od strane nekih teoretičara koji su se, baveći se filozofijom matematike, dotakli teme matematičkog znanja. Neki od njih govore o nužnosti uzročnog uvjeta za opravdanje, čime se stvaraju uvjeti za obnavljanje starog sukoba empirista i racionalista. Uzročna teorija je, isticanjem uvjeta uzročnosti kao nužnog za opravdanost, dala poticaj suvremenim empiristima da krenu čak i na do tada nedodirljive spoznajne temelje matematike. Međutim, u kom smislu možemo govoriti o opravdanosti kao uzročnosti kad je riječ o matematičkom znanju? Da li uzročnošću-čulnošću možemo opravdati matematički iskaz 2+2=4? Je li nam za znanje tog iskaza neophodna čulnost, vizualna predodžba jabuka ili klikera koje zbrajamo na našim prvim satovima matematike u školi? Stoje li stvari isto i s iskazom da se kroz bilo koje dvije točke može povući točno jedan pravac, ili da je zbroj kutova bilo kojeg trokuta kut čija je mjera jednaka zbroju mjera dvaju pravih kutova? Iako je u ovom radu, uglavnom, dan pregled stavova autora koji pokušavaju govoriti o primjeni uzročne teorije u shvaćanju matematičkog znanja, ideja koja se podržava u njemu jest da je znanje, iskazano matematičkim tvrđenjem, dobiveno i preneseno dokazom. Dokaz, sam po sebi, jamac je istine. On nas uvjerava u točnost matematičkih tvrdnji. Dokazujući spoznajemo. Najveći dio onoga što znamo zasnovano je dokazom na prethodnim znanjima . Zbog prethodnog možemo reći da je znanje u matematici po svojoj prirodi drugačije od znanja u empirijskim znanostima, to jest da ne iziskuje uzročnu vezu koja se smatra nužnim uvjetom za znanje u tim znanostima. (shrink)

In 2020, Daniele Molinini published a paper outlining two types of mathematical objectivity. One could say that with this paper Molinini not only separated two mathematical concepts in terms of terminology and content, but also contrasted two mathematical-philosophical contexts, the traditional-idealistic and the modern-practical. Since the first context was the theoretical basis for a large number of analyses that we find in the framework of the philosophy of mathematics, the space was now offered to re-examine such analyses in the second (...) context. More specifically, with respect to the second context, we will analyse the strength of one of the few explicit Platonic arguments that seeks to justify the ontological status of mathematical objects and the central claim of mathematical Platonism about the existence of mathematical objects. (shrink)

Alan Baker argues that mathematical objects play an indispensable explanatory role in science. There are several examples cited in the literature as solid candidates for such a role. We discuss two such examples and show that they are very different in their strength and (im)perfection, although both are recognized by the scientific community as examples of the best scientific explanations of particular phenomena. More specifically, it will be shown that the explanation of the cicada case has serious shortcomings compared with (...) the explanation of the case of Königsberg’s bridges. We will argue that the latter is a perfectly reliable scientific explanation that employs mathematical reasoning whereas the former is not. (shrink)

This paper analyses two definitions of contingency. Both definitions have been widely accepted and used as to identify contingent events. One of them is primarily of a philosophical character, whereas the other is more commonly used in mathematics. Evidently, these two definitions do not describe the same set of phenomena, and neither of them determines the completely intuitive notion of contingency.Namely, carefully selected examples testify that the first definition is too narrow and the second too wide. These facts have certain (...) epistemological consequences. They must, therefore, serve as a warning for using the definitions only in a restrictive and cautious way when detecting random beliefs – those we cannot identify as knowledge. (shrink)

Ever since its beginnings, mathematics has occupied a special position among all sciences, natural, as well as social sciences and humanities. It has not only provided a role model in terms of methodology, particularly when it comes to natural sciences, but other sciences have always relied on mathematics extensively both in their development and for solving various open questions. The beginning of the 21st century foregrounded the issue of the so-called explanatory role of mathematics in science. However, the reference literature (...) features only a few examples as illustration of this role. This paper aims at showing that those examples, even though they are used for illustrating precisely the same purpose, also illustrate various explanatory scopes which mathematical tools can reach within a scientific explanation. Some of these examples also show how mathematics, unfortunately, provides false credibility to scientific explanations. (shrink)

The contemporary Platonists in the philosophy of mathematics argue that mathematical objects exist. One of the arguments by which they support this standpoint is the so-called Enhanced Indispensability Argument (EIA). This paper aims at pointing out the difficulties inherent to the EIA. The first is contained in the vague formulation of the Argument, which is the reason why not even an approximate scope of the set objects whose existence is stated by the Argument can be established. The second problem is (...) reflected in the vagueness of the very term indispensability, which is essential to the Argument. The paper will remind of a recent definition of the concept of indispensability of a mathematical object, reveal its deficiency and propose an improvement of this definition. Following this, we will deal with one of the consequences of the arbitrary employment of the concept of indispensability of a mathematical theory. We will propose a definition of this concept as well, in accordance with the common intuition about it. Eventually, on the basis of these two definitions, the paper will describe the relation between these two concepts, in the attempt to clarify the conceptual apparatus of the EIA. (shrink)

Recently, psychologists have explored moral concepts including obligation, blame, and ability. While little empirical work has studied the relationships among these concepts, philosophers have widely assumed such a relationship in the principle that “ought” implies “can,” which states that if someone ought to do something, then they must be able to do it. The cognitive underpinnings of these concepts are tested in the three experiments reported here. In Experiment 1, most participants judge that an agent ought to keep a promise (...) that he is unable to keep, but only when he is to blame for the inability. Experiment 2 shows that such “ought” judgments correlate with judgments of blame, rather than with judgments of the agent’s ability. Experiment 3 replicates these findings for moral “ought” judgments and finds that they do not hold for nonmoral “ought” judgments, such as what someone ought to do to fulfill their desires. These results together show that folk moral judgments do not conform to a widely assumed philosophical principle that “ought” implies “can.” Instead, judgments of blame play a modulatory role in some judgments of obligation. (shrink)

Deceptionism about lying is the view that all lies are intended to deceive. This view sits uneasily with some cases that seem to involve lies not intended to deceive. We call these lies bald-faced because the liar lies while believing that the hearer knows that they are lying. The most recent deceptionist argument put forward by Rudnicki and Odrowąż-Sypniewska (this journal) defends the view that all genuine bald-faced lies are intended to deceive some of their hearers. I argue that this (...) argument is interesting but problematic: its premises do not support the view that all bald-faced lies are intended to deceive but rather only that some people who bald-faced lie to institutions or large audiences intend to deceive someone. Also, genuine bald-faced lies addressed at institutions are intended to (non-deceptively) manipulate institutions rather than deceive anyone. (shrink)

The book presents two fundamental theories that characterize the cultural-historical perspective in cognitive semantics: the Four-Level Theory of Cognitive Development (FLTCD) and the Sociocultural Theory of Lexical Complexes (STLC) as well as their application to the analysis of specific material. In particular, the book analyzes the sociocultural history of the machine metaphor, specifically its use in the texts of René Descartes and Francis Bacon. The practical embodiment of STLC is demonstrated through the analysis of lexical complexes such as otkryvat' 'to (...) open,' kamen' 'stone,' and intelligencija 'intelligentsia.' In the final chapter of the monograph, FLTCD and STLC are used for the diachronic analysis of semantic change. The monograph will be of interest to a wide range of linguists, psychologists, cultural anthropologists, and philosophers who consider language as a sociocultural phenomenon. (shrink)

Set theory -- Logic -- Proofs -- Functions -- Group theory -- Linear algebra.

The paper turns attention to some very general questions that concern the nature of logic – it deals with the problem of the identity of logic. It suggests that we can view the notion of value as one through which we can approach the elusive issues which surround the question of the nature of logic. The first part of the paper addresses the question of the value of logic as a discipline. In other words – it aims at answering the (...) question what is (or could/should be) the benefit of exercising logic. The second part focuses on the question of what role values play (or could/should play) ‘inside’ of logic. It suggests that the elusive and general term “value” can perhaps turn out quite useful in the project of delineation of the realm of logic. The conclusion can be formulated in the provocative slogan: logic can be seen as a kind of general formal theory of values. (shrink)

This book contains 86 essays and papers by the Russian sculptor and hermeneutic philosopher Vladimir Zimmerling (1931-2017) addressed the issues in aesthetics, ethics and cultural history. The apparatus includes the introductory article, the commentary, the name and the subject indexes prepared by the book editor, Anton Zimmerling. The appendix contains 70 pictures of Vladimir Zimmerling's sculptures. Vladimir Zimmerling's conception is build on the combination of the empiricism principle with the elements of hermeneutics and metalinguistic criticism. His essays (...) and papers focus on the foundations of aesthetics and ethics. Vladimir Zimmerling was one of the pioneers of the analytic approach to the poetics of Ossip Mandelstam with his paper "Промер" ["The Measurement"], (1974-1975) devoted to 10 difficult Mandelstam's poems including "Грифельная Ода", "Слепая ласточка бросается к ногам", "Я слово позабыл, что я хотел сказать". (shrink)

The small, the tiny, and the infinitesimal have been the object of both fascination and vilification for millenia. One of the most vitriolic reviews in mathematics was that written by Errett Bishop about Keisler’s book Elementary Calculus: an Infinitesimal Approach. In this skit we investigate both the argument itself, and some of its roots in Bishop George Berkeley’s criticism of Leibnizian and Newtonian Calculus. We also explore some of the consequences to students for whom the infinitesimal approach is congenial. The (...) casual mathematical reader may be satisfied to read the text of the five act play, whereas the others may wish to delve into the 130 footnotes, some of which contain elucidation of the mathematics or comments on the history. (shrink)

O alfabeto deste livro não segue uma ordenação típica. Em vez disso, ele percorre um caminho de colisões, da escrita do que se entrega só como espanto e impacto. Trata-se de uma amostra da vasta produção de Vladimir Safatle, feita de fragmentos, suas “escritas em farrapos” que misturam as muitas facetas de seu pensamento – política, ética, psicanálise, estética, filosofia, crítica cultural. Para quem já acompanha o trabalho de décadas do filósofo, o livro é uma surpresa. O rigor acadêmico (...) de suas outras produções dá lugar a uma escrita de tateamento, com certo componente lúdico que nos leva a uma espécie de ensaísmo de pequenas formas. Para quem está pouco familiarizado com essa produção, a obra é um generoso convite a conhecê-la. (shrink)

In The Burning Bush, Glazov conducts a profoundly original inquiry into Vladimir Solovyov's attitude toward Judaism. Solovyov (1853-1900) was one of the most remarkable figures of the 19th century: He was the most important Russian speculative thinker of that century, publishing major works on theoretical philosophy, the philosophy of religion, and ethics; he also produced sensitive literary criticism and incisive essays on current political, social, and ecclesiastical questions. The eminent theologian Hans Urs von Balthasar designated Solovyov as the greatest (...) artist of conceptual order and organization--after Thomas Aquinas--in the entire history of thought, a thinker who borrows from all systems after purging them of their negations. Solovyov was also the first major Russian thinker to enter into ecumenical dialogue with Jewish scholars and theologians, and Glazov's main concern is (1) to translate as completely as possible all of Solovyov's writings on Judaism and to annotate these texts by identifying persons, places, and citations, especially in the Biblical and rabbinic literature; and (2) to synthesize the information gleaned from these writings with key recollections of Solovyov's attitudes toward Jews and Judaism by his immediate family, friends, and early biographers. Glazov collects, translates, and comments on all the relevant primary texts: writings, letters, pamphlets, protests, political documents, and prayers which relate to Solovyov's work on Jewish matters. (shrink)

ABSTRACTThe psychological and philosophical literature exploring the role of social influence in moral judgments suggests that conformity in moral judgments is common and, in many cases, seems to b...

The research analyzes the process of formation of the ethics committee as a new institution in the system of regulation of genetic research. The external factors of this process are the increasing digitalization of medical and research practices, as well as the special situation that is developing in the field of genomic research and the use of genetic technologies, where issues of philosophy, jurisprudence and administration have generated many fundamentally new, and sometimes unexpected contexts. The author shows the similarity and (...) difference of approaches to the inclusion of the ethics committee in the national regulatory systems of different countries and determines the prospects for further integration of the new institution into normative and administrative-regulatory and law enforcement practices. The research applies all the main methods of system analysis and structural and functional analysis, as well as the comparative legal method. At the stage of generalization of empirical material, the author turns to the means and methods of philosophical phenomenology and phenomenological sociology. The study revealed that the ethics committee may have different institutional and regulatory functions in a variety of management and legal systems. Being hybrid in nature, the ethics committee performs various functions, and in various state legal systems and traditions it can combine elements of legislative, executive and judicial power. At times, the ethics committee may go beyond the scope of both a purely administrative and exclusively legal regulator. All this indicates that the integration of this institution into the legal system and into a variety of social practices is far from being completed. (shrink)

This paper examines Gadamer's and Davidson's dialogical models of interpretation. It shows them to be comparable, but importantly dissimilar with respect to the kind of agreement they require for communication to be possible. It is argued that this difference entails different concepts of alterity: they model not only how we talk, but implicitly who we can intelligibly talk to. Another important contribution of this paper is to uncover a distinction in Gadamer between two kinds of agreement missed so far by (...) all commentators. The final section of this paper defends a second thesis, namely that the degree of agreement required by the models is proportional to the conceptual difference it can make intelligible. Hence, the extent of graspable cultural difference is not only an empirical matter, but is entailed by our choice of model. (shrink)

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