This book offers a comprehensive account of logic that addresses fundamental issues concerning the nature and foundations of the discipline. The authors claim that these foundations can not only be established without the need for strong metaphysical assumptions, but also without hypostasizing logical forms as specific entities. They present a systematic argument that the primary subject matter of logic is our linguistic interaction rather than our private reasoning and it is thus misleading to see logic as revealing "the laws of (...) thought". In this sense, fundamental logical laws are implicit to our "language games" and are thus more similar to social norms than to the laws of nature. Peregrin and Svoboda also show that logical theories, despite the fact that they rely on rules implicit to our actual linguistic practice, firm up these rules and make them explicit. By carefully scrutinizing the project of logical analysis, the authors demonstrate that logical rules can be best seen as products of the so called reflective equilibrium. They suggest that we can profit from viewing languages as "inferential landscapes" and logicians as "geographers" who map them and try to pave safe routes through them. This book is an essential resource for scholars and researchers engaged with the foundations of logical theories and the philosophy of language. (shrink)

We examine some of Connes’ criticisms of Robinson’s infinitesimals starting in 1995. Connes sought to exploit the Solovay model S as ammunition against non-standard analysis, but the model tends to boomerang, undercutting Connes’ own earlier work in functional analysis. Connes described the hyperreals as both a “virtual theory” and a “chimera”, yet acknowledged that his argument relies on the transfer principle. We analyze Connes’ “dart-throwing” thought experiment, but reach an opposite conclusion. In S , all definable sets of reals are (...) Lebesgue measurable, suggesting that Connes views a theory as being “virtual” if it is not definable in a suitable model of ZFC. If so, Connes’ claim that a theory of the hyperreals is “virtual” is refuted by the existence of a definable model of the hyperreal field due to Kanovei and Shelah. Free ultrafilters aren’t definable, yet Connes exploited such ultrafilters both in his own earlier work on the classification of factors in the 1970s and 80s, and in Noncommutative Geometry, raising the question whether the latter may not be vulnerable to Connes’ criticism of virtuality. We analyze the philosophical underpinnings of Connes’ argument based on Gödel’s incompleteness theorem, and detect an apparent circularity in Connes’ logic. We document the reliance on non-constructive foundational material, and specifically on the Dixmier trace −∫ (featured on the front cover of Connes’ magnum opus) and the Hahn–Banach theorem, in Connes’ own framework. We also note an inaccuracy in Machover’s critique of infinitesimal-based pedagogy. (shrink)

The article attempts to raise a question and give an answer to it regarding the evaluation of the philosophical creativity of Hermann Cohen, the German-Jewish thinker of the late XIX - early XX century. Moreover, following the philosophical style of Cohen himself, the question posed and discussed in the article is not idle, but it contains a hypothesis that forms our answer in a certain way. It is important to identify the difficulties and intellectual determinants that prevent the formation of (...) a clear and unambiguous answer. At the same time these difficulties contain an initiating moment for opening a philosophical debate. The historical and philosophical reasons that make the very beginning of the discussion of the question more complex, are considered. The article, of course, cannot claim to be an exhaustive answer on such a fundamental topic, which is contained in the designated question. But the article itself, and the articles following it in the section devoted to the work of Herman Cohen, may be indicate that the time for this discussion has come. (shrink)

In this study, voluntary and involuntary visual attention focused on different interpretations of a bistable image, were investigated using magnetoencephalography. A Necker cube with sinusoidally modulated pixels' intensity in the front and rear faces with frequencies 6.67 Hz and 8.57 Hz, respectively, was presented to 12 healthy volunteers, who interpreted the cube as either left- or right-oriented. The tags of these frequencies and their second harmonics were identified in the average Fourier spectra of the MEG data recorded from the visual (...) cortex. In the first part of the experiment, the subjects were asked to voluntarily control their attention by interpreting the cube orientation as either being on the left or right. Accordingly, we observed the dominance of the corresponding spectral component, and voluntary attention performance was measured. In the second part of the experiment, the subjects were asked to focus their gaze on a red marker at the center of the cube image without putting forth effort in its interpretation. The alternation of the dominant spectral energies at the second harmonics of the stimulation frequencies was treated as changes in the cube orientation. Based on the results of the first experimental stage and using a wavelet analysis, we developed a method which allowed us to identify the currently perceived cube orientation. Finally, we characterized involuntary attention using the distribution of dominance times when focusing attention on one of the cube orientations, which was related to voluntary attention performance and brain noise. In particular, we confirmed our hypothesis that higher attention performance is associated with stronger brain noise. (shrink)

The logic of single-conclusion proofs () is introduced. It combines the verification property of proofs with the single valuedness of proof predicate and describes the operations on proofs induced by modus ponens rule and proof checking. It is proved that is decidable, sound and complete with respect to arithmetical proof interpretations based on single-valued proof predicates. The application to arithmetical inference rules specification and -admissibility testing is considered. We show that the provability in gives the complete admissibility test for the (...) rules which can be specified by schemes in -language. The test is supplied with the ground proof extraction algorithm which eliminates the admissible rules from a -proof by utilizing the information from the corresponding -proofs. (shrink)

Our investigation is concerned with the finite model property with respect to admissible rules. We establish general sufficient conditions for absence of fmp w. r. t. admissibility which are applicable to modal logics containing K4: Theorem 3.1 says that no logic λ containing K4 with the co-cover property and of width > 2 has fmp w. r. t. admissibility. Surprisingly many, if not to say all, important modal logics of width > 2 are within the scope of this theorem–K4 itself, (...) S4, GL, K4.1, K4.2, S4.1, S4.2, GL.2, etc. Thus the situation is completely opposite to the case of the ordinary fmp–the absolute majority of important logics have fmp, but not with respect to admissibility. As regards logics of width ≤ 2, there exists a zone for fmp w. r. t. admissibility. It is shown that all modal logics A of width ≤ 2 extending S4 which are not sub-logics of three special tabular logics have fmp w.r.t. admissibility. (shrink)

ABSTRACT Two models of the Aristotelian syllogistic in arithmetic of natural numbers are built as realizations of an old Leibniz idea. In the interpretation, called Scholastic, terms are replaced by integers greater than 1, and s.Ap is translated as “s is a divisor of p”, sIp as “g.c.d. > 1”. In the interpretation, called Leibnizian, terms are replaced by proper divisors of a special “Universe number” u < 1, and sAp is translated as “s is divisible by p”, sIp as (...) ‘l.c.m. < u”. Both interpretations are proved to be adequate to the Aristotelian syllogistic. They are extended to syllogistic including term negation and term conjunction as well. (shrink)

Traditionalists affirm that in self-deception I intend to deceive myself; but, on the standard account of interpersonal deception, according to which deceiver intend to make their target believe a falsehood, traditionalism generates paradoxes, arising from the fact that I will surely know that I want to make myself believe a falsehood. In this thesis, I argue that these well-known paradoxes need not arise under my manipulativist account of deception. In particular, I defend traditionalism about self-deception by showing that what causes (...) paradoxes is not the idea that self-deception is an intrapersonal analogue of interpersonal deception but rather our incorrect conceptions of deception, interpersonal deception, and lying. I show, by way of counterexamples, that the essence of deception is not ending up epistemically worse off but rather being intentionally manipulated into forming or retaining a certain truth-evaluable mental state. Vitally, contra the standard view, the deceiver need not hold that the mental state he intends to produce in the deceived involves a falsehood; in fact, the targeted effect may involve a proposition believed by the deceiver to be true or about whose truth the deceiver suspends belief. Any phenomenon rightly called self-deception, I argue, involves an action in which the person intentionally manipulates (by way of a trick) her own way of forming or retaining some truth-evaluable mental state of her own (belief or a belief-like thought). Thus, on the manipulativist view, a self-deceiver may non-paradoxically intend to deceive himself: the relevant intention is to affect a particular truth-evaluable thought by way of non-deviantly manipulating his agential use of his own cognitive capacities. While all cases of self-deception involve intentional manipulation of the self by the self, how this manipulative trick works out varies in different kinds of cases. In some cases, the self-deceptive manipulative trick is not intentional under that description, a description that captures the so-called deflationary view. Although the manipulativist account allows for numerous different strategies of self-deception, and is consistent with both traditionalism and deflationism, it cannot, by itself, vindicate the idea of lying to oneself. On the standard conception, lying to myself is practically impossible (if the mind is not partitioned) and this is because the very forming the intention to lie to myself – as including the intention to make myself believe my own lie – seems very unlikely. Arguably, people will not φ if they think that φ-ing is impossible. I argue that some kinds of behaviour typically understood as self-deception are actually cases in which the person is lying to herself without the intention to deceive herself; rather, she avoids legitimising an unfavourable state of affairs by openly affirming its contrary. It may also be the case, however, that some lies to oneself are aimed at deceiving – this is because, as I argue, liars need not assert what they believe is false; hence, by lying to myself, I may intend to increase my confidence in the belief I already hold. Finally, the motive for self-deception is always a matter of preserving the person’s endorsed idealised picture of reality. This account allows me to explain all possible cases of self-deception. In the last chapter, I apply my theory to some paradigmatic cases first outlined in my introduction. (shrink)

In this article the cosmological and metaphysical dimensions of the Logos concept in the Hellenic and Patristic traditions are explored. Heraclitus initially depicted the logos as the ontological link between the One and the many, with the logos thus serving as the foundation of both rational discourse and natural law. This concept was elaborated and modified by a number of eminent Hellenic and Christian thinkers. Among them count Plato, Philo of Alexandria, the New Testament authors John and Paul, Plotinus, Athenagoras, (...) Justin Martyr, Clement of Alexandria, Augustine of Hippo, Dionysius the Areopagite, Maximus the Confessor and John Scottus Eriugena. (shrink)

The aim of this paper is to look from the point of view of admissibility of inference rules at intermediate logics having the finite model property which extend Heyting's intuitionistic propositional logic H. A semantic description for logics with the finite model property preserving all admissible inference rules for H is given. It is shown that there are continuously many logics of this kind. Three special tabular intermediate logics λ, 1 ≥ i ≥ 3, are given which describe all tabular (...) logics preserving admissibility: a tabular logic λ preserves all admissible rules for H iff 7λ has width not more than 2 and is not included in each λ. MSC: 03B55, 03B20. (shrink)

Článek reflektuje Hayekovy výklady o povaze pravidel. Ukazuje, že jeho pojetí pravidel je extrémně široké a vazba mezi pravidly a pravidelnostmi je nepřijatelně úzká. Následně je nastíněno alternativní - užší - vymezení pojmu pravidla. Nakonec je podrobeno kritice Hayekovo příliš úzké chápání pojmu normativních pravidel a je navrženo jeho širší vymezení.

A través del método etimológico de Vico es posible ver relaciones entre un enfoque materialista y los temas de la infancia y el mundo primitivo, lo que implica un interés por cuestiones históricas vinculadas al mundo agrícola y religioso de los orígenes y cuestiones cognitivas vinculadas a las relaciones entre tacto, visión e intelecto. La etimología de cogitare como “recoger” y de intelligere como “leer” proporciona las bases para una teoría de la cognición decididamente aplicada a la Dipintura de la (...) Ciencia nueva, que sirve de introducción a la obra y que revela el horizonte gnoseológico de sus pretensiones ya puestas a prueba en sus primeros textos, especialmente en lo que se refiere al tema de la racionalidad y del ingenio humano. (shrink)

The keynote idea of the theses is contained in the author’s assumption that modern philosophy doesn’t meet its claiming pretensions: to be universal form of knowledge. First of all philosophy is connected not with knowledge but with ideas and secondly being authentic it “exists only in everyday life”.1 In orderthat philosophy could realize its innate essence corresponding conditions of social being should exist but they are still absent and therefore philosophy is absent as well. Its place is occupied by metaphysics (...) which is free movement of thinking that has no definiteness as the condition of being of any form of thought. That iswhy we watch crisis state of “philosophy” which becomes apparent in vagueness of its subject: “philosophy is not only one, there are many of them”. The author supposes that philosophy as the highest relation of mankind to objective reality is the only one. Philosophy lowered down from the heaven (Platon, Ciceron) in the field of human being must raise people not only to purity of thought, but mainly to purity of their activity both with each other and with nature. Then real interaction of men and nature will take place. This will be the beginning of spiritualization of the Universe. It may exist only under the conditions of social uniformity as historical form of Weltanschauung (world outlook) that removes religious form. Realization of its being supposes fundamental change of social life. It is necessary that private property should be replaced with social property in the sphere of social production. Only under these conditions philosophy may appear and exist as historical form of Weltanschauung. (shrink)

. We demonstrate that a comprehensive nonstandard set theory can be developed in the standard $\displaystyle{\in}$ -language. As an illustration, a nonstandard ${\sf Law of Large Numbers}$ is obtained.

We study models of HST . This theory admits an adequate formulation of the isomorphism propertyIP, which postulates that any two elementarily equivalent internally presented structures of a well-orderable language are isomorphic. We prove that IP is independent of HST and consistent with HST.

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)

The English Synopsis is after the text of the book. The book presents an original and generalizing substantive vision of the philosophy of science through the prism of a detailed analysis of the polysystem structure of scientific theories. Theories are considered, firstly, as complex specialized forms of developed scientific thinking about the realities studied by natural science, secondly, as constantly improving tools for producing new knowledge in interaction with experimental research, and thirdly, as carriers of ordered and verified knowledge. Emphasis (...) is placed on their nominal and ontic subsystems. The book develops personal and joint research of the authors (theoretical physicist and philosopher), the experience of teaching philosophy of physics at NaUKMA, philosophy of science at the Higher School of Philosophy at the H. Skovoroda Institute of Philosophy of the National Academy of Sciences of Ukraine and theoretical physics at the National Technical University "Ihor Sikorsky Kyiv Polytechnic Institute". The research is based on a significant source base covering works of modern Western researchers in natural science and philosophy of science. For students, teachers, and scientists who are interested in the problems of modern philosophy of science and have a certain amount of scientific knowledge. It will also be useful for high school students who are eager to become scientists. (shrink)

Tato stať se zabývá implicitním vztahem pojmu nutnosti a náhodnosti (bytí jsoucího) a pojmu zákona (bytí jsoucího) v Marxově filosofii spjaté (svázané) s explicitním vztahem pojmu nutnosti a náhodnosti (bytí lidsky jsoucího v ekonomicko-společenské bytné sféře) a pojmu zákona (bytí lidsky jsoucího v ekonomicko-společenské bytné sféře) v Marxově politické ekonomii a ukazuje její ontologicko-nomologické přednosti, poukazujíc však na její antropologicko-ontologické nedostatky, spjaté zvláště s jejím historicismem (s "bídou historicismu").

Iznimni utjecaj tehnologije na ljudski život oduvijek je bio paradoksalan. Primjerice, tehnologija je jedan od činitelja koji pridonosi neizvjesnosti budućnosti uslijed unutarnje proturječnosti tehničkog sustava i društva. Naime, što je tehnologija moćnija to je svijet uznemireniji. Pojedini autori izražavaju mišljenje da je upravo tehnodiskurs u stvari diskurs čovječnosti i način njezina poboljšanja. Unatoč ovome, pojedini autori, humanisti prije svega, misle da se tehnologija može ispuniti tradicionalnim vrijednostima. U stvari, oni smatraju da današnja kultura ima samo djelatnu vrijednost odjeljenu od tradicije (...) koja je oblikovana tehničkim napretkom i ekonomskim potrebama. Kultura je snažna oblikovateljica ljudskoga ponašanja jer je temelj svjesnih i nesvjesnih uvjerenja. Ona je put »ispravnih« načina života. Ne ugrožava li razvoj tehnike i tehnologije taj put »ispravnih« načina života?The extraordinary influence of technology on the human life has always been a paradox. For example, one of the factors contributing to an increase of uncertainty of the future of technology is internal contradictions of the technical system and society. For instance, a vulnerability to accidents grows proportionally with the size of organizations. Similarly, the more powerful a technology is, the more it disturbs the world. Some people think that the technodiscourse is a discourse about humanity and the ways of advancing it. Some humanists, on the other hand, think that the technology can be saturated with traditional values. Today’s culture has just an operational value detached from tradition, molded by the technical progress and economic needs. Culture is a powerful shaper of human behavior because it is the foundation of conscious and unconscious beliefs. It is the way of ‘proper’ ways to live. Can we do something in that way? We think we can. (shrink)

V celej Heideggerovej tvorbe predstavuje recepcia dejín filozofie dominantný rozmer jeho filozofického u?enia. Autor štúdie sa zamýš?a nad problémom, ?i Heidegger mohol úspešne zav?ši? dokon?enie svojho diela Bytie a ?as ako ho pôvodne ohlásil pri prvom vydaní . Zis?uje, že nenaplnenie pôvodných zámerov k druhej nenapísanej ?asti práce nebolo vôbec náhodným dôsledkom. H?adanie odpovede na otázku bytia v druhej polovici práce Bytie a ?as sústredením sa na filozofické u?enia Kanta, Descarta a Aristotela nemohlo prinies? o?akávané výsledky, preto sa Heidegger po (...) obrate sústredil najmä na recepciu chápania bytia v diele Hegela, Leibniza, Herakleita a Parmenida. V tejto súvislosti autor zis?uje, že ani táto vážna zmena základnej orientácie na dejiny filozofie nemohla by? úspešne zav?šená hlavným problémom Heideggerovej filozofie – premyslie? bytie bez jestvujúcna a tak prejs? od metafyziky jestvujúcna k metafyzike Bytia. (shrink)

This note is about the “calculational style” of presenting proofs introduced by Dijkstra and Scholten and adopted in some books on theoretical computer science. We define the concept of a calculation, which is a formal counterpart of the idea of a calculational proof. The definition is in terms of a new formalization DS of predicate logic. Any proof tree in the system DS can be represented as a sequence of calculations. This fact shows that any logically valid predicate formula has (...) a calculational proof. (shrink)

Ovaj tekst nastoji da nijansira dihotomiju izmedju pojmova istorije i pravde koja je uobicajena u interpretaciji Hobzovog misljenja. Hobzov kriticki stav prema istoriji objasnjava se njegovom polemikom protiv nasledja klasicne antike, koja stoji u vezi s njegovim projektom stroge nauke o moralu i politici. Medjutim, Hobzovo shvatanje pravde ne moze se zasnovati bez izvesnih faktickih, empirijskih elemenata; ono se ne svodi na neku cisto racionalnu konstrukciju. Ovi elementi otvaraju Hobzovo misljenje prema problematici stvarne istorije; za Hobza, najvazniji predstavnici takve vrste (...) istorije su Tukidid i Tacit. Konacno, istorijska dimenzija Hobzovog misljenja dopusta nam da kod njega prepoznamo i jedan siri pojam pravde, koji probija granice pravde koja proizlazi iz ugovora. (shrink)

Для Макса Вебера «рациональная бюрократия» есть идеальный тип организации общества. Однако идеальный тип не позволяет заполнить провал между властью и обществом, который называется отчуждением. Это - миф, и когда Макс Вебер говорит о рациональности, то в основе этого лежат не требования научности, но отсылка к некоей культурной аксиологии. Этот миф можно критиковать, анализируя конкретное поведение бюрократов, обычно мало рациональное, но также ставя под вопрос и саму культуру, которая хочет быть или даже претендует быть рационалистической. В России чудовищность бюрократии является следствием (...) кризиса культуры. Pour Max Weber la « bureaucratie rationnelle » est un type idéal d’organisation de la société. Mais ce type idéal ne permet pas de combler le hiatus entre pouvoir et société, lequel s’appelle aliénation. C’est un mythe, et si Max Weber parle de rationalité, ce n’est pas en vertu d’une exigence scientifique mais par référence à une axiologie culturelle. On peut donc le critiquer en analysant le comportement concret des bureaucrates -lequel est souvent fort peu rationnel -mais également en mettant en question une culture qui se veut ou se prétend rationaliste. En Russie, la monstruosité de la bureaucratie est la conséquence d’une crise de la culture. According to Max Weber, “rational bureaucracy” is an ideal-type of social organization. But this ideal-type cannot bridge the gap between power and society, something we could call alienation. It is a myth, and if Max Weber resorts to the concept of rationality, it is not because of any scientific need, but by reference to a cultural axiology. He can therefore be criticized by analyzing the actual behavior of bureaucrats, which often is less than rational, but also by challenging a culture that wants or claims to be rationalistic. In Russia, the monstrosity of bureaucracy is the consequence of a crisis of culture. (shrink)

Let D be a division ring such that the number of conjugacy classes of the multiplicative group D ∗ is equal to the power of D ∗ . Suppose that H is the group GL or PGL, where V is a vector space of infinite dimension ϰ over D . We prove, in particular, that, uniformly in κ and D , the first-order theory of H is mutually syntactically interpretable with the theory of the two-sorted structure 〈κ,D〉 in the second-order (...) logic with quantification over arbitrary relations of power ⩽κ . A certain analogue of this results is proved for the groups ΓL and PΓL . These results imply criteria of elementary equivalence for infinite-dimensional classical groups of types H= ΓL , PΓL , GL, PGL over division rings, and solve, for these groups, a problem posed by U. Felgner. It follows from the criteria that if H≡H then κ 1 and κ 2 are second-order equivalent as sets. (shrink)

The paper offers an interpretation of Plato’s Necessity in the Timaeus according to which Necessity is an entity which manifests itself in different ways at different stages of the creation of the Universe. The main argument aims to show that Necessity gains at least two different meanings in the course of the creation as described by Plato – that of limiting consequences and that of purposeless motion ; that despite the fact that Necessity is not a self-sustained principle, it has (...) its origin in chōra which is a condition of limiting material spatiality; that the important question what the effects of Necessity in the already created world are should be asked but cannot be easily answered on the basis of what Plato explicitly says. (shrink)

Prvi deo ovog rada, objavljen u prethodnom broju casopisa, bio je posvecen razmatranju religijskog porekla dvojnosti 'duha' i 'slova', a zatim i pitanju njenog znacenja u kontekstu filozofije ranog nemackog idealizma. Ovaj, drugi i zakljucni deo rada usredsredjuje se na eticke implikacije tog pitanja, posto je suprotstavljanje 'duha2 Kantovog sistema njegovom 'slovu', uz cesta pozivanja na novozavetno ispunjenje mojsijevskog zakona ljubavlju i verom predstavljalo jednu od osnovnih strategija kriticara Kantove teorije morala. Krajnja konsekvenca ovog pravca kritike Kanta lezi u ukidanju (...) autoriteta transcendentne moralne norme. Ovaj korak, kojim se istovremeno ponistava autoritet teksta kao takvog, a time i stav komentara kao literarnog zanra moze se uociti vec u Hegelovim mladalackim teoloskim spisima, u kojima se zastupa ukidanje transcendencije moralnog zakona njegovim inkorporiranjem u slobodnu subjektivnost koja egzistira u zajednici verujucih hriscana. (shrink)

We prove two theorems concerning expressive power of relational and functional languages. The theorems have interesting consequences for the history of philosophy and logic.