This chapter argues that the distinction between ambitious and modest transcendental arguments, developed and deployed by various authors in the wake of Stroud’s influential critique of transcendental reasoning, may be pointless when applied to transcendental arguments from performative inconsistency that have moral statements as their conclusions. If moral truth is assertorically constrained, then any modest moral transcendental argument from performative inconsistency can be converted into an ambitious moral transcendental argument. The chapter provides an account of performative inconsistency and suggests an (...) alternative to the widespread reading of transcendental conditionals in terms of an ‘if-then’-sentences whose antecedents express a proposition to the effect that some x is possible and whose consequents express a statement to the effect that some y is actual. (shrink)

This article informally presents a solution to the paradoxes of truth and shows how the solution solves classical paradoxes (such as the original Liar) as well as the paradoxes that were invented as counterarguments for various proposed solutions (“the revenge of the Liar”). This solution complements the classical procedure of determining the truth values of sentences by its own failure and, when the procedure fails, through an appropriate semantic shift allows us to express the failure in a classical two-valued language. (...) Formally speaking, the solution is a language with one meaning of symbols and two valuations of the truth values of sentences. The primary valuation is a classical valuation that is partial in the presence of the truth predicate. It enables us to determine the classical truth value of a sentence or leads to the failure of that determination. The language with the primary valuation is precisely the largest intrinsic fixed point of the strong Kleene three-valued semantics (LIFPSK3). The semantic shift that allows us to express the failure of the primary valuation is precisely the classical closure of LIFPSK3: it extends LIFPSK3 to a classical language in parts where LIFPSK3 is undetermined. Thus, this article provides an argumentation, which has not been present in contemporary debates so far, for the choice of LIFPSK3 and its classical closure as the right model for the truth predicate. In the end, an erroneous critique of Kripke-Feferman axiomatic theory of truth, which is present in contemporary literature, is pointed out. (shrink)

Starting from the idea that functions are formally similar to actions in that they are described and explained in a similar way, so that both admit of an accordion effect, I turn to Anscombe’s insight that the point of practical reasoning is to render explicit the relation between the different descriptions of an action generated by the accordion effect. The upshot is, roughly, that an item has a function if what it does can be accounted for by functional reasoning. Put (...) differently, a part of a system has a function if what it does is a functional part of what the system does. (shrink)

The aim of Modality and Explanatory Reasoning (MER) is to shed light on metaphysical necessity and the broader class of modal properties to which it belongs. This topic is approached with two goals: to develop a new and reductive analysis of modality, and to understand the purpose and origin of modal thought. I argue that a proper understanding of modality requires us to reconceptualize its relationship to causation and other forms of explanation such as grounding, a relation that connects metaphysically (...) fundamental facts to non-fundamental ones. While many philosophers have tried to give modal analyses of causation and explanation, often in counterfactual terms, I argue that we obtain a more plausible, explanatorily powerful and unified theory if we regard explanation as more fundamental than modality. The function of modal thought is to facilitate a common type of thought experiment – counterfactual reasoning – that allows us to investigate explanatory connections and which is closely related to the controlled experiments of empirical science. Necessity is defined in terms of explanation, and modal facts often reflect underlying facts about explanatory relationships. The study of modal facts is important for philosophy not because these facts are of much metaphysical interest in their own right, but largely because they provide evidence about explanatory connections. (shrink)

The Swiss linguist Ferdinand de Saussure (1857-1913) revolutionized the study of language, signs, and discourse in the twentieth century. He successfully reconstructed the proto-Indo-European vowel system, advanced a conception of language as a system of arbitrary signs made meaningful through kinetic interrelationships, and developed a theory of the anagram so profound it gave rise to poststructural literary criticism. The roots of these disparate, even contradictory achievements lie in the thought of Early German Romanticism, which Saussure consulted for its insight into (...) the nature of meaning and discourse. Conducting the first comprehensive analysis of Saussure's intellectual heritage, Boris Gasparov links Sassurean notions of cognition, language, and history to early Romantic theories of cognition and the transmission of cultural memory. In particular, several fundamental categories of Saussure's philosophy of language, such as the differential nature of language, the mutability and immutability of semiotic values, and the duality of the signifier and the signified, are rooted in early Romantic theories of "progressive" cognition and child cognitive development. Consulting a wealth of sources only recently made available, Gasparov casts the seeming contradictions and paradoxes of Saussure's work as a genuine tension between the desire to bring linguistics and semiotics in line with modernist epistemology on the one hand, and Jena Romantics' awareness of language's dynamism and its transcendence of the boundaries of categorical reasoning on the other. Advancing a radical new understanding of Saussure, Gasparov reveals aspects of the intellectual's work previously overlooked by both his followers and his postmodern critics. (shrink)

The public generally regards the media with suspicion and distrust. Therefore, the media's primary concern is to regain that trust through the production of sincerity. Advancing the field of media studies in a truly innovative way, Boris Groys focuses on the media's affect of sincerity and its manufacture of trust to appease skeptics. Groys identifies forms of media sincerity and its effect on politics, culture, society, and conceptions of the self. He relies on different philosophical writings thematizing the gaze (...) of the other, from the theories of Heidegger, Sartre, Mauss, and Bataille to the poststructuralist formulations of Lacan and Derrida. He also considers media "states of exception" and their creation of effects of sincerity--a strategy that feeds the media's predilection for the extraordinary and the sensational, further fueling the public's suspicions. Emphasizing the media's production of emotion over the presentation (or lack thereof) of "facts," Groys launches a timely study boldly challenging the presumed authenticity of the media's worldview. (shrink)

In this article I develop an elementary system of axioms for Euclidean geometry. On one hand, the system is based on the symmetry principles which express our a priori ignorant approach to space: all places are the same to us, all directions are the same to us and all units of length we use to create geometric figures are the same to us. On the other hand, through the process of algebraic simplification, this system of axioms directly provides the Weyl’s (...) system of axioms for Euclidean geometry. The system of axioms, together with its a priori interpretation, offers new views to philosophy and pedagogy of mathematics: it supports the thesis that Euclidean geometry is a priori, it supports the thesis that in modern mathematics the Weyl’s system of axioms is dominant to the Euclid’s system because it reflects the a priori underlying symmetries, it gives a new and promising approach to learn geometry which, through the Weyl’s system of axioms, leads from the essential geometric symmetry principles of the mathematical nature directly to modern mathematics. (shrink)

In this handbook, I put into practice my philosophical views on children's mathematics. The handbook contains brief instructions and examples of mathematical activities. In the INSTRUCTIONS section, instructions are given on how, and in part why that way, to help preschool children in their mathematical development. In the ACTIVITIES section, there are examples of activities through which the child develops her mathematical abilities.

Boris Kment takes a new approach to the study of modality that emphasises the origin of modal notions in everyday thought. He argues that the concepts of necessity and possibility originate in counterfactual reasoning, which allows us to investigate explanatory connections. Contrary to accepted views, explanation is more fundamental than modality.

I propose a general alethic theory of epistemic risk according to which the riskiness of an agent’s credence function encodes her relative sensitivity to different types of graded error. After motivating and mathematically developing this approach, I show that the epistemic risk function is a scaled reflection of expected inaccuracy. This duality between risk and information enables us to explore the relationship between attitudes to epistemic risk, the choice of scoring rules in epistemic utility theory, and the selection of priors (...) in Bayesian epistemology more generally. (shrink)

This paper analyzes the historical context and systematic importance of Kant's hypothetical use of reason. It does so by investigating the role of hypotheses in Kant's philosophy of science. We first situate Kant’s account of hypotheses in the context of eighteenth-century German philosophy of science, focusing on the works of Wolff, Meier, and Crusius. We contrast different conceptions of hypotheses of these authors and elucidate the different theories of probability informing them. We then adopt a more systematic perspective to discuss (...) Kant's idea that scientific hypotheses must articulate real possibilities. We argue that Kant's views on the intelligibility of scientific hypotheses constitute a valuable perspective on scientific understanding and the constraints it imposes on scientific rationality. (shrink)

This article is a study of the compatibility of the theory and practice of Marxism-Leninism and Orthodox Christianity. The great importance of this topic is due to its direct connection with the improvement of society and the ongoing controversy on this issue with attempts to integrate communism with Christianity. The work provides a historical and theological analysis based on a critical study of the works of the founders of Marxism-Leninism, their associates, historical and theological works, as well as historical documents (...) on this issue. The article examines the approaches of the teachings of Orthodox Christianity, as well as Marxism-Leninism to atheism, materialism, religion and the Church. For this purpose, the relevant texts of Holy Scripture, the opinions of the Church fathers and the views of the founders and followers of Marxism-Leninism are studied. The novelty of this study is that some documents are considered for the first time in the context of the problem under study. In addition, a more detailed and systematic historical and theological analysis of the comparison of the teachings of Marxism-Leninism and Orthodox Christianity on this topic is carried out in comparison with the available works. The purpose of the work is to study historical and theological works, as well as historical documents related to the problem under study. The article concludes that Marxism-Leninism in this matter is not compatible with Christianity and is directly opposed to it. Since the Second World War in the USSR, relations between the state and the Church have improved from time to time, but the official state course on Marxism-Leninism did not leave the possibility of their reconciliation. Currently, there are attempts to produce a symbiosis of these two teachings. Many Communists have a positive attitude towards the Church, so a dialogue between them is possible and necessary. But as long as the ideology of the Communists remains Marxism-Leninism, antagonistic to Christianity and any religion in general, in their ranks will always remain hostile to religion. Therefore, the synthesis of these teachings is impossible. (shrink)

We further investigate a divisibility relation on the set of BN ultrafilters on the set of natural numbers. We single out prime ultrafilters (divisible only by 1 and themselves) and establish a hierarchy in which a position of every ultrafilter depends on the set of prime ultrafilters it is divisible by. We also construct ultrafilters with many immediate successors in this hierarchy and find positions of products of ultrafilters.

Analysing several characteristic mathematical models: natural and real numbers, Euclidean geometry, group theory, and set theory, I argue that a mathematical model in its final form is a junction of a set of axioms and an internal partial interpretation of the corresponding language. It follows from the analysis that (i) mathematical objects do not exist in the external world: they are our internally imagined objects, some of which, at least approximately, we can realize or represent; (ii) mathematical truths are not (...) truths about the external world but specifications (formulations) of mathematical conceptions; (iii) mathematics is first and foremost our imagined tool by which, with certain assumptions about its applicability, we explore nature and synthesize our rational cognition of it. (shrink)

While there are satisfactory answers to the question “How should we teach children mathematics?”, there are no satisfactory answers to the question “What mathematics should we teach children?”. This paper provides an answer to the last question for preschool children (early childhood), although the answer is also applicable to older children. This answer, together with an appropriate methodology on how to teach mathematics, gives a clear conception of the place of mathematics in the children’s world and our role in helping (...) children develop their mathematical abilities. Briefly, children’s mathematics consists of the world of children’s internal activities that they eventually purposefully organize in order to understand and control the outside world and organize their overall activities in it. We need to support a child in mathematical activities that she does spontaneously and in which she shows interest, and we need to teach her mathematics that she is interested in developing through these activities. In doing so, we must be fully aware that the child’s mathematics is part of the child’s world of internal activities and is not outside of it. We help the child develop mathematical abilities by developing them in the context of her world and not outside of it. From the point of view of this conception, the standards established today are limiting and too focused on numbers and geometric figures: these topics are too prominent and elaborated, and other mathematical contents are subordinated to them. Adhering to the standards, we drastically limit the mathematics of the child’s world, hamper the correct mathematical development of a child, and we can turn her away from mathematics. (shrink)

We continue the research of an extension of the divisibility relation to the Stone‐Čech compactification. First we prove that ultrafilters we call prime actually possess the algebraic property of primality. Several questions concerning the connection between divisibilities in and nonstandard extensions of are answered, providing a few more equivalent conditions for divisibility in. Results on uncountable chains in are proved and used in a construction of a well‐ordered chain of maximal cardinality. Probably the most interesting result is the existence of (...) a chain of type in. Finally, we consider ultrafilters without divisors in and among them find the greatest class. (shrink)

If definitive evidence concerning treatment effectiveness becomes available from an ongoing randomized clinical trial, then the trial could be stopped early, with the public release of results benefiting current and future patients. However, stopping an ongoing trial based on accruing outcome data requires methodological rigor to preserve validity of the trial conclusions. This has led to the use of formal interim monitoring procedures, which include inefficacy monitoring that will stop a trial early when the experimental treatment appears not to be (...) working. For participants, inefficacy monitoring is especially important as it ensures that they are not being treated worse than if they had not enrolled on the trial. We discuss the importance of reporting with trial results the formal interim inefficacy monitoring guidelines that were utilized, and, if none were used, the reasons for their absence. A survey of two leading medical journals suggests that this is not current practice. (shrink)

We construct and study structures imitating the field of complex numbers with exponentiation. We give a natural, albeit non first-order, axiomatisation for the corresponding class of structures and prove that the class has a unique model in every uncountable cardinality. This gives grounds to conjecture that the unique model of cardinality continuum is isomorphic to the field of complex numbers with exponentiation.

In this paper, I make a contribution to a naturalistically-minded theory of truthmakers by proposing a solution to the nasty problem of truthmakers for negative truths. After formulating the difficulty, I consider and reject a number of solutions to the problem, including Armstrong's states of affairs of totality, incompatibility accounts, and JC Beall 's polarity view. I then defend the position that absences of truthmakers are real and are responsible for making negative truths true. According to the positive account of (...) absences I offer, absences of contingent states of affairs are causally relevant mind-independent features of the physical world, located within space and time, and capable of being discovered by scientific inquiry. Recognition of the reality of absences strengthens truthmaker theory as a naturalistic metaphysics, as truth and falsity of each and every contingent proposition finds an ontological grounding in some region of the physical universe. (shrink)

In this paper we develop a general theory of algorithmic fairness. Drawing on Johnson King and Babic’s work on moral encroachment, on Gary Becker’s work on labor market discrimination, and on Strawson’s idea of resentment and indignation as responses to violations of the demand for goodwill toward oneself and others, we locate attitudes to fairness in an agent’s utility function. In particular, we first argue that fairness is a matter of a decision-maker’s relative concern for the plight of people from (...) different groups, rather than of the outcomes produced for different groups. We then show how an agent’s preferences, including in particular their attitudes to error, give rise to their decision thresholds. Tying these points together, we argue that the agent’s relative degrees of concern for different groups manifest in a difference in decision thresholds applied to these groups. (shrink)