The main goal of this paper is to provide an abstract framework for constructing proof systems for various many-valued logics. Using the framework it is possible to generate strongly complete proof systems with respect to any finitely valued deterministic and non-deterministic logic. I provide a couple of examples of proof systems for well-known many-valued logics and prove the completeness of proof systems generated by the framework.

This paper critically examines and evaluates Yacin Hamami’s reconstruction of the standard view of mathematical rigor. We will argue that the reconstruction offered by Hamami is premised on a strong and controversial epistemological thesis and a strong and controversial thesis in the philosophy of mind. Secondly, we will argue that Hamami’s reconstruction of the standard view robs it of its original philosophical rationale, i.e. making sense of the notion of rigor in mathematical practice.

The aim of this paper is to study a particular family of non-deterministic semantics for modal logics that has eight truth-values. These eight-valued semantics can be traced back to Omori and Skurt (2016), where a particular member of this family was used to characterize the normal modal logic K. The truth-values in these semantics convey information about a proposition’s truth/falsity, whether the proposition is necessary/not necessary, and whether it is possible/not possible. Each of these triples is represented by a unique (...) value. In this paper we will study which modal logics can be obtained by changing the interpretation of the $$\Box $$ modality, assuming that the interpretation of other connectives stays constant. We will show what axioms are responsible for a particular interpretations of $$\Box $$. Furthermore, we will study subsets of these axioms. We show that some of the combinations of the axioms are equivalent to well-known modal axioms. We apply the level-valuation technique to all of the systems to regain the closure under the rule of necessitation. We also point out that some of the resulting logics are not sublogics of S5 and comment briefly on the corresponding frame conditions that are forced by these axioms. Ultimately, we sketch a proof of meta-completeness for all of these systems. (shrink)

According to the dialetheist argument from the inconsistency of informal mathematics, the informal version of the Gödelian argument leads us to a true contradiction. On one hand, the dialetheist argues, we can prove that there is a mathematical claim that is neither provable nor refutable in informal mathematics. On the other, the proof of its unprovability is given in informal mathematics and proves that very sentence. We argue that the argument fails, because it relies on the unjustified and unlikely assumption (...) that the informal Gödel sentence is informally provable. (shrink)

Classical logic of formal provability includes Löb’s theorem, but not reflection. In contrast, intuitions about the inferential behavior of informal provability (in informal mathematics) seem to invalidate Löb’s theorem and validate reflection (after all, the intuition is, whatever mathematicians prove holds!). We employ a non-deterministic many-valued semantics and develop a modal logic T-BAT of an informal provability operator, which indeed does validate reflection and invalidates Löb’s theorem. We study its properties and its relation to known provability-related paradoxical arguments. We also (...) argue that T-BAT is a fairly sensible candidate for a formal logic of informal provability. (shrink)

BAT is a logic built to capture the inferential behavior of informal provability. Ultimately, the logic is meant to be used in an arithmetical setting. To reach this stage it has to be extended to a first-order version. In this paper we provide such an extension. We do so by constructing non-deterministic three-valued models that interpret quantifiers as some sorts of infinite disjunctions and conjunctions. We also elaborate on the semantical properties of the first-order system and consider a couple of (...) its strengthenings. It turns out that obtaining a sensible strengthening is not straightforward. We prove that most strategies commonly used for strengthening non-deterministic logics fail in our case. Nevertheless, we identify one method of extending the system which does not. (shrink)

Recently, in an ongoing debate about informal provability, non-deterministic logics of informal provability BAT and CABAT were developed to model the notion. CABAT logic is defined as an extension of BAT logics and itself does not have independent and decent semantics. The aim of the paper is to show that, semantically speaking, both logics are rather complex and they can be characterized by neither finitely many valued deterministic semantics nor possible word semantics including neighbourhood semantics.

Provability logics are, roughly speaking, modal logics meant to capture the formal principles of various provability operators or predicates.

Brain activity determines which relations between objects in the environment are perceived as differences and similarities in colour, smell, sound, etc. According to selectionism, brain activity does not create those relations; it only selects which of them are perceptually available to the subject on a given occasion. In effect, selectionism entails that perceptual experience is diaphanous, i.e. that sameness and difference in the phenomenal character of experience is exhausted by sameness and difference in the perceived items. It has been argued (...) that diaphaneity is undermined by phenomenological considerations and empirical evidence. This paper considers five prominent arguments of this sort and shows that none of them succeeds. (shrink)

In this paper, we consider how an agent may manage a questioning agenda in a situation where multiple information sources are available. We work within the framework of formal dialogue systems with the underpinning of Inferential Erotetic Logic. Firstly, we present the formal dialogue system DL(IEL)mult for managing multi-agent information retrieval. Then, we extend the proposed system so that it is capable of representing group and individual levels for the question decomposition process. We also propose two measures for evaluating information (...) sources: their cooperativeness and success levels; next, we analyse how the choice of agents may influence the way in which a solution for a given problem is reached. (shrink)

According to the predictive coding theory of cognition , brains are predictive machines that use perception and action to minimize prediction error, i.e. the discrepancy between bottom–up, externally-generated sensory signals and top–down, internally-generated sensory predictions. Many consider PCT to have an explanatory scope that is unparalleled in contemporary cognitive science and see in it a framework that could potentially provide us with a unified account of cognition. It is also commonly assumed that PCT is a representational theory of sorts, in (...) the sense that it postulates that our cognitive contact with the world is mediated by internal representations. However, the exact sense in which PCT is representational remains unclear; neither is it clear that it deserves such status—that is, whether it really invokes structures that are truly and nontrivially representational in nature. In the present article, I argue that the representational pretensions of PCT are completely justified. This is because the theory postulates cognitive structures—namely action-guiding, detachable, structural models that afford representational error detection—that play genuinely representational functions within the cognitive system. (shrink)

This paper centers around the notion that internal, mental representations are grounded in structural similarity, i.e., that they are so-called S-representations. We show how S-representations may be causally relevant and argue that they are distinct from mere detectors. First, using the neomechanist theory of explanation and the interventionist account of causal relevance, we provide a precise interpretation of the claim that in S-representations, structural similarity serves as a “fuel of success”, i.e., a relation that is exploitable for the representation using (...) system. Then, we discuss crucial differences between S-representations and indicators or detectors, showing that—contrary to claims made in the literature—there is an important theoretical distinction to be drawn between the two. (shrink)

We study the intersection type assignment system as defined by Barendregt, Coppo and Dezani. For the four essential variants of the system (with and without a universal type and with and without subtyping) we show that the emptiness (inhabitation) problem is recursively unsolvable. That is, there is no effective algorithm to decide if there is a closed term of a given type. It follows that provability in the logic of "strong conjunction" of Mints and Lopez-Escobar is also undecidable.

In the past centuries Maṇḍana Miśra was regarded as the most prominent figure of the advaita school of philosophy, to the extent that the whole system of advaita was frequently described by his name as ‘maṇḍana-matam’ (‘the view of Maṇḍana’). Nowadays advaita is almost exclusively associated, if not identified, with the name of Maṇḍana’s contemporary Śaṅkara. Both thinkers philosophizing along advaita lines, their views on the ultimate being, the highest bliss, ignorance etc. were substantially different. The present paper is intended (...) as a bird’s eye view on the whole of Maṇḍana’s legacy, including his Sphoṭasiddhi, being his contribution to the grammatical tradi­tion of Bhartṛhari. It is also aimed at finding the reason why in the hierarchy of eminent advaita thinkers Maṇḍana was eventually supplanted by Śaṅkara and his œuvre unacknowledged. (shrink)

Modernity and What Has Been Lost comes out of a conference held at the Jagiellonian University in Krakw̤, Poland, on June 4-5, 2009 that sought to identify Leo Strauss's intellectual background in re: the repudiation of a modern idea of homogenous, universal state (considered as an illegitimate synthesis of Jerusalem and Athens, i.e., the claims of Reason and Revelation). The world we live in, molded by science and historical relativism, may be described as hostile to human dignity or perfection, or (...) abhorrent to those who love the search for wisdom. Straussian teaching consisted in the steady effort to reopen "the quarrel between the Ancients and the Moderns," and refers to the esoteric way of writing practiced by the most profound thinkers of the past which has been apparently forgotten in the last three centuries. Strauss binds the concept of natural right with the question of maintenance of conditions for philosophizing, and it probably seems to him that such defense of philosophy is the highest task in our times. However, one must be well aware that philosophizing always means a perilous way of life. Indeed, it may be destructive of the city (polis) itself as far as the city exists due to some crucial beliefs the philosopher might put in doubt. Reflecting on those issues, Strauss engaged in several highly important debates with his contemporaries, in an open way with, e.g., Carl Schmitt, Karl Lw̲ith and Alexandre Kojv̈e, and more tacitly with Martin Heidegger"--Provided by publisher. (shrink)

The title of this article refers to one of the best-known essays written by David Hume, That Politics may be reduced to a Science. Hume assumed that politics was a science because it admitted of some general truths, which could not be varied by human beings. He adopted a similar stance, albeit indirectly, in the case of economics, discovering several general truths concerning the origins of wealth, money and international trade. At times, however, he was far from being consistent and (...) this undermined these truths. Consequently, it can be argued that, from his perspective, economics was a science on a theoretical level, but it lost this character at a more practical level. Similar doubts can be raised when it comes to Hume’s role in the history of economic thought. In some respects he was an original thinker, but several of his key concepts resembled to some extent ideas that had been put forward by ‘mercantilists’, especially those ‘mercantilists’ who were active in his native Scotland in the first decade of the 18 th century. (shrink)

I borrow part of the title of my paper from Susan Sontag. In 2003, a year before her death, Susan Sontag published an essay entitled Regarding the Pain of Others. There she takes up the subject of the moral significance of presenting the views of war, violent human death exposed to the lenses of cameras. Her approach to the contemporary issue of mediatisation through the image of the sight of human suffering provokes a question: Do we need teleethics today, the (...) ethics of remote moral relations? Using the method of comparative analysis in the area of cultural determinants of ethics, I draw attention to the contemporary challenges that the culture of late modernity imposes on the morality of everyday life. My thesis is this: The images of human suffering provided by the media reveal the imperfection of our morality. As moral subjects, we are not prepared to respond to the suffering of human beings absent from face-to-face relationships. So, we need teleethics. The paper is devoted to this issue. (shrink)

Perceptual experience usually comes with “phenomenal force”, a strong sense that it reflects reality as it is. Some philosophers have argued that it is in virtue of possessing phenomenal force that perceptual experiences are able to non‐inferentially justify beliefs. In this article, I introduce an alternative, inferentialist take on the epistemic role of phenomenal force. Drawing on Bayesian modeling in cognitive science, I argue that the sense of reality that accompanies conscious vision can be viewed as epistemically appraisable in light (...) of its rational etiology. (shrink)

The idea that concepts play a significant role in some perceptions is widespread but everybody seems to differ as to where to draw the line. Some researchers say that the difference between direct and indirect, concept driven acts of perception manifests itself whenever we perceive abstract or general properties. Others point at second order properties or causal properties. I call this inability to precisely differentiate between acts of direct and indirect perception “The Division Problem”. Furthermore there is always a question (...) as to how widespread indirect perceptions are. Can we attribute them to prelingual cognitive systems? I call this second problem “The Distribution Problem”. -/- The main aim of the paper is providing a solution to both problems by proposing a naturalistic explication of the notion of “concept”. -/- I propose to identify the role concepts were supposed to play in perception with a mechanism of “soft detection”. Unlike hard detectors which react to a specific target in virtue of their constitution and placement in the system, soft detectors are understood as dynamic categorization devices enabling the cognitive system to selectively react to an undetectable property via flexible exploitation of data from hard detectors. -/- I conclude by showing how the notion of soft detection retains some of the aspects traditionally attributed to concepts and how does it differ from similar accounts known from contemporary literature. (shrink)

What would it look like for researchers to take non-human animal rights seriously? Recent discussions foster the impression that scientific practice needs to be reformed to make animal research ethical: just as there is ethically rigorous human research, so there can be ethically rigorous animal research. We argue that practically little existing animal research would be ethical and that ethical animal research is not scalable. Since animal research is integral to the existing scientific paradigm, taking animal rights seriously requires a (...) radical, wholesale reimagining of science.Trial registration: ClinicalTrials.gov identifier: NCT05340426. (shrink)

Despite the fact that the notion of internal representation has - at least according to some - a fundamental role to play in the sciences of the mind, not only has its explanatory utility been under attack for a while now, but it also remains unclear what criteria should an explanation of a given cognitive phenomenon meet to count as a representational explanation in the first place. The aim of this article is to propose a solution to this latter problem. (...) I will assume that representational explanations should be construed as a form of mechanistic explanations and proceed by proposing a general sketch of a functional architecture of a representational cognitive mechanism. According to the view on offer here, representational mechanisms are mechanisms that meet four conditions: the structural resemblance condition, the action-guidance condition, the decouplability condition, and the error-detection condition. (shrink)

This book presents a new approach to semantics based on Kazimierz Ajdukiewicz’s Directival Theory of Meaning, which in effect reduces semantics of the analysed language to the combination of its syntax and pragmatics. The author argues that the DTM was forgotten because for many years philosophers didn’t have conceptual tools to appreciate its innovative nature, and that the theory was far ahead of its time. The book shows how a redesigned and modernised version of the DTM can deliver a new (...) solution to the problem of defining linguistic meaning and that the theory can be understood as a new type of functional role semantics. The defining feature of the DTM is that it presents meaning as a product of constraints on the usage of words. According to the DTM meaning is not use, but the avoidance of misuse. Readers will see how the DTM was shelved for reasons that we don’t find so dramatic anymore, and how it contains enough original ideas and solutions to warrant developing it into a full-blown contemporary account. It is shown how many of the underlying ideas of the theory have been embraced later by philosophers and treated simply as brute facts about natural languages or even as new philosophical discoveries. Philosophers of language and researchers with an interest in how languages and the mind work will find this book a fascinating read. (shrink)

Psychedelic substances elicit powerful, uncanny conscious experiences that are thought to possess therapeutic value. In those who undergo them, these altered states of consciousness often induce shifts in metaphysical beliefs about the fundamental structure of reality. The contents of those beliefs range from contentious to bizarre, especially when considered from the point of view of naturalism. Can chemically induced, radically altered states of consciousness provide reasons for or play some positive epistemic role with respect to metaphysical beliefs? In this paper, (...) I discuss a view that has been underexplored in recent literature. I argue that psychedelic states can be rationally integrated into one’s epistemic life. Consequently, updating one’s metaphysical beliefs based on altered states of consciousness does not have to constitute an instance of epistemic irrationality. (shrink)

The evolutionary origin of synapses and neurons is an enigmatic subject that inspires much debate. Non-bilaterian metazoans, both with and without neurons and their closest relatives already contain many components of the molecular toolkits for synapse functions. The origin of these components and their assembly into ancient synaptic signaling machineries are particularly important in light of recent findings on the phylogeny of non-bilaterian metazoans. The evolution of synapses and neurons are often discussed only from a metazoan perspective leaving a considerable (...) gap in our understanding. By taking an integrative approach we highlight the need to consider different, but extremely relevant phyla and to include the closest unicellular relatives of metazoans, the ichthyosporeans, filastereans and choanoflagellates, to fully understand the evolutionary origin of synapses and neurons. This approach allows for a detailed understanding of when and how the first pre- and postsynaptic signaling machineries evolved. The evolutionary origin of synapses and neurons is an enigmatic subject that inspires much debate. Most of our knowledge and recent discussions are biased towards a metazoan perspective, leaving a considerable gap in our understanding. Recent work has now revealed important insights into the emergence and co-regulation of complex synaptic signaling machineries from studies in the closest unicellular relatives of metazoans. (shrink)

Śankara did not comment on the first s ū tra in his Brahmas ū trabh āṣ ya, which was a common practice in such cases; rather, he started by defining two terms: ‘superimposition’ and ‘ignorance’, in a special introductory chapter known to a wider audience as Adhy ā sabh āṣ ya. The question arises as to why he deemed it necessary to precede his commentary to the initial s ū tra with these additional elucidations. Bh ā mat ī, Vācaspati Miśra’s (...) commentary on Mah ā s ū trabh āṣ ya, seems to shed some light on the problem. According to the doctrine of advaita, the phrase ‘desire to know Brahman’ in the first s ū tra seems prima facie to have no meaning. Thus, the introductory commentary is an explanation of an idea of Brahman which is foreign to advaita. (shrink)

The issue of liberation is a recurrent theme in all schools of Indian classical thought. In case of advaita-vedānta it is deeply rooted in ontology. The problem of ontological status of the world was the bone of contention for two competing non‑dualist schools of vedānta — vivaraṇa and bhāmatī. Maṇḍana’s Brahmasiddhi can be regarded as an important source of inspiration for the latter. The present paper is an analysis of Maṇḍana’s statements pertaining to the issue of mukti in contrast with (...) those of Śankara, the exponent of advaita commonly considered the creator and the most prominent representative of the school. (shrink)

Debunking arguments aim to undermine common sense beliefs by showing that they are not explanatorily or causally linked to the entities they are purportedly about. Rarely are facts about the aetiology of common sense beliefs invoked for the opposite aim, that is, to support the reality of entities that furnish our manifest image of the world. Here I undertake this sort of un-debunking project. My focus is on the metaphysics of ordinary physical objects. I use the view of perception as (...) approximate Bayesian inference to show how representations of ordinary objects can be extracted from sensory input in a rational and truth-tracking manner. Drawing an analogy between perception construed as Bayesian hypothesis testing and scientific inquiry, I sketch out how some of the intuitions that traditionally inspired arguments for scientific realism also find application with regards to proverbial tables and chairs. (shrink)

The aim of this paper is to present a proof to the conclusion that is impossible to traverse an infinite series (in particular, an infinite series of past moments). This may also show (given additional assumptions) that the series of past moments cannot be infinite. In the first section I formulate five theses concerning traversing, successive addition and successive subtraction and I present the idea of the argument: if it were possible to traverse an infinite past, it should be in (...) principle possible to go back, which is, however, impossible. The main body of the paper is concerned with working out a simple mathematical representation of some structural features of processes like traversing and successive addition. I also make a crucial distinction between completion of a process at a particular time and its timeless "completion" in infinite time. In section V, I present the formal proof and defend it against a possible objection of question-begging. Finally, I suggest that my argume. (shrink)

Recently, it has been objected that naïve realism is inconsistent with an empirically well-supported claim that mental states of the same fundamental kind as ordinary conscious seeing can occur unconsciously (SFK). The main aim of this paper is to establish the following conditional claim: if SFK turns out to be true, the naïve realist can and should accommodate it into her theory. Regarding the antecedent of this conditional, I suggest that empirical evidence renders SFK plausible but not obvious. For it (...) is possible that what is currently advocated as unconscious perception of the stimulus is in fact momentaneous perceptual awareness (or residual perceptual awareness) of the stimulus making the subject prone to judge in some way rather than another, or to act in some way rather than another. As to the apodosis, I show that neither the core of naïve realism nor any of its main motivations is undermined if SFK is assumed. On the contrary, certain incentives for endorsing naïve realism become more tempting on this assumption. Since the main motivations for naïve realism retain force under SFK, intentionalism is neither compulsory nor the best available explanation of unconscious perception. (shrink)

In this paper, I use the predictive processing theory of perception to tackle the question of how perceptual states can be rationally involved in cognition by justifying other mental states. I put forward two claims regarding the epistemological implications of PP. First, perceptual states can confer justification on other mental states because the perceptual states are themselves rationally acquired. Second, despite being inferentially justified rather than epistemically basic, perceptual states can still be epistemically responsive to the mind-independent world. My main (...) goal is to elucidate the epistemology of perception already implicit in PP. But I also hope to show how it is possible to peacefully combine central tenets of foundationalist and coherentist accounts of the rational powers of perception while avoiding the well-recognized pitfalls of either. (shrink)

The article presents issues concerning the interpretation of the phenomenon of wealth in the context of Christian thought. From beginning, philosophical thought has been engaged in problems of tangible property and its influence on the human condition. The great philosophers indicated a way that the person should refer to the goods of this world. Plato, Aristotle, Seneca – each of them, according to his own vision of man and the world, referred in his texts to the problem of wealth. Equally (...) significant contributions has been made by the monotheistic religions, Judaism and Christianity. Along with the development of the Church, this phenomenon stood out as an essential point of teaching. Primitive and post-apostolic church, to some extent out of necessity, took polemics with the outside world. Separating faith from matters of management, with its beginning in the Enlightenment, shaken the moral underpinnings of the deeds related to wealth. Marxist philosophy gave impulse to another reflection of the Church over economic phenomena. Leon XIII and his Rerum novarum are a milestone in Catholic thought on negative phenomena within the economy. The Holy Father portrayed threats resulting from the Marxist concept, showing an anthropological concept which was appropriate from the point of view of the Christianity. Social and later encyclicals, treat issues related to wealth from the Christian anthropology standpoint. (shrink)