The paradox of material implication has remained unresolved since antiquity because it was believed that the nature of implication was entailment. The article shows that this nature is opposition and therefore the name "implication" should be replaced with the name "competition". A solution to the paradox is provided along with appropriate changes in nomenclature, the addition of connectives and the postulate that the biconditional take over the role of the previous implication. In addition, changes to the (...) nomenclature of logic gates reflecting the competition in electronics are proposed. (shrink)

This paper is concerned with the paradox of decrease. Its aim is to defend the answer to this puzzle that was propounded by its originator, namely, the Stoic philosopher Chrysippus. The main trouble with this answer to the paradox is that it has the seemingly problematic implication that a material thing could perish due merely to extrinsic change. It follows that in order to defend Chrysippus’ answer to the paradox, one has to explain how it could be that Theon (...) is destroyed by the amputation without changing intrinsically. In this paper, I shall answer this challenge by appealing to the broadly Aristotelian idea that at least some of the proper parts of a material substance are ontologically dependent on that substance. I will also appeal to this idea in order to offer a new solution to the structurally similar paradox of increase. In this way, we will end up with a unified solution to two structurally similar paradoxes. (shrink)

This paper resolves a paradox concerning colour constancy. On the one hand, our intuitive, pre-theoretical concept holds that colour constancy involves invariance in the perceived colours of surfaces under changes in illumination. On the other, there is a robust scientific consensus that colour constancy can persist in cerebral achromatopsia, a profound impairment in the ability to perceive colours. The first stage of the solution advocates pluralism about our colour constancy capacities. The second details the close relationship between colour constancy and (...) contrast. The third argues that achromatopsics retain a basic type of colour constancy associated with invariants in contrast processing. The fourth suggests that one person-level, conscious upshot of such processing is the visual awareness of chromatic contrasts ‘at’ the edges of surfaces, implicating the ‘colour for form’ perceptual function. This primitive type of constancy sheds new light on our most basic perceptual capacities, which mark the lower borders of representational mind. (shrink)

Silence is a multifaceted concept which is not merely as an absence of sound but a presence with significant ontological, existential, and phenomenological implications. Through a thematic analysis, this paper deconstructs silence into various dimensions—its ontology, linguistic universality, and its function as cessation of speech, a form of listening, an act of kenosis, a form of ascesis, and a way of life. The study employs philosophical discourse and mathematical notation to delve into these aspects, demonstrating that while each perspective sheds (...) light on certain facets of silence, none can comprehensively encapsulate its essence. The research underscores the paradoxical nature of silence. It is both a universal phenomenon recognised across cultures and an intimate, personal experience that resists definitive categorisation. The paper concludes that the true nature of silence, particularly when considering the state of "being silent," remains indefinable and elusive, inviting deeper contemplation on its role in human experience. (shrink)

Discussions of the implications of sexual reproduction have appeared throughout the history of evolutionary biology, from Darwin to Weismann, Fisher, Muller, Maynard Smith, and Williams. The latest of these appearances highlighted an evolutionary paradox that had previously been overlooked. In many animal and plant species reproduction is obligately sexual and also half the offspring are male, yet the males contribute nothing but genes to reproduction. If asexual mutants of such a species were to produce as many asexual offspring on average (...) as sexual females in that species produce daughters and sons, the growth rate of their population would be twice as large. Whereas half the offspring of sexual females are noncontributory males, all the offspring of such an asexual mutant would contribute to growth rate. Nevertheless, sexual reproduction prevails in most species and is not lost evolutionarily. (shrink)

The aim of this text is to offer an explanation of Gödel's Theorem according to the schemes and notations of the original article. There are many good didactic explanations of the theorem that reveal its central points and implications, but these are difficult to recognize when reading the original work, due to the complexity of its formulation and the author's economical style in explaining the steps of his argument. An exposition of the central concepts will be made, as well as (...) a detailed explanation of the main points of the algebraic development of the proof, which will allow the non-specialist reader to find the well-known paradox from them. (shrink)

Lewis Carroll’s 1895 paper, 'What the Tortoise Said to Achilles' is widely regarded as a classic text in the philosophy of logic. This special issue of 'The Carrollian' publishes five newly commissioned articles by experts in the field. The original paper is reproduced, together with contemporary correspondence relating to the paper and an extensive bibliography.

Paradoxes have played an important role both in philosophy and in mathematics and paradox resolution is an important topic in both fields. Paradox resolution is deeply important because if such resolution cannot be achieved, we are threatened with the charge of debilitating irrationality. This is supposed to be the case for the following reason. Paradoxes consist of jointly contradictory sets of statements that are individually plausible or believable. These facts about paradoxes then give rise to a deeply (...) troubling epistemic problem. Specifically, if one believes all of the constitutive propositions that make up a paradox, then one is apparently committed to belief in every proposition. This is the result of the principle of classical logical known as ex contradictione (sequitur) quodlibetthat anything and everything follows from a contradiction, and the plausible idea that belief is closed under logical or material implication (i.e. the epistemic closure principle). But, it is manifestly and profoundly irrational to believe every proposition and so the presence of even one contradiction in one’s doxa appears to result in what seems to be total irrationality. This problem is the problem of paradox-induced explosion. In this paper it will be argued that in many cases this problem can plausibly be avoided in a purely epistemic manner, without having either to resort to non-classical logics for belief (e.g. paraconsistent logics) or to the denial of the standard closure principle for beliefs. The manner in which this result can be achieved depends on drawing an important distinction between the propositional attitude of belief and the weaker attitude of acceptance such that paradox constituting propositions are accepted but not believed. Paradox-induced explosion is then avoided by noting that while belief may well be closed under material implication or even under logical implication, these sorts of weaker commitments are not subject to closure principles of those sorts. So, this possibility provides us with a less radical way to deal with the existence of paradoxes and it preserves the idea that intelligent agents can actually entertain paradoxes. (shrink)

This study explored the experiences of the newly-hired faculty in the university to acquire an in-depth and profound understanding of these experiences. It involved eight purposively chosen faculty in a semi-structured interview and focus group discussion documented in voice and video recorders. Using Colaizzi’s seven step-approach to data analysis, results revealed three paradoxical themes: the joys and struggles of teaching, successes and pains of learning, and the privileges and challenges of serving. On the one hand, the joys and struggles of (...) teaching were brought about by their adjustments in instruction. On the other hand, successes and pains of learning centered on professional growth. Finally, the privileges and challenges of serving incorporated the experiences in research, production, and extension. Generally, these teachers have experienced ups and downs in their first two years of teaching at a higher education institution. On the basis of study findings, implications and recommendations are discussed. (shrink)

Unlike almost all other philosophers of science, Karl Popper sought to contribute to natural philosophy or cosmology – a synthesis of science and philosophy. I consider his contributions to the philosophy of science and quantum theory in this light. There is, however, a paradox. Popper’s most famous contribution – his principle of demarcation – in driving a wedge between science and metaphysics, serves to undermine the very thing he professes to love: natural philosophy. I argue that Popper’s philosophy of science (...) is, in this respect, defective. Science cannot proceed without making highly problematic metaphysical assumptions concerning the comprehensibility and knowability of the universe. Precisely because these assumptions are problematic, rigour requires that they be subjected to sustained critical scrutiny, as an integral part of science itself. Popper’s principle of demarcation must be rejected. Metaphysics and philosophy of science become a vital part of science. Natural philosophy is reborn. A solution to the problem of what it means to say a theory is unified is proposed, a problem Popper failed to solve. In The Logic of Scientific Discovery, Popper made important contributions to the interpretation of quantum theory, especially in connection with Heisenberg's uncertainty relations. Popper's advocacy of natural philosophy has important implications for education. (shrink)

The possibility of algorithmic consciousness depends on the assumption that conscious states can be copied or repeated by sufficiently duplicating their underlying physical states, leading to a variety of paradoxes, including the problems of duplication, teleportation, simulation, self-location, the Boltzmann brain, and Wigner’s Friend. In an effort to further elucidate the physical nature of consciousness, I challenge these assumptions by analyzing the implications of special relativity on evolutions of identical copies of a mental state, particularly the divergence of these (...) evolutions due to quantum fluctuations. By assuming the supervenience of a conscious state on some sufficient underlying physical state, I show that the existence of two or more instances, whether spacelike or timelike, of the same conscious state leads to a logical contradiction, ultimately refuting the assumption that a conscious state can be physically reset to an earlier state or duplicated by any physical means. Several explanatory hypotheses and implications are addressed, particularly the relationships between consciousness, locality, physical irreversibility, and quantum no-cloning. (shrink)

This paper investigates the responses of GPT-4, a state-of-the-art AI language model, to ten prominent philosophical paradoxes, and evaluates its capacity to reason and make decisions in complex and uncertain situations. In addition to analyzing GPT-4's solutions to the paradoxes, this paper assesses the model's Theory of Mind (ToM) capabilities by testing its understanding of mental states, intentions, and beliefs in scenarios ranging from classic ToM tests to complex, real-world simulations. Through these tests, we gain insight into AI's (...) potential for social reasoning and its capacity for more sophisticated forms of human-AI interaction. The paper also explores the limitations and biases of AI-generated reasoning and its implications for our comprehension of complex philosophical problems. (shrink)

I defend the hypothesis that the semantic paradoxes, the paradoxes about collections, and the sorites paradoxes, are all paradoxes of reference fixing: they show that certain conventionally adopted and otherwise functional reference-fixing principles cannot provide consistent assignments of reference to certain relevant expressions in paradoxical cases. I note that the hypothesis has interesting implications concerning the idea of a unified account of the semantic, collection and sorites paradoxes, as well as about the explanation of their (...) “recalcitrance”. I also note that it does not necessarily imply that one should not expect the sometimes hoped for “unique” solution to a paradox of these kinds. (shrink)

Lewis Carroll, both logician and writer, suggested a logical paradox containing furthermore two connotations (connotations or metaphors are inherent in literature rather than in mathematics or logics). The paradox itself refers to implication demonstrating that an intermediate implication can be always inserted in an implication therefore postponing its ultimate conclusion for the next step and those insertions can be iteratively and indefinitely added ad lib, as if ad infinitum. Both connotations clear up links due to the shared (...) formal structure with other well-known mathematical observations: (1) the paradox of Achilles and the Turtle; (2) the transitivity of the relation of equality. Analogically to (1), one can juxtapose the paradox of the Liar (for Lewis Carroll’s paradox) and that of the arrow (for “Achilles and the Turtle”), i.e. a logical paradox, on the one hand, and an aporia of motion, on the other hand, suggesting a shared formal structure of both, which can be called “ontological”, on which basis “motion” studied by physics and “conclusion” studied by logic can be unified being able to bridge logic and physics philosophically in a Hegelian manner: even more, the bridge can be continued to mathematics in virtue of (2), which forces the equality (for its property of transitivity) of any two quantities to be postponed analogically ad lib and ad infinitum. The paper shows that Hilbert arithmetic underlies naturally Lewis Carroll’s paradox admitting at least three interpretations linked to each other by it: mathematical, physical and logical. Thus, it can be considered as both generalization and solution of his paradox therefore naturally unifying the completeness of quantum mechanics (i.e. the absence of hidden variables) and eventual completeness of mathematics as the same and isomorphic to the completeness of propositional logic in relation to set theory as a first-order logic (in the sense of Gödel (1930)’s completeness theorems). (shrink)

This paper examines Hegel’s claim that philosophy “has no other object than God‘ as a claim about the essentiality of the idea of God to philosophy. On this idealist interpretation, even atheistic philosophies would presuppose rationally evaluable ideas of God, despite denials of the existence of anything corresponding to those ideas. This interpretation is then applied to Hegel’s version of idealism in relation to those of two predecessors, Leibniz and Kant. Hegel criticizes the idea of the Christian God present within (...) his predecessors in terms of his own heterodox reading of the Trinity in order to resolve a paradox affecting them -- the “paradox of perspectivism‘. (shrink)

This paper studies proof systems for the logics of super-strict implication ST2–ST5, which correspond to C.I. Lewis’ systems S2–S5 freed of paradoxes of strict implication. First, Hilbert-style axiomatic systems are introduced and shown to be sound and complete by simulating STn in Sn and backsimulating Sn in STn, respectively(for n=2,...,5). Next, G3-style labelled sequent calculi are investigated. It is shown that these calculi have the good structural properties that are distinctive of G3-style calculi, that they are sound (...) and complete, and it is shown that the proof search for G3. ST2 is terminating and therefore the logic is decidable. (shrink)

My aim in this paper is to move toward a relational moral theory of harm through examination of a common yet underexplored form of child maltreatment: childhood psychological abuse. I draw on relational theory to consider agential, intrapersonal, and interpersonal ways in which relational harms develop and evolve both in intimate relationships and in conditions of oppression. I set forth three distinctive yet interconnected forms of relational harm that childhood psychological abuse causes: harm to the relational agency of individuals, harm (...) to the relationships individuals hold with themselves, especially with regard to how they respect, know, and trust themselves, and harm to interpersonal relationships of both a direct and indirect nature in present and future timeframes. I close by noting that while relationships can be the site of human brutality that destroys the relational self, paradoxically and promisingly, they also can be a primary means of the relational reconstitution of the self. Ultimately, relational analyses of the harms of childhood psychological abuse reveal several key elements of a relational theory of harm and demonstrate the significance of relational harms for moral philosophy. (shrink)

In his recent article in Philosophy and Public Affairs, 'The Paradox of Voting and Ethics of Political Representation', Alexander A. Guerrero argues it is rational to vote because each voter should want candidates they support to have the strongest public mandate possible if elected to office, and because every vote contributes to that mandate. The present paper argues that two of Guerrero's premises require correction, and that when those premises are corrected several provocative but compelling conclusions follow about the rationality (...) of voting and duties of elected officials: (A) Voting is typically rational for the members of a political party’s base; (B) Voting is often (but not always) irrational for “swing” voters (i.e. independent voters who are not affiliated with any political party, as well as “undecided” voters who are considering voting across party lines); and (C) Elected officials have a moral duty to respond to changing levels of popular support once in office, as indicated by properly monitored and corroborated public opinion polls of constituents, functioning more as delegates the lower their level of popular support. Finally, I suggest that the last of these conclusions has wide-ranging implications for political ethics. I illustrate these implications by focusing on the questions -- under debate in the 2016 US Presidential election cycle -- of whether a sitting President has a moral duty to nominate or not nominate a new Supreme Court justice during his or her final year in office, and similarly, whether US Senators have a moral duty to obstruct, or not obstruct, confirmation of the President’s eventual nominee. (shrink)

It will be shown in this article that an ontological approach for some problems related to the interpretation of Quantum Mechanics (QM) could emerge from a re-evaluation of the main paradox of early Greek thought: the paradox of Being and non-Being, and the solutions presented to it by Plato and Aristotle. More well known are the derivative paradoxes of Zeno: the paradox of motion and the paradox of the One and the Many. They stem from what was perceived by (...) classical philosophy to be the fundamental enigma for thinking about the world: the seemingly contradictory results that followed from the co-incidence of being and non-being in the world of change and motion as we experience it, and the experience of absolute existence here and now. The most clear expression of both stances can be found, again following classical thought, in the thinking of Heraclitus of Ephesus and Parmenides of Elea. The problem put forward by these paradoxes reduces for both Plato and Aristotle to the possibility of the existence of stable objects as a necessary condition for knowledge. Hence the primarily ontological nature of the solutions they proposed: Plato’s Theory of Forms and Aristotle’s metaphysics and logic. Plato’s and Aristotle’s systems are argued here to do on the ontological level essentially the same: to introduce stability in the world by introducing the notion of a separable, stable object, for which a ‘principle of contradiction’ is valid: an object cannot be and not-be at the same place at the same time. So it becomes possible to forbid contradiction on an epistemological level, and thus to guarantee the certainty of knowledge that seemed to be threatened before. After leaving Aristotelian metaphysics, early modern science had to cope with these problems: it did so by introducing “space” as the seat of stability, and “time” as the theater of motion. But the ontological structure present in this solution remained the same. Therefore the fundamental notion ‘separable system’, related to the notions observation and measurement, themselves related to the modern concepts of space and time, appears to be intrinsically problematic, because it is inextricably connected to classical logic on the ontological level. We see therefore the problems dealt with by quantum logic not as merely formal, and the problem of ‘non-locality’ as related to it, indicating the need to re-think the notions system, entity, as well as the implications of the operation ‘measurement’, which is seen here as an application of classical logic (including its ontological consequences) on the material world. (shrink)

The aim of this paper is to clarify the truth-functional interpretation of the logical connective of the material implication. The importance of such clarification lies in the fact that it allows avoiding the supposed paradoxes introduced by C. I. Lewis (1918). I argue that an adequate understanding of the history and purposes of logic is enough to dissolve them away. The defense is based on an exposition of propositional compositionalism. To compare, I also present Stalnaker’s (1968) alternative that (...) seeks to explain the implicit concept of conditionality of conditionals assertions. In order to reinforce my aim I expound the twelve different meanings of ‘implication’ stated by Corcoran (1993) in order to hold that a proper understanding of these meanings allows us to avoid ambiguities and confusions. Finally, I expect to show that despite the possible alternatives, compositionalism is still the best explanation for the truth-functionality account of logical connectives. (shrink)

The black hole information loss paradox is a catch-all term for a family of puzzles related to black hole evaporation. For almost 50 years, the quest to elucidate the implications of black hole evaporation has not only sustained momentum, but has also become increasingly populated with proposals that seem to generate more questions than they purport to answer. Scholars often neglect to acknowledge ongoing discussions within black hole thermodynamics and statistical mechanics when analyzing the paradox, including the interpretation of Bekenstein-Hawking (...) entropy, which is far from settled. To remedy the dialectical gridlock, I have formulated an overarching, unified framework, which I call ``Black Hole Paradoxes'', that integrates the debates and taxonomizes the relevant `camps' or philosophical positions. -/- I demonstrate that black hole evaporation within Hawking's semi-classical framework insinuates how late-time Hawking radiation is an entangled global system, a contradiction in terms. The relevant forms of information loss are associated with a decrease in maximal Boltzmann entropy and an increase in global von Neumann entropy respectively, which engender what I've branded the ``paradox of phantom entanglement''. Prospective solutions are then tasked with demonstrating how late-time Hawking radiation is either exclusively an entangled subsystem, in which a black hole remnant lingers as an information safehouse, or exclusively an unentangled global system, in which information is evacuated to the exterior. -/- The disagreement between safehouse and evacuation solutions boils down to the statistical interpretation of thermodynamic black hole entropy, i.e., Bekenstein-Hawking entropy. Safehouse solutions attribute Bekenstein-Hawking entropy to a minority of black hole degrees of freedom, those that are associated with the horizon. Evacuation solutions, in contrast, attribute Bekenstein-Hawking entropy to all black hole degrees of freedom. I argue that the interpretation of Bekenstein-Hawking entropy is the litmus test to vet the overpopulated proposal space. So long as any proposal rejecting Hawking's original calculation independently derives black hole evaporation, globally conserves degrees of freedom and entanglement, preserves a version of semi-classical gravity at sub-Planckian scales, and describes black hole thermodynamics in statistical terms, then it counts as a genuine solution to the paradox. (shrink)

According to the most common interpretation of the simulation argument, we are very likely to live in an ancestor simulation. It is interesting to ask if some families of simulations are more likely than others inside the space of all simulations. We argue that a natural probability measure is given by computational complexity: easier simulations are more likely to be run. Remarkably this allows us to extract experimental predictions from the fact that we live in a simulation. For instance we (...) show that it is very likely that humanity will not achieve interstellar travel and that humanity will not meet other intelligent species in the universe, in turn explaining the Fermi's Paradox. On the opposite side, experimental falsification of any of these predictions would constitute evidence against our reality being a simulation. (shrink)

This article discusses the logic of the Epimenides Paradox using a graphical representation of the logical operators involved. The graphical representation of the Logical Operators is the one used in digital electronics. This method of investigation is very effective in revealing the hidden error in the reasoning that leads to the contradiction. The article explains the vicious circle that the mind goes through when trying to analyze the Paradox. Finally, the article proposes a solution of the Paradox with final conclusions (...) that are not paradoxical but simply counterintuitive. The endless deduction is generated by subsequent evaluations that take place on different levels. In its evaluation the Mind alternates a level of logical evaluation with a level of semantic evaluation. (shrink)

A sorites argument is a symptom of the vagueness of the predicate with which it is constructed. A vague predicate admits of at least one dimension of variation (and typically more than one) in its intended range along which we are at a loss when to say the predicate ceases to apply, though we start out confident that it does. It is this feature of them that the sorites arguments exploit. Exactly how is part of the subject of this paper. (...) The majority of philosophers writing on vagueness take it to be a kind of semantic phenomenon. If we are right, they are correct in this assumption, which is surely the default position, but they have not so far provided a satisfactory account of the implications of this or a satisfactory diagnosis of the sorites arguments. Other philosophers have urged more exotic responses, which range from the view that the fault lies not in our language, but in the world, which they propose to be populated with vague objects which our semantics precisely reflects, to the view that the world and language are both perfectly in order, but that the fault lies with our knowledge of the properties of the words we use (epistemicism). In contrast to the exotica to which some philosophers have found themselves driven in an attempt to respond to the sorites puzzles, we undertake a defense of the commonsense view that vague terms are semantically vague. Our strategy is to take fresh look at the phenomenon of vagueness. Rather than attempting to adjudicate between different extant theories, we begin with certain pre-theoretic intuitions about vague terms, and a default position on classical logic. The aim is to see whether (i) a natural story can be told which will explain the vagueness phenomenon and the puzzling nature of soritical arguments, and, in the course of this, to see whether (ii) there arises any compelling pressure to give up the natural stance. We conclude that there is a simple and natural story to be told, and we tell it, and that there is no good reason to abandon our intuitively compelling starting point. The importance of the strategy lies in its dialectical structure. Not all positions on vagueness are on a par. Some are so incredible that even their defenders think of them as positions of last resort, positions to which we must be driven by the power of philosophical argument. We aim to show that there is no pressure to adopt these incredible positions, obviating the need to respond to them directly. If we are right, semantic vagueness is neither surprising, nor threatening. It provides no reason to suppose that the logic of natural languages is not classical or to give up any independently plausible principle of bivalence. Properly understood, it provides us with a satisfying diagnosis of the sorites argumentation. It would be rash to claim to have any completely novel view about a topic so well worked as vagueness. But we believe that the subject, though ancient, still retains its power to inform and challenge us. In particular, we will argue that taking seriously the central phenomenon of predicate vagueness—the “boundarylessness” of vague predicates—on the commonsense assumption that vagueness is semantic, leads ineluctably to the view that no sentences containing vague expressions (henceforth ‘vague sentences’) are truth-evaluable. This runs counter to much of the literature on vagueness, which commonly assumes that, though some applications of vague predicates to objects fail to be truth-evaluable, in clear positive and negative cases vague sentences are unproblematically true or false. It is clarity on this, and related points, that removes the puzzles associated with vagueness, and helps us to a satisfying diagnosis of why the sorites arguments both seem compelling and yet so obviously a bit of trickery. We give a proof that semantically vague predicates neither apply nor fail-to-apply to anything, and that consequently it is a mistake to diagnose sorites arguments, as is commonly done, by attempting to locate in them a false premise. Sorites arguments are not sound, but not unsound either. We offer an explanation of their appeal, and defend our position against a variety of worries that might arise about it. The plan of the paper is as follows. We first introduce an important distinction in terms of which we characterize what has gone wrong with vague predicates. We characterize what we believe to be our natural starting point in thinking about the phenomenon of vagueness, from which only a powerful argument should move us, and then trace out the consequences of accepting this starting point. We consider the charge that among the consequences of semantic vagueness are that we must give up classical logic and the principle of bivalence, which has figured prominently in arguments for epistemicism. We argue there are no such consequences of our view: neither the view that the logic of natural languages is classical, nor any plausible principle of bivalence, need be given up. Next, we offer a diagnosis of what has gone wrong in sorites arguments on the basis of our account. We then present an argument to show that our account must be accepted on pain of embracing (in one way or another) the epistemic view of “vagueness”, i.e., of denying that there are any semantically vague terms at all. Next, we discuss some worries that may arise about the intelligibility of our linguistic practices if our account is correct. We argue none of these worries should force us from our intuitive starting point. Finally, we cast a quick glance at other forms of semantic incompleteness. (shrink)

Resolving the Ross and Prior paradoxes proved to be a difficult task. Its first two stages, involving the identification of the true natures of the implication and truth values, are described in the articles "Solving the Paradox of Material Implication – 2024" and "Solving Jörgensen's Dilemma – 2024". This article describes the third stage, which involves the discovery of missing modal operators and the Classical Modal Calculus. Finally, procedures for solving both paradoxes are provided.

The problem analysed in this paper is whether we can gain knowledge by using valid inferences, and how we can explain this process from a model-theoretic perspective. According to the paradox of inference (Cohen & Nagel 1936/1998, 173), it is logically impossible for an inference to be both valid and its conclusion to possess novelty with respect to the premises. I argue in this paper that valid inference has an epistemic significance, i.e., it can be used by an agent to (...) enlarge his knowledge, and this significance can be accounted in model-theoretic terms. I will argue first that the paradox is based on an equivocation, namely, it arises because logical containment, i.e., logical implication, is identified with epistemological containment, i.e., the knowledge of the premises entails the knowledge of the conclusion. Second, I will argue that a truth-conditional theory of meaning has the necessary resources to explain the epistemic significance of valid inferences. I will explain this epistemic significance starting from Carnap’s semantic theory of meaning and Tarski’s notion of satisfaction. In this way I will counter (Prawitz 2012b)’s claim that a truth-conditional theory of meaning is not able to account the legitimacy of valid inferences, i.e., their epistemic significance. (shrink)

Some analogous higher-order versions of Skolem’s paradox will be introduced. The generalizability of two solutions for Skolem’s paradox will be assessed: the course-book approach and Bays’ one. Bays’ solution to Skolem’s paradox, unlike the course-book solution, can be generalized to solve the higher-order paradoxes without any implication about the possibility or order of a language in which mathematical practice is to be formalized.

The focus in this essay will be upon the paradoxes, and foremostly in set theory. A central result is that the librationist set theory £ extension \Pfund $\mathscr{HR}(\mathbf{D})$ of \pounds \ accounts for \textbf{Neumann-Bernays-Gödel} set theory with the \textbf{Axiom of Choice} and \textbf{Tarski's Axiom}. Moreover, \Pfund \ succeeds with defining an impredicative manifestation set $\mathbf{W}$, \emph{die Welt}, so that \Pfund$\mathscr{H}(\mathbf{W})$ %is a model accounts for Quine's \textbf{New Foundations}. Nevertheless, the points of view developed support the view that the truth- (...) class='Hi'>paradoxes and the set-paradoxes have common origins, so that the librationist resolutions of the set theoretic paradoxes are at the same time resolutions of the truth theoretic paradoxes. Both the librationist resolutions of the set theoretic paradoxes and the truth theoretic paradoxes have non-trivial philosophical implications: librationist set theories have the consequence that there are no absolutely uncountable sets, and librationist truth theories allow the use of syntactical modalities in ways which circumvent limitations as those of \parencite{Montague1963}, and a truth predicate which is useful for more precise philosophical discourse. (shrink)

We study a new formal logic LD introduced by Prof. Grzegorczyk. The logic is based on so-called descriptive equivalence, corresponding to the idea of shared meaning rather than shared truth value. We construct a semantics for LD based on a new type of algebras and prove its soundness and completeness. We further show several examples of classical laws that hold for LD as well as laws that fail. Finally, we list a number of open problems. -/- .

In this chapter I explore what painful art can tell us about the nature and importance of human welfare. My goal is not so much to defend a new solution to the paradox of tragedy, as it is to explore the implications of the kinds of solutions that I find attractive. Both nonhedonic compensatory theories and constitutive theories explain why people seek out painful art, but they have troublesome implications. On some narrow theories of well-being, they imply that painful art (...) is bad for us. Accordingly, we may rightly wonder if it rational for people to watch melodramas or to listen to love songs. One might think that we should generally avoid unpleasant works of art. This implication flirts with absurdity. I show how it can be avoided by making a distinction between well-being and worth. (shrink)

The truth-functional hypothesis states that indicative conditional sentences and the material implication have the same truth conditions. Haze (2011) has rejected this hypothesis. He claims that a self-referential conditional, coupled with a plausible assumption about its truth-values and the assumption that the truth-functional hypothesis is true, lead to a liar’s paradox. Given that neither the self-referential conditional nor the assumption about its truth-values are problematic, the culprit of the paradox must be the truth-functional hypothesis. Therefore, we should reject it. (...) In this paper I argue that, contrary to what Haze thinks, the truth-functional hypothesis is not to blame. In fact, no liar’s paradox emerges when the truth-functional hypothesis is true; it emerges only if it is false. (shrink)

The discrepancy between individual women and the stereotypes attributed to the group as a ‎whole has become progressively greater and more explicit over the course of history. The stereotypes remain the same age-old ‎allegations whilst the ‎developments in the occupations of women and the traits they have opportunity to express have increased the distance between women and those ascribed traits. Stereotypes’ abstention from revision in light of contrary evidence constitutes an epistemic paradox for it entails conflict between the stereotypical knowledge (...) and empirical evidence, as well as between the stereotypical knowledge and other empirical knowledges. This paradox of stubbornness also raises the question as to the epistemic source of stereotypes. For, people at young ages encounter evidence which should have formed a more complex knowledge regarding women rather than the pervasive stereotypical knowledge. It is this extremity of absurdness of stereotypes regarding women that is utile to understanding stereotypes as a whole. The epistemic paradox that is engrained in all stereotypes is exposed uncompromisingly by this group. The paradox cannot be dismissed with excuses of having a small basis of evidence, such as may be said regarding other social groups with which one may have had minimal or no contact. Thus, stereotypes of women provide a limit case to understanding the epistemology of this paradoxical form of knowledge. The traits and epistemic phenomena which render stereotypes epistemically puzzling and intriguing is the relationship between knowledges. Stereotypical knowledge regarding women as a group conflict with one’s experience-founded knowledges of particular women, deeming the corporate body of knowledge incoherent. Quine’s theory of knowledge, with its holistic empirical approach endorsing conceptual schemes, provides fertile ground for this analysis. The novelty in his account is his establishment of the criteria of coherency, which shifts the focal point of epistemic inquiry away from the adequacy of individual knowledges with empirical evidence to the intra-knowledge relationships themselves. In his empiricism, Quine rather examines the interactions between knowledges and the overarching coherence of the body of knowledge as a holistic unit. Quine creates place in his account for mechanism which provide for the epistemic incongruences of stubbornness and conflict found between stereotypical knowledges and empirical evidence. These very mechanisms are what this paper requests to examine. Quine, ultimately, formulates knowledge as a collectively held fabric consisting of relations and of posits – socially constructed mechanisms which are empirically-irreducible and implemented pragmatically for the organisation of empirical evidence. According to Quine, the fabric formation is a conceptual scheme sourced in social heritage. People are bestowed with an eclectic framework of ‎knowledge to pragmatically merge between an inherited, collective conceptual scheme and the personally experienced empirical evidence. This paper will delve into Quine’s fabric of knowledge, its relations, and inner-mechanisms. The finding of stereotypes to be an age-old posit entrenched pragmatically – thus stubbornly – in the collective conceptual scheme, will explain the epistemic paradoxes they entail and offer insight to their revision in light of empiric reality and its women. (shrink)

Loneliness in medicine is a serious problem not just for patients, for whom illness is intrinsically isolating, but also for physicians in the contemporary condition of medicine. We explore this problem by investigating the ideal physician-patient relationship, whose analogy with friendship has held enduring normative appeal. Drawing from Talbot Brewer and Nir Ben-Moshe, we argue that this appeal lies in a dynamic form of companionship incompatible with static models of friendship-like physician-patient relationships: a mutual refinement of embodied virtue that draws (...) both persons together. The ideal physician-patient relationship has a dialectical character that fosters each member's improvement of phenomenologically recognizing and embodying moral virtues. A key component of this dynamic is a commitment to the common goal of the patient's health, realized through joint interactivities and conversations over time. The physician's presence to the patient's suffering—understood best as an alienating phenomenological condition for the patient—orients and discloses possibilities for virtuous caregiving by structuring the meanings of the goals, conversations, and joint narrative constitutive of their relationship. Presence to suffering, paradoxically, is perhaps an important prerequisite for this dynamic partnership. These activities dialectically build an interpretive horizon of understanding through which moral goods and character refinement—in and for the other—may become revealed for both persons in their shared being-in-the-world. This analysis of suffering, mood, and revealing of (possible) moral goods has implications for addressing the modern problem of loneliness for patients and physicians, who are increasingly inhibited from building flourishing relationships with each other. (shrink)

Supererogatory acts—good deeds “beyond the call of duty”—are a part of moral common sense, but conceptually puzzling. I propose a unified solution to three of the most infamous puzzles: the classic Paradox of Supererogation (if it’s so good, why isn’t it just obligatory?), Horton’s All or Nothing Problem, and Kamm’s Intransitivity Paradox. I conclude that supererogation makes sense if, and only if, the grounds of rightness are multi-dimensional and comparative.

This chapter discusses the fundamental question of the defense industry’s role and legitimacy for societies. It begins with a parable of a psychopath doing something self-serving that has beneficial moral consequences. Analogously, it is argued, the defense industry profiting by selling weapons that can kill people makes it useful in solving moral problems not solvable by people with ordinary moral scruples. Next, the chapter argues that while the defense industry is a business, it is also implicated in the security of (...) its home nations. In addition, its products can be used for good or evil. Thus, it must navigate conflicting values, with the result that the rules often thought to rightly regulate the industry—codes of business ethics, engineering ethics, procurement ethics, plus laws of the land, and dicta of conscience—need supplementing by general moral reflection. This chapter argues for a principle that tells how to decide when to violate the rules, for a theory of rational choice on which choosing by this principle is rational, and for teaching that theory to defense industry employees to ensure their ethical behavior. (shrink)

Jonathan Lowe has argued that a particular variation on C.I. Lewis' notion of strict implication avoids the paradoxes of strict implication. We show that Lowe's notion of implication does not achieve this aim, and offer a general argument to demonstrate that no other variation on Lewis' notion of constantly strict implication describes the logical behaviour of natural-language conditionals in a satisfactory way.

Recently, the problem of national identity has been actualized, but here is a the question: identity to what? Traditions, religion, mentality? Ideals, perhaps? Inspired by the best examples of national historical thought, the author offers an an original approach to deciphering the Russian "cultural code". В последнее время актуализируется проблема национальной идентичности, но вот вопрос: идентичности чему? Традициям, религии, менталитету? Идеалам, может быть? Воодушевленный лучшими образцами отечественной исторической мысли, автор предлагает оригинальный подход к расшифровке русского «культурного кода».

How to say no less, no more about conditional than what is needed? From a logical analysis of necessary and sufficient conditions (Section 1), we argue that a stronger account of conditional can be obtained in two steps: firstly, by reminding its historical roots inside modal logic and set-theory (Section 2); secondly, by revising the meaning of logical values, thereby getting rid of the paradoxes of material implication whilst showing the bivalent roots of conditional as a speech-act based (...) on affirmations and rejections (Section 3). Finally, the two main inference rules for conditional, viz. Modus Ponens and Modus Tollens, are reassessed through a broader definition of logical consequence that encompasses both a normal relation of truth propagation and a weaker relation of falsity non-propagation from premises to conclusion (Section 3). (shrink)

The theological misappropriation of Christianity as a civilizing force occurs when individuals convert to Christianity due to deception that ignores the faith-based aspect of Christianity. The history of Western education in India illustrates the hidden curriculum that Christian missionaries employed to disrupt the Indian educational system. This unnerving pedagogy points to the need for a postcolonial theoretical framework that relates the inescapable hybridity of religion and culture where Orientalism has the potential to occur. To press the ongoing urgency of this (...) discussion, I convey how the history of British India connects to my lived-reality as an American Hindu. Overall, I point to hybridity as a lived paradox of ambiguous conflict that embraces interfaith relations. I offer implications for Christian missionaries today to foster authentic interfaith connections without engaging in colonizing ideologies. (shrink)

Illusionism is the view that conscious experience is some sort of introspective illusion. According to illusionism, there is no conscious experience, but it merely seems like there is conscious experience. This would suggest that much phenomenological enquiry, including work on phenomenological psychopathology, rests on a mistake. Some philosophers have argued that illusionism is obviously false, because seeming is itself an experiential state, and so necessarily presupposes the reality of conscious experience. In response, the illusionist could suggest that the relevant sort (...) of seeming here is not an experiential state, but is a cognitive state, such as a judgement or a belief, which is fully amenable to a physical or functionalist analysis. Herein, I argue that this response is unsuccessful and fails to undermine the reality of conscious experience. Nonetheless, the response does raise the problem of how a judgement or belief about the character of a conscious experience, even if it is true, can be justified if the conscious experience has no causal role in the formation of the judgement or belief. This is not a new problem, but is a reiteration of an old problem that is known in the philosophy of mind literature as the paradox of phenomenal judgement. I consider how the paradox of phenomenal judgement can be resolved and how the judgement or belief about conscious experience can be justified with appeal to the notion of acquaintance. (shrink)

It is widely accepted that there is what has been called a non-hypocrisy norm on the appropriateness of moral blame; roughly, one has standing to blame only if one is not guilty of the very offence one seeks to criticize. Our acceptance of this norm is embodied in the common retort to criticism, “Who are you to blame me?”. But there is a paradox lurking behind this commonplace norm. If it is always inappropriate for x to blame y for a (...) wrong that x has committed, then all cases in which x blames x (i.e. cases of self-blame) are rendered inappropriate. But it seems to be ethical common-sense that we are often, sadly, in position (indeed, excellent, privileged position) to blame ourselves for our own moral failings. And thus we have a paradox: a conflict between the inappropriateness of hypocritical blame, and the appropriateness of self-blame. We consider several ways of resolving the paradox, and contend none is as defensible as a position that simply accepts it: we should never blame ourselves. In defending this startling position, we defend a crucial distinction between self-blame and guilt. (shrink)

It is common to think that what theory of linguistic vagueness is correct has implications for debates in philosophy of law. I disagree. I argue that the implications of particular theories of vagueness on substantive issues of legal theory and practice are less far-reaching than often thought. I focus on four putative implications discussed in the literature concerning (i) the value of vagueness in the law, (ii) the possibility and value of legal indeterminacy, (iii) the possibility of the rule of (...) law, and (iv) strong discretion. I conclude with some methodological remarks. Delineating questions about conventional meaning, the metaphysics/metasemantics of (legal) content determination, and norms of legal interpretation and judicial practice can motivate clearer answers and a more refined understanding of the space of overall theories of vagueness, interpretation, and law. (shrink)

Philosophers have long argued that duties to oneself are paradoxical, as they seem to entail an incoherent power to release oneself from obligations. I argue that self-release is possible, both as a matter of deontic logic and of metaethics.

The coordinated attack scenario and the electronic mail game are two paradoxes of common knowledge. In simple mathematical models of these scenarios, the agents represented by the models can coordinate only if they have common knowledge that they will. As a result, the models predict that the agents will not coordinate in situations where it would be rational to coordinate. I argue that we should resolve this conflict between the models and facts about what it would be rational to (...) do by rejecting common knowledge assumptions implicit in the models. I focus on the assumption that the agents have common knowledge that they are rational, and provide models to show that denying this assumption suffices for a resolution of the paradoxes. I describe how my resolution of the paradoxes fits into a general story about the relationship between rationality in situations involving a single agent and rationality in situations involving many agents. (shrink)

In the article I deal with some paradoxes and errors caused by improper usage of logical and philosophical terms appearing in the arguments for existence of god and other philosophical issues. I point at rst some paradoxes coming om improper usage of propositional calculus as an instrument for analysis of a natural language. this language is actually not using simple sentences but rather propositional functions, their logical connections, and some replacements for variables in them. We still have to (...) deal with so called paradox of material implication. the second paragraph provides formal and metatheoretical critics of Charles Sanders Peirce’s theory of deduction, induction and abduction. I argue that what Peirce and his followers call abduction is actually deduction or some reasoning unable to describe in terms of the logic used by them. Both syllogistic and inferential theory of abduction generate some paradoxes and contradictions. In the last paragraph also some paradoxes and contradictions resulting om the theory of causation by Jan Łukasiewicz are presented. the central issue of the article is erroneous usage of the implication: in logical paraphrases of a natural language, in description of the scienti c reasoning, and in description of causality. However, my objective is not to solve all problems mentioned above but rather to open a discussion over them. (shrink)

*As mentioned in Peter Coy's NYT essay "When Being Good Is Just a Matter of Being Lucky" (2023) -/- ----- -/- How is the problem of free will related to the problem of moral luck? In this essay, I answer that question and outline a new solution to the paradox of moral luck, the source-paradox solution. This solution both explains why the paradox arises and why moral luck does not exist. To make my case, I highlight a few key connections (...) between the paradox of moral luck and two related problems, namely the problem of free will and determinism and the paradox of self-creation. Piecing together intuitions, arguments, and insights from recent work on each of these three problems, I argue that the type of control necessary for moral responsibility can only be had by someone who is a genuine source of his own actions, but the relevant notion of sourcehood admits no coherent characterization. If our commonsense view of moral responsibility is incoherent, it is unsurprising that our commitment to the existence of morally responsible agents commits us to some paradoxical things—e.g. to both the existence and impossibility of moral luck. For more information about this article, please write to gmail account: kristin.mickelson.42. (shrink)

Extending on an earlier paper [Found. Phys. Ltt., 16(4) 343–355, (2003)], it is argued that instants of time and the instantaneous (including instantaneous relative position) do not actually exist. This conclusion, one which is also argued to represent the correct solution to Zeno’s motion paradoxes, has several implications for modern physics and for our philosophical view of time, including that time and space cannot be quantized; that contrary to common interpretation, motion and change are compatible with the “block” universe (...) and relativity; and that time, space, and space-time too, cannot exist. Instead, motion and change become the major players. (shrink)

Most theories of suspense implicitly or explicitly have as a background assumption what I call suspense realism, i.e., that suspense is itself a genuine, distinct emotion. I claim that for a theory of suspense to entail suspense realism is for that theory to entail a contradiction, and so, we ought instead assume a background of suspense eliminativism, i.e., that there is no such genuine, distinct emotion that is the emotion of suspense. More precisely, I argue that i) any suspense realist (...) (...) theory must resolve the paradox of suspense, ii) if suspense is itself a genuine, distinct emotion, then in order to resolve the paradox of suspense it must be a radically sui generis genuine, distinct emotion, iii) according to any minimally adequate theory of the emotions, there can be no radically sui generis emotion, and so iv) there can be no genuine, distinct emotion that is the emotion of suspense. Quite simply, if a theory of suspense must entail suspense realism, then we ought to be eliminativists about suspense. This I call the Paradox of Suspense Realism, which I take to constitute a productive viability condition for any theory of suspense, i.e., any viable theory of suspense must be mutatis mutandis compatible with suspense eliminativism. (shrink)

Saying that x is ineffable seems to be paradoxical – either I cannot say anything about x, not even that it is ineffable – or I can say that it is ineffable, but then I can say something and it is not ineffable. In this article, I discuss Alston’s version of the paradox and a solution proposed by Hick which employs the concept of formal and substantial predicates. I reject Hick’s proposal and develop a different account based on some passages (...) from Pseudo-Dionysius’ Mystica Theologia. ‘God is ineffable’ is a metalinguistic statement concerning propositions about God: not all propositions about God are expressible in a human language. (shrink)