We provide a logical matrix semantics and a Gentzen-style sequent calculus for the first-degree entailments valid in W. T. Parry’s logic of Analytic Implication. We achieve the former by introducing a logical matrix closely related to that inducing paracomplete weak Kleene logic, and the latter by presenting a calculus where the initial sequents and the left and right rules for negation are subject to linguistic constraints.

It is well known that the following features hold of AR + T under the strong Kleene scheme, regardless of the way the language is Gödel numbered: 1. There exist sentences that are neither paradoxical nor grounded. 2. There are 2ℵ0 fixed points. 3. In the minimal fixed point the weakly definable sets (i.e., sets definable as {n∣ A(n) is true in the minimal fixed point where A(x) is a formula of AR + T) are precisely the Π1 1 sets. (...) 4. In the minimal fixed point the totally defined sets (sets weakly defined by formulae all of whose instances are true or false) are precisely the ▵1 1 sets. 5. The closure ordinal for Kripke's construction of the minimal fixed point is ωCK 1. In contrast, we show that under the weak Kleene scheme, depending on the way the Gödel numbering is chosen: 1. There may or may not exist nonparadoxical, ungrounded sentences. 2. The number of fixed points may be any positive finite number, ℵ0, or 2ℵ0 . 3. In the minimal fixed point, the sets that are weakly definable may range from a subclass of the sets 1-1 reducible to the truth set of AR to the Π1 1 sets, including intermediate cases. 4. Similarly, the totally definable sets in the minimal fixed point range from precisely the arithmetical sets up to precisely the ▵1 1 sets. 5. The closure ordinal for the construction of the minimal fixed point may be ω, ωCK 1, or any successor limit ordinal in between. In addition we suggest how one may supplement AR + T with a function symbol interpreted by a certain primitive recursive function so that, irrespective of the choice of the Godel numbering, the resulting language based on the weak Kleene scheme has the five features noted above for the strong Kleene language. (shrink)

This paper extends Fitting's epistemic interpretation of some Kleene logics, to also account for Paraconsistent Weak Kleene logic. To achieve this goal, a dualization of Fitting's "cut-down" operator is discussed, rendering a "track-down" operator later used to represent the idea that no consistent opinion can arise from a set including an inconsistent opinion. It is shown that, if some reasonable assumptions are made, the truth-functions of Paraconsistent Weak Kleene coincide with certain operations defined in this track-down fashion. Finally, further (...) reflections on conjunction and disjunction in the weak Kleene logics accompany this paper, particularly concerning their relation with containment logics. These considerations motivate a special approach to defining sound and complete Gentzen-style sequent calculi for some of their four-valued generalizations. (shrink)

In this paper, I consider a family of three-valued regular logics: the well-known strong and weak S.C. Kleene’s logics and two intermedi- ate logics, where one was discovered by M. Fitting and the other one by E. Komendantskaya. All these systems were originally presented in the semantical way and based on the theory of recursion. However, the proof theory of them still is not fully developed. Thus, natural deduction sys- tems are built only for strong Kleene’s logic (...) both with one (A. Urquhart, G. Priest, A. Tamminga) and two designated values (G. Priest, B. Kooi, A. Tamminga). The purpose of this paper is to provide natural deduction systems for weak and intermediate regular logics both with one and two designated values. (shrink)

In this article, the attempts by David Lewis and Brian Loar to make perspicuous the logical form of sentences ascribing propositional attitudes to individuals are set out and criticized. Both work within the assumption of the truth of 'type' physicalism, and require that logically perspicuous attitude ascriptions be compatible with the demands of such a doctrine. It is argued that neither carry out this task successfully - Lewis's perspicuous ascriptions have counter-intuitive implications, while Loar's avoidance of these undermines type physicalism (...) itself. (shrink)

As these opening quotes acknowledge, the Prisoner’s Dilemma (PD) represents a core puzzle within the formal mathematics of game theory.3 Its rise in conspicuity is evident figure 2.1 above demonstrating a relatively steady rise in incidences of the phrase’s usage between 1960 to 1995, with a stable presence persisting into the twenty first century. This famous two-person “game,” with a stock narrative cast in terms of two prisoners who each independently must choose whether to remain silent or speak, each advancing (...) self-interest at the expense of the other and thereby achieving a mutually suboptimal outcome, mires any social interaction it is applied to into perplexity. The logic of this game proves the inverse of Adam Smith’s invisible hand: individuals acting on self interest will achieve a mutually suboptimal outcome. However, as this chapter illuminates, the assumptions underlying game theory drive this conclusion. (shrink)

Tong Shijun holds a concept of dialectics which can also be found in Mao’s writings and in classical Chinese philosophy. Tong, however, is ambivalent in his attitude to dialectics in this sense, and for this reason he recommends Chinese philosophy to focus more on formal logic. My point will be that with another concept of dialectics Tong can have dialectics without giving up on logic and epistemology. This argument is given substance by an analysis of texts by Mao, (...) Tong and Hegel. (shrink)

David Lewis presented Convention as an alternative to the conventionalism characteristic of early-twentieth-century analytic philosophy. Rudolf Carnap is well known for suggesting the arbitrariness of any particular linguistic convention for engaging in scientific inquiry. Analytic truths are self-consistent, and are not checked against empirical facts to ascertain their veracity. In keeping with the logical positivists before him, Lewis concludes that linguistic communication is conventional. However, despite his firm allegiance to conventions underlying not just languages but also social customs, he pioneered (...) the view that convening need not require any active agreement to participate. Lewis proposed that conventions arise from “an exchange of manifestations of a propensity to conform to a regularity” (87–8). In reasserting the conventional quality of languages and other practices resting on mutual expectations, Lewis comfortably works within the analytic tradition. Yet he also deviates from his predecessors because his conventionalist approach is comprehensively grounded in instrumentalism. Lewis adopts an extension of David Hume's desire-belief psychology articulated in rational choice theory. He develops his philosophy of convention relying on the highly formal mid-twentieth-century expected utility and game theories. This attempt to account for language and social customs wholly in terms of instrumental rationality has the implication of reducing normativity to preference satisfaction. Lewis’ approach continues in the trend of undermining normative political philosophy because institutions and practices arise spontaneously, without the deliberate involvement of agents. Perhaps Lewis’ Convention is best seen as a resurgent form of analytic philosophy, characterized by “a style of argument, hostility to [ambitious] metaphysics, focus on language, and the dominance of logic and formalization” that solves the dilemma of “combining the analytic inheritance…with normative concerns” by reducing normativity to individuals’ preference fulfillment consistent with the axioms of rational choice. (shrink)

Open theists argue that God's relationship to time, as conceived in classical theism, is erroneous. They explain that it is contradictory for an atemporal being to act in a temporal universe, including experiencing its temporal successions. Contrary to the atemporalists, redemptive history has shown that God interacts with humans in time. This relational nature of God nullifies the classical notion of God as timelessly eternal. Therefore, it lacks a philosophical and theological basis. Because God is in time, He does not (...) know all future contingencies and, therefore, changes. This study examines open theism's appropriation of the A and B theories of time to the divine-human relationship. The study argues that divine temporality does not solve the tension of divine-human relationships, especially in relation to the future. Further, historical divine temporality does not negate the fact of divine atemporality. It mainly stems from God's choice to create temporal creatures and His relationship with them. Furthermore, if it is not logically and metaphysically contradictory for an omnipresent being to act in space, then it follows that an atemporal being can act in time. Whether time is understood from the metric or psychological point of view, it does not transcend God, and therefore, the limitation it places on human creatures with respect to the future does not apply to God. Lastly, although a few philosophers reject the notion of eternity as timelessly eternal, the doctrine has a philosophical and theological basis in the Scripture. (shrink)

Justification logics are modal-like logics with the additional capability of recording the reason, or justification, for modalities in syntactic structures, called justification terms. Justification logics can be seen as explicit counterparts to modal logics. The behavior and interaction of agents in distributed system is often modeled using logics of knowledge and time. In this paper, we sketch some preliminary ideas on how the modal knowledge part of such logics of knowledge and time could be replaced with an appropriate justification (...) class='Hi'>logic. (shrink)

There are three questions associated with Simpson’s Paradox (SP): (i) Why is SP paradoxical? (ii) What conditions generate SP?, and (iii) What should be done about SP? By developing a logic-based account of SP, it is argued that (i) and (ii) must be divorced from (iii). This account shows that (i) and (ii) have nothing to do with causality, which plays a role only in addressing (iii). A counterexample is also presented against the causal account. Finally, the causal and (...) logic-based approaches are compared by means of an experiment to show that SP is not basically causal. (shrink)

The thesis deals with the concept of truth and the paradoxes of truth. Philosophical theories usually consider the concept of truth from a wider perspective. They are concerned with questions such as - Is there any connection between the truth and the world? And, if there is - What is the nature of the connection? Contrary to these theories, this analysis is of a logical nature. It deals with the internal semantic structure of language, the mutual semantic connection of sentences, (...) above all the connection of sentences that speak about the truth of other sentences and sentences whose truth they speak about. Truth paradoxes show that there is a problem in our basic understanding of the language meaning and they are a test for any proposed solution. It is important to make a distinction between the normative and analytical aspect of the solution. The former tries to ensure that paradoxes will not emerge. The latter tries to explain paradoxes. Of course, the practical aspect of the solution is also important. It tries to ensure a good framework for logical foundations of knowledge, for related problems in Artificial Intelligence and for the analysis of the natural language. Tarski’s analysis emphasized the T-scheme as the basic intuitive principle for the concept of truth, but it also showed its inconsistency with the classical logic. Tarski’s solution is to preserve the classical logic and to restrict the scheme: we can talk about the truth of sentences of a language only inside another essentially richer metalanguage. This solution is in harmony with the idea of reflexivity of thinking and it has become very fertile for mathematics and science in general. But it has normative nature | truth paradoxes are avoided in a way that in such frame we cannot even express paradoxical sentences. It is also too restrictive because, for the same reason we cannot express a situation in which there is a circular reference of some sentences to other sentences, no matter how common and harmless such a situation may be. Kripke showed that there is no natural restriction to the T-scheme and we have to accept it. But then we must also accept the riskiness of sentences | the possibility that under some circumstances a sentence does not have the classical truth value but it is undetermined. This leads to languages with three-valued semantics. Kripke did not give any definite model, but he gave a theoretical frame for investigations of various models | each fixed point in each three-valued semantics can be a model for the concept of truth. The solutions also have normative nature | we can express the paradoxical sentences, but we escape a contradiction by declaring them undetermined. Such a solution could become an analytical solution only if we provide the analysis that would show in a substantial way that it is the solution that models the concept of truth. Kripke took some steps in the direction of finding an analytical solution. He preferred the strong Kleene three-valued semantics for which he wrote it was "appropriate" but did not explain why it was appropriate. One reason for such a choice is probably that Kripke finds paradoxical sentences meaningful. This eliminates the weak Kleene three valued semantics which corresponds to the idea that paradoxical sentences are meaningless, and thus indeterminate. Another reason could be that the strong Kleene three valued semantics has the so-called investigative interpretation. According to this interpretation, this semantics corresponds to the classical determination of truth, whereby all sentences that do not have an already determined value are temporarily considered indeterminate. When we determine the truth value of these sentences, then we can also determine the truth value of the sentences that are composed of them. Kripke supplemented this investigative interpretation with an intuition about learning the concept of truth. That intuition deals with how we can teach someone who is a competent user of an initial language (without the predicate of truth T) to use sentences that contain the predicate T. That person knows which sentences of the initial language are true and which are not. We give her the rule to assign the T attribute to the former and deny that attribute to the latter. In that way, some new sentences that contain the predicate of truth, and which were indeterminate until then, become determinate. So the person gets a new set of true and false sentences with which he continues the procedure. This intuition leads directly to the smallest fixed point of strong Kleene semantics as an analytically acceptable model for the logical notion of truth. However, since this process is usually saturated only on some transfinite ordinal, this intuition, by climbing on ordinals, increasingly becomes a metaphor. This thesis is an attempt to give an analytical solution to truth paradoxes. It gives an analysis of why and how some sentences lack the classical truth value. The starting point is basic intuition according to which paradoxical sentences are meaningful (because we understand what they are talking about well, moreover we use it for determining their truth values), but they witness the failure of the classical procedure of determining their truth value in some "extreme" circumstances. Paradoxes emerge because the classical procedure of the truth value determination does not always give a classically supposed (and expected) answer. The analysis shows that such an assumption is an unjustified generalization from common situations to all situations. We can accept the classical procedure of the truth value determination and consequently the internal semantic structure of the language, but we must reject the universality of the exterior assumption of a successful ending of the procedure. The consciousness of this transforms paradoxes to normal situations inherent to the classical procedure. Some sentences, although meaningful, when we evaluate them according to the classical truth conditions, the classical conditions do not assign them a unique value. We can assign to them the third value, \undetermined", as a sign of definitive failure of the classical procedure. An analysis of the propagation of the failure in the structure of sentences gives exactly the strong Kleene three-valued semantics, not as an investigative procedure, as it occurs in Kripke, but as the classical truth determination procedure accompanied by the propagation of its own failure. An analysis of the circularities in the determination of the classical truth value gives the criterion of when the classical procedure succeeds and when it fails, when the sentences will have the classical truth value and when they will not. It turns out that the truth values of sentences thus obtained give exactly the largest intrinsic fixed point of the strong Kleene three-valued semantics. In that way, the argumentation is given for that choice among all fixed points of all monotone three-valued semantics for the model of the logical concept of truth. An immediate mathematical description of the fixed point is given, too. It has also been shown how this language can be semantically completed to the classical language which in many respects appears a natural completion of the process of thinking about the truth values of the sentences of a given language. Thus the final model is a language that has one interpretation and two systems of sentence truth evaluation, primary and final evaluation. The language through the symbol T speaks of its primary truth valuation, which is precisely the largest intrinsic fixed point of the strong Kleene three valued semantics. Its final truth valuation is the semantic completion of the first in such a way that all sentences that are not true in the primary valuation are false in the final valuation. (shrink)

How do we prepare engineering students to make ethical and responsible decisions in their professional work? This paper presents an approach that enhances engineering students’ engagement with ethical reasoning by simulating decision-making in a complex scenario. The approach has two principal inspirations. The first is Anthony Weston’s scenario-based teaching. Weston’s concept of a scenario is a situation that changes in response to choices made by participants, according to an inner logic. Scenarios can dynamically explore open-ended complex problems without imposing (...) predetermined results, allowing students to apply their ethical reasoning in a more realistic fashion. The second inspiration is Thi Nguyen’s theory of games. According to Nguyen, games are the “art of agency,” meaning that they provide a structure under which some result is agreed to be valuable, along with prescribed ways of achieving that result, in a relatively low-stakes and temporary social arrangement. By playing many games, Nguyen argues, we can develop a “library of agency,” that is to say, a set of values and means to achieving them that can inform how we make high-stakes decisions in real life. Engaging with carefully designed game scenarios, then, can enable students to practice making ethical decisions within a structured framework, which unfolds in response to their choices, while their decisions are driven by some defined goal. This roleplaying game–based approach thus allows students to build their own ethical libraries of agency, in preparation for professional decision-making. The approach is illustrated using a specific example recently deployed in a seminar on engineered living materials (building materials that incorporate living tissues). The scenario uses techniques from tabletop roleplaying games (e.g. Dungeons & Dragons) for outcome resolution, adventure design, and character creation. Through the game, students practice making difficult decisions in a humanitarian context. (shrink)

Recently, a number of philosophers have argued that we can and should “consequentialize” non-consequentialist moral theories, putting them into a consequentialist framework. I argue that these philosophers, usually treated as a group, in fact offer three separate arguments, two of which are incompatible. I show that none represent significant threats to a committed non-consequentialist, and that the literature has suffered due to a failure to distinguish these arguments. I conclude by showing that the failure of the consequentializers’ arguments has implications (...) for disciplines, such as economics, logic, decision theory, and linguistics, which sometimes use a consequentialist structure to represent non-consequentialist ethical theories. (shrink)

In Pietroski ( 2018 ) a simple representation language called SMPL is introduced, construed as a hypothesis about core conceptual structure. The present work is a study of this system from a logical perspective. In addition to establishing a completeness result and a complexity characterization for reasoning in the system, we also pinpoint its expressive limits, in particular showing that the fourth corner in the square of opposition (“ Some_not ”) eludes expression. We then study a seemingly small extension, called (...) SMPL +, which allows for a minimal predicate-binding operator. Perhaps surprisingly, the resulting system is shown to encode precisely the concepts expressible in first-order logic. However, unlike the latter class, the class of SMPL + expressions admits a simple procedural (context-free) characterization. Our contribution brings together research strands in logic—including natural logic, modal logic, description logic, and hybrid logic—with recent advances in semantics and philosophy of language. (shrink)

We address the need for a model by considering two competing theories regarding the origin of life: (i) the Metabolism First theory, and (ii) the RNA World theory. We discuss two interrelated points, namely: (i) Models are valuable tools for understanding both the processes and intricacies of origin-of-life issues, and (ii) Insights from models also help us to evaluate the core objection to origin-of-life theories, called “the inefficiency objection”, which is commonly raised by proponents of both the Metabolism First theory (...) and the RNA World theory against each other. We use Simpson’s Paradox (SP) as a tool for challenging this objection. We will use models in various senses, ranging from taking them as representations of reality to treating them as theories/accounts that provide heuristics for probing reality. In this paper, we will frequently use models and theories interchangeably. Additionally, we investigate Conway’s Game of Life and contrast it with our SP-based approach to emergence-of-life issues. Finally, we discuss some of the consequences of our view. A scientific model is testable in three senses: (i) a logical sense, (ii) a nomological sense, and (iii) a current technological sense. The SP-based model is testable in the first two senses but it is not feasible to test it using current technology. (shrink)

No serious discussion of the forces shaping Schleiermacher could overlook the influence that Romanticism had on the formulation of his thought. Seeing the Enlightenment’s confidence in human reason as an obstacle to the effective communication of the gospel, he contrastingly understood Romanticism as an ally, for it emphasized passion over reason — imagination and inspiration over logic. The Enlightenment’s enshrinement of human reason as the autonomous source for truth had advanced naturalistic rationalism as its sole determinant. With the ascendancy (...) of this rationalism came an attendant depreciation of other avenues of knowledge, leaving no possibility for its existence outside of the empirical. This state of affairs produced a climate that had starved the soul. -/- In the Romanticists, Schleiermacher found others that shared his views: a great value placed on inward feeling and the importance of the growth of the individual. Schleiermacher’s efforts sought to gain a hearing among his contemporaries by contextualizing the Christian faith within the paradigm of Romanticism, bringing about the emergence of a movement that would embrace a subjectified view of truth. -/- This work advances the proposal that much of the thought currently associated with postmodernism finds its first cogent expression in the writings of the German theologian Friedrich Schleiermacher (1768-1834). Widely hailed as the Father of Modern Theology, his influences in the areas of thought that would eventually combine to produce postmodernism have been ignored by both Christian and non-Christian scholars. (shrink)

Review of "The Construction of Logical Space", by Augustin Rayo. Oxford: OxfordUniversity Press, 2013. Pp. xix+220. H/b$35.00.

Faith has many aspects. One of them is whether absolute logical proof for God’s existence is a prerequisite for the proper establishment and individual acceptance of a religious system. The treatment of this question, examined here in the Jewish context of Rabbi Prof. Eliezer Berkovits, has been strongly influenced in the modern era by the radical foundationalism and radical skepticism of Descartes, who rooted in the Western mind the notion that religion and religious issues are “all or nothing” questions. Cartesianism, (...) which surprisingly became the basis of modern secularism, was criticized by the classical American pragmatists. Peirce, James and Dewey all rejected the attempt to achieve infallible absolute knowledge, as well as the presumptuousness of establishing such a knowledge by means of casting Cartesian hyperbolic doubt. They advocated an alternative approach which was more holistic and humane. This paper lays out Descartes’s approach and the pragmatists’ critique. Despite the place that pragmatic considerations hold in Jewish tradition, some thinkers reject the relevance of these ideas. Yet Berkovits’s thought suggest a different path. He rejected Descartes’ radical skepticism and his radical foundationalism, in favor of a moderate foundationalism, which allows for a belief in God alongside constructive doubts. Similar to Peirce’s conception of the fixation of belief, Berkovits views local doubts (distinct from the hyperbolic doubt) as necessary for thought. Berkovits’s understanding of the biblical human-divine encounter, following Rosenzweig, Buber, and Heschel, is conceptualized here as “encounter theology”. Berkovits criticizes the propositionalist attempts to prove God’s existence logically, as well as the presumptuousness of basing religious belief on the teleological world-order. However, Berkovits’s conception of the ‘caring God’ is not provable, and thus defined as a pragmatic ‘postulate’. The article concludes by considering Berkovits’s “encounter theology”. In contrast to the approach described by Haym Soloveitchik, of halakhic stringency and lack of subjective experience of God’s face, Berkovits’s approach is dialogic through and through. (shrink)

After years of neglect, alienation has again reached the agenda of critical thought. In my case, I recognize alienation as a challenge for education in contemporary societies. To obtain conceptual resources to overcome this challenge, I have revisited the comprehensive 20 th century discussion of alienation. Today, alienation is naturally discussed as an existential condition of human being, but still in the 1980s, there was a strong Marxist current that claimed alienation to be implied by capitalism, in particular by the (...) institution of private property and the social division of labor, and that alienation therefore should be criticized as part of the critique of capitalism and political economy and possibly overcome. Today, under the hegemony of neo-liberal capitalism, this critical and processual concept of alienation is more relevant than ever. Hence, in the present work I argue that the basic logic of Marx's idea of alienation still has critical potential. The argument forms a long engagement with mainly 20 th century literature, departing from the very idea of capitalism, considering the ideas of history, education and democracy, discussing how to distinguish and translate key terms, considering why alienation became an object of controversy among Marxists, offering an interpretation of Marx's critique relevant for contemporary society, thus considering alienation a consequence of working under conditions of private property, i.e. being a human being in a capitalist society, and finally presenting Marx's idea of communism as relevant to the contemporary educational agenda. (shrink)

As the debate between realists and empiricists in the philosophy of science drags on, one point of consensus has emerged: no one wants to be a manifestationalist. The manifestationalist is a kind of radical empiricist who argues that science provides theories that aim neither at a true picture of the entire world, nor even an empirically adequate picture that captures the world in all its observable respects. For manifestationalists, science aims only at providing theories that are true to the observed (...) aspects of reality. If the guiding idea of empiricism is that experience, and experience alone, provides us with knowledge about the world, then manifestationalism is an exceptionally strict empiricist perspective on science. Manifestationalism has primarily served within a reductio: certain empiricist views and arguments, when taken to their logical conclusion, lead to manifestationalism and so cannot be correct. The reductio works only because manifestationalism is widely agreed to be a non-starter. However, this consensus against manifestationalism is based on a single argument. We contest this assessment of manifestationalism and show that the primary argument against manifestationalism fails to hit its target. We do not intend to offer a manifesto for manifestationalism. Rather, we aim to vindicate it from a false accusation. Manifestationalism may not be the correct view of science, but the objections levied against it so far can be met. (shrink)

We look at extensions (i.e., stronger logics in the same language) of the Belnap–Dunn four-valued logic. We prove the existence of a countable chain of logics that extend the Belnap–Dunn and do not coincide with any of the known extensions (Kleene’s logics, Priest’s logic of paradox). We characterise the reduced algebraic models of these new logics and prove a completeness result for the first and last element of the chain stating that both logics are determined by a (...) single finite logical matrix. We show that the last logic of the chain is not finitely axiomatisable. (shrink)

“Probably Peirce’s best-known works are the first two articles in a series of six that originally were collectively entitled Illustrations of the Logic of Science and published in Popular Science Monthly from November 1877 through August 1878. The first is entitled ‘The Fixation of Belief’ and the second is entitled ‘How to Make Our Ideas Clear.’ In the first of these papers Peirce defended, in a manner consistent with not accepting naive realism, the superiority of the scientific method over (...) other methods of overcoming doubt and ‘fixing belief.’” — Robert Burch, “Charles Sanders Peirce,” entry in the Stanford Encyclopedia of Philosophy (2021 revision) -/- “Pragmatist epistemologies often explore how we can carry out inquiries in a self-controlled and fruitful way. (Where much analytic epistemology centres around the concept of knowledge, considered as an idealised end-point of human thought, pragmatist epistemology centres around the concept of inquiry, considered as the process of knowledge-seeking and how we can improve it.) So pragmatists often provide rich accounts of the capacities or virtues that we must possess in order to inquire well, and the rules or guiding principles that we should adopt. A canonical account is Peirce’s classic early paper ‘The Fixation of Belief‘. Here Peirce states that inquiry is a struggle to replace doubt with “settled belief“, and that the only method of inquiry that can make sense of the fact that at least some of us are disturbed by inconsistent beliefs, and will subsequently reflect upon which methods of fixing belief are correct is the Method of Science, which draws on the Pragmatic Maxim described above. This contrasts with three other methods of fixing belief: i) refusing to consider evidence contrary to one’s favored beliefs (the Method of Tenacity), ii) accepting an institution’s dictates (the Method of Authority), iii) developing the most rationally coherent or elegant-seeming belief-set (the A Priori Method).“ — Catherine Legg, “Pragmatism,” entry in the Stanford Encyclopedia of Philosophy (2021 revision). (shrink)

The alien in science fiction has not often been seen as part of an imperial colonial discourse. By examining John W. Campbell’s founding golden age SF text, “Who Goes There?” (1938), this paper explores the ways in which the alien adheres to an invisible mythos of whiteness that has come to be seen through a colonizing logic as isomorphic with the human. Campbell’s alien-monster comes to disseminate and invade both self and world and as such serves as an interrogation (...) of what whites have done through colonization. It is thus part and parcel of imperial domination and discourse and appears as the very nightmare of whiteness in the form of its liminal and estranged shadow side. Part of what has made Campbell’s text so influential is that it offers a new type of alien invasion in the figure of “contagion,” which speaks “to the transition from colonial to postcolonial visions of modernity and its attendant catastrophes” (Rieder, 124), and which can be further examined as a race metaphor in American SF—indeed, as the white man’s fear of racial mixing that has a long and dehumanizing history. Through its threat of mixture, I read the alien as a creolizing figure that both troubles and undoes the white/black, human/nonhuman binary in science fiction, which I also read as being a creolizing, i.e., hybrid and plastic, genre. (shrink)

In spite of its everyday connotations, the term independence as republicans understand it is not a celebration of individualism or self-reliance but embodies an acknowledgement of the importance of personal and social relationships in people’s lives. It reflects our connectedness rather than separateness and is in this regard a relational ideal. Properly understood, independence is a useful concept in addressing a fundamental problem in social philosophy that has preoccupied theorists of relational autonomy, namely how to reconcile the idea of individual (...) human agency with the inevitable and necessary influence of other people, both directly and indirectly. I derive my account from the work of Mary Wollstonecraft and Catharine Macaulay, whose contributions have remained largely overlooked by current republican theorists. I have three purposes in this chapter. First, I set out the relational character of independence. Secondly, I outline a republican approach to the problem of structural social threats to agency. Finally, I hope to establish the basis for a fruitful dialogue between republicans and relational autonomy theorists on the requirements and dynamics of individual agency and freedom in oppressive social situations. I identify three distinctive features of the internal logic of freedom as independence that give it a relational character: it always locates the person within a community; there is a mediating role played by the notion of arbitrariness in connecting individual and collective perspectives; a causal relationship exists linking each person’s freedom as independence such that that the dependence of one class of persons jeopardizes the independence of the whole community. (shrink)

Marsilius of Inghen’s account of imaginable impossibilities became paradigmatic in logic, semantics, and metaphysics throughout the later Middle Ages and well into the early modern period. The present study focuses on imaginable impossibilities in 14th-century logic, underlining the relevance of Marsilius of Inghen’s innovative approach through a comparison with the semantic accounts proposed by other mid-14th-century Parisian nominalists, namely John Buridan and Albert of Saxony. In particular, this paper tracks the specific issue of the admissibility of absolute impossibilities (...) – such as the chimera – within Marsilius of Inghen’s semantic analysis, proving that there is a sense in which the chimera is indeed treatable. The present study does so by analysing the issues involved in impossibilities on the levels of signification, supposition, and extended reference. In doing so it provides a clearer picture of the problems involved, where they emerge and why, as well as of the significance and range of Marsilius of Inghen’s approach. (shrink)

This review of Richard Tuck's Free Riding conveys Tuck's crucial distinction between the logic of collective action which fails due to the problem of causal negligibility, and free riding, which has been modeled as a Prisoner's Dilemma and involves casually impacting another actor in an adverse manner. Tuck also distinguishes the practice of voting which he argues neither fails due to the worry of causal negligibility or due to free riding; instead it represents a problem of achieving sufficiency of (...) votes representing a minimum winning coalition. This article clarifies how the problem of collective action resembles perfect free market competition which is defined to be characterized by a state in which no single agent can impact the price of a good. Similarly, in a large scale collective action, no single actor can have a causal impact on the outcome of the vast enterprise. This inability to make a difference due to the negligibility of each individual's causal power differentiates collective action and the tragedy of the commons from other social problems. (shrink)

In this paper , the authors explore neutrosophic statistics, that was initiated by Florentin Smarandache in 1998 and developed in 2014, by presenting various examples of several statistical distributions, from the work [1]. The paper is presented with more case studies, by means of which this neutrosophic version of statistical distribution becomes more pronounced.

Uses erotetic logic to model the courtroom objection "Improper Cross!". -/- Readers downloading the article should also please download the erratum et corrigendum, which is locally available.

Note: The author holds the copyright, and there was no agreement, express or implied, not to use a facsimile PDF. -/- Using erotetic logic, the paper defines the "the whole truth" in a manner consistent with U.S. Supreme Court precedent. It cannot mean "the whole story," as witnesses in an adversary system are permitted /only/ to answer the questions put to them, nor are they permitted to speculate, add irrelevant material, etc. Nor can it mean not to add an (...) admixture of falsity, as that is already included in "nothing but the truth," and, strictly speaking, in "the truth," as any such as admixture renders the whole thing false (given bivalence is presupposed) by &-introduction. (shrink)

As the journal is effectively defunct, I am uploading a full-text copy, but only of my abstract and article, and some journal front matter. -/- Note that the pagination in the PDF version differs from the official pagination because A4 and 8.5" x 11" differ. -/- Traditionally, imperatives have been handled with deontic logics, not the logic of propositions which bear truth values. Yet, an imperative is issued by the speaker to cause (stay) actions which change the state of (...) affairs, which is, in turn, described by propositions that bear truth values. Thus, ultimately, imperatives affect truth values. In this paper, we put forward an idea that allows us to reason with imperatives using classical logic by constructing a one-to-one correspondence between imperatives and a particular class of declaratives. (shrink)

We look at extensions (i.e., stronger logics in the same language) of the Belnap–Dunn four-valued logic. We prove the existence of a countable chain of logics that extend the Belnap–Dunn and do not coincide with any of the known extensions (Kleene’s logics, Priest’s logic of paradox). We characterise the reduced algebraic models of these new log- ics and prove a completeness result for the first and last element of the chain stating that both logics are determined by (...) a single finite logical matrix. We show that the last logic of the chain is not finitely axiomatisable. (shrink)

We propose a natural definition of what it means in a constructive context for a Banach space to be reflexive, and then prove a constructive counterpart of the Milman-Pettis theorem that uniformly convex Banach spaces are reflexive.

Throughout this research, imposing the training of an Artificial Neural Network (ANN) to play tic-tac-toe bored game, by training the ANN to play the tic-tac-toe logic using the set of mathematical combination of the sequences that could be played by the system and using both the Gradient Descent Algorithm explicitly and the Elimination theory rules implicitly. And so on the system should be able to produce imunate amalgamations to solve every state within the game course to make better of (...) results of winnings or getting draw. (shrink)

We extend the framework of Inductive Logic to Second Order languages and introduce Wilmers' Principle, a rational principle for probability functions on Second Order languages. We derive a representation theorem for functions satisfying this principle and investigate its relationship to the first order principles of Regularity and Super Regularity.

This has been made available gratis by the publisher. -/- This piece gives the raison d'etre for the development of the converters mentioned in the title. Three reasons are given, one linguistic, one philosophical, and one practical. It is suggested that at least /two/ independent converters are needed. -/- This piece ties together the extended paper "Abstracts from Logical Form I/II," and the short piece providing the comprehensive theory alluded to in the abstract of that extended paper in "Pragmatics, Montague, (...) and 'Abstracts from Logical Form'" by motivating the entire project from beginning to end. (shrink)

In this article I define a strong conditional for classical sentential logic, and then extend it to three non-classical sentential logics. It is stronger than the material conditional and is not subject to the standard paradoxes of material implication, nor is it subject to some of the standard paradoxes of C. I. Lewis’s strict implication. My conditional has some counterintuitive consequences of its own, but I think its pros outweigh its cons. In any case, one can always augment one’s (...) language with more than one conditional, and it may be that no single conditional will satisfy all of our intuitions about how a conditional should behave. Finally, I suspect the strong conditional will be of more use for logic rather than the philosophy of language, and I will make no claim that the strong conditional is a good model for any particular use of the indicative conditional in English or other natural languages. Still, it would certainly be a nice bonus if some modified version of the strong conditional could serve as one. -/- I begin by exploring some of the disadvantages of the material conditional, the strict conditional, and some relevant conditionals. I proceed to define a strong conditional for classical sentential logic. I go on to adapt this account to Graham Priest’s Logic of Paradox, to S. C. Kleene’s logic K3, and then to J. Łukasiewicz’s logic Ł, a standard version of fuzzy logic. (shrink)

Paul Boghossian (1997) has argued that there is much to be said on behalf of the notion of analyticity so long as we distinguish epistemic analyticity and metaphysical analyticity. In particular, (1) epistemic analyticity isn’t undermined by Quine’s critique of the analytic-synthetic distinction, (2) it can explain the a prioricity of logic, and (3) epistemic analyticity can’t be rejected short of embracing semantic irrealism. In this paper, we argue that all three of these claims are mistaken.

This paper aims to analyze the relationship between applied social sciences and practical wisdom. Utilizing conceptual analysis methodology, it begins by defining application, action, and practice, then delves into the conceptual analysis of applied social sciences and practical wisdom. The concept of phronesis in Aristotle's philosophy and practical wisdom in Muslim philosophers are studied and analyzed. By examining different definitions of practical wisdom among Muslim scholars and comparing their views with those of Aristotle, the paper evaluates their perspectives. Subsequently, it (...) focuses on exploring the relationship between applied social sciences and practical wisdom, analyzing their points of divergence and convergence. Considering the inherent nature of applied social sciences as technological and practical, contrasted with the virtue-based nature of practical wisdom, the paper raises the question of whether phronesis can logically benefit from pure applied social sciences as theoretical wisdom to guide individuals towards virtuous action. It also questions whether this scenario could be considered a form of applied social sciences. (shrink)

We examine the set of formula-to-formula valid inferences of Classical Logic, where the premise and the conclusion share at least a propositional variable in common. We review the fact, already proved in the literature, that such a system is identical to the first-degree entailment fragment of R. Epstein's Relatedness Logic, and that it is a non-transitive logic of the sort investigated by S. Frankowski and others. Furthermore, we provide a semantics and a calculus for this logic. (...) The semantics is defined in terms of a \-matrix built on top of a 5-valued extension of the 3-element weak Kleene algebra, whereas the calculus is defined in terms of a Gentzen-style sequent system where the left and right negation rules are subject to linguistic constraints. (shrink)

The vision of natural kinds that is most common in the modern philosophy of biology, particularly with respect to the question whether species and other taxa are natural kinds, is based on a revision of the notion by Mill in A System of Logic. However, there was another conception that Whewell had previously captured well, which taxonomists have always employed, of kinds as being types that need not have necessary and sufficient characters and properties, or essences. These competing views (...) employ different approaches to scientific methodologies: Mill’s class-kinds are not formed by induction but by deduction, while Whewell’s type-kinds are inductive. More recently, phylogenetic kinds (clades, or monophyletic-kinds) are inductively projectible, and escape Mill’s strictures. Mill’s version represents a shift in the notions of kinds from the biological to the physical sciences. (shrink)

In this paper a class of languages which are formal enough for mathematical reasoning is introduced. Its languages are called mathematically agreeable. Languages containing a given MA language L, and being sublanguages of L augmented by a monadic predicate, are constructed. A mathematical theory of truth (shortly MTT) is formulated for some of those languages. MTT makes them fully interpreted MA languages which posses their own truth predicates. MTT is shown to conform well with the eight norms formulated for theories (...) of truth in the paper 'What Theories of Truth Should be Like (but Cannot be)', by Hannes Leitgeb. MTT is also free from infinite regress, providing a proper framework to study the regress problem. Main tools used in proofs are Zermelo-Fraenkel (ZF) set theory and classical logic. (shrink)

Adrian Piper argues that the Humean conception can be made to work only if it is placed in the context of a wider and genuinely universal conception of the self, whose origins are to be found in Kant’s Critique of Pure Reason. This conception comprises the basic canons of classical logic, which provide both a model of motivation and a model of rationality. These supply necessary conditions both for the coherence and integrity of the self and also for unified (...) agency. The Kantian conception solves certain intractable problems in decision theory by integrating it into classical predicate logic, and provides answers to longstanding controversies in metaethics concerning moral motivation, rational final ends, and moral justification that the Humean conception engenders. In addition, it sheds light on certain kinds of moral behavior – for example, the whistleblower – that the Humean conception is at a loss to explain. (shrink)

A theory of truth is introduced for a first--order language L of set theory. Fully interpreted metalanguages which contain their truth predicates are constructed for L. The presented theory is free from infinite regress, whence it provides a proper framework to study the regress problem. Only ZF set theory, concepts definable in L and classical two-valued logic are used.

In this paprer a class of so called mathematically acceptable (shortly MA) languages is introduced First-order formal languages containing natural numbers and numerals belong to that class. MA languages which are contained in a given fully interpreted MA language augmented by a monadic predicate are constructed. A mathematical theory of truth (shortly MTT) is formulated for some of these languages. MTT makes them fully interpreted MA languages which posses their own truth predicates, yielding consequences to philosophy of mathematics. MTT is (...) shown to conform well with the eight norms presented for theories of truth in the paper 'What Theories of Truth Should be Like (but Cannot be)' by Hannes Leitgeb. MTT is also free from infinite regress, providing a proper framework to study the regress problem. (shrink)

In his book After Finitude, Quentin Meillassoux criticizes post-Kantian philosophy for its inability to explain how science is able to describe a world without human beings. This paper addresses that challenge through a consideration of Heidegger’s thought and his thinking about science. It is argued that the disagreement between Meillassoux and Heidegger comes down to a question of first philosophy and the priority of logic or ontology in philosophy. Ultimately, Heidegger’s emphasis on ontology in philosophy is superior in its (...) ability to give a more comprehensive account of science and thinking about things themselves. (shrink)

This essay examines the development of Reformed treatments of the affections in the period of early orthodoxy (ca. 1565-1640). I argue that discussion of the affections during this period grew within the broad framework of the Aristotelian psychology and certain polemical concerns initially established by early Reformed theologians. With the advent of Protestant universities and academies, Reformed ethicists and theologians treated the affections in greater detail, with a majority drawing on a generally Thomistic approach to the nature and division of (...) the affections, although not without a dissenting Scotistic minority. (shrink)