Traditional monotheism appears to many to involve contradiction in basic 'omni' properties (e.g. omnipotence and too-heavy stones, etc.). A glut-theoretic account of such problems treats them as gluts (dual to familiar truth-value gaps): 'omnipotence' is both true of and false of God. Many philosophers, glut theorists and otherwise, acknowledge that such a glut-theoretic account of at least some traditional omni-god problems is natural, at least in the abstract. But what about the problem of evil? The unanimous view even among (...) glut theorists (including myself until now) has long been clear: gluts have nothing to offer in response to the problem of evil even if they are involved in true theology elsewhere. This paper refutes said view by advancing a simple glut-theoretic response to the target problem of evil on the assumption that gluts are involved in the theology elsewhere (notably, at 'omnipotent' or 'omniscient' or both). (shrink)

1 IntroductionNumerous solutions have been proposed to the semantic paradoxes. Two that are frequently singled out and compared are the following. The first is that according to which paradoxical sentences are neither true nor false — as it is sometimes put, they are semantic gaps. The second is that according to which paradoxical sentences are both true and false — as it is sometimes put, they are semantic gluts. Calling the first of these a solution is, in fact, somewhat (...) misleading: it is rather like calling an opening gambit a game of chess. For the solution runs into severe problems almost immediately, and so can be only the first of a series of moves made to defend the original weak opening. Nonetheless, the symmetry involved in the gap and glut solutions is obvious enough to make the comparison a natural one. (shrink)

In this paper, I examine the deep theological faultline generated by divergent understandings of the divine attributes among two early antagonistic Muslim groups – the traditionalists (main...

This paper deals with predicate logics involving two truth values (here referred to as bivalent logics). Sequent calculi for these logics rely on a general notion of sequent that helps to make the principles of excluded middle and non-contradiction explicit. Several formulations of the redundancy of cut are possible in these sequent calculi. Indeed, four different forms of cut can be distinguished. I prove that only two of them hold for positive sequent calculus (which is both paraconsistent and paracomplete) while (...) all of them hold for classical sequent calculus. As for complete and consistent sequent calculi (which are respectively paraconsistent and paracomplete), I prove that they only admit one form of cut in addition to the two that hold for positive sequent calculus. (shrink)

When are two formal theories of broadly logical concepts, such as truth, equivalent? The paper investigates a case study, involving two well-known variants Kripke-Feferman truth. The first, KF+CONS, features a consistent but partial truth predicate. The second, KF+COMP, an inconsistent but complete truth predicate. It is well-known that the two truth predicates are dual to each other. We show that this duality reveals a much stricter correspondence between the two theories: they are intertraslatable. Intertranslatability under natural assumptions coincides with definitional (...) equivalence, and is arguably the strictest notion of theoretical equivalence different from logical equivalence. The case of KF+CONS and KF+COMP raises a puzzle: the two theories can be proved to be strictly related, yet they appear to embody remarkably different conceptions of truth. We discuss the significance of the result for the broader debate on formal criteria of conceptual reducibility for theories of truth. (shrink)

Consider the following sentence schema:This sentence entails that ϕ.Call a sentence which is obtained from this schema by the substitution of an arbitrary, contingent sentence, s, for ϕ, the sentence CS. Thus, This sentence entails that s.Now ask the following question: Is CS true?One sentence classically entails a second if and only if it is impossible for both the first to be true and the second to be false. Thus ‘Xanthippe is a mother’ entails ‘Xanthippe is female’ if and only (...) if it is impossible for both ‘Xanthippe is a mother’ to be true and ‘Xanthippe is female’ to be false. CS makes a claim about a purported entailment. Thus, CS is true if and only if it is impossible for both the sentence it mentions as entailing a second to be true and the sentence it mentions as being entailed by the first to be false. In other words, CS is true if and only if it is impossible for both CS to be true and s to be false. In yet other words, CS is false if and only if it is possible for both CS to be true and s to be false. (shrink)

Radical glut and gap theorists deny—in opposite ways—that the liar sentence has exactly one of the two values true and not true. I describe a scenario where a signalman finds himself in a situation analogous to the liar paradox: if he lights a fire at a certain time, that is analogous to the liar being true, and if he does not, that is analogous to the liar not being true. It is obvious that he must make exactly one of those (...) states of affairs come about. It is argued that there are no relevant differences between the liar and the signalman’s dilemma, implying that the glut and gap theorists are wrong about the former. A further point is that whether or not the liar is true/the signalman lights the fire, language/the signalman is misleading relative to the conditions under which the liar/the fire “ought” to be true/lit. (shrink)

When are two formal theories of broadly logical concepts, such as truth, equivalent? The paper investigates a case study, involving two well-known variants of Kripke–Feferman truth. The first, \, features a consistent but partial truth predicate. The second, \, an inconsistent but complete truth predicate. It is known that the two truth predicates are dual to each other. We show that this duality reveals a much stricter correspondence between the two theories: they are intertraslatable. Intertranslatability, under natural assumptions, coincides with (...) definitional equivalence, and is arguably the strictest notion of theoretical equivalence different from logical equivalence. The case of \ and \ raises a puzzle: the two theories can be proved to be strictly related, yet they appear to embody remarkably different conceptions of truth. We discuss the significance of the result for the broader debate on formal criteria of conceptual reducibility for theories of truth. (shrink)

This paper applies what I call the shrieking method (a refined version of an idea with roots in Priest's work) to one of – if not the – issues confronting glut-theoretic approaches to paradox (viz., the problem of ‘just true’ or, what comes to the same, ‘just false’). The paper serves as a challenge to formulate a problem of ‘just true’ that isn't solved by shrieking (as advanced in this paper), if such a problem be thought to exist.

Can God change the past? The standard Aquinas line answers this question negatively: God cannot change the past since such an act implies a contradiction; thus is not within the purview of God's omnipotence. While the Aquinas line is well-known, there are other, non-standard solutions to this question. In this paper, I look into such answers. In particular, I explore those answers that employ the resources of gappy and glutty logics. I show how these solutions are motivated and how each (...) offers an alternative conception of what it is for God to be omnipotent. Finally, I consider and reply to potential issues that may be raised against these non-standard answers. (shrink)

Weber, Colyvan, and Priest have advanced glutty approaches to the sorites, on which the truth about the penumbral region of a soritical series is inconsistent. The major benefit of a glut-based approach is maintaining the truth of all sorites premisses while none the less avoiding, in a principled fashion, the absurdity of the sorites conclusion. I agree that this is a major virtue of the target glutty approach; however, I think that it can be had without gluts. If correct, (...) this result weighs heavily against the proposed glutty approach, at least given the default-consistency principle that all target glutty philosophers accept: posit gluts only if there is no consistent theory that enjoys the same virtues as the would-be glutty solution. (shrink)

Today, complaints about information overload – associated with an overwhelming deluge of data – are commonplace. Early modernists have reacted to these concerns by showing that similar ones have arisen before. While this perspective is useful, it leaves out what was novel about the concept of information overload, which relied on a historically specific model of the human being. I trace the term’s history back to 1960, when the American psychologist and systems theorist James Grier Miller published his article on (...) ‘information input overload and psychopathology’. In Grier Miller’s usage, the idea of information overload signalled as much a reconceptualization of human beings as communication channels whose capacity could be overwhelmed as it did concerns about the volume of reading material to manage. Through his work, and the broader subsequent adoption of the term in academic and journalistic venues, I show how ‘information overload’ reflected intellectual and social trends specific to its time. (shrink)

Do inconsistent laws, which are in the form of inconsistent legal obligations, provide us with good reasons for accepting the possibility of legal gluts, which are true legal statements whose negations are also true? Given the contingencies of the law, it is unlikely that many will deny the possibility of inconsistent legal obligations, but it remains an ongoing debate whether these lead to any legal gluts. In a recent debate, Graham Priest [Priest, G. 2006. In ‘Contradiction’. In First (...) printed by Martinus Nijhoff in 1987. 2nd ed. Oxford: Oxford University Press; Priest, G. 2017. ‘Where Laws Conflict: An Application of the Method of Chunk and Permeate’. In Law and the New Logics, edited by H. Glenn, and L. Smith, 168–180. Cambridge: Cambridge University Press] has argued from inconsistent obligations to legal gluts and JC Beall [Beall, JC 2017. ‘On inconsistent laws and gluts’. In Law and the New Logics, edited by H. Glenn, and L. Smith, 199–207. Cambridge: Cambridge University Press.], while he has acknowledged that there are inconsistent obligations, has argued against Priest’s arguments for legal gluts. In this paper, after reviewing the debate, I adjudicate it and provide reasons for resisting Beall’s arguments again Priest thereby providing a possibility for legal gluts. (shrink)

We characterize the notion of validity relatively to models, for comprehension axioms, containing gluts.

Belnap-Dunn logic, sometimes also known as First Degree Entailment, is a four-valued propositional logic that complements the classical truth values of True and False with two non-classical truth values Neither and Both. The latter two are to account for the possibility of the available information being incomplete or providing contradictory evidence. In this paper, we present a probabilistic extension of BD that permits agents to have probabilistic beliefs about the truth and falsity of a proposition. We provide a sound and (...) complete axiomatization for the framework defined and also identify policies for conditionalization and aggregation. Concretely, we introduce four-valued equivalents of Bayes’ and Jeffrey updating and also suggest mechanisms for aggregating information from different sources. (shrink)

This paper compares two proposed solutions to the liar paradox, both of which involve revisions to classical semantics. The first, that of truth value gaps, denies that all sentences are true or false. The second, that of truth value gluts, asserts that some sentences are true and false. A natural question about these proposals is, ?Do they offer equally good (or bad) solutions, or is one better than the other?? Parsons 1990 suggested an answer to this question, arguing that (...) for every problem for one solution, there is a parallel problem for the other. Since then, several people have given arguments for and against the idea that the two face parallel problems. This paper advances the debate in two ways. First, it answers four attempts by Graham Priest to reject the parallel. In particular, it discusses alleged advantages for the gap solution with regard to the teleological account of truth, an extended liar paradox, Berry's paradox, and inexpressibility. Second, it discusses where, if anywhere, the parallel may be broken. (shrink)

JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with the scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact [email protected].

The liar paradox results from a line of reasoning that starts with the liar sentence, ‘This sentence is false’ and ends with a contradictory conclusion, ‘The liar sentence is both true and false’. There have been solutions to the paradox that preserve the standard conception of truth and the classical notion of logical validity. In this paper, I explore nonstandard solutions to it. In particular, I focus on two non-classical solutions to the liar paradox; viz., the gappy and the glutty (...) solutions. According to the gappy solution, the liar sentence is neither true nor false, and the reasoning that leads to the paradoxical conclusion is unsound. On the other hand, according to the glutty solution, the paradoxical conclusion is correct, but any subsequent reasoning from it is invalid. I show some ways of motivating each of these solutions. Next, I show what each implies about the notions of truth and validity, and how each solves the paradox. Finally, I highlight some of the more recent problems that could be pitted against each of these solutions. (shrink)

One of the few points of agreement to be found in mainstream responses to the logical and semantic problems generated by vagueness is the view that if any modification of classical logic and semantics is required at all then it will only be such as to admit underdetermined reference and truth-value gaps. Logics of vagueness including many valued logics, fuzzy logics, and supervaluation logics all provide responses in accord with this view. The thought that an adequate response might require the (...) recognition of cases of overdetermination and truth value gluts has few supporters. This imbalance lacks justification. As it happens, Jaskowski's paraconsistent discussive logic-a logic which admits truth value gluts-can be defended by reflecting on similarities between it and the popular supervaluationist analysis of vagueness already in the philosophical literature. A simple dualisation of supervaluation semantics results in a paraconsistent logic of vagueness based on what has been termed subvaluational semantics. (shrink)

This paper studies the question: How should one handle inconsistencies that derive from the inadequacy of the criteria by which one approaches the world. I compare several approaches. The adaptive logics defined from CLuN appear to be superior to the others in this respect. They isolate inconsistencies rather than spreading them, and at the same time allow for genuine deductive steps from inconsistent and mutually inconsistent premises. Yet, the systems based on CLuN seem to introduce an asymmetry betweennegated and non-negated (...) formulas, and this seems hard to justify. To clarify and understand the source of the asymmetry, the epistemological presuppositions of CLuN, viz. inadequate criteria, are investigated. This leads to a new type of paraconsistent logic that involves gluts with respect to all logical symbols. The larger part of the paper is devoted to this logic, to the adaptive logics defined from it, and to the properties of these systems. While the resulting logics are sensible and display interesting features, the search for variants of the justification leads to an unexpected justification for CLuN. (shrink)

This paper is an attempt to show that the subvaluation theory isnot a good theory of vagueness. It begins with a short review of supervaluation and subvaluation theories and procedes to evaluate the subvaluation theory. Subvaluationism shares all the main short-comings of supervaluationism.Moreover, the solution to the sorites paradox proposed by subvaluationists isnot satisfactory. There is another solution which subvaluationists could availthemselves of, but it destroys the whole motivation for using a paraconsistentlogic and is not different from the one offered (...) by supervaluationism. (shrink)

Critical thinking instructors are faced with an overwhelming number of textbooks to choose from for their courses. Many of these texts do not reflect an awareness of current scholarship in critical thinking and informal logic. I argue that instructors should only adopt textbooks that reflect a sound theoretical understanding of the topic by acknowledging the central role of critical thinking dispositions, offering a more nuanced approach to the teaching of fallacies and of inference, stressing dialectic and argument revision, focusing on (...) the analysis and evaluation of real arguments, and broadening the scope of critical thinking beyond argument analysis and evaluation. To support instructors in this regard, I critique one popular textbook now in its sixth edition that does not satisfy many of these criteria, Munson and Black (2012), and applaud one new textbook that I find does succeed on many of these fronts, Bailin and Battersby (2010). (shrink)

In “Sideways Music”, Ned Markosian presents the aesthetic value variance of sideways music as a case against what the Spacetime Thesis—the thesis that time is one of four similar dimensions that make up spacetime. Critics have already raised worries about the premises of his argument. In this paper, I focus on Markosian’s assumed aesthetic realism. I argue that there is a version of aesthetic realism—a version that admits aesthetic value gluts—that is consistent with both the Spacetime Thesis and the (...) aesthetic variance of sideways music. If this is right, then sideways music may simply be a non-issue for proponents of the Spacetime Thesis. (shrink)

The central thesis of JC Beall’s paraconsistent Christology is that Christ, being human and divine, is a contradictory being, and a rational Christology can accept it, since logic nowadays does not exclude the possibility of true contradictions. In this paper, I move from Beall’s theory and I present an alternative view. I quote seven statements of the so-called ‘Athanasian Creed’ which synthesizes the results of conciliar Christology. The aim of the Creed is to combat monophysitism by stressing the duplicity and (...) unity of Christ: two (incompatible) natures inseparably joined in only one person. I note that the two-in-one principle, so intended, may be seen as an ancestor of what has been called ‘conjunctive paraconsistency’, whereby there could be true contradictions but contradictories cannot be separately true. I specifically oppose this view to Beall’s idea of Christ’s human divinity (or divine humanity) as a glut, showing that in the conjunctive account, true contradictions do not require any overlapping or joint ascription of truth and falsity. (shrink)

In a recent paper, Jc Beall has employed what he calls ‘shriek rules’ in a putative solution to the long-standing ‘just false’ problem for glut theory. The purpose of this paper is twofold: firstly, I distinguish the ‘just false’ problem from another problem, with which it is often conflated, which I will call the ‘exclusion problem’. Secondly, I argue that shriek rules do not help glut theorists with either problem.

This book argues that the standard (orthodox) doctrine of incarnation (of "God enfleshed") is best understood along glut-theoretic lines: the incarnate God is a contradictory being. Example: because God, the Christ figure is all-knowing; but because human, ignorant. And so on. Standard theological theory in the tradition recognizes the apparent contradiction in its core doctrines; Beall argues that the appearance should be accepted as veridical.

One longstanding problem for glut theorists is the problem of ‘just true.’ On Beall's conservative version of glut theory advanced in Spandrels of Truth , he addresses the problem in two steps. The first is a rejection of the problem: he claims that the only general notion of ‘just true’ is just truth itself. On that view, the alleged problem of ‘just true’ is reduced to the problem of truth itself, which has a solution—glut theory. The second step is to (...) acknowledge that there is a notion of ‘just true’ which is more limited but nonetheless meets all reasonable criteria demanded by those who advance the longstanding just-true objection. Marcus Rossberg disagrees. According to Rossberg, a just-true operator ought to iterate and be non-arbitrary in ways that Beall's proposed just-true operator is not. My aim in this paper is to construct a new conditional in terms of which a new just-true operator may be defined, a necessity operator, and to show that it meets all of the target desiderata of the debate. I then use that new operator to address the arbitrariness worries raised by Rossberg. (shrink)

Gegenstand der "Phänomenologie des Geistes" ist die 'Wissenschaft der Erfahrung des Bewußtseins', d.i. der Aufstieg der Gestalten vernünftiger Erkenntnis von der Stufe der naiven Wahrnehmung bis zur Höhe des absoluten Wissens. Von diesem ersten reifen Werk Hegels sagte Bloch, es sei "voll Jugend ohne gleichen, voll Überfülle und Glut, dichterisch durchaus, wissenschaftlich durchaus, in einzigartiger, morgendlicher Gärung ... Nirgends kann genauer gesehen werden, was großer Gedanke im Aufgang ist, und nirgends ist sein Lauf bereits vollständiger." – Die Einleitung gibt eine (...) genaue Rekonstruktion der Entstehungsgeschichte des Werks, außerdem eine klare Nachzeichnung des Argumentationsganges des Textes, die nicht nur die schwierige Lektüre erleichtert, sondern auch an den derzeitigen Interpretationsstand heranführt. (shrink)

Proponents of “truth-value glut” responses to the paradoxes of self-reference, such as Priest [6, 7] argue that “truth-value gap” analyses of the paradoxes fall foul of the strengthened liar paradox: “this sentence is not true.” If we pay attention to the role of assertion and denial and the behaviour of negation in both “gap” and “glut” analyses, we see that the situation with these approaches has a pleasing symmetry: gap approaches take some denials to fail to be expressible by negation, (...) and glut approaches take some negations to not express denials. But in the light of this symmetry, considerations against a gap view point to parallel considerations against a glut view. Those who find some reason to prefer one view over another (and this is almost everyone) must find some reason to break this symmetry. (shrink)

We cast doubts on the suggestion, recently made by Graham Priest, that glut theorists may express disagreement with the assertion of A by denying A. We show that, if denial is to serve as a means to express disagreement, it must be exclusive, in the sense of being correct only if what is denied is false only. Hence, it can’t be expressed in the glut theorist’s language, essentially for the same reasons why Boolean negation can’t be expressed in such a (...) language either. We then turn to an alternative proposal, recently defended by Beall (in Analysis 73(3):438–445, 2013; Rev Symb Log, 2014), for expressing truth and falsity only, and hence disagreement. According to this, the exclusive semantic status of A, that A is either true or false only, can be conveyed by adding to one’s theory a shrieking rule of the form A & ~A |- \bot, where \bot entails triviality. We argue, however, that the proposal doesn’t work either. The upshot is that glut theorists face a dilemma: they can either express denial, or disagreement, but not both. Along the way, we offer a bilateral logic of exclusive denial for glut theorists—an extension of the logic commonly called LP. (shrink)

This article introduces, studies, and applies a new system of logic which is called ‘HYPE’. In HYPE, formulas are evaluated at states that may exhibit truth value gaps and truth value gluts. Simple and natural semantic rules for negation and the conditional operator are formulated based on an incompatibility relation and a partial fusion operation on states. The semantics is worked out in formal and philosophical detail, and a sound and complete axiomatization is provided both for the propositional and (...) the predicate logic of the system. The propositional logic of HYPE is shown to contain first-degree entailment, to have the Finite Model Property, to be decidable, to have the Disjunction Property, and to extend intuitionistic propositional logic conservatively when intuitionistic negation is defined appropriately by HYPE’s logical connectives. Furthermore, HYPE’s first-order logic is a conservative extension of intuitionistic logic with the Constant Domain Axiom, when intuitionistic negation is again defined appropriately. The system allows for simple model constructions and intuitive Euler-Venn-like diagrams, and its logical structure matches structures well-known from ordinary mathematics, such as from optimization theory, combinatorics, and graph theory. HYPE may also be used as a general logical framework in which different systems of logic can be studied, compared, and combined. In particular, HYPE is found to relate in interesting ways to classical logic and various systems of relevance and paraconsistent logic, many-valued logic, and truthmaker semantics. On the philosophical side, if used as a logic for theories of type-free truth, HYPE is shown to address semantic paradoxes such as the Liar Paradox by extending non-classical fixed-point interpretations of truth by a conditional as well-behaved as that of intuitionistic logic. Finally, HYPE may be used as a background system for modal operators that create hyperintensional contexts, though the details of this application need to be left to follow-up work. (shrink)

This paper is a contribution to the emerging field of comparative metaethics, which aims to analyse the metaethical views of philosophical traditions outside the Western mainstream. It argues that the metaethical views implicit in the mediaeval Chinese school of Tiantai Buddhism can be reconstructed in contemporary terms in order to develop two novel views. These views are moral dialetheism and moral trivialism. The taxonomy of contemporary metaethical views, in epistemic terms, is exhausted by either partial success, or complete error, theories. (...) They claim, respectively, either that some moral judgments are true (and some false) or that all moral judgments are false. There are also noncognitivist and nonfactualist views, claiming that all moral judgments are technically neither true nor false. In opposition to this moral truth gap, moral dialetheism and moral trivialism offer a moral truth glut. These views say, respectively, that some moral judgments and their negations are true and that all moral judgments and their negations are true. The upshot of this metaethical reconstruction of Tiantai Buddhism is that it allows us to complete the contemporary metaethical taxonomy, and to contribute to the therapeutic goal of finding ways to utilize metaethical reflection for the sake of release from the pathologies of morality. (shrink)

In Philosophical Logic, the Liar Paradox has been used to motivate the introduction of both truth value gaps and truth value gluts. Moreover, in the light of “revenge Liar” arguments, also higher-order combinations of generalized truth values have been suggested to account for so-called hyper-contradictions. In the present paper, Graham Priest's treatment of generalized truth values is scrutinized and compared with another strategy of generalizing the set of classical truth values and defining an entailment relation on the resulting sets (...) of higher-order values. This method is based on the concept of a multilattice. If the method is applied to the set of truth values of Belnap's “useful four-valued logic”, one obtains a trilattice, and, more generally, structures here called Belnap-trilattices. As in Priest's case, it is shown that the generalized truth values motivated by hyper-contradictions have no effect on the logic. Whereas Priest's construction in terms of designated truth values always results in his Logic of Paradox, the present construction in terms of truth and falsity orderings always results in First Degree Entailment. However, it is observed that applying the multilattice-approach to Priest's initial set of truth values leads to an interesting algebraic structure of a “bi-and-a-half” lattice which determines seven-valued logics different from Priest's Logic of Paradox. (shrink)

This volume examines the concept of falsification as a central notion of semantic theories and its effects on logical laws. The point of departure is the general constructivist line of argument that Michael Dummett has offered over the last decades. From there, the author examines the ways in which falsifications can enter into a constructivist semantics, displays the full spectrum of options, and discusses the logical systems most suitable to each one of them. While the idea of introducing falsifications into (...) the semantic account is Dummett's own, the many ways in which falsificationism departs quite radically from verificationism are here spelled out in detail for the first time. The volume is divided into three large parts. The first part provides important background information about Dummett’s program, intuitionism and logics with gaps and gluts. The second part is devoted to the introduction of falsifications into the constructive account and shows that there is more than one way in which one can do this. The third part details the logical effects of these various moves. In the end, the book shows that the constructive path may branch in different directions: towards intuitionistic logic, dual intuitionistic logic and several variations of Nelson logics. The author argues that, on balance, the latter are the more promising routes to take. "Kapsner’s book is the first detailed investigation of how to incorporate the notion of falsification into formal logic. This is a fascinating logico-philosophical investigation, which will interest non-classical logicians of all stripes." Graham Priest, Graduate Center, City University of New York and University of Melbourne. (shrink)

In this paper I urge friends of truth-value gaps and truth-value gluts – proponents of paracomplete and paraconsistent logics – to consider theories not merely as sets of sentences, but as pairs of sets of sentences, or what I call ‘bitheories,’ which keep track not only of what holds according to the theory, but also what fails to hold according to the theory. I explain the connection between bitheories, sequents, and the speech acts of assertion and denial. I illustrate (...) the usefulness of bitheories by showing how they make available a technique for characterising different theories while abstracting away from logical vocabulary such as connectives or quanti- fiers, thereby making theoretical commitments independent of the choice of this or that particular non-classical logic. (shrink)

Infectious logics are systems that have a truth-value that is assigned to a compound formula whenever it is assigned to one of its components. This paper studies four-valued infectious logics as the basis of transparent theories of truth. This take is motivated as a way to treat different pathological sentences differently, namely, by allowing some of them to be truth-value gluts and some others to be truth-value gaps and as a way to treat the semantic pathology suffered by at (...) least some of these sentences as infectious. This leads us to consider four distinct four-valued logics: one where truth-value gaps are infectious, but gluts are not; one where truth-value gluts are infectious, but gaps are not; and two logics where both gluts and gaps are infectious, in some sense. Additionally, we focus on the proof theory of these systems, by offering a discussion of two related topics. On the one hand, we prove some limitations regarding the possibility of providing standard Gentzen sequent calculi for these systems, by dualizing and extending some recent results for infectious logics. On the other hand, we provide sound and complete four-sided sequent calculi, arguing that the most important technical and philosophical features taken into account to usually prefer standard calculi are, indeed, enjoyed by the four-sided systems. (shrink)

In this paper, I will present a Fitch–style natural deduction proof theory for modal paralogics (modal logics with gaps and/or gluts for negation). Besides the standard classical subproofs, the presented proof theory also contains modal subproofs, which express what would follow from a hypothesis, in case it would be true in some arbitrary world.

When I began to think about a book on Kant and the life sciences, the idea that Kant would ever have been influenced by the ideas coming out of this field seemed impossible to believe. In fact, I spent an entire Summer determined to prove that my thesis was wrong. The problem was, I kept finding evidence in support of it (fully one third of Kant’s Organicism is devoted to a glut of historical research filling up the endnotes, research stemming, (...) for the most part, from an initial disbelief in my own hypothesis). Most of the scholars who had considered this connection before me had had their training in the history of science. My situation was different, I had been trained in philosophy. I knew my Descartes but I had never read Harvey; I had written on Locke but I had never heard of Ray…. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Josiah Royce in FocusDwayne A. TunstallJosiah Royce in Focus Jacquelyn Ann K. Kegley. Bloomington, IN: Indiana University Press, 2008.Josiah Royce in Focus reads like a sequel to Jacquelyn Ann K. Kegley’s earlier book on Royce’s public philosophy, Genuine Individuals and Genuine Communities. As she did in Genuine Individuals and Genuine Communities, Kegley does a remarkable job of interpreting Royce’s philosophy such that it has [End Page 127] contemporary (...) relevance for academic philosophy, conflict resolution, psychology, and the religion-science dialogue. Yet, unlike with her earlier book, Kegley devotes over two-thirds of this book to the task of weaving together Royce’s life and educational experiences with his thought. This integration of Royce’s life with his thought allows the reader to glimpse just how Royce is “a model philosopher: a scholar and a committed teacher, as well as a philosopher much concerned about public issues and basic human concerns” (xiv). Kegley does this while introducing the reader to many dimensions of Royce, including Royce the son, Royce the father, Royce the first-generation Californian, Royce the first-rate historian of California, Royce the amateur novelist, and Royce the world traveler. Amazingly, she uses Royce’s life to illuminate his philosophical thought without psychologizing Royce and hence avoids the all-too-common urge to reduce people’s philosophical ideas to mere rationalizations of their own preferences and desires. This is to be applauded in the age of Oprah, the proliferation of memoirs, and the apparent glut of self-help books.The first five chapters constitute Kegley’s portrait of Royce the person and Royce the thinker. In chapter 1, “Royce as a Frontier Californian and Intellectual Pioneer: Forging Self and Thought in a New and Developing Land,” she introduces the reader to Royce the first-generation Californian and intellectual pioneer. Here she persuasively links his California frontier upbringing; his early educational experiences in California at the Lincoln School (San Francisco) and the University of California, Berkeley; his studies in Germany; and his graduate studies at Johns Hopkins to his concerns about social conflicts and his lifelong attempt to resolve those conflicts to better the communities in which they occur (7–12).Indeed, she persuasively argues that Royce had already formulated the central insights of his philosophy by the time of his arrival at Harvard University in 1882. Kegley’s interpretation of Royce’s intellectual development owes much to Randall Auxier’s recent work on Royce’s thought. In Auxier’s interpretation of Royce’s thought, Royce had formulated the central intellectual insights of his philosophy—especially his ethics, philosophy or religion, and public philosophy—years before The Religious Aspect of Philosophy was published in 1885. This account of Royce’s intellectual development differs somewhat from Frank M. Oppenheim’s account. Oppenheim’s account depicts Royce’s intellectual development as a series of interrelated yet momentous “maximal intellectual insights.” Each of these insights marks a noticeable shift in his intellectual development. Oppenheim thinks that, of all the maximal intellectual insights Royce had throughout his career, the [End Page 128] most momentous one is the 1912 Peircean insight. This insight leads Royce to convert to Peircean semiotics and clarify his moral philosophy and philosophy of religion with Peirce’s theory of interpretation. In Oppenheim’s account, The Sources of Religious Insight (1912) and The Problem of Christianity (1913) are the glorious fruits of his Peircean insight. What Kegley has done in chapter 1 is to provide an account of Royce’s intellectual development that supersedes Oppenheim’s account. Indeed, her account of Royce’s intellectual development could possibly change how scholars study Royce’s thought, much in the same way that John E. Smith’s Royce’s Social Infinite did from the early 1950s until recently.In chapter 2, “The Self,” Kegley depicts Royce as a late nineteenth- and early twentieth-century psychologist whose ideas are still relevant today. She reminds the reader throughout this chapter that Royce is a pioneer in psychology, given that his book Outlines of Psychology (1903) advances an approach to psychology that sidesteps faculty psychology and that he is one of the first psychologists, along with William James... (shrink)

The recent work of logician Jc Beall marks a paradigm shift within the fields of analytic theology and philosophy of religion. Thanks to Beall’s work, the long held (and generally unquestioned) assumption that theology is governed by (or closed under) the classical account of logic, is no longer free for the assumption. More importantly, by dropping this unquestioned commitment to the classical account, Beall’s work has uncovered natural and well-motivated solutions to some of monotheistic theologies’ most difficult and longstanding problems. (...) That said, much of Beall’s work (and the work of others who have followed his lead) has been paraconsistent, utilizing glut-theoretic (contradictory) models to solve theologies problems. In this essay, my plan is to go paracomplete, with the aim of exploring a yet to be explored solution to the infamous foreknowledge and freedom problem. My solution finds its roots in the recent work Jc Beall and Aaron Cotnoir (‘God of the Gaps’, Analysis, 2017). Specifically, in this essay I will explore a gap-theoretic solution to the foreknowledge and freedom problem; one in which it is neither true nor false that God has foreknowledge. By utilizing Beall’s and Cotnoir’s model — which sees limit claims on God’s omni-properties as either just false or gappy — a natural and well-motivated solution to the foreknowledge and freedom problem emerges. Moreover, by utilizing the Beall-Cotnoir gap-theoretic model, not only is the foreknowledge and freedom problem circumvented, but an interesting and novel account of divine omniscience emerges. (shrink)

A liquid modernity, where the traditional certainties have become fluid and blurred, presents a major challenge for education. The world is changing so quickly that homo sapiens, learning animal par excellence, can no longer rely on strategies acquired through learning experiences, let alone those derived from traditional values or wisdom. The excess of useless information creates a glut. When saturation level is reached, accumulation ceases to be a sign of wealth and becomes undesirable. Knowledge is confined - discarded like refuse (...) - in the infinite capacity of cyber-computers. What should we humans keep and what should we reject in this process? In times of liquid modernity, how and what should our children be taught in order to be able to develop survival strategies throughout their lives? (shrink)

Paraconsistent approaches have received little attention in the literature on vagueness (at least compared to other proposals). The reason seems to be that many philosophers have found the idea that a contradiction might be true (or that a sentence and its negation might both be true) hard to swallow. Even advocates of paraconsistency on vagueness do not look very convinced when they consider this fact; since they seem to have spent more time arguing that paraconsistent theories are at least as (...) good as their paracomplete counterparts, than giving positive reasons to believe on a particular paraconsistent proposal. But it sometimes happens that the weakness of a theory turns out to be its mayor ally, and this is what (I claim) happens in a particular paraconsistent proposal known as subvaluationism. In order to make room for truth-value gluts subvaluationism needs to endorse a notion of logical consequence that is, in some sense, weaker than standard notions of consequence. But this weakness allows the subvaluationist theory to accommodate higher-order vagueness in a way that it is not available to other theories of vagueness (such as, for example, its paracomplete counterpart, supervaluationism). (shrink)