It is valuable for inquiry to have researchers who are committed advocates of their own theories. However, in light of pervasive disagreement, such a commitment is not well explained by the idea that researchers believe their theories. Instead, this commitment, the rational attitude to take toward one’s favored theory during the course of inquiry, is what I call endorsement. Endorsement is a doxastic attitude, but one which is governed by a different type of epistemic rationality. This inclusive epistemic rationality is (...) sensitive to reasons beyond those to think the particular proposition in question is true. Instead, it includes extrinsic epistemic reasons, which concern the health of inquiry more generally. Such extrinsic reasons include the distribution of cognitive labor that a researcher will contribute to by endorsing a particular theory. Recognizing endorsement and inclusive epistemic rationality thus allows us to smooth a tension between individual rationality and collective rationality. It does so by showing how it can be epistemically rational to endorse a theory on the basis of the way this endorsement will benefit collective inquiry. I provide a decision theoretic treatment for inclusive epistemic rationality and endorsement which illustrates how this can be accomplished. (shrink)

It might be thought that we could argue for the consistency of a mathematical theory T within T, by giving an inductive argument that all theorems of T are true and inferring consistency. By Gödel's second incompleteness theorem any such argument must break down, but just how it breaks down depends on the kind of theory of truth that is built into T. The paper surveys the possibilities, and suggests that some theories of truth give far more intuitive diagnoses of (...) the breakdown than do others. The paper concludes with some morals about the nature of validity and about a possible alternative to the idea that mathematical theories are indefinitely extensible. (shrink)

In this article, I consider the possibility of interpreting Hegel’s dialectic as dialetheism. After a first basic recapitulation about the meaning of the words ‘dialetheism’ and ‘dialectic’ and a consideration of Priest’s own account of the relation between dialectical and dialetheic logic in 1989, I discuss some controversial issues, not directly considered by Priest. As a matter of fact, the reflection on paraconsistent logics and dialetheism has enormously grown in recent years. In addition, the reception of Hegel’s logic and metaphysics (...) has also impressively improved. So I suggest that the discussion about the binomial dialectic/dialetheism should be reopened, on these new bases. (shrink)

According to tradition, logic is normative for reasoning. According to many contemporary philosophers of logic, there is more than one correct logic. What is the relationship between these two strands of thought? This paper makes two claims. First, logic is doubly normative for reasoning because, in addition to constraining the combinations of beliefs that we may have, logic also constrains the methods by which we may form them. Second, given that logic is doubly normative for reasoning, a wide array of (...) logical pluralisms are inconsistent with the normativity of logic as they entail contradictory claims about how agents ought to reason. Thus, if logic is normative for reasoning, these pluralisms are untenable. (shrink)

Logical realism is a view about the metaphysical status of logic. Common to most if not all the views captured by the label ‘logical realism’ is that logical facts are mind- and language-independent. But that does not tell us anything about the nature of logical facts or about our epistemic access to them. The goal of this paper is to outline and systematize the different ways that logical realism could be entertained and to examine some of the challenges that these (...) views face. It will be suggested that logical realism is best understood as a metaphysical view about the logical structure of the world, but this raises an important question: does logical realism collapse into standard metaphysical realism? It will be argued that this result can be accommodated, even if it cannot be altogether avoided. (shrink)

One response to the problem of logical omniscience in standard possible worlds models of belief is to extend the space of worlds so as to include impossible worlds. It is natural to think that essentially the same strategy can be applied to probabilistic models of partial belief, for which parallel problems also arise. In this paper, I note a difficulty with the inclusion of impossible worlds into probabilistic models. Under weak assumptions about the space of worlds, most of the propositions (...) which can be constructed from possible and impossible worlds are in an important sense inexpressible; leaving the probabilistic model committed to saying that agents in general have at least as many attitudes towards inexpressible propositions as they do towards expressible propositions. If it is reasonable to think that our attitudes are generally expressible, then a model with such commitments looks problematic. (shrink)

At some step in proving the Liar Paradox in natural language, a sentence is derived that seems overdetermined with respect to its semantic value. This is complemented by Tarski’s Theorem that a formal language cannot consistently contain a naive truth predicate given the laws of logic used in proving the Liar paradox. I argue that proofs of the Eubulidean Liar either use a principle of truth with non-canonical names in a fallacious way or make a fallacious use of substitution of (...) identicals. Tarski never committed the first fallacy and may have himself considered it fallacious. Nevertheless, I clarify that it is fallacious. I then argue substitution of identicals needs to be restricted within the scope of the truth predicate. A logic for truth implementing this restriction is a monotonic extension of a classical first order logic, or indeed a formalizable fragment of natural language. Proofs of Tarski’s Indefinability of Truth theorem are invalid in this logic. This approach generalizes to invalidate proofs of Liar-like paradoxes, particularly the predicate form of the Knower paradox. Consequently, such a logic can be further extended in a way that avoids Montague’s theorem for such a system. Yet, the semantic status of a Liar sentence is not fully resolved. It is no longer overdetermined; it is now underdetermined. (shrink)

The Liar paradox is an obstacle to a theory of truth, but a Liar sentence need not contain a semantic predicate. The Pinocchio paradox, devised by Veronique Eldridge-Smith, was the first published paradox to show this. Pinocchio’s nose grows if, and only if, what Pinocchio is saying is untrue. What happens if Pinocchio says that his nose is growing? Eldridge-Smith and Eldridge-Smith : 212-5, 2010) posed the Pinocchio paradox against the Tarskian-Kripkean solutions to the Liar paradox that use language hierarchies. (...) Eldridge-Smith : 306-8, 2011) also set the Pinocchio paradox against semantic dialetheic solutions to the Liar. Beall argued the Pinocchio story was just an impossible story. Eldridge-Smith : 749-752, 2012b) responded that unless the T-schema is a necessary truth of some sort, the Pinocchio principle is possible. Luna : 77–86, 2016) argues that the Pinocchio contradiction proves the principle is false. D’Agostini & Ficara discuss a more plausible physical truth-tracking trait, the Blushing Liar, and argue that the Pinocchio contradiction is not a metaphysical dialetheia. I respond to Luna, and D’Agostini & Ficara, and prove that the Pinocchio paradox is a counterexample to hierarchical solutions to the Liar. (shrink)

The concept of hypodox is dual to the concept of paradox. Whereas a paradox is incompatibly overdetermined, a hypodox is underdetermined. Indeed, many particular paradoxes have dual hypodoxes. So, naively the dual of Russell’s Paradox is whether the set of all sets that are members of themselves is self-membered. The dual of the Liar Paradox is the Truth-teller, and a hypodoxical dual of the Heterological paradox is whether ‘autological’ is autological. I provide some analysis of the duality and I search (...) for modal hypodoxes as duals to known paradoxes. I also try to continue this search further by mapping the relations between some paradoxes and hypodoxes in duality squares. This investigation increases the known extension of the concept of hypodox, and the duality relation between paradoxes and hypodoxes assists in finding some of these. (shrink)

The philosophical difficulties presented by self-deception are vexed and multifaceted. One such difficulty is what I call the ‘doxastic problem’ of self-deception. Solving the doxastic problem involves determining whether someone in a state of self-deception that ∼p both believes that p and believes that ∼p, simply holds one or the other belief, or, as I will argue, holds neither. This final option, which has been almost entirely overlooked to-date, is what I call ‘ nondoxasticism ’ about self-deception. In this article, (...) I present a negative case for nondoxasticism according to which, in the paradigm case of self-deception, there is no explanatory need to attribute the self-deceived person either their undesired belief that p, or their desired belief that ∼p. Folk psychology is replete with concepts other than belief, and if we bear this in mind, it becomes clear that the explanatory roles for which the self-deceived person's purported beliefs have traditionally been enlisted can be comfortably filled without recourse to belief. (shrink)

This paper discusses the neo-logicist approach to the foundations of mathematics by highlighting an issue that arises from looking at the Bad Company objection from an epistemological perspective. For the most part, our issue is independent of the details of any resolution of the Bad Company objection and, as we will show, it concerns other foundational approaches in the philosophy of mathematics. In the first two sections, we give a brief overview of the "Scottish" neo-logicist school, present a generic form (...) of the Bad Company objection and introduce an epistemic issue connected to this general problem that will be the focus of the rest of the paper. In the third section, we present an alternative approach within philosophy of mathematics, a view that emerges from Hilbert's Grundlagen der Geometrie (1899, Leipzig: Teubner; Foundations of geometry (trans.: Townsend, E.). La Salle, Illinois: Open Court, 1959.). We will argue that Bad Company-style worries, and our concomitant epistemic issue, also affects this conception and other foundationalist approaches. In the following sections, we then offer various ways to address our epistemic concern, arguing, in the end, that none resolves the issue. The final section offers our own resolution which, however, runs against the foundationalist spirit of the Scottish neo-logicist program. (shrink)

This paper explores allowing truth value assignments to be undetermined or "partial" and overdetermined or "inconsistent", thus returning to an investigation of the four-valued semantics that I initiated in the sixties. I examine some natural consequence relations and show how they are related to existing logics, including ukasiewicz's three-valued logic, Kleene's three-valued logic, Anderson and Belnap's relevant entailments, Priest's "Logic of Paradox", and the first-degree fragment of the Dunn-McCall system "R-mingle". None of these systems have nested implications, and I investigate (...) twelve natural extensions containing nested implications, all of which can be viewed as coming from natural variations on Kripke's semantics for intuitionistic logic. Many of these logics exist antecedently in the literature, in particular Nelson 's "constructible falsity". (shrink)

Both I and Belnap, motivated the "Belnap-Dunn 4-valued Logic" by talk of the reasoner being simply "told true" (T) and simply "told false" (F), which leaves the options of being neither "told true" nor "told false" (N), and being both "told true" and "told false" (B). Belnap motivated these notions by consideration of unstructured databases that allow for negative information as well as positive information (even when they conflict). We now experience this on a daily basis with the Web. But (...) the 4-valued logic is deductive in nature, and its matrix is discrete: there are just four values. In this paper I investigate embedding the 4-valued logic into a context of probability. Jøsang's Subjective Logic introduced uncertainty to allow for degrees of belief, disbelief, and uncertainty. We extend this so as to allow for two kinds of uncertainty— that in which the reasoner has too little information (ignorance) and that in which the reasoner has too much information (conflicted). Jøsang's "Opinion Triangle" becomes an "Opinion Tetrahedron" and the 4-values can be seen as its vertices. I make/prove various observations concerning the relation of non-classical "probability" to non-classical logic. (shrink)

Two epistemic principles are Knowledge Exclusion and Belief Exclusion. Knowledge Exclusion says that it is necessarily the case that if an agent knows that p, then she does not believe that ∼p, and Belief Exclusion says that it is necessarily the case that if an agent believes that q, then she does not believe that ∼q. Many epistemologists find it reasonable to reject the latter principle and accept the former. I argue that this is in fact not reasonable by proposing (...) a case in which an agent can use that she has contradictory beliefs towards a proposition as decisive evidence for that proposition. A natural response is that this case conflicts with common assumptions about the relation between knowledge, contradictory beliefs and rationality. I reply by drawing ideas from Lasonen-Aarnio’s remarks on unreasonable knowledge to explain why these common assumptions do not threaten my argument. (shrink)

The present article critically examines three aspects of Graham Priest's dialetheic analysis of very important kinds of limitations (the limit of what can be expressed, described, conceived, known, or the limit of some operation or other). First, it is shown that Priest's considerations focusing on Hegel's account of the infinite cannot be sustained, mainly because Priest seems to rely on a too restrictive notion of object. Second, we discuss Priest's treatment of the paradoxes in Cantorian set-theory. It is shown that (...) Priest does not address the issue in full generality; rather, he relies on a reading of Cantor which implicitly attributes a very strong principle concerning quantification over arbitrary domains to Cantor. Third, the main piece of Priest's work, the so-called “inclosure schema”, is investigated. This schema is supposed to formalize the core of many well-known paradoxes. We claim, however, that formally the schema is not sound. (shrink)

The sciences occasionally generate discoveries that undermine their own assumptions. Two such discoveries are characterized here: the discovery of apophenia by cognitive psychology and the discovery that physical systems cannot be locally bounded within quantum theory. It is shown that such discoveries have a common structure and that this common structure is an instance of Priest’s well-known Inclosure Schema. This demonstrates that science itself is dialetheic: it generates limit paradoxes. How science proceeds despite this fact is briefly discussed, as is (...) the connection between our results and the realism-antirealism debate. We conclude by suggesting a position of epistemic modesty. (shrink)

The idea of omnipotence plays a crucial role within the framework of classical theism. God is typically considered omnipotent, that is, able to perform any action. Sometimes, it is said that for God there is no difference between will and action; everything he wishes happens. However, as one reflects on the concept of omnipotence, some rather complex questions arise; the range of God’s possible “actions” is not clear. What are the boundaries of the power of an omnipotent being, if these (...) boundaries exist at all? In this paper, we will examine an interesting question: is it possible that two omnipotent beings exist? Or, does the property of omnipotence necessarily imply the uniqueness of its instantiation? Intuitively, the existence of more than one omnipotent being seems to be contradictory. However, we will demonstrate that under some conditions the existence of two omnipotent beings is possible. (shrink)

It is argued, on the basis of new counterexamples, that neither knowledge nor epistemic justification (or “epistemic rationality”) can reasonably be thought to be closed under logical implication. The argument includes an attempt to reconcile the fundamental intuitions of the opposing parties in the debate.

Dentro del conjunto de las lógicas no clásicas, las lógicas paraconsistentes han suscitado de manera particular el interés de diversos filósofos. Además de las definiciones tradicionales, en los últimos años, se han propuesto nuevas maneras de caracterizar a la paraconsistencia. Lo que tienen en común todas estas definiciones es que alguna forma de la regla o de la metarregla de explosión debe ser rechazada. En este artículo, presentaré dichas definiciones y evaluaré el rol que juegan la negación y la transitividad (...) en ellas. Finalmente, propondré una nueva caracterización de la paraconsistencia, la que llamaré paraconsistencia pura y mostraré que la regla de monotonía juega un rol crucial en todas las presentaciones de dicho concepto. (shrink)

In this paper I’ll explore the relation between ω-inconsistency and plain inconsistency, in the context of theories that intend to capture semantic concepts. In particular, I’ll focus on two very well known inconsistent but non-trivial theories of truth: LP and STTT. Both have the interesting feature of being able to handle semantic and arithmetic concepts, maintaining the standard model. However, it can be easily shown that both theories are ω- inconsistent. Although usually a theory of truth is generally expected to (...) be ω-consistent, all conceptual concerns don’t apply to inconsistent theories. Finally, I’ll explore if it’s possible to have an inconsistent, butω-consistent theory of truth, restricting my analysis to substructural theories. (shrink)

I argue that medieval solutions to the limit decision problem imply four-dimensionalism, i.e. the view according to which substances that persist through time are extended through time as well as through space, and have different temporal parts at different times.

In this paper I argue that it’s impossible for there to be a single universal theory of meaning for a language. First, I will consider some minimal expressiveness requirements a language must meet to be able to express semantic claims. Then I will argue that in order to have a single unified theory of meaning, these expressiveness requirements must be satisfied by a language which the semantic theory itself applies to. That is, we would need a language which can express (...) its own meaning. It has been well-known since Tarski that theories of meaning whose central notion is truth can’t be expressed in a language which they apply to. Here, I develop Quine’s formulation of the Liar Paradox in grammatical terms and use this to extend Tarski’s result to all theories of meaning. This general version of the paradox can be formalised as a special case of the Lawvere Fixed-Point Theorem applied to a categorial grammar. Taken together with the initial arguments, I infer that a universal theory of meaning is impossible and conclude the paper with a brief discussion on what alternatives are available. (shrink)

In his Lectures on the History of Philosophy, Hegel develops a subtle analysis of Megarian paradoxes: the Liar, the Veiled Man and the Sorites. In this paper, we focus on Hegel's interpretation of...

Stratified properties such as ‘happy unhappiness’, ‘ungrounded ground’, ‘fortunate misfortune’, and evidently ‘true falsity’ may generate dialetheias (true contradictions). The aim of the article is to show that if this is the case, then we will have a special, conjunctive, kind of dialetheia: a true state description of the form ‘Fa and not Fa’ (for some property F and object a), wherein the two conjuncts, separately taken, are to be held untrue. The particular focus of the article is on happy (...) unhappiness: people suffering from (or enjoying) happy unhappiness (if there is some situation or state of mind of this kind) cannot be truly said ‘happy’ or ‘unhappy’, but we can say they are both. In the first section three cases of conjunctive stratification are presented; in the second section the logic of stratified contradictions is explored. The last section focuses on eudemonistic ascriptions: stated that a is happy to be unhappy (or unhappy to be happy), should we say a is happy? unhappy? both? neither? (shrink)

The mathematical concept of pragmatic truth, first introduced in Mikenberg, da Costa and Chuaqui (1986), has received in the last few years several applications in logic and the philosophy of science. In this paper, we study the logic of pragmatic truth, and show that there are important connections between this logic, modal logic and, in particular, Jaskowski's discussive logic. In order to do so, two systems are put forward so that the notions of pragmatic validity and pragmatic truth can be (...) accommodated. One of the main results of this paper is that the logic of pragmatic truth is paraconsistent. The philosophical import of this result, which justifies the application of pragmatic truth to inconsistent settings, is also discussed. (shrink)

This paper defends a rational account of conceivability according to which conceiving is a kind of modal thinking that is distinct from imagining effectively allowing us to think beyond what we can imagine, and that we are subject to rational rather than experiential constraints when we do so. Defending this view involves appealing to the perspective of an idealized agent and I’ll argue that this appeal is not worrisome given an “objective” view of propositional justification.

Putative examples of true contradictions in the social world have been given by dialetheists such as Graham Priest, Richard Routley, and Val Plumwood. However, we feel that it has not been decisively argued that these examples are in fact true contradictions rather than merely apparent. In this paper we adopt a new strategy to show that there are some true contradictions in the social world, and hence that dialetheism is correct. The strategy involves showing that a group of sincere dialetheists (...) can, given an appropriately formed institution, bootstrap contradictions into existence. We discuss objections and consider the implications of this finding for debates over logic. (shrink)

The divine attributes of omniscience and omnipotence have faced objections to their very consistency. Such objections rely on reasoning parallel to semantic paradoxes such as the Liar or to set-theoretic paradoxes like Russell's paradox. With the advent of paraconsistent logics, dialetheism—the view that some contradictions are true—became a major player in the search for a solution to such paradoxes. This paper explores whether dialetheism, armed with the tools of paraconsistent logics, has the resources to respond to the objections levelled against (...) the divine attributes. (shrink)

ABSTRACT We critically review two extant paradigms for understanding the systematic interaction between modality and tense, as well as their respective modifications designed to do justice to the contingency of time’s structure and composition. We show that on either type of theory, as well as their respective modifications, some principles prove logically valid whose truth might sensibly be questioned on metaphysical grounds. These considerations lead us to devise a more general logical framework that allows accommodation of those metaphysical views that (...) its predecessors rule out by fiat. (shrink)

In 1986, Mikenberg et al. introduced the semantic notion of quasi-truth defined by means of partial structures. In such structures, the predicates are seen as triples of pairwise disjoint sets: the set of tuples which satisfies, does not satisfy and can satisfy or not the predicate, respectively. The syntactical counterpart of the logic of partial truth is a rather complicated first-order modal logic. In the present article, the notion of predicates as triples is recursively extended, in a natural way, to (...) any complex formula of the first-order object language. From this, a new definition of quasi-truth is obtained. The proof-theoretic counterpart of the new semantics is a first-order paraconsistent logic whose propositional base is a 3-valued logic belonging to hierarchy of paraconsistent logics known as Logics of Formal Inconsistency, which was proposed by Carnielli and Marcos in 2002. (shrink)

According to an influential contextualist solution to skepticism advanced by Keith DeRose, denials of skeptical hypotheses are, in most contexts, strong yet insensitive. The strength of such denials allows for knowledge of them, thus undermining skepticism, while the insensitivity of such denials explains our intuition that we do not know them. In this paper we argue that, under some well-motivated conditions, a negated skeptical hypothesis is strong only if it is sensitive. We also consider how a natural response on behalf (...) of DeRose appears to be equally available to his primary rival (viz., the sensitivity theorist). (shrink)

This paper presents a semantical analysis of the Weak Kleene Logics Kw3 and PWK from the tradition of Bochvar and Halldén. These are three-valued logics in which a formula takes the third value if at least one of its components does. The paper establishes two main results: a characterisation result for the relation of logical con- sequence in PWK – that is, we individuate necessary and sufficient conditions for a set.

The present paper focuses on Graham Priest’s claim that even primitive recursive relations may be inconsistent. Although he carefully presented his claim using the expression “may be,” Priest made a definite claim that even numerical equations can be inconsistent. His argument relies heavily on the fact that there is an inconsistent model for arithmetic. After summarizing Priest’s argument for the inconsistent primitive recursive relation, I first discuss the fact that his argument has a weak foundation to explain that the existence (...) of a model for some relations does not guarantee that they are primitive recursive. Moreover, since his identity relation is a combination of a standard identity and a congruence relation, it does not simply represent the standard identity function. Then, I argue that his identity relation cannot be both inconsistent and primitive recursive. Furthermore, I extend the argument to the general case that there is no inconsistent primitive recursive relation. These arguments show that the standard notions of “function” and “primitive recursive function” do not fit Priest’s inconsistent model. New definitions are necessary to show the existence of a dialetheic primitive recursive relation. (shrink)

One diagnosis of Fitch’s paradox of knowability is that it hinges on the factivity of knowledge: that which is known is true. Yet the apparent role of factivity and non-factive analogues in related paradoxes of justified belief can be shown to depend on familiar consistency and positive introspection principles. Rejecting arguments that the paradox hangs on an implausible consistency principle, this paper argues instead that the Fitch phenomenon is generated both in epistemic logic and logics of justification by the interaction (...) of analogues of the knowability principle and positive introspection theses that are characteristic of, even if not entailed by, epistemic internalism. (shrink)

In this paper we intend to outline an introduction to Situation Theory as an approach to the liar paradoxes. This idea was first presented by the work of Barwise and Etchemendy ). First we introduce the paradoxes in their most appealing and important versions. Second we show that non-classical approaches on the problem usually get puzzled by the revenge problem on one side and loss of expressive power on the other side. Last, we present Situation Theory and try to show (...) how it is capable of solving the old paradoxes and blocking revenge. The price we pay on this view is universality, since it would allow a new revenge situated liar. We don’t intend to address the problem of universality here, but we try at least to motivate the reader to make sense of this theory. (shrink)

This paper contributes to the study of paracompleteness and paraconsistency. We present two logics that address the following questions in novel ways. How can the paracomplete theorist characterize the formulas that defy excluded middle while maintaining that not all formulas are of this kind? How can the paraconsistent theorist characterize the formulas that obey explosion while still maintaining that there are some formulas not of this kind?

This note motivates a logic for a theory that can express its own notion of logical consequence—a ‘syntactically closed’ theory of naive validity. The main issue for such a logic is Curry’s paradox, which is averted by the failure of contraction. The logic features two related, but different, implication connectives. A Hilbert system is proposed that is complete and non-trivial.

Although “theory” has been the prevalent unit of analysis in the meta-study of science throughout most of the twentieth century, the concept remains elusive. I further explore the leitmotiv of several authors in this issue: that we should deal with theorizing (rather than theory) in biology as a cognitive activity that is to be investigated naturalistically. I first contrast how philosophers and biologists have tended to think about theory in the last century or so, and consider recent calls to upgrade (...) the role of theory in the life sciences against the background of the recent “data deluge” in molecular biology, systems biology, etc. I then review thinking about theory in biology in relation to physical theory as a positive or negative exemplar. I conclude by discussing various aspects of a positive program for “naturalizing theorizing.”. (shrink)

I here present and defend what I call the Triviality Theory of Truth, to be understood in analogy with Matti Eklund’s Inconsistency Theory of Truth. A specific formulation of is defended and compared with alternatives found in the literature. A number of objections against the proposed notion of meaning-constitutivity are discussed and held inconclusive. The main focus, however, is on the problem, discussed at length by Gupta and Belnap, that speakers do not accept epistemically neutral conclusions of Curry derivations. I (...) first argue that the facts about speakers’ reactions to such Curry derivations do not constitute a problem for the Triviality Theory specifically. Rather, they follow from independent, uncontroversial facts. I then propose a solution which coheres with the theory as I understand it. Finally, I consider a normative reading of their objection and offer a response. (shrink)

Guided by questions of scope, this paper provides an overview of what is known about both the scope and, consequently, the limits of Gödel’s famous first incompleteness theorem.