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)

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.

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.

In order to develop an account of scientific rationality, two problems need to be addressed: (i) how to make sense of episodes of theory change in science where the lack of a cumulative development is found, and (ii) how to accommodate cases of scientific change where lack of consistency is involved. In this paper, we sketch a model of scientific rationality that accommodates both problems. We first provide a framework within which it is possible to make sense of scientific revolutions, (...) but which still preserves some (partial) relations between old and new theories. The existence of these relations help to explain why the break between different theories is never too radical as to make it impossible for one to interpret the process in perfectly rational terms. We then defend the view that if scientific theories are taken to be quasi-true, and if the underlying logic is paraconsistent, it's perfectly rational for scientists and mathematicians to entertain inconsistent theories without triviality. As a result, as opposed to what is demanded by traditional approaches to rationality, it's not irrational to entertain inconsistent theories. Finally, we conclude the paper by arguing that the view advanced here provides a new way of thinking about the foundations of science. In particular, it extends in important respects both coherentist and foundationalist approaches to knowledge, without the troubles that plague traditional views of scientific rationality. (shrink)

Though the social world is real and objective, the way that social facts arise out of other facts is in an important way shaped by human thought, talk and behaviour. Building on recent work in social ontology, I describe a mechanism whereby this distinctive malleability of social facts, combined with the possibility of basic human error, makes it possible for a consistent physical reality to ground an inconsistent social reality. I explore various ways of resisting the prima facie case for (...) social inconsistency. I conclude, however, that the prima facie case survives scrutiny, and draw out some of the ramifications. (shrink)

Given any proposition, is it possible to have rationally acceptable attitudes towards it? Absent reasons to the contrary, one would probably think that this should be possible. In this paper I provide a reason to the contrary. There is a proposition such that, if one has any opinions about it at all, one will have a rationally unacceptable set of propositional attitudes—or if one doesn’t, one will end up being cognitively imperfect in some other manner. The proposition I am concerned (...) with is a self-referential propositional attitude ascription involving the propositional attitude of rejection. Given a basic assumption about what constitutes irrationality, and a few assumptions about the nature of cognitively ideal agents, a paradox results. This paradox is superficially like the Liar, but it is importantly different in that no alethic notions are involved at all. As such, it stands independent of the Liar and is not a ‘revenge’ version of it. After setting out the paradox I discuss possible responses. After considering several I argue that one is best off simply accepting that the paradox shows us something surprising and interesting about rationality: that some cognitive shortfall is unavoidable even for ideal agents. I argue that nothing disastrous follows from accepting this conclusion. (shrink)

I consider here several versions of finitism or conceptions that try to work around postulating sets of infinite size. Restricting oneself to the so-called potential infinite seems to rest either on temporal readings of infinity (or infinite series) or on anti-realistic background assumptions. Both these motivations may be considered problematic. Quine’s virtual set theory points out where strong assumptions of infinity enter into number theory, but is implicitly committed to infinity anyway. The approaches centring on the indefinitely large and the (...) use of schemata would provide a work-around to circumvent usage of actual infinities if we had a clear understanding of how schemata work and where to draw the conceptual line between the indefinitely large and the infinite. Neither of this seems to be clear enough. Versions of strict finitism in contrast provide a clear picture of a (realistic) finite number theory. One can recapture standard arithmetic without being committed to actual infinities. The major problem of them is their usage of a paraconsistent logic with an accompanying theory of inconsistent objects. If we are, however, already using a paraconsistent approach for other reasons (in semantics, epistemology or set theory), we get finitism for free. This strengthens the case for paraconsistency. (shrink)

I begin with an explication of "thought experiment". I then clarify the role that intuitions play in thought experiments by addressing two important issues: (1) the informativeness of thought experiments and (2) the legitimacy of the method of thought experiments in philosophy and the natural sciences. I defend a naturalistic account of intuitions that provides a plausible explanation of the informativeness of thought experiments, which, in turn, allows thought experiments to be reconstructed as arguments. I also specify criteria for distinguishing (...) bad "intuition pumps" from legitimate thought experiments. These criteria help us to avoid being seduced by the dangerous suggestive power of misleading intuitions. (shrink)

In a universal logic containing naive semantics the semantic antinomies will be provable. Although being provable they are not assertiblebecause of some pragmatic constraints on assertion I will argue for. Furthermore, since it is not acceptable that the thesis of dialethism is a dialethiaitself, what it would be according to naive semantics and the prefered logical systems of dialethism, a corresponding restriction on proof theory isnecessary.

The work of Luciano Floridi lies at the interface of philosophy, information science and technology, and ethics, an intersection whose existence and significance he was one of the first to establish. His closely related concepts of a philosophy of information (PI), informational structural realism, information logic (IL), and information ethics (IE) provide a new ontological perspective from which moral concerns can be addressed, especially but not limited to those arising in connection with the new information and communication technologies. In this (...) paper, I relate Floridi's approach to another novel perspective, namely, that of an extension of logic to complex real processes, including those of information production and transfer. This non-propositional, non-truth-functional logic (logic in reality (LIR)) is grounded in the fundamental dualism (dynamic opposition) inherent in energy and accordingly present at all levels of reality. The LIR description of the dynamics of processes and their evolution is relevant to what Floridi refers to as the possible non-linguistic aspects of information. It suggests answers to some of Floridi's “outstanding problems” in PI related to the ontological status of information and how it is used in cognition. Floridi's IL retains the formal structure of the doxastic and epistemic logics from which he correctly distinguishes it and is the basis for his conceptual PI. However, LIR fulfills Floridi's implied requirement that logic be regarded as a natural phenomenon dealing with other natural phenomena, recovering its original philosophical function. LIR provides a logical foundation for discussion of ethical questions based on kinds of information that complements IL. Both are reconsiderations of logic that, as Marijuan suggests, may be necessary for the advancement of information technology in an ethical direction (cf. also Brenner). IE focuses on entities as constituted by information in an overall strategy that generalizes the concept of moral agents. LIR and its related ontology naturalize critical aspects of Floridi's theses, especially, the moral value of being as such and a non-separable joint responsibility of individuals and groups. I compare IE to other current approaches to ethics and information technology (e.g., phenomenological and social constructivist). Ethical information is defined “ecologically” in process terms as reality in a physical space (cf. Floridi), with an intentional “valence,” positive and negative, in the morally valued interaction between producer and receiver. LIR is neither topic-neutral nor context independent and can support an ethics involving apparently contradictory perspectives (e.g., internalist and externalist). Ethics involves practical reasoning, and unlike standard logics, LIR supports Magnani's approach to abductive reasoning in rational moral decision making. The basis of moral responsibility and the consequent behavior of individuals involved in information and communications technologies is the same logical–metaphysical principle of dynamic opposition instantiated at other levels of reality. The way moral responsibilities are actively accepted (or not) by individuals supervenes on their primitive psychological structure, which in turn reflects an evolutionary development grounded in the fundamental dualism of the physical world. The paper concludes with some suggestions of areas of philosophical research, such as causality, identity, and the ontological turn, where convergence of the Floridi and LIR approaches might be envisaged. Their overall motivation is the same, namely, the development of strategies for reinforcing and increasing ethical sensitivity wherever possible. The ethical information concept outlined in the paper supports the function of IE, assigned to it by Floridi, of potentially determining what is right and what is wrong. (shrink)

According to David Lewis, the argument from temporary intrinsics is ‘the principal and decisive objection against endurance’. I focus on eternalist endurantism, discussing three different ways the eternalist endurantist can try to avoid treating temporary intrinsics as relational. Two of them, generally known as ‘adverbialism’ and ‘SOFism’, are familiar and controversial. I scrutinize them and argue that Lewis’ scepticism about them is well founded. Then, I sketch a further, to some extent new, version of eternalist endurantism, where the key idea (...) is that intrinsic monadic properties had simpliciter by objects are eternal, time-transcendent properties in Fine’s sense, i.e., properties had by objects regardless of time. Eternal properties of an object are ipso facto sempiternal. When something is P at one time and not P at another, it is radically indeterminate whether it is P simpliciter or not. I argue that an account along these lines is better placed to treat intrinsic monadic properties of changing objects than any other known alternatives insofar as it recognizes that something is P simpliciter ; it is able to account for x’s being P at a time in terms of something’s being P simpliciter; it has an answer to the question ‘is \ simpliciter?’ when x is P at one time and not P at another. I conclude that endurantism is no less at ease with intrinsics than perdurantism is. (shrink)

There are two no-change objections that can be raised against the B-theory of time. One stems from the observation that in a B-theoretic scenario changes of determinations can only be represented by propositions which have eternal truth values. The other derives from the principle that nothing can vary over a period of time if it doesn’t instantiate a state of change at all the instants of time which compose it. Here I argue that both objections apply to all comparative conceptions (...) of change, regardless of whether they take tense seriously or not. It follows that, contrary to what is widely believed, A-theoretic accounts of time are not immune to no-change objections, just in virtue of being realist about tense. A-theorists must either accept the conclusion that time, according to their account, does not flow, or put forward an account of flow that is not comparative. A number of difficulties with both of these options are discussed. (shrink)

I provide an interpretation of Wittgenstein's much criticized remarks on Gödel's First Incompleteness Theorem in the light of paraconsistent arithmetics: in taking Gödel's proof as a paradoxical derivation, Wittgenstein was right, given his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. I show that the models of paraconsistent arithmetics (obtained via the Meyer-Mortensen (...) collapsing filter on the standard model) match with many intuitions underlying Wittgensteins philosophy of mathematics, such as its strict finitism and the insistence on the decidability of any meaningful mathematical question. (shrink)

I present a possible worlds semantics for a hyperintensional belief revision operator, which reduces the logical idealization of cognitive agents affecting similar operators in doxastic and epistemic logics, as well as in standard AGM belief revision theory. (Revised) belief states are not closed under classical logical consequence; revising by inconsistent information does not perforce lead to trivialization; and revision can be subject to ‘framing effects’: logically or necessarily equivalent contents can lead to different revisions. Such results are obtained without resorting (...) to non-classical logics, or to non-normal or impossible worlds semantics. The framework combines, instead, a standard semantics for propositional S5 with a simple mereology of contents. (shrink)

I want to model a finite, fallible cognitive agent who imagines that p in the sense of mentally representing a scenario—a configuration of objects and properties—correctly described by p. I propose to capture imagination, so understood, via variably strict world quantifiers, in a modal framework including both possible and so-called impossible worlds. The latter secure lack of classical logical closure for the relevant mental states, while the variability of strictness captures how the agent imports information from actuality in the imagined (...) non-actual scenarios. Imagination turns out to be highly hyperintensional, but not logically anarchic. Section 1 sets the stage and impossible worlds are quickly introduced in Sect. 2. Section 3 proposes to model imagination via variably strict world quantifiers. Section 4 introduces the formal semantics. Section 5 argues that imagination has a minimal mereological structure validating some logical inferences. Section 6 deals with how imagination under-determines the represented contents. Section 7 proposes additional constraints on the semantics, validating further inferences. Section 8 describes some welcome invalidities. Section 9 examines the effects of importing false beliefs into the imagined scenarios. Finally, Sect. 10 hints at possible developments of the theory in the direction of two-dimensional semantics. (shrink)

In his famous work on vagueness, Russell named “fallacy of verbalism” the fallacy that consists in mistaking the properties of words for the properties of things. In this paper, I examine two (clusters of) mainstream paraconsistent logical theories – the non-adjunctive and relevant approaches –, and show that, if they are given a strongly paraconsistent or dialetheic reading, the charge of committing the Russellian Fallacy can be raised against them in a sophisticated way, by appealing to the intuitive reading of (...) their underlying semantics. The meaning of “intuitive reading” is clarified by exploiting a well-established distinction between pure and applied semantics. If the proposed arguments go through, the dialetheist or strong paraconsistentist faces the following Dilemma: either she must withdraw her claim to have exhibited true contradictions in a metaphysically robust sense – therefore, inconsistent objects and/or states of affairs that make those contradictions true; or she has to give up realism on truth, and embrace some form of anti-realistic (idealistic, or broadly constructivist) metaphysics. Sticking to the second horn of the Dilemma, though, appears to be promising: it could lead to a collapse of the very distinction, commonly held in the literature, between a weak and a strong form of paraconsistency – and this could be a welcome result for a dialetheist. (shrink)

Philosophical dialetheism, whose main exponent is Graham Priest, claims that some contradictions hold, are true, and it is rational to accept and assert them. Such a position is naturally portrayed as a challenge to the Law of Non-Contradiction (LNC). But all the classic formulations of the LNC are, in a sense, not questioned by a typical dialetheist, since she is (cheerfully) required to accept them by her own theory. The goal of this paper is to develop a formulation of the (...) Law which appears to be unquestionable, in the sense that the Priestian dialetheist is committed to accept it without also accepting something inconsistent with it, on pain of trivialism—that is to say, on pain of lapsing into the position according to which everything is the case. This will be achieved via (a) a discussion of Priest's dialetheic treatment of the notions of rejection and denial; and (b) the characterization of a negation via the primitive intuition of content exclusion. Such a result will not constitute a cheap victory for the friends of consistency. We may just learn that different things have been historically conflated under the label of 'Law of Non-Contradiction'; that dialetheists rightly attack some formulations of the Law, and orthodox logicians and philosophers have been mistaken in assimilating them to the indisputable one. (shrink)

I propose a comprehensive account of negation as a modal operator, vindicating a moderate logical pluralism. Negation is taken as a quantifier on worlds, restricted by an accessibility relation encoding the basic concept of compatibility. This latter captures the core meaning of the operator. While some candidate negations are then ruled out as violating plausible constraints on compatibility, different specifications of the notion of world support different logical conducts for negations. The approach unifies in a philosophically motivated picture the following (...) results: nothing can be called a negation properly if it does not satisfy Contraposition and Double Negation Introduction; the pair consisting of two split or Galois negations encodes a distinction without a difference; some paraconsistent negations also fail to count as real negations, but others may; intuitionistic negation qualifies as real negation, and classical Boolean negation does as well, to the extent that constructivist and paraconsistent doubts on it do not turn on the basic concept of compatibility but rather on the interpretation of worlds. (shrink)

Is there a notion of contradiction—let us call it, for dramatic effect, “absolute”—making all contradictions, so understood, unacceptable also for dialetheists? It is argued in this paper that there is, and that spelling it out brings some theoretical benefits. First it gives us a foothold on undisputed ground in the methodologically difficult debate on dialetheism. Second, we can use it to express, without begging questions, the disagreement between dialetheists and their rivals on the nature of truth. Third, dialetheism has an (...) operator allowing it, against the opinion of many critics, to rule things out and manifest disagreement: for unlike other proposed exclusion-expressing-devices (for instance, the entailment of triviality), the operator used to formulate the notion of absolute contradiction appears to be immune both from crippling expressive limitations and from revenge paradoxes—pending a rigorous nontriviality proof for a formal dialetheic theory including it. (shrink)

We present the inconsistency-adaptive deontic logic DP r , a nonmonotonic logic for dealing with conflicts between normative statements. On the one hand, this logic does not lead to explosion in view of normative conflicts such as O A ∧ O ∼A, O A ∧ P ∼A or even O A ∧ ∼O A. On the other hand, DP r still verifies all intuitively reliable inferences valid in Standard Deontic Logic (SDL). DP r interprets a given premise set ‘as normally (...) as possible’ with respect to SDL. Whereas some SDL-rules are verified unconditionally by DP r , others are verified conditionally. The latter are applicable unless they rely on formulas that turn out to behave inconsistently in view of the premises. This dynamic process is mirrored by the proof theory of DP r. (shrink)

The study of truth is often seen as running on two separate paths: the nature path and the logic path. The former concerns metaphysical questions about the ‘nature’, if any, of truth. The latter concerns itself largely with logic, particularly logical issues arising from the truth-theoretic paradoxes. Where, if at all, do these two paths meet? It may seem, and it is all too often assumed, that they do not meet, or at best touch in only incidental ways. It is (...) often assumed that work on the metaphysics of truth need not pay much attention to issues of paradox and logic; and it is likewise assumed that work on paradox is independent of the larger issues of metaphysics. Philosophical work on truth often includes a footnote anticipating some resolution of the paradox, but otherwise tends to take no note of it. Likewise, logical work on truth tends to have little to say about metaphysical presuppositions, and simply articulates formal theories, whose strength may be measured, and whose properties may be discussed. In practice, the paths go their own ways. Our aim in this paper is somewhat modest. We seek to illustrate one point of intersection between the paths. Even so, our aim is not completely modest, as the point of intersection is a notable one that often goes unnoticed. We argue that the ‘nature’ path impacts the logic path in a fairly direct way. What one can and must say about the logic of truth is influenced, or even in some cases determined, by what one says about the metaphysical nature of truth. In particular, when it comes to saying what the well-known Liar paradox teaches us about truth, background conceptions — views on ‘nature’ — play a significant role in constraining what can be said. This paper, in rough outline, first sets out some representative ‘nature’ views, followed by the ‘logic’ issues (viz., paradox), and turns to responses to the Liar paradox. What we hope to illustrate is the fairly direct way in which the background ‘nature’ views constrain — if not dictate — responses to the main problem on the ‘logic’ path.. (shrink)

In this paper, we distinguish two versions of Curry's paradox: c-Curry, the standard conditional-Curry paradox, and v-Curry, a validity-involving version of Curry's paradox that isn’t automatically solved by solving c-curry. A unified treatment of curry paradox thus calls for a unified treatment of both c-Curry and v-Curry. If, as is often thought, c-Curry paradox is to be solved via non-classical logic, then v-Curry may require a lesson about the structure—indeed, the substructure—of the validity relation itself.

The paper reviews a number of approaches for handling restricted quantification in relevant logic, and proposes a novel one. This proceeds by introducing a novel kind of enthymematic conditional.

Mark Balaguer argues for full blooded platonism (FBP), and argues that FBP alone can solve Benacerraf's familiar epistemic challenge. I note that if FBP really can solve Benacerraf's epistemic challenge, then FBP is not alone in its capacity so to solve; RFBP—really full blooded platonism—can do the trick just as well, where RFBP differs from FBP by allowing entities from inconsistent mathematics. I also argue briefly that there is positive reason for endorsing RFBP.

In his “Deep Inconsistency?” Eklund attacks arguments to the effect that some contradictions are true, and especially those based on the liar paradox, to be found in Priest’ In Contradiction. The point of this paper is to evaluate his case.

Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, a (...) position which has profound implications for many linguists as well as for philosophers. We should not search for one true logic, since there are many. (shrink)

Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, a (...) position which has profound implications for many linguists as well as for philosophers. We should not search for one true logic, since there are many. (shrink)

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