The article is an extended critical discussion of Kevin Scharp’s Replacing Truth. Scharp’s case for the claim that the concept of truth is inconsistent is criticized, and so is his case for the claim that the concept of truth must be replaced because of its inconsistency.

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)

Plato’s view on pleasure in the Republic emerges in the course of developing the third proof of his central thesis that the just man is happier than the unjust. Plato presents it as the “greatest and most decisive” proof of his central thesis, so one might expect to find an abundance of scholarly work on it. Paradoxically, however, this argument has received little attention from scholars, and what has been written on it has generally been harshly critical. I believe that (...) this treatment of the argument has been unfair and that the relevant passages deserve a more careful and charitable interpretation. In this paper, I take up two serious charges that scholars have leveled against this proof, that it is inconsistent and that it involves a “fatal ambiguity”. I show that these charges result from misinterpreting Plato’s text, and I offer an alternative interpretation of the relevant passages. In doing so, I hope to shed some light on the complexities involved in Plato’s unappreciated third proof. (shrink)

In order to reason in a non-trivializing way with contradictions, para- consistent logics reject some classically valid inferences. As a way of re- covering some of these inferences, Graham Priest ([Priest, 1991]) proposed to nonmonotonically strengthen the Logic of Paradox by allowing the se- lection of “less inconsistent” models via a comparison of their respective inconsistent parts. This move recaptures a good portion of classical logic in that it does not block, e.g., disjunctive syllogism, unless it is applied to contradictory (...) assumptions. In Priest’s approach the inconsistent parts of models are compared in an extensional way by considering their inconsis- tent objects. This distinguishes his system from the standard format of (inconsistency-)adaptive logics pioneered by Diderik Batens, according to which (atomic) contradictions validated in models form the basis of their comparison. A well-known problem for Priest’s extensional approach is its lack of the Strong Reassurance property, i.e., for specific settings there may be infinitely descending chains of less and less inconsistent models, thus never reaching a minimally inconsistent model. In this paper, we demonstrate that Strong Reassurance holds for the extensional approach under a cardinality-based comparison of the incon- sistent parts of models. Furthermore, we introduce and investigate the metatheory of the class of first-order nonmonotonic inconsistency-tolerant construct over the extensional or quantitative comparisons of their respec- tive models. Core model-theoretic properties for these logics, such as the Löwenheim-Skolem theorems, along with other nonmonotonic properties, are further studied. (shrink)

Opponents of abortion are commonly said to be inconsistent in their beliefs or actions, and to fail in their obligations to prevent the deaths of embryos and fetuses from causes other than induced...

The Uniform Determination of Death Act (UDDA) provides that “an individual who has sustained either (1) irreversible cessation of circulatory and respiratory functions or (2) irreversible cessation of all functions of the entire brain, including the brain stem, is dead.” We show that the UDDA contains two conflicting interpretations of the phrase “cessation of functions.” By one interpretation, what matters for the determination of death is the cessation of spontaneous functions only, regardless of their generation by artificial means. By the (...) other, what matters is the cessation of both spontaneous and artificially supported functions. Because each UDDA criterion uses a different interpretation, the law is conceptually inconsistent. A single consistent interpretation would lead to the conclusion that conscious individuals whose respiratory and circulatory functions are artificially supported are actually dead, or that individuals whose brain is entirely and irreversibly destroyed may be alive. We explore solutions to mitigate the inconsistency. (shrink)

During multiple testing, researchers often adjust their alpha level to control the familywise error rate for a statistical inference about a joint union alternative hypothesis (e.g., “H1,1 or H1,2”). However, in some cases, they do not make this inference. Instead, they make separate inferences about each of the individual hypotheses that comprise the joint hypothesis (e.g., H1,1 and H1,2). For example, a researcher might use a Bonferroni correction to adjust their alpha level from the conventional level of 0.050 to 0.025 (...) when testing H1,1 and H1,2, find a significant result for H1,1 (p < 0.025) and not for H1,2 (p > .0.025), and so claim support for H1,1 and not for H1,2. However, these separate individual inferences do not require an alpha adjustment. Only a statistical inference about the union alternative hypothesis “H1,1 or H1,2” requires an alpha adjustment because it is based on “at least one” significant result among the two tests, and so it refers to the familywise error rate. Hence, an inconsistent correction occurs when a researcher corrects their alpha level during multiple testing but does not make an inference about a union alternative hypothesis. In the present article, I discuss this inconsistent correction problem, including its reduction in statistical power for tests of individual hypotheses and its potential causes vis-à-vis error rate confusions and the alpha adjustment ritual. I also provide three illustrations of inconsistent corrections from recent psychology studies. I conclude that inconsistent corrections represent a symptom of statisticism, and I call for a more nuanced inference-based approach to multiple testing corrections. (shrink)

This paper introduces new logical systems which axiomatize a formal representation of inconsistency (here taken to be equivalent to contradictoriness) in classical logic. We start from an intuitive semantical account of inconsistent data, fixing some basic requirements, and provide two distinct sound and complete axiomatics for such semantics, LFI1 and LFI2, as well as their first-order extensions, LFI1* and LFI2*, depending on which additional requirements are considered. These formal systems are examples of what we dub Logics of Formal (...) class='Hi'>Inconsistency (LFI) and form part of a much larger family of similar logics. We also show that there are translations from classical and paraconsistent first-order logics into LFI1* and LFI2*, and back. Hence, despite their status as subsystems of classical logic, LFI1* and LFI2* can codify any classical or paraconsistent reasoning. (shrink)

The badness of having conflicting emotions is a familiar theme in academic ethics, clinical psychology, and commercial self-help, where emotional harmony is often put forward as an ideal. Many philosophers give emotional harmony pride of place in their theories of practical reason.1 Here we offer a defense of a particular species of emotional conflict, namely, ambivalence. We articulate an conception of ambivalence, on which ambivalence is unresolved inconsistent desire (§1) and present a case of appropriate ambivalence (§2), before considering two (...) alternative defenses of emotional conflict (§3). We then argue that inconsistent desires can be fitting (§4) and that it can be reasonable not to resolve inconsistent desires (§5), before considering an objection (§6) and concluding the discussion (§7). (shrink)

The paper discusses the Inconsistency Theory of Truth (IT), the view that “true” is inconsistent in the sense that its meaning-constitutive principles include all instances of the truth-schema (T). It argues that (IT) entails that anyone using “true” in its ordinary sense is committed to all the (T)-instances and that any theory in which “true” is used in that sense entails the (T)-instances (which, given classical logic, entail contradictions). More specifically, I argue that theorists are committed to the meaning-constitutive (...) principles of logical constants, relative to the interpretation they intend thereof (e.g., classical), and that theories containing logical constants entail those principles. Further, I argue, since there is no relevant difference from the case of “true”, inconsistency theorists’ uses of “true” commit them to the (T)-instances. Adherents of (IT) are recommended, as a consequence, to eschew the truth-predicate. I also criticise Matti Eklund’s account of how the semantic value of “true” is determined, which can be taken as an attempt to show how “true” can be consistently used, despite being inconsistent. (shrink)

Direct reference theory faces serious prima facie counterexamples which must be explained away (e.g., that it is possible to know a priori that Hesperus = Phosphorus). This is done by means of various forms of pragmatic explanation. But when those explanations that provisionally succeed are generalized to deal with analogous prima facie counterexamples concerning the identity of propositions, a fatal dilemma results. Either identity must be treated as a four-place relation (contradicting what just about everyone, including direct reference theorists, takes (...) to be essential to identity). Or direct reference theorists must incorporate a view that was rejected in pretty much our first lesson about identity—namely, that Hesperus at twilight is not identical to Hesperus at dawn. One way of the other, the direct reference theory is thus inconsistent with basic principles concerning the logic of identity, which nearly everyone, including direct reference theorists, take as starting points. (shrink)

Inferentialists about scientific representation hold that an apparatus’s representing a target system consists in the apparatus allowing “surrogative inferences” about the target. I argue that a serious problem for inferentialism arises from the fact that many scientific theories and models contain internal inconsistencies. Inferentialism, left unamended, implies that inconsistent scientific models have unlimited representational power, since an inconsistency permits any conclusion to be inferred. I consider a number of ways that inferentialists can respond to this challenge before suggesting my (...) own solution. I develop an analogy to exploitable glitches in a game. Even though inconsistent representational apparatuses may in some sense allow for contradictions to be generated within them, doing so violates the intended function of the apparatus’s parts and hence violates representational “gameplay.”. (shrink)

In the article ”Inconsistency of N from a not-finitist point of view” we have shown the inconsistency of N, going through a denial. Here we delete this indirect step and essentially repeat the same proof. Contextually we find a contradiction about natural number definition. Then we discuss around the rejection of infinity.

This dissertation has two main goals. The first is to provide a practice-based analysis of the field of inconsistent mathematics: what motivates it? what role does logic have in it? what distinguishes it from classical mathematics? is it alternative or revolutionary? The second goal is to introduce and defend a new conception of inconsistent mathematics - queer incomaths - as a particularly effective answer to feminist critiques of classical logic and mathematics. This sets the stage for a genuine revolution in (...) mathematics, insofar as it suggests the need for a shift in mainstream attitudes about the role of logic and ethics in the practice of mathematics. (shrink)

This paper demonstrates that there is an inconsistency in functionalism in psychology and philosophy of mind. Analogous inconsistencies can be expected in functionalisms in biology and social theory. (edited).

How do opinion diversity and belief polarisation affect epistemic group decision-making, particularly if decisions must be made without delay and on the basis of permissive evidence? In an agent-based model, we track the consistency of group opinions aggregated through sentence-wise majority voting. Simulations on the model reveal that high opinion diversity, but not polarisation, incurs a significant inconsistency risk. These results indicate that epistemic group decisions based on permissive evidence can be particularly difficult for diverse groups. The results also (...) improve our understanding of what can reasonably be expected of expert groups, and where expert advice might have limits. (shrink)

A contradiction is obtained, considering the axiom of infinity, then ℕ and Peano axioms, together a list of ℕ subsets and with inclusion relation and union operation. Natural numbers constitute an infinite set, ℕ, but we show the union of its proper subsets, with a specific form, isn’t an infinite set. Also we get a simpler explanation and a symbolic representation. Lastly, inconsistency of Peano successor axiom is a consequence of rejecting infinity.

One of the most expected properties of a logical system is that it can be algebraizable, in the sense that an algebraic counterpart of the deductive machinery could be found. Since the inception of da Costa's paraconsistent calculi, an algebraic equivalent for such systems have been searched. It is known that these systems are non self-extensional (i.e., they do not satisfy the replacement property). More than this, they are not algebraizable in the sense of Blok-Pigozzi. The same negative results hold (...) for several systems of the hierarchy of paraconsistent logics known as Logics of Formal Inconsistency (LFIs). Because of this, these logics are uniquely characterized by semantics of non-deterministic kind. This paper offers a solution for two open problems in the domain of paraconsistency, in particular connected to algebraization of LFIs, by obtaining several LFIs weaker than C1, each of one is algebraizable in the standard Lindenbaum-Tarski's sense by a suitable variety of Boolean algebras extended with operators. This means that such LFIs satisfy the replacement property. The weakest LFI satisfying replacement presented here is called RmbC, which is obtained from the basic LFI called mbC. Some axiomatic extensions of RmbC are also studied, and in addition a neighborhood semantics is defined for such systems. It is shown that RmbC can be defined within the minimal bimodal non-normal logic E+E defined by the fusion of the non-normal modal logic E with itself. Finally, the framework is extended to first-order languages. RQmbC, the quantified extension of RmbC, is shown to be sound and complete w.r.t. BALFI semantics. (shrink)

Several authors maintain that we are capable of having inconsistent intentional states, either in cases of illusion, in certain cases of imagination, or because the observable world is (partly) inconsistent and we perceive it as such. These views are all premised on the assumption that inconsistent intentional states—even if acknowledged—are peculiar and have nothing essential to do with our perceptual capacities. In the present article, I would like to present, and argue for, a much stronger thesis: that inconsistent intentional states (...) underlie the possibility of having intentional content in mind. I argue for this thesis based on a Husserlian phenomenological analysis of our grasp of objects, which I formulate in terms of incompatibility semantics. (shrink)

The problem of how to accommodate inconsistencies has attracted quite a number of researchers, in particular, in the area of database theory. The problem is also of concern in the study of belief change. For inconsistent beliefs are ubiquitous. However, comparatively little work has been devoted to discussing the problem in the literature of belief change. In this paper, I examine how adequate the AGM theory is as a logical framework for belief change involving inconsistencies. The technique is to apply (...) to Grove’s sphere system, a semantical representation of the AGM theory, logics that do not infer everything from contradictory premises, viz., paraconsistent logics. I use three paraconsistent logics and discuss three sphere systems that are based on them. I then examine the completeness of the postulates of the AGM theory with respect to the systems. At the end, I discuss some philosophical implications of the examination. (shrink)

We propose a theoretical model to explain the usage of time-inconsistent behavior as a strategy to exploit others when reputation and trust have secondary effects on the economic outcome. We consider two agents with time-consistent preferences exploiting common resources. Supposing that an agent is believed to have time-inconsistent preferences with probability p, we analyze whether she uses this misinformation when she has the opportunity to use it. Using the model originally provided by Levhari and Mirman (Bell J Econ 11(1):322–334, 1980), (...) we determine the optimal degree of present bias that the agent would like to have while pretending to have time-inconsistent preferences and we provide the range of present-bias parameter under which deceiving is optimal. Moreover, by allowing the constant relative risk aversion class of utility form, we characterize the distinction between pretending to be naive and sophisticated. (shrink)

I argue that William Craig’s defence of the moral argument is internally inconsistent. In the course of defending the moral argument, Craig criticizes non-theistic moral realism on the grounds that it posits the existence of certain logically necessary connections but fails to provide an adequate account of why such connections hold. Another component of Craig’s defence of the moral argument is an endorsement of a particular version of the divine command theory. Craig’s version of DCT posits certain logically necessary connections (...) but Craig fails to provide an adequate account of why these connections hold. Thus, Craig’s critique of non-theistic moral realism is at odds with his DCT. Since the critique and DCT are both essential elements of his defence of the moral argument, that defence is internally inconsistent. (shrink)

Opponents of abortion are often described as ‘inconsistent’ (hypocrites) in terms of their beliefs, actions and/or priorities. They are alleged to do too little to combat spontaneous abortion, they should be adopting cryopreserved embryos with greater frequency and so on. These types of arguments—which we call ‘inconsistency arguments’—conform to a common pattern. Each specifies what consistent opponents of abortion would do (or believe), asserts that they fail to act (or believe) accordingly and concludes that they are inconsistent. Here, we (...) show that inconsistency arguments fail en masse. In short, inconsistency arguments typically face four problems. First, they usually fail to account for diversity among opponents of abortion. Second, they rely on inferences about consistency based on isolated beliefs shared by some opponents of abortion (and these inferences often do not survive once we consider other beliefs opponents of abortion tend to hold). Third, inconsistency arguments usually ignore the diverse ways in which opponents of abortion might act on their beliefs. Fourth, inconsistency arguments criticise groups of people without threatening their beliefs (eg, that abortion is immoral). Setting these problems aside, even supposing inconsistency arguments are successful, they hardly matter. In fact, in the two best-case scenarios—where inconsistency arguments succeed—they either encourage millions of people to make the world a (much) worse place (from the critic’s perspective) or promote epistemically and morally irresponsible practices. We conclude that a more valuable discussion would be had by focusing on the arguments made by opponents of abortion rather than opponents themselves. (shrink)

In different papers, David Liggins and Chris Daly tell philosophers what they should not do. There is no sign of them withdrawing any of these prohibitions, but I show that they fail to be consistent when asserting them. The inconsistency concerns when a philosopher should defer to the empirical findings of science.

This chapter argues that the distinction between ambitious and modest transcendental arguments, developed and deployed by various authors in the wake of Stroud’s influential critique of transcendental reasoning, may be pointless when applied to transcendental arguments from performative inconsistency that have moral statements as their conclusions. If moral truth is assertorically constrained, then any modest moral transcendental argument from performative inconsistency can be converted into an ambitious moral transcendental argument. The chapter provides an account of performative inconsistency (...) and suggests an alternative to the widespread reading of transcendental conditionals in terms of an ‘if-then’-sentences whose antecedents express a proposition to the effect that some x is possible and whose consequents express a statement to the effect that some y is actual. (shrink)

In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes. In this paper I show that a number of logics are susceptible to a strengthened version of Curry's paradox. This can be adapted to provide a proof theoretic analysis of the omega-inconsistency in Lukasiewicz's continuum valued logic, allowing us to better evaluate which logics are suitable for a naïve truth theory. On this basis I identify two natural subsystems of Lukasiewicz logic which individually, (...) but not jointly, lack the problematic feature. (shrink)

Mark Schroeder has argued that all reasonable forms of inconsistency of attitude consist of having the same attitude type towards a pair of inconsistent contents (A-type inconsistency). We suggest that he is mistaken in this, offering a number of intuitive examples of pairs of distinct attitudes types with consistent contents which are intuitively inconsistent (B-type inconsistency). We further argue that, despite the virtues of Schroeder's elegant A-type expressivist semantics, B-type inconsistency is in many ways the more (...) natural choice in developing an expressivist account of moral discourse. We close by showing how to adapt ordinary formality-based accounts of logicality to define a B-type account of logical inconsistency and distinguish it from both semantic and pragmatic inconsistency. In sum, we provide a roadmap of how to develop a successful B-type expressivism. (shrink)

In this article we derived an important example of the inconsistent countable set in second order ZFC (ZFC_2) with the full second-order semantics. Main results: (i) :~Con(ZFC2_); (ii) let k be an inaccessible cardinal, V is an standard model of ZFC (ZFC_2) and H_k is a set of all sets having hereditary size less then k; then : ~Con(ZFC + E(V)(V = Hk)):.

If a subject’s belief system is inconsistent, does it follow that the subject’s beliefs (all of them) are unjustified? It seems not. But, coherentist theories of justification (at least some of them) imply otherwise, and so, it seems, are open to counterexample. This is the “Problem of Justified Inconsistent Beliefs”. I examine two main versions of the Problem of Justified Inconsistent Beliefs, and argue that coherentists can give at least a promising line of response to each of them.

This paper deals with a relatively recent trend in the history of analytic philosophy, philosophical logic, and theory of science: the philosophical study of the role of inconsistency in empirical science. This paper is divided in three sections that correspond to the three types of inconsistencies identified: (i) factual, occurring between theory and observations, (ii) external, occurring between two mutually contradictory theories, and (iii) internal, characterising theories that entail mutually contradictory statements.

The most pressing difficulty coherentism faces is, I believe, the problem of justified inconsistent beliefs. In a nutshell, there are cases in which our beliefs appear to be both fully rational and justified, and yet the contents of the beliefs are inconsistent, often knowingly so. This fact contradicts the seemingly obvious idea that a minimal requirement for coherence is logical consistency. Here, I present a solution to one version of this problem.

I propose that an irreducible property of physical space — consistency — is the origin of logic. I propose that an inconsistent space is inconceivable and that this inconceivability can be recognized as the force behind logical propositions. The implications of this argument are briefly explored and then applied to address two paradoxes: Zeno of Elea’s paradox regarding the race between Achilles and the Tortoise, and Lewis Carroll’s paradox regarding the Tortoise’s conversation with Achilles after the race. I conclude that (...) Achilles would have won on both accounts, in the race and the argument, by invoking the consistency of space as the foundation of both movement across space and logical argument. (shrink)

Presentists argue that only present entities exist absolutely and unrestrictedly. Presentism, which itself is a temporal analog of the modal doctrine of actualism, is an ontological idea about time and existence against theories such as eternalism, possibilism, and growing block theory. Thus, presentists deny the existence of atemporal or timeless entities and describe presentism as a version of the (A-theory), which makes a difference between present, past, and future. Also, presentists are not able to ontologically, justify the existence of some (...) entities such as Socrates and the year 3000 in the past and the future and the relations involving non-present objects like ‘Abraham Lincoln was taller than Napoleon Bonaparte’. However, presentism is altered via the addition of an abstract four-dimensional manifold of ersatz time, which is a type of (B-theory) series, to identify all ontological entities and justify the dynamic world. This inquiry is an attempt to put a completely different perspective on presentism and, the result obtained that despite the new conceptualization of time, there is an inconsistency between time and being in presentism. Therefore, presentists have failed to determine the ontological identification of cross-temporal relations, reference and propositions, and truth-makers. Also, whatever the final outcome of the debate between presentism and other views is significantly eternalism, according to ersatz presentism, it is hard to make sense of the idea that things change from one moment to the next. (shrink)

The existential insecurity of human beings has induced them to create protective spheres of symbols: myths, religions, values, belief systems, theories, etc. Rationality is one of the key factors contributing to the construction of civilisation in technical and symbolic terms. As Hankiss (2001) has emphasised, protective spheres of symbols may collapse – thus causing a profound social crisis. Social and political transformations had a tremendous impact at the end of the 20th century. As a result, management theories have been revised (...) in order to deal with transition and uncertainty. Francis Fukuyama's (2000) approach is supportive of hierarchical organisation as the best solution when facing a 'disruption'. The notion of Homo Hierarchicus has been based on, allegedly, rational presumptions. This paper contributes to the discussion on hierarchy within contemporary organisations. It criticises so-called 'natural' and 'rational' necessities justifying hierarchy. A key issue identified by the paper is the formalisation of language in claiming value-free knowledge and 'detached' observation as the basis for neutral rationality and aspired efficiency. This should be seriously reconsidered as hindering rather than aiding understanding of social complexity. All in all, Homo Hierarchicus appears to be misleading rather than helping symbolic sphere or construct. (shrink)

An important strand in philosophy of science takes scientific explanation to consist in the conveyance of some kind of information. Here I argue that this idea is also implicit in some core arguments of mechanists, some of whom are proponents of an ontic conception of explanation that might be thought inconsistent with it. However, informational accounts seem to conflict with some lay and scientific commonsense judgments and a central goal of the theory of explanation, because information is relative to the (...) background knowledge of agents. Sometimes we make lay judgments about whether a model is an explanation simpliciter, not just an explanation relative to some particular agent. And as philosophers of explanation, we would like a philosophical account to tell us when a model is an explanation simpliciter, not just when a model is an explanation relative to some particular agent. Thus, even if one’s account of explanation is not concerned with explanation qua communicative or speech act, the account’s reliance on the concept of information generates a prima facie conflict between the claims that 1) explanation is the conveyance of information, 2) information is relative to the background knowledge of an agent, and 3) some models are explanations not relative to the background knowledge of any particular agent. I sketch a solution to this puzzle by distinguishing informationally what I call “explanation simpliciter” from what I call “explanation-to,” relativizing the latter to an individual’s background knowledge and the former to what I call “total scientific background knowledge”. (shrink)

This paper challenges Francis Hutcheson's and John Clarke of Hull's alleged demonstrations that William Wollaston's moral theory is inconsistent. It also present a form of the inconsistency objection that fares better than theirs, namely, that of Thomas Bott (1688-1754). Ultimately, the paper shows that Wollaston's moral standard is not what some have thought it to be; that consequently, his philosophy withstands the best-known efforts to expose it as inconsistent; and further, that one of the least-known British moralists is more (...) important than hitherto thought, in that he uncovers the inconsistency Clarke and Hutcheson try in vain to elicit. (shrink)

According to what I call the ‘argument from public bads’, if a researcher deceived subjects in the past, there is a chance that subjects will discount the information that a subsequent researcher provides, thus compromising the validity of the subsequent researcher’s experiment. While this argument is taken to justify an existing informal ban on explicit deception in experimental economics, it can also apply to implicit deception, yet implicit deception is not banned and is sometimes used in experimental economics. Thus, experimental (...) economists are being inconsistent when they appeal to the argument from public bads to justify banning explicit deception but not implicit deception. (shrink)

The logics of formal inconsistency (LFIs, for short) are paraconsistent logics (that is, logics containing contradictory but non-trivial theories) having a consistency connective which allows to recover the ex falso quodlibet principle in a controlled way. The aim of this paper is considering a novel semantical approach to first-order LFIs based on Tarskian structures defined over swap structures, a special class of multialgebras. The proposed semantical framework generalizes previous aproaches to quantified LFIs presented in the literature. The case of (...) QmbC, the simpler quantified LFI expanding classical logic, will be analyzed in detail. An axiomatic extension of QmbC called QLFI1o is also studied, which is equivalent to the quantified version of da Costa and D'Ottaviano 3-valued logic J3. The semantical structures for this logic turn out to be Tarkian structures based on twist structures. The expansion of QmbC and QLFI1o with a standard equality predicate is also considered. (shrink)

In this paper we present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language in such a way that consistency may be logically independent of non-contradiction. We defend the view according to which logics of formal inconsistency may be interpreted as theories of logical consequence of an epistemological character. We also argue that in order to (...) philosophically justify paraconsistency there is no need to endorse dialetheism, the thesis that there are true contradictions. Furthermore, we show that mbC, a logic of formal inconsistency based on classical logic, may be enhanced in order to express the basic ideas of an intuitive interpretation of contradictions as conflicting evidence. (shrink)

The well-known empiricist apories of the lawfulness of nature prevent an adequate philosophical interpretation of empirical science until this day. Clarification can only be expected through an immanent refutation of the empiricist point of view. My argument is that Hume’s claim, paradigmatic for modern empiricism, is not just inconsequent, but simply contradictory: Empiricism denies that a lawlike character of nature can be substantiated. But, as is shown, anyone who claimes experience to be the basis of knowledge (as the empiricist naturally (...) does), has, in fact, always already presupposed the lawfullness of nature, i.e. has assumed the ontology of a nature lawful in itself. If lawfulness is, more closely, understood as dependency on conditions, then the functional character of the laws of nature is involved with the consequence that verification is not to be taken as a mere repetition of measurements but as clarification of the conditional structure of the physical process. Furthermore the functionality of the laws of nature also includes a statement on their invariance (relative to certain transformations) and so their lawlikeness. This throws a new light on the problem of induction. Seen in this way it is hardly surprising that the notorious neglect of the functional aspect in empiricism has led to fundamental problems with the concept of the law of nature. (shrink)

Despite being very common in both public and private argumentation, accusations of selective application of general premises, also known as “whataboutisms”, have been mostly overlooked in argumentation studies, where they are, at most, taken as accusations of inconsistency. Here I will defend an account according to which allegations of this sort can express the suspicion that the argumentation put forward by one party does not reflect his or her actual standpoint and reasons. Distinguishing this kind of argumentative moves is (...) important for evaluating its appropriateness in critical discussions where knowing the honest opinion of arguers is relevant, as in political controversies or interpersonal communication. (shrink)

The word “populism” commonly elicits images of hordes of angry townspeople with pitchforks and torches. That is the classic picture of “the mob,” bolstered by countless movie and television productions, and it is clearly based on such historical events as the English civil wars, the sans-culottes’ terror, the Bolshevik revolution, and the recent genocides in Rwanda and Burundi. Many of the leaders involved in fostering such horrors are seen as radical democrats whose successors today should also be feared. In this (...) paper, I argue that any mob takeovers of the feared sort are actually antithetical to radical democracy. This is because an authentically democratic regime, even of the most extreme type, is necessarily inconsistent with “mobocracy” or any sort of “tyranny of the majority” given its essential procedural aspects. It is argued, in fact, that leaders of legitimately democratic movements have generally been quite vapid because of the fallibilistic, plebiscitary proceduralism inherent in any authentic attempt to require government policy to reflect the “general will.” And this vapidity is argued to inhere regardless of the extent of rhetorical powers of the advocate or advocacy. (shrink)

The few people familiar with the pseudo-Platonic dialogue Axiochus generally have a low opinion of it. It's easy to see why: the dialogue is a mish-mash of Platonic, Epicurean and Cynic arguments against the fear of death, seemingly tossed together with no regard whatsoever for their consistency. As Furley notes, the Axiochus appears to be horribly confused. Whereas in the Apology Socrates argues that death is either annihilation or a relocation of the soul, and is a blessing either way, "the (...) Socrates of the Axiochus wants to have it both ways": death is both annihilation and a release of the soul from the body into a better realm. This may be used to construct a valid argument for the conclusion that death is not evil, but at the expense of having a contradiction as one of its premises. But D. S. Hutchinson has recently proposed that these inconsistencies shouldn't surprise us if we view the Axiochus as "an unconventional version of a very conventional genre--the consolation letter." In this paper I expand on Hutchinson's brief suggestion and argue that the Axiochus can be rehabilitated by paying attention to its genre. Although the Axiochus does display many similarities to the consolation letter, the shift from letter to dialogue does--pace Hutchinson--significantly affect what's going on. Within the dialogue, Socrates behaves toward Axiochus in a way similar to the way the author of a consolation letter behaves towards the letter's reader: he is willing to use inconsistent arguments, borrowed from any source, in order to soothe the patient. However, in depicting this type of consolatory relationship between Socrates and Axiochus, the dialogue itself is not aiming at consoling its readers. Instead, it should be seen as displaying for the reader's consideration a certain type of consolatory argumentative practice. -/- Socrates notes that Axiochus is "very much in need of consolation" (365a), and he uses any means necessary to accomplish this task. Socrates exhibits many ways in which he is willing to sacrifice argumentative hygiene for the sake of therapeutic effectiveness. These include: -/- * Use of arguments with inconsistent premises, presented in propria persona. * Appeals to emotion * Tailoring arguments to the audience. * Presenting invalid arguments so as to induce unjustified but comforting beliefs. * Evasion. In these respects, I think that Socrates' argumentative practice is best compared to PH III 280-1, where Sextus Empiricus says that the skeptic will deliberately use logically weak arguments as long as they work. Dorothy Tarrant claims that what links the Socrates of the Axiochus to Socrates as he appears elsewhere in the Platonic corpus is his evident care for the welfare of his interlocutor's psyche. But this concern takes a quite different form in the Axiochus than it usually does. As with Sextus, psychic therapy in the Axiochus involves relief from pain. The primary difference between them is that Socrates, unlike Sextus, is not aiming at producing epochê in his patient. (shrink)

Recently, there has been some discussion of how Dutch Book arguments might be used to demonstrate the rational incoherence of certain hidden variable models of quantum theory. In this paper, we argue that the 'form of inconsistency' underlying this alleged irrationality is deeply and comprehensively related to the more familiar 'inconsistency' phenomenon of contextuality. Our main result is that the hierarchy of contextuality due to Abramsky and Brandenburger corresponds to a hierarchy of additivity/convexity-violations which yields formal Dutch Books (...) of different strengths. We then use this result to provide a partial assessment of whether these formal Dutch Books can be interpreted normatively. (shrink)

Can a perceptual experience justify (epistemically) a belief? More generally, can a nonbelief justify a belief? Coherentists answer in the negative: Only a belief can justify a belief. A perceptual experience can cause a belief but cannot justify a belief. Coherentists eschew all noninferential justification—justification independent of evidential support from beliefs—and, with it, the idea that justification has a foundation. Instead, justification is holistic in structure. Beliefs are justified together, not in isolation, as members of a coherent belief system. The (...) main question of the paper is whether coherentism is consistent. I set out an apparent inconsistency in coherentism and then give a resolution to that apparent inconsistency. (shrink)

I present an approach to our conceiving absolute impossibilities—things which obtain at no possible world—in terms of ceteris paribus intentional operators: variably restricted quantifiers on possible and impossible worlds based on world similarity. The explicit content of a representation plays a role similar in some respects to the one of a ceteris paribus conditional antecedent. I discuss how such operators invalidate logical closure for conceivability, and how similarity works when impossible worlds are around. Unlike what happens with ceteris paribus counterfactual (...) conditionals, the closest worlds are relevantly closest belief-worlds: closest to how things are believed to be, rather than to how they are. Also, closeness takes into account apriority and the opacity of intentional contexts. (shrink)

In this paper, two axiomatic theories T− and T′ are constructed, which are dual to Tarski’s theory T+ (1930) of deductive systems based on classical propositional calculus. While in Tarski’s theory T+ the primitive notion is the classical consequence function (entailment) Cn+, in the dual theory T− it is replaced by the notion of Słupecki’s rejection consequence Cn− and in the dual theory T′ it is replaced by the notion of the family Incons of inconsistent sets. The author has proved (...) that the theories T+, T−, and T′ are equivalent. (shrink)

In this paper I apply the concept of _inter-Model Inconsistency in Set Theory_ (MIST), introduced by Carolin Antos (this volume), to select positions in the current universe-multiverse debate in philosophy of set theory: I reinterpret H. Woodin’s _Ultimate L_, J. D. Hamkins’ multiverse, S.-D. Friedman’s hyperuniverse and the algebraic multiverse as normative strategies to deal with the situation of de facto inconsistency toleration in set theory as described by MIST. In particular, my aim is to situate these positions (...) on the spectrum from inconsistency avoidance to inconsistency toleration. By doing so, I connect a debate in philosophy of set theory with a debate in philosophy of science about the role of inconsistencies in the natural sciences. While there are important differences, like the lack of threatening explosive inferences, I show how specific philosophical positions in the philosophy of set theory can be interpreted as reactions to a state of inconsistency similar to analogous reactions studied in the philosophy of science literature. My hope is that this transfer operation from philosophy of science to mathematics sheds a new light on the current discussion in philosophy of set theory; and that it can help to bring philosophy of mathematics and philosophy of science closer together. (shrink)

Hypocrisy is a ubiquitous feature of moral and political life, and accusations of hypocrisy a ubiquitous feature of moral and political discourse. Yet it has been curiously under-theorized in analytic philosophy. Fortunately, the last decade has seen a boomlet of articles that address hypocrisy in order to explain and justify conditions on the so-called “standing” to blame (Wallace 2010; Friedman 2013; Bell 2013; Todd 2017; Herstein 2017; Roadevin 2018; Fritz and Miller 2018). Nevertheless, much of this more recent literature does (...) not adequately address the question, “what is hypocrisy?” In this paper, I develop and defend an account of hypocrisy as vicious, value-expressing inconsistency. I show how this account solves some traditional and some novel philosophical puzzles concerning hypocrisy and affords a deeper understanding of the features of hypocrisy emphasized by other prominent accounts. (shrink)