For centuries, inconsistencies were seen as a hindrance to good reasoning, and their role in the sciences was ignored. In recent years, however, logicians as well as philosophers and historians have showed a growing interest in the matter. Central to this change were the advent of paraconsistent logics, the shift in attention from finished theories to construction processes, and the recognition that most scientific theories were at some point either internally inconsistent or incompatible with other accepted findings. The new interest (...) gave rise to important questions. How is `logical anarchy' avoided? Is it ever rational to accept an inconsistent theory? In what sense, if any, can inconsistent theories be considered as true? The present collection of papers is the first to deal with this kind of questions. It contains case studies as well as philosophical analyses, and presents an excellent overview of the different approaches in the domain. (shrink)

Peter Vickers examines 'inconsistent theories' in the history of science--theories which, though contradictory, are held to be extremely useful. He argues that these 'theories' are actually significantly different entities, and warns that the traditional goal of philosophy to make substantial, general claims about how science works is misguided.

This paper discusses the problem of inconsistencies in the metaphorical conceptualizations of time that involve motion within the framework of conceptual metaphor theory (CMT). It demonstrates that the TIME AS A PURSUER metaphor contrasts with the reverse variant TIME AS AN OBJECT OF PURSUIT, just as the MOVING TIME metaphor contrasts with the MOVING OBSERVER variant. Such metaphorical conceptualizations of time functioning as pairs of minimally differing variants based on Figure-Ground reversal are, strictly speaking, inconsistent with one another. Looking at (...) these inconsistencies from a wider perspective suggests that time may belong to a separate category of conceptual phenomena. This paper puts forward a proposal to approach time from the perspective of “phenomena of the third kind”, which according to Keller’s thesis include conceptual establishments resulting from human cognition, but not of human design. (shrink)

It has recently been argued by Davey (2014) that inconsistency is never tolerated in science, but only discretely isolated. But when talking about inconsistencies in science, not much attention has been paid to the inconsistencies between theory and observation. Here I will argue that inconsistency toleration actually takes place in science, and that when we examine actual inconsistent theories, inconsistencies between theory and observation look anything but homogeneous. I will argue, appealing to certain properties of empirical theories, especially (...) holism, that at least two sub-types of inconsistencies regarding theory and observation can be distinguished: those that satisfy a criterion of observational independence and those that do not. (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)

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.

In certain finite extensive games with perfect information, Cristina Bicchieri (1989) derives a logical contradiction from the assumptions that players are rational and that they have common knowledge of the theory of the game. She argues that this may account for play outside the Nash equilibrium. She also claims that no inconsistency arises if the players have the minimal beliefs necessary to perform backward induction. We here show that another contradiction can be derived even with minimal beliefs, so there (...) is no paradox of common knowledge specifically. These inconsistencies do not make play outside Nash equilibrium plausible, but rather indicate that the epistemic specification must incorporate a system for belief revision. Whether rationality is common knowledge is not the issue. (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...

Several writers have argued that the state lacks the moral standing to hold socially deprived offenders responsible for their crimes because the state would be hypocritical in doing so. Yet the state is not disposed to make an unfair exception of itself for committing the same sorts of crimes as socially deprived offenders, so it is unclear that the state is truly hypocritical. Nevertheless, the state is disposed to inconsistently hold its citizens responsible, blaming or punishing socially deprived offenders more (...) often or more harshly than other offenders, even when the crimes are the same. The state’s stable disposition to inconsistently hold offenders responsible undermines its standing to hold offenders responsible for the same reasons that hypocrisy undermines standing; instead of making an unfair exception of itself, the state makes an unfair exception of others. Strikingly, this means that the state lacks the standing to hold anyone responsible for a crime for which it is unfairly disposed to hold citizens responsible inconsistently, not just socially deprived offenders. Thus, it is even more urgent that the state regain its moral standing by working toward a justice system that holds offenders responsible consistently. (shrink)

I erect a framework within the semantic view of theories for explaining the empirical success of internally inconsistent models and theories, with scientific realism in mind. The framework is an instance of the ‘content-driven’ approach to inconsistency, advocated by both Norton (Philos Sci 54:327–350, 1987) and Smith (Stud Hist Philos Sci 19:429–445, 1988a, In: Fine A, Leplin J (eds) PSA1988, 1988b), whose ideas my analysis aims to clarify and substantiate.

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)

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 concept of measuring inconsistency in information was developed by John Grant in a 1978 paper in the context of first-order logic. For more than 20 years very little was done in this area until in the early 2000s a number of AI researchers started to formulate new inconsistency measures primarily in the context of propositional logic knowledge bases. The aim of this volume is to survey what has been done so far, to expand inconsistency measurement to (...) other formalisms, to connect it with related topics, and to provide ideas for further research in a topic that is particularly relevant now in view of the many inconsistencies in the massive amount of information available. The book contains 11 chapters. The first chapter, by John Grant, gives his original motivation for starting this field, explains why it was formulated in a highly mathematical manner, presents important material that was omitted from the original paper, and provides ideas about the use of dimensions in measuring inconsistency. The second chapter, by Matthias Thimm, is a survey that covers most of the research on inconsistency measures up to 2017. The other 9 chapters, all by experts either in inconsistency measures, or in the topic under consideration, or both, connect inconsistency measures with argumentation, disjunctive logic programming, fuzzy logic systems, modal logics, multiset representation, paraconsistent consequence, probabilistic logic, relational databases, and spatio-temporal databases."-- back cover. (shrink)

Background The review of human participant research by Research Ethics Committees or Institutional Review Boards is a complex multi-faceted process that cannot be reduced to an algorithm. However, this does not give RECs/ IRBs permission to be inconsistent in their specific requirements to researchers or in their final opinions. In England the Health Research Authority coordinates 67 committees, and has adopted a consistency improvement plan including a process called “Shared Ethical Debate” where multiple committees review the same project. Committee reviews (...) are compared for consistency by analysing the resulting minutes. Methods We present a description of the ShED process. We report an analysis of minutes created by research ethics committees participating in two ShED exercises, and compare them to minutes produced in a published “mystery shopper” exercise. We propose a consistency score by defining top themes for each exercise, and calculating the ratio between top themes and total themes identified by each committee for each ShED exercise. Results Our analysis highlights qualitative differences between the ShED 19, ShED 20 and “mystery shopper” exercises. The quantitative measure of consistency showed only one committee across the three exercises with more than half its total themes as top themes. The average consistency scores for the three exercises were 0.23, 0.35 and 0.32. There is a statistically significant difference between the ShED 19 exercise, and the ShED 20 and mystery shopper exercises. Conclusions ShED exercises are effective in identifying inconsistency between ethics committees and we describe a scoring method that could be used to quantify this. However, whilst a level of inconsistency is probably inevitable in research ethics committee reviews, studies must move beyond the ShED methodology to understand why inconsistency occurs, and what an acceptable level of inconsistency might be. (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)

The main thesis of this paper is that we sometimes are disposed to accept false and even jointly inconsistent claims by virtue of our semantic competence, and that this comes to light in the sorites and liar paradoxes. Among the subsidiary theses are that this is an important source of indeterminacy in truth conditions, that we must revise basic assumptions about semantic competence, and that classical logic and bivalence can be upheld in the face of the sorites paradox.

In theorizing about racial pejoratives, an initially attractive view is that pejoratives have the same reference as their “neutral counterparts”. Call this the identity thesis. According to this thesis, the terms “kike” and “Jew”, for instance, pick out the same set of people. To be a Jew just is to be a kike, and so to make claims about Jews just is to make claims about kikes. In this way, the two words are synonymous, and so make the same contribution (...) to the truth-conditions of sentences containing them. While the fundamental claim for the identity thesis that Jews are kikes sounds anti-semitic, it need not be actually anti-semitic. The identity thesis is usually bolstered with the further claim that the pejorative aspect of “kike” and other such terms is located elsewhere than in truth-conditional content, so what makes “kike” a bad word is a non-truth-conditional association with anti-semitism that is not shared with the word “Jew”. The exact nature and location of the negative moral content of pejoratives is a matter of some dispute among identity theorists. But whatever the intuitive appeal of the identity theory for those persuaded by such views, it is nevertheless inconsistent. (shrink)

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

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)

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)

Inconsistency robustness is information system performance in the face of continually pervasive inconsistencies---a shift from the previously dominant paradigms of inconsistency denial and inconsistency elimination attempting to sweep them under the rug. Inconsistency robustness is a both an observed phenomenon and a desired feature: Inconsistency Robustness is an observed phenomenon because large information-systems are required to operate in an environment of pervasive inconsistency. Inconsistency Robustness is a desired feature because we need to improve (...) the performance of large information system. This volume has revised versions of refereed articles and panel summaries from the first two International Symposia on Inconsistency Robustness conducted under the auspices of the International Society for Inconsistency Robustness. The articles are broadly based on theory and practice, addressing fundamental issues in inconsistency robustness. The field of Inconsistency Robustness aims to provide practical rigorous foundations for computer information systems dealing with pervasively inconsistent information.". (shrink)

In this work, the first of a series, we study the nature of informal inconsistency in physics, focusing mainly on the foundations of quantum theory, and appealing to the concept of quasi-truth. We defend a pluralistic view of the philosophy of science, grounded on the existence of inconsistencies and on quasi-truth. Here, we treat only the ‘classical aspects’ of the subject, leaving for a forthcoming paper the ‘non-classical’ part.

An argument for Trivialism, the view that natural languages are logically inconsistent, is provided that does not rely on contentious empirical assumptions about natural language terms such as “and” or “or.” Further, the view is defended against an important objection recently mounted against it by Thomas Hofweber.

Most opposition to induced abortion turns on the belief that human fetuses are persons from conception. On this view, the moral status of the fetus alone requires those in a position to provide aid—gestational mothers—to make tremendous sacrifices to benefit the fetus. Recently, critics have argued that this pro-life position requires more than opposition to induced abortion. Pro-life theorists are relatively silent on the issues of spontaneous abortion, surplus in vitro fertilisation human embryos, and the suffering and death of born (...) persons due to lack of access to food, shelter and medical care. Colgrove et al call such arguments inconsistency arguments, arguing they ‘do not matter’ and mischaracterise them as ad hominem attacks. Here, I argue these are better understood as moral dilemmas. While some critics argue pro-life inaction is evidence that they do not really believe human fetuses are persons, I contend this inaction is likely the result of resolvable confusion rather than moral negligence. (shrink)

Mathias Frisch provides the first sustained philosophical discussion of conceptual problems in classical particle-field theories. Part of the book focuses on the problem of a satisfactory equation of motion for charged particles interacting with electromagnetic fields. As Frisch shows, the standard equation of motion results in a mathematically inconsistent theory, yet there is no fully consistent and conceptually unproblematic alternative theory. Frisch describes in detail how the search for a fundamental equation of motion is partly driven by pragmatic considerations (like (...) simplicity and mathematical tractability) that can override the aim for full consistency. The book also offers a comprehensive review and criticism of both the physical and philosophical literature on the temporal asymmetry exhibited by electromagnetic radiation fields, including Einstein's discussion of the asymmetry and Wheeler and Feynman's influential absorber theory of radiation. Frisch argues that attempts to derive the asymmetry from thermodynamic or cosmological considerations fail and proposes that we should understand the asymmetry as due to a fundamental causal constraint. The book's overarching philosophical thesis is that standard philosophical accounts that strictly identify scientific theories with a mathematical formalism and a mapping function specifying the theory's ontology are inadequate, since they permit neither inconsistent yet genuinely successful theories nor thick causal notions to be part of fundamental physics. (shrink)

A critic may attack an arguer personally by pointing out that the arguer’s position is pragmatically inconsistent: the arguer does not practice what he preaches. A number of authors hold that such attacks can be part of a good argumentative discussion. However, there is a difficulty in accepting this kind of contribution as potentially legitimate, for the reason that there is nothing wrong for a protagonist to have an inconsistent position, in the sense of committing himself to mutually inconsistent propositions. (...) If so, any such charge seems to be irrelevant. The questions to be answered in this essay are: what, if any, is the dialectical rationale for this type of criticism, and in what situations, if any, is this kind of charge dialectically legitimate? It will be shown that these attacks can be dialectically legitimate, in special circumstances, and that they can be seen as strategic␣manoeuvres where a party attempts to reconcile his dialectical and his rhetorical objectives. (shrink)

In this paper, I will characterize a new class of inconsistency-adaptive logics, namely inconsistency-adaptive modal logics. These logics cope with inconsistencies in a modal context. More specifically, when faced with inconsistencies, inconsistency-adaptive modal logics avoid explosion, but still allow the derivation of sufficient consequences to adequately explicate the part of human reasoning they are intended for.

The paper examines philosophical issues that arise in contexts where one has many different models for treating the same system. I show why in some cases this appears relatively unproblematic (models of turbulence) while others represent genuine difficulties when attempting to interpret the information that models provide (nuclear models). What the examples show is that while complementary models needn’t be a hindrance to knowledge acquisition, the kind of inconsistency present in nuclear cases is, since it is indicative of a (...) lack of genuine theoretical understanding. It is important to note that the differences in modeling do not result directly from the status of our knowledge of turbulent flows as opposed to nuclear dynamics—both face fundamental theoretical problems in the construction and application of models. However, as we shall, the ‘problem context(s)’ in which the modeling takes plays a decisive role in evaluating the epistemic merit of the models themselves. Moreover, the theoretical difficulties that give rise to inconsistent as opposed to complementary models (in the cases I discuss) impose epistemic and methodological burdens that cannot be overcome by invoking philosophical strategies like perspectivism, paraconsistency or partial structures. (shrink)

In this paper, I compare how it is that inconsistencies are handled in mathematics to how they are handled in chemistry. In mathematics, they are very precisely formulated and identified, unlike in chemistry. So the chemists can learn from the precision and the very well-worked out strategies developed by logicians and deployed by mathematicians to cope with inconsistency. Some lessons can also be learned by the mathematicians from the chemists. Mathematicians tend to be intolerant towards inconsistencies. There are some (...) philosophers of chemistry who attribute to chemists, collectively, a more tolerant attitude towards inconsistency, and so, mathematicians can learn from the chemists’ attitude to inform their choice of strategies. (shrink)

Les principaux aspects de l’Etat Providence sont identifiés. Parce que les mêmes individus et les mêmes couches de la population bénéficient de la redistribution en même temps qu’ils sont frappés d’impôts, la “société malaxée” est une expression qui convient mieux aux démocraties modernes que ne l’est “l’Etat Providence”. Le développement historique du phénomène est retracé.. Le bismarckisme marque le tournant de l’idée originelle avec son image optimiste de l’homme sous sa forme moderne de la “société malaxée”. L’assistance sociale est un (...) phénomène induit par la démocratie. Le Léviathan se révèle être une vache à lait ; il s’étend de plus en plus et devient incroyablement gourmand. L’explication de l’émergence de la “société malaxée” met l’accent sur des facteurs intellectuels, en particulier sur la théorie politique du libéralisme. Le déclin du libéralisme peut être en partie expliqué par le caractère “dissolu” du libéralisme classique et de ses successeurs. L’article recherche la manière de renforcer le libéralisme. L’ébauche du libéralisme “strict” par Jasay est esquissée et analysée. Elle fournit le fondement d’un système de règles morales déontologiques. Un tel système est-il indispensable pour un ordre social compatible avec l’idée d’une société libre? Ou est-ce que la démocratie peut résoudre le problème? Cette question mène à une analyse de la dynamique de la méthode démocratique du choix collectif. Les remèdes susceptibles de favoriser l’émergence d’une société moins coercitive sont examinés.Central features of the welfare state are described. Since most redistribution now benefits the same persons and strata as it taxes, “Churning Society” is a more telling label for modern democracies than is the “welfare state”. The historical development of the phenomenon is sketched. Churning society is a democracy-induced phenomenon. Leviathan turns into a Milch Cow; it grows and grows and becomes incredibly voracious. The explanation of the rise of the churning society focuses on the intellectual factors, in particular on the political theory of liberalism. The decline of liberalism can be in part explained by the “looseness” of classical liberalism and its successors. The article inquires: how can liberalism be strengthened? Jasay’s design of “strict” liberalism is outlined and analyzed. It provides the basis of a system of deontological moral rules. Is such a system indispensable for a social order that is compatible with the idea of a free society? Or can democracy solve the problem? This question leads to an analysis of the dynamics of the democratic method of collective choice. Remedies are discussed that might help the emergence of a less unfree society. (shrink)

Meditations, aphorisms, maxims, notes, and comments construct a philosophy of thought congruent with the inconsistency of our reality. Those who continue to think never return to their point of departure. —Inconsistencies These 130 short texts—aphoristic, interlacing, and sometimes perplexing—target a perennial philosophical problem: Our consciousness and our experience of reality are inconsistent, fragmentary, and unstable; God is dead, and our identity as subjects discordant. How can we establish a new mode of thought that does not cling to new gods (...) or the false security of rationality? Marcus Steinweg, as he did in his earlier book The Terror of Evidence, constructs a philosophical position from fragments, maxims, meditations, and notes, formulating a philosophy of thought that expresses and enacts the inconsistency of our reality. Steinweg considers, among other topics, life as a game (“To think is to play because no thought is firmly grounded”); sexuality (“wasteful, contradictory, and contingent”); desire (”Desire has a thousand names; It's earned none of them”); reality (“overdetermined and excessively complex”); and world (“a nonconcept”). He disposes of philosophy in one sentence (“Philosophy is a continual process of its own redefinition.”) but spends multiple pages on “A Tear in Immanence,” invoking Nietzsche, Heidegger, Sartre, and others. He describes “Wandering with Foucault” (“Thought entails wandering as well as straying into madness”) and brings together Derrida and Debord. He poses a question: “Why should a cat be more mysterious than a dog?” and later answers one: “Beauty is truth because truth is beauty.” By the end, we have accompanied Steinweg on converging trains of thought. “Thinking means continuing to think,” he writes, adding “But thinking can only pose questions by answering others.” The question of inconsistency? Asked and answered, and asked. (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)

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)

Every theory of rationality worth taking seriously implies that it is in some way irrational to accept contradictions. In this essay, the author examines how exactly this basic idea should be spelled out. He argues for two claims. First, it is not practically irrational to accept a contradiction in the sense of causing oneself to have contradictory beliefs. Second, it is moreover not theoretically irrational to accept a contradiction in the sense of having contradictory beliefs, if the contradictoriness of the (...) relevant beliefs is inaccessible to the person. The contradictoriness of a set of beliefs is accessible to a person only if this person possesses the general cognitive capacities to realise that the beliefs are contradictory. (shrink)

The paper explains how a paraconsistent logician can appropriate all classical reasoning. This is to take consistency as a default assumption, and hence to work within those models of the theory at hand which are minimally inconsistent. The paper spells out the formal application of this strategy to one paraconsistent logic, first-order LP. (See, Ch. 5 of: G. Priest, In Contradiction, Nijhoff, 1987.) The result is a strong non-monotonic paraconsistent logic agreeing with classical logic in consistent situations. It is shown (...) that the logical closure of a theory under this logic is trivial only if its closure under LP is trivial. (shrink)

This is a philosophical and historical investigation of the role of inconsistent representations of the same scientific phenomenon. The logical difficulties associated with the simultaneous application of inconsistent models are discussed. Internally inconsistent scientific proposals are characterized as structures whose application is necessarily tied to the confirming evidence that each of its components enjoys and to a vision of the general form of the theory that will resolve the inconsistency. Einstein's derivation of the black body radiation law is used (...) as an example application of such a strategy and is contrasted with planck's derivation. (shrink)

In this paper we discuss the process of building a joint probability distribution from an input set of low-dimensional probability distributions. Since the solution of the problem for a consistent input set of probability distributions is known we concentrate on a setup where the input probability distributions are inconsistent. In this case the iterative proportional fitting procedure (IPFP), which converges in the consistent case, tends to come to cycles. We propose a new algorithm that converges even in inconsistent case. The (...) important property of the algorithm is that it can be efficiently implemented exploiting decomposability of considered distributions. (shrink)

It is widely recognized that scientific theories are often associated with strictly inconsistent models, but there is little agreement concerning the epistemic consequences. Some argue that model inconsistency supports a strong perspectivism, according to which claims serving as interpretations of models are inevitably and irreducibly perspectival. Others argue that in at least some cases, inconsistent models can be unified as approximations to a theory with which they are associated, thus undermining this kind of perspectivism. I examine the arguments for (...) perspectivism, and contend that its strong form is defeasible in principle, not merely in special cases. The argument rests on the plausibility of scientific knowledge concerning non-perspectival, dispositional facts about modelled systems. This forms the basis of a novel suggestion regarding how to understand the knowledge these models afford, in terms of a contrastive theory of what-questions. (shrink)

This paper discusses a conception of physics as a collection of theories that, from a logical point of view, is inconsistent. It is argued that this logical conception of the relations between physical theories is too crude. Mathematical subtleties allow for a much more nuanced and sophisticated understanding of the relations between different physical theories.

Nicholas Rescher has argued we must tolerate inconsistency because of our cognitive limitations. He has also produced, together with R. Brandom, a serious attempt at exploring the logic of inconsistency. Inconsistency tolerance calls for a systematic rewriting of our logical doctrines: it requires a paraconsistent logic. However, having given up all aggregation of premises, Rescher's proposal for a paraconsistenl logic fails to account for the reductive reasoning Rescher appeals to in his account of inconsistency tolerance. A (...) non-adjunctive logic developed by P.K. Schotch and RE. Jennings provides just what Rescher's logic is lacking: It allows a tolerant attitude toward inconsistency while giving an account of reductive reasoning. (shrink)

Logical paradoxes – like the Liar, Russell's, and the Sorites – are notorious. But in Paradoxes and Inconsistent Mathematics, it is argued that they are only the noisiest of many. Contradictions arise in the everyday, from the smallest points to the widest boundaries. In this book, Zach Weber uses “dialetheic paraconsistency” – a formal framework where some contradictions can be true without absurdity – as the basis for developing this idea rigorously, from mathematical foundations up. In doing so, Weber directly (...) addresses a longstanding open question: how much standard mathematics can paraconsistency capture? The guiding focus is on a more basic question, of why there are paradoxes. Details underscore a simple philosophical claim: that paradoxes are found in the ordinary, and that is what makes them so extraordinary. (shrink)

The debate on probabilistic measures of coherence has focused on evaluating sets of consistent propositions. In this paper we draw attention to the largely neglected question of whether such measures concur with intuitions on test cases involving inconsistent propositions and whether they satisfy general adequacy constraints on coherence and inconsistency. While it turns out that, for the vast majority of measures in their original shape, this question must be answered in the negative, we show that it is possible to (...) adapt many of them in order to improve their performance. (shrink)