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)

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)

Buchanan highlighted the inconsistencies that arise when public services are financed by general taxation. Citizens increase their demand for services, even though citizens are reticent to increase taxation. Buchanan invited readers to explore the impact of different assumptions of politicians’ behaviour. In this chapter, attention focuses on the way that vote maximising governments are likely to respond to the divorce between receipt and payment for services. Buchanan illustrated his analysis with reference to the National Health Service in the UK. Predictions (...) are tested with reference to the pattern of excess demand in the National Health Service between 1970 and 2012. (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)

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)

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)

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)

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)

This is a discussion of different ways of working out the idea that the semantic paradoxes show that natural languages are somehow “inconsistent”. I take the workable form of the idea to be that there are expressions such that a necessary condition of understanding them is that one be inclined to accept inconsistent claims (an conception also suggested by Matti Eklund). I then distinguish “simple” from “complex” forms of such views. On a simple theory, such expressions are meaningless, while on (...) a complex theory they are not. I argue that complex theories are incompatible with truth conditional semantics and that simple theories are only coherent when the inconsistent claims are metalingusitic attributions of meaning. I close with a discussion of the version of the simple metalinguistic theory I have defended in “Understanding the Liar” and other papers. (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.

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)

Even when inconsistencies are present in our premise set, we can sensibly distinguish between good and bad arguments relying on these premises. In making this distinction, the inconsistency-adaptive approach of Batens strikes a particularly nice balance between inconsistency-tolerance and inferential strength. In this paper, we use the machinery of Batens’ approach to extend the paraconsistent approach to dialogical logic as developed by Rahman and Carnielli. In bringing these frameworks closer together, we obtain a dynamic mechanism for the systematic (...) study of dialogues in which two parties exchange arguments over a central claim, in the possible presence of inconsistencies. (shrink)

In a recent article M. Colyvan has argued that Quinean forms of scientific realism are faced with an unexpected upshot. Realism concerning a given class of entities, along with this route to realism, can be vindicated by running an indispensability argument to the effect that the entities postulated by our best scientific theories exist. Colyvan observes that among our best scientific theories some are inconsistent, and so concludes that, by resorting to the very same argument, we may incur a commitment (...) to inconsistent entities. Colyvan's argument could be interpreted, and in part is presented, as a reductio of Quinean scientific realism; yet, Colyvan in the end manifests some willingness to bite the bullet, and provides some reasons why we shouldn't feel too uncomfortable with those entities. In this paper we wish to indicate a way out to the scientific realist, by arguing that no indispensability argument of the kind suggested by Colyvan is actually available. To begin with, in order to run such an indispensability argument we should be justified in believing that an inconsistent theory is true; yet, in so far as the logic we accept is a consistent one it is arguable that our epistemic predicament could not be possibly one in which we are justified in so believing. Moreover, also if our logic admitted true contradictions, as Dialetheism does, it is arguable that Colyvan's indispensability argument could not rest on a true premise. As we will try to show, dialetheists do not admit true contradictions for cheap: they do so just as a way out of paradox, namely whenever we are second-level ignorant as to the metaphysical possibility of evidence breaking the parity among two or more inconsistent claims; Colyvan's examples, however, are not of this nature. So, even under the generous assumption that Dialetheism is true, we will conclude that Colyvan's argument doesn't achieve its surprising conclusion. (shrink)

In section I, I argue that the principal reason why inconsistency is a fault is that it involves having at least one false belief. In section 2, I argue that inconsistency need not be a serious epistemic fault. The argument in section 2 is based on the notion that what matters epistemically is always in the final analysis an item's effect on attaining the goal of truth. In section 3 I describe two cases in which it is best (...) from an epistemic point of view to knowingly retain inconsistent beliefs. In section 4 my goal is to put into perspective the charge that relativism ought to be rejected because it involves one in inconsistency. (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.

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)

This paper concerns the relationship between transitivity of entailment, omega-inconsistency and nonstandard models of arithmetic. First, it provides a cut-free sequent calculus for non-transitive logic of truth STT based on Robinson Arithmetic and shows that this logic is omega-inconsistent. It then identifies the conditions in McGee for an omega-inconsistent logic as quantified standard deontic logic, presents a cut-free labelled sequent calculus for quantified standard deontic logic based on Robinson Arithmetic where the deontic modality is treated as a predicate, proves (...) omega-inconsistency and shows thus, pace Cobreros et al., that the result in McGee does not rely on transitivity. Finally, it also explains why the omega-inconsistent logics of truth in question do not require nonstandard models of arithmetic. (shrink)

I provide a method of measuring the inconsistency of a set of sentences from 1-consistency, corresponding to complete consistency, to 0-consistency, corresponding to the explicit presence of a contradiction. Using this notion to analyze the lottery paradox, one can see that the set of sentences capturing the paradox has a high degree of consistency (assuming, of course, a sufficiently large lottery). The measure of consistency, however, is not limited to paradoxes. I also provide results for general sets of sentences.

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 develops in certain directions the work of Meyer in [3], [4], [5] and [6]. In those works, Peano’s axioms for arithmetic were formulated with a logical base of the relevant logic R, and it was proved finitistically that the resulting arithmetic, called R♯, was absolutely consistent. It was pointed out that such a result escapes incau- tious formulations of Goedel’s second incompleteness theorem, and provides a basis for a revived Hilbert programme. The absolute consistency result used as a (...) model arithmetic modulo two. Modulo arithmetics are not or- dinarily thought of as an extension of Peano arithmetic, since some of the propositions of the latter, such as that zero is the successor of no number, fail in the former. Consequently a logical base which, unlike classical logic, tolerates contradictory theories was used for the model. The logical base for the model was the three-valued logic RM3, which has the advantage that while it is an extension of R, it is finite valued and so easier to handle. The resulting model-theoretic structure is interesting in its own right in that the set of sentences true therein consti- tutes a negation inconsistent but absolutely consistent arithmetic which is an extension of R♯. In fact, in the light of the result of [6], it is an extension of Peano arithmetic with a base of a classical logic, P♯. A generalisation of the structure is to modulo arithmetics with the same logical base RM3, but with varying moduli. We first study the properties of these arithmetics in this paper. The study is then generalised by vary- ing the logical base, to give the arithmetics RMni, of logical base RMn and modulus i. Not all of these exist, however, as arithmetical properties and logical properties interact, as we will show. The arithmetics RMni give rise, on intersection, to an inconsistent arithmetic RMω which is not of modulo i for any i. We also study its properties, and, among other results, we show by finitistic means that the more natural relevant arithmetics R♯ and R♯♯ are incomplete. In the rest of the paper we apply these techniques to several topics, particularly relevant quantum arithmetic in which we are able to show that the law of distribution remains unprovable. Aside from its intrinsic interest, we regard the present exercise as a demonstration that inconsistent theories and models are of mathematical worth and interest. (shrink)

Inconsistent Commitments and Commitment to Inconsistencies.

The first mention of the concept of an inconsistency measure for sets of formulas in first-order logic was given in 1978, but that paper presented only classifications for them. The first actual inconsistency measure with a numerical value was given in 2002 for sets of formulas in propositional logic. Since that time, researchers in logic and AI have developed a substantial theory of inconsistency measures. While this is an interesting topic from the point of view of logic, (...) an important motivation for this work is also that some intelligent systems may encounter inconsistencies in their operation. This research deals primarily with propositional knowledge bases, that is, finite sets of propositional logic formulas. The goal of this paper is to extend the concept of inconsistency measure in a formal way to sets of formulas with the modal operators “necessarily” and “possibly” applied to propositional logic formulas. We use frames for the semantics, but in a way that is different from the way that frames are commonly used in modal logics, in order to facilitate measuring inconsistency. As a set of formulas may have different inconsistency measures for different frames, we define the concept of a standard frame that can be used for all finite sets of formulas in the language. We do this for two languages. The first language, AMPL, contains formulas where a prefix of operators is applied to a propositional logic formula. The second language, CMPL, adds connectives that can be applied to AMPL formulas in a limited way. We show how to extend propositional logic inconsistency measures to such sets of formulas. Finally, we define a new concept, weak inconsistency measure, and show how to compute it. (shrink)

In this paper I present an argument for belief in inconsistent objects. The argument relies on a particular, plausible version of scientific realism, and the fact that often our best scientific theories are inconsistent. It is not clear what to make of this argument. Is it a reductio of the version of scientific realism under consideration? If it is, what are the alternatives? Should we just accept the conclusion? I will argue (rather tentatively and suitably qualified) for a positive answer (...) to the last question: there are times when it is legitimate to believe in inconsistent objects. (shrink)

Classical logic is explosive in the face of contradiction, yet we find ourselves using inconsistent theories. Mark Colyvan, one of the prominent advocates of the indispensability argument for realism about mathematical objects, suggests that such use can be garnered to develop an argument for commitment to inconsistent objects and, because of that, a paraconsistent underlying logic. I argue to the contrary that it is open to a classical logician to make distinctions, also needed by the paraconsistent logician, which allow a (...) more nuanced ranking of theories in which inconsistent theories can have different degrees of usefulness and productivity. Facing inconsistency does not force us to adopt an underlying paraconsistent logic. Moreover we will see that the argument to best explanation deployed by Colyvan in this context is unsuccessful. I suggest that Quinean approach which Colyvan champions will not lead to the revolutionary doctrines Colyvan endorses. (shrink)

William Simkulet has recently criticised Colgrove et al’s defence against what they have called inconsistency arguments—arguments that claim opponents of abortion (OAs) act in ways inconsistent with their underlying beliefs about human fetuses (eg, that human fetuses are persons at conception). Colgrove et al presented three objections to inconsistency arguments, which Simkulet argues are unconvincing. Further, he maintains that OAs who hold that the fetus is a person at conception fail to act on important issues such as the (...) plight of frozen embryos, poverty and spontaneous abortion. Thus, they are morally negligent. In response, we argue that Simkulet has targeted a very narrow group of OAs, and so his criticisms are inapplicable to most OAs. We then explain why his responses to each of Colgrove et al’s objections do not succeed, even for this restricted group. Finally, we note that Simkulet fails to provide evidence for his claims regarding OAs’ supposed failures to act, and we show that OAs veritably do invest resources into these important issues. We conclude that Colgrove et al’s reasons for rejecting inconsistency arguments (en masse) remain intact. (shrink)

Research Ethics Committees (RECs) are frequently a focus of complaints from researchers, but evidence about the operation and decisions of RECs tends to be anecdotal. We conducted a systematic study to identify and compare the ethical issues raised in 54 letters to researchers about the same 18 applications submitted to three RECs over one year. The most common type of ethical trouble identified in REC letters related to informed consent, followed by scientific design and conduct, care and protection of research (...) participants, confidentiality, recruitment and documentation. Community considerations were least frequently raised. There was evidence of variability in the ethical troubles identified and the remedies recommended. This analysis suggests that some principles may be more institutionalized than others, and offers some evidence of inconsistency between RECs. Inconsistency is often treated as evidence of incompetence and caprice, but a more sophisticated understanding of the role of RECs and their functioning is required. (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...

Chemists do not aim at testing preconceptions or theoretical hypotheses only; they first and foremost produce and determine the object of chemical investigation: they learn through making. They never cease to create and stabilize heterogeneous devices, methods, models, and theories in order to act upon the world. Chemical bodies cannot be studied in isolation; their properties constitutively depend on what surrounds and acts upon them. Starting from the specificity of chemical practices, this paper investigates the meaning of consistency, inconsistency, (...) and that of the ceteris paribus clause, in this domain of science. In so doing, it defends the idea that studying what we call ‘a lack of consistency’ should always include the scrutiny of: the way a particular scientific practice is stabilized, and the ontological or pragmatic assumptions about the entities and processes upon which this practice revolves. (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)

Branching time logics have been studied in computer science since the 1980s primarily to model the tree of computations for discrete transition systems. Inconsistency measures for propositional log...

Consistency is one of the key concepts of logic; logicians have put a great deal of effort into proving the consistency of many logics. Understanding what causes inconsistency is also important; some logicians have developed paraconsistent logics that, unlike classical logics, allow some contradictions without making all formulas provable. Another direction of research studies inconsistency by measuring the amount of inconsistency of sets of formulas. While the initial attempt in 1978 was too ambitious in trying to do (...) this for first-order logic, this research got a substantial boost when an inconsistency measure was proposed for propositional logic in 2002. Since then, researchers in logic and artificial intelligence have made many interesting proposals and found related issues. Almost all of this work has been done for propositional logic. The purpose of this paper is to extend inconsistency measures to logics that also contain operators, such as modal operators. We use the terminology “generalized propositional logic” for such logics. We show how to extend propositional inconsistency measures to sets of formulas in any such generalized propositional logic. Examples are used to illustrate how various modal operators, including spatial and tense operators, fit into this framework. We also show that the addition of operators leads to a weak type of inconsistency. In all cases, the calculations for several inconsistency measures are given. (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)

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.

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)

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.

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)

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)

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.

This paper identifies major inconsistencies in the threefold argument that Glaucon presents in defence of Thrasymachus in the second book of Plato’s Republic. Specifically, the paper argues for three claims. Firstly, it argues that in his account of the origin of justice Glaucon treats the consequences of justice as necessary, while in the test case he merely emphasizes incidental consequences. Secondly, the paper argues that in setting up the test case of the perfectly unjust man and the perfectly just man (...) Glaucon—despite claiming to be restating Thrasymachus’ claims, and also to be presenting the ordinary view of justice — uses some Socratic assumptions about the nature of justice. That is, although Gyges’ example follows directly from the first part of the argument and, in particular, from the claim that justice is grounded in convention, the unshakably just man of the test example is supposed to be motivated by justice itself. Finally, it is argued that the test case and Gyges' example are at variance with respect to public recognition: in the test case Glaucon suggests that most people would respect and admire a man who seemed to be perfectly just, while in his discussion of Gyges he intimates that tyrannical power strengthens itself not by the false appearance of perfect justice, but by appealing to a secret and yet widespread admiration for unpunished injustice. (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)

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)

Is logical consistency required for a set of beliefs or propositions to be categorically coherent? An affirmative answer is often assumed by mainstream epistemologists, and yet it is unclear why. Cases like the lottery and the preface call into question the assumption that beliefs must be consistent in order to be epistemically rational. And thus it is natural to wonder why all inconsistent sets of propositions are incoherent. On the other hand, Easwaran and Fitelson have shown that particular kinds of (...) inconsistency entail the epistemically ‘irrationality’ of holding certain sets of beliefs. In cases of the latter kind of inconsistency, it seems more reasonable to insist that such sets of beliefs or propositions are categorically incoherent. What the precise relationship is between coherence and consistency depends on the nature of the coherence relation. We shall examine recent attempts to explicate the coherence relation in terms of probabilistic measures of confirmation or agreement to see what they can teach us about the relationship between coherence and consistency. We shall show that some probabilistic measures of coherence allow for inconsistent sets to be categorically coherent, while satisfying plausible epistemic rationality constraints. Other probabilistic measures of coherence impose very strong logical consistency requirements, and some measures are tolerant of most forms of inconsistency. As we try to understand what distinguishes coherence measures in this respect, we will also draw some important lessons about Bayesian confirmation measures and differences in the way that they treat contradictory propositions. (shrink)

In this article, I reply to the charge, made in Analysis by Anthony Hatzimoysis, that my criticism of Sartre's Sketch for a Theory of the Emotions is unwarranted. I argued that Sartre offers two lines of reasoning about emotional experience that are in clear conflict with each other. Hatzimoysis counters that we can and should read Sartre's text in a way that avoids attributing inconsistency to Sartre. In response, I argue that Hatzimoysis' suggestion about how one might read the (...) text does not in fact remove the central inconsistency. Pace Hatzimoysis, the inconsistency that I identified remains. (shrink)