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 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 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)

An argument for the rationality of religious belief in the existence of God is defended. After reviewing three preconditions for rational belief, I show reasons to privilege the criterion of consistency. Taking the inconsistency of the religious belief in God and the belief in the scientific world picture as the impediment to a rational belief in God, I propose that we can overcome this objection by assuming, firstly, that God is a universal class. This allows us to put the problem (...) of God in set-theoretic terms, such that the antinomy that follows from such an assumption can be overcome by assuming that God is not a subject but a strict class that cannot be individuated. I conclude that that the self-contradictory nature of God does not prevent the believer from making a rational, ethical assessment that the contradiction resides in the possibility of using language to explain his existence, but that this does not make belief in the existence of God unjustifiable – on the contrary. In this way, we can say statements that claim God exists are justifiable. (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)

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 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 his Treatise of Human Nature Hume argues for a provocative account of the soul; the soul - or self, as he prefers to call it - is nothing but a bundle of perceptions. But this bold thesis, concedes Hume, gives rise to a predicament concerning two incompatible propositions, or principles as he calls them: one on the nature of perceptions, the other on the capabilities of the mind: "In short, there are two principles, which I cannot render consistent; nor (...) is it in my power to renounce either of them, viz. that all our distinct perceptions are distinct existences, and that the mind never perceives any real connexion among distinct existences". But the situation is not hopeless, thinks Hume. Someone might be able to show that these principles are actually consistent: "Others, perhaps, or myself, upon more mature reflection, may discover some hypothesis, that will reconcile those contradictions". (Treatise 636, my emphasis) My paper is an attempt to throw light on this important component in Hume’s analysis of his account of the self. In the course of our investigation of Hume's suggestion that an hypothesis can resolve his contradiction we will learn more about his conception of a contradiction - ultimately enriching our understanding of his account of the soul. (shrink)

Hans Frei, one of the most influential American theologians of the twentieth century, is generally considered a founder of postliberal theology. Frei never set forth his thinking systematically, and he has been criticized for being inconsistent, contradictory, and insufficiently rigorous. Jason Springs seeks here to offer a re-evaluation of Frei's work. Arguing that Hans Frei's theology cannot be understood without a meticulous consideration of the complex equilibrium of his theological and philosophical interests and influences, Springs vindicates Frei's christologically (...) motivated engagement with Ludwig Wittgenstein, Clifford Geertz, and Erich Auerbach, as well as his use of ordinary language philosophy and non-foundational philosophical insights, while illuminating his indebtedness to Karl Barth's theology. Moreover, by placing Frei's work in critical conversation with developments in pragmatist thought and cultural theory since his death, this re-reading aims to resolve many of the misunderstandings that vex his theological legacy. What emerges from Toward a Generous Orthodoxy is a sharpened account of the christologically anchored, interdisciplinary, and conversational character of Frei's theology, one he came to describe as a "generous orthodoxy"--modeling a way for academic theological voices to take seriously both their vocation to the Christian church and their roles as interlocutors in academic discourse. (shrink)

C. I. Lewis (I883-I964) was the first major figure in history and philosophy of logic—-a field that has come to be recognized as a separate specialty after years of work by Ivor Grattan-Guinness and others (Dawson 2003, 257).Lewis was among the earliest to accept the challenges offered by this field; he was the first who had the philosophical and mathematical talent, the philosophical, logical, and historical background, and the patience and dedication to objectivity needed to excel. He was blessed with (...) many fortunate circumstances, not least of which was entering the field when mathematical logic, after only six decades of toil, had just reaped one of its most important harvests with publication of the monumental Principia Mathematica. It was a time of joyful optimism which demanded an historical account and a sober philosophical critique. Lewis was one of the first to apply to mathematical logic the Aristotelian dictum that we do not understand a living institution until we see it growing from its birth. (shrink)

Two systems of belief change based on paraconsistent logics are introduced in this article by means of AGM-like postulates. The first one, AGMp, is defined over any paraconsistent logic which extends classical logic such that the law of excluded middle holds w.r.t. the paraconsistent negation. The second one, AGMo , is specifically designed for paraconsistent logics known as Logics of Formal Inconsistency (LFIs), which have a formal consistency operator that allows to recover all the classical inferences. Besides the three usual (...) operations over belief sets, namely expansion, contraction and revision (which is obtained from contraction by the Levi identity), the underlying paraconsistent logic allows us to define additional operations involving (non-explosive) contradictions. Thus, it is defined external revision (which is obtained from contraction by the reverse Levi identity), consolidation and semi-revision, all of them over belief sets. It is worth noting that the latter operations, introduced by S. Hansson, involve the temporary acceptance of contradictory beliefs, and so they were originally defined only for belief bases. Unlike to previous proposals in the literature, only defined for specific paraconsistent logics, the present approach can be applied to a general class of paraconsistent logics which are supraclassical, thus preserving the spirit of AGM. Moreover, representation theorems w.r.t. constructions based on selection functions are obtained for all the operations. (shrink)

This article is a preliminary presentation of conjunctive paraconsistency, the claim that there might be non-explosive true contradictions, but contradictory propositions cannot be considered separately true. In case of true ‘p and not p’, the conjuncts must be held untrue, Simplification fails. The conjunctive approach is dual to non-adjunctive conceptions of inconsistency, informed by the idea that there might be cases in which a proposition is true and its negation is true too, but the conjunction is untrue, Adjunction fails. (...) While non-adjunctivism is a well-known option, the other view is not so much studied nowadays, but it was not unknown in the tradition, and there are some positive suggestions, in recent literature, that the position is plausible and deserves to be developed. The article compares conjunctivism, non-adjunctivism and dialetheism, then focuses on some possible justifications, costs and benefits of the conjunctive view. (shrink)

This paper reflects on metametaphysics and as such develops a metametameta-physical view: that quietist metametaphysics requires dialetheism, and in turn a paraconsistent logic. I demonstrate this using Carnap’s metametaphysical position in his 'Empiricism, Semantics and Ontology' as an example, with regard to how it exhibits self-reference and results in inconsistency. I show how applying Carnap’s position to itself produces a dilemma, both horns of which lead to a contradiction. Such inconsistency commonly arises from meta-theories with global scope, as the 'meta' (...) approach aims to transcend the scope of that which it is theorizing about, whilst the global nature will place itself back within the scope of that which it is theorizing about, which together result in the theory referring to itself whilst refuting itself. I argue that any global metametaphysical theory that draws a limit to thought will face self-reference problems leading to contradictory realms. My conclusion is conditional: If we want to meta-philosophize in such a way and treat quietist meta-theories as being true, then we need to be dialetheist and utilize a paraconsistent logic in order to accommodate the contradictions that result from such theorizing. (shrink)

This is a corrected version of the final proofs. I've fixed a number of typos, and corrected a blunder in chapter 4. In chapter 4 I say that 'this is this' is analytic, and 'this is not this' is antonymous. This is inconsistent with what I say in chapter 5, and not what I actually think. Rather, 'this is this' is taugologous, and 'this is not this' is contradictory. Analyticity and autnonmy are sense properties while tautologousness and contradictoriness (...) are formal logical properties. Heading, ToC and Index updated accordingly. (Oxford will make these corrections in their online version and in future print runs.). (shrink)

Reid argues that Hume’s claim that justice is an artificial virtue is inconsistent with the fact that gratitude is a natural sentiment. This chapter shows that Reid’s argument succeeds only given a philosophy of mind and action that Hume rejects. Among other things, Reid assumes that one can conceive of one of a pair of contradictories only if one can conceive of the other—a claim that Hume denies. So, in the case of justice, the disagreement between Hume and Reid (...) is, at bottom, a disagreement over their respective conceptions of how the human mind works at its most fundamental level. (shrink)

Physical dimensions like “mass”, “length”, “charge”, represented by the symbols [M], [L], [Q], are not numbers, but used as numbers to perform dimensional analysis in particular, and to write the equations of physics in general, by the physicist. The law of excluded middle falls short of explaining the contradictory meanings of the same symbols. The statements like “m tends to 0”, “r tends to 0”, “q tends to 0”, used by the physicist, are inconsistent on dimensional grounds because (...) “m”, “r”, “q” represent quantities with physical dimensions of [M], [L], [Q] respectively and “0” represents just a number—devoid of physical dimension. Consequently, due to the involvement of the statement “q tends to 0'', where q is the test charge” in the definition of electric field leads to either circular reasoning or a contradiction regarding the experimental verification of the smallest charge in the Millikan–Fletcher oil drop experiment. Considering such issues as problematic, by choice, I make an inquiry regarding the basic language in terms of which physics is written, with an aim of exploring how truthfully the verbal statements can be converted to the corresponding physico-mathematical expressions, where “physico-mathematical” signifies the involvement of physical dimensions. Such investigation necessitates an explanation by demonstration of “self inquiry”, “middle way”, “dependent origination”, “emptiness/relational existence”, which are certain terms that signify the basic tenets of Buddhism. In light of such demonstration I explain my view of “definition”; the relations among quantity, physical dimension and number; meaninglessness of “zero quantity” and the associated logico-linguistic fallacy; difference between unit and unity. Considering the importance of the notion of electric field in physics, I present a critical analysis of the definitions of electric field due to Maxwell and Jackson, along with the physico-mathematical conversions of the verbal statements. The analysis of Jackson’s definition points towards an expression of the electric field as an infinite series due to the associated “limiting process” of the test charge. However, it brings out the necessity of a postulate regarding the existence of charges, which nevertheless follows from the definition of quantity. Consequently, I explain the notion of undecidable charges that act as the middle way to resolve the contradiction regarding the Millikan–Fletcher oil drop experiment. In passing, I provide a logico-linguistic analysis, in physico-mathematical terms, of two verbal statements of Maxwell in relation to his definition of electric field, which suggests Maxwell’s conception of dependent origination of distance and charge ) and that of emptiness in the context of relative vacuum. This work is an appeal for the dissociation of the categorical disciplines of logic and physics and on the large, a fruitful merger of Eastern philosophy and Western science. Nevertheless, it remains open to how the reader relates to this work, which is the essence of emptiness. (shrink)

There is no question that Fichte's theory of conscience is central to his system of ethics. Yet his descriptions of its role in practical deliberation appear inconsistent, if not contradictory. Many scholars have claimed that for Fichte conscience plays a material role by providing the content of our moral obligations—the Material Function View. Some have denied this, however, claiming that conscience only plays a formal role by testing our moral convictions in any given case—the Formal Function View. My (...) aim in this paper is to offer a new contribution to this debate. I begin by supplying further evidence in support of the view that conscience only plays a formal function in Fichte's ethics. Then I call attention to a deeper problem this view faces, namely, that it invites an infinite regress by making one's conviction a matter of higher-order reflection. The key to overcoming this threat, I argue, lies in Fichte's doctrine of feeling, whereby the criterion of one's conviction lies, not in a cognitive state, but in an affective state. In closing, I discuss the relevance of Fichte's theory for current debates over the nature of moral error and moral deference. (shrink)

ABSTRACT This paper deals with the problem of characterizing the content of experience as either conceptual or non-conceptual in -/- Kant’s transcendenta -/- l philosophy, a topic widely debated in contemporary philosophy. I start out with -/- Kant’s pre -/- -critical discussions of space and time in which he develops a specific notion of non-conceptual content. Secondly, I show that this notion of non-conceptual intuitional content does not seem to match well with the Transcendental Deduction. This incongruity results in three (...) interrelated problems that are -/- inherent to Kant’s -/- Transcendental Deduction in the -/- Critique -/- 1 -/- : the ‘Independency Disagreement’, the ‘Conceptualism Contradiction’ and the ‘Intuition Inconsistency’. -/- These three problems derive from apparently contradictory claims concerning the possibility of non-conceptual content. Contemporary Kantian conceptualists and non-conceptualists tend to take a stance at either side of the dilemma rather than trying to dissolve these tensions. In response to this, I propose a new solution to these difficulties based on a distinction between two kinds of conceptualism. This will reveal why Kant is a non-conceptualist in one significant sense, but also why he is still better regarded a conceptualist. -/- . (shrink)

Girolamo Saccheri (1667--1733) was an Italian Jesuit priest, scholastic philosopher, and mathematician. He earned a permanent place in the history of mathematics by discovering and rigorously deducing an elaborate chain of consequences of an axiom-set for what is now known as hyperbolic (or Lobachevskian) plane geometry. Reviewer's remarks: (1) On two pages of this book Saccheri refers to his previous and equally original book Logica demonstrativa (Turin, 1697) to which 14 of the 16 pages of the editor's "Introduction" are devoted. (...) At the time of the first edition, 1920, the editor was apparently not acquainted with the secondary literature on Logica demonstrativa which continued to grow in the period preceding the second edition \ref[see D. J. Struik, in Dictionary of scientific biography, Vol. 12, 55--57, Scribner's, New York, 1975]. Of special interest in this connection is a series of three articles by A. F. Emch [Scripta Math. 3 (1935), 51--60; Zbl 10, 386; ibid. 3 (1935), 143--152; Zbl 11, 193; ibid. 3 (1935), 221--333; Zbl 12, 98]. (2) It seems curious that modern writers believe that demonstration of the "nondeducibility" of the parallel postulate vindicates Euclid whereas at first Saccheri seems to have thought that demonstration of its "deducibility" is what would vindicate Euclid. Saccheri is perfectly clear in his commitment to the ancient (and now discredited) view that it is wrong to take as an "axiom" a proposition which is not a "primal verity", which is not "known through itself". So it would seem that Saccheri should think that he was convicting Euclid of error by deducing the parallel postulate. The resolution of this confusion is that Saccheri thought that he had proved, not merely that the parallel postulate was true, but that it was a "primal verity" and, thus, that Euclid was correct in taking it as an "axiom". As implausible as this claim about Saccheri may seem, the passage on p. 237, lines 3--15, seems to admit of no other interpretation. Indeed, Emch takes it this way. (3) As has been noted by many others, Saccheri was fascinated, if not obsessed, by what may be called "reflexive indirect deductions", indirect deductions which show that a conclusion follows from given premises by a chain of reasoning beginning with the given premises augmented by the denial of the desired conclusion and ending with the conclusion itself. It is obvious, of course, that this is simply a species of ordinary indirect deduction; a conclusion follows from given premises if a contradiction is deducible from those given premises augmented by the denial of the conclusion---and it is immaterial whether the contradiction involves one of the premises, the denial of the conclusion, or even, as often happens, intermediate propositions distinct from the given premises and the denial of the conclusion. Saccheri seemed to think that a proposition proved in this way was deduced from its own denial and, thus, that its denial was self-contradictory (p. 207). Inference from this mistake to the idea that propositions proved in this way are "primal verities" would involve yet another confusion. The reviewer gratefully acknowledges extensive communication with his former doctoral students J. Gasser and M. Scanlan. ADDED 14 March 14, 2015: (1) Wikipedia reports that many of Saccheri's ideas have a precedent in the 11th Century Persian polymath Omar Khayyám's Discussion of Difficulties in Euclid, a fact ignored in most Western sources until recently. It is unclear whether Saccheri had access to this work in translation, or developed his ideas independently. (2) This book is another exemplification of the huge difference between indirect deduction and indirect reduction. Indirect deduction requires making an assumption that is inconsistent with the premises previously adopted. This means that the reasoner must perform a certain mental act of assuming a certain proposition. It case the premises are all known truths, indirect deduction—which would then be indirect proof—requires the reasoner to assume a falsehood. This fact has been noted by several prominent mathematicians including Hardy, Hilbert, and Tarski. Indirect reduction requires no new assumption. Indirect reduction is simply a transformation of an argument in one form into another argument in a different form. In an indirect reduction one proposition in the old premise set is replaced by the contradictory opposite of the old conclusion and the new conclusion becomes the contradictory opposite of the replaced premise. Roughly and schematically, P,Q/R becomes P,~R/~Q or ~R, Q/~P. Saccheri’s work involved indirect deduction not indirect reduction. (3) The distinction between indirect deduction and indirect reduction has largely slipped through the cracks, the cracks between medieval-oriented logic and modern-oriented logic. The medievalists have a heavy investment in reduction and, though they have heard of deduction, they think that deduction is a form of reduction, or vice versa, or in some cases they think that the word ‘deduction’ is the modern way of referring to reduction. The modernists have no interest in reduction, i.e. in the process of transforming one argument into another having exactly the same number of premises. Modern logicians, like Aristotle, are concerned with deducing a single proposition from a set of propositions. Some focus on deducing a single proposition from the null set—something difficult to relate to reduction. (shrink)

A new puzzle about material constitution is presented and its implications are discussed. The moral of the story is that familiar intuitions supporting a neo-Aristotelian view of the material world are contradictory. To accommodate these intuitions is to embrace inconsistency. Therefore, neo-Aristotelianism is worse off for its intuitive appeal. Furthermore, the puzzle is used to argue for an account of ordinary modal thought and language that’s reconstructive, or ameliorative.

This paper investigates the argument that substantiates Nietzsche's refusal of teh Kantian concept of thing in itself. As Maudmarie Clark points out, Nietzsche dismisses this notion because he views it as self-contradictory. The main concern of the paper will be to account for this position. In particular, the two main theses defended here are that the argument underlying Nietzsche's claim is that the concept of thing in itself amounts to the inconsistent idea of a propertyless thing and that (...) this argument is a sound one. Finally, I will show that the reading proposed allows a deflationary response to the objection that Nietzsche's will to power is simply a new version of the post-Kantian thing in itself.Dieser Aufsatz untersucht die Argumentation, die Nietzsches Zurückweisung des kantischen Begriffs des Dings an sich untermauert. Wie Maudmarie Clark betont, berwift Nietzsche diesen Begriff als selbstwidersprüchlich. Hauptanliegen des Aufsatzes ist, dies deutlich zu machen. Insbesondere werden folgende zwei Thesen vertrenen: dass das Nietzsches Position zugrundeliegende Argument darin besteht, der Begriff des Dings an sich sei der inkonsistente Begriff eines eigenschaftslosen Dings; dass dieses Argument stichhaltig ist. Schließlich wird gezeigt, dass diese Interpretation eine delfationäre Antwort auf den Einwand ermöglicht, Nietzsches Wille zur Macht sei einfach eine neue Variante des postkantischen Dings an sich. (shrink)

In this paper, we criticize Hans Jonas’s analogy between God’s power and the operation of physical forces. We wonder why, if omnipotence had proved to be "a self-contradictory concept", does Jonas still need to invoke the occurrence of horrendous evils to support the view that "God is not all powerful". We suggest that "God’s retreating into himself in order to give room to the world, renouncing his being and divesting himself of his deity" are beautiful but inconsistent metaphors (...) of creation. Our central claim is that God’s alleged retirement, even if it were conceivable, would not the least diminish his responsibility in the occurrence of evil. (shrink)

Study represents an application of the neutrosophic method, for solving the contradiction between communication and information. In addition, it recourse to an appropriate method of approaching the contradictions: Extensics, as the method and the science of solving the contradictions. The research core is the reality that the scientific research of communication-information relationship has reached a dead end. The bivalent relationship communicationinformation, information-communication has come to be contradictory, and the two concepts to block each other. After the critical examination of (...) conflicting positions expressed by many experts in the field, the extensic and inclusive hypothesis is issued that information is a form of communication. The object of communication is the sending of a message. The message may consist of thoughts, ideas, opinions, feelings, beliefs, facts, information, intelligence or other significational elements. When the message content is primarily informational, communication will become information or intelligence. The arguments of supporting the hypothesis are: a) linguistic (the most important being that there is "communication of information" but not "information of communication"; also, it is clarified and reinforced the over situated referent, that of the communication as a process), b) systemic-procedural (in the communication system is developing an information system; the informing actant is a type of communicator, the information process is a communication process), c) practical (the delimitation eliminates the efforts of disparate and inconsistent understanding of the two concepts), d) epistemological arguments (the possibility of intersubjective thinking of reality is created), linguistic arguments, e) logical and realistic arguments (it is noted the situation that allows to think coherently in a system of concepts - derivative series or integrative groups) f) and arguments from historical experience (the concept of communication has temporal priority, it appears 13 times in Julius Caesar’s writings ). In an axiomatic conclusion, the main arguments are summarized in four axioms: three are based on the pertinent observations of specialists, and the fourth is a relevant application of Florentin Smarandache’s neutrosophic theory. (shrink)

In this essay, I argue that there are two more or less distinct theories of the State in Hegel. The first, and better known, is developed in the Philosophy of Right, wherein Hegel endorses the notion of a coercive, centralised, and hierarchical 'Ideal State'. This is precisely the theory which certain radical Hegelians of the nineteenth century (e.g., Marx and Bakunin) viewed with such deep suspicion. The second, which has not received as much attention by commentators, appears in the Phenomenology (...) and other early writings. Although this theory introduces many of the key components of Hegel's later political philosophy, it is nonetheless far more radical in its political implications--most important, in its gesturing toward a society which makes room for the realisation of the stateless, classless vision of anarchist communism. The point is not to demonstrate that Hegel is inconsistent or self-contradictory, but show that there are elements of creative tension within his political theory which are not only sufficient to vindicate him from the criticisms of Marx and Bakunin, but also to re-contextualise him as a radical precursor. As I shall argue, the kind of society that emerges in the final chapters of the Phenomenology need not contain the elements of coercion and class struggle which appear in the Philosophy of Right and repulse Marx and Bakunin. On the contrary, such a society may be understood as prefiguring the classless, stateless society which both Marx and Bakunin ultimately endorse. (shrink)

Thomas Hobbes’ theory of punishment plays a constitutive role in the Leviathan’s theory of state sovereignty. Despite this, Hobbes’ justification for punishment is widely found to be discrepant, weak, inconsistent, and contradictory. Two dominant tendencies in the scholarship attempt to stabilize the Leviathan’s justification for the state’s right to punish by either identifying it with the sovereign’s right to war or by elaborating a theory of authorization within the state. In contrast, by tracing the deployments of the metaphor (...) that Hobbes utilizes to evoke the state’s right to punish in the Leviathan (i.e. that of the nerves of the Leviathan) this paper finds that these two accounts can be made to be consistent with each other — thereby destabilizing the grounds upon which the theory of punishment can be founded. (shrink)

Cases of non-traditional family-making offer a rich seam for thinking about normative parenthood. Gamete donors are genetically related to the resulting offspring but are not thought to be normative parents. Gestational surrogates are also typically not thought to be normative parents, despite having gestated a child. Adoptive parents are typically thought to be normative parents even though they are neither genetically nor gestationally related to their child. Philosophers have paid attention to these kinds of cases. But they have not paid (...) attention to what the people who have engaged in these forms of family-making have to say about what they’re doing and, more specifically, how they answer the questions: “Who is the normative parent? And why?” Paying attention to their answers reveals two things. First, accounts of parenthood from people involved in two forms of non-traditional family-making – reproduction with gestational surrogacy and reproduction with donated eggs – are mutually inconsistent. This is not surprising. What is surprising is that the contradictory aspects of the views evince a common commitment to, as I shall put it, naturalizing parenthood. The central goal of this paper is to explain what that means, but rough idea is that in naturalizing parenthood, prospective parents aim to put the features that make someone a normative parent beyond the reach of human agency. I conclude by briefly suggesting that we should think of the grounds of normative parenthood – and the very task of theorizing about the grounds of normative parenthood – in a way that avoids the need to naturalize altogether. (shrink)

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

“There is no use in trying,” said Alice; “one can’t believe impossible things.” “I dare say you haven’t had much practice,” said the Queen. “When I was your age, I always did it for half an hour a day. Why, sometimes I’ve believed as many as six impossible things before breakfast”. Lewis Carroll, Through the Looking Glass. -/- It is a rather common view among philosophers that one cannot, properly speaking, be said to believe, conceive, imagine, hope for, or seek (...) what is impossible. -/- Some philosophers, for instance George Berkeley and the early Wittgenstein, thought that logically contradictory propositions lack cognitive meaning (informational content) and cannot, therefore, be thought or believed. Philosophers who do not go as far as Berkeley and Wittgenstein in denying that impossible propositions or states of affairs are thinkable, may still claim that it is impossible to rationally believe an impossible proposition. On a classical “Cartesian” view of belief, belief is a purely mental state of the agent holding true a proposition p that she “grasps” and is directly acquainted with. But if the agent is directly acquainted with an impossible proposition, then, presumably, she must know that it is impossible. But surely no rational agent can hold true a proposition that she knows is impossible. Hence, no rational agent can believe an impossible proposition. Thus it seems that on the Cartesian view of propositional attitudes as inner mental states in which proposition are immediately apprehended by the mind, it is impossible for a rational agent to believe, imagine or conceive an impossible proposition. -/- Ruth Barcan Marcus (1983) has suggested that a belief attribution is defeated once it is discovered that the proposition, or state of affairs that is believed is impossible. According to her intuition, just as knowledge implies truth, belief implies possibility. -/- It is commonplace that people claim to believe propositions that later turn out to be impossible. According to Barcan Marcus, the correct thing to say in such a situation is not: I once believed that A but I don’t believe it any longer since I have come to realize that it is impossible that A. What one should say is instead: It once appeared to me that I believed that A, but I did not, since it is impossible that A. Thus, Barcan Marcus defends what we might call Alice’s thesis: Necessarily, for any proposition p and any subject x, if x believes p, then p is possible. -/- Alice’s thesis that it is impossible to hold impossible beliefs, seems to come into conflict with our ordinary practices of attributing beliefs. Consider a mathematical example. Some mathematicians believe that CH (the continuum hypothesis) is true and others believe that it is false. But if CH is true, then it is necessarily true; and if it is false, then it is necessarily false. Regardless of whether CH is true or false, the conclusion seems to be that there are mathematicians who believe impossible propositions. -/- Examples of apparent beliefs in impossible propositions outside of mathematics are also easy to come by. Consider, for example, Kripke’s (1999) story of the Frenchman Pierre who without realizing it has two different names ‘London’ and ‘Londres’ for the same city, London. After having arrived in London, Pierre may assent to ‘Londres is beautiful and London is not beautiful’ without being in any way irrational. It seems reasonably to infer from this that Pierre believes that Londres is beautiful and London is not beautiful. But since ‘Londres’ and ‘London’ are rigid designators for the same city, it seems to follow from this that Pierre believes the inconsistent proposition that we may express as ‘London is both beautiful and not beautiful’. (shrink)

Joshua Glasgow argues against the existence of races. His experimental philosophy asks subjects questions involving racial categorization to discover the ordinary concept of race at work in their judgments. The results show conflicting information about the concept of race, and Glasgow concludes that the ordinary concept of race is inconsistent. I conclude, rather, that Glasgow’s results fit perfectly fine with a social-kind view of races as real social entities. He also presents thought experiments to show that social-kind views give (...) the wrong results, but intuitions might differ on which results are the wrong ones, and social-kind views can resist the implications he derives from these cases. Widespread false beliefs about a concept or category need not undermine anything’s existence, and a sufficiently context-sensitive approach to races will allow for competing criteria for race-membership in different contexts without contradictory criteria in any one context. Glasgow’s arguments are therefore unsuccessful. (shrink)

Nicholas Rescher claims that rational decision theory “may leave us in the lurch”, because there are two apparently acceptable ways of applying “the standard machinery of expected-value analysis” to his Dr. Psycho paradox which recommend contradictory actions. He detects a similar contradiction in Newcomb’s problem. We consider his claims from the point of view of both Bayesian decision theory and causal decision theory. In Dr. Psycho and in Newcomb’s Problem, Rescher has used premisses about probabilities which he assumes to (...) be independent. From the former point of view, we show that the probability premisses are not independent but inconsistent, and their inconsistency is provable within probability theory alone. From the latter point of view, we show that their consistency can be saved, but then the contradictory recommendations evaporate. Consequently, whether one subscribes to evidential or causal decision theory, rational decision theory is not in any way vitiated by Rescher’s arguments. (shrink)

Searle proposes an argument in order to prove the existence of universals and thereby solve the problem of universals: From every meaningful general term P(x) follows a tautology Vx[P(x) v -P(x)], which entails the existence of the corresponding universal P. To be convincing, this argument for existence must be valid, it must presume true premises and it must be free of any informal fallacy. First, the validity of the argument for existence in its non-modal interpretation will be proven with the (...) help of the formal deductive system F. Secondly, it will be shown that a self-contradictory tautology concept is employed, which renders the premises meaningless. Consequently, the inconsistency will be emended through redefinition and the argument's ensuing correctness will be demonstrated. Finally, it will be shown that the argument for existence presupposes the existence of universals in its premise and hence begs the question. (shrink)

Most formalisms for representing common-sense knowledge allow incomplete and potentially inconsistent information. When strong negation is also allowed, contradictory conclusions can arise. A criterion for deciding between them is needed. The aim of this paper is to investigate an inherent and autonomous comparison criterion, based on specificity as defined in [POO 85, SIM 92]. In contrast to other approaches, we consider not only defeasible, but also strict knowledge. Our criterion is context-sensitive, i. e., preference among defeasible rules is (...) determined dynamically during the dialectical analysis.We show how specificity can be defined in terms of two different approaches: activation sets and derivation trees. This allows us to get a syntactic criterion that can be implemented in a computationally attractive way. The resulting definitions may be applied in general rulebased formalisms. We present theorems linking both characterizations. Finally we discuss other frameworks for defeasible reasoning in which preference handling is considered explicitly. (shrink)

The paper argues for the plausibility of the thesis that there are no genuine moral dilemmas. In particular, I examine Bernard Williams’ objection that agentregret in a situation of conflict among contradictory moral obligations would prove the existence of such dilemmas. Contrary to Williams’claim, agentregret in these situations is not sufficient to establish the existence of such moral dilemmas. Williams’ argument cannot undermine the logical consistency of moral theories, nor their capacity to solve moral conflicts. I also consider Monika (...) Betzler’s proposal that agentregret can be considered ‘rational in a looser sense’ without implying an inconsistency in moral theory. In order to discuss the plausibility of this proposal, I focus on the interpretation of agentregret as an emotional response which also restores offended moral integrity. I claim, in conclusion, that it is reasonable to assume this proposal, insofar as moral theory can determine some criteria of judgement which allow a distinction between authentic and false modalities of integration. (shrink)

Priest's theory of motion is based on Leibniz's Continuity Condition (LCC), which states that any state that exists at each instant in a continuous set of moments also exists at its temporal limit. If we accept the CCL, a free-falling pen would have to be simultaneously in motion and at rest at the instant of change: the critical moment when it hits the ground, thus passing from the state of motion to that of rest. This seems to be a (...) class='Hi'>contradictory state of affairs, which is precisely what Priest claims to be the case. In this article, I discuss the logical possibility of empirically testing whether such a contradictory state of affairs occurs. (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 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.

In this chapter, I grant Jc Beall’s assertion that the best understanding of the doctrine of the incarnation posits that Christ is a contradictory being, in the sense that it has him satisfying complementary pairs of predicates. I also argue, however, that by attending to a distinction between predicate negation and sentence negation, this view can be upheld without positing any classical logical contradictions. I argue that the resulting Christological view has several advantages over Beall’s: It is more conservative (...) about avoiding contradiction, exhibits greater logical neutrality, and comports better with Christian tradition. (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.

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)

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...

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).

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)

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)

This article explores the contradictory nature of the ghost in Hamlet and shows how Shakespeare seeks to manipulate the reader’s response in Hamlet by using contradictions and ambiguities. The article also explores the ways in which the reader responds to these contradictions and reconstructs a palpable world in the impalpable world of the text. These contradictions compel the reader to participate in the composition of the text and make him keep changing his own approach to the work with the (...) result that the more he reads the play, the deeper he finds himself entrenched in contradictions. As he fails to grasp the logic of events, the reader relates his own world to the text instead of relating the events of the text to his world and recreates his own world. Therefore, he can easily detach himself from the text and let his imagination run loose as the play proves too vague for him to comprehend. In reading Hamlet, the imagination runs wild and travels far beyond the text to an extent where the reader perceives things, which stand not within but utterly outside the text. Eventually, the reality achieved by the reader in the course of reading the play is only the reality which dwells in the innermost recesses of his mind. (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.

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)

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)

While social geographers have convincingly made the case that space is not an external constant, but rather is produced through inter-relations, anthropologists and sociologists have done much to further an understanding of time, as itself constituted through social interaction and inter-relation. Their work suggests that time is not an apolitical background to social life, but shapes how we perceive and relate to others. For those interested in exploring issues such as identity, community and difference, this suggests that attending to how (...) temporal discourses are utilised in relation to these issues is a key task. This article seeks to contribute to an expansion of the debate about time and sociality by contributing an analysis of a variety of ways in which Gloria Anzaldúa utilises temporal concepts as part of her work of rethinking social identity and community. In particular, I suggest that in contesting homogeneous identity, Anzaldúa also implicitly contests linear temporal frameworks. Further, in creating new frameworks for identity, I suggest the possibility of discerning an alternative approach to time in her work that places difference at the heart of simultaneity. I suggest that the interconnection between concepts of time and community within Anzaldúa’s work indicates, more broadly, that attempts to rework understandings of relationality must be accompanied by reworked accounts of temporality. (shrink)

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)

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)