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

The relationship between inconsistency and Lehrerian coherence is scrutinized. Like most coherence theorists of epistemic justification, Lehrer contends that consistency is necessary for coherence. Despite this contention, minimally inconsistent belief-sets prove coherent and rationally acceptable on Lehrer's account of coherence. Lehrer is left with the following dilemma: If consistency is necessary for coherence, then (i) he must revise his account of coherence accordingly and, more importantly, (ii) such coherence is nof necessary for justification, since intuitively we are justified in (...) accepting such minimally inconsistent belief-sets. If, on the other hand, minimally inconsistent acceptance systems can be coherent, then to prevent pairwise inconsistent statements form readily cohering with such systems, Lehrer must deny that rational acceptance is closed under deduction. (shrink)

The aim in this paper is to define an Abductive Question-Answer System for the minimal logic of formal inconsistency \. As a proof-theoretical basis we employ the Socratic proofs method. The system produces abductive hypotheses; these are answers to abductive questions concerning derivability of formulas from sets of formulas. We integrated the generation of and the evaluation of hypotheses via constraints of consistency and significance being imposed on the system rules.

This paper proposes a new account of bounded or minimal doxastic rationality (in the sense of Cherniak 1986), based on the notion that beliefs are answers to questions (à la Yalcin 2018). The core idea is that minimally rational beliefs are linked through thematic connections, rather than entailment relations. Consequently, such beliefs are not deductively closed, but they are closed under parthood (where a part is an entailment that answers a smaller question). And instead of avoiding all inconsistency, (...) minimally rational believers only avoid blatant inconsistencies (where some beliefs are blatantly inconsistent when they contradict one another on a particular question). Rather than cohering into a single overall world view, beliefs are more loosely connected in what is best described as a web of questions. This view of minimally rational belief naturally gives rise to an account of deductive inquiry on which deductive reasoning is a matter of posing new questions. (shrink)

For millennia self has been conjectured to be necessary for consciousness. But scant empirical evidence has been adduced to support this hypothesis. Inconsistent explications of “self” and failure to design apt experiments have impeded progress. Advocates of phenomenological psychiatry, however, have helped explicate “self,” and employed it to explain some psychopathological symptoms. In those studies, “self” is understood in a minimalist sense, sheer “for-me-ness.” Unfortunately, explication of the “minimal self” (MS) has relied on conceptual analysis, and applications to psychopathology (...) have been hermeneutic, allowing for many degrees of interpretive latitude. The result is that MS’s current scientific status is analogous to that of the “atom,” at the time when “atom” was just beginning to undergo transformation from a philosophical to a scientific concept. Fortunately, there is now an opportunity to promote a similar transformation for “MS.” Discovery of the brain’s Default Mode Network (DMN) opened the door to neuroimaging investigations of self. Taking the DMN and other forms of intrinsic activity as a starting point, an empirical foothold can be established, one that spurs experimental research and that enables extension of research into multiple phenomena. New experimental protocols that posit “MS” can help explain phenomena hitherto not thought to be related to self, thereby hastening development of a mature science of self. In particular, targeting phenomena wherein consciousness is lost and recovered, as in some cases of Unresponsive Wakefulness Syndrome (UWS), allow for design of neuroimaging probes that enable detection of MS during non-conscious states. These probes, as well as other experimental protocols applied to NREM Sleep, General Anesthesia (GA), and the waking state, provide some evidence to suggest that not only can self and consciousness dissociate, MS might be a necessary precondition for conscious experience. Finally, these findings have implications for the science of consciousness: it has been suggested that “levels of consciousness” (LoC) is not a legitimate concept for the science of consciousness. But because we have the conceptual and methodological tools with which to refine investigations of MS, we have the means to identify a possible foundation—a bifurcation point—for consciousness, as well as the means by which to measure degrees of distance from that foundation. These neuroimaging investigations of MS position us to better assess whether LoC has a role to play in a mature science of consciousness. (shrink)

Graham Priest has formulated the minimally inconsistent logic of paradox (MiLP), which is paraconsistent like Priest’s logic of paradox (LP), while staying closer to classical logic. We present logics that stand to (the propositional fragments of) strong Kleene logic (K3) and the logic of first-degree entailment (FDE) as MiLP stands to LP. That is, our logics share the paracomplete and the paraconsistent-cum-paracomplete nature of K3 and FDE, respectively, while keeping these features to a minimum in order to stay closer to (...) classical logic. We give semantic and sequent-calculus formulations of these logics, and we highlight some reasons why these logics may be interesting in their own right. (shrink)

The relationship between inconsistency and Lehrerian coherence is scrutinized. Like most coherence theorists of epistemic justification, Lehrer contends that consistency is necessary for coherence. Despite this contention, minimally inconsistent belief-sets prove coherent and rationally acceptable on Lehrer's account of coherence. Lehrer is left with the following dilemma: If consistency is necessary for coherence, then (i) he must revise his account of coherence accordingly and, more importantly, (ii) such coherence is nof necessary for justification, since intuitively we are justified in (...) accepting such minimally inconsistent belief-sets. If, on the other hand, minimally inconsistent acceptance systems can be coherent, then to prevent pairwise inconsistent statements form readily cohering with such systems, Lehrer must deny that rational acceptance is closed under deduction. (shrink)

In this paper we study an alternative approach to the concept of abstract logic and to connectives in abstract logics. The notion of abstract logic was introduced by Brown and Suszko —nevertheless, similar concepts have been investigated by various authors. Considering abstract logics as intersection structures we extend several notions to their κ -versions, introduce a hierarchy of κ -prime theories, which is important for our treatment of infinite connectives, and study different concepts of κ -compactness. We are particularly interested (...) in non-topped intersection structures viewed as semi-lattices with a minimal meet-dense subset, i.e., with a minimal generator set. We study a chain condition which is sufficient for a minimal generator set, implies compactness of the logic, and in regular logics is equivalent to compactness of the consequence relation together with the existence of a inconsistent set, where κ is the cofinality of the cardinality of the logic. Some of these results are known in a similar form in the context of closure spaces, we give extensions to intersection structures and to big cardinals presenting new proofs based on set-theoretical tools. The existence of a minimal generator set is crucial for our way to define connectives. Although our method can be extended to further non-classical connectives we concentrate here on intuitionistic and infinite ones. Our approach leads us to the concept of the set of complete theories which is stable under all considered connectives and gives rise to the definition of the topological space of the logic. Topological representations of abstract logics by means of this space remain to be further investigated. (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)

Concentrating on the views of Christopher Stone, who advocates moral pluralism, and J. Baird Callicott, who criticizes Stone’s views, I argue that the debate has been confused by a conflation of three different positions, here called minimal, moderate, and extreme moral pluralism. Minimal pluralism is uncontroversial because all known moral theories are minimally pluralistic. Extreme pluralism is defective in the ways that Callicott alleges and, moreover, is inconsistent with integrity in the moral life. However, moderate pluralism of the (...) sort that I advance in Environmental Justice is distinct from extreme pluralism and free of its defects. It is also consistent with Callicott’s version of Aldo Leopold’s land ethic, which is itself moderately pluralistic. (shrink)

Concentrating on the views of Christopher Stone, who advocates moral pluralism, and J. Baird Callicott, who criticizes Stone’s views, I argue that the debate has been confused by a conflation of three different positions, here called minimal, moderate, and extreme moral pluralism. Minimal pluralism is uncontroversial because all known moral theories are minimally pluralistic. Extreme pluralism is defective in the ways that Callicott alleges and, moreover, is inconsistent with integrity in the moral life. However, moderate pluralism of the (...) sort that I advance in Environmental Justice is distinct from extreme pluralism and free of its defects. It is also consistent with Callicott’s version of Aldo Leopold’s land ethic, which is itself moderately pluralistic. (shrink)

In this paper I present two new strategies for inconsistencyadaptive logics: the reliable sufficient information strategy of ACLuN3 andthe minimally abnormal sufficient information strategy of ACLuN4. I giveproof theory and semantics for both ACLuN3 and ACLuN4. I also compare them with the well-known inconsistency-adaptive logics ACLuN1 andACLuN2.

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

Those who deny that the provision of protection services could be supplied through either the market or some other nonmonopolistic device must therefore endorse some sort of state. And those within that group who maintain that the provision of such services to everyone within a given territory is the only proper function of government must therefore advocate a minimal, or laissez-faire, state. However, an examination of the arguments of three of the better-known contemporary minarchists discloses problems of internal (...) class='Hi'>inconsistency which render them unsound, even on their own.. (shrink)

It is shown that all those theses of traditional logic which were rejected by Russell in terms of a preferred interpretation of 'all' and 'some', in fact lead to inconsistency in any formal system of traditional logic satisfying certain minimal conditions. Hence, Russell's refutation is ultimately independent of his interpretation. Further, the derivation of each of the refutable theses depends crucially on the Bochenski/Lukasiewicz postulate 'Some _A are _A'. If this postulate is removed, the theses which remain are (...) exactly those which translate into theses of quantification theory. (shrink)

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

In this paper we present some algorithms for computing minimal conflicts. First of all we discuss the relationship between minimal conflicts and minimally inconsistent subsets. Then we introduce an algorithm for computing all minimally inconsistent subsets, which is applied to generating all minimal conflicts. Furthermore, an algorithm for computing all minimal conflicts using structured description is introduced, and its correctness is proved; its time complexity is also shown. The algorithm using structured description terminates in polynomial time (...) for some special system, such as the tree–structured systems. The algorithms are also complared with related works. (shrink)

Minimally inconsistent LP (MiLP) is a nonmonotonic paraconsistent logic based on Graham Priest's logic of paradox (LP). Unlike LP, MiLP purports to recover, in consistent situations, all of classical reasoning. The present paper conducts a proof-theoretic analysis of MiLP. I highlight certain properties of this logic, introduce a simple sequent system for it, and establish soundness and completeness results. In addition, I show how to use my proof system in response to a criticism of this logic put forward by JC (...) Beall. (shrink)

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

Let random vectors \ represent joint measurements of certain subsets \ of properties\ in different contexts\. Such a system is traditionally called noncontextual if there exists a jointly distributed set \ of random variables such that \ has the same distribution as \ for all \ A trivial necessary condition for noncontextuality and a precondition for many measures of contextuality is that the system is consistently connected, i.e., all \ measuring the same property \ have the same distribution. The contextuality-by-default (...) approach allows defining more general measures of contextuality that apply to inconsistently connected systems as well, but at the price of a higher computational cost. In this paper we propose a novel measure of contextuality that shares the generality of the CbD approach and the computational benefits of the previously proposed negative probability approach. The present approach differs from CbD in that instead of considering all possible joints of the double-indexed random variables \, it considers all possible approximating single-indexed systems \. The degree of contextuality is defined based on the minimum possible probabilistic distance of the actual measurements \ from \. We show that this measure, called the optimal approximation measure, agrees with a certain measure of contextuality of the CbD approach for all systems where each property enters in exactly two contexts. The OA measure can be calculated far more efficiently than the CbD measure and even more efficiently than the NP measure for sufficiently large systems. We also define a variant, the OA-NP measure of contextuality that agrees with the NP measure for consistently connected systems while extending it to inconsistently connected systems. (shrink)

This article provides a critical evaluation of the central components of Integrative Bioethics, a project aiming at a bioethical framework reconceptualization. Its proponents claim that this new system of thought has developed a better bioethical methodology than mainstream Western bioethics, a claim that we criticize here. We deal especially with the buzz words of Integrative Bioethics – pluriperspectivism, integrativity, orientational knowledge, as well as with its underlying theory of moral truth. The first part of the paper looks at what the (...) claims of a superior methodology consist in. The second reveals pluriperspectivism and integrativity to be underdeveloped, hazy terms, but which seem to be underpinned by two theses – the incommensurability and the inclusiveness theses. These theses we critically scrutinize. We then consider strategies the project's proponents might apply to curb these theses in order to acquire minimal consistency for their framework. This part of the article also deals with the conception of moral truth that drives the theory, a position equally burdened with inconsistencies. In the last part of the article, we observe the concept of orientational knowledge, and develop two interpretations of its possible meaning. We claim that, following the first interpretation, Integrative Bioethics is completely descriptive, in which case it is informative and important, but hardly bioethics; if it is normative, following the second interpretation, it is bioethics as we already know it, but merely clad in rhetorical embellishments. We conclude that there is nothing new about this project, and that its inconsistencies are reason enough for its abandonment. (shrink)

This article provides a critical evaluation of the central components of Integrative Bioethics, a project aiming at a bioethical framework reconceptualization. Its proponents claim that this new system of thought has developed a better bioethical methodology than mainstream Western bioethics, a claim that we criticize here. We deal especially with the buzz words of Integrative Bioethics – pluriperspectivism, integrativity, orientational knowledge, as well as with its underlying theory of moral truth. The first part of the paper looks at what the (...) claims of a superior methodology consist in. The second reveals pluriperspectivism and integrativity to be underdeveloped, hazy terms, but which seem to be underpinned by two theses – the incommensurability and the inclusiveness theses. These theses we critically scrutinize. We then consider strategies the project's proponents might apply to curb these theses in order to acquire minimal consistency for their framework. This part of the article also deals with the conception of moral truth that drives the theory, a position equally burdened with inconsistencies. In the last part of the article, we observe the concept of orientational knowledge, and develop two interpretations of its possible meaning. We claim that, following the first interpretation, Integrative Bioethics is completely descriptive, in which case it is informative and important, but hardly bioethics; if it is normative, following the second interpretation, it is bioethics as we already know it, but merely clad in rhetorical embellishments. We conclude that there is nothing new about this project, and that its inconsistencies are reason enough for its abandonment. (shrink)

N. Kamide introduced a pair of classical and constructive logics, each with a peculiar type of negation: its double negation behaves as classical and intuitionistic negation, respectively. A consequence of this is that the systems prove contradictions but are non-trivial. The present paper aims at giving insights into this phenomenon by investigating subsystems of Kamide’s logics, with a focus on a system in which the double negation behaves as the negation of minimal logic. We establish the negation inconsistency (...) of the system and embeddability of contradictions from other systems. In addition, we attempt at an informational interpretation of the negation using the dimathematical framework of H. Wansing. (shrink)

The so-called paradoxes of material implication have motivated the development of many non-classical logics over the years, such as relevance logics, paraconsistent logics, fuzzy logics and so on. In this note, we investigate some of these paradoxes and classify them, over minimal logic. We provide proofs of equivalence and semantic models separating the paradoxes where appropriate. A number of equivalent groups arise, all of which collapse with unrestricted use of double negation elimination. Interestingly, the principle ex falso quodlibet, and (...) several weaker principles, turn out to be distinguishable, giving perhaps supporting motivation for adopting minimal logic as the ambient logic for reasoning in the possible presence of inconsistency. (shrink)

The present paper is devoted to computational aspects of propositional inconsistency-adaptive logics. In particular, we prove (relativized versions of) some principal results on computational complexity of derivability in such logics, namely in cases of CLuN r and CLuN m , i.e., CLuN supplied with the reliability strategy and the minimal abnormality strategy, respectively.

We investigate an approach for drawing logical inference from inconsistent premisses. The main idea in this approach is that the inconsistencies in the premisses should be interpreted as uncertainty of the information. We propose a mechanism, based on Kinght’s [14] study of inconsistency, for revising an inconsistent set of premisses to a minimally uncertain, probabilistically consistent one. We will then generalise the probabilistic entailment relation introduced in [15] for propositional languages to the first order case to draw logical inference (...) from a probabilistic set of premisses. We will show how this combination can allow us to limit the effect of uncertainty introduced by inconsistent premisses to only the reasoning on the part of the premise set that is relevant to the inconsistency. (shrink)

Wijdicks and colleagues1 recently presented the Full Outline of UnResponsiveness (FOUR) scale as an alternative to the Glasgow Coma Scale (GCS)2 in the evaluation of consciousness in severely brain-damaged patients. They studied 120 patients in an intensive care setting (mainly neuro-intensive care) and claimed that “the FOUR score detects a locked-in syndrome, as well as the presence of a vegetative state.”1 We fully agree that the FOUR is advantageous in identifying locked-in patients given that it specifically tests for eye movements (...) or blinking on command. This is welcomed given that misdiagnosis of the locked-in syndrome has been shown to occur in more than half of the cases (see Laureys and colleagues3 for review). As for the diagnosis of the vegetative state, the scale explicitly tests for visual pursuit, and hence can disentangle the vegetative state from the minimally conscious state (MCS). The diagnostic criteria for MCS have been proposed4 only recently, but Wijdicks and colleagues1 do not mention the existence of this clinical entity in their article. As for the vegetative state, MCS can be encountered in the acute or subacute setting as a transitional state on the way to further recovery, or it can be a more chronic or even permanent condition. The MCS refers to patients showing inconsistent, albeit clearly discernible, minimal behavioral evidence of consciousness (eg, localization of noxious stimuli, eye fixation or tracking, reproducible movement to command, or nonfunctional verbalization).4 The FOUR scale does not test for all of the behavioral criteria required to diagnose MCS.4 It is known from the literature (see Majerus and colleagues5 for review) that about a third of patients diagnosed with vegetative state are actually in MCS, and this misdiagnosis can lead to major clinical, therapeutic, and ethical consequences. We tested the ability of the newly proposed FOUR scale to correctly diagnose the vegetative state in an acute (intensive care and neurology ward) and chronic (neurorehabilitation) setting.. (shrink)

I argue that a general logic of definitions must tolerate ω‐inconsistency. I present a semantical scheme, S, under which some definitions imply ω‐inconsistent sets of sentences. I draw attention to attractive features of this scheme, and I argue that S yields the minimal general logic of definitions. I conclude that any acceptable general logic should permit definitions that generate ω‐inconsistency. This conclusion gains support from the application of S to the theory of truth.

It is widely assumed that the use of deception in research is always inconsistent with obtaining valid consent. In addition, guidelines and regulations permit research without valid consent only when it poses no greater than minimal risk. Current practice thus prohibits studies that use deception and pose greater than minimal risk, including studies that rely on deceptive methods to evaluate experimental treatments. To assess whether these prohibitions are justified, the present paper evaluates five arguments that might be thought (...) to support the assumption that deception is always inconsistent with valid consent. Analysis of these arguments reveals that deception is frequently, but not always, inconsistent with obtaining valid consent for research. This conclusion suggests that, in order to avoid unnecessarily blocking valuable research, current policies and practice should be revised to recognize the conditions under which the use of deception can be consistent with obtaining research participants’ valid consent. (shrink)

We prove that the minimal Logic of Formal Inconsistency $\mathsf{QmbC}$ validates a weaker version of Fraïssé’s theorem. LFIs are paraconsistent logics that relativize the Principle of Explosion only to consistent formulas. Now, despite the recent interest in LFIs, their model-theoretic properties are still not fully understood. Our aim in this paper is to investigate the situation. Our interest in FT has to do with its fruitfulness; the preservation of FT indicates that a number of other classical semantic properties (...) can be also salvaged in LFIs. Further, given that FT depends on truth-functionality, whether full FT holds for $\mathsf{QmbC}$ becomes a challenging question. (shrink)

“Philosophical perspectivism” is surely one of Nietzsche's most important insights regarding the limits of human knowledge. However, the perspectivist thesis combined with a minimal realist metaphysical position produces what Brian Leiter calls the 'Received View': an epistemologically incoherent misinterpretation of Nietzsche which pervades the secondary literature. In order to salvage the thesis of perspectivism, Leiter argues that we must commit Nietzsche to an anti-realist metaphysical position. I argue that Leiter's proposed solution is (1) epistemically weak, and (2) inconsistent with (...) much of Nietzsche's views on truth, knowledge and the psychological make-up of human beings. I argue that we need to abandon the scheme/content distinction on which both the Received View and Leiter's anti-realist construal of perspectivism are predicated and instead construe perspectives as environments of power. (shrink)

In this paper, we approach the problem of classical recapture for LP and K3 by using normality operators. These generalize the consistency and determinedness operators from Logics of Formal Inconsistency and Underterminedness, by expressing, in any many-valued logic, that a given formula has a classical truth value (0 or 1). In particular, in the rst part of the paper we introduce the logics LPe and Ke3 , which extends LP and K3 with normality operators, and we establish a classical (...) recapture result based on the two logics. In the second part of the paper, we compare the approach in terms of normality operators with an established approach to classical recapture, namely minimal inconsistency. Finally, we discuss technical issues connecting LPe and Ke3 to the tradition of Logics of Formal Inconsistency and Underterminedness. (shrink)

In this paper, we shall consider the so-called cancellation view of negation and the inferential role of contradictions. We will discuss some of the problematic aspects of negation as cancellation, such as its original presentation by Richard and Valery Routley and its role in motivating connexive logic. Furthermore, we will show that the idea of inferential ineffectiveness of contradictions can be conceptually separated from the cancellation model of negation by developing a system we call qLPm, a combination of Graham Priest’s (...) minimally inconsistent Logic of Paradox with q-entailment as introduced by Grzegorz Malinowski. (shrink)

The dissertation deals with problems in "logic", more precisely, it deals with particular formal systems aiming at capturing patterns of valid reasoning. Sequent calculi were proposed to characterize logical connectives via introduction rules. These systems customarily also have structural rules which allow one to rearrange the set of premises and conclusions. In the "structurally free logic" of Dunn and Meyer the structural rules are replaced by combinatory rules which allow the same reshuffling of formulae, and additionally introduce an explicit marker (...) for the application of the rule---the combinator. The dissertation gives syntactic extensions of such systems introducing conjunction and disjunction . Cut elimination is proved for these systems. ;Syntactic systems as a rule are accompanied by a semantics which interprets them. The extended systems are supplied with semantics using algebraic methods. First, the Lindenbaum algebras are formed, and then these algebras are represented in an algebra of sets. This gives a so called Kripke-style semantics for the systems. The representation for the distributive extension utilizes well-known techniques; it uses sets of prime filters and set theoretical operations on them to deal with conjunction and disjunction, plus a ternary accessibility relation to accommodate the intensional operators as fusion and implication. The representation theorem is proven generally, i.e., for arbitrary sets of combinators using the "squeeze lemma" of Routley and Meyer. ;The non-distributive calculi require a different representation since union and intersection are distributive. Two previous representations for lattices are overviewed, and a modification of the Hartonas-Dunn representation is successfully augmented with the intensional operations. Instead of sets of filters, sets of pairs of minimally inconsistent filters and ideals are used and the representation theorem is proven. The representation results provide soundness and completeness for the systems. The dissertation also investigates properties of dual combinators , proving a series of lemmas about dual combinatory systems not being Church-Rosser and being inconsistent. Combinatorially definable classes of lambda-terms are considered as well. (shrink)

In 1970, K. Kunen, working in the context of Kelley–Morse set theory, showed that the existence of a nontrivial elementary embedding j:V→V is inconsistent. In this paper, we give a finer analysis of the implications of his result for embeddings V→V relative to models of ZFC. We do this by working in the extended language , using as axioms all the usual axioms of ZFC , along with an axiom schema that asserts that j is a nontrivial elementary embedding. Without (...) additional axiomatic assumptions on j, we show that that the resulting theory is weaker than an ω-Erdös cardinal, but stronger than n-ineffables. We show that natural models of ZFC+BTEE give rise to Schindler’s remarkable cardinals. The approach to inconsistency from ZFC+BTEE forks into two paths: extensions of ZFC+BTEE+Cofinal Axiom and ZFC+BTEE+¬Cofinal Axiom, where Cofinal Axiom asserts that the critical sequence is cofinal in the ordinals. We describe near-minimal inconsistent extensions of each of these theories. The path toward inconsistency from ZFC+BTEE+¬Cofinal Axiom is paved with a sequence of theories of increasing large cardinal strength. Indeed, the extensions of the theory ZFC +“j is a nontrivial elementary embedding” form a hierarchy of axioms, ranging in strength from Con to the existence of a cardinal that is super-n-huge for every n, to inconsistency. This hierarchy is parallel to the usual hierarchy of large cardinal axioms, and can be used in the same way. We also isolate several intermediate-strength axioms which, when added to ZFC+BTEE, produce theories having strengths in the vicinity of a measurable cardinal of high Mitchell order, a strong cardinal, ω Woodin cardinals, and n-huge cardinals. We also determine precisely which combinations of axioms, of the form result in inconsistency. (shrink)

This paper sketches the antilogism of Christine Ladd-Franklin and historical advancement about antilogism, mainly constructs an axiomatic system Atl based on first-order logic with equality and the wholly-exclusion and not-wholly-exclusion relations abstracted from the algebra of Ladd-Franklin, with soundness and completeness of Atl proved, providing a simple and convenient tool on syllogistic reasoning. Atl depicts the empty class and the whole class differently from normal set theories, e.g. ZFC, revealing another perspective on sets and set theories. Two series of Dotterer (...) and the theorem proved by Russinoff are re-characterized in antilogistic formulas corresponding to the square of opposition and twenty-four moods of syllogism. Then the restricted equivalence between two forms of antilogism and minimal inconsistency is built up, implying the internal connection between antilogisms and minimal inconsistency and leaving two related conjectures not proved. Besides, this paper provides a new explanation for the reason why contrariety, subcontrariety, and subalternation and the nine special moods require the non-empty assumption. (shrink)

According to unconditional motivational internalism, there is an a priori constraint on an agent's forming a sincere moral judgement, namely that she is, at least to some minimal extent, motivated to act as it dictates. In order to undermine this internalist position, proponents of motivational externalism typically appeal to the possibility of the amoralist—i.e. an individual who makes sincere moral judgements, but who is completely unmoved to act accordingly. This strategy is known as the challenge of amoralism. Against this (...) strategy, I will argue that in order to represent a genuine case of amoralism, and a credible counterexample to unconditional motivational internalism, an agent would have to simultaneously satisfy an epistemically inconsistent set of conditions. Thus, the conclusion I will attempt to defend in this paper is that the challenge of amoralism does not succeed in posing a legitimate threat to unconditional motivational internalism. (shrink)

Amidst the many brain events evoked by a visual stimulus, which are specifically associated with conscious perception, and which merely reflect non-conscious processing? Several recent neuroimaging studies have contrasted conscious and non-conscious visual processing, but their results appear inconsistent. Some support a correlation of conscious perception with early occipital events, others with late parieto-frontal activity. Here we attempt to make sense of those dissenting results. On the basis of a minimal neuro-computational model, the global neuronal workspace hypothesis, we propose (...) a taxonomy which distinguishes between vigilance and access to conscious report, as well as between subliminal, preconscious and conscious processing. We suggest that these distinctions map onto different neural mechanisms, and that conscious perception is systematically associated with a sudden surge of parieto-frontal activity causing top-down amplification. (shrink)

Let serious propositional contingentism (SPC) be the package of views which consists in (i) the thesis that propositions expressed by sentences featuring terms depend, for their existence, on the existence of the referents of those terms, (ii) serious actualism—the view that it is impossible for an object to exemplify a property and not exist—and (iii) contingentism—the view that it is at least possible that some thing might not have been something. SPC is popular and compelling. But what should we say (...) about possible worlds, if we accept SPC? Here, I first show that a natural view of possible worlds, well-represented in the literature, in conjunction with SPC is inadequate. Though I note various alternative ways of thinking about possible worlds in response to the first problem, I then outline a second more general problem—a master argument—which generally shows that any account of possible worlds meeting very minimal requirements will be inconsistent with compelling claims about mere possibilia which the serious propositional contingentist should accept. (shrink)

ven a cursory look at the extensive literature on mindreading in nonhuman animals reveals considerable variation both in what mindreading abilities are taken to be, and in what is taken as evidence for them. Claims that seem to contradict each other are often not inconsistent with each other when examined more closely. And sometimes theorists who seem to be on the same side are actually talking at cross-purposes. The first aim of this paper is to tackle some important framework questions (...) about how exactly the mindreading hypothesis is to be stated. It emerges in sections 1 and 2 that there are three importantly different versions of the mindreading hypothesis that need to be distinguished. The first (which I call minimal mindreading) occurs when a creature’s behavior covaries with the psychological states of other participants in social exchanges. The presence of minimal mindreading is not in itself evidence for the presence of what I term substantive mindreading. Substantive mindreading involves attributions of mental states. There are different levels of substantive mindreading, varying according to the category of mental state attributions that they involve. Section 2 explores different types of substantive mindreading, according to the extent to which they involve explicitly representing the agent’s backgtround psychological profile. This gives us a principled way of distinguishing propositional attitude mindreading from perceptual mindreading. -/- It is clear that much of the reasoning behind attributions of mindreading abilities to nonlinguistic creatures is analogical in nature. We see in section 3 that much of the discussion in this area proceeds on the basis of a double analogy between animal cognition and human cognition. Researchers assume both that animals solve many problems of social coordination that are analogous to problem solved by humans and that since humans solve those problems using mindreading strategies, so too do non-human animals. How we apply the second analogy, of course, depends upon our interpretation of the particular mindreading strategies that humans employ – in particular, it depends upon the centrality of propositional attitude psychology (or folk psychology) in human social understanding and social coordination. There are good reasons for thinking that the role of propositional attitude psychology in human social life is very much over-stated. This has repercussions for how we think about substantive mindreading in nonhuman animals. It very much weakens the analogical case for identifying propositional attitude mindreading in nonlinguistic creatures. -/- Suspicion of claims of propositional attitude mindreading in non-human animals turns out to be well-founded. In section 4 I present a revised version of an argument I have given elsewhere (Bermúdez 2003) to show that the most sophisticated form of substantive mindreading (the type of mindreading that exploits the concepts of propositional attitude psychology) is only available to language-using creatures. (shrink)