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)

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

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

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

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

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)

The paper presents an analysis of the ethics of abortion and infanticide. The work considers two main approaches: the argument of J.J. Thomson on the right to use his body and the absence of responsibilities regarding the fetus, and the argument about the difference in the moral status of the fetus and the adult, which are used both in the argumentation of supporters and opponents of abortion. The paper shows the fallacy of the first approach, and also, in order for (...) the second approach to remain internally consistent, we must agree that infanticide is permissible. (shrink)

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

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

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

According to the two-systems account of mindreading, our mature perspective-taking abilities are subserved by two distinct mindreading systems: a fast but inflexible, “implicit” system, and a flexible but slow “explicit” one. However, the currently available evidence on adult perspective-taking does not support this account. Specifically, both Level-1 and Level-2 perspective-taking show a combination of efficiency and flexibility that is deeply inconsistent with the two-systems architecture. This inconsistency also turns out to have serious consequences for the two- (...) class='Hi'>systems framework as a whole, both as an account of our mature mindreading abilities and of the development of those abilities. What emerges from this critique is a conception of context-sensitive, spontaneous mindreading that may provide insight into how mindreading functions in complex social environments. This in turn offers a bulwark against skepticism about the role of mindreading in everyday social cognition. (shrink)

We investigate the structure common to causal theories that attempt to explain a (part of) the world. Causality implies conservation of identity, itself a far from simple notion. It imposes strong demands on the universalizing power of the theories concerned. These demands are often met by the introduction of a metalevel which encompasses the notions of 'system' and 'lawful behaviour'. In classical mechanics, the division between universal and particular leaves its traces in the separate treatment of cinematics and dynamics. This (...) analysis is applied to the mechanical theories of Newton and Leibniz, with some surprising results. (shrink)

Rawls’s consideration not to include the choice of economic systems as part of a theory of justice is inconsistent with his comments on redistribution and the political effects of economic inequality. When Rawls’s discussion of economic systems and his discussion of economic inequalities is examined, it is apparent that the selection of economic systems is a pertinent topic for a theory of justice. The propensity for the primary social good of self-respect to be satisfied can be (...) affected by the selection of economic systems. Rawls has incorrectly determined the selection of economic systems to be unimportant if different economic systems can be more advantageous to the satisfaction of self-respect than others. When socialism and Rawls’s version of regulated capitalism are compared, socialism is a maximin solution, and accordingly will be selected by people within the original position under the veil of ignorance. (shrink)

Memory evolved to supply useful, timely information to the organism’s decision-making systems. Therefore, decision rules, multiple memory systems, and the search engines that link them should have coevolved to mesh in a coadapted, functionally interlocking way. This adaptationist perspective suggested the scope hypothesis: When a generalization is retrieved from semantic memory, episodic memories that are inconsistent with it should be retrieved in tandem to place boundary conditions on the scope of the generalization. Using a priming paradigm and (...) a decision task involving person memory, the authors tested and confirmed this hypothesis. The results support the view that priming is an evolved adaptation. They further show that dissociations between memory systems are not—and should not be—absolute: Independence exists for some tasks but not others. (shrink)

This article considers whether the international legal human rights system founded on liberal individualism, as endorsed by liberal theorists, can function as a fair universal legal regime. This question is examined in relation to the collective right to self-determination demanded by indigenous peoples, who are paradigmatic decent nonliberal peoples. Indigenous peoples’ collective right to self-determination has been internationally recognized in the Declaration on the Rights of Indigenous Peoples, which was adopted by the United Nations in 2007. This historic event may (...) seem to exemplify the international legal human rights system’s ability to function as a truly global legal regime applicable cross-culturally to all well-ordered societies, whether liberal or nonliberal. The article argues, however, that the collective right to self-determination advocated by indigenous peoples for the sake of cultural integrity is inconsistent with the international legal human rights system founded on liberal individualism. By showing the plausibility of indigenous peoples’ defense of their cultural integrity, this article suggests that the international legal human rights system ought to be reconceptualized to reflect a genuine international consensus on human rights among all well-ordered societies if it is to function as a just mechanism for global governance. (shrink)

In this paper, we theoretically address the relevance of unintentional and inconsistent interactional elements in human–robot interactions. We argue that elements failing, or poorly succeeding, to reproduce a humanlike interaction create significant consequences in human–robot relational patterns and may affect human–human relations. When considering social interactions as systems, the absence of a precise interactional element produces a general reshaping of the interactional pattern, eventually generating new types of interactional settings. As an instance of this dynamic, we study the (...) absence of metacommunicative abilities in social artifacts. Then, we analyze the pragmatic consequences of the aforementioned absence through the lens of Paul Watzlawick’s interactionist theory. We suggest that a fixed complementary interactional setting may be produced because of the asymmetric understanding, between robots and humans, of metacommunication. We highlight the psychological implications of this interactional asymmetry within Jessica Benjamin’s concept of “mutual recognition”. Finally, we point out the possible shift of dysfunctional interactional patterns from human–robot interactions to human–human ones. (shrink)

This paper investigates the fundamental idea at stake in current bioeconomies such as Europe's Bio-Based Economy (BBE). We argue that basing an economy upon ecology is an ambivalent effort, causing confusion and inconsistencies, and that the dominant framing of the damaged biosphere as a market-failure in bioeconomies such as the BBE is problematic. To counter this dominant narrative, we present alternative conceptualisations of bio-economies and indicate which concepts are overlooked. We highlight the specific contradictions and discrepancies in the relation between (...) economy and ecology, and then work towards outlining a genuine and consistent conceptualisation of the BBE. The philosophical perspective of Emmanuel Levinas is employed to develop a more profound understanding of the tensions at stake; Levinas' work is compared with that of Nicholas Georgescu-Roegen's work on bioeconomics, and found to be of complementary value. Our hypothesis is that, rather than the impossible, absolute amalgamation of economy and ecology striven for today, a principal heterogeneity between humankind and nature must be acknowledged if a bioeconomy that truly operates within the carrying capacity of planet Earth is to be achieved. (shrink)

When the U.S. conducts warfare, elements of a force are drawn from different services and work together as a single team to accomplish an assigned mission. To achieve such unified action, it is necessary that the doctrines governing the actions of members of specific services be both consistent with and subservient to joint Doctrine. Because warfighting today increasingly involves not only live forces but also automated systems, unified action requires that information technology that is used in joint warfare must (...) be aligned with joint doctrine. It requires also that the separate information systems used by the different elements of a joint force must be interoperable, in the sense that data and information that is generated by each element must be usable (understandable, processable) by all the other elements that need them. Currently, such interoperability is impeded by multiple inconsistencies among the different data and software standards used by warfighters. We describe here the on-going project of creating a Joint Doctrine Ontology (JDO), which uses joint doctrine to provide shared computer-accessible content valid for any field of military endeavor, organization, and information system. JDO addresses the two previously mentioned requirements of unified action by providing a widely applicable benchmark for use by developers of information systems that will both guarantee alignment with joint doctrine and support interoperability. (shrink)

Legal positivists maintain that the legality of a rule is fundamentally determined by social facts. Yet for much of legal history, ordinary officials used legal terminology in ways that seem inconsistent with positivism. Judges regularly cited, analyzed, and predicated their decisions on the ‘laws of justice’ which they claimed had universal legal import. This practice, though well-documented by historians, has received surprisingly little philosophical attention; I argue that it invites explanation from positivists. After taxonomizing the positivist’s explanatory options, I (...) suggest that the most viable option appeals to conceptual change: classical Romans, early modern Europeans, founding-era Americans were not using ‘law’ (or ‘lex’ or ‘jus’) to refer to the subject matter of contemporary legal philosophy. But the strategy is costly. It renders positivism’s truth surprisingly parochial. And it supplies new reasons for doubting positivist accounts of contemporary practices, including the treatment of moral principles in modern adjudication. (shrink)

To eliminate incompleteness, undecidability and inconsistency from formal systems we only need to convert the formal proofs to theorem consequences of symbolic logic to conform to the sound deductive inference model. -/- Within the sound deductive inference model there is a (connected sequence of valid deductions from true premises to a true conclusion) thus unlike the formal proofs of symbolic logic provability cannot diverge from truth.

Questions concerning the validity of religious beliefs.

Logic systems that can handle contradictions were being used for some time without having a general technical name. One of the main proposers of these systems, Newton da Costa, asked Francisco Miró Quesada to suggest him a name for those systems. In the historical letter that here we translate into English for the first time, Miró Quesada suggests three names to da Costa for this purpose: ‘ultraconsistent’, ‘metaconsistent’, and ‘paraconsistent’; explaining their pros and cons. -/- Paper based (...) on a letter by Francisco Miró Quesada Cantuarias to Newton da Costa, edited, translated, and annotated by Luis Felipe Bartolo Alegre. (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)

The programmatic statement put forward in von Wright's last works on deontic logic introduces the perspective of logical pragmatics, which has been formally explicated here and extended so to include the role of norm-recipient as well as the role of norm-giver. Using the translation function from the language of deontic logic to the language of set-theoretical approach, the connection has been established between the deontic postulates, on one side, and the perfection properties of the norm-set and the counter-set, on the (...) other side. In the study of conditions of rational norm-related activities it has been shown that diverse dynamic second-order norms related to the concept of the consistency norm-system hold: -- the norm-giver ought to restore ``classical'' consistency by revising an inconsistent system, -- the norm-recipient ought to preserve an inconsistent system by revision of its logic so that inconsistency does not imply destruction of the system. Dialetheic deontic logic of Priest is a suitable logic for the purpose since it preserves other perfection properties of the system. (shrink)

In this paper two systems of AGM-like Paraconsistent Belief Revision are overviewed, both defined over Logics of Formal Inconsistency (LFIs) due to the possibility of defining a formal consistency operator within these logics. The AGM° system is strongly based on this operator and internalize the notion of formal consistency in the explicit constructions and postulates. Alternatively, the AGMp system uses the AGM-compliance of LFIs and thus assumes a wider notion of paraconsistency - not necessarily related to the notion of (...) formal consistency. (shrink)

A rational man’s beliefs are not logically consistent, and he does not believe all the logical consequences of his beliefs. This is because in any situational context, we only accept certain believed sentences. Within that context, we insist that sentences be logically consistent, and we accept the logical consequences of the other sentences we accept in that context. But such sentences do not have to be consistent with sentences we accept in other contexts, nor will we always accept in that (...) context the logical consequences of sentences that we accept in other contexts. We go through many different situational contexts in the course of a day. For example, in trying to start a car with a dead battery, explaining why the car won’t start may form one context, while explaining how to start it may form a different context; sentences we accept in the first context may be logically inconsistent with sentences we accept in the second. (shrink)

There are two foundational, but not fully developed, ideas in paraconsistency, namely, the duality between paraconsistent and intuitionistic paradigms, and the introduction of logical operators that express meta-logical notions in the object language. The aim of this paper is to show how these two ideas can be adequately accomplished by the Logics of Formal Inconsistency (LFIs) and by the Logics of Formal Undeterminedness (LFUs). LFIs recover the validity of the principle of explosion in a paraconsistent scenario, while LFUs recover the (...) validity of the principle of excluded middle in a paracomplete scenario. We introduce definitions of duality between inference rules and connectives that allow comparing rules and connectives that belong to different logics. Two formal systems are studied, the logics mbC and mbD, that display the duality between paraconsistency and paracompleteness as a duality between inference rules added to a common core– in the case studied here, this common core is classical positive propositional logic (CPL + ). The logics mbC and mbD are equipped with recovery operators that restore classical logic for, respectively, consistent and determined propositions. These two logics are then combined obtaining a pair of logics of formal inconsistency and undeterminedness (LFIUs), namely, mbCD and mbCDE. The logic mbCDE exhibits some nice duality properties. Besides, it is simultaneously paraconsistent and paracomplete, and able to recover the principles of excluded middle and explosion at once. The last sections offer an algebraic account for such logics by adapting the swap-structures semantics framework of the LFIs the LFUs. This semantics highlights some subtle aspects of these logics, and allows us to prove decidability by means of finite non-deterministic matrices. (shrink)

The measurement problem concerns an apparent conflict between the two fundamental principles of quantum mechanics, namely the Schrödinger equation and the measurement postulate. These principles describe inconsistent behavior for quantum systems in so-called "measurement contexts." Many theorists have thought that the measurement problem can only be resolved by proposing a mechanistic explanation of (genuine or apparent) wavefunction collapse that avoids explicit reference to "measurement." However, I argue here that the measurement problem dissolves if we accept Humeanism about laws (...) of nature. On a Humean metaphysics, there is no conflict between the two principles, nor is there any inherent problem with the concept of "measurement" figuring into the account of collapse. (shrink)

Recently Feferman has outlined a program for the development of a foundation for naive category theory. While Ernst has shown that the resulting axiomatic system is still inconsistent, the purpose of this note is to show that nevertheless some foundation has to be developed before naive category theory can replace axiomatic set theory as a foundational theory for mathematics. It is argued that in naive category theory currently a ‘cookbook recipe’ is used for constructing categories, and it is explicitly (...) shown with a formalized argument that this “foundationless” naive category theory therefore contains a paradox similar to the Russell paradox of naive set theory. (shrink)

The inconsistent relation between word frequency and free recall performance and the non-monotonic relation found between the two cannot all be explained by current theories. We propose a theoretical framework that can explain all extant results. Based on an ecological psychology analysis of the free recall situation in terms of environmental and informational resources available to the participants, we propose that because participants’ cognitive system has been shaped by their native language, free recall performance is best understood as the (...) end result of relational properties that preexist the experimental situation and of the way the words from the experimental list interact with those. In addition to this, we borrow from predictive coding theory the idea that the brain constantly predicts “what is coming next” so that it is mainly prediction errors that will propagate information forward. Our ecological psychology analysis indicates there will be “prediction errors” because the word frequency distribution in an experimental word list is inevitably different from the particular Zipf’s law distribution of the words in the language that shaped participants’ brains. We further propose the particular distributional discrepancies inherent to a given word list will trigger, as a function of the words that are included in the list, their order, and of the words that are absent from the list, a surprisal signal in the brain, something that is isomorphic to the concept of Bayesian surprise. The precise moment when Bayesian surprise is triggered will determine to what word of the list that Bayesian surprise will be associated with, and the word the Bayesian surprise will be associated with will benefit from it and become more memorable as a direct function of the magnitude of the surprisal. Two experiments are presented that show a proxy of Bayesian surprise explains the free recall performance and that no effect of word frequency is found above and beyond the effect of that proxy variable. We then discuss how our view can account for all data extant in the literature on the effect of word frequency on free recall. (shrink)

In western philosophy and beyond, a tension between pluralism and monism has sparked many developments and debates. Pluralism of norms, of forms of knowledge, of aesthetic and moral values, of interests etc. has often been pitted against monism. Monism usually implies a hierarchical order of such norms etc. After having traced the origin of this tension between pluralism and monism in ancient tragedy and philosophy, I’m asking in this article whether a rejection of monism and embrace of pluralism necessarily raises (...) the specter of inconsistency and contradiction. The threat of inconsistency need not be associated with pluralism as even with regard to logic an argument can be made for a ‘multiplicity of logics’, as van Lambalgen and Stenning argue in several places. They refer to the varieties in reasoning that can be observed in humans and which are partly due to there being ‘dual systems’ of reasoning: System 1 processes information fast, automatized, and emotional, while System 2 is rather slow, more deliberative, and more rational. In contrast to a widely held view, the authors argue that System 1 processing is not without logic, even though it is a different form of logic from System 2. In addition, the multiplicity of logics they discuss is related to the multiple semantics required for distinct domains of reasoning. This perspective raises the subsequent question how this pluralism can be available while maintaining consistency, how should the available options be configured or related to each other? In the remainer of this chapter I’m addressing several such options for configurating pluralism like: non-foundational pluralism and foundational pluralism, moderate or temporary pluralism, antagonistic pluralism, incompatible pluralism, incommensurable pluralism, ‘Anything goes’ pluralism, complementary pluralism, integrative pluralism, and interactive pluralism. The discussion and examples of these options show that irrespective of its domain, the encounter with different configurations of pluralism shows how some forms of pluralism are likely to be productive, whereas others are less so - which is an important lesson given the prominent pluralism of pluralisms in philosophy and beyond. (shrink)

There is a curious bifurcation in the literature on ground and its logic. On the one hand, there has been a great deal of work that presumes that logical complexity invariably yields grounding. So, for instance, it is widely presumed that any fact stated by a true conjunction is grounded in those stated by its conjuncts, that any fact stated by a true disjunction is grounded in that stated by any of its true disjuncts, and that any fact stated by (...) a true double negation is grounded in that stated by the doubly-negated formula. This commitment is encapsulated in the system GG axiomatized and semantically characterized by [deRosset and Fine, 2023] (following [Fine, 2012]). On the other hand, there has been a great deal of important formal work on “flatter” theories of ground, yielding logics very different from GG [Correia, 2010] [Fine, 2016, 2017b]. For instance, these theories identify the fact stated by a self-conjunction $$(\phi \wedge \phi )$$ with that stated by its conjunct $$\phi $$. Since, in these systems, no fact grounds itself, the “flatter” theories are inconsistent with the principles of GG. This bifurcation raises the question of whether there is a single notion of ground suited to fulfill the philosophical ambitions of grounding enthusiasts. There is, at present, no unified semantic framework employing a single conception of ground for simultaneously characterizing both GG and the “flatter” approaches. This paper fills this gap by specifying such a framework and demonstrating its adequacy. (shrink)

This thesis starts with three challenges to the structuralist accounts of applied mathematics. Structuralism views applied mathematics as a matter of building mapping functions between mathematical and target-ended structures. The first challenge concerns how it is possible for a non-mathematical target to be represented mathematically when the mapping functions per se are mathematical objects. The second challenge arises out of inconsistent early calculus, which suggests that mathematical representation does not require rigorous mathematical structures. The third challenge comes from renormalisation (...) group (RG) explanations of universality. It is argued that the structural mapping between the world and a highly abstract minimal model adds little value to our understanding of how RG obtains its explanatory force. I will address the first and second challenges from the similarity perspective. The similarity account captures representations as similarity relations, providing a more flexible and broader conception of representation than structuralism. It is the specification of the respect and degree of similarity that forges mathematics into a context of representation and directs it to represent a specific system in reality. Structuralism is treatable as a tool for explicating similarity rela-tions set-theoretically. The similarity account, combined with other approaches (e.g., Nguyen and Frigg’s extensional abstraction account and van Fraassen’s pragmatic equivalence), can dissolve the first challenge. Additionally, I will make a structuralist response to the second challenge, and suggestions regarding the role of infinitesimals from the similarity perspective. In light of the similarity account, I will propose the “hotchpotch picture” as a method-ological reflection of our study of representation and explanation. Its central insight is to dissect a representation or an explanation into several aspects and use different theories (that are usually thought of competing) to appropriate each of them. Based on the hotchpotch picture, RG explanations can be dissected to the “indexing” and “inferential” conceptions of explanation, which are captured or characterised by structural mappings. Therefore, structuralism accommodates RG explanations, and the third challenge is resolved. (shrink)

Before the Darwinian revolution species were thought to be universals. Since then, numerous attempts have been made to propose new definitions. The twentieth-century German philosopher Nicolai Hartmann defined 'species' as an individual system of processes and a process of life of a higher-order. To provide a clear understanding of Hartmann's conception of species, I first present his method of definition. Then I look at Hartmann's Philosophie der Natur (1950) to present his concepts of "organism" and "species." And I end the (...) paper by pointing out two possible systematic inconsistencies. (shrink)

Charges of inconsistency are frequently made against opponents of abortion for failing to ‘live out’ their beliefs. One such popular charge is that opponents of abortion are inconsistent for failing to ‘adopt the babies they don’t want aborted’—in this chapter, I will focus on a slightly broader version of this charge. I will understand adoption* broadly to include adopting and/or fostering children, as well as concretely supporting the systems involved in facilitating adoption and foster care through financial means, (...) volunteering, and/or advocacy. I will argue that opponents of abortion do not have special obligations to adopt* for the reasons often presumed, and thus are not inconsistent for failing to do so. However, I will go on to argue that they nevertheless have compelling reasons to do so—to decrease future abortions and oppose abortion with integrity. (shrink)

How is it possible that beginning from the negation of rational thoughts one comes to produce knowledge? This problem, besides its intrinsic interest, acquires a great relevance when the representation of a knowledge is settled, for example, on data and automatic reasoning. Many treatment ways have been tried, as in the case of the non-monotonic logics; logics that intend to formalize an idea of reasoning by default, etc. These attempts are incomplete and are subject to failure. A possible solution would (...) be to formulate a logic of the irrational, which offers a model for reasoning permitting to support contradictions as well as to produce knowledge from such situations. An intuition underlying the foundation of such a logic consists of the da Costa's paraconsistent logics presenting however, a different deduction theory and a whole distinct semantics, called here "the semantics of possible translations". The present proposing, following our argumentation, intends to enlight all this question, by a whole satisfactory logical point of view, being practically applicable and philosophically acceptable.Como é possível que a partir da negação do racional se possa obter conhecimento adicional? Esse problema, além de seu interesse intrínseco, adquire uma relevância adicional quando o encontramos na representação do conhecimento em bases de dados e raciocínio automático, por exemplo. Nesse caso, diversas tentativas de tratamento têm sido propostas, como as lógicas não-monotônicas, as lógicas que tentam formalizar a ideia do raciocínio por falha . Tais tentativas de solução, porém, são falhas e incompletas; proponho que uma solução possível seria formular uma lógica do irracional, que oferecesse um modelo para o raciocínio permitindo não só suportar contradições, como conseguir obter conhecimento, a partir de tais situações. A intuição subjacente à formulação de tal lógica são as lógicas paraconsistentes de da Costa, mas com uma teoria da dedução diferente e uma semântica completamente distinta . Tal proposta, como pretendo argumentar, fornece um enfoque para a questão que é ao mesmo tempo completamente satisfatório, aplicável do ponto de vista prático e aceitável do ponto de vista filosófico. (shrink)

In this book, we approach different topics related to neutrosophics, such as: Neutrosophic Set, Intuitionistic Fuzzy Set, Inconsistent Intuitionistic Fuzzy Set, Picture Fuzzy Set, Ternary Fuzzy Set, Pythagorean Fuzzy Set, Atanassov’s Intuitionistic Fuzzy Set of second type, Spherical Fuzzy Set, n-HyperSpherical Neutrosophic Set, q-Rung Orthopair Fuzzy Set, truth-membership, indeterminacy-membership, falsehood-nonmembership, Regret Theory, Grey System Theory, Three-Ways Decision, n-Ways Decision, Neutrosophy, Neutrosophication, Neutrosophic Probability, Refined Neutrosophy, Refined Neutrosophication, Nonstandard Analysis; (Theory, NeutroTheory, AntiTheory), S-denying an Axiom, Multispace with Multistructure, and so (...) on. (shrink)

Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory was firstly proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. (...) Since then, the single valued neutrosophic set theory has been extensively studied in books and monographs, the properties of neutrosophic sets and their applications, by many authors around the world. Also, an international journal - Neutrosophic Sets and Systems started its journey in 2013. Neutrosophic triplet was first defined in 2016 by Florentin Smarandache and Mumtaz Ali and they also introduced the neutrosophic triplet groups in the same year. For every element “x” in a neutrosophic triplet set A, there exist a neutral of “x” and an opposite of “x”. Also, neutral of “x” must be different from the classical neutral element. Therefore, the NT set is different from the classical set. Furthermore, a NT of “x” is showed by . This first volume collects original research and applications from different perspectives covering different areas of neutrosophic studies, such as decision making, Triplet, topology, and some theoretical papers. This volume contains three sections: NEUTROSOPHIC TRIPLET, DECISION MAKING, AND OTHER PAPERS. (shrink)

David Furley's work on the cosmologies of classical antiquity is structured around what he calls "two pictures of the world." The first picture, defended by both Plato and Aristotle, portrays the universe, or all that there is (to pan), as identical with our particular ordered world-system. Thus, the adherents of this view claim that the universe is finite and unique. The second system, defended by Leucippus and Democritus, portrays an infinite universe within which our particular kosmos is only one of (...) countless kosmoi. Aristotle's argument in De caelo I.9 that the world is necessarily unique is an important contribution to this debate. This argument holds interest because it shows Aristotle wrestling with an apparent inconsistency in his own philosophy, as deeply-held convictions within his cosmology collide with an equally deeply-held conviction within his metaphysics. The following three principles, each of which Aristotle appears committed to, are inconsistent: -/- The cosmic uniqueness principle. The world is necessarily unique. The cosmic form principle. The world is an ordered, structured unity. As such, the world has a form. The possibility of multiple instantiation principle. For all F, if F is a form, it is possible that there exist multiple Fs. In De caelo I.9, Aristotle argues that we can establish the uniqueness of the universe, reject the multiple instantiation principle, yet still retain the distinction between 'this world' and 'world in general,' if the following is true (as it is): the world takes up all the matter that exists. Aristotle illustrates this argument with one of the stranger analogies in his corpus: imagine an aquiline nose that takes up all the flesh in the universe. If this were so, then there could not exist any other aquiline objects whatsoever. (For this reason, we dub the De caelo I.9 argument the 'Cosmic Nose argument.') This paper is an interpretation of how this argument is supposed to proceed and an assessment of its success. The first section states the problem Aristotle is confronted with, sorts through Aristotle's various statements of the Cosmic Nose argument, which exhibit some sloppiness, and reconstructs charitably a single argument. We also spend some time examining the significance of Aristotle's example of a gigantic aquiline nose. We argue that, even charitably reconstructed, the argument appears to commit a serious modal fallacy. The remainder of the paper explores whether this modal fallacy can be overcome. We conclude that, although not a cogent argument for the uniqueness of the world (as this would require a significant revision of our current astronomy), the Cosmic Nose argument does succeed on its own terms. However, it should not be regarded as a free-standing argument for the uniqueness of the world. Instead, it depends crucially on the earlier argument in De caelo I.8 for the universe's uniqueness; De caelo I.9 should be viewed as an attempt to extend the conclusion of De caelo I.8 and to show how this conclusion can be made consistent with Aristotle's metaphysical principles about the nature of form. (shrink)

Considering the set of natural numbers ℕ, then in the context of Peano axioms, starting from inequalities between finite sets, we find a fundamental contradiction, about the existence of ℕ, from a not-finitist point of view.

Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. In the past years the fields of neutrosophics have been extended and applied in various fields, such as: artificial intelligence, data mining, soft computing, decision making in incomplete / indeterminate / inconsistent information systems, image processing, computational modelling, robotics, medical diagnosis, biomedical (...) engineering, investment problems, economic forecasting, social science, humanistic and practical achievements. There are about 7,000 neutrosophic researchers, within 89 countries around the globe, that have produced about 4,000 publications and tenths of PhD and MSc theses, within more than two decades. This is the sixth volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation, with an introduction contains a short history of neutrosophics, together with links to the main papers and books. -/- ES: Este es el Sexto volumen de la Enciclopedia de Investigadores Neutróficos, editados a partir de materiales ofrecidos por los autores que respondieron a la invitación del editor. Los autores se enumeran alfabéticamente. La introducción contiene una breve historia de la neutrosófica, y en especial se sus impacto en latinoamérica junto con enlaces a los principales artículos y libros. Conjunto neutrosófico, lógica neutrosófica, probabilidad neutrosófica, estadística neutrosófica, medida neutrosófica, precálculo neutrosófico, cálculo neutrosófico, psicología neutrosófica, sociología neutrosófica etc., están ganando una atención significativa en resolver muchos problemas de la vida real que implican incertidumbre, imprecisión, vaguedad, incompletitud, inconsistencia e indeterminación. En los últimos años, los campos de la neutrosófica se han ampliado y aplicado en diversos campos, tales como: inteligencia artificial, minería de datos, software informática, toma de decisiones en forma incompleta / indeterminada / inconsistente sistemas de información, procesamiento de imágenes, modelado computacional, robótica, diagnóstico médico, ingeniería biomédica, problemas de inversión, previsión económica, ciencias sociales, humanística y la validación y consolidación del conocimiento científico. (shrink)

Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. In the past years the fields of neutrosophics have been extended and applied in various fields, such as: artificial intelligence, data mining, soft computing, decision making in incomplete / indeterminate / inconsistent information systems, image processing, computational modelling, robotics, medical diagnosis, biomedical (...) engineering, investment problems, economic forecasting, social science, humanistic and practical achievements. There are about 7,000 neutrosophic researchers, within 89 countries around the globe, that have produced about 4,000 publications and tenths of PhD and MSc theses, within more than two decades. This is the fifth volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation, with an introduction contains a short history of neutrosophics, together with links to the main papers and books. (shrink)

The empirical study of belief is emerging at a rapid clip, uniting work from all corners of cognitive science. Reliance on belief in understanding and predicting behavior is widespread. Examples can be found, inter alia, in the placebo, attribution theory, theory of mind, and comparative psychological literatures. Research on belief also provides evidence for robust generalizations, including about how we fix, store, and change our beliefs. Evidence supports the existence of a Spinozan system of belief fixation: one that is automatic (...) and independent of belief rejection. Independent research supports the existence of a system of fragmented belief storage: one that relies on large numbers of causally isolated, context-sensitive stores of belief in memory. Finally, empirical and observational data support at least two systems of belief change. One system adheres, mostly, to epistemological norms of updating; the other, the psychological immune system, functions to guard our most centrally held beliefs from potential inconsistency with newly formed beliefs. Refining our under- standing of these systems can shed light on pressing real-world issues, such as how fake news, propaganda, and brainwashing exploit our psychology of belief, and how best to construct our modern informational world. (shrink)

David Lewis is a natural target for those who believe that findings in quantum physics threaten the tenability of traditional metaphysical reductionism. Such philosophers point to allegedly holistic entities they take both to be the subjects of some claims of quantum mechanics and to be incompatible with Lewisian metaphysics. According to one popular argument, the non-separability argument from quantum entanglement, any realist interpretation of quantum theory is straightforwardly inconsistent with the reductive conviction that the complete physical state of the (...) world supervenes on the intrinsic properties of and spatio-temporal relations between its point-sized constituents. Here I defend Lewis's metaphysical doctrine, and traditional reductionism more generally, against this alleged threat from quantum holism. After presenting the non-separability argument from entanglement, I show that Bohmian mechanics, an interpretation of quantum mechanics explicitly recognized as a realist one by proponents of the non-separability argument, plausibly rejects a key premise of that argument. Another holistic worry for Humeanism persists, however, the trouble being the apparently holistic character of the Bohmian pilot wave. I present a Humean strategy for addressing the holistic threat from the pilot wave by drawing on resources from the Humean best system account of laws. (shrink)

In `Essence and Modality', Kit Fine proposes that for a proposition to be metaphysically necessary is for it to be true in virtue of the nature of all objects whatsoever. Call this view Fine's Thesis. This paper is a study of Fine's Thesis in the context of Fine's logic of essence (LE). Fine himself has offered his most elaborate defense of the thesis in the context of LE. His defense rests on the widely shared assumption that metaphysical necessity obeys the (...) laws of the modal logic S5. In order to get S5 for metaphysical necessity, he assumes a controversial principle about the nature of all objects. I will show that the addition of this principle to his original system E5 leads to inconsistency with an independently plausible principle about essence. In response, I develop a theory that avoids this inconsistency while allowing us to maintain S5 for meta- physical necessity. However, I conclude that our investigation of Fine's Thesis in the context of LE motivates the revisionary conclusion that metaphysical necessity obeys the principles of the modal logic S4, but not those of S5. I argue that this constitutes a distinctively essentialist challenge to the received view that the logic of metaphysical necessity is S5. (shrink)

The Integrated Information Theory of consciousness (IIT) claims that consciousness is identical to maximal integrated information, or maximal Φ. One objection to IIT is based on what may be called the intrinsicality problem: consciousness is an intrinsic property, but maximal Φ is an extrinsic property; therefore, they cannot be identical. In this paper, I show that this problem is not unique to IIT, but rather derives from a trilemma that confronts almost any theory of consciousness. Given most theories of consciousness, (...) the following three claims are inconsistent. INTRINSICALITY: Consciousness is intrinsic. NON-OVERLAP: Conscious systems do not overlap with other conscious systems (a la Unger’s problem of the many). REDUCTIONISM: Consciousness is constituted by more fundamental properties (as per standard versions of physicalism and Russellian monism). In view of this, I will consider whether rejecting INTRINSICALITY is necessarily less plausible than rejecting NON-OVERLAP or REDUCTIONISM. I will also consider whether IIT is necessarily committed to rejecting INTRINSICALITY or whether it could also accept solutions that reject NON-OVERLAP or REDUCTIONISM instead. I will suggest that the best option for IIT may be a solution that rejects REDUCTIONISM rather than INTRINSICALITY or NON-OVERLAP. (shrink)

Within the United States, the most prominent justification for criminal punishment is retributivism. This retributivist justification for punishment maintains that punishment of a wrongdoer is justified for the reason that she deserves something bad to happen to her just because she has knowingly done wrong—this could include pain, deprivation, or death. For the retributivist, it is the basic desert attached to the criminal’s immoral action alone that provides the justification for punishment. This means that the retributivist position is not reducible (...) to consequentialist considerations nor in justifying punishment does it appeal to wider goods such as the safety of society or the moral improvement of those being punished. A number of sentencing guidelines in the U.S. have adopted desert as their distributive principle, and it is increasingly given deference in the “purposes” section of state criminal codes, where it can be the guiding principle in the interpretation and application of the code’s provisions. Indeed, the American Law Institute recently revised the Model Penal Code so as to set desert as the official dominate principle for sentencing. And courts have identified desert as the guiding principle in a variety of contexts, as with the Supreme Court’s enthroning retributivism as the “primary justification for the death penalty.” While retributivism provides one of the main sources of justification for punishment within the criminal justice system, there are good philosophical and practical reasons for rejecting it. One such reason is that it is unclear that agents truly deserve to suffer for the wrongs they have done in the sense required by retributivism. In the first section, I explore the retributivist justification of punishment and explain why it is inconsistent with free will skepticism. In the second section, I then argue that even if one is not convinced by the arguments for free will skepticism, there remains a strong epistemic argument against causing harm on retributivist grounds that undermines both libertarian and compatibilist attempts to justify it. I maintain that this argument provides sufficient reason for rejecting the retributive justification of criminal punishment. I conclude in the third section by briefly sketching my public health-quarantine model, a non-retributive alternative for addressing criminal behavior that draws on the public health framework and prioritizes prevention and social justice. I argue that the model is not only consistent with free will skepticism and the epistemic argument against retributivism, it also provides the most justified, humane, and effective way of dealing with criminal behavior. (shrink)

Canonical defenders of the principle of sufficient reason (PSR), such as Leibniz and Spinoza, are metaphysical foundationalists of one stripe or another. This is curious since the PSR—which says that everything has a ground, cause, or explanation—in effect, denies fundamental entities. In this paper, I explore the apparent inconsistency between metaphysical foundationalism and approaches to metaphysical system building that are driven by a commitment to the PSR. I do so by analyzing how Indian Buddhist philosophers arrive at foundationalist and anti-foundationalist (...) positions motivated by implicit commitments to different versions of the PSR. I begin by introducing the Buddhist principle of dependent origination (pratītyasamutpāda) as a proto-PSR that is restricted to causal explanation. Next, I show how Vasubandhu’s Sautrāntika Abhidharma metaphysics is shaped by a qualified commitment to both causal and metaphysical grounding versions of the PSR. I then reveal how Nāgārjuna’s Madhyamaka metaphysics is driven by an unrestricted and exceptionless commitment to causal and metaphysical grounding versions of the PSR. Finally, I consider how Nāgārjuna’s account may put him in a unique position to respond to a common contemporary objection to the PSR from necessitarianism. I conclude by addressing a competing interpretation on which Nāgārjuna is best understood as an anti-rationalist rather than an uber-rationalist, as I characterize him. (shrink)

As is well-known, the formal system in which Frege works in his Grundgesetze der Arithmetik is formally inconsistent, Russell’s Paradox being derivable in it.This system is, except for minor differ...