What is it to know someone? Epistemologists rarely take up this question, though recent developments make such inquiry possible and desirable. This paper advances an account of how such interpersonal knowledge goes beyond mere propositional and qualitative knowledge about someone, giving a central place to second-personal treatment. It examines what such knowledge requires, and what makes it distinctive within epistemology as well as socially. It assesses its theoretic value for several issues in moral psychology, epistemic injustice, and philosophy of mind. (...) And it offers an account of the complex content in play if interpersonal knowledge is to be understood in terms of its mental states and their functions. (shrink)

Epistemologists have shown increased interest in the epistemic significance of disagreement, and in particular, in whether there is a rational requirement concerning belief revision in the face of peer disagreement. This article examines some of the general issues discussed by epistemologists, and then considers how they may or may not apply to the case of religious disagreement, both within religious traditions and between religious (and non-religious) views.

Hope, in its propositional construction "I hope that p," is compatible with a stated chance for the speaker that not-p. On fallibilist construals of knowledge, knowledge is compatible with a chance of being wrong, such that one can know that p even though there is an epistemic chance for one that not-p. But self-ascriptions of propositional hope that p seem to be incompatible, in some sense, with self-ascriptions of knowing whether p. Data from conjoining hope self-ascription with outright assertions, with (...) first- and third-person knowledge ascriptions, and with factive predicates suggest a problem: when combined with a plausible principle on the rationality of hope, they suggest that fallibilism is false. By contrast, the infallibilist about knowledge can straightforwardly explain why knowledge would be incompatible with hope, and can offer a simple and unified explanation of all the linguistic data introduced here. This suggests that fallibilists bear an explanatory burden which has been hitherto overlooked. (shrink)

Surprisingly little has been written about hedged assertion. Linguists often focus on semantic or syntactic theorizing about, for example, grammatical evidentials or epistemic modals, but pay far less attention to what hedging does at the level of action. By contrast, philosophers have focused extensively on normative issues regarding what epistemic position is required for proper assertion, yet they have almost exclusively considered unqualified declaratives. This essay considers the linguistic and normative issues side-by-side. We aim to bring some order and clarity (...) to thinking about hedging, so as to illuminate aspects of interest to both linguists and philosophers. In particular, we consider three broad questions. 1) The structural question: when one hedges, what is the speaker’s commitment weakened from? 2) The functional question: what is the best way to understand how a hedge weakens? And 3) the taxonomic question: are hedged assertions genuine assertions, another speech act, or what? (shrink)

Recent epistemology has focused almost exclusively on propositional knowledge. This paper considers an underexplored area of epistemology, namely knowledge of persons: if propositional knowledge is a state of mind, consisting in a subject's attitude to a (true) proposition, the account developed here thinks of interpersonal knowledge as a state of minds, involving a subject's attitude to another (existing) subject. This kind of knowledge is distinct from propositional knowledge, but it exhibits a gradability characteristic of context-sensitivity, and admits of shifty thresholds. (...) It is supported by a wide range of unexplored linguistic data and intuitive cases; and it promises to illuminate debates within epistemology, philosophy of religion, and ethics. (shrink)

Some philosophers oppose recent arguments for the Knowledge Norm of Assertion by claiming that assertion, being an act much like any other, will be subject to norms governing acts generally, such as those articulated by Grice for the purpose of successful, cooperative endeavours. But in fact, Grice is a traitor to their cause; or rather, they are his dissenters, not his disciples. Drawing on Grice's unpublished papers, I show that he thought of asserting as a special linguistic act in need (...) of its own norm, and he tied his maxim of Quality to knowledge. I also develop a simple Gricean-inspired argument showing that the Quality maxim is not dependent on the Cooperative Principle. If it is not thus dependent, then the Cooperative Principle cannot be the explanation of, or source of normativity for, the Quality maxim. Thus, leveraging the insights informing the maxim of Quality actually provides the resources for a distinctive positive case that knowledge is the constitutive norm of assertion. (shrink)

Many epistemologists are enamored with a defeat condition on knowledge. In this paper we present some implementation problems for defeatism, understood along either internalist or externalist lines. We then propose that one who accepts a knowledge norm of belief, according to which one ought to believe only what one knows, can explain away much of the motivation for defeatism. This is an important result, because on the one hand it respects the plausibility of the intuitions about defeat shared by many (...) in epistemology; but on the other hand, it obviates the need to provide a unified account of defeat which plays well with the most plausible views of how knowledge fits with evidential probability. (shrink)

Expert testimony figures in recent debates over how best to understand the norm of assertion and the domain-specific epistemic expectations placed on testifiers. Cases of experts asserting with only isolated second-hand knowledge (Lackey 2011, 2013) have been used to shed light on whether knowledge is sufficient for epistemically permissible assertion. I argue that relying on such cases of expert testimony introduces several problems concerning how we understand expert knowledge, and the sharing of such knowledge through testimony. Refinements are needed to (...) clarify exactly what principles are being tested by such cases; but once refined, such cases raise more questions than they answer. (shrink)

Recent epistemology offers an account of what it is to know other persons. Such views hold promise for illuminating several issues in philosophy of religion, and for advancing a distinctive approach to religious epistemology. This paper develops an account of interpersonal knowledge, and clarifies its relation to propositional and qualitative knowledge. I then turn to our knowledge of God and God's knowledge of us, and compare my account of interpersonal knowledge with important work by Eleonore Stump on "Franciscan" knowledge. I (...) examine how interpersonal knowledge may figure in liturgical practice, in diffusing the problem of divine hiddenness, and in motivating a novel understanding of divine love. I also explore the possibility of epistemic injustice arising from dismissal or neglect of our religious testimony to one another, or of divine testimony to humanity, focusing specifically on the import of interpersonal knowledge. (shrink)

The problem of evil is the most prominent argument against the existence of God. Skeptical theists contend that it is not a good argument. Their reasons for this contention vary widely, involving such notions as CORNEA, epistemic appearances, 'gratuitous' evils, 'levering' evidence, and the representativeness of goods. We aim to dispel some confusions about these notions, in particular by clarifying their roles within a probabilistic epistemology. In addition, we develop new responses to the problem of evil from both the phenomenal (...) conception of evidence and the knowledge-first view of evidence. (shrink)

Traditional definitions of lying require that a speaker believe that what she asserts is false. Sam Fox Krauss seeks to jettison the traditional belief requirement in favour of a necessary condition given in a credence-accuracy framework, on which the liar expects to impose the risk of increased inaccuracy on the hearer. He argues that this necessary condition importantly captures nearby cases as lies which the traditional view neglects. I argue, however, that Krauss's own account suffers from an identical drawback of (...) being unable to explain nearby cases; and even worse, that account fails to distinguish cases of telling lies from cases of telling the truth. (shrink)

Hope is an attitude with a distinctive epistemological dimension: it is incompatible with knowledge. This chapter examines hope as it relates to knowledge but also to probability and inductive considerations. Such epistemic constraints can make hope either impossible, or, when hope remains possible, they affect how one’s epistemic situation can make hope rational rather than irrational. Such issues are especially relevant to when hopefulness may permissibly figure in practical deliberation over a course of action. So I consider cases of second-order (...) inductive reflection on when one should, or should not, be hopeful for an outcome with which one has a long record of experience: in other words, what is the epistemology behind when one should, if ever, stop hoping for outcomes which have failed one many times in the past? (shrink)

Assertion is governed by an epistemic norm requiring knowledge. This idea has been hotly debated in recent years, garnering attention in epistemology, philosophy of language, and linguistics. This chapter presents and extends the main arguments in favor of the knowledge norm, from faulty conjunctions, several conversational patterns, judgments of permission, excuse, and blame, and from showing how. (Paired with a chapter by Peter J. Graham and Nikolaj J. L. L. Pedersen, "Knowledge is Not Our Norm of Assertion.").

This chapter covers contemporary work on disagreement, detailing both the conceptual and normative issues in play in the debates in mainstream analytic epistemology, and how these relate to religious diversity and disagreement. §1 examines several sorts of disagreement, and considers several epistemological issues: in particular, what range of attitudes a body of evidence can support, how to understand higher-order evidence, and who counts as an epistemic “peer”. §2 considers how these questions surface when considering disagreements over religion, including debates over (...) the nature of evidence and truth in religion, epistemic humility, concerns about irrelevant influences and about divine hiddenness, and arguments over exclusivism, inclusivism, and pluralism. Finally, §3 summarizes the contributors’ essays in this volume. (shrink)

Epistemologists focus primarily on cases of knowledge, belief, or credence where the evidence which one possesses, or on which one is relying, plays a fundamental role in the epistemic or normative status of one's doxastic state. Recent work in epistemology goes beyond the evidence one possesses to consider the relevance for such statuses of evidence which one does not possess, particularly when there is a sense in which one should have had some evidence. I focus here on Sanford Goldberg's approach (...) ("Should Have Known," Synthese, forthcoming; and "On the Epistemic Significance of Evidence You Should Have Had," Episteme 2016, this issue); but the discussion will interest anyone working on epistemic defeat. (shrink)

Linda Zagzebski's "Epistemic Authority" (Oxford University Press, 2012) brings together issues in social epistemology with topics in moral and political philosophy as well as philosophy of religion. In this paper I criticize her discussion of self-trust and rationality, which sets up the main argument of the book; I consider how her view of authority relates to some issues of epistemic authority in testimony; and I raise some concerns about her treatment of religious epistemology and religious authority in particular.

The lottery and preface paradoxes pose puzzles in epistemology concerning how to think about the norms of reasonable or permissible belief. Contextualists in epistemology have focused on knowledge ascriptions, attempting to capture a set of judgments about knowledge ascriptions and denials in a variety of contexts (including those involving lottery beliefs and the principles of closure). This article surveys some contextualist approaches to handling issues raised by the lottery and preface, while also considering some of the difficulties encountered by those (...) approaches. (shrink)

This essay expands upon the suggestion that Lessing's infamous ‘ditch’ is actually three ditches: temporal, metaphysical, and existential gaps. It examines the complex problems these ditches raise, and then proposes that Kierkegaard's Fragments and Postscript exhibit a similar triadic organizational structure, which may signal a deliberate attempt to engage and respond to Lessing's three gaps. Viewing the Climacean project in this way offers an enhanced understanding of the intricacies of Lessing's rationalist approach to both religion and historical truth, and illuminates (...) Climacus's subjective response to Lessing. (shrink)

Assertion is widely regarded as an act associated with an epistemic position. To assert is to represent oneself as occupying this position and/or to be required to occupy this position. Within this approach, the most common view is that assertion is strong: the associated position is knowledge or certainty. But recent challenges to this common view present new data that are argued to be better explained by assertion being weak. Old data widely taken to support assertion being strong has also (...) been challenged. This paper examines such challenges and finds them wanting. Far from diminishing the case for strong assertion, carefully considering new and old data reveals that assertion is as strong as ever. (shrink)

The paper compares the suitability of two different epistemologies of counterfactuals—(EC) and (W)—to elucidate modal knowledge. I argue that, while both of them explain the data on our knowledge of counterfactuals, only (W)—Williamson’s epistemology—is compatible with all counterpossibles being true. This is something on which Williamson’s counterfactual-based account of modal knowledge relies. A first problem is, therefore, that, in the absence of further, disambiguating data, Williamson’s choice of (W) is objectionably biased. A second, deeper problem is that (W) cannot satisfactorily (...) elucidate modal knowledge. Third, from a naturalistic perspective, the nature of this second problem favours (EC) against (W). (shrink)

The Knowledge Norm or Knowledge Account of Assertion (KAA) has received added support recently from data on prompting assertion (Turri 2010) and from a refinement suggesting that assertions ought to express knowledge (Turri 2011). This paper adds another argument from parenthetical positioning, and then argues that KAA’s unified explanation of some of the earliest data (from Moorean conjunctions) adduced in its favor recommends KAA over its rivals.

We study shared intentions in what we call “loose groups”. These are groups that lack a codified organizational structure, and where the communication channels between group members are either unreliable or not completely open. We start by formulating two desiderata for shared intentions in such groups. We then argue that no existing account meets these two desiderata, because they assume either too strong or too weak an epistemic condition, that is, a condition on what the group members know and believe (...) about what the others intend, know, and believe. We propose an alternative, pooled knowledge, and argue that it allows formulating conditions on shared intentions that meet the two desiderata. (shrink)

The knowledge account of assertion - roughly: one should not assert what one does not know - can explain a variety of Moorean conjunctions, a fact often cited as evidence in its favor. David Sosa ("Dubious Assertions," Phil Studies, 2009) has objected that the account does not generalize satisfactorily, since it cannot explain the infelicity of certain iterated conjunctions without appealing to the controversial "KK" principle. This essay responds by showing how the knowledge account can handle such conjunctions without use (...) of the KK principle. (shrink)

John N. Williams (1994) and Matthew Weiner (2005) invoke predictions in order to undermine the normative relevance of knowledge for assertions; in particular, Weiner argues, predictions are important counterexamples to the Knowledge Account of Assertion (KAA). I argue here that they are not true counterexamples at all, a point that can be agreed upon even by those who reject KAA.

According to the early Yogācāra, following non-conceptual awareness, the advanced bodhisattva is said to attain a state characterized by a "subsequent awareness". Yogācāra thinkers identify this state with ultimate knowledge of causality and view it as involving a unique kind of conceptual activity and propositional attitudes, which are very different, however, from ordinary conceptual awareness insofar as they do not involve vikalpa. Translated back into the terms of some version of the contemporary debate between conceptualists and nonconceptualists, this would amount (...) to something like the claim that we can use concepts in a non-conceptual way. But how can we make sense... (shrink)

In this paper, we define projection and bidirectional projection measures between interval rough neutrosophic sets and prove their basic properties. Then two new multi attribute decision making strategies are proposed based on interval rough neutrosophic projection and bidirectional projection measures respectively. Then the proposed methods are applied for solving multi attribute decision making problems. Finally, a numerical example is solved to show the feasibility, applicability and effectiveness of the proposed strategies.

Competitive negotiators frequently use tactics which others view as "unethical", in that these tactics either violate standards of truth telling or violate the perceived rules of negotiation. This paper sought to determine how business students viewed a number of marginally ethical negotiating tactics, and to determine the underlying factor structure of these tactics. The factor analysis of these tactics revealed five clear factors which were highly similar across the two samples, and which parallel (to a moderate degree) categories of tactics (...) proposed by earlier theory. Data from one sample also permitted comparisons of the appropriateness of certain tactics across gender, nationality, ethnic origin and perception of one's negotiating style. (shrink)

In the proof-theoretic semantics approach to meaning, harmony , requiring a balance between introduction-rules (I-rules) and elimination rules (E-rules) within a meaning conferring natural-deduction proof-system, is a central notion. In this paper, we consider two notions of harmony that were proposed in the literature: 1. GE-harmony , requiring a certain form of the E-rules, given the form of the I-rules. 2. Local intrinsic harmony : imposes the existence of certain transformations of derivations, known as reduction and expansion . We propose (...) a construction of the E-rules (in GE-form) from given I-rules, and prove that the constructed rules satisfy also local intrinsic harmony. The construction is based on a classification of I-rules, and constitute an implementation to Gentzen’s (and Pawitz’) remark, that E-rules can be “read off” I-rules. (shrink)

Coleridge rarely mentions Hegel in his philosophical writings and seems to have read very little of Hegel's work. Yet I argue that Coleridge's criticisms of Schelling's philosophy—as recorded in letters and marginalia—betray remarkable intellectual affinities with his nearly exact contemporary Hegel, particularly in their shared doubts about Schelling's foundationalist intuitionism. With this background in place, I seek to demonstrate that volume one of Coleridge's Biographia Literaria is a radically self-undermining text: its philosophical argument, far from slavishly recapitulating Schelling's philosophy, remains (...) haunted by a quasi-Hegelian skepticism toward intuition even as it advances intuition as the foundation of its theoretical edifice. (shrink)

One of the predominant debates in AI Ethics is the worry and necessity to create fair, transparent and accountable algorithms that do not perpetuate current social inequities. I offer a critical analysis of Reuben Binns’s argument in which he suggests using public reason to address the potential bias of the outcomes of machine learning algorithms. In contrast to him, I argue that ultimately what is needed is not public reason per se, but an audit of the implicit moral assumptions of (...) societies within which algorithms are built and applied. Public justification is appealing since it offers us the possibility to align the decision-making outcomes of the algorithm with the core moral values of stakeholders within a constitutional democratic society. My concern is that the common moral principles that form the foundation of public reason are not necessarily neutral, as they still express specific moral ideals and normative standards even if there is moral agreement by society as a whole, or among different stakeholders within society. Appealing to such normative standards may thus still lead to algorithmic outcomes being biased as common moral values may very well still be discriminatory even though they are formed from a consensus, and even if public reason is applied as a kind of filter for potential algorithmic outcomes. Hence, I argue that these implicit moral norms within society that we take as a given in public reasoning, need to be audited from generation to generation in order to effectively mitigate potential algorithmic bias. (shrink)

During the Winter of 2011 I visited SADAF and gave a series of talks based on the central chapters of my manuscript on the Yablo paradox. The following year, I visited again, and was pleased and honored to find out that Eduardo Barrio and six of his students had written ‘responses’ that addressed the claims and arguments found in the manuscript, as well as explored new directions in which to take the ideas and themes found there. These comments reflect my (...) thoughts on these responses (also collected in this issue), as well as my thoughts on further issues that arose during the symposium that was based on the papers and during the many hours I spent talking and working with Eduardo and his students. Durante el invierno de 2011, visité SADAF y dí una serie de conferencias sobre los capítulos centrales de mi manuscrito sobre la paradoja de Yablo. El año siguiente, visité Buenos aires nuevamente y tuve el placer y el honor de descubrir que Eduardo Barrio y seis de sus estudiantes habían escrito respuestas que abordan las afirmaciones y argumentos de mi manuscrito, además de explorar nuevas direcciones en las cuales considerar las ideas y temas encontrados allí. El presente trabajo refleja mis pensamientos sobre estas respuestas (también incluidas en este volumen), así como mis ideas sobre otras cuestiones que surgieron durante el simposio en el que se presentaron los artículos y en las muchas horas que nosotros discutimos y trabajamos con Eduardo y sus estudiantes. (shrink)

Comics comprise a hybrid art form descended from printmaking and mostly made using print technologies. But comics are an art form in their own right and do not belong to the art form of printmaking. We explore some features art comics and fine art prints do and do not have in common. Although most fine art prints and comics are multiple artworks, it is not obvious whether the multiple instances of comics and prints are artworks in their own right. The (...) comparison of comics and fine art prints provides a promising test for assessing how hybrid art forms develop more generally, and for assessing how they differ from closely related nonhybrid cousins. (shrink)

The paper briefly surveys the sentential proof-theoretic semantics for fragment of English. Then, appealing to a version of Frege’s context-principle (specified to fit type-logical grammar), a method is presented for deriving proof-theoretic meanings for sub-sentential phrases, down to lexical units (words). The sentential meaning is decomposed according to the function-argument structure as determined by the type-logical grammar. In doing so, the paper presents a novel proof-theoretic interpretation of simple type, replacing Montague’s model-theoretic type interpretation (in arbitrary Henkin models). The domains (...) of derivations are collections of derivations in the associated “dedicated” natural-deduction proof-system, and functions therein (with no appeal to models, truth-values and elements of a domain). The compositionality of the semantics is analyzed. (shrink)

Charitable interpreters of David Hume set aside his sprinkles of piety. Better to read him as lying than as clumsily inconsistent. We argue that the attribution of lies can pay dividends in historical scholarship no matter how strongly the theorist condemns lying. Accordingly, we show that our approach works even with one of the strongest condemners of lying: Immanuel Kant. We argue that Kant lied in his scholarly work and even in the first Critique. And we defend the claim that (...) this lie attribution, strange as it may sound, amounts to a kind of scholarly charity. (shrink)

Immanuel Kant promised, ‘as Your Majesty's loyal subject’, to abstain from all public lectures about religion. All past commentators agree this phrase permitted Kant to return to the topic after the King died. But it is not part of the ‘at-issue content’. Consequently, ‘as Your Majesty's loyal subject’ is no more an escape clause than the corresponding phrase in ‘I guarantee, as your devoted fan, that these guitar strings will not break’. Just as the guarantee stands regardless of whether the (...) guarantor ceases to be your devoted fan, the compliance conditions of Kant's promise are not affected by Kant's ceasing to be the king's loyal subject. For good or ill, Kant made a lying promise to King Friedrich Wilhelm II in 1794. (shrink)

Ce texte est le fruit d’une collaboration entre un astrophysicien, Jean-René Roy, et un philosophe de l’éducation, Normand Baillargeon. Ils ont en commun d’avoir été marqués par la fréquentation des oeuvres de Mario Bunge, auxquelles ils attachent un grand prix, sur un plan personnel, d’abord, mais aussi, et c’est ce qu’ils veulent rappeler dans ces pages : parce qu’ils estiment que les oeuvres de Bunge contribuent de manière extrêmement forte et positive à rendre plus salubre la vie de l’esprit, en (...) enrichissant notre intellect et en luttant contre diverses formes troublantes d’obscurantisme qui y sévissent parfois, notamment dans les domaines familiers aux deux auteurs. (shrink)

Notions such as Sunyata, Catuskoti, and Indra's Net, which figure prominently in Buddhist philosophy, are difficult to readily accommodate within our ordinary thinking about everyday objects. Famous Buddhist scholar Nagarjuna considered two levels of reality: one called conventional reality and the other ultimate reality. Within this framework, Sunyata refers to the claim that at the ultimate level objects are devoid of essence or "intrinsic properties", but are interdependent by virtue of their relations to other objects. Catuskoti refers to the claim (...) that four truth values, along with contradiction, are admissible in reasoning. Indra's Net refers to the claim that every part of a whole is reflective of the whole. Here we present category theoretic constructions which are reminiscent of these Buddhist concepts. The universal mapping property definition of mathematical objects, wherein objects of a universe of discourse are defined not in terms of their content, but in terms of their relations to all objects of the universe is reminiscent of Sunyata. The objective logic of perception, with perception modeled as [a category of] two sequential processes (sensation followed by interpretation), and with its truth value object of four truth values, is reminiscent of the Buddhist logic of Catuskoti. The category of categories, wherein every category has a subcategory of sets with zero structure within which every category can be modeled, is reminiscent of Indra's Net. Our thorough elaboration of the parallels between Buddhist philosophy and category theory can facilitate better understanding of Buddhist philosophy, and bring out the broader philosophical import of category theory beyond mathematics. (shrink)

According to Essentialism, an object’s properties divide into those that are essential and those that are accidental. While being human is commonly thought to be essential to Socrates, being a philosopher plausibly is not. We can motivate the distinction by appealing—as we just did—to examples. However, it is not obvious how best to characterize the notion of essential property, nor is it easy to give conclusive arguments for the essentiality of a given property. In this paper, I elaborate on these (...) issues and explore the way in which essential properties behave in relation to other related properties, like sufficient-for-existence properties and individual essences. (shrink)

We define consciousness as the category of all conscious experiences. This immediately raises the question: What is the essence in which every conscious experience in the category of conscious experiences partakes? We consider various abstract essences of conscious experiences as theories of consciousness. They are: (i) conscious experience is an action of memory on sensation, (ii) conscious experience is experiencing a particular as an exemplar of a general, (iii) conscious experience is an interpretation of sensation, (iv) conscious experience is referring (...) sensation to an object as its cause, and (v) conscious experience is a model of stimulus. Corresponding to each one of these theories we obtain a category of models of conscious experiences: (i) category of actions, (ii) category of idempotents, (iii) category of two sequential maps, (iv) category of brain-generalized figures, and (v) functor categories with intuition as base and conceptual repertoire as exponent, respectively. For each theory of consciousness we also calculate its truth value object and characterize the objective logic intrinsic to the corresponding category of models of consciousness experiences. (shrink)

Pace Necessitism – roughly, the view that existence is not contingent – essential properties provide necessary conditions for the existence of objects. Sufficiency properties, by contrast, provide sufficient conditions, and individual essences provide necessary and sufficient conditions. This paper explains how these kinds of properties can be used to illuminate the ontological status of merely possible objects and to construct a respectable possibilist ontology. The paper also reviews two points of interaction between essentialism and modal logic. First, we will briefly (...) see the challenge that arises against S4 from flexible essential properties; as well as the moves available to block it. After this, the emphasis is put on the Barcan Formula (BF), and on why it is problematic for essentialists. As we will see, Necessitism can accommodate both (BF) and essential properties. What necessitists cannot do at the same time is to continue to understanding essential properties as providing necessary conditions for the existence of individuals; against what might be for some a truism. (shrink)

In this paper we compare the propositional logic of Frege’s Grundgesetze der Arithmetik to modern propositional systems, and show that Frege does not have a separable propositional logic, definable in terms of primitives of Grundgesetze, that corresponds to modern formulations of the logic of “not”, “and”, “or”, and “if…then…”. Along the way we prove a number of novel results about the system of propositional logic found in Grundgesetze, and the broader system obtained by including identity. In particular, we show that (...) the propositional connectives that are definable in terms of Frege’s horizontal, negation, and conditional are exactly the connectives that fuse with the horizontal, and we show that the logical operators that are definable in terms of the horizontal, negation, the conditional, and identity are exactly the operators that are invariant with respect to permutations on the domain that leave the truth-values fixed. We conclude with some general observations regarding how Frege understood his logic, and how this understanding differs from modern views. (shrink)

Notions such as śūnyatā, catuṣkoṭi, and Indra's net, which figure prominently in Buddhist philosophy, are difficult to readily accommodate within our ordinary thinking about everyday objects. Famous Buddhist scholar Nāgārjuna considered two levels of reality: one called conventional reality, and the other ultimate reality. Within this framework, śūnyatā refers to the claim that at the ultimate level objects are devoid of essence or "intrinsic properties", but are interdependent by virtue of their relations to other objects. Catuṣkoṭi refers to the claim (...) that four truth values, including contradiction, are admissible in reasoning. Indra's net refers to the claim that every part of a whole is reflective of the whole. Here we present category theoretic constructions that are reminiscent of these Buddhist concepts. The universal mapping property definition of mathematical objects, wherein objects of a universe of discourse are defined not in terms of their content, but in terms of their relations to all objects of the universe is reminiscent of śūnyatā. The objective logic of perception, with perception modeled as [a category of] two sequential processes (sensation followed by interpretation), and with its truth value object of four truth values, is reminiscent of the Buddhist logic of catuṣkoṭi. The category of categories, wherein every category has a subcategory of sets with zero structure within which every category can be modeled, is reminiscent of Indra's net. Our thorough elaboration of the parallels between Buddhist philosophy and category theory can facilitate better understanding of Buddhist philosophy, and bring out the broader philosophical import of category theory beyond mathematics. (shrink)

In this paper, the sine, cosine and cotangent similarity measures of interval rough neutrosophic sets is proposed. Some properties of the proposed measures are discussed. We have proposed multi attribute decision making approaches based on proposed similarity measures. To demonstrate the applicability, a numerical example is solved.

At the turn of the nineteenth century, Friedrich Schlegel developed an influential theory of irony that anticipated some of the central concerns of postmodernity. His most vocal contemporary critic, the philosopher Hegel, sought to demonstrate that Schlegel’s theory of irony tacitly relied on certain problematic aspects of Fichte’s philosophy. While Schlegel’s theory of irony has generated seemingly endless commentary in recent critical discourse, Hegel’s critique of Schlegelian irony has gone neglected. This essay’s primary aim is to defend Hegel’s critique of (...) Schlegel by isolating irony’s underlying Fichtean epistemology. Drawing on Søren Kierkegaard’s The Concept of Irony in the final section of this essay, I argue that Hegel’s critique of irony can motivate a dialectical hermeneutics that offers a powerful alternative both to Paul de Man’s poststructuralist hermeneutics and to recent cultural-studies-oriented criticism that tends to reduce literary texts to sociohistorical epiphenomena. (shrink)

In this paper, we define correlation coefficient measure between any two rough neutrosophic sets. We also prove some of its basic properties.. We develop a new multiple attribute group decision making method based on the proposed correlation coefficient measure. An illustrative example of medical diagnosis is solved to demonstrate the applicability and effecriveness of the proposed method.

Our conscious experiences are qualitative and unitary. The qualitative universals given in particular experiences, i.e. qualia, combine into the seamless unity of our conscious experience. The problematics of quality and cohesion are not unique to consciousness studies. In mathematics, the study of qualities (e.g., shape) resulting from quantitative variations in cohesive spaces led to the axiomatization of cohesion and quality. Using the mathematical definition of quality, herein we model qualia space as a categorical product of qualities. Thus modeled qualia space (...) is a codomain space wherein composite qualities (e.g. shape AND color) of conscious experiences can be valued. As part of characterizing the qualia space, we provide a detailed exemplification of the mathematics of quality and cohesion in terms of the categories of idempotents and reflexive graphs. More specifically, with qualities as commutative triangles formed of cohesion-preserving functors, first we calculate the product of commutative triangles. Next, we explicitly show that the category of idempotents is a quality type. Lastly, as part of showing that the category of reflexive graphs is cohesive, we characterize the adjointness between functors relating cohesive graphs to discrete sets. In conclusion, our category theoretic construction of qualia space is a formalization of the binding of qualitative features (colors and shapes) into the cohesive objects (colored-shapes) of conscious experiences. Compared to the feature-vector accounts of conscious experiences, our product-of-qualities account of consciousness is a substantial theoretical advance. (shrink)

Due to the influence of Nathan Salmon’s views, endorsement of the “flexibility of origins” thesis is often thought to carry a commitment to the denial of S4. This paper rejects the existence of this commitment and examines how Peacocke’s theory of the modal may accommodate flexibility of origins without denying S4. One of the essential features of Peacocke’s account is the identification of the Principles of Possibility, which include the Modal Extension Principle (MEP), and a set of Constitutive Principles. Regarding (...) their modal status, Peacocke argues for the necessity of MEP, but leaves open the possibility that some of the Constitutive Principles be only contingently true. Here, I show that the contingency of the Constitutive Principles is inconsistent with the recursivity of MEP, and this makes the account validate S4. It is also shown that, compatibly with the necessity of the Constitutive Principles, the account can still accommodate intuitions about flexibility of origins. However, the account we end up with once those intuitions are consistently accommodated may not be satisfactory, and this opens up the debate about whether or not artefacts allow for some variation in their origins. (shrink)