Mind, according to cognitive neuroscience, is a set of brain functions. But, unlike sets, our minds are cohesive. Moreover, unlike the structureless elements of sets, the contents of our minds are structured. Mutual relations between the mental contents endow the mind its structure. Here we characterize the structural essence and the logical form of the mind by focusing on thinking. Examination of the relations between concepts, propositions, and syllogisms involved in thinking revealed the reflexive graph structure of the (...) conceptual mind. Objective logic of the conceptual mind is calculated from its structure. Noteworthy features of the logic of conceptual mind are: degrees of truth, varieties of negation, admission of contradiction, and the failure of a de Morgan's law. Furthermore, cohesion of the conceptual mind follows from its reflexive graph structure. Our characterization of the structure and logic of mind constitutes a substantial refinement of the contemporary cognitive neuroscientific conceptualization of the mind as a set. (shrink)

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)

This paper deals with higher-order vagueness in Williamson's 'logic of clarity'. Its aim is to prove that for 'fixed margin models' (W,d,α ,[ ]) the notion of higher-order vagueness collapses to second-order vagueness. First, it is shown that fixed margin models can be reformulated in terms of similarity structures (W,~). The relation ~ is assumed to be reflexive and symmetric, but not necessarily transitive. Then, it is shown that the structures (W,~) come along with naturally defined maps h and (...) s that define a Galois connection on the power set PW of W. These maps can be used to define two distinct boundary operators bd and BD on W. The main theorem of the paper states that higher-order vagueness with respect to bd collapses to second-order vagueness. This does not hold for BD, the iterations of which behave in quite an erratic way. In contrast, the operator bd defines a variety of tolerance principles that do not fall prey to the sorites paradox and, moreover, do not always satisfy the principles of positive and negative introspection. (shrink)

Modeling mechanisms is central to the biological sciences – for purposes of explanation, prediction, extrapolation, and manipulation. A closer look at the philosophical literature reveals that mechanisms are predominantly modeled in a purely qualitative way. That is, mechanistic models are conceived of as representing how certain entities and activities are spatially and temporally organized so that they bring about the behavior of the mechanism in question. Although this adequately characterizes how mechanisms are represented in biology textbooks, contemporary biological research practice (...) shows the need for quantitative, probabilistic models of mechanisms, too. In this paper we argue that the formal framework of causal graph theory is well-suited to provide us with models of biological mechanisms that incorporate quantitative and probabilistic information. On the ba-sis of an example from contemporary biological practice, namely feedback regulation of fatty acid biosynthesis in Brassica napus, we show that causal graph theoretical models can account for feedback as well as for the multi-level character of mechanisms. However, we do not claim that causal graph theoretical representations of mechanisms are advantageous in all respects and should replace common qualitative models. Rather, we endorse the more balanced view that causal graph theoretical models of mechanisms are useful for some purposes, while being insufficient for others. (shrink)

A graph-theoretic account of logics is explored based on the general notion of m-graph (that is, a graph where each edge can have a finite sequence of nodes as source). Signatures, interpretation structures and deduction systems are seen as m-graphs. After defining a category freely generated by a m-graph, formulas and expressions in general can be seen as morphisms. Moreover, derivations involving rule instantiation are also morphisms. Soundness and completeness theorems are proved. As a consequence of (...) the generality of the approach our results apply to very different logics encompassing, among others, substructural logics as well as logics with nondeterministic semantics, and subsume all logics endowed with an algebraic semantics. (shrink)

Generative AI has proven itself as an efficient innovation in many fields including writing and even analyzing data. For spatial computing, it provides a potential solution for solving such issues related to data manipulation and analysis within the spatial computing domain. This paper aims to discuss the probabilities of applying generative AI to graph-based spatial computing; to describe new approaches in detail; to shed light on their use cases; and to demonstrate the value that they add. This technique thus (...) incorporates graph theory, generative models to model spatial relations, generate new spatial forms and improve on spatial decision-making processes. The paper surveys such methods, describes typical applications, and outlines further development of the subject. (shrink)

A graph-theoretic account of fibring of logics is developed, capitalizing on the interleaving characteristics of fibring at the linguistic, semantic and proof levels. Fibring of two signatures is seen as a multi-graph (m-graph) where the nodes and the m-edges include the sorts and the constructors of the signatures at hand. Fibring of two models is a multi-graph (m-graph) where the nodes and the m-edges are the values and the operations in the models, respectively. Fibring of (...) two deductive systems is an m-graph whose nodes are language expressions and the m-edges represent the inference rules of the two original systems. The sobriety of the approach is confirmed by proving that all the fibring notions are universal constructions. This graph-theoretic view is general enough to accommodate very different fibrings of propositional based logics encompassing logics with non-deterministic semantics, logics with an algebraic semantics, logics with partial semantics and substructural logics, among others. Soundness and weak completeness are proved to be preserved under very general conditions. Strong completeness is also shown to be preserved under tighter conditions. In this setting, the collapsing problem appearing in several combinations of logic systems can be avoided. (shrink)

Peirce’s Existential Graphs provide a geometrical understanding of a variety of logics (classical, intuitionistic, modal, fi rst-order). The geometrical interpretation is given by topological transformations of closed (Jordan) curves on the plane, but it can be extended to other surfaces (sphere, cylinder, torus, etc.) The result provides the appearance of new logics related to the shapes of the surfaces. Going beyond, one can draw existential graphs over general Riemann Surfaces, and, introducing tools from algebraic geometry (Sheaves, Grothendieck Toposes, Elementary Toposes), (...) one can try to capture both the logics and the geometrical shapes through a new Topos of Existential Graphs over Riemann Surfaces, and through the classifi er subobject of the topos. We off er new perspectives (concepts, defi nitions, examples, conjectures) along this road. -/- Os Grafos Existenciais de Peirce oferecem uma compreensão geométrica de uma variedade de lógicas (clássica, intuicionista, modal, de primeira ordem). A sua interpretação geométrica é dada por transformações topológicas de curvas fechadas (Jordan) no plano, mas pode ser estendida a outras superfícies (esfera, cilindro, toro etc.). Além disso, é possível desenhar grafos existenciais sobre superfícies de Riemann gerais e, introduzindo ferramentas da geometria algébrica (Feixes, Toposes de Grothendieck, Toposes Elementares), é possível tentar capturar as lógicas nas formas geométricas por meio de um novo Topos de Grafos Existenciais sobre Superfícies de Riemann e por meio do subobjeto classifi cador do topos. Oferecemos novas perspectivas (conceitos, defi nições, exemplos, conjecturas) ao longo desse caminho. (shrink)

In this paper, we analyze and discuss Schopenhauer’s n-term diagrams for eristic dialectics from a graph-theoretical perspective. Unlike logic, eristic dialectics does not examine the validity of an isolated argument, but the progression and persuasiveness of an argument in the context of a dialogue or even controversy. To represent these dialogue situations, Schopenhauer created large maps with concepts and Euler-type diagrams, which from today’s perspective are a specific form of graphs. We first present the original method with Euler-type diagrams, (...) then give the most important graph-theoretical definitions, then discuss Schopenhauer’s diagrams graph-theoretically and finally give an example of how the graphs or diagrams can be used to analyze dialogues. (shrink)

Self-reflexive videogames are videogames designed to materialize critical and/or satirical perspectives on the ways in which videogames themselves are designed, played, sold, manipulated, experienced, and understood as social objects. This essay focuses on the use of virtual worlds as mediators, and in particular on the use of videogames to guide and encourage reflections on technical, interactive, and thematic conventions in videogame design and development. Structurally, it is composed of two interconnected parts: -/- 1) In the first part of this (...) essay, I will discuss NECESSARY EVIL (Gualeni et al., 2013), an experimental videogame that I designed as a self-reflexive virtual artifact. With the objective of clarifying the philosophical aspirations of self-reflexive videogames – and in order to understand how those aspirations can be practically pursued – I will dissect and examine the design decisions that contributed to the qualities of NECESSARY EVIL as an example of “playable philosophy”. -/- 2) Taking off from the perspectives on self-reflexive videogames offered in the first part of the essay, the second half will focus on virtual worlds as viable mediators of philosophical thought more in general. In this section, I will argue that, both through the practice of game design and through the interactive experiences of virtual worlds, twenty-first century philosophers have the possibility to challenge the often-unquestioned understanding of written discourse as the only context in which philosophical thought can emerge and be developed. (shrink)

The classical rule of Repetition says that if you take any sentence as a premise, and repeat it as a conclusion, you have a valid argument. It's a very basic rule of logic, and many other rules depend on the guarantee that repeating a sentence, or really, any expression, guarantees sameness of referent, or semantic value. However, Repetition fails for token-reflexive expressions. In this paper, I offer three ways that one might replace Repetition, and still keep an interesting notion (...) of validity. Each is a fine way to go for certain purposes, but I argue that one in particular is to be preferred by the semanticist who thinks that there are token-reflexive expressions in natural languages. (shrink)

In this book, the authors systematically define the new notion of linguistic graphs associated with a linguistic set of a linguistic variable. We can also define the notion of directed linguistic graphs and linguistic-weighted graphs. Chapter two discusses all types of linguistic graphs, linguistic dyads, linguistic triads, linguistic wheels, complete linguistic graphs, linguistic connected graphs, disconnected linguistic graphs, linguistic components of the graphs and so on. Further, we define the notion of linguistic subgraphs of a linguistic graph. However, like (...) usual graphs, we will not be able to arbitrarily connect any two linguistic words of a linguistic set associated with a linguistic variable. They can be related or adjacent depending on the linguistic variable associated with the linguistic set. This is an exceptional feature of a linguistic graph. (shrink)

Many results have been obtained on isolated graphs and complete graphs. In this paper, a necessary and sufficient condition will be proved for a single valued neutrosophic graph to be an isolated single valued neutrosophic graph.

We argue that C. Darwin and more recently W. Hennig worked at times under the simplifying assumption of an eternal biosphere. So motivated, we explicitly consider the consequences which follow mathematically from this assumption, and the infinite graphs it leads to. This assumption admits certain clusters of organisms which have some ideal theoretical properties of species, shining some light onto the species problem. We prove a dualization of a law of T.A. Knight and C. Darwin, and sketch a decomposition result (...) involving the internodons of D. Kornet, J. Metz and H. Schellinx. A further goal of this paper is to respond to B. Sturmfels’ question, “Can biology lead to new theorems?”. (shrink)

From the Editor’s Introduction: "The Internal Limitations of Human Understanding." We carry, unavoidably, the limits of our understanding with us. We are perpetually confined within the horizons of our conceptual structure. When this structure grows or expands, the breadth of our comprehensions enlarges, but we are forever barred from the wished-for glimpse beyond its boundaries, no matter how hard we try, no matter how much credence we invest in the substance of our learning and mist of speculation. -/- The limitations (...) in view here are not due to the mere finitude of our understanding of ourselves and of the world in which we live. They are limitations that come automatically and necessarily with any form of understanding. They are, as we shall see, part and parcel of any organization or ordering of data that we call information. -/- The consequences of these limitations are varied: As a result of them, hermeneutics cannot help but be hermetic; scientific theories of necessity are circumscribed by the boundaries of the ideas that define them; formal systems must choose between consistency and comprehensiveness; philosophical study, because it includes itself within its own proper subject matter, is forced to be reflexive in its self-enclosure. The fundamental dynamic shared by all forms of understanding testifies to an internal limitative keystone. (shrink)

Can you find an xy-equation that, when graphed, writes itself on the plane? This idea became internet-famous when a Wikipedia article on Tupper’s self-referential formula went viral in 2012. Under scrutiny, the question has two flaws: it is meaningless (it depends on typography) and it is trivial (for reasons we will explain). We fix these flaws by formalizing the problem, and we give a very general solution using techniques from computability theory.

Metaphysical graphical structuralism is the view that at some fundamental level the world is a mathematical graph of nodes and edges. Randall Dipert has advanced a graphical structuralist theory of fundamental particulars and Alexander Bird has advanced a graphical structuralist theory of fundamental properties. David Oderberg has posed a powerful challenge to graphical structuralism: that it entails the absurd inexistence of the world or the absurd cessation of all change. In this paper I defend graphical structuralism. A sharper formulation, (...) some theorems about such structures, and careful attention to the interaction of metaphysical and mathematical features, shows that the absurdities depend on assumptions that are not essential to the view and brings to light a surprising fact about the necessary structure of fundamental properties. (shrink)

As the author has previously argued, a statement of form “Y is X” can often be taken as hyperbolic for a notably high degree of likeness between Y and X, or, instead, as hyperbolically stating how important Y is as a part of X. The present article goes further and argues that these types of hyperbole, as well as various others, are just special cases of reflexive hyperbole, a style that appears not previously to have been explored in its (...) own right. The article therefore serves to introduce this style and to unify under it various more specific, disparate-seeming types of hyperbole, revealing their deep similarity. They all rest in a uniform way on a special property that some relationships have, namely of being reflexive in a broadened sense. The relationship of likeness is reflexive in the standard sense that any entity bears the relationship to itself with maximum possible strength. But some other relationships of interest in this article are only reflexive in a broader way that relaxes these universality and maximality requirements to an extent. The article also explains how reflexive hyperbole about likeness is a novel addition to the theory of metaphor, involving a distinctive interpretative process with special effects, and how reflexive hyperbole about part importance is not reducible to whole-for-part metonymy, because the latter does not systematically access sufficiently important parts. In addition, the article briefly considers the defaultness or otherwise of reflexive hyperbolic interpretations. (shrink)

The lattice operations of join and meet were defined for set partitions in the nineteenth century, but no new logical operations on partitions were defined and studied during the twentieth century. Yet there is a simple and natural graph-theoretic method presented here to define any n-ary Boolean operation on partitions. An equivalent closure-theoretic method is also defined. In closing, the question is addressed of why it took so long for all Boolean operations to be defined for partitions.

Once upon a time, coherentism was the dominant response to the regress problem in epistemology, but in recent decades the view has fallen into disrepute: now almost everyone is a foundationalist (with a few infinitists sprinkled here and there). In this paper, I sketch a new way of thinking about coherentism, and show how it avoids many of the problems often thought fatal for the view, including the isolation objection, worries over circularity, and concerns that the concept of coherence is (...) too vague or metaphorical for serious theoretical use. The key to my approach is to take a familiar tool from discussions of the regress problem -- namely, directed graphs depicting the support relations between beliefs -- and to use that tool in a more sophisticated manner than it is standardly employed. (shrink)

Reichenbachian approaches to indexicality contend that indexicals are "token-reflexives": semantic rules associated with any given indexical-type determine the truth-conditional import of properly produced tokens of that type relative to certain relational properties of those tokens. Such a view may be understood as sharing the main tenets of Kaplan's well-known theory regarding content, or truth-conditions, but differs from it regarding the nature of the linguistic meaning of indexicals and also regarding the bearers of truth-conditional import and truth-conditions. Kaplan has criticized these (...) approaches on different counts, the most damaging of which is that they make impossible a "logic of demonstratives". The reason for this is that the token-reflexive approach entails that not two tokens of the same sentential type including indexicals are guaranteed to have the same truth-conditions. In this paper I rebut this and other criticisms of the Reichenbachian approach. Additionally, I point out that Kaplan's original theory of "true demonstratives" is empirically inadequate, and claim that any modification capable of accurately handling the linguistic data would have similar problems to those attributed to the Reichenbachian approach. This is intended to show that the difficulties, no matter how real, are not caused by idiosincracies of the "token-reflexive" view, but by deep facts about indexicality. (shrink)

This article examines contemporary Buddhist defences of the idea that consciousness is reflexively aware or self-aware. Call this the Self-Awareness Thesis. A version of this thesis was historically defended by Dignāga but rejected by Prāsaṅgika Mādhyamika Buddhists. Prāsaṅgikas historically advanced four main arguments against this thesis. In this paper I consider whether some contemporary defence of the Self-Awareness Thesis can withstand these Prāsaṅgika objections. A problem is that contemporary defenders of the Self-Awareness Thesis have subtly different accounts with different assessment (...) criteria. I start by providing a fourfold taxonomy of these different views and then progressively show how each can withstand Prāsaṅgika objections. And I conclude by giving reasons to think that even some Prāsaṅgikas can accept some version of the Self-Awareness Thesis. (shrink)

The term ‘reflexivity’ continues to maintain an interpretive hegemony in discussions on modernity and the Self. As a form of praxis, applications of reflexivity frequently rely upon an acknowledged awareness of one’s self-conscious attitudes, dispositions, behaviors and motives. This paper will take aim at such contentions, exploring the extent to which examples of racism rely upon a level of reflexivity, best encapsulated in Žižek’s ‘reflexive racism’. Specifically, it is highlighted how examples of non- racism/anti-racism assert the formal promotion of (...) a monadic subject, solely adept at ‘uncovering’ and ‘relinquishing’ their racism (disavowal); and, an equally unhelpful social constructionism, which depoliticizes racism by relocating and relativizing it to a particular socio-historical context (deferment). In outlining this response, specific attention is given to Lacan’s subject of enunciation and subject of the enunciated, from which it is concluded that it is in the obfuscation of one’s ‘position of enunciation’ that examples of reflexive racism reside. (shrink)

In this paper, we propose a new concept named the uniform single valued neutrosophic graph. An illustrative example and some properties are examined. Next, we develop an algorithmic approach for computing the complement of the single valued neutrosophic graph. A numerical example is demonstrated for computing the complement of single valued neutrosophic graphs and uniform single valued neutrosophic graph.

ABSTRACT: The Reflexive Theory of Perception (RTP) claims that perception of an object or property X by an organism Z consists in Z being caused by X to acquire some disposition D toward X itself. This broadly behavioral perceptual theory explains perceptual intentionality and correct versus incorrect, plus successful versus unsuccessful, perception in a plausible evolutionary framework. The theory also undermines cognitive and perceptual modularity assumptions, including informational or purely epistemic views of perception in that, according to the RTP, (...) any X-caused and X-directed dispositions are genuinely perceptual—including affective, attitudinal, and immediately activated purely action-directed behavioral dispositions. Thus the RTP has the potential to provide the foundations for a broadly behavioral counter-revolution in cognitive science. (shrink)

In this article, following on from earlier debates in the journal regarding the ‘thorny issue’ of epochē and bracketing in sociological phenomenological research, we consider more generally the challenges of engaging in reflexivity and bracketing when undertaking ethnographic ‘insider’ research, or research in familiar settings. We ground our discussion and illustrate some of the key challenges by drawing on the experience of undertaking this research approach with a group of competitive swimmers, who were participating in a British university performance swimming (...) programme at the time of the doctoral study. The primary researcher was highly familiar with the phenomenon of competitive swimming, having been both a competitive swimmer and swimming coach. Some of the key elements of a sociological phenomenological approach to studying physical-cultural embodiment are first delineated, before addressing the considerable challenges of engaging in sustained reflexivity and bracketing, using the swimming research for illustrative purposes. We suggest some practical ways in which researchers in sport and physical cultures might approach epochē and bracketing in ethnographic ‘insider’ research. -/- KEYWORDS: Sociological phenomenology, competitive swimming, insider research, epochē/bracketing. (shrink)

Our aim is to provide a sequent calculus whose external consequence relation coincides with the three-valued paracomplete logic `of nonsense' introduced by Dmitry Bochvar and, independently, presented as the weak Kleene logic K3W by Stephen C. Kleene. The main features of this calculus are (i) that it is non-reflexive, i.e., Identity is not included as an explicit rule (although a restricted form of it with premises is derivable); (ii) that it includes rules where no variable-inclusion conditions are attached; and (...) (iii) that it is hybrid, insofar as it includes both left and right operational introduction as well as elimination rules. (shrink)

Synonymy, at its most basic, is sameness of meaning. A token-reflexive expression is an expression whose meaning assigns a referent to its tokens by relating each particular token of that particular expression to its referent. In doing so, the formulation of its meaning mentions the particular expression whose meaning it is. This seems to entail that no two token-reflexive expressions are synonymous, which would constitute a strong objection against token-reflexive semantics. In this paper, I propose and defend (...) a notion of synonymy for token-reflexive expressions that allows such expressions to be synonymous, while being a fairly conservative extension of the customary notion of synonymy. (shrink)

The field of machine perception is based on standard informational and computational approaches to perception. But naturalistic informational theories are widely regarded as being inadequate, while purely syntactic computational approaches give no account of perceptual content. Thus there is a significant need for a novel, purely naturalistic perceptual theory not based on informational or computational concepts, which could provide a new paradigm for mechanistic perception. Now specifically evolutionary naturalistic approaches to perception have been—perhaps surprisingly—almost completely neglected for this purpose. Arguably (...) perceptual mechanisms enhance evolutionary fitness by facilitating sensorily mediated causal interactions between an organism Z and items X in its environment. A ‘reflexive’ theory of perception of this kind is outlined, according to which an organism Z perceives an item X just in case X causes a sensory organ zi of Z to cause Z to acquire a disposition toward the very same item X that caused the perception. The rest of the paper shows how an intuitively plausible account of mechanistic perception can be developed and defended in terms of the reflexive theory. Also, a compatibilist option is provided for those who wish to preserve a distinct informational concept of perception. (shrink)

This essay offers a unified philosophical account of observer effects in social science. When agents are aware their behavior is subject to scientific inquiry they often act in ways that render measurements of them unreliable. This is the problem of reflexive measurement. In order to develop this novel account, I provide a general characterization of reflexivity which encompasses the full scope of scientific practice: theorizing, prediction, measurement, etc. The characterization captures the insights of contemporary philosophers of science working on (...) reflexive prediction alongside observations by scientists grappling with observer-type effects in the course of their research. (shrink)

A consideration of the relationship between conscious self-aware systems and art. I introduce my art practice and demonstrate the connections language has to self-conscious reflexivity. The document of research can be considered part of a creative practice that also uses language as a material. The specialist use and subversive manipulation of information in science and art as practiced in the service of culture are discussed to show how this informed the creation of Access Restricted-Operational Reasons as a response to my (...) environment. (shrink)

Charles Peirce's diagrammatic logic — the Existential Graphs — is presented as a tool for illuminating how we know necessity, in answer to Benacerraf's famous challenge that most ‘semantics for mathematics’ do not ‘fit an acceptable epistemology’. It is suggested that necessary reasoning is in essence a recognition that a certain structure has the particular structure that it has. This means that, contra Hume and his contemporary heirs, necessity is observable. One just needs to pay attention, not merely to individual (...) things but to how those things are related in larger structures, certain aspects of which relations force certain other aspects to be a certain way. (shrink)

Cognitive scientists claim to have discovered a large number of cognitive biases, which have a tendency to mislead reasoners. Might cognitive scientists themselves be subject to the very biases they purport to discover? And how should this alter the way they evaluate their research as evidence for the existence of these biases? In this paper, we posit a new paradox (the ‘Self-Reflexive Bias Paradox’), which bears a striking resemblance to some classical logical paradoxes. Suppose that research R appears to (...) be good evidence for the existence of bias B, but if B exists, then R would have been subject to B. Thus, it seems sensible for the researcher to reject R as good evidence for the existence of B. However, rejecting R for this reason admits the existence of B. We examine four putative cognitive biases and criticisms of them, each of which seem to be subject to self-reflexivity. In two cases, we argue, paradox is avoidable. In the remaining two, we cannot find a way to avoid the paradox, which poses a practical obstacle to scientific inquiry and results in an intriguing theoretical quandary. (shrink)

Causal theories of perception typically have problems in explaining deviant causal chains. They also have difficulty with other unusual putative cases of perception involving prosthetic aids, defective perception, scientifically extended cases of perception, and so on. But I show how a more adequate reflexive causal theory, in which objects or properties X cause a perceiver to acquire X-related dispositions toward that very same item X, can provide a plausible and principled perceptual explanation of all of these kinds of cases. (...) A critical discussion of David Lewis's perceptual descriptivist views is also provided, including a defense of the logical possibility of systematic misperception or perceptual error for a perceiver, in spite of its empirical improbability. (shrink)

From my ongoing "Metalogical Plato" project. The aim of the diagram is to make reasonably intuitive how the Socratic elenchos (the logic of refutation applied to candidate formulations of virtues or ruling knowledges) looks and works as a whole structure. This is my starting point in the project, in part because of its great familiarity and arguable claim to being the inauguration of western philosophy; getting this point less wrong would have broad and deep consequences, including for philosophy’s self-understanding. -/- (...) (i.) is the first pass at elenchos in which the Socratic interlocutor does not reflect on knowledge being the crux of the problem. (ii.) is the second, rarer, reflective pass in which they are, making the investigation explicitly about knowledge. Its centrality in the Charmides makes that neglected dialogue of superlative importance. This structure is also the gateway through which the discussion/dialectic crosses into the Agathology (discussion of the form of the good) at Republic 505. -/- The problem of elenchos, then, grasped as a whole structure, is that it seems that knowledge can neither satisfactorily be included in nor excluded from its own scope. The development of the ti esti (“what is ---?”) question leads to the introduction of knowledge into its own scope (i. implicitly, as goodness contrasted with blind rule-following ii. explicitly qua knowledge) while the development of the dual peri tinos (“----about what?) question leads to K’s elimination from its own scope. The introductions are motivated to avoid contradiction, but produce regress; the eliminations are motivated to avoid regress, but produce contradiction. In scholarship, and in the history of philosophy, the ti esti question is universally recognized, to the point of being identified with philosophy’s origin and essence; the peri tinos question is neglected textually and never recognized as the equal dual to the ti esti. This, I claim, has blocked the development of a nontrivial logical appreciation of what Plato's Socrates is up to. (One rather disastrous effect of this neglect is taking Aristotle as the beginning of the development of logic, rather than, correctly, for the beginning of logic’s fatal separation from mathematics and dialectic.) -/- Further, because of this monopticism of the ti esti, the function of consistency in the elenchos has not been understood, even with respect to the ti esti. The ti esti is actually in search of completeness, given a norm of consistency; the peri tinos is in search of consistency, given a norm of completeness. Only appreciating the two questions as dual allows space in the structure to clarify these different orientations relative to consistency. (And, dually, to completeness, whose function in the elenchos is generally entirely missed by scholars and relegated to discussions of eros; it's not out of place there, of course, but its significance is secured here.) Recognizing the duality of the ti esti and peri tinos questions is thus the royal road, in the Socratic-Platonic context, to catching sight of what we post-Cantorians can recognize as the metalogical duality of consistency and completeness. (The salutary disruptive effects of this Plato-Cantor proximity have, of course, been traced in complementary ways by Badiou.) -/- Note that the diagram is supposed to provide a relatively accessible orientation, not to stand on its own, and certainly not to be the last word on any subject. An important qualification (telegraphed in the previous paragraph) is that what elenchos shows is not finally circular or paradoxical, though the problem first presents as such (stubbornly, obdurately, as "difficult" Plato's Socrates always says with characteristic understatement). What is depicted here is meant, at a first pass, to be the shape of that first presentation, the form of the problem of elenchos, rather than of its solution. It's not an accident that this problem strongly resembles "Russell's paradox" (not Russell's not a paradox.) Problem is to solution as RP is to the diagonal theorems. (shrink)

This paper will investigate the basic question of the nature of perception, as theoretically approached from a purely naturalistic standpoint. An adequate theory must not only have clear application to a world full of pre-existing biological examples of perception of all kinds, from unicellular perception to conscious human perception, but it must also satisfy a series of theoretical or philosophical constraints, as enumerated and discussed in Section 1 below. A perceptual theory invoking _reflexive dispositions_--that is, dispositions directed toward the very (...) same worldly perceived objects or properties that caused them--will be defended as one legitimate such naturalistic theory. (shrink)

The Introduction to the collection of papers, _Reflexivity: A Source-book in Self-reference_. The Introduction studies the limits of our understanding that we carry unavoidably with us. We are perpetually confined within the horizons of our conceptual structure. When this structure grows or expands, the breadth of our comprehensions enlarges, but we are forever barred from the wished-for glimpse beyond its boundaries, no matter how hard we try, no matter how much credence we invest in the substance of our learning and (...) mist of speculation. (shrink)

The ability to engage in reflexive thought—in thought about thought or about other mental states more generally—is regarded as a complex intellectual achievement that is beyond the capacities of most nonhuman animals. To the extent that reflexive thought capacities are believed necessary for the possession of many other psychological states or capacities, including consciousness, belief, emotion, and empathy, the inability of animals to engage in reflexive thought calls into question their other psychological abilities. This chapter attacks the (...) idea that reflexive thought is required in this pervasive way and holds that supposing that it is derives from a tendency among philosophers and scientists toward overcomplication. Against this tendency, it recommends an aponoian framework, from apó, “away from” and noûs, “intelligence” or “thought,” arguing that seemingly complex psychological abilities are often not as complex as they seem, and do not require the ability to engage in reflexive thought. (shrink)

Plotinus argues that materialism cannot explain reflexive cognition. He argues that mere bodies cannot engage in the self-reflexive activity of both cognizing some content and being cognitively aware of cognizing this content. Short of outright denying the cognitive unity underlying this phenomenon of self-awareness, materialism is in trouble. However, Plotinus bases his argument on the condition that material bodies are capable of a spatial unity at most, and while this condition has purchase on ancient materialists, it would be (...) rejected today. After considering objections based on our contemporary understanding of a material body, I amend Plotinus' argument to focus instead on the core materialist commitment to external efficient-causal relations. This amended argument regains its urgency for materialism, while retaining the spirit of Plotinus' view. (shrink)

This paper reconstructs Sartre’s account of the “circuit of ipseity” as an integral theory of the experiential, agentive and normative aspects of self-consciousness. At the core of this theory is a conception of human (self-)consciousness as lacking, and the correlation between lacking and ideal. In Section 1, I show how this theory manages to satisfy the apparently incompatible requirements generated by the idea of a pre-reflective cogito. Section 2 discusses practical self-consciousness, in particular the agent’s consciousness of herself as self-determined (...) in the projection and pursuit of ends, and how this is accounted for in Sartre’s theory by the correlation of lack and ideal. Section 3 first clarifies the Sartrean conception of the ideal by comparing it with Korsgaard’s, and then reconstructs Sartre’s account of practical normativity by showing how it can be read as emerging from a critical engagement with Heidegger. (shrink)

We recall and improve our 2019 and 2020 concepts of n-SuperHyperGraph, Plithogenic nSuperHyperGraph, n-Power Set of a Set, and we present some application from the real world. The nSuperHyperGraph is the most general form of graph today and it is able to describe the complex reality we live in, by using n-SuperVertices (groups of groups of groups etc.) and nSuperHyperEdges (edges connecting groups of groups of groups etc.).

This paper develops a version of the self-refutation argument against relativism in the teeth of the prevailing response by relativists: that this argument begs the question against them. It is maintained that although weaker varieties of relativism are not self-refuting, strong varieties are faced by this argument with a choice between making themselves absolute (one thing is absolutely true - relativism); or reflexive (relativism is 'true for' the relativist). These positions are in direct conflict. The commonest response, Reflexive (...) Relativism, is shown to be vulnerable to an iterated version of the self-refutation argument. As a result, Reflexive Relativism possesses only the appearance of content, being either incoherent, or a regressively disguised version of Absolute Relativism. Concluding remarks on Absolute Relativism acknowledge this to be a bare, formal possibility, but claim that in fact it must represent one of a range of weaker varieties of relativism that alone remain tenable. (shrink)

Drawing on what we know about priming effects, informational encapsulation, lucid dreaming, imaginative practice, and the “mirror box” illusion, this article argues that self-reflexive fictions may enhance our capacity for simultaneous belief and disbelief, a capacity of surprising importance for human flourishing.

In graph theory, the concept of domination is essential in a variety of domains. It has broad applications in diverse fields such as coding theory, computer net work models, and school bus routing and facility lo cation problems. If a fuzzy graph fails to obtain acceptable results, neutrosophic sets and neutrosophic graphs can be used to model uncertainty correlated with indeterminate and inconsistent information in arbitrary real-world scenario. In this study, we consider the concept of domination as it (...) relates to single-valued neutrosophic incidence graphs (SVNIGs). Given the importance of domination and its utilization in numerous fields, we propose the application of dominating sets in SVNIG with valid edges. We present some relevant definitions such as those of valid edges, cardinality, and isolated vertices in SVNIG along with some examples. Furthermore, we also show a few significant sets connected to the dominating set in an SVNIG such as independent and irredundant sets. We also investigate a relationship between the concepts of dominating sets and domination numbers as well as irredundant and independence sets in SVNIGs. Finally, a real-life deployment of domination in SVNIGsis investigated in relation to COVID-19 vaccination locations as a practical application. (shrink)

Evaluativism (Carruthers 2018) and reflexive imperativism (Barlassina and Hayward 2019) agree that valence—the (un)pleasantness of experiences—is a natural kind shared across all affective states. But they disagree about what valence is. For evaluativism, an experience is pleasant/unpleasant in virtue of representing its worldly object as good/bad; for reflexive imperativism, an experience is pleasant/unpleasant in virtue of commanding its subject to get more/less of itself. I argue that reflexive imperativism is superior to evaluativism according to Carruthers’s own standards. (...) He maintains that a theory of valence should account for its phenomenology and role in imagination-based decision-making. I show that it is reflexive imperativism, rather than evaluativism, that fits this explanatory bill. (shrink)

The rule account of self-conscious thought holds that a thought is self-conscious if and only if it contains a token of a concept-type that is governed by a reflexive rule. An account along these lines was discussed in the late 70s. Nevertheless, very few philosophers endorse it nowadays. I shall argue that this summary dismissal is partly unjustified. There is one version of the rule account that can explain a key epistemic property of self-conscious thoughts: Guarantee. Along the way, (...) I will rebut a number of objections and introduce two constraints on how the reflexive rule is implemented. (shrink)

If I am aware that p, say, that it is raining, is it the case that I must be aware that I am aware that p? Does introspective or object-awareness entail the apprehension of mental states as being of some kind or another: self-monitoring or intentional? That is, are cognitive events implicitly self-aware or is “self-awareness” just another term for metacognition? Not surprisingly, intuitions on the matter vary widely. This paper proposes a novel solution to this classical debate by reframing (...) the problem of self-knowledge in terms of the relation between phenomenal concepts and phenomenal knowledge. Concepts of consciousness such as “introspective awareness” and “reflexive self-awareness” are grounded in phenomenal experiences rather than physical events and processes. As such they yield a different kind of self-knowledge than what can be gained by applying externalist conceptual schemas to understanding the mind. I argue that Dharmakīrti’s theory of content can be seen as endorsing the efficacy of phenomenal experience as a vehicle for self-knowledge. (shrink)

We provide here irrefutable facts that prove the falsehood of the claims published in [1] by Dehmer and Mowshowitz (DM) against our paper published in [2]. We first prove that Dehmer’s definition of node probability [3] is flawed. In addition, we show that it was not Dehmer in [3] who proposed this definition for the first time. We continue by proving how the use of Dehmer’s definition does not reveal all the physico-mathematical richness of the walk entropy of graphs. Finally, (...) we show a few facts about the failure of DM themselves to cite properly the relevant literature in their field. We also show here how the Editors of Complexity have failed to manage the publication of [1] in an appropriate way according to the accepted guidelines given in the Code of Conduct and Best Practice Guidelines for Journal Editors, published by the Committee on Publication Ethics (COPE). (shrink)

Some have argued that a subject has an inner awareness of its conscious mental states by virtue of the non-introspective, reflexive awareness that any conscious state has of itself. But, what exactly is it like to have a ubiquitous and reflexive inner awareness of one’s conscious states, as distinct from one’s outer awareness of the apparent world? This essay derives a model of ubiquitous inner awareness (UIA) from Sebastian Watzl’s recent theory of attention as the activity of structuring (...) consciousness into an experiential center and periphery. I develop Watzl’s theory into an account of UIA by suggesting that a subject is acquainted with its own conscious mental states through being reflexively aware of how these states are structured by attention into a unified subjective perspective. I favorably compare this Watzl-inspired account of UIA against other contemporary analytic and classical Buddhist accounts of reflexive awareness and subjective character, which variously ground the inner awareness of conscious states on their intrinsic phenomenal quality of “for-me-ness,” their affective/hedonic valence, or a subject’s disposition to introspect them. The Watzl-inspired account also accommodates possible counter-examples to Watzl’s theory posed by states of minimal phenomenal experience such as lucid dreamless sleep and non-dual meditative awareness. (shrink)