At the beginning of the 20th century, Gestalt psychologists put forward the concept of psychoneural isomorphism, which was meant to replace Fechner’s obscure notion of psychophysical parallelism and provide a heuristics that may facilitate the search for the neural correlates of the mind. However, the concept has generated much confusion in the debate, and today its role is still unclear. In this contribution, I will attempt a little conceptual spadework in clarifying the concept of psychoneural isomorphism, focusing exclusively (...) on conscious visual perceptual experience and its neural correlates. Firstly, I will outline the history of our concept, and its alleged metaphysical and epistemic roles. Then, I will clarify the nature of isomorphism and rule out its metaphysical role. Finally, I will review some epistemic roles of our concept, zooming in on the work of Jean Petitot, and suggest that it does not play a relevant heuristic role. I conclude suggesting that psychoneural isomorphism might be an indicator of robustness for certain mathematical descriptions of perceptual content. (shrink)

An isomorphism is built between the separable complex Hilbert space (quantum mechanics) and Minkowski space (special relativity) by meditation of quantum information (i.e. qubit by qubit). That isomorphism can be interpreted physically as the invariance between a reference frame within a system and its unambiguous counterpart out of the system. The same idea can be applied to Poincaré’s conjecture (proved by G. Perelman) hinting another way for proving it, more concise and meaningful physically. Mathematically, the isomorphism means (...) the invariance to choice, the axiom of choice, well-ordering, and well-ordering “theorem” (or “principle”) and can be defined generally as “information invariance”. (shrink)

We compare the medieval projects of commentaries and disputations with the modern projects of formal ontology and of mathematics.

The Gestalt principle of isomorphism reveals the primacy of subjective experience as a valid source of evidence for the information encoded neurophysiologically. This theory invalidates the abstractionist view that the neurophysiological representation can be of lower dimensionality than the percept to which it gives rise.

In RG forum, one senior professor of physics posted a project called: “Future science and technology.” As a response, one of us (VC) wrote in reply: “I think one of future science's tasks is to discover the link between entanglement and classical electromagnetic theory. This is to fulfill Einstein's position that present QM theory is incomplete, a new one must be found. We are on a way to that goal.” Therefore, in this paper we will discuss how entanglement can be (...) explained in terms of Maxwell-Dirac isomorphism. This short review may be considered as Einstein’s dream of completing QM in a classical picture. (shrink)

This paper reviews some major episodes in the history of the spatial isomorphism problem of dynamical systems theory. In particular, by analysing, both systematically and in historical context, a hitherto unpublished letter written in 1941 by John von Neumann to Stanislaw Ulam, this paper clarifies von Neumann's contribution to discovering the relationship between spatial isomorphism and spectral isomorphism. The main message of the paper is that von Neumann's argument described in his letter to Ulam is the very (...) first proof that spatial isomorphism and spectral isomorphism are not equivalent because spectral isomorphism is weaker than spatial isomorphism: von Neumann shows that spectrally isomorphic ergodic dynamical systems with mixed spectra need not be spatially isomorphic. (shrink)

The problem of the formal connection between electrodynamics and wave mechanics has attracted the attention of a number of authors, especially there are some existing proofs on Maxwell-Dirac isomorphism. Here the author will review two derivations of Maxwell-Dirac isomorphism i.e. by Hans Sallhofer and Volodimir Simulik. A few plausible extensions will be discussed too.

In this article I examine two mathematical definitions of observational equivalence, one proposed by Charlotte Werndl and based on manifest isomorphism, and the other based on Ornstein and Weiss’s ε-congruence. I argue, for two related reasons, that neither can function as a purely mathematical definition of observational equivalence. First, each definition permits of counterexamples; second, overcoming these counterexamples will introduce non-mathematical premises about the systems in question. Accordingly, the prospects for a broadly applicable and purely mathematical definition of observational (...) equivalence are unpromising. Despite this critique, I suggest that Werndl’s proposals are valuable because they clarify the distinction between provable and unprovable elements in arguments for observational equivalence. (shrink)

Many philosophers and psychologists have attempted to elucidate the nature of mental representation by appealing to notions like isomorphism or abstract structural resemblance. The ‘structural representations’ that these theorists champion are said to count as representations by virtue of functioning as internal models of distal systems. In his 2007 book, Representation Reconsidered, William Ramsey endorses the structural conception of mental representation, but uses it to develop a novel argument against representationalism, the widespread view that cognition essentially involves the manipulation (...) of mental representations. Ramsey argues that although theories within the ‘classical’ tradition of cognitive science once posited structural representations, these theories are being superseded by newer theories, within the tradition of connectionism and cognitive neuroscience, which rarely if ever appeal to structural representations. Instead, these theories seem to be explaining cognition by invoking so-called ‘receptor representations’, which, Ramsey claims, aren’t genuine representations at all—despite being called representations, these mechanisms function more as triggers or causal relays than as genuine stand-ins for distal systems. I argue that when the notions of structural and receptor representation are properly explicated, there turns out to be no distinction between them. There only appears to be a distinction between receptor and structural representations because the latter are tacitly conflated with the ‘mental models’ ostensibly involved in offline cognitive processes such as episodic memory and mental imagery. While structural representations might count as genuine representations, they aren’t distinctively mental representations, for they can be found in all sorts of non-intentional systems such as plants. Thus to explain the kinds of offline cognitive capacities that have motivated talk of mental models, we must develop richer conceptions of mental representation than those provided by the notions of structural and receptor representation. (shrink)

Despite its enormous practical success, many physicists and philosophers alike agree that the quantum theory is full of contradictions and paradoxes which are difficult to solve consistently. Even after 90 years, the experts themselves still do not all agree what to make of it. The area of disagreement centers primarily around the problem of describing observations. Formally, the so-called quantum measurement problem can be defined as follows: the result of a measurement is a superposition of vectors, each representing the quantity (...) being observed as having one of its possible values. The question that has to be answered is: how this superposition can be reconciled with the fact that in practice we only observe one value. How is the measuring instrument prodded into making up its mind which value it has observed? Among some alternatives to resolve the above QM measurement problem, a very counterintuitive one was suggested by Hugh Everett in his 1955 Princeton dissertation, which was subsequently called the Many-Worlds Interpretation of QM (MWI). In this paper we will not discuss all possible scenarios to solve the measurement problem, but we will only shortly discuss Everett’s MWI, because it has led to heated debates on possibility of multiverses, beyond the Universe we live in. We also discuss two alternatives against MWI proposal: (a) the so-called scale symmetry theory, (b) the Maxwell-Dirac isomorphism. In last section, we also discuss shortly MWI hypothesis from philosophical perspective. (shrink)

It is known, despite special theory of relativity has been widely accepted, in our recent draft submitted to this journal it is shown that some experiments have been carried out suggesting superluminal wave propagation, which make Minkowski lightcone not valid anymore. Therefore, it seems worth to reconsider the connection between elastic wave and electromagnetic wave equations, as in their early development. In this paper we will start with Maxwell-Dirac isomorphism, then we will find its connection with elastic wave equations.

Expressions are synonymous if they have the same semantic content. Complex expressions are synonymously isomorphic in Alonzo Church’s sense if one is obtainable from the other by a sequence of alphabetic changes of bound variables or replacements of component expressions by syntactically simple synonyms. Synonymous isomorphism provides a very strict criterion for synonymy of sentences. Several eminent philosophers of language hold that synonymous isomorphism is not strict enough. These philosophers hold that ‘Greeks prefer Greeks’ and ‘Greeks prefer Hellenes’ (...) express different propositions even if they are synonymously isomorphic. They hold that the very recurrence (multiple occurrence) of ‘Greeks’ contributes to the proposition expressed something that indicates the very recurrence in question. Kit Fine argues that this thesis, which he labels semantic relationism calls for a radically new conception of semantics. I have argued that the relevant phenomenon is wholly pragmatic, entirely non-semantic. Here I supplement the case with a new argument. No cognition without recognition—or almost none. With this observation, standard Millianism has sufficient resources to confront Frege’s puzzle and related problems without injecting pragmatic phenomena where they do not belong. (shrink)

We approach the topic of solution equivalence of propositional problems from the perspective of non-constructive procedural theory of problems based on Transparent Intensional Logic (TIL). The answer we put forward is that two solutions are equivalent if and only if they have equivalent solution concepts. Solution concepts can be understood as a generalization of the notion of proof objects from the Curry-Howard isomorphism.

This chapter challenges the common claim that vicious forms of argumentative practice, like interpersonal arrogance and discursive polarisation, are caused by martial metaphors, such as ARGUMENT AS WAR. I argue that the problem isn’t the metaphor, but our wider practices of metaphorising and the ways they are deformed by invidious cultural biases and prejudices. Drawing on feminist argumentation theory, I argue that misogynistic cultures distort practices of metaphorising in two ways. First, they spotlight some associations between the martial and argumentative (...) domains while occluding others, resulting in a sort of myopia. Second, those cultures interfere with a phenomenon I label normative isomorphism – the capacity of some structural metaphors to enable (and often encourage) a transfer of normative chracater traits from the source domain to the target domain. Crucially, the normative status of character trait often changes across domains—traits that are virtuous in the martial domain are often vicious in the argumentative domain, and vice versa. Sexist myopia tends to deform practices of metaphorising by interfering with normative isomorphism by privileging the transfer across domains of traits that recapitulate invidious cultural constructions of masculinity in terms of aggression, domination, and violence. Basically, the problem isn’t the metaphors, but the cultures. (shrink)

Artificial intelligence has historically been conceptualized in anthropomorphic terms. Some algorithms deploy biomimetic designs in a deliberate attempt to effect a sort of digital isomorphism of the human brain. Others leverage more general learning strategies that happen to coincide with popular theories of cognitive science and social epistemology. In this paper, I challenge the anthropomorphic credentials of the neural network algorithm, whose similarities to human cognition I argue are vastly overstated and narrowly construed. I submit that three alternative supervised (...) learning methods—namely lasso penalties, bagging, and boosting—offer subtler, more interesting analogies to human reasoning as both an individual and a social phenomenon. Despite the temptation to fall back on anthropomorphic tropes when discussing AI, however, I conclude that such rhetoric is at best misleading and at worst downright dangerous. The impulse to humanize algorithms is an obstacle to properly conceptualizing the ethical challenges posed by emerging technologies. (shrink)

In his 1935 book Principles of Gestalt Psychology, Kurt Koffka stated that empirical research in perceptual psychology should begin with “a phenomenological analysis,” which in turn would put constraints on the “true theory.” In this paper, I take this statement as a point of departure to investigate in what sense Gestalt psychologists practiced a phenomenological analysis and how they saw it related to theory construction. I will contextualize the perceptual research in Gestalt psychology vis-a-vis Husserlian phenomenology on the one hand (...) and mainstream psychophysics on the other, and I will argue that Gestalt psychologists practiced a form of “frontloading” phenomenology: Instead of requiring experimental subjects to engage in experiential reflections, such reflections were—in a sense—already engrained in the experimental designs used by researchers. This type of phenomenology was decidedly anti-“introspectionist” and as such was compatible with some of Husserl’s basic commitments, while at the same time bearing a surprising resemblance with the methods employed by psychophysicists like E. Boring and S.S. Stevens. This latter point will prompt me to explore what the difference between Gestalt-psychology and psychophysics amounted to. My analysis will reveal some disagreements and misunderstandings, especially with regard to the notions of isomorphism and introspection. (shrink)

An approach to implementing variational Bayesian inference in biological systems is considered, under which the thermodynamic free energy of a system directly encodes its variational free energy. In the case of the brain, this assumption places constraints on the neuronal encoding of generative and recognition densities, in particular requiring a stochastic population code. The resulting relationship between thermodynamic and variational free energies is prefigured in mind–brain identity theses in philosophy and in the Gestalt hypothesis of psychophysical isomorphism.

In this paper, I contest increasingly common "realist" interpretations of Hegel's theory of "the concept" (der Begriff), offering instead a "isomorphic" conception of the relation of concepts and the world. The isomorphism recommended, however, is metaphysically deflationary, for I show how Hegel's conception of conceptual form creates a conceptually internal standard for the adequacy of concepts. No "sideways-on" theory of the concept-world relationship is envisioned. This standard of conceptual adequacy is also "graduated" in that it allows for a lack (...) of fit between concept and world. The possibility for a "maximally isomorphic" fit between concept and world obtains through the teleological realization of concepts, which marks especially the "artificial" world of human culture (law, art, religion, etc.). Some of the most seemingly exaggerated claims Hegel makes about the concept, I contend, can be understood when we consider the significance Hegel ascribes to human making, which is provided for in his conceptual theory. But my framework provides an interpretive key for the way Hegel sees concepts imperfectly realized in the natural world as well. (shrink)

According to the thesis of temporal isomorphism, the experienced order of events in the world and the order in which experiences are processed in the brain are the same. The thesis is encompassed in the brain-time view, a popular view on the literature of the temporal illusions. The view is commonly contrasted with the event-time view, which maintains that the experienced order of events reflects the order in which the events occur in the world. This chapter focuses on the (...) conflict between the two views in the contexts of perceptual asymmetry in visual perception and temporal order judgment tasks. It is argued that both views mean slightly different things in these contexts. Accordingly, it is possible for one to endorse both the brain-time view and the event-time view at the same time. On the broader perspective, the chapter illustrates how time order is employed differently by various perceptual processes, resulting in different characteristics from implicit and explicit time perception. (shrink)

This work addresses a broad range of questions which belong to four fields: computation theory, general philosophy of science, philosophy of cognitive science, and philosophy of mind. Dynamical system theory provides the framework for a unified treatment of these questions. ;The main goal of this dissertation is to propose a new view of the aims and methods of cognitive science--the dynamical approach . According to this view, the object of cognitive science is a particular set of dynamical systems, which I (...) call "cognitive systems". The goal of a cognitive study is to specify a dynamical model of a cognitive system, and then use this model to produce a detailed account of the specific cognitive abilities of that system. The dynamical approach does not limit a-priori the form of the dynamical models which cognitive science may consider. In particular, this approach is compatible with both computational and connectionist modeling, for both computational systems and connectionist networks are special types of dynamical systems. ;To substantiate these methodological claims about cognitive science, I deal first with two questions in two different fields: What is a computational system? What is a dynamical explanation of a deterministic process? ;Intuitively, a computational system is a deterministic system which evolves in discrete time steps, and which can be described in an effective way. In chapter 1, I give a formal definition of this concept which employs the notions of isomorphism between dynamical systems, and of Turing computable function. In chapter 2, I propose a more comprehensive analysis which is based on a natural generalization of the concept of Turing machine. ;The goal of chapter 3 is to develop a theory of the dynamical explanation of a deterministic process. By a "dynamical explanation" I mean the specification of a dynamical model of the system or process which we want to explain. I start from the analysis of a specific type of explanandum--dynamical phenomena--and I then use this analysis to shed light on the general form of a dynamical explanation. Finally, I analyze the structure of those theories which generate explanations of this form, namely dynamical theories. (shrink)

Panmicropsychism is the view that the fundamental physical ingredients of our universe are also its fundamental phenomenal ingredients. Since there is only a limited number of fundamental physical ingredients, panmicropsychism seems to imply that there exists only a small set (palette) of basic phenomenal qualities. How does this limited palette of basic phenomenal qualities give rise to our rich set of experiences? This is known as ‘the palette problem’. One class of solutions to this problem, large-palette solutions, simply denies that (...) the palette is limited. These solutions assume that all types of phenomenal qualities (color, sound, odor, taste, etc., and presumably also types not experienced by humans) were created fully formed at the birth of our universe. On this view, brains evoke conscious experiences by sampling primordial, preexisting phenomenal spaces. My main claim in this paper is that, by analogy with the mathematical description of the fundamental physical ingredients of our universe, which exhibits simplicity, symmetry, and beauty, panmicropsychists should expect the mathematical description of the fundamental phenomenal ingredients of our universe to exhibit similar features. The goal of this paper is to exemplify this claim using what is arguably the simplest of all types of phenomenal qualities—color. Specifically, I utilize phenomenological data on color to construct the maximally symmetric mathematical description of phenomenal color space. I then show that this mathematical description is isomorphic to the mathematical description of two-state quantum systems in a mixed state. Based on this isomorphism, I suggest that color may be the phenomenal dual aspect of two-state quantum systems. (shrink)

A principle, according to which any scientific theory can be mathematized, is investigated. Social science, liberal arts, history, and philosophy are meant first of all. That kind of theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In thus used, the term “theory” includes all hypotheses as yet unconfirmed as already rejected. The investigation of the sketch of a possible proof of the principle demonstrates that it should be accepted rather (...) a metamathematical axiom about the relation of mathematics and reality. The main statement is formulated as follows: Any scientific theory admits isomorphism to some mathematical structure in a way constructive. Its investigation needs philosophical means. Husserl’s phenomenology is what is used, and then the conception of “bracketing reality” is modelled to generalize Peano arithmetic in its relation to set theory in the foundation of mathematics. The obtained model is equivalent to the generalization of Peano arithmetic by means of replacing the axiom of induction with that of transfinite induction. The sketch of the proof is organized in five steps: a generalization of epoché; involving transfinite induction in the transition between Peano arithmetic and set theory; discussing the finiteness of Peano arithmetic; applying transfinite induction to Peano arithmetic; discussing an arithmetical model of reality. Accepting or rejecting the principle, two kinds of mathematics appear differing from each other by its relation to reality. Accepting the principle, mathematics has to include reality within itself in a kind of Pythagoreanism. These two kinds are called in paper correspondingly Hilbert mathematics and Gödel mathematics. The sketch of the proof of the principle demonstrates that the generalization of Peano arithmetic as above can be interpreted as a model of Hilbert mathematics into Gödel mathematics therefore showing that the former is not less consistent than the latter, and the principle is an independent axiom. The present paper follows a pathway grounded on Husserl’s phenomenology and “bracketing reality” to achieve the generalized arithmetic necessary for the principle to be founded in alternative ontology, in which there is no reality external to mathematics: reality is included within mathematics. That latter mathematics is able to self-found itself and can be called Hilbert mathematics in honour of Hilbert’s program for self-founding mathematics on the base of arithmetic. The principle of universal mathematizability is consistent to Hilbert mathematics, but not to Gödel mathematics. Consequently, its validity or rejection would resolve the problem which mathematics refers to our being; and vice versa: the choice between them for different reasons would confirm or refuse the principle as to the being. An information interpretation of Hilbert mathematics is involved. It is a kind of ontology of information. The Schrödinger equation in quantum mechanics is involved to illustrate that ontology. Thus the problem which of the two mathematics is more relevant to our being is discussed again in a new way A few directions for future work can be: a rigorous formal proof of the principle as an independent axiom; the further development of information ontology consistent to both kinds of mathematics, but much more natural for Hilbert mathematics; the development of the information interpretation of quantum mechanics as a mathematical one for information ontology and thus Hilbert mathematics; the description of consciousness in terms of information ontology. (shrink)

This article surveys recent literature by Parsons, McGee, Shapiro and others on the significance of categoricity arguments in the philosophy of mathematics. After discussing whether categoricity arguments are sufficient to secure reference to mathematical structures up to isomorphism, we assess what exactly is achieved by recent ‘internal’ renditions of the famous categoricity arguments for arithmetic and set theory.

This paper accomplishes two goals. First, I elucidate Edmund Husserl’s theory of inauthentic judgments from his 1890 “On the Logic of Signs.” It will be shown how inauthentic judgments are distinct from other signitive experiences, in such a manner that when Husserl seeks to account for them, he is forced to revise the general structure of his philosophy of meaning and in doing so, is also able to realize novel insights concerning the nature of signification. Second, these conclusions are revealed (...) to be the foundation of Husserl’s pure logical grammar, found in the 1901 “Fourth Logical Investigation.” In his analysis of inauthentic judgments, Husserl already recognized, albeit in a problematic way and for entirely different reasons, many of the central tenets of the 1901 work concerning categoremata and syncategoremata, matter and form, and the isomorphism between them. (shrink)

This paper develops a criterion for sameness of Fregean senses. I consider three criteria: logical equivalence, intensional isomorphism, and epistemic equipollence. I reject the first two and argue for a version of the third.

The notion of empathy has been explicated in different ways in the current debate on how to understand others. Whereas defenders of simulation-based approaches claim that empathy involves some kind of isomorphism between the empathizer’s and the target’s mental state, defenders of the phenomenological account vehemently deny this and claim that empathy allows us to directly perceive someone else’s mental states. Although these views are typically presented as being opposed, I argue that at least one version of a simulation-based (...) approach—the account given by de Vignemont and Jacob—is compatible with the direct-perception view. My argument has two parts: My first step is to show that the conflict between these accounts is not—as it seems at first glance—a disagreement on the mechanism by which empathy comes about. Rather, it is due to the fact that their proponents attribute two very different roles to empathy in understanding others. My second step is to introduce Stein’s account of empathy. By not restricting empathy to either one of these two roles, her process model of empathy helps to see how the divergent intuitions that have been brought forward in the current debate could be integrated. (shrink)

This paper explores the defects in fuzzy (hyper) graphs (as complex (hyper) networks) and extends the fuzzy (hyper) graphs to fuzzy (quasi) superhypergraphs as a new concept.We have modeled the fuzzy superhypergraphs as complex superhypernetworks in order to make a relation between labeled objects in the form of details and generalities. Indeed, the structure of fuzzy (quasi) superhypergraphs collects groups of labeled objects and analyzes them in the form of the part to part of objects, the part of objects to (...) the whole group of objects, and the whole to the whole group of objects at the same time. We have investigated the properties of fuzzy (quasi) superhypergraphs based on any positive real number as valued fuzzy (quasi) superhypergraphs, considering the complement of valued fuzzy (quasi) superhypergraphs, the notation of isomorphism of valued fuzzy (quasi) superhypergraphs based on the permutations, and we have presented the isomorphic conditions of (self complemented) valued fuzzy (quasi) superhypergraphs. The concept of impact membership value of fuzzy (quasi) superhypergraphs is introduced in this study and it is applied in designing the real problem in the real world. Finally, the problem of business superhypernetworks is presented as an application of fuzzy valued quasi superhypergraphs in the real world. (shrink)

What is a logical constant? The question is addressed in the tradition of Tarski's definition of logical operations as operations which are invariant under permutation. The paper introduces a general setting in which invariance criteria for logical operations can be compared and argues for invariance under potential isomorphism as the most natural characterization of logical operations.

One particular topic in the literature on Frege’s conception of sense relates to two apparently contradictory theses held by Frege: the isomorphism of thought and language on one hand and the expressibility of a thought by different sentences on the other. I will divide the paper into five sections. In (1) I introduce the problem of the tension in Frege’s thought. In (2) I discuss the main attempts to resolve the conflict between Frege’s two contradictory claims, showing what is (...) wrong with some of them. In (3), I analyze where, in Frege’s writings and discussions on sense identity, one can find grounds for two different conceptions of sense. In (4) I show how the two contradictory theses held by Frege are connected with different concerns, compelling Frege to a constant oscillation in terminology. In (5) I summarize two further reasons that prevented Frege from making the distinction between two conceptions of sense clear: (i) the antipsychologism problem and (ii) the overlap of traditions in German literature contemporary to Frege about the concept of value. I conclude with a hint for a reconstruction of the Fregean notion of ‘thought’ which resolves the contradiction between his two theses. (shrink)

This study explores the interface between conscious and nonconscious mental processes using phenomenological analysis, information processing cognitive psychology, connectionism and traditional aesthetic theories. It attempts to explain how global, evaluative information--especially the primitive feeling of 'rightness' or 'making sense'--is represented in consciousness. ;Many lines of evidence confirm and extend William James' nucleus/fringe model of consciousness: surrounding clear experience in focal attention is a fringe of vague experience. Context information in general, and the feeling of rightness in particular, occupy the fringe. (...) The fringe is vague because it works to finesse consciousness' limited capacity to articulate experience, and the fringe is elusive or 'ungraspable' because it helps to call new information into consciousness. The phenomenology of the fringe is thus a consequence of its cognitive functions. ;Meaningfulness is proposed to be a summary index of cognitive integration, signalling consciousness about the degree of global compatibility or 'fit' between a given content in the focus of attention and its nonconscious context. Though very similar to goodness-of-fit in a connectionist network, Meaningfulness is proposed to play an active feedback role in cognition, while goodness-of-fit, as currently used, is a passive measure of network integration. ;This analysis predicts that an intense feeling of Meaningfulness will have a characteristic 'profile,' and this profile is evident in many accounts of aesthetic experience: a feeling of unity and coherence that cannot be captured adequately in words, but which nevertheless seems to be a source of profound, and often "spiritual," knowledge. ;Many philosophical theories try to explain the unistic, ineffable, noetic, and transcendent aspects of the aesthetic. Platonic and Aristotelian traditions are considered, but the primary focus is on Kant. The Critique of Judgment created modern aesthetics, and in many ways it is remarkably compatible with current cognitive analysis. ;Beyond clarifying the cognitive foundation of aesthetic experience, this study offers new arguments against epiphenomenalism, provides further reason to doubt rule-based accounts of nonconscious processing, explains the isomorphism in aesthetic and mystical phenomenology, and develops a method to investigate consciousness called convergent phenomenology. (shrink)

El objetivo de este artículo es presentar una demostración de un teorema clásico sobre álgebras booleanas y ordenes parciales de relevancia actual en teoría de conjuntos, como por ejemplo, para aplicaciones del método de construcción de modelos llamado “forcing” (con álgebras booleanas completas o con órdenes parciales). El teorema que se prueba es el siguiente: “Todo orden parcial se puede extender a una única álgebra booleana completa (salvo isomorfismo)”. Donde extender significa “sumergir densamente”. Tal demostración se realiza utilizando cortaduras de (...) Dedekind siguiendo el texto “Set Theory” de Jech, y otras ideas propias del autor de este artículo. Adicionalmente, se formulan algunas versiones débiles del axioma de elección relacionadas con las álgebras booleanas, las cuales son también de gran importancia para la investigación en teoría de conjuntos y teoría de modelos, pues estas son poderosas técnicas de construcción de modelos, como por ejemplo, el teorema de compacidad (permite construir modelos no estándar, etc) y el teorema del ultrafiltro, que permite construir ultraproductos (pueden ser usados para investigar problemas de cardinales grandes, etc). Se presentan algunas referencias de problemas abiertos sobre el tema. -/- The objective of this paper is to present a demonstration of a classical theorem on boolean algebras and partial orders of current relevance in set theory, as for example, for applications of model construction method called forcing" (with boolean algebras complete or with partial orders). The theorem to be proved is as follows: Any partial order can be extended to a single complete boolean algebra (up to isomorphism)". Where to extend means embed densely". Such a demonstration is done using Dedekind's cuts following the text Set Theory" of Jech, and other ideas of the author of this article. In addition, some weak versions of the axiom of choice related to boolean algebras are formulated, which are also of great importance for the research in set theory and model theory, since this are powerful model construction techniques, such as the compactness theorem (allows the construction of non-standard models, etc.) and the ultralter theorem, which allows the construction of ultraproducts (can be used to investigate problems of large cardinals, etc). Some references of open problems on the subject are presented. (shrink)

‘Radical enactivism’ (Hutto and Myin 2013, 2017) eschews representational content for all ‘basic’ mental activities. Critics have argued that this view cannot make sense of the workings of the imagination. In their recent book (2017), Hutto and Myin respond to these critics, arguing that some imaginings can be understood without attributing them any representational content. Their response relies on the claim that a system can exploit a structural isomorphism between two things without either of those things being a semantically (...) evaluable representation of the other. I argue that even if this claim is granted, there remains a problem for radically enactive accounts of imagining, namely that the active establishing and maintenance of a structural isomorphism seems to require representational content even if the exploitation of such an isomorphism, when established, does not. (shrink)

● Sergio Cremaschi, The non-existing Island. I discuss the way in which the cleavage between the Continental and the Anglo-American philosophies originated, the (self-)images of both philosophical worlds, the converging rediscoveries from the Seventies, as well as recent ecumenic or anti-ecumenic strategies. I argue that pragmatism provides an important counter-instance to both the familiar self-images and to the fashionable ecumenic or anti-ecumenic strategies. My conclusions are: (i) the only place where Continental philosophy exists (as Euro-Communism one decade ago) is America; (...) (ii) less obviously, also analytic philosophy does not exist, or does no more exist as a current or a paradigm; what does exist is, on the one hand, philosophy of language and, on the other, philosophy of mind, that is, two disciplines; (iii) the dissolution of analytic philosophy as a school has been extremely fruitful, precisely in so far as it has left room for disciplines and research programmes; (iv) what is left, of the Anglo-American/Continental cleavage is primarily differences in styles, depending partly on intellectual traditions, partly owing to sociology, history, institutional frameworks; these differences should not be blurred by rash ecumenism; besides, theoretical differences are alive as ever, but within both camps; finally, there is indeed a lag (not a difference) in the appropriation of intellectual techniques by most schools of 'Continental' philosophy, and this should be overcome through appropriation of what the best 'analytic' philosophers have produced. ● Michael Strauss, Language and sense-perception: an aspect of analytic philosophy. To test an assertion about one fact by comparing it with perceived reality seems quite unproblematic. But the very possibility of such a procedure is incompatible with the intellectualistic basis of logical positivism and atomism (as it is for example to be found in Russell's Analysis of Mind). According to the intellectualistic approach pure sensation is meaningless. Sensation receives its meaning and order from the intellect through interpretation, which is performed with the help of linguistic tools, i.e. words and sentences. Before being interpreted, sensation is not a picture or a representation, it is neither true nor false, neither an illusion nor knowledge; it does not tell us anything; it is a lifeless and order-less matter. But how can a thought (or a proposition) be compared with such a lifeless matter? This difficulty confronts the intellectualist, if on the one hand he admits the necessity of comparing thought with sense-perception, and on the other hand presupposes that we possess only intellectual and no immediate perceptual understanding of what we see and hear. In this paper I give a critical exposition of three attempts, made by Russell, Neurath and Wittgenstein, to solve this problem. The first attempt adheres to strict conventionalism, the second tends to naturalism and the third leads to an amended, very moderate version of conventionalism. This amended conventionalism looks at sense impressions as being a peculiar language, which includes primary symbols, i.e. symbols not founded on convention and not being in need of interpretation. ● Ernst Tugendhat, Phenomenology and language analysis. The paper, first published in German in 1970, by which Tugendhat gave a start to the German rediscovery of analytic philosophy. The author stages a confrontation between phenomenology and language analysis. He argues that language analysis does not differ from phenomenology as far as the topics dealt with are concerned; instead, both currents are quite different in method. The author argues that language-analytic philosophy does not simply lay out of the mainstream of transcendental philosophy, but that instead it challenges this tradition on the very level of foundations. The author criticizes the linguistic-analytic approach centred on the subject as well as any object-centred approach, while proposing inter-subjective understanding through language as the new universal framework. This is, when construed in so general terms, the same program of hermeneutics, though in a more basic version. ● Jürgen Habermas, Language game, intention and meaning. On a few suggestions by Sellars and Wittgenstein. The paper, first published in German in 1975, in which Habermas announces his own linguistic turn through a discovery of speech acts. In this essay the author wants to work out a categorical framework for a communicative theory of society; he takes Wittgenstein's concept of language game as a Leitfade and, besides, he takes advantage also of Wilfried Sellars's quasi-transcendental account of the genesis of intentionality. His goal is to single out the problems connected with a theory of consciousness oriented in a logical-linguistic sense. ● Zvie Bar-On, Isomorphism of speech acts and intentional states. This essay presents the problem of the formal relationship between speech acts and intentional states as an essential part of the perennial philosophical question of the relation between language and thought. I attempt to show how this problem had been dealt with by two prominent philosophers of different camps in our century, Edmund Husserl and John Searle. Both of them wrote extensively about the theory of intentionality. I point out an interesting, as it were unintended, continuity of their work on that theory. Searle started where Husserl left off 80 years earlier. Their meeting point could be used as the first clue in our search. They both adopted in effect the same distinction between two basic aspects of the intentional experience: its content or matter, and its quality or mode. Husserl did not yet have the concept of a speech act as contradistinguished from an intentional state. The working hypothesis, however, which he suggested, could be used as a second clue for the further elaboration of the theory. The relationship of the two levels, the mental and the linguistic, which remained for Husserl in the background only, became the cornerstone of Searle' s inquiry. He employed the speech act as the model and analysed the intentional experience by means of the conceptual apparatus of his own theory of speech acts. This procedure enabled him to mark out a number of parallelisms and correlations between the two levels. This procedure explains the phenomenon of the partial isomorphism of speech acts and intentional states. ● Roberta de Monticelli, Ontology. A dialogue among the linguistic philosopher, the naturalist, and the phenomenological philosopher. This paper proposes a comparison between two main ways of conceiving the role and scope of that fundamental part of philosophy (or of "first" philosophy) which is traditionally called "ontology". One way, originated within the analytic tradition, consists of two main streams, namely philosophy of language and (contemporary) philosophy of mind, the former yielding "reduced ontology" and the latter "neo-Aristotelian ontology". The other way of conceiving ontology is exemplified by "phenomenological ontology" (more precisely, the Husserlian, not the Heideggerian version). Ontology as a theory of reference ("reduced" ontology, or ontology as depending on semantics) is presented and justified on the basis of some classical thesis of traditional philosophy of language (from Frege to Quine). "Reduced ontology" is shown to be identifiable with one level of a traditional, Aristotelian ontology, namely the one which corresponds to one of the four "senses of being" listed in Aristotle's Metaphysics: "being" as "being true". This identification is justified on the basis of Franz Brentano's "rules for translation" of the Aristotelian table of judgements in terms of (positive and negative) existential judgments such as are easily translatable into sentences of first order predicate logic. The second part of the paper is concerned with "neo-Aristotelian ontology", i.e. with naturalism and physicalism as the main ontological options underlying most of contemporary discussion in the philosophy of mind. The qualification of such options as "neo-Aristotelian" is justified; the relationships between "neo-Aristotelian ontology" and "reduced ontology" are discussed. In the third part the fundamental tenet of "phenomenological ontology" is identified by the thesis that a logical theory of existence and being does capture a sense of "existing" and "being" which, even though not the basic one, is grounded in the basic one. An attempt is done of further clarifying this "more basic" sense of "being". An argument making use of this supposedly "more basic" sense is advanced in favour of a "phenomenological ontology". ● Kuno Lorenz, Analytic Roots in Dialogic Constructivism. Both in the Vienna Circle ad in Russell's early philosophy the division of knowledge into two kinds (or two levels), perceptual and conceptual, plays a vital role. Constructivism in philosophy, in trying to provide a pragmatic foundation - a knowing-how - to perceptual as well as conceptual competences, discovered that this is dependent on semiotic tools. Therefore, the "principle of method" had to be amended by the "principle of dialogue". Analytic philosophy being an heir of classical empiricism, conceptually grasping the "given", and constructive philosophy being an heir of classical rationalism, perceptually providing the "constructed", merge into dialogical constructivism, a contemporary development of ideas derived especially from the works of Charles S. Peirce (his pragmatic maxim as a means of giving meaning to signs) and of Ludwig Wittgenstein (his language games as tools of comparison for understanding ways of life). 7. Albrecht Wellmer, "Autonomy of meaning" and "principle of charity" from the viewpoint of the pragmatics of language. In this essay I present an interpretation of the principle of the autonomy of meaning and of the principle of charity, the two main principles of Davidson's semantic view of truth, showing how both principles may fit in a perspective dictated by the pragmatics of language. I argue that (I) the principle of the autonomy of meaning may be thoroughly reformulated in terms of the pragmatics of language, (ii) the principle of charity needs a supplement in terms of pragmatics of language in order to become really enlightening as a principle of interpretation. Besides, I argue that: (i) on the one hand, the fundamental thesis of Habermas on the pragmatic theory of meaning ("we understand a speech act when we know what makes it admissible") is correlated with the seemingly intentionalist thesis according to which we understand a speech act when we know what a speaker means; (ii) on the other hand, to say that the meaning competence of a competent speaker is basically a competence about a potential of reasons (or also of possible justifications) which is inherently connected with the meaning of statements, or with their use in utterances. ● Rüdiger Bubner, The convergence of analytic and hermeneutic philosophy This paper argues that the analytic philosophy does not exist, at least as understood by its original programs. Differences in the analytic camp have always been bigger than they were believed to be. Now these differences are coming to the fore thanks to a process of dissolution of dogmatism. Philosophical analysis is led by its own inner logic towards questions that may be fairly qualified as hermeneutic. Recent developments in analytic philosophy, e.g. Davidson, seem to indicate a growing convergence of themes between philosophical analysis and hermeneutics; thus, the familiar opposition of Anglo-Saxon and Continental philosophy might soon belong to history. The fact of an ongoing appropriation of analytical techniques by present-day German philosophers may provide a basis for a powerful argument for the unity of philosophizing, beyond its strained images privileging one technique of thinking and rejecting the remainder. Actual philosophical practice should take the dialogue between the two camps more seriously; in fact, the processes described so far are no danger to philosophical work. They may be a danger for parochial approaches to philosophizing; indeed, contrary to what happens in the natural sciences, Thomas Kuhn's "normal science" developing within the framework of one fixed paradigm is not typical for philosophical thinking. And in philosophy innovating revolutions are symptoms more of vitality than of crisis. ● Karl-Otto Apel, The impact of analytic philosophy on my intellectual biography. In my paper I try to reconstruct the history of my Auseinandersetzung mit - as I called it - "language-analytical" philosophy (including even Peircean semiotics) since the late Fifties. The heuristics of my study was predetermined by two main motives of my beginnings: the hermeneutic turn of phenomenology and the transformation of "transcendental philosophy" in the light of the "language a priori". Thus, I took issue with the early and the later Wittgenstein, logical positivism, and post-Wittgensteinian and post-empiricist philosophy of science (i.e. G.H. von Wright and the renewal of the "explanation vs understanding controversy" as well as the debate between Th. Kuhn and Popper/Lakatos); besides, with speech act theory and the debate about "transcendental arguments" since Strawson. The "pragmatic turn", started already by C.L. Morris and the later Carnap, led me to study also the relationship between Wittgensteinian "use" theory of meaning and of truth. This resulted on my side in something like a program of "transcendental semiotics", i.e. "transcendental pragmatics" and "transcendental hermeneutics". ● Ben-Ami Scharfstein, A doubt on both their houses: the blindness to non-western philosophies. The burden of my criticism is that contemporary European philosophers of all kinds have continued to think as if there were no true philosophy but that of the West. For the most part, the existentialists have been oblivious of their Eastern congeners; the hermeneuticians have yet to stretch their horizons beyond the most familiar ones; and the analysts remain unaware of the analyses and linguistic sensitivities of the ancient non-European philosophers. Briefly, ignorance still blinds almost all contemporary Western philosophers to the rich, variegated philosophical traditions outside of their familiar orbit. Both Continental and Anglo-Americans have lost the breadth of view that once characterized such thinkers as Herder and the Humboldts. The blindness that has resulted is not simply that of individual Western philosophers but of our whole, still parochial philosophical culture. (shrink)

The objective of this document is to present three introductory notes on set theory: The first note presents an overview of this discipline from its origins to the present, in the second note some considerations are made about the evaluation of reasoning applying the first-order Logic and Löwenheim's theorems, Church Indecidibility, Completeness and Incompleteness of Gödel, it is known that the axiomatic theories of most commonly used sets are written in a specific first-order language, that is, they are developed within (...) the framework of first-order logic, so this note is relevant; and the third note refers to the presence of mathematical platonism in the axioms of ZFC and in the axioms of "complete ordered field", it is known that the last axioms mentioned characterize (except isomorphism) the real number system and are currently used to develop the real Analysis in the context of set theory. It is hoped that this article will be of pedagogical utility for students interested in set theory and in the philosophy of mathematics (that are beginning in the subject). (shrink)

In this paper the class of Fidel-structures for the paraconsistent logic mbC is studied from the point of view of Model Theory and Category Theory. The basic point is that Fidel-structures for mbC (or mbC-structures) can be seen as first-order structures over the signature of Boolean algebras expanded by two binary predicate symbols N (for negation) and O (for the consistency connective) satisfying certain Horn sentences. This perspective allows us to consider notions and results from Model Theory in order to (...) analyze the class of mbC-structures. Thus, substructures, union of chains, direct products, direct limits, congruences and quotient structures can be analyzed under this perspective. In particular, a Birkhoff-like representation theorem for mbC-structures as subdirect poducts in terms of subdirectly irreducible mbC-structures is obtained by adapting a general result for first-order structures due to Caicedo. Moreover, a characterization of all the subdirectly irreducible mbC-structures is also given. An alternative decomposition theorem is obtained by using the notions of weak substructure and weak isomorphism considered by Fidel for Cn-structures. (shrink)

I defend a theory of mental representation that satisfies naturalistic constraints. Briefly, we begin by distinguishing (i) what makes something a representation from (ii) given that a thing is a representation, what determines what it represents. Representations are states of biological organisms, so we should expect a unified theoretical framework for explaining both what it is to be a representation as well as what it is to be a heart or a kidney. I follow Millikan in explaining (i) in terms (...) of teleofunction, explicated in terms of natural selection. -/- To explain (ii), we begin by recognizing that representational states do not have content, that is, they are neither true nor false except insofar as they both “point to” or “refer” to something, as well as “say” something regarding whatever it is they are about. To distinguish veridical from false representations, there must be a way for these separate aspects to come apart; hence, we explain (ii) by providing independent theories of what I call f-reference and f-predication (the ‘f’ simply connotes ‘fundamental’, to distinguish these things from their natural language counterparts). -/- Causal theories of representation typically founder on error, or on what Fodor has called the disjunction problem. Resemblance or isomorphism theories typically founder on what I’ve called the non-uniqueness problem, which is that isomorphisms and resemblance are practically unconstrained and so representational content cannot be uniquely determined. These traditional problems provide the motivation for my theory, the structural preservation theory, as follows. F-reference, like reference, is a specific, asymmetric relation, as is causation. F-predication, like predication, is a non-specific relation, as predicates typically apply to many things, just as many relational systems can be isomorphic to any given relational system. Putting these observations together, a promising strategy is to explain f-reference via causal history and f-predication via something like isomorphism between relational systems. -/- This dissertation should be conceptualized as having three parts. After motivating and characterizing the problem in chapter 1, the first part is the negative project, where I review and critique Dretske’s, Fodor’s, and Millikan’s theories in chapters 2-4. Second, I construct my theory about the nature of representation in chapter 5 and defend it from objections in chapter 6. In chapters 7-8, which constitute the third and final part, I address the question of how representation is implemented in biological systems. In chapter 7 I argue that single-cell intracortical recordings taken from awake Macaque monkeys performing a cognitive task provide empirical evidence for structural preservation theory, and in chapter 8 I use the empirical results to illustrate, clarify, and refine the theory. (shrink)

"Realitas formalis/realitas obiectiva. The Paradox of Descartes’ Representationism" The paper discusses some aspects of the highly original theory of representation, developed by Descartes in his ‘Meditations’, and based on the ontological isomorphism of ideas and their material correlates. In the course of the analysis it is shown that the Cartesian theory involves unavoidable problems with discrimination or correlation of the objects in question, which is connected with the problem of constitutiveness of their modes of existence. Consequently, the conclusion of (...) the paper is that representationism based on the isomorphistic theory of representation turns out to be self-contradictory. (shrink)

This paper accomplishes two goals. First, I elucidate Edmund Husserl’s theory of inauthentic judgments from his 1890 “On the Logic of Signs (Semiotic).” It will be shown how inauthentic judgments are distinct from other signitive experiences, in such a manner that when Husserl seeks to account for them, he is forced to revise the general structure of his philosophy of meaning and in doing so, is also able to realize novel insights concerning the nature of signification. Second, these conclusions are (...) revealed to be the foundation of Husserl’s pure logical grammar, found in the 1901 “Fourth Logical Investigation.” In his analysis of inauthentic judgments, Husserl already recognized, albeit in a problematic way and for entirely different reasons, many of the central tenets of the 1901 work concerning categoremata and syncategoremata, matter and form, and the isomorphism between them. (shrink)

In this Master's dissertation, I try to show that the causal theory of memory, which is the only theory developed so far that at first view seems more plausible and that could be integrated with psychological explanations and investigations of memory, shows some conceptual and ontological problems that go beyond the internal inconsistencies that each version can present. On one hand, the memory phenomenon analyzed is very limited: in general it is reduced to the conscious act of remembering expressed in (...) a propositional format: the idea of an agent who can control his memory reports, in contrast to a passive subject who merely retrieve his encoded memories, is not even considered. Furthermore, the representational function of memory is the only function taken into account; and all the diachronic changes that could entail a dynamic conception of memory are ignored, as is the consideration of context in a broad sense of the term. On the other hand, causal theories make some implicit assumptions that are obviously questionable (e.g., the difference between facts and events) and leave some of their key concepts unexplained, like the nature of the causality, the isomorphism between the memory trace and the memory event, etc. Nonetheless, the principal point that we criticized is the idea of a correspondence between a past event or representation of it, the correspondent memory trace and the memory representation of it. Psychological models of memory, with the exception of the spatial analogy, question some of these assumptions and suggest that memory information is organized in a way other than that implied by the causal theory. But it is distributed connectionism that actually challenges the causal theory of memory, not only through some of its basic postulates, like the superpositional conception of memory traces, their mutual influence and constant state of change, but also because it is compatible with a more situated approach to memory phenomena as well as with the idea that memory in reality accomplishes a variety of functions that go beyond the representational one. The explicit and implicit ideas provided by distributed connectionism, together with the previous criticisms that we made to of causal theory, clearly suggest the possibility of developing another kind of philosophical theory of memory, different from existing theories. This task, nonetheless, implies: (a) A much deeper study of connectionism principles and memory models, as well as of the rival candidate, symbolism, plus the evaluation of these models in the light of psychological and neurophysiological empirical research, which unfortunately I have not dealt with in this work. (b) An analysis of the metaphysical nature of events and facts, in order to see if we should decide in favor of a realist or a non-realist account. It is also clear that this decision can’t be taken without an examination of perception studies (and not exclusively philosophical ones) which would be crucial for determining what is encoded in memory, and studies devoted to language, which, I suspect, plays an important role in the segmentation of reality. (c) A clarification of the notion of causality, because we wouldn’t like to deny any kind entail the complete disappearance of boundaries between memory and imagination. And even if I suspect that my future work will question the existence of absolute boundaries between these two capacities, the notion of causality can’t be completely erase from the theory of memory without erasing the memory phenomenon itself. But this causality, as we’ve already showed, can’t consist in the naïve conception adopted by the causal accounts of memory, nor can it be explained in counterfactual terms. If we think of the reconsolidation concept, of the interdependence between all the memory system, and of the deciding influence of context, it’s almost sure that more than one notion of causality will need to be invoked in order to explain memory. (d) Because I do not want to reduce the study of memory exclusively to cases of remembering, it’s essential to analyze how memory intervenes not only in imagination, but also in perception, reasoning and future projection, for example. In this respect, we could quote the interesting articles of Atance & O’Neill (2001) and Bucker & Carroll (2006), the first concerning the relationship between episodic memory and episodic future thinking, the second concerning the relationship between episodic memory and all kinds of self-projection, such as navigation and theory of mind, relations that would also have to be explored from a philosophical perspective, in particular to overcome the tendency to suppose that representation is the only function of memory. I will also mention the necessity of combining the notion of metamemory with that of memory to some extent; as I have already remarked, it is implausible to suppose that a subject who consciously remembers something is unable to exert any kind of control over his memory reports. (e) Finally, in order to integrate a situated conception of memory into a philosophical account, it will also be indispensable to take into consideration what is known as “everyday memory research” as well as studies in social and collective memory. (shrink)

Neutrosophic theory has many applications in graph theory, bipolar single valued neutrosophic graphs (BSVNGs) is the generalization of fuzzy graphs and intuitionistic fuzzy graphs, SVNGs. In this paper we introduce some types of BSVNGs, such as subdivision BSVNGs, middle BSVNGs, total BSVNGs and bipolar single valued neutrosophic line graphs (BSVNLGs), also investigate the isomorphism, co weak isomorphism and weak isomorphism properties of subdivision BSVNGs, middle BSVNGs, total BSVNGs and BSVNLGs.

In this article, I re-examine Kant’s many senses of cognition, thought, and object in order to better understand his account of logic, and, in particular, transcendental logic. In laying out the multiple and conflicting ways Kant defines each of those terms, the relation between transcendental logic and pure general logic can be revealed as analogous to, and, indeed, linked to, the isomorphism that exists between the categories of the understanding and the logical forms of judgment, which are equivalent if (...) one ignores the manifold of intuition. This means transcendental logic is a general logic, even as a logic of (some) cognizing. (shrink)

Set-theoretic and category-theoretic foundations represent different perspectives on mathematical subject matter. In particular, category-theoretic language focusses on properties that can be determined up to isomorphism within a category, whereas set theory admits of properties determined by the internal structure of the membership relation. Various objections have been raised against this aspect of set theory in the category-theoretic literature. In this article, we advocate a methodological pluralism concerning the two foundational languages, and provide a theory that fruitfully interrelates a `structural' (...) perspective to a set-theoretic one. We present a set-theoretic system that is able to talk about structures more naturally, and argue that it provides an important perspective on plausibly structural properties such as cardinality. We conclude the language of set theory can provide useful information about the notion of mathematical structure. (shrink)

It has often been said that metaphors are based on analogies, but the nature of this relation has never been made precise. This article rigorously and formally specifies two semantic relations that do obtain between some metaphors and analogies. We argue that analogies often provide conditions of meaningfulness and truth for metaphors. An analogy is treated as an isomorphism from a source to topic domain. Metaphors are thought of as surface structures. Formal analogical conditions of meaningfulness and truth are (...) fully and rigorously worked out for several grammatical classes of metaphors. By providing analogical meaningfulness and truth conditions for metaphors, this article shows that truth-conditional semantics can be extended to metaphors. (shrink)

According to the Thomistic tradition, the Principle of Totality (TPoT) articulates a secondary principle of natural law which guides the exercise of human ownership or dominium over creation. In its general signification, TPoT is a principle of distributive justice determining the right ordering of wholes to their parts. In the medical field it is traditionally understood as entailing an absolute prohibition of bodily mutilation as irrational and immoral, and an imperfect obligation to use the parts of one’s body for the (...) perfection of the bodily whole. TPoT is thus a key element of the system of principles within which an individual exercises her right to life: it helps specify the nature, scope and limits of those actions by which an agent permissibly acts in order to preserve her life. While the Thomistic tradition and the Catholic Church have drawn clear conclusions from the principle regarding, e.g., direct sterilization and non-therapeutic experimentation on human subjects, less attention has been given to the implications of TPoT for non-therapeutic procedures that may positively impact biological functioning or supra-biological goals–that is, for human “enhancement.” We will explore the degree to which TPoT non-univocally guides our use of both artifacts and bodies. We will argue that a careful analysis of these distinct kinds of totalities suggests that the application of TPoT to artifacts and bodies is strongly isomorphic, which is what tempts advocates of the Principle of Autonomy to invalidly infer the absolute dominium of the individual over her body. The inference is invalid because this isomorphism also includes a principle of intrinsic value whose function is to resist the instrumentalization of both artifacts and bodies in some contexts; we are not even related to artifacts as advocates of absolute autonomy believe we are, let alone to our bodies. Rather, the limits of human dominium are determined by the nature and finalities, inherent or acquired, of the objects in question, and it will be argued that articulating these limits raises important, understudied, and fascinating questions about the permissibility of various kinds of human enhancement. (shrink)

The claim that we want to put forward is that Thomas Kuhn ’s growth of knowledge concept is drawn upon Heidegger’s epistemology. To bolster the tenet the corresponding works of both thinkers are considered. As a result, the one-to-one correspondence between the key propositions of Heideggerian epistemology and the basic tenets of Kuhn ’s growth of knowledge model is dawned. The tenets under consideration include the holistic nature of a paradigm, the incommensurability thesis, conventional status of a paradigm caused by (...) pragmatist way of its vocabulary justification and even the basic instance – connection between Aristotelean and Newtonian mechanics. It is conjectured that an indirect influence of Heidegger upon Kuhn should be taken into account to explain the isomorphism. For instance, through the works of Alexandre Koyré admired by Kuhn. As is well-known, Koyré had close professional links with another Russian émigré – Alexandre Kojev – who presented in his 1933-1939 Paris lectures Hegel’s “Phenomenology of Spirit” seen through the cognitive lens of Heideggerian phenomenology. Key words: Martin Heidegger, Thomas Kuhn, growth of knowledge, paradigm, incommensurability thesis, holism, pragmatism. (shrink)

Set-theoretic and category-theoretic foundations represent different perspectives on mathematical subject matter. In particular, category-theoretic language focusses on properties that can be determined up to isomorphism within a category, whereas set theory admits of properties determined by the internal structure of the membership relation. Various objections have been raised against this aspect of set theory in the category-theoretic literature. In this article, we advocate a methodological pluralism concerning the two foundational languages, and provide a theory that fruitfully interrelates a ‘structural’ (...) perspective to a set-theoretic one. We present a set-theoretic system that is able to talk about structures more naturally, and argue that it provides an important perspective on plausibly structural properties such as cardinality. We conclude the language of set theory can provide useful information about the notion of mathematical structure. (shrink)

The topics approached in this collection of papers are: neutrosophic sets; neutrosophic logic; generalized neutrosophic set; neutrosophic rough set; multigranulation neutrosophic rough set (MNRS); neutrosophic cubic sets; triangular fuzzy neutrosophic sets (TFNSs); probabilistic single-valued (interval) neutrosophic hesitant fuzzy set; neutro-homomorphism; neutrosophic computation; quantum computation; neutrosophic association rule; data mining; big data; oracle Turing machines; recursive enumerability; oracle computation; interval number; dependent degree; possibility degree; power aggregation operators; multi-criteria group decision-making (MCGDM); expert set; soft sets; LA-semihypergroups; single valued trapezoidal neutrosophic number; (...) inclusion relation; Q-linguistic neutrosophic variable set; vector similarity measure; fundamental neutro-homomorphism theorem; neutro-isomorphism theorem; quasi neutrosophic triplet loop; quasi neutrosophic triplet group; BE-algebra; cloud model; fuzzy measure; clustering algorithm; and many more. (shrink)

In his 1927 Analysis of Matter and elsewhere, Russell argued that we can successfully infer the structure of the external world from that of our explanatory schemes. While nothing guarantees that the intrinsic qualities of experiences are shared by their objects, he held that the relations tying together those relata perforce mirror relations that actually obtain (these being expressible in the formal idiom of the Principia Mathematica). This claim was subsequently criticized by the Cambridge mathematician Max Newman as true but (...) trivial, insofar as from a closed body of observations (or “Ramsey sentence”) one can always generate other equally-satisfactory networks of relations, provided they respect the original set’s cardinality. Since any model thus generated will be empirically adequate, “[t]he defence is therefore driven back from the fairly safe fictitious-real classification to the much less tenable ‘trivial’ and ‘important’” (Newman 1928). Given the definitional rigour afforded by the initial appeal to isomorphism (via one-to-one correspondences in extension), the received assessment, shared by Russell himself, is that retreating to a pragmatic adjudication would betoken a fatal blow. However, I suggest that reliance on “importance” can be avoided if we incorporate an impersonal criterion of diachronic precedence. When collecting observations, an ordinality emerges alongside the cardinality which gives that underived structure an irrevocable epistemological privilege. Hence, I argue that, all other things being equal, any construct parasitic on an antecedent theory ought to be regarded as inferior/dispensable, since it was generated by an algorithm lacking the world-involving pedigree of its host structure. (shrink)

Any philosophy of science ought to have something to say about the nature of mathematics, especially an account like constructive empiricism in which mathematical concepts like model and isomorphism play a central role. This thesis is a contribution to the larger project of formulating a constructive empiricist account of mathematics. The philosophy of mathematics developed is fictionalist, with an anti-realist metaphysics. In the thesis, van Fraassen's constructive empiricism is defended and various accounts of mathematics are considered and rejected. Constructive (...) empiricism cannot be realist about abstract objects; it must reject even the realism advocated by otherwise ontologically restrained and epistemologically empiricist indispensability theorists. Indispensability arguments rely on the kind of inference to the best explanation the rejection of which is definitive of constructive empiricism. On the other hand, formalist and logicist anti-realist positions are also shown to be untenable. It is argued that a constructive empiricist philosophy of mathematics must be fictionalist. Borrowing and developing elements from both Philip Kitcher's constructive naturalism and Kendall Walton's theory of fiction, the account of mathematics advanced treats mathematics as a collection of stories told about an ideal agent and mathematical objects as fictions. The account explains what true portions of mathematics are about and why mathematics is useful, even while it is a story about an ideal agent operating in an ideal world; it connects theory and practice in mathematics with human experience of the phenomenal world. At the same time, the make-believe and game-playing aspects of the theory show how we can make sense of mathematics as fiction, as stories, without either undermining that explanation or being forced to accept abstract mathematical objects into our ontology. All of this occurs within the framework that constructive empiricism itself provides the epistemological limitations it mandates, the semantic view of theories, and an emphasis on the pragmatic dimension of our theories, our explanations, and of our relation to the language we use. (shrink)

This essay examines the philosophical significance of Ω-logic in Zermelo-Fraenkel set theory with choice (ZFC). The dual isomorphism between algebra and coalgebra permits Boolean-valued algebraic models of ZFC to be interpreted as coalgebras. The modal profile of Ω-logical validity can then be countenanced within a coalgebraic logic, and Ω-logical validity can be defined via deterministic automata. I argue that the philosophical significance of the foregoing is two-fold. First, because the epistemic and modal profiles of Ω-logical validity correspond to those (...) of second-order logical consequence, Ω-logical validity is genuinely logical, and thus vindicates a neo-logicist conception of mathematical truth in the set-theoretic multiverse. Second, the foregoing provides a modal-computational account of the interpretation of mathematical vocabulary, adducing in favor of a realist conception of the cumulative hierarchy of sets. (shrink)