Is it possible to construct an alternative framework for the description of physical reality that is not based on space and time? According to Kant, because of the incorrigibility of the spatiotemporal scheme, the contents of any such alternative will be beyond our cognitive grasp. Nonetheless, the possibility of constructing such a descriptive scheme poses itself as an intriguing challenge. In this paper, we attempt to answer this challenge by exploiting an analytical tool extensively used by physicists and engineers: the (...) utilisation of multiple representations of the same data using integral transforms – for example, the Fourier transform. According to the spectral picture we propose, frequencies and wavelengths, related to time and space by the Fourier transform, form an adequate alternative basis for describing physical systems, and one that is of equal richness to the spatiotemporal picture. Furthermore, the routine use of Fourier analysis applied to familiar physical systems suggests ways in which sense organs might be constructed such that they naturally give rise to a spectral representation of the world. Although we might never be able to imagine perceiving the world in this way, we can nonetheless describe the contents of such a mode of perception and relate them precisely to our own world-view. Hence, we suggest in a Kantian spirit, that the spatiotemporal description of the world is not unique. (shrink)

Is it possible to construct an alternative framework for the description of physical reality that is not based on space and time? According to Kant, because of the incorrigibility of the spatiotemporal scheme, the contents of any such alternative will be beyond our cognitive grasp. Nonetheless, the possibility of constructing such a descriptive scheme poses itself as an intriguing challenge. In this paper, we attempt to answer this challenge by exploiting an analytical tool extensively used by physicists and engineers: the (...) utilisation of multiple representations of the same data using integral transforms – for example, the Fourier transform. According to the “spectral” picture we propose, frequencies and wavelengths, related to time and space by the Fourier transform, form an adequate alternative basis for describing physical systems, and one that is of equal richness to the spatiotemporal picture. Furthermore, the routine use of Fourier analysis applied to familiar physical systems suggests ways in which sense organs might be constructed such that they naturally give rise to a spectral representation of the world. Although we might never be able to imagine perceiving the world in this way, we can nonetheless describe the contents of such a mode of perception and relate them precisely to our own world-view. Hence, we suggest in a Kantian spirit, that the spatiotemporal description of the world is not unique. (shrink)

The regional brain networks and the underlying neurophysiological mechanisms subserving the cognition of visual narrative in humans have largely been studied with non-invasive brain recording. In this study, we specifically investigated how regional and cross-regional cortical activities support visual narrative interpretation using intracranial stereotactic electroencephalograms recordings from thirteen human subjects (6 females, and 7 males). Widely distributed recording sites across the brain were sampled while subjects were explicitly instructed to observe images from fables presented in “sequential” order, and a set (...) of images drawn from multiple fables presented in “scrambled” order. Broadband activity mainly within the frontal and temporal lobes were found to encode if a presented image is part of a visual narrative (sequential) or random image set (scrambled). Moreover, the temporal lobe exhibits strong activation in response to visual narratives while the frontal lobe is more engaged when contextually novel stimuli are presented. We also investigated the dynamics of interregional interactions between visual narratives and contextually novel series of images. Interestingly, the interregional connectivity is also altered between sequential and scrambled sequences. Together, these results suggest that both changes in regional neuronal activity and cross-regional interactions subserve visual narrative and contextual novelty processing. (shrink)

Evidence from studies of the processing of topographic and classifier constructions in sign language sentences provides a model of how a mental scene description can be represented linguistically, but it also raises questions about how this can be related to spatial linguistic descriptions in spoken languages and their processing. This in turn provides insights into models of the evolution of language.

The paper argues that cognitive states of biological systems are inherently temporal. Three adequacy conditions for neuronal models of representation are vindicated: the compositionality of meaning, the compositionality of content, and the co-variation with content. Classicist and connectionist approaches are discussed and rejected. Based on recent neurobiological data, oscillatory networks are introduced as a third alternative. A mathematical description in a Hilbert space framework is developed. The states of this structure can be regarded as conceptual representations satisfying the three (...) conditions. (shrink)

Theories of relations between language and conceptual development benefit from empirical evidence for concepts available in infancy, but such evidence is comparatively scarce. Here, we examine early representations of specific concepts, namely, sets of dynamic events corresponding either to predicates involving two variables with a reversible, asymmetric relation between them (such as the set of all events that correspond to a linguistic phrase like “a dog is pushing a car,”) or to comparatively simpler, one-variable predicates (such as the (...) set of events corresponding to a phrase like “a dog is jumping.”). We develop a non-linguistic, anticipatory eye-tracking task that can be administered to both infants and adults, and we use this task to gather evidence for the formation and use of such one-and two-place-predicate classes (which we refer to as event sortals) in 12–24-mo-old infants, and in adults with and without concurrent verbal prose shadowing. Using visually similar stimuli for both the simpler (one-place) and the more complex (reversible, asymmetric, two-place) concepts, we find that infants only show evidence for forming and generalizing one-place event sortals, and, while adults succeed with both kinds in the absence of verbal shadowing, shadowing hampers their ability to form and use the asymmetric two-place event sortals. In a subsequent experiment with adults, we find that if the shadowing material is grammatically impoverished, adults now succeed in forming and using both one- and two-place event sortals. We discuss implications of these results for theories of concept acquisition, and the role of language in this process. (shrink)

Constructs developed for the semantics of artificial languages are often proposed as the proper description of aspects of the semantics of natural languages. Most of us are familiar with the claims that conjunction, disjunction, negation, and material implication in standard versions of propositional calculus describe the meaning of “and”, “or”, “not”, and “if …, then …” in English. The argument for such claims is not only that these constructs account for meanings in English but that they offer the advantage of (...) well-understood formal apparatus for the explication of meaning in natural language. The argument against such claims is that explications based on this apparatus leave important aspects of the meaning of “and”, “or”, “not”, and “if …, then …” unexplicated. It is charged that the advantage of a well-understood formalism is secured at the expense of truth. Many of the most significant issues in philosophic logic are or depend on questions about whether constructs from artificial languages provide adequate semantic descriptions for natural languages. (shrink)

Post algebras of order + as a semantic foundation for +-valued predicate calculi were examined in [5]. In this paper Post spaces of order + being a modification of Post spaces of order n2 (cf. Traczyk [8], Dwinger [1], Rasiowa [6]) are introduced and Post fields of order + are defined. A representation theorem for Post algebras of order + as Post fields of sets is proved. Moreover necessary and sufficient conditions for the existence of representations preserving a given (...) set of infinite joins and infinite meets are established and applied to Lindenbaum-Tarski algebras of elementary theories based on +-valued predicate calculi in order to obtain a topological characterization of open theories. (shrink)

Neural correlates exist for a basic component of logical formulae, PREDICATE(x). Vision and audition research in primates and humans shows two independent neural pathways; one locates objects in body-centered space, the other attributes properties, such as colour, to objects. In vision these are the dorsal and ventral pathways. In audition, similarly separable “where” and “what” pathways exist. PREDICATE(x) is a schematic representation of the brain's integration of the two processes of delivery by the senses of the location of an (...) arbitrary referent object, mapped in parietal cortex, and analysis of the properties of the referent by perceptual subsystems. The brain computes actions using a few “deictic” variables pointing to objects. Parallels exist between such nonlinguistic variables and linguistic deictic devices. Indexicality and reference have linguistic and nonlinguistic (e.g., visual) versions, sharing the concept of attention. The individual variables of logical formulae are interpreted as corresponding to these mental variables. In computing action, the deictic variables are linked with “semantic” information about the objects, corresponding to logical predicates. Mental scene descriptions are necessary for practical tasks of primates, and preexist language phylogenetically. The type of scene descriptions used by nonhuman primates would be reused for more complex cognitive, ultimately linguistic, purposes. The provision by the brain's sensory/perceptual systems of about four variables for temporary assignment to objects, and the separate processes of perceptual categorization of the objects so identified, constitute a pre-adaptive platform on which an early system for the linguistic description of scenes developed. Key Words: argument; attention; deictic; dorsal; logic; neural; object; predicate; reference; ventral. (shrink)

Despite the fact that human daily emotions are co-occurring by nature, most neuroscience studies have primarily adopted a univariate approach to identify the neural representation of emotion (emotion experience within a single emotion category) without adequate consideration of the co-occurrence of different emotions (emotion experience across different emotion categories simultaneously). To investigate the neural representations of multivariate emotion experience, this study employed the inter-situation representational similarity analysis (RSA) method. Researchers used an EEG dataset of 78 participants who watched 28 (...) video clips and rated their experience on eight emotion categories. The EEG-based electrophysiological representation was extracted as the power spectral density (PSD) feature per channel in the five frequency bands. The inter-situation RSA method revealed significant correlations between the multivariate emotion experience ratings and PSD features in the Alpha and Beta bands, primarily over the frontal and parietal-occipital brain regions. The study found the identified EEG representations to be reliable with sufficient situations and participants. Moreover, through a series of ablation analyses, the inter-situation RSA further demonstrated the stability and specificity of the EEG representations for multivariate emotion experience. These findings highlight the importance of adopting a multivariate perspective for a comprehensive understanding of the neural representation of human emotion experience. (shrink)

The present study investigates the types of verb and symbolic representational strategies used by 10 deaf signing adults and 13 deaf signing children who described in Italian Sign Language 45 video clips representing nine action types generally communicated by five general verbs in spoken Italian. General verbs, in which the same sign was produced to refer to several different physical action types, were rarely used by either group of participants. Both signing children and adults usually produced specific depicting predicates (...) by incorporating, through a representational strategy, the object and/or the modality of the action into the sign. As for the different types of representational strategies, the adults used the hand-as-object strategy more frequently than the children, who, in turn, preferred to use the hand-as-hand strategy, suggesting that different degrees of cognitive complexity are involved in these two symbolic strategies. Addressing the symbolic iconic strategies underlying sign formation could provide new insight into the perceptual and cognitive processes of linguistic meaning construction. The findings reported here support two main assumptions of cognitive linguistics applied to sign languages: there is a strong continuity between gestures and language; lexical units and depicting constructions derive from the same iconic core mechanism of sign creation. (shrink)

The description of named entities in terminological knowledge bases has never been addressed in any depth in terminology. Firm preconceptions, rooted in philosophy, about the only referential function of proper names have presumably led to disparage their inclusion in terminology resources, despite the relevance of named entities having been highlighted by prominent figures in the discipline of terminology. Scholars from different branches of linguistics depart from the conservative stance on proper names and have foregrounded the need for a novel approach, (...) more linguistic than philosophical, to describing proper names. Therefore, this paper proposed a linguistic and terminological approach to the study of named entities when used in scientific discourse, with the purpose of representing them in EcoLexicon, an environmental knowledge base designed according to the premises of Frame-based Terminology. We focused more specifically on named rivers mentioned in a coastal engineering corpus. Inclusion of named entities in terminological knowledge bases requires analyzing the context that surrounds them in specialized texts because these contexts convey specialized knowledge about named entities. For the semantic representation of context, this paper thus analyzed the local syntactic and semantic contexts that surrounded potamonyms in coastal engineering texts and described the semantic annotation of the predicate-argument structure of sentences where a potamonym was mentioned. The semantic variables annotated were the following: semantic category of the arguments; semantic role of the arguments; semantic relation between the arguments; and lexical domain of the verbs. This method yielded valuable insight into the different semantic roles that named rivers played, the entities and processes that participated in the events educed by potamonyms through verbs, and how they all interacted. Furthermore, since arguments are specialized terms and verbs are relational constructs, the analysis of argument structure led to the construction of semantic networks that depicted specialized knowledge about named rivers. These conceptual networks were then used to craft the thematic description of potamonyms. Accordingly, the semantic network and the thematic description not only constituted the representation of a potamonym in EcoLexicon, but also allowed the geographic contextualization of specialized concepts in the terminological resource. (shrink)

This study investigates the online narratives Hong Kong employers construct around foreign domestic helpers and aims to compensate for the existing gap in discursive research and mainstream media, which tend to focus on the perspective of FDHs. It examines how employers portrayed FDHs both positively and negatively, as well as how they represented themselves in online environments. Critical discourse analysis was used to analyse more than 2000 Facebook posts on the subject of FDHs, identifying discursive strategies used in constructing both (...) power dynamics and identities. The findings revealed that nomination strategies dominated the discourse, constructing both the in- and out-group identities of FDHs. Other strategies, such as predication and augmentation, showed how employers portrayed themselves as opportunity-givers and food critics, which further contributed to the inferior self-perception of FDHs. The study concludes that employers have developed a sense of ideological ambivalence, in which they perceived FDHs as motherly figures while simultaneously maintaining their superior status. (shrink)

We continue work of our earlier paper :219–241, 2009) where abstract logics and particularly intuitionistic abstract logics are studied.logics can be topologized in a direct and natural way. This facilitates a topological study of classes of concrete logics whenever they are given in abstract form. Moreover, such a direct topological approach avoids the often complex algebraic and lattice-theoretic machinery usually applied to represent logics. Motivated by that point of view, we define in this paper the category of intuitionistic abstract logics (...) with stable logic maps as morphisms, and the category of implicative spectral spaces with spectral maps as morphisms. We show the equivalence of these categories and conclude that the larger categories of distributive abstract logics and distributive sober spaces are equivalent, too. (shrink)

Starting from an abstract setting for the Lüders-von Neumann quantum measurement process and its interpretation as a probability conditionalization rule in a non-Boolean event structure, the author derived a certain generalization of operator algebras in a preceding paper. This is an order-unit space with some specific properties. It becomes a Jordan operator algebra under a certain set of additional conditions, but does not own a multiplication operation in the most general case. A major objective of the present paper is the (...) search for such examples of the structure mentioned above that do not stem from Jordan operator algebras; first natural candidates are matrix algebras over the octonions and other nonassociative rings. Therefore, the case when a nonassociative commutative multiplication exists is studied without assuming that it satisfies the Jordan condition. The characteristics of the resulting algebra are analyzed. This includes the uniqueness of the spectral resolution as well as a criterion for its existence, subalgebras that are Jordan algebras, associative subalgebras, and more different levels of compatibility than occurring in standard quantum mechanics. However, the paper cannot provide the desired example, but contribute to the search by the identification of some typical differences between the potential examples and the Jordan operator algebras and by negative results concerning some first natural candidates. The possibility that no such example exists cannot be ruled out. However, this would result in an unexpected new characterization of Jordan operator algebras, which would have a significant impact on quantum axiomatics since some customary axioms (e.g., power-associativity or the sum postulate for observables) might turn out to be redundant then. (shrink)

In the context of Hurford's claim that “some feature of language structure maps onto a feature of primitive mental representations,” I will argue that Hurford's focus on 1-place predicates as the basis of the “mental representations of situations in the world” is problematic, particularly with respect to spatiotemporal events. A solution is proposed.

A sentence like every circle is blue might be understood in terms of individuals and their properties or in terms of a relation between groups. Relatedly, theorists can specify the contents of universally quantified sentences in first-order or second-order terms. We offer new evidence that this logical first-order vs. second-order distinction corresponds to a psychologically robust individual vs. group distinction that has behavioral repercussions. Participants were shown displays of dots and asked to evaluate sentences with each, every, or all combined (...) with a predicate. We find that participants are better at estimating how many things the predicate applied to after evaluating sentences in which universal quantification is indicated with every or all, as opposed to each. We argue that every and all are understood in second-order terms that encourage group representation, while each is understood in first-order terms that encourage individual representation. Since the sentences that participants evaluate are truth-conditionally equivalent, our results also bear on questions concerning how meanings are related to truth-conditions. (shrink)

I argue that maps do not feature predication, as analyzed by Frege and Tarski. I take as my foil (Casati and Varzi, Parts and places, 1999), which attributes predication to maps. I argue that the details of Casati and Varzi’s own semantics militate against this attribution. Casati and Varzi emphasize what I call the Absence Intuition: if a marker representing some property (such as mountainous terrain) appears on a map, then absence of that marker from a map coordinate signifies absence (...) of the corresponding property from the corresponding location. Predication elicits nothing like the Absence Intuition. “F(a)” does not, in general, signify that objects other than a lack property F. On the basis of this asymmetry, I argue that attaching a marker to map coordinates is a different mode of semantic composition than attaching a predicate to a singular term. (shrink)

In this paper I argue that noun complement modality cannot be treated as dependent on the meanings of lexical embedding predicates or of abstract performatives. Using two types of complement modalities, I show that their meanings and restrictions remain distinct and invariable regardless of the meanings of their embedding predicates. Then, using embedding predicates that can take both types of modalities, I show that the embedding predicates retain their meanings, regardless of the different modalities of their (...) complements, and they can undergo deletions requiring their identity. (shrink)

Human agents draw a variety of inferences effortlessly, spontaneously, and with remarkable efficiency – as though these inferences were a reflexive response of their cognitive apparatus. Furthermore, these inferences are drawn with reference to a large body of background knowledge. This remarkable human ability seems paradoxical given the complexity of reasoning reported by researchers in artificial intelligence. It also poses a challenge for cognitive science and computational neuroscience: How can a system of simple and slow neuronlike elements represent a large (...) body of systemic knowledge and perform a range of inferences with such speed? We describe a computational model that takes a step toward addressing the cognitive science challenge and resolving the artificial intelligence paradox. We show how a connectionist network can encode millions of facts and rules involving n-ary predicates and variables and perform a class of inferences in a few hundred milliseconds. Efficient reasoning requires the rapid representation and propagation of dynamic bindings. Our model (which we refer to as SHRUTI) achieves this by representing (1) dynamic bindings as the synchronous firing of appropriate nodes, (2) rules as interconnection patterns that direct the propagation of rhythmic activity, and (3) long-term facts as temporal pattern-matching subnetworks. The model is consistent with recent neurophysiological evidence that synchronous activity occurs in the brain and may play a representational role in neural information processing. The model also makes specific psychologically significant predictions about the nature of reflexive reasoning. It identifies constraints on the form of rules that may participate in such reasoning and relates the capacity of the working memory underlying reflexive reasoning to biological parameters such as the lowest frequency at which nodes can sustain synchronous oscillations and the coarseness of synchronization. (shrink)

In order to represent legal knowledge adequately, it is vital to create a formal device that can freely construct an individual concept directly from a predicate expression. For this purpose, a Compound Predicate Formula (CPF) is formulated for use in legal expert systems. In this paper, we willattempt to explain the nature of CPFs by rigorous logical foundation, i.e., establishing their syntax and semantics precisely through the use of appropriate examples. We note the advantages of our system over other such (...) systems and discuss the significance of CPFs with regard to the formalization of legal reasonings using examples from the United Nations Convention for the International Sale of Goods. (shrink)

We give an extension of the Jónsson‐Tarski representation theorem for both normal and non‐normal modal algebras so that it preserves countably many infinite meets and joins. In order to extend the Jónsson‐Tarski representation to non‐normal modal algebras we consider neighborhood frames instead of Kripke frames just as Došen's duality theorem for modal algebras, and to deal with infinite meets and joins, we make use of Q‐filters, which were introduced by Rasiowa and Sikorski, instead of prime filters. By means (...) of the extended representation theorem, we show that every predicate modal logic, whether it is normal or non‐normal, has a model defined on a neighborhood frame with constant domains, and we give a completeness theorem for some predicate modal logics with respect to classes of neighborhood frames with constant domains. Similarly, we show a model existence theorem and a completeness theorem for infinitary modal logics which allow conjunctions of countably many formulas. (shrink)

Providing more human-like concept learning in machines has always been one of the most significant goals of machine learning paradigms and of human-machine interaction techniques. This article attempts to provide a logical specification of conceptual mappings from humans’ minds into machines’ knowledge bases. We will focus on the representation of the mappings (transformations) relying on First-Order Predicate Logic. Additionally, the structure of concepts in the common ground between humans and machines will be analysed. It seems quite necessary to pay (...) attention to the philosophy of constructivism and constructivist models of knowing. This research constructs a conceptual ground for expressing and analysing concepts in the common ground between humanistic and informatics sciences and in the context of human-machine interplays. (shrink)

The results of Cubitt et al. on the spectral gap problem add a new chapter to the issue of undecidability in physics, as they show that it is impossible to decide whether the Hamiltonian of a quantum many-body system is gapped or gapless. This implies, amongst other things, that a reductionist viewpoint would be untenable. In this paper, we examine their proof and a few philosophical implications, in particular ones regarding models and limitative results. In more detail, we examine (...) the way these theorems model many-body quantum systems, and we question what, if anything, is the physical counterpart of the models used by Cubitt et al. We argue that these models are non-representational and that, even if they are so artificial that it is hard to imagine a physical system arising from them, they nonetheless offer an opportunity to learn about the world and the relation between mathematics and reality. On this basis, we draw the conclusion that their results do not undermine the reductionist viewpoint in a strong sense but leave the question open in a weak sense. (shrink)

The threads of linguistic philosophy in Being and Time oppose the prevailing tendency to understand language philosophically within the confines of representational epistemology. In elaborating on the ontological aspects of the view of human beings as inhabiting a linguistically articulated world, the paper stresses the peculiar status of the “fore-structure of understanding” in the discursive articulation as an existential phenomenon of being-in-the-world.

Marx's call for a materialism capable of engaging reality as ‘sensuous human activity’ opens a question about the role of representation in relation to data. Images have increasingly been seen as significant forms of data in the history of education. Derrida's theory of the spectre—a variation on the positions established in his earlier works on the trace, the supplement and differance—offers a way of rethinking visual images, their relations with existing discourses of knowledge and with positioned subjects who makes (...) sense. Two early twentieth-century photographs are explored here in relation to ideas derived from Derrida as an exercise in the philosophy of representation. (shrink)

Recently, there’s been a lot of interest in a research program that tries to understand propositional representation in terms of the subject’s performance of sub-propositional mental acts like reference and predication (e. g. Burge 2010, Hanks 2015, Soames 2010, 2015). For example, on one version of the view, for a subject to predicate the property of being a composer of Arvo just is what it is to perform the to the basic propositional act of judging that Arvo is a (...) composer (e. g. Hanks 2015). In this paper I first present my own version of this view and contrast it with alternatives. I then argue that we must clearly separate the thin predication-resultant notion of judging (S(emantic)-judgment) from a much richer notion used in epistemology (E(pistemic)-judgment). The former is just the act of thinking a forceful thought. The latter is the act of making up one’s mind about how things are, a way of concluding theoretical or doxastic deliberation. I argue that these two acts differ in three ways: levels of propositional attitude, objective vs. subjective norms, and the possibility of sub-personal occurrence. (shrink)

We show that Bohr's principle of complementarity between position and momentum descriptions can be formulated rigorously as a claim about the existence of representations of the canonical commutation relations. In particular, in any representation where the position operator has eigenstates, there is no momentum operator, and vice versa. Equivalently, if there are nonzero projections corresponding to sharp position values, all spectral projections of the momentum operator map onto the zero element.

Monoidal t-norm based logic $\mathbf {MTL}$ is the weakest t-norm based residuated fuzzy logic, which is a $[0,1]$ -valued propositional logical system having a t-norm and its residuum as truth function for conjunction and implication. Monadic fuzzy predicate logic $\mathbf {mMTL\forall }$ that consists of the formulas with unary predicates and just one object variable, is the monadic fragment of fuzzy predicate logic $\mathbf {MTL\forall }$, which is indeed the predicate version of monoidal t-norm based logic $\mathbf {MTL}$. The (...) main aim of this paper is to give an algebraic proof of the completeness theorem for monadic fuzzy predicate logic $\mathbf {mMTL\forall }$ and some of its axiomatic extensions. Firstly, we survey the axiomatic system of monadic algebras for t-norm based residuated fuzzy logic and amend some of them, thus showing that the relationships for these monadic algebras completely inherit those for corresponding algebras. Subsequently, using the equivalence between monadic fuzzy predicate logic $\mathbf {mMTL\forall }$ and S5-like fuzzy modal logic $\mathbf {S5(MTL)}$, we prove that the variety of monadic MTL-algebras is actually the equivalent algebraic semantics of the logic $\mathbf {mMTL\forall }$, giving an algebraic proof of the completeness theorem for this logic via functional monadic MTL-algebras. Finally, we further obtain the completeness theorem of some axiomatic extensions for the logic $\mathbf {mMTL\forall }$, and thus give a major application, namely, proving the strong completeness theorem for monadic fuzzy predicate logic based on involutive monoidal t-norm logic $\mathbf {mIMTL\forall }$ via functional representation of finitely subdirectly irreducible monadic IMTL-algebras. (shrink)

The aim of this paper is to present a strongly complete first order functional predicate calculus generalized to models containing not only ordinary classical total functions but also arbitrary partial functions. The completeness proof follows Henkin’s approach, but instead of using maximally consistent sets, we define saturated deductively closed consistent sets . This provides not only a completeness theorem but a representation theorem: any SDCCS defines a canonical model which determine a unique partial value for every predicate symbol and (...) any function symbol. Any SDCCS can thus be interpreted as an epistemic state. (shrink)

Kripke completeness of some infinitary predicate modal logics is presented. More precisely, we prove that if a normal modal logic above is -persistent and universal, the infinitary and predicate extension of with BF and BF is Kripke complete, where BF and BF denote the formulas pi pi and x x, respectively. The results include the completeness of extensions of standard modal logics such as , and its extensions by the schemata T, B, 4, 5, D, and their combinations. The proof (...) is obtained by extending the correspondence between the representation of modal algebras and the completeness of propositional modal logic to infinite. (shrink)

In §93 of The Principles of Mathematics, Bertrand Russell observes that “the variable is a very complicated logical entity, by no means easy to analyze correctly”. This assessment is borne out by the fact that even now we have no fully satisfactory understanding of the role of variables in a compositional semantics for first-order logic. In standard Tarskian semantics, variables are treated as meaning-bearing entities; moreover, they serve as the basic building blocks of all meanings, which are constructed out of (...) variable assignments. But this has disquieting consequences, including Fine’s antinomy of the variable and an undue dependence of meanings on language. Here I develop an alternative, Fregean version of predicate logic that uses the traditional quantifier–variable apparatus for the expression of generality, possesses a fully compositional, non-representational semantics, and is not subject to the antinomy of the variable. The advantages of Fregean over Tarskian predicate logic are due to the former’s treating variables not as meaningful lexical items, but as mere marks of punctuation, similar to parentheses. I submit that this is indeed how the variables of predicate logic should be construed. (shrink)

El artículo intenta establecer las configuraciones que asume el humanismo crítico en la escritura de Aimé Césaire en la encrucijada de la diferencia colonial, entendida desde una perspectiva decolonial, y a partir de una noción de espectralidad que deriva y se diferencia de las perspectivas derrideanas. Así entonces, se destaca el hecho de que la escritura de Césaire produce una fuerte impugnación de los procesos de la representación colonial y abre el campo de la experiencia política y cultural signada por (...) la heterogeneidad. The article tries to establish the settings that the critical humanism assumes in Aimé Césaire´s writing at the crossroads of the colonial difference, which is understood from a decolonial perspective, and from a notion of spectrality which derives and differs from the Derridean perspective. So then, the article remarks the fact that Césaire´s writing produces a strong challenge to the processes of colonial representation and it opens the field of political and cultural experience marked by heterogeneity. (shrink)

Why is a red face not really red? How do we decide that this book is a textbook or not? Conceptual spaces provide the medium on which these computations are performed, but an additional operation is needed: Contrast. By contrasting a reddish face with a prototypical face, one gets a prototypical ‘red’. By contrasting this book with a prototypical textbook, the lack of exercises may pop out. Dynamic contrasting is an essential operation for converting perceptions into predicates. The existence (...) of dynamic contrasting may contribute to explaining why lexical meanings correspond to convex regions of conceptual spaces. But it also explains why predication is most of the time opportunistic, depending on context. While off-line conceptual similarity is a holistic operation, the contrast operation provides a context-dependent distance that creates ephemeral predicative judgments that are essential for interfacing conceptual spaces with natural language and with reasoning. (shrink)

In this dissertation, I provide the logical foundation for a solution to the mind-body problem, a solution which is directly based upon Wilfrid Sellars' analogical theory of thought and sensation. Chapters I-IV are devoted to an interpretation, analysis, and constructive criticism of Sellars' notions of the inner thought episode and the sensing state. My analysis is offered in support of three general contentions: I argue that the postulation of inner thought episodes and sensing states is necessary for adequate explanations of (...) agent behavior; I hope to show how the analogical theory of inner thought episodes and sensing states actually generates a legitimate problem concerning the relationship between the mental and the physical; and I demonstrate the importance of the notion of analogy in philosophical theory construction. I suggest that the role of analogy provides the key for the solution to the mind-body problem. ;Chapter One is essentially introductory in nature. I offer an interpretation and reconstruction of Sellars' illustrative story entitled "The Jonesean Myth" . The "Myth" provides a suitable representation of Sellars' overall philosophy of mind. But perhaps more importantly, the "Myth" is a paradigm example of what I shall call the analogical method of inquiry, a method employed for the introduction of the notions of inner thought episodes and sensing states. In brief, I want to show how the "Myth" provides the logical basis for a theory adequate for explanations of the mental activity of agents. ;Chapters II and III are closely related. In Chapter II, I present a theory of linguistic representation which will serve as the analogical base for the introduction and characterization of the inner thought episode. In Chapter III, I develop the notion of the inner thought episode , and I examine its nature and status as a theoretical construct. Chapters II and III are thus related by the Sellarsian thesis that the concept of mental representation is to be understood in terms which apply, primarily, to characterizations of the features of the linguistic framework presented in Chapter II. ;In Chapter IV, I argue, again following Sellars' lead, that the explication of the notion of the perceptual thought episode requires the introduction of a second distinct sort of inner episode, namely, that of the sense experience or sensing state. The argument offered in Chapter IV is designed to show that sensing states are theoretical constructs, the reference to which is essential for explanations concerning the occurrence and nature of perceptual representations. Sensing states are introduced and characterized by an analogical extension of families of predicates which are suitable for the identification and description of ordinary physical objects . ;In Chapter V, I propose a solution to the mind-body problem, as the latter is generated by the analysis given to the thought episode and the sensing state . In general terms, I argue that any purported solution to the mind-body problem must provide an explanatory basis for agent behavior, and it is for this reason that I reject "reductionistic" theories of mind of the kind represented by logical behaviorism, type-identity physicalism, and Turing Machine functionalism. My solution, instead, involves a commitment to what I shall call token physicalism, a thesis which is contingent upon the development of a theory of neurophysiology which is rich enough to capture, in an analogical sense, both the intentional features of the thought episode, and the occurrent-like qualities which are exemplified by the sensing state. (shrink)