I am going to attempt to argue, given certain premises, there are reasons, not only empirical, but also logical, for expecting a certain division of labor in the processing of information by the human brain. This division of labor consists specifically of a functional bifurcation into what may be called, to a first approximation, "verbal" and "nonverbal" modes of information- processing. That this dichotomy is not quite satisfactory, however, will be one of the principal conclusions of this chapter, for I (...) shall attempt to show that metaphor, which in its most common guise is a literary, and hence a fortiori a "verbal" phenomenon, may in fact be more a function of the "nonverbal" than the "verbal" mode. (For alternative attempts to account for cognitive lateralization, see e.g. Bever, 1975; Wickelgren, 1975; Pendse, 1978.). (shrink)
The relationship between self-consciousness, Aristotelian ontology, and Cartesian duality is far closer than it has been thought to be. There is no valid inference either from considerations of Aristotle's hylomorphism or from the phenomenological distinction between body and living body, to the undermining of Cartesian dualism. Descartes' conception of the self as both a reasoning and willing being informs his conception of personhood; a person for Descartes is an unanalysable, integrated, self-conscious and autonomous human being. The claims that Descartes (...) introspectively encounters the self and that the Cartesian extent of inner space is self-contained are profound errors, distortions through the lenses of modern theories. (shrink)
This paper explores relationships between many-valued logic and fuzzy topology from the viewpoint of duality theory. We first show a fuzzy topological duality for the algebras of Łukasiewicz n -valued logic with truth constants, which generalizes Stone duality for Boolean algebras to the n -valued case via fuzzy topology. Then, based on this duality, we show a fuzzy topological duality for the algebras of modal Łukasiewicz n -valued logic with truth constants, which generalizes Jónsson-Tarski (...) class='Hi'>duality for modal algebras to the n -valued case via fuzzy topology. We emphasize that fuzzy topological spaces naturally arise as spectrums of algebras of many-valued logics. (shrink)
Some of the basic terminology of Yogācāra philosophy needs reevaluation. Whereas commentaries almost universally gloss the term dvaya ('duality') with some version of the phrase grāhya grāhaka ca (lit. 'grasped and grasper', but usually translated as 'subject and object'), in fact this gloss is absent from the earliest strata. The term and its gloss are derived from separate streams of Yogācāra reasoning - one from discussions of linguistic conceptualization and the other from discussions of perception. Once we see that (...) these two are distinct, it becomes clear that the commentarial literature asserts their identity in order to philosophically unify Yogācāra thought. One upshot of this is that even in this later assertion 'duality' refers not to the distinction between internal and external reality (as in 'textbook' Yogācāra), but to the falsely projected distinction between mental subjects and mental objects. (shrink)
From a logical point of view, Stone duality for Boolean algebras relates theories in classical propositional logic and their collections of models. The theories can be seen as presentations of Boolean algebras, and the collections of models can be topologized in such a way that the theory can be recovered from its space of models. The situation can be cast as a formal duality relating two categories of syntax and semantics, mediated by homming into a common dualizing object, (...) in this case 2. In the present work, we generalize the entire arrangement from propositional to first-order logic. Boolean algebras are replaced by.. (shrink)
A key working hypothesis in neuroscience is ‘materialistic reductionism’, i.e., the assumption whereby all physiological, behavioral or cognitive phenomena is produced by localized neurochemical brain activation (but not vice versa). However, analysis of sub-threshold Weber’s psychophysical stimulation indicates its computational irreducibility to the direct interaction between psychophysical stimulation and any neuron/s. This is because the materialistic-reductionistic working hypothesis assumes that the determination of the existence or non-existence of any psychophysical stimulation [s] may only be determined through its direct interaction [di1] (...) with a given neuron/s [N] that together forms the ‘neural registry’ computational level [NR/di1]. But, this implies that in cases of (initial) sub-threshold (sensory-specific) psychophysical stimulation which is increased above the sensory-specific threshold but below Weber’s psychophysical ‘dv’—the psychophysical computational processing [PCP] produces an apparently ‘computationally indeterminate’ output. This is because materialistic reductionism asserts the contingency of PCP upon the existence of a direct interaction between ‘s’ and ‘N’ within the NR/di1 level, but in the special case of Weber’s sub-threshold psychophysical stimulation the same PCP/di1 also asserts the non-existence of ‘s’ (as demanded by Weber’s psychophysical law). However, given robust empirical evidence indicating the capability of PCP to determine whether (or not) ‘s’ exists, we must conclude that PCP may not be carried out from within NR’s direct interaction between a particular psychophysical stimulation and any set of neuron/s in the brain. Hence, the Duality Principle asserts the conceptual irreducibility of sub-threshold psychophysical stimulation to any direct NR/di1: s-N interaction, thereby challenging the current materialistic-reductionistic assumption. (shrink)
This essay touches on a number of topics in philosophy of quantum field theory from the point of view of the LSZ asymptotic approach to scattering theory. First, particle/field duality is seen to be a property of free field theory and not of interacting QFT. Second, it is demonstrated how LSZ side-steps the implicationsof Haag's theorem. Finally, a recent argument due to Redhead (1995), Malament (1996) and Arageorgis (1995) against the concept of localized particle states is addressed. Briefly, the (...) argument observes thatthe Reeh–Schlieder theorem entails that correlations between spacelike separatedvacuum expectation values of local field operators are always present,and this, according to the above authors, dictates against the notion of a localizedparticle state. I claim that this moral is excessive and that a coherentnotion of localized particles is given by the LSZ approach. The underlyingmoral to be drawn from this analysis is that questions concerning theontology of interacting QFT cannot be appropriately addressed if one restrictsoneself to the free theory. (shrink)
We generalize Priestley duality for distributive lattices to a duality for distributive meet-semilattices. On the one hand, our generalized Priestley spaces are easier to work with than Celani’s DS-spaces, and are similar to Hansoul’s Priestley structures. On the other hand, our generalized Priestley morphisms are similar to Celani’s meet-relations and are more general than Hansoul’s morphisms. As a result, our duality extends Hansoul’s duality and is an improvement of Celani’s duality.
This paper defines a category of bounded distributive lattice-ordered grupoids with a left-residual operation that corresponds to a weak system in the family of relevant logics. Algebras corresponding to stronger systems are obtained by adding further postulates. A duality theoey piggy-backed on the Priestley duality theory for distributive lattices is developed for these algebras. The duality theory is then applied in providing characterizations of the dual spaces corresponding to stronger relevant logics.
In this note, we give a representation of distributive Ockham algebras via natural hom-functors. In order to do this, we describe two different structures (one algebraic, and the other order-topological) on the set of subsets of the natural numbers. The topological duality previously obtained by A. Urquhart is used throughout.
In this paper we continue the investigation of monadic Heyting algebras which we started in [2]. Here we present the representation theorem for monadic Heyting algebras and develop the duality theory for them. As a result we obtain an adequate topological semantics for intuitionistic modal logics over MIPC along with a Kripke-type semantics for them. It is also shown the importance and the effectiveness of the duality theory for further investigation of monadic Heyting algebras and logics over MIPC.
Priestley duality can be used to study subalgebras of Heyting algebras and related structures. The dual concept is that of congruence on the dual space and the congruence lattice of a Heyting space is dually isomorphic to the subalgebra lattice of the dual algebra. In this paper we continue our investigation of the congruence lattice of a Heyting space that was undertaken in [10], [8] and [12]. Our main result is a characterization of the modularity of this lattice (Theorem (...) 2.12). Partial results about its complementedness are also given, and among other things a characterization of those finite Heyting algebras with a complemented subalgebra lattice (Theorem 3.5). (shrink)
Part I of this paper is developed in the tradition of Stone-type dualities, where we present a new topological representation for general lattices (influenced by and abstracting over both Goldblatt's [17] and Urquhart's [46]), identifying them as the lattices of stable compact-opens of their dual Stone spaces (stability refering to a closure operator on subsets). The representation is functorial and is extended to a full duality.In part II, we consider lattice-ordered algebras (lattices with additional operators), extending the Jónsson and (...) Tarski representation results [30] for Boolean algebras with Operators. Our work can be seen as developing, and indeed completing, Dunn's project of gaggle theory [13, 14]. We consider general lattices (rather than Boolean algebras), with a broad class of operators, which we dubb normal, and which includes the Jónsson-Tarski additive operators. Representation of l-algebras is extended to full duality. (shrink)
In this paper, we develop a duality for the varieties of a Łukasiewicz n + 1-valued modal System. This duality is an extension of Stone duality for modal algebras. Some logical consequences (such as completeness results, correspondence theory...) are then derived and we propose some ideas for future research.
This paper is a study of duality in the absence of canonicity. Specifically it concerns double quasioperator algebras, a class of distributive lattice expansions in which, coordinatewise, each operation either preserves both join and meet or reverses them. A variety of DQAs need not be canonical, but as has been shown in a companion paper, it is canonical in a generalized sense and an algebraic correspondence theorem is available. For very many varieties, canonicity (as traditionally defined) and correspondence lead (...) on to topological dualities in which the topological and correspondence components are quite separate. It is shown that, for DQAs, generalized canonicity is sufficient to yield, in a uniform way, topological dualities in the same style as those for canonical varieties. However topology and correspondence are no longer separable in the same way. (shrink)
In a recent article in The European Legacy, Mark Cortes Favis argued that the figure of Kierkegaard expressed a tension between two aspects of writing?the Socratic and the Platonic. While Favis is correct to see a duality in Kierkegaard's writing, his article does not fully answer the problem of how we can account for our interpretation of this tension. Given that the duality within Kierkegaard's writing transgresses the boundaries of author and reader, we cannot easily circumscribe any claims (...) on his writing without considering its effect on our reading. Rather, the characteristic duality of his authority manifests itself in a number of ways in the task of identifying the philosophical meaning of his texts. Kierkegaard's relationship to Socrates is thus symptomatic of a number of figural dualities that pervade interpretations of his work. By surveying the ways in which these interpretations draw on the axiom of duality in order to ascribe an authority to Kierkegaard's texts, I suggest Favis's argument that Kierkegaard's writing expresses both Socratic and Platonic aspects should be placed within the wider duality at work in the interpretation of Kierkegaard's work. (shrink)
This paper presents duality results between categories of neighbourhood frames for modal logic and categories of modal algebras (i.e. Boolean algebras with an additional unary operation). These results extend results of Goldblatt and Thomason about categories of relational frames for modal logic.
In order to shed light on the issue of crony corruption in the context of economic transition, I focus on the puzzle of China's unique experience of economic transition characterized by the duality forms and effects of crony corruption underlying local corporatism in a dual-track (i.e., market and political tracks) transition. I argue that the duality of local corporatism derives from the duality of crony corruption. First, the early form of local corporatism as state-business public alliance is (...) embedded in informal crony corruption as positive for the purpose of wealth growth in the initial phase of economic transition with public and private interests aligned as compatible. Second, the later form of local corporatism as official-manager private collusion is embedded in quasi-formal crony corruption as negative for the purpose of wealth transfer in the later phase with public and private interests in conflict as incompatible. The duality of crony corruption in the two phases of economic transition is caused by the interplay between formal and informal factors and between economic and political factors. My contribution is twofold. First, I explain China's transition in terms of crony corruption underlying local corporatism. Second, I develop an integrated framework of crony corruption concerning its content, process, antecedent and consequence. (shrink)
We give a coalgebraic view of the restricted Priestley duality between Heyting algebras and Heyting spaces. More precisely, we show that the category of Heyting spaces is isomorphic to a full subcategory of the category of all -coalgebras, based on Boolean spaces, where is the functor which maps a Boolean space to its hyperspace of nonempty closed subsets. As an appendix, we include a proof of the characterization of Heyting spaces and the morphisms between them.
A. M. Pitts in [Pi] proved that HA op fp is a bi-Heyting category satisfying the Lawrence condition. We show that the embedding $\Phi: HA^\mathrm{op}_\mathrm{fp} \longrightarrow Sh(\mathbf{P_0,J_0})$ into the topos of sheaves, (P 0 is the category of finite rooted posets and open maps, J 0 the canonical topology on P 0 ) given by $H \longmapsto HA(H,\mathscr{D}(-)): \mathbf{P_0} \longrightarrow \text{Set}$ preserves the structure mentioned above, finite coproducts, and subobject classifier, it is also conservative. This whole structure on HA op (...) fp can be derived from that of Sh(P 0 ,J 0 ) via the embedding Φ. We also show that the equivalence relations in HA op fp are not effective in general. On the way to these results we establish a new kind of duality between HA op fp and a category of sheaves equipped with certain structure defined in terms of Ehrenfeucht games. Our methods are model-theoretic and combinatorial as opposed to proof-theoretic as in [Pi]. (shrink)
We develop a Priestley-style duality theory for different classes of algebras having a bilattice reduct. A similar investigation has already been realized by B. Mobasher, D. Pigozzi, G. Slutzki and G. Voutsadakis, but only from an abstract category-theoretic point of view. In the present work we are instead interested in a concrete study of the topological spaces that correspond to bilattices and some related algebras that are obtained through expansions of the algebraic language.
The Priestley duality for Wajsberg algebras is developed. The Wajsberg space is a De Morgan space endowed with a family of functions that are obtained in rather natural way.As a first application of this duality, a theorem about unicity of the structure is given.
A Priestley duality is developed for the variety j of all modal lattices. This is achieved by restricting to j a known Priestley duality for the variety of all bounded distributive lattices with a meet-homomorphism. The variety j was first studied by R. Beazer in 1986.The dual spaces of free modal lattices are constructed, paralleling P.R. Halmos'' construction of the dual spaces of free monadic Boolean algebras and its generalization, by R. Cignoli, to distributive lattices with a quantifier.
The duality theory established by Halmos in [2] for boolean hemimorphism applies of course to the diagonalizable algebra, because ντν is an hemimorphism. For commodity in working on diagonalizable algebras we recall the basic facts and give the characteristic conditions on the dual of ντν.
For a sufficiently large class of formal systems a duality theorem is proved. We consider such formal set theories $\widetilde{\scr{T}}$ [2] which, at least, satisfy the following conditions: 1. The theory $\widetilde{\scr{T}}$ contains its own (either bounded or introduced by a definition) substantive constant U, for which $\vdash \forall x[x\in U]$ or $\vdash \forall x[x\subset U]$ . 2. The operation of "complement", denoted by C, is defined with respect to U. 3. For any formula (resp. a term), A ⊦ (...) A ↔ ⅂⅂ A (resp. ⊦ CCA = A), and some basic conclusions follow. (shrink)
The main goal of this paper is to explain the link between the algebraic models and the Kripke-style models for certain classes of propositional non-classical logics. We consider logics that are sound and complete with respect to varieties of distributive lattices with certain classes of well-behaved operators for which a Priestley-style duality holds, and present a way of constructing topological and non-topological Kripke-style models for these types of logics. Moreover, we show that, under certain additional assumptions on the variety (...) of the algerabic models of the given logics, soundness and completeness with respect to these classes of Kripke-style models follows by using entirely algebraical arguments from the soundness and completeness of the logic with respect to its algebraic models. (shrink)
A duality between Pawlak's knowledge representation systems and certain information systems of logical type, called bi-consequence systems is established. As an application a first-order characterization of some informational relations is given and a completeness theorem for the corresponding modal logic INF is proved. It is shown that INF possesses finite model property and hence is decidable.
This paper illustrates how Priestley duality can be used in the transfer of an optimal natural duality from a minimal generating algebra for a quasi-variety to other generating algebras. Detailed calculations are given for the quasi-variety of Kleene algebras and the quasi-varieties n of pseudocomplemented distributive lattices (n 1).
Both syntactic and semantic solutions are given for the entailment problem of duality theory. The test algebra theorem provides both a syntactic solution to the entailment problem in terms of primitive positive formulae and a new derivation of the corresponding result in clone theory, viz. the syntactic description of $\operatorname{Inv(Pol}(R))$ for a given set R of finitary relations on a finite set. The semantic solution to the entailment problem follows from the syntactic one, or can be given in the (...) form of an algorithm. It shows, in the special case of a purely relational type, that duality-theoretic entailment is describable in terms of five constructs, namely trivial relations, intersection, repetition removal, product, and retractive projection. All except the last are concrete, in the sense that they are described by a quantifier-free formula. It is proved that if the finite algebra $\underline{M}$ generates a congruence-distributive variety and all subalgebras of $\underline{M}$ are subdirectly irreducible, then concrete constructs suffice to describe entailment. The concept of entailment appropriate to strong dualities is also introduced, and described in terms of coordinate projections, restriction of domains, and composition of partial functions. (shrink)
A topological duality is presented for a wide class of lattice-ordered structures including lattice-ordered groups. In this new approach, which simplifies considerably previous results of the author, the dual space is obtained by endowing the Priestley space of the underlying lattice with two binary functions, linked by set-theoretical complement and acting as symmetrical partners. In the particular case of l-groups, one of these functions is the usual product of sets and the axiomatization of the dual space is given by (...) very simple first-order sentences, saying essentially that both functions are associative and that the space is a residuated semigroup with respect to each of them. (shrink)
The main goal of this paper is to explain the link between the algebraic and the Kripke-style models for certain classes of propositional logics. We start by presenting a Priestley-type duality for distributive lattices endowed with a general class of well-behaved operators. We then show that finitely-generated varieties of distributive lattices with operators are closed under canonical embedding algebras. The results are used in the second part of the paper to construct topological and non-topological Kripke-style models for logics that (...) are sound and complete with respect to varieties of distributive lattices with operators in the above-mentioned classes. (shrink)
Recently, a number of epistemologists have argued that there are no non-conceptual elements in representational content. On their view, the only sort of non-conceptual elements are components of sub-personal organic hardware that, because they enjoy no veridical role, must be construed epistemologically irrelevant. By reviewing a 35-year-old debate initiated by Dagfinn F.
In consciousness studies, the first-person perspective, seen as a way to approach consciousness, is often seen as nothing but a variant of the third-person perspective. One of the most important advocates of this view is Dennett. However, as I show in critical interaction with Dennett’s view, the first-person perspective and the third-person perspective are different ways of asking questions about themes. What these questions are is determined by the purposes that we have when we ask them. Since our purposes are (...) different according to the perspective we take, each perspective has a set of leading questions of its own. This makes that the first-person perspective is an approach of consciousness that is substantially different from the third-person perspective, and that one cannot be reduced to the other. These perspectives are independent, although complementary approaches of the mind. (shrink)
[About the book] This book explores the idea that we have two minds - automatic, unconscious, and fast, the other controlled, conscious, and slow. In recent years there has been great interest in so-called dual-process theories of reasoning and rationality. According to such theories, there are two distinct systems underlying human reasoning - an evolutionarily old system that is associative, automatic, unconscious, parallel, and fast, and a more recent, distinctively human system that is rule-based, controlled, conscious, serial, and slow. Within (...) the former, processes the former, processes are held to be innate and to use heuristics that evolved to solve specific adaptive problems. In the latter, processes are taken to be learned, flexible, and responsive to rational norms. Despite the attention these theories are attracting, there is still poor communication between dual-process theorists themselves, and the substantial bodies of work on dual processes in cognitive psychology and social psychology remain isolated from each other. This book brings together leading researchers on dual processes to summarize the state-of-the-art, highlight key issues, present different perspectives, explore implications, and provide a stimulus to further work. It includes new ideas about the human mind both by contemporary philosophers interested in broad theoretical questions about mental architecture and by psychologists specialising in traditionally distinct and isolated fields. For all those in the cognitive sciences, this is a book that will advance dual-process theorizing, promote interdisciplinary communication, and encourage further applications of dual-process approaches. (shrink)
In 1909, Einstein derived a formula for the mean square energy fluctuation in blackbody radiation. This formula is the sum of a wave term and a particle term. In a key contribution to the 1926 Dreim¨.
In the view of the author, the main problem of semiotics is the understanding and advancing of understanding. To contribute to the solution of this problem, a distinction is suggested between two types of understanding: enlogy and empathy. The subject of enlogy reduces what he understands to himself as a code: he hears only what he is himself. The subject of empathy reduces what she understands to herself as a text: she sees only what she is striving to become. Enlogy (...) is possible due to the identity of the communicants as a present unified code. Empathy is possible due to the identity of the communicants as a future common text. Mastering the code is a by-product of empathy; the texts rests on the enlogy that already is possible. Enlogy and empathy do not pereceive each other as understanding. Therefore their mutual understanding remains the hardest problem of understanding. To fulfil its task, semiotics has to address this problem. (shrink)
NON-DUALISM, DUALISM AND MONISM Q.1 What do the following terms, often used by the Vedanta: dualism, monism, monotheism and non-dualism, mean? A. Every philosophical or cosmological vision which affirms two opposing and irreducible ...
The basic notions in Prior’s Ockhamist and Peircean logics of branching-time are the notion of moment and that of history (or course of events). In the tree semantics, histories are defined as maximal linearly ordered sets of moments. In the geometrical approach, both moments and histories are primitive entities and there is no set theoretical (and ontological) dependency of the latter on the former. In the topological approach, moments can be defined as the elements of a rank 1 base of (...) a non-Archimedean topology on the set of histories. In this paper, it will be shown that the topological approach, and hence the other approaches, can be reconstructed in a framework in which the basic notions are those of history and of relative closeness relation among histories. (shrink)
The final version of the paper is published pp. 117-166 in: Myrdene Anderson and Floyd Merrell (eds.): On Semiotic Modeling . Mouton de Gruyter, Berlin and New York, 1991.
In this autoethnographic essay, I reflect on my brief personal experiences of conducting field research on ways in which way a small group of Tibetan Buddhist monks enact a monastic total institution in Ladakh, India. More specifically, I analyze my experiences in view of the relationship between dual and nondual mind, as discussed by Henry Vyner (2002) in Anthropology of Consciousness, and use this analysis to develop preliminary insights into the ways in which a Tibetan Buddhist monastery is constituted.
The grammar of spatial and temporal concepts cannot, it is argued, be the same in their application to the (manifest) world as perceived and to the (nether) world of unobservable causes as modelled in physics. A parallel case is the dual meaning of colour words, for hues and for material dispositions. The keys to differentiating the two main ranges of uses of 's' and 't' are: differences in criteria of numerical and qualitative identity in the two 'worlds'; differences in the (...) logic of indexicals in each context; the explanatory role of powers. The differences can be illustrated in a close analysis of the concept of velocity. (shrink)
In this paper we describe the Priestley space of a quasi-Stone algebra and use it to show that the class of finite quasi-Stone algebras has the amalgamation property. We also describe the Priestley space of the free quasi-Stone algebra over a finite set.
(1) The idea that diffraction of matter particles can only be understood in terms of a temporary wave transformation or 'double manifestation' is an uneconomical ad hoc hypothesis, shattered already in 1923 by the unitary quantum theory of diffraction of Duane which in 1926 became part of the quantum mechanics, with a statistical interpretation of wave-like appearances. (2) Bohr's re-interpretation of Heisenberg's uncertainty of prediction as an indeterminacy of existence rests on an illegitimate literal translation of a wave result into (...) particle language which is at variance with experience as well as with the statistical interpretation. (3) The fact that one can transform the simple and unitary particle mechanics into a complicated wavelike form is only a weak substitute for genuine dualism -- as if one would see dualism in the transformability from the geo- to the heliocentric reference system. (4) The strongest argument against a symmetry of the particle and the wave theory of matter is the explainability of the former in terms of simple postulates of invariance, leaving the wave formalism as a purely ad hoc construction. (shrink)
. Relational semantics for nonclassical logics lead straightforwardly to topological representation theorems of their algebras. Ortholattices and De Morgan lattices are reducts of the algebras of various nonclassical logics. We define three new classes of topological spaces so that the lattice categories and the corresponding categories of topological spaces turn out to be dually isomorphic. A key feature of all these topological spaces is that they are ordered relational or ordered product topologies.
Methods developed in a previous paper are employed to define an exact correspondence between the states of a deterministic cellular automaton in 1+1 dimensions and those of a bosonic quantum field theory. The result may be used to argue that quantum field theories may be much closer related to deterministic automata than what is usually thought possible.
The grammar of spatial and temporal concepts cannot, it is argued, be the same in their application to the (manifest) world as perceived and to the (nether) world of unobservable causes as modelled in physics. A parallel case is the dual meaning of colour words, for hues and for material dispositions. The keys to differentiating the two main ranges of uses of 's' and 't' are: differences in criteria of numerical and qualitative identity in the two 'worlds'; differences in the (...) logic of indexicals in each context; the explanatory role of powers. The differences can be illustrated in a close analysis of the concept of velocity. (shrink)
The paper suggests a revision of the notion of harmony, a major necessary condition in proof-theoretic semantics for a natural-deduction proof-system to qualify as meaning conferring, when moving to a bilateral proof-system. The latter considers both forces of assertion and denial as primitive, and is applied here to positive logics, lacking negation altogether. It is suggested that in addition to the balance between (positive) introduction and elimination rules traditionally imposed by harmony, a balance should be imposed also on: (i) negative (...) introduction and elimination rules, and (ii) positive and negative introduction rules. The paper suggests a proof-theoretical definition of duality (not referring to truthtables), using which double harmony is defined. The paper proves that in a doubly-harmonious system, the coordination rule, typical to bilateral systems, is admissible. (shrink)
Employing the theory of Birkhoff polarities as a model of model theory yields an inductively defined dual structure which is a formalization of semantics and which allows for simple proofs of some new results for model theory.
: Julia Ward (1819-1910) and Ednah Dow Littlehale (1824-1904), lifelong friends, wrote and lectured on many of the same issues, traveled across the country to lend support to causes, and taught together at the Concord School of Philosophy. Despite their close association and mutual efforts on similar issues, I argue that their philosophical principles were essentially different, in particular their approaches to an understanding of God, society, the sexes, art, and science.
Dualistic approaches to the mind-body relationship are commonplace; however, the adoption of dualistic thinking can often obscure aspects of the way the organism functions as a whole biological entity. Future versions of the emulation theory will, it is hoped, address some of these issues, including the nature of process noise, how distinct iterations can occur, and how to deal with non-emulated aspects of motor control.
