A Propositional Logic with Relative Identity Connective and a Partial Solution to the Paradox of Analysis

We construct a a system PLRI which is the classical propositional logic supplied with a ternary construction , interpreted as the intensional identity of statements and in the context . PLRI is a refinement of Roman Suszko’s sentential calculus with identity (SCI) whose identity connective is a binary one. We provide a Hilbert-style axiomatization of this logic and prove its soundness and completeness with respect to some algebraic models. We also show that PLRI can be used to give a partial solution to the paradox of analysis. Presented by Jacek Malinowski     

The Undecidability of Propositional Adaptive Logic

We investigate and classify the notion of final derivability of two basic inconsistency-adaptive logics. Specifically, the maximal complexity of the set of final consequences of decidable sets of premises formulated in the language of propositional logic is described. Our results show that taking the consequences of a decidable propositional theory is a complicated operation. The set of final consequences according to either the Reliability Calculus or the Minimal Abnormality Calculus of a decidable propositional premise set is in general undecidable, and can be -complete. These classifications are exact. For first order theories even finite sets of premises can generate such consequence sets in either calculus.     

The Red and The Real

It is often claimed that principles of individuation imply essential properties of the things individuated. For example, sets are individuated by their members, hence sets have their members essentially. But how does this inference work? First I discuss the form of such inferences, and conclude that the essentialist inference is not a purely formal matter: although there is a form which all principles of individuation have in common, it is not true that any statement of that form is a principle of individuation, and hence there is no valid inference based purely on that form. However, I argue that there is a viable version of the essentialist inference nonetheless. The resources for a proper reconstruction of this type of inference can be gathered from reflections upon the role principles of individuation play in the project of the ontologist: such principles turn out to carry a modal weight similar to that of definitions or conceptual truths. It follows that, no matter how austere the ontology, some portion of essentialist modality is inevitable.     

The Logic of Causal Explanation An Axiomatization

Three-valued (strong-Kleene) modal logic provides the foundation for a new approach to formalizing causal explanation as a relation between partial situations. The approach makes fine-grained distinctions between aspects of events, even between aspects that are equivalent in classical logic. The framework can accommodate a variety of ontologies concerning the relata of causal explanation. I argue, however, for a tripartite ontology of objects corresponding to sentential nominals: facts, tropes (or facta or states of affairs), and situations (or events). I axiomatize the relations and use canonical models to demonstrate completeness.     

The expressibility of fragments of Hybrid Graph Logic on finite digraphs

Hybrid Graph Logic is a logic designed for reasoning about graphs and is built from a basic modal logic, augmented with the use of nominals and a facility to verify the existence of paths in graphs. We study the finite model theory of Hybrid Graph Logic. In particular, we develop pebble games for Hybrid Graph Logic and use these games to exhibit strict infinite hierarchies involving fragments of Hybrid Graph Logic when the logic is used to define problems involving finite digraphs. These fragments are parameterized by the quantifier-rank of formulae along with the numbers of propositional symbols and nominals that are available. We ascertain exactly the relative definability of these parameterized fragments of the logic.     

The Greatest Extension of S4 into which Intuitionistic Logic is Embeddable

This paper gives a characterization of those quasi-normal extensions of the modal system S4 into which intuitionistic propositional logic Int is embeddable by the Gödel translation. It is shown that, as in the normal case, the set of quasi-normal modal companions of Int contains the greatest logic, M*, for which, however, the analog of the Blok-Esakia theorem does not hold. M* is proved to be decidable and Halldén-complete; it has the disjunction property but does not have the finite model property.     

Hegel and Sellars on the Unity of Things

ABSTRACT

I have claimed previously that Hegel and Sellars are both, in the end, monistic visionaries, though with radically different visions of the grand unity of things. In this paper I explain and defend that claim. Section one differentiates several kinds of monism; section two discusses Hegel’s vision of the underlying unity of thing, while section three does the same for Sellars. The compare-and-contrast assignment is brought to completion in section four.     

The Logic and Meaning of Plurals. Part II

In this sequel to “The logic and meaning of plurals. Part I”, I continue to present an account of logic and language that acknowledges limitations of singular constructions of natural languages and recognizes plural constructions as their peers. To this end, I present a non-reductive account of plural constructions that results from the conception of plurals as devices for talking about the many. In this paper, I give an informal semantics of plurals, formulate a formal characterization of truth for the regimented languages that results from augmenting elementary languages with refinements of basic plural constructions of natural languages, and account for the logic of plural constructions by characterizing the logic of those regimented languages.

The Class of Extensions of Nelson's Paraconsistent Logic

The article is devoted to the systematic study of the lattice εN4_⊥ consisting of logics extending N4_⊥. The logic N4_⊥ is obtained from paraconsistent Nelson logic N4 by adding the new constant ⊥ and axioms ⊥ → p, p → ∼ ⊥. We study interrelations between εN4_⊥ and the lattice of superintuitionistic logics. Distinguish in εN4_⊥ basic subclasses of explosive logics, normal logics, logics of general form and study how they are relate. The author acknowledges support by the Alexander von Humboldt-Stiftung and by Counsil for Grants under RF President, project NSh - 2112.2003.1.     

The Sporting Exploration of the World; Toward a Fundamental Ontology of the Sporting Human Being

ABSTRACT

My perspective in this paper is to look at sport and other physical activities as a way of exploring and experimenting with the environing world. The human being is basically the homo movens – born to move. Furthermore, the homo movens is the homo ludens – an active and playful being that explores the world in different ways and in a variety of environments. The ludic exploration of the world starts with children’s play and goes all the way up to full-blown versions of rule-based sports, then on to various physical activities into old age. My point of departure is Heidegger’s notion of being-in-the-world which suggests that humans are never isolated individuals but are always in a deep way connected with a ‘world’. The ‘world’ of sport comes in different versions. By use of a phenomenological approach I try to show that the sporting exploration of the world takes place in four ontologically different dimensions or ‘worlds’. Here I distinguish between individual sports, encounter sports, team sports and nature sports, and I argue that the I-Me, I-You, I-Society and I-Nature relations that are exemplified in these four types of sports have different ontological characteristics. While the discussion is inspired by Heidegger’s ideas I argue that the ways of ‘worldmaking’ in sport are more ontologically diverse than Heidegger opened up for. Heidegger described the relation of Dasein to itself and to other human beings and argued that we deal with the environment in a practical and a theoretical mode. I expand on this and present a more coherent picture of four different dimensions in the human being’s sporting exploration of the world.     

The Logic of Quantum Measurements in terms of Conditional Events

This paper shows that the non-Boolean logic of quantum measurementsis more naturally represented by a relatively new 4-operationsystem of Boolean fractions—conditional events—thanby the standard representation using Hilbert Space. After therequirements of quantum mechanics and the properties of conditionalevent algebra are introduced, the quantum concepts of orthogonality,completeness, simultaneous verifiability, logical operations,and deductions are expressed in terms of conditional eventsthereby demonstrating the adequacy and efficacy of this formulation.Since conditional event algebra is nearly Boolean and consistsmerely of ordered pairs of standard events or propositions,quantum events and the so-called "superpositions" of statesneed not be mysterious, and are here fully explicated. Conditionalevent algebra nicely explains these non-standard "superpositions"of quantum states as conjunctions or disjunctions of conditionalevents, Boolean fractions, but does not address the so-called"entanglement phenomena" of quantum mechanics, which remainphysically mysterious. Nevertheless, separating the latter phenomenafrom superposition issues adds clarity to the interpretationof quantum entanglement, the phenomenon of influence propagatedat faster than light speeds. With such treacherous possibilitiespresent in all quantum situations, an observer has every reasonto be completely explicit about the environmental–instrumentalconfiguration, the conditions present when attempting quantummeasurements. Conditional event algebra allows such explicationwithout the physical and algebraic remoteness of Hilbert space.     

中医气论的本质是关系本体论

学界在对中医气论的阐释中常将气作为核心,把"气"当作具有第一性的"实体实在"。这种观点非常容易产生原子论和实体主义倾向,与中医学的临床实践相违背。现代科学的进展和中医学实践证明,原子论和实体主义的思想实际上并不符合客观世界的真实情况。若是从系统科学中"关系实在"的视角来看,作为"关系实在"的气化才应该是气论的核心,气论的本质应该是关系本体论。确定中医学理论在现代语境之中的定位,有助于深入发掘我国优秀的传统思想,并可促进中医现代化,由此来推动中医学的复兴。     

The many-worlds theory of consciousness

This paper sketches a new and somewhat heterodox metaphysical theory of consciousness: the “many-worlds theory”. It drops the assumption that all conscious subjects’ experiences are features of one and the same world and instead associates different subjects with different “first-personally centred worlds”. We can think of these as distinct “first-personal realizers” of a shared “third-personal world”, where the latter is supervenient, in a sense to be explained. This is combined with a form of modal realism, according to which different subjects’ first-personally centred worlds are all real, though only one of them is present for each subject. The theory offers a novel way of capturing the irreducibly subjective nature of conscious experience without lapsing into solipsism. The paper also looks at some scientific theories of consciousness, such as integrated information theory, through the proposed lens and reconsiders the hard problem of consciousness.     

Algebras of Intervals and a Logic of Conditional Assertions

Intervals in boolean algebras enter into the study of conditional assertions (or events) in two ways: directly, either from intuitive arguments or from Goodman, Nguyen and Walker's representation theorem, as suitable mathematical entities to bear conditional probabilities, or indirectly, via a representation theorem for the family of algebras associated with de Finetti's three-valued logic of conditional assertions/events. Further representation theorems forge a connection with rough sets. The representation theorems and an equivalent of the boolean prime ideal theorem yield an algebraic completeness theorem for the three-valued logic. This in turn leads to a Henkin-style completeness theorem. Adequacy with respect to a family of Kripke models for de Finetti's logic, ukasiewicz's three-valued logic and Priest's Logic of Paradox is demonstrated. The extension to first-order yields a short proof of adequacy for Körner's logic of inexact predicates.     

A broad assessment of theory of mind in adolescence: The complexity of mindreading

The aim of this research was to provide an articulated assessment of several different ToM components, namely first- vs. third-person, egocentric vs. allocentric, and first- vs. second-order ToM, in preadolescence and adolescence. Our expectations for the sample of 80 juveniles that participated in the research were that: (1) ToM abilities would improve with age; (2) participants would perform better at first-person than at third-person tasks; (3) participants would perform better at first-order than at second-order tasks; (4) girls will perform systematically better than boys. We also explored possible differences in performance (5) in the allocentric vs. the egocentric perspectives as well as (6) in the comprehension of different types of mental states, namely desires, beliefs and positive and negative emotions. Overall our expectations were confirmed. Our data confirmed that all ToM aspects we investigated keep maturing during preadolescence and adolescence.     

Categorical Ontology of Levels and Emergent Complexity: An Introduction

An overview of the following three related papers in this issue presents the Emergence of Highly Complex Systems such as living organisms, man, society and the human mind from the viewpoint of the current Ontological Theory of Levels. The ontology of spacetime structures in the Universe is discussed beginning with the quantum level; then, the striking emergence of the higher levels of reality is examined from a categorical—relational and logical viewpoint. The ontological problems and methodology aspects discussed in the first two papers are followed by a rigorous paper based on Category Theory, Algebraic Topology and Logic that provides a conceptual and mathematical basis for a Categorical Ontology Theory of Levels. The essential links and relationships between the following three papers of this issue are pointed out, and further possible developments are being considered.     

The Elimination of Self-Reference: Generalized Yablo-Series and the Theory of Truth

Although it was traditionally thought that self-reference is a crucial ingredient of semantic paradoxes, Yablo (1993, 2004) showed that this was not so by displaying an infinite series of sentences none of which is self-referential but which, taken together, are paradoxical. Yablo’s paradox consists of a countable series of linearly ordered sentences s(0), s(1), s(2),... , where each s(i) says: For each k > i, s(k) is false (or equivalently: For no k > i is s(k) true). We generalize Yablo’s results along two dimensions. First, we study the behavior of generalized Yablo-series in which each sentence s(i) has the form: For Q k > i, s(k) is true, where Q is a generalized quantifier (e.g., no, every, infinitely many, etc). We show that under broad conditions all the sentences in the series must have the same truth value, and we derive a characterization of those values of Q for which the series is paradoxical. Second, we show that in the Strong Kleene trivalent logic Yablo’s results are a special case of a more general fact: under certain conditions, any semantic phenomenon that involves self-reference can be emulated without self-reference. Various translation procedures that eliminate self-reference from a non-quantificational language are defined and characterized. An Appendix sketches an extension to quantificational languages, as well as a new argument that Yablo’s paradox and the translations we offer do not involve self-reference.     

传统异化逻辑与主体性形而上学的共生性--论《1844年经济学哲学手稿》对启蒙辩证法的初始突破

主体性形而上学与传统异化逻辑的对峙是主体-客体对立的必然理论后果,二者之间的张力维持有赖于启蒙以来的时代精神也即抽象主体性的支撑。一旦抽象主体性被消解,主体神话被揭穿,异化就自然而然僭越为本体性存在。惟有马克思的历史辩证法才能走出主客二分的主体性与传统异化逻辑对立之悖论。在《1844年经济学哲学手稿》中,马克思就已经对传统异化逻辑做了初始性的突破。     

Variable Perception of White Noise in Ambiguous Phonetic Contexts: The Case of /p/ and /f/

The roles of spectro-temporal coherence, lexical status, and word position in the perception of speech in acoustic signals containing a mixture of speech and nonspeech sounds were investigated. Stimuli consisted of nine (non)words in which either white noise was inserted only into the silent interval preceding and/or following the onset of vocalic transitions ambiguous between /p/ and /f/, or in which white noise overlaid the entire utterance. Ten listeners perceived 85% /f/s when noise was inserted only into the silent interval signaling a stop closure, 47% /f/s when noise overlaid the entire (non)words, and 1% in the control condition that contained no noise. Effects of spectro-temporal coherence seemed to have dominated perceptual outcomes, although the lexical status and position of the critical phoneme also appeared to affect responses. The results are explained more adequately by the theory of Auditory Scene Analysis than by the Motor Theory of Speech Perception.     

科学心理学的观念与人文科学的逻辑奠基

科学心理学观念的普遍兴起,是19世纪中叶错综复杂的思想史背景的产物。只有在人类思想及其历史作为整体的关系背景中,才能澄清这个观念的内在本性。也只有在系统地接受这个背景的制约关系中,这个观念才能获得其真理的实现。能否在人类思想作为整体中胜任并执行其理论职能,成为我们检验一种心理学体系之真理性的途径之一:科学心理学观念只有实现为现象学心理学,才能执行其为人文科学奠基的逻辑职能; 反之亦然。这个关系还从否定方面暗示着,一切以异化的形式实现的心理学,都不可能真正承担起为人文科学奠基的逻辑职能,并因而违背了我们的常识。