We develop a relativistic perspective on structures of quantum observables, in terms of localization systems of Boolean coordinatizing charts. This perspective implies that the quantum world is comprehended via Boolean reference frames for measurement of observables, pasted together along their overlaps. The scheme is formalized categorically, as an instance of the adjunction concept. The latter is used as a framework for the specification of a categorical equivalence signifying an invariance in the translational code of communication between Boolean localizing contexts and (...) quantum systems. Aspects of the scheme semantics are discussed in relation to logic. The interpretation of coordinatizing localization systems, as structure sheaves, provides the basis for the development of an algebraic differential geometric machinery suited to the quantum regime. (shrink)

We analyse the two definitions of generalized quantifiers for logics of dependence and independence that have been proposed by F. Engström, comparing them with a more general, higher order definition of team quantifier. We show that Engström’s definitions can be identified, by means of appropriate lifts, with special classes of team quantifiers. We point out that the new team quantifiers express a quantitative and a qualitative component, while Engström’s quantifiers only range over the latter. We further argue that Engström’s definitions (...) are just embeddings of the first-order generalized quantifiers into team semantics, and fail to capture an adequate notion of team-theoretical generalized quantifier, save for the special cases in which the quantifiers are applied to flat formulas. We also raise several doubts concerning the meaningfulness of the monotone/nonmonotone distinction in this context. In the appendix we develop some proof theory for Engström’s quantifiers. (shrink)

Recently, two apparently quite different duality-based approaches to automata minimisation have appeared. One is based on ideas that originated from the controllability-observability duality from systems theory, and the other is based on ideas derived from Stone-type dualities specifically linking coalgebras with algebraic structures derived from modal logics. In the present paper, we develop a more abstract view and unify the two approaches. We show that dualities, or more generally dual adjunctions, between categories can be lifted to dual adjunctions between categories (...) of coalgebras and algebras, and from there to automata with initial as well as final states. As in the Stone-duality approach, algebras are essentially logics for reasoning about the automata. By exploiting the ability to pass between these categories, we show that one can minimize the corresponding automata. We give an abstract minimisation algorithm that has several instances, including the celebrated Brzozowski minimisation algorithm. We further develop three examples that have been treated in previous works: deterministic Kripke frames based on a Stone-type duality, weighted automata based on the self-duality of semimodules, and topological automata based on Gelfand duality. As a new example, we develop alternating automata based on the discrete duality between sets and complete atomic Boolean algebras. (shrink)

Abramsky, S., Domain theory in logical form, Annals of Pure and Applied Logic 51 1–77. The mathematical framework of Stone duality is used to synthesise a number of hitherto separate developments in theoretical computer science.• Domain theory, the mathematical theory of computation introduced by Scott as a foundation for detonational semantics• The theory of concurrency and systems behaviour developed by Milner, Hennesy based on operational semantics.• Logics of programsStone duality provides a junction between semantics and logics . Moreover, the (...) underlying logic is geometric, which can be computationally interpreted as the logic of observable properties—i.e., properties which can be determined to hold of a process on the basis of a finite amount of information about its execution.These ideas lead to the following programme. A metalanguage is introduced, comprising• types = universes of discourse for various computational situations;• terms = PROGRAMS = syntactic intensions for models or points. A standard denotational interpretation of the metalanguage is given, assigning domains to types and domain elements to terms. The metalanguage is also given a logical interpretation, in which types are interpreted as propositional theories and terms are interpreted via a program logic, which axiomatises the properties they satisfy. The two interpretations are related by showing that they are Stone duals of each other. Hence, semantics and logic are guaranteed to be in harmony with each other, and in fact each determines the other up to isomorphism. This opens the way to a whole range of applications. Given a denotational description of a computational situation in our metalanguage, we can turn the handle to obtain a logic for that situation. (shrink)

Theory of Mind (ToM), the cognitive capacity to attribute internal mental states to oneself and others, is a crucial component of social skills. Its formal study has become important, witness recent research on reasoning and information update by intelligent agents, and some proposals for its formal modelling have put forward settings based on Epistemic Logic (EL). Still, due to intrinsic idealisations, it is questionable whether EL can be used to model the high-order cognition of ‘real’ agents. This manuscript proposes (...) a framework that takes visibility, memory, perspective and communication as the main factors underpinning mental attributions. This is more in-line with findings in cognitive science and allows us to model well-known False-Belief Tasks that are typically used in testing people's ToM. We discuss some of the framework's technical features, arguing why it does justice to empirical observations. (shrink)

Open peer commentary on the article “Second-Order Science: Logic, Strategies, Methods” by Stuart A. Umpleby. Upshot: Second-order science requires a specific methodology. It thereby reverses the classical observer-observed relation in favor of the observed - i.e., the first-order observers - if the principle of autopoiesis is acknowledged.

It is a paradox, whose importance familiarity fails to diminish, that the most highly developed and useful scientific theories are ostensibly expressed in terms of objects never encountered in experience. The line traced by a draughtsman, no matter how accurate, is seen beneath the microscope as a kind of corrugated trench, far removed from the ideal line of pure geometry. And the “point-planet” of astronomy, the “perfect gas” of thermodynamics, or the “pure species” of genetics are equally remote from exact (...) realization. Indeed the unintelligibility at the atomic or sub-atomic level of the notion of a rigidly demarcated boundary shows that such objects not merely are not but could not be encountered. While the mathematician constructs a theory in terms of “perfect” objects, the experimental scientist observes objects of which the properties demanded by theory are and can, in the very nature of measurement, be only approximately true. As Duhem remarks, mathematical deduction is not useful to the physicist if interpreted rigorously. It is necessary to know that its validity is unaltered when the premise and conclusion are only “approximately true.” But the indeterminacy thus introduced, it is necessary to add in criticism, will invalidate the deduction unless the permissible limits of variation are specified. To do so, however, replaces the original mathematical deduction by a more complicated mathematical theory in respect of whose interpretation the same problem arises, and whose exact nature is in any case unknown. (shrink)

a single life-span. Philosophers, then, do not see more or know more, and they do not see less or know less. They aim to see less detail and more of the abstract. Their details, if you like, are abstractions. Walking on God’s earth as a pedestrian, as a farmer working his fields or as a passer-by, one’s picture of one’s surroundings is every bit as intelligent as that of the pilot riding the sky. The views of the field are radically (...) different, however. One sees only a specific field and in all lively detail: the exact pattern of the land, or even the exact outline of a given leaf, grasshopper, grain of sand even. Acquaintance with minute detail is not without its price: details may stand in the way of conjuring the big picture. It may be difficult to compare whichever field one happens to be in with far off fields, with respect to their size or shape or any other quality. One may wish to inquire if far off fields were already planted, harvested, or even if they exist. A pedestrian may find it hard or even impossible to do so. The pedestrian view contains fine points that the pilot’s map never would, but it does not necessarily contain more information, for it lacks the general context. After all, there are only so many items that one can observe and account for at a single glance, a single map, a single book, a single life-span. (shrink)

Scientists collect evidence in order to confirm or falsify scientific theories. Unfortunately, scientific evidence may sometimes be false or deceiving and as a consequence lead individuals to believe in a false theory. By interaction between scientists, such false beliefs may spread through the entire community. There is currently a debate about the effect of various network configurations on the epistemic reliability of scientific communities. To contribute to this debate from a logical perspective, this paper introduces an epistemic logical framework of (...) observation, interaction and belief revision in scientific communities. The presented sound and complete system provides the formal tools for qualitative analysis of the social dynamics of scientific inquiry. Furthermore, this paper includes detailed suggestions for future applications of the framework. (shrink)

A textbook on the principles of logical reasoning and scientific method, including chapters covering topics such as argumentation, inductive and deductive reasoning, and scientific observation and experimentation. The book is intended for students of philosophy, logic, and the natural sciences. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other (...) nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

Scientists obtain a great deal of the evidence they use by observingnatural and experimentally generated objects and effects. Much of thestandard philosophical literature on this subject comes from20th century logical positivists and empiricists, theirfollowers, and critics who embraced their issues and accepted some oftheir assumptions even as they objected to specific views. Theirdiscussions of observational evidence tend to focus on epistemologicalquestions about its role in theory testing. This entry follows theirlead even though observational evidence also plays important andphilosophically interesting roles (...) in other areas including scientificdiscovery and the application of scientific theories to practicalproblems. (shrink)

Rational agents base their actions on information from observation, inference, introspection, or other sources. But this information comes in different kinds, and it is usually handled by different logical mechanisms. We discuss how to integrate external ‘updating information’ and internal ‘elucidating information’ into one system of dynamic epistemic logic, by distinguishing two basic informational actions: ‘bare seeing’ versus ‘conscious realization’.

Patrick Heelan, with background in quantum theory and in hermeneutic phenomenology, investigated not only the hermeneutical philosophy of science but also the parallels between quantum mechanics and human experience in general and the logic of changes of worldview. Heelan’s closeness to Aristotle and Lonergan, often neglected, is discussed, and issues concerning Heelan’s treatment of the social context of science are raised.

Antoine Arnauld and Pierre Nicole were philosophers and theologians associated with Port-Royal Abbey, a centre of the Catholic Jansenist movement in seventeenth-century France. Their enormously influential Logic or the Art of Thinking, which went through five editions in their lifetimes, treats topics in logic, language, theory of knowledge and metaphysics, and also articulates the response of 'heretical' Jansenist Catholicism to orthodox Catholic and Protestant views on grace, free will and the sacraments. In attempting to combine the categorical theory (...) of the proposition with a Cartesian account of knowledge, their Logic represents the classical view of judgment which inspired the modern transformation in logic and semantic theory by Frege, Russell, Wittgenstein and recent philosophers. This edition presents a new translation of the text, together with a historical introduction and suggestions for further reading. (shrink)

This paper addresses the question whether the past couple of decades of formal research in belief revision offers evidence of a new psychologism in logic. In the first part I examine five potential arguments in favour of this thesis and find them all wanting. In the second part of the paper I argue that belief revision research has climbed up a hierarchy of models for the change of doxastic states that appear to be clearly normative at the bottom, but (...) are more amenable to an empirical-descriptive interpretation on higher levels. I conclude that this observation might offer a foothold for the thesis that there is a new psychologism in logic. (shrink)

It is well known that no consistent normal modal logic contains (as theorems) both ♦A and ♦¬A (for any formula A). Here we observe that this claim can be strengthened to the following: for any formula A, either no consistent normal modal logic contains ♦A, or else no consistent normal modal logic contains ♦¬A.

A vital step to successfully orienting Deleuze with biosemiotics (and theories of biological complexity overall) is to discover a coherent scientific throughline in his work that also accounts for the aesthetic/creative dimension of his philosophy. This requires the heterodox move (from a Deleuzean point of view) of giving priority to the organism. I argue that Deleuze’s treatment of the organism does more than signal a superficial relation to biological complexity theory that, as a result of his nuanced take on the (...) matter, undermines the value of the organic body to his system. Instead, we can recognize a working theory of autopoiesis in the early Deleuze that scaffolds as well as substantiates his later ethological and biosemiotic observations and reveals a definite, albeit minimal, notion of subjectivity in his work. Most importantly, reorienting his logic of sense as a logic of _sense-making_, or the context-dependent signification between system and environment (Thompson, 2007 ), allows us to begin the work of mining a scientific throughline in Deleuze’s work akin to biological complexity theory that is of value to both Deleuze studies and biosemiotics. (shrink)

In this paper we present two families of probability logics (denoted _QLP_ and \(QLP^{ORT}\) ) suitable for reasoning about quantum observations. Assume that \(\alpha \) means “O = a”. The notion of measuring of an observable _O_ can be expressed using formulas of the form \(\square \lozenge \alpha \) which intuitively means “if we measure _O_ we obtain \(\alpha \) ”. In that way, instead of non-distributive structures (i.e., non-distributive lattices), it is possible to relay on classical logic extended (...) with the corresponding modal laws for the modal logic \({\textbf{B}}\). We consider probability formulas of the form \(CS_{z_{1},\rho _{1}; \ldots ; z_{m},\rho _{m}} \square \lozenge \alpha \) related to an observable _O_ and a possible world (vector) _w_: if _a_ is an eigenvalue of _O_, \(w_{1}\),..., \(w_{m}\) form a base of a closed subspace of the considered Hilbert space which corresponds to eigenvalue _a_, and if _w_ is a linear combination of the basis vectors such that \(w=c_{1}\cdot w_{1}+ \cdots + c_{m}\cdot w_{m}\) for some \(c_{i}\in {\mathbb {C}}\), then \(\Vert c_{1}-z_{1}\Vert \le \rho _{1}\),..., \(\Vert c_{m}-z_{m}\Vert \le \rho _{m}\), and the probability of obtaining _a_ while measuring _O_ in the state _w_ is equal to \(\Sigma _{i=1}^{m}\Vert c_{i}\Vert ^{2}\). Formulas are interpreted in reflexive and symmetric Kripke models equipped with probability distributions over families of subsets of possible worlds that are orthocomplemented lattices, while for \(QLP^{ORT}\) also satisfy ortomodularity. We give infinitary axiomatizations, prove the corresponding soundness and strong completeness theorems, and also decidability for _QLP_-logics. (shrink)

The aim of the article is to present the results of research conducted as part of the project Polonica Philosophica Orientalia: namely, to give an overview of the most important logical and metaphysical treatises written in Vilnius between the sixteenth and eighteenth centuries that are currently accessible in some of the Vilnius libraries. Although the research focused primarily on the Vilnius University Library and its resources, some interesting results were also obtained while researching the Wróblewski Library of the Lithuanian Academy (...) of Sciences. Most sources containing information about the state and the nature of metaphysical and logical investigations conducted in Vilnius during the period discussed are the manuscripts of lecture courses delivered for the students of Vilnius University and other schools. The analysis of those manuscripts has revealed a strong and long-lasting influence of scholastic Aristotelianism in both logic and metaphysics. Namely, up to the mid-eighteenth century, the main questions discussed in logic were Aristotelian syllogism, the square of opposition and the medieval topics of semantical antinomies, modalities and supposition theory, while investigations into metaphysical issues were limited to commentaries on Aristotle’s theoretical treatises without seriously questioning their main theses. In the second part of the eighteenth century, a moderate shift towards subjectivism and psychologism was observed in both of these disciplines. This was influenced by modern epistemologists. Logicians and metaphysicians of Vilnius University developed an interest in the topics of human understanding and cognition. However, this shift did not take a radical form – while the majority of eighteenth-century authors sought a combination of scholastic and modern ideas, a critical and even hostile stance towards modern philosophy and science is still noticeable in many of the analysed sources. An overview of the research supported by statistical data is followed by some preliminary remarks on how and where investigation of this topic might be continued in the future. (shrink)

Very often in frameworks for and presentations of The Brothers Karamazov, the modern reading public attempts to divide characters by their ability to reason. Usually Ivan is remembered for his reason, pitted against Dmitri’s passion. Adapting some terminology from mathematical logic, I propose and trace a different approach to reason in Dostoevsky’s text, to recast its canonical characters into alternative, though still fluid, categories. This exercise aims not to reinscribe or to reinterpret Dostoevsky’s novel but rather to reconsider an (...) aspect of reasoning, specifically modes or forms of logic. With an admittedly imperfect mapping of characters onto these logical structures, this article encourages the ways in which we can trouble notions of stable reason and sound logic as they operate in the novel. (shrink)

In prior work [7] we considered networks of agents who have knowledge bases in first order logic, and report facts to their neighbors that are in their common languages and are provable from their knowledge bases, in order to help a decider verify a single sentence. In report complete networks, the signatures of the agents and the links between agents are rich enough to verify any deciderʼs sentence that can be proved from the combined knowledge base. This paper introduces (...) a more general setting where new observations may be added to knowledge bases and the decider must choose a sentence from a set of alternatives. We consider the question of when it is possible to prepare in advance a finite plan to generate reports within the network. We obtain conditions under which such a plan exists and is guaranteed to produce the right choice under any new observations. (shrink)

In the debate on our engagement with and appreciation of fiction films, the thesis that the viewer of a fiction film imagines observing fictional events, and the thesis that these events are imagined to be presented by a narrator, are usually taken as two components of one theoretical package, which philosophers such as George Wilson and Jerrold Levison defend, while philosophers such as Gregory Currie and Berys Gaut reject. This paper argues that the two theses can be disentangled and investigates (...) their logical connection. The investigation shows that the second thesis entails the first but there is no entailment the other way around. Endorsing the first thesis is thus compatible with two options, namely endorsing the second thesis or abandoning it. However, the paper argues that if we endorse the first thesis, endorsing the second provides us with a more compelling explanation of our engagement with and appreciation of fiction films. (shrink)

Major figures of twentieth-century philosophy were enthralled by the revolution in formal logic, and many of their arguments are based on novel mathematical discoveries. Hilary Putnam claimed that the Löwenheim-Skølem theorem refutes the existence of an objective, observer-independent world; Bas van Fraassen claimed that arguments against empiricism in philosophy of science are ineffective against a semantic approach to scientific theories; W. V. O. Quine claimed that the distinction between analytic and synthetic truths is trivialized by the fact that any (...) theory can be reduced to one in which all truths are analytic. This book dissects these and other arguments through in-depth investigation of the mathematical facts undergirding them. It presents a systematic, mathematically rigorous account of the key notions arising from such debates, including theory, equivalence, translation, reduction, and model. The result is a far-reaching reconceptualization of the role of formal methods in answering philosophical questions. (shrink)

ABSTRACT:This study examines whether the empirical evidence on the relationship between corporate social performance (CSP) and corporate financial performance (CFP) differs depending on the publication outlet in which that evidence appears. This moderator meta-analysis, based on a total sample size of 33,878 observations, suggests that published CSP-CFP findings have been shaped by differences in institutional logics in different subdisciplines of organization studies. In economics, finance, and accounting journals, the average correlations were only about half the magnitude of the findings published (...) in Social Issues in Management, Business Ethics, or Business and Society journals (mean corrected correlation coefficientof.22 vs..49, respectively). Specifically, economists did not find null or negative CSP-CFP correlations, and average findings published in general management outlets (=.41) were closer to Social Issues in Management, Business Ethics, and Business and Society results than to findings reported in economics, finance, and accounting journals. (shrink)

This paper presents a model for the structure of universal frameworks in logic, mathematics, and physics that are closed to logical conclusion by the mechanism of paradox across a dualism of elements. The prohibition takes different forms defined by the framework of observation inherent to the structure. Forms include either prohibition to conclusion on the logical relationship of internal elements or prohibition to conclusion based on the existence of an element not included in the framework of a first element. (...) The model is applied to logical arguments in philosophy, mathematics, and physics and is initially a geometrical analysis of quantum theory and its application in experiment. Conclusion from the analysis is extended to give insight into the complexity of infinities above the two-dimensional boundary of the model. (shrink)

The often observed complexity gap between the expressiveness of a logical formalism and its exponentially harder expression complexity is proven for all logical formalisms which satisfy natural closure conditions. The expression complexity of the prefix classes of second-order logic can thus be located in the corresponding classes of the weak exponential hierarchies; further results about expression complexity in database theory, logic programming, nonmonotonic reasoning, first-order logic with Henkin quantifiers and default logic are concluded. The proof method (...) illustrates the significance of quantifier-free interpretations in descriptive complexity theory. (shrink)

1. One sometimes finds, in popular literature, the statement that formal logic is called formal because it studies the forms of thought: concepts, judgments, inferences. To confine the definition in this way would, to say the least, be an inaccuracy. Study of concepts and other forms of thought is generally assumed to be a task of philosophy; and it attains its highest development in dialectical philosophy. The fact is that statements such as the one we have cited are usually (...) followed by the explanation that formal logic studies thoughts — concepts, judgments, inferences — in terms of their formal structure and construction, that is, of various general ways of connecting parts of their concrete content. And it is observed that the logical structure of thought emerges as the result of abstraction, the identification and separation of the general from a multiplicity of individual facts differing in content, and that it is then recorded in terms of formulas. (shrink)

John Leslie presents a thought experiment to show that chances are sometimes observer-relative in a paradoxical way. The pivotal assumption in his argument – a version of the weak anthropic principle – is the same as the one used to get the disturbing Doomsday argument off the ground. I show that Leslie's thought experiment trades on the sense/reference ambiguity and is fallacious. I then describe a related case where chances are observer-relative in an interesting way. But not in a paradoxical (...) way. The result can be generalized: At least for a very wide range of cases, the weak anthropic principle does not giverise to paradoxical observer-relative chances. This finding could be taken to give new indirect support to the doomsday argument. (shrink)

With the advent of classical logic we are continuing to observe an adherence to the laws of logic. Moreover, the system of classical logic exhibits a prominent role within analytic philosophy. Given that the laws of logic have persistently endured in actively defining classical logic and its preceding system of logic, it begs the question as to whether it actually proves to be consistent with Islam. To consider this inquiry in a broader manner; it (...) would be an investigation into the consistency between Islam and the logic which has been the predominant driving force of analytic philosophy. Despite the well documented engagement and novel contributions made in the field of logic by Arab and Islamic theologians/logicians, I think this question deserves examination not just in terms of classical logic but also from perspectives which go beyond classical logic, namely, non-classical logic. Doing so, would I believe, retain this inquiry within the purview of analytic philosophy despite the reference to non-classical logic. To be more specific, this question would be directed toward the Islamic theologian who espouses the system of classical logic in attempting to make sense of an absolute ineffable God of Islam. The inquiry would seek to determine if classical logic is consistent (amenable) in making sense of an absolute ineffable God of Islam. This would principally involve an analysis which determines whether the metaphysical assumptions of the laws of logic (more specifically the law of non-contradiction) are consistent in making sense of an absolute ineffable God of Islam. I shall argue that it is inconsistent. I shall establish my position on this matter by demonstrating why classical logic is inconsistent (not amenable) with an absolute ineffable God of Islam. Although, I am principally concerned with classical logic, my argument is as applicable to all earlier systems of logic as much as it is to classical logic. This is on the basis that both systems of logic, namely, all preceding systems and classical logic, consider the laws of logic as defining features. (shrink)

In this paper, I show that a kind of perfect logical competence is observed in the Babylonian tablets used for forecasting. In these documents, we see an intuition of some algebraic structures that are used for inferring prognoses as logical conclusions. The paper is based mainly on the omen series reconstructed by N. De Zorzi. It is shown that in composing these divination lists there was implicitly used the Boolean algebra.

This paper contains five observations concerning the intended meaning of the intuitionistic logical constants: (1) if the explanations of this meaning are to be based on a non-decidable concept, that concept should not be that of `proof"; (2) Kreisel"s explanations using extra clauses can be significantly simplified; (3) the impredicativity of the definition of → can be easily and safely ameliorated; (4) the definition of → in terms of `proofs from premises" results in a loss of the inductive character of (...) the definitions of ∨ and ∃ and (5) the same occurs with the definition of ∀ in terms of `proofs with free variables". (shrink)

The finding that people tend to prefer logically valid conclusions over invalid ones is known in the literature as the logic‐liking effect and has traditionally been interpreted as evidence for the notion of so‐called logical intuitions. Results of more recent empirical studies investigating conditional and categorical syllogisms suggest, however, that previous instances of the logic‐liking effect can be accounted for by a confound in terms of surface‐feature atmosphere. But the true nature of this atmosphere effect has so far (...) remained largely elusive. Here, we address this issue and introduce two variants of disjunctive syllogisms that enable us to deconfound validity, possibility of the conclusion, and surface‐feature atmosphere, which has been impossible with simple disjunctive syllogisms used in earlier studies. Three experiments, in which participants were asked to provide liking and logic ratings for these arguments, revealed that the logic‐liking effect in disjunctive syllogisms can be explained by an atmosphere confound in combination with implied demand to consider logicality when judging likability. We also observed a strong atmosphere effect in logic ratings over and above an effect of logical validity per se. Furthermore, atmosphere effects appear to be induced only by specific surface features, namely those that are ecologically valid, if fallible, predictors for logicality. We conclude that acquired atmosphere heuristics provide proxies for logical validity that reasoners often take at face value. A comparison of the present results with previous findings from experiments that focused on conditional and categorical syllogisms additionally indicates that these atmosphere heuristics are used irrespective of an argument's complexity. (shrink)

Process logic described by A. V. Smirnov is based on materials from the arab-muslim cul­ture as a whole. Process logic is contrasted with the substance logic which forms the foundation of European culture as a whole. It has been proven theoretically that any situation could be interpreted using any logic of sense. The article provides an empirical illustration of the use of the process logic in a consultation of a preschool educational in­stitution psychologist on problems (...) connected with a mental disorder of one of the pupils of the institution. On the basis of this single example it is demonstrated how process logic allows the shift of the focus of attention retaining the rational basis of the actions. Situa­tions relating to the health are difficult to describe using substantial logic as the course of the disease depends on the actions of the patient and on the actions of people in his/her immediate surroundings. This limits the usability of the law of identity which is funda­mental to substantial logic. The disease is “not that very same” disease – it is changing as the result of the actions. This creates a persistent uncertainty which is of remarkable im­portance in pediatric healthcare, where the actions of the parents are complicating the sit­uation much more significantly compared to the adult healthcare. In contrast to this, process logic allows us to observe the course of the ailment as such, as being a process, which eliminates the uncertainty. The process determines the actions regarding the ail­ment as well as their evaluation. If an action is changing the course of the ailment to the better we consider it successful. In the case described, the logic of understanding the situation used by the consultant has changed the client’s logic of understanding the situation. The person stopped seeing the problem as something rigid and insurmount­able. The change of the logic didn’t require any special training of the client. It follows that the shift of understanding from the substance logic to the process logic can help to solve practical pediatric problems. (shrink)

The observation that the standard solution of the paradox of the Liar is not satisfactory as a pragmatic solution of a semantic problem restores its former status as a semantic antinomy. Since the antinomy originates from Tarski's T scheme, a conservative modification of the standard semantics is looked for, which would prevent applying the scheme T to anomalous statements. Two such modifications are considered. The first is simpler and implies Kleene's weak tables for three-valued logic. The second, more complex (...) but also more intuitive, agrees with Kleene's strong tables. This undermines the seemingly natural intuition that a sentence and the sentence attributing truth to it have the same truth conditions, which is compatible only with the weak tables. (shrink)

Since Kripke, philosophers have distinguished a priori true statements from necessarily true ones. A statement is a priori true if its truth can be established before experience, and necessarily true if it could not have been false according to logical or metaphysical laws. This distinction can be captured formally using two-dimensional semantics. There is a natural way to extend the notions of apriority and necessity so they can also apply to questions. Questions either can or cannot be resolved before experience, (...) and either are or are not about necessary facts. Classical two-dimensionalism has no account of question meanings, so it has to be combined with a framework for question semantics in order to capture these observations. It is shown in [14] how two-dimensional semantics can be combined with inquisitive semantics, in which questions are analyzed in terms of information. The present paper investigates the logic of two-dimensional inquisitive semantics, and provides a complete proof system. (shrink)

This paper defends a version of J. H. Randall’s thesis that modern empiricism is rooted in the Scholastic regressus method epitomized by Jacopo Zabarella in De Regressu (1578). Randall’s critics note that the empirical practice of Galileo and his contemporaries does not follow Zabarella. However, Zabarella’s account of the regressus is imprecise, which permitted an interpretation introducing empirical hypothesis testing into the framework. The discourse surrounding Galileo’s lunar observations in Sidereus Nuncius (1610) suggests that both Galileo and his interlocutors amended (...) the regressus method in this way, such that a developmental narrative links Scholastic logic to Galilean science. (shrink)

Open peer commentary on the article “Second-Order Science: Logic, Strategies, Methods” by Stuart A. Umpleby. Upshot: The evaluation of what we knew is an urgent and evolving issue. The issues discussed by Umpleby have been raised earlier, particularly in the social sciences. Arguably, in some quarters they are exaggerated. But an awareness of observer effects is of great importance and is greatly enhanced by second-order cybernetics applied more widely as second-order science.

The first line of Merleau-Ponty 's 1951-52 lecture "The Question of Method in Child Psychology" readt, "In child psychology (as in psychopathology, the psychology of primitives, and the psychology ofwomen), the situation ofthe object of study is so different from that ofthe observer that it cannot be grasped on its own terms." Is there any hope for a feminist reading of Merleau-Ponty's psychology with such a statement, or are women relegated in Merleau-Ponty's corpus alongside the childlike, the insane, and the (...) primitive? This paper endeavors to demonstrate that Merleau-Ponty 's understanding of the psychology of women is not a false or bigoted placing of women in an infant-like position. Rather, he demonstrates that it is precisely this relationship of man to woman that must be the starting point of analysis for both a philosophy and psychology of sex. (shrink)

The article raises the question of the theoretical and cognitive foundations of sociological observation in the system-communication theory of Niklas Luhmann. Observation of society in its entirety is possible only from within itself, and therefore its observer (sociologist, artist, writer, moralist, politician or participant in a social movement) is necessarily included in the observed object itself. This circumstance gives rise to the paradox of self-applicability or self-reference in their social specification, since generalizing statements about society, if they claim to be (...) universal in description, are always applicable to the statements themselves. It is substantiated that the paradoxes of self- applicability and self-reference, without receiving their resolution, are never- theless performatively realized both in social reality itself and in its theoretical representation, and ensure the function of the social system — reflection of the system and the possibility of comparing one’s own observation resources with the methods of observation of adjacent communication systems. Following logic of self-observation, social theory is supplemented by a self-referential theoretical complex (sub-discipline), called “Self-Descriptions” (the fifth book of N. Luhmann’s fundamental work “Societies of Society”). This additional theory specializes in reconstructing the semantics of the concept of society, how society — in its communications, religion, mass media, art, politics, but today primarily in the optics of science — looked and looks at itself. Such inclu- sion of “Self-Description” (“shorthand”, “scene description”) in the corpus of social theory, as its integral and equal part with the function of describing the formation, semantics and theoretical resources of the theory of society itself, has become an important theoretical innovation in the field of social theory. (shrink)

The aim of this paper is to present a new logic-based understanding of the connection between classical kinematics and relativistic kinematics. We show that the axioms of special relativity can be interpreted in the language of classical kinematics. This means that there is a logical translation function from the language of special relativity to the language of classical kinematics which translates the axioms of special relativity into consequences of classical kinematics. We will also show that if we distinguish a (...) class of observers in special relativity and exclude the non-slower-than light observers from classical kinematics by an extra axiom, then the two theories become definitionally equivalent. Furthermore, we show that classical kinematics is definitionally equivalent to classical kinematics with only slower-than-light inertial observers, and hence by transitivity of definitional equivalence that special relativity theory extended with “Ether” is definitionally equivalent to classical kinematics. So within an axiomatic framework of mathematical logic, wee xplicitly show that the transition from classical kinematics to relativistic kinematics is the knowledge acquisition that there is no “Ether”, accompanied by a redefinition of the concepts of time and space. (shrink)

Generating new ideas—innovation and novelty—is central to what those of us practicing science hope to accomplish. We call it research, but what we really aim for is new-search—learning new things about the world and how it works. Charles Peirce gave the name “abduction” to what he described as the only logical operation that introduces any new idea. In this paper, I will focus on an unconventional understanding of abduction, one that goes beyond its usual meaning and concerns the situation when (...) a surprising observation becomes reconfigured as an unintended experiment about a new research problem that previously was not being studied and possibly was unknown. For science, the consequences can be the beginning of a new field of investigation. For the researcher, the consequences can be life-changing. (shrink)

This paper shows that the non-Boolean logic of quantum measurements is more naturally represented by a relatively new 4-operation system of Boolean fractions—conditional events—than by the standard representation using Hilbert Space. After the requirements of quantum mechanics and the properties of conditional event algebra are introduced, the quantum concepts of orthogonality, completeness, simultaneous verifiability, logical operations, and deductions are expressed in terms of conditional events thereby demonstrating the adequacy and efficacy of this formulation. Since conditional event algebra is nearly (...) Boolean and consists merely of ordered pairs of standard events or propositions, quantum events and the so-called “superpositions” of states need not be mysterious, and are here fully explicated. Conditional event algebra nicely explains these non-standard “superpositions” of quantum states as conjunctions or disjunctions of conditional events, Boolean fractions, but does not address the so-called “entanglement phenomena” of quantum mechanics, which remain physically mysterious. Nevertheless, separating the latter phenomena from superposition issues adds clarity to the interpretation of quantum entanglement, the phenomenon of influence propagated at faster than light speeds. With such treacherous possibilities present in all quantum situations, an observer has every reason to be completely explicit about the environmental–instrumental configuration, the conditions present when attempting quantum measurements. Conditional event algebra allows such explication without the physical and algebraic remoteness of Hilbert space. (shrink)