Esta enciclopédia abrange, de uma forma introdutória mas desejavelmente rigorosa, uma diversidade de conceitos, temas, problemas, argumentos e teorias localizados numa área relativamente recente de estudos, os quais tem sido habitual qualificar como «estudos lógico-filosóficos». De uma forma apropriadamente genérica, e apesar de o território teórico abrangido ser extenso e de contornos por vezes difusos, podemos dizer que na área se investiga um conjunto de questões fundamentais acerca da natureza da linguagem, da mente, da cognição e do raciocínio humanos, bem (...) como questões acerca das conexões destes com a realidade não mental e extralinguística. A razão daquela qualificação é a seguinte: por um lado, a investigação em questão é qualificada como filosófica em virtude do elevado grau de generalidade e abstracção das questões examinadas (entre outras coisas); por outro, a investigação é qualificada como lógica em virtude de ser uma investigação logicamente disciplinada, no sentido de nela se fazer um uso intenso de conceitos, técnicas e métodos provenientes da disciplina de lógica. O agregado de tópicos que constitui a área de estudos lógico-filosóficos é já visível, pelo menos em parte, no Tractatus Logico-Philosophicus de Ludwig Wittgenstein, uma obra publicada em 1921. E uma boa maneira de ter uma ideia sinóptica do território disciplinar abrangido por esta enciclopédia, ou pelo menos de uma porção substancial dele, é extrair do Tractatus uma lista dos tópicos mais salientes aí discutidos; a lista incluirá certamente tópicos do seguinte género, muitos dos quais se podem encontrar ao longo desta enciclopédia: factos e estados de coisas; objectos; representação; crenças e estados mentais; pensamentos; a proposição; nomes próprios; valores de verdade e bivalência; quantificação; funções de verdade; verdade lógica; identidade; tautologia; o raciocínio matemático; a natureza da inferência; o cepticismo e o solipsismo; a indução; as constantes lógicas; a negação; a forma lógica; as leis da ciência; o número. (shrink)

An Objectivity Principle (O) and a Locality Principle (L) are considered with respect to two simple, but fundamental Gedanken experiments, namely a “Welcher-Weg” Gedanken experiment and an Einstein-Podolsky-Rosen (EPR) Gedanken experiment. It is shown that, if both principles (O) and (L) are assumed to be valid, a contradiction, in the EPR case Bell’s inequality, can be derived implying that at least one of the two principles (O) and (L) has to be denied. It is shown that, if (O) is denied, (...) (L) is preserved in the EPR-Gedanken experiment. For a more adequate discussion, in particular of (L), the two experiments are described in Minkowskian space-time of special relativity. (shrink)

The main aim of the paper is to solve a problem posed in Di Nola et al. (Multiple Val. Logic 8:715–750, 2002) whether every pseudo BL-algebra with two negations is good, i.e. whether the two negations commute. This property is intimately connected with possessing a state, which in turn is essential in quantum logical applications. We approach the solution by describing the structure of pseudo BL-algebras and pseudo hoops as important families of quantum structures. We show when a pseudo hoop (...) can be embedded into the negative cone of the reals. We give an equational base characterizing representable pseudo hoops. We also describe some subvarieties: normal-valued, and varieties where each maximal filter is normal. We produce some noncommutative covers and extend the area where each algebra is good. Finally, we show that there are uncountably many subvarieties of pseudo BL-algebras having members that are not good. (shrink)

The main goal of quantum logic is the bottom-up reconstruction of quantum mechanics in Hilbert space. Here we discuss the question whether quantum logic is an empirical structure or a priori valid. There are good reasons for both possibilities. First, with respect to the possibility of a rational reconstruction of quantum mechanics, quantum logic follows a priori from quantum ontology and can thus not be considered as a law of nature. Second, since quantum logic allows for a reconstruction of quantum (...) mechanics, self-referential consistency requires that the empirical content of quantum mechanics must be compatible with the presupposed quantum ontology. Hence, quantum ontology contains empirical components that are also contained in quantum logic. Consequently, in this sense quantum logic is also a law of nature. (shrink)

Using the mathematical notion of an entity to represent states in quantum and classical mechanics, we show that, in a strict sense, proper superpositions are possible in classical mechanics.

This article offers a critical review of various ontological-relativist arguments, mostly deriving from the work of W. V. Quine and Thomas K hn. I maintain that these arguments are (1) internally contradictory, (2) incapable of accounting for our knowledge of the growth of scientific knowledge, and (3) shown up as fallacious from the standpoint of a causal-realist approach to issues of truth, meaning, and interpretation. Moreover, they have often been viewed as lending support to such programmes as the 'strong' sociology (...) of knowledge and the turn towards wholesale cultural-relativist doctrines, whether of the Wittgensteinian ('language-games') or Heideggerian (depth-hermeneutic) varieties. Thus Richard Rorty recommends that we should henceforth drop all that old-fashioned talk of 'truth', 'knowledge', or 'reality', since whatever warrants those descriptions from time to time is just the product of some currently favoured language-game or range of elective metaphors. Such ideas have little in common with Quine's general outlook of robust physicalism, nor again - though the case is less clear - with Kuhn's reconsidered approach to these issues as set forth in his 1969 Postscript to The Structure of Scientific Revolutions . However, both thinkers have left themselves open to misconstrual by adopting a sceptical-relativist fallback position in response to the well-known problems with logical empiricism. This essay therefore reviews those problems with reference to alternative, more adequate accounts of what is involved in the process of scientific discovery and theory-change. (shrink)

The author investigates which methods of naming objects are possible in the language of physics on the basis of the real physical conditions and to which extend objects thereby can be identified. It is shown that in the language of classical physics naming by designation is always possible. But this implies only the temporal identity of objects, not the "trans - world" - identity, which is important for modalities. In the language of quantum physics naming by designation is no longer (...) applicable to individuals but only to classes of equivalent objects. And for these classes temporal identity as well as the "trans - world" - identity can be produced, which means that an adequate semantics can be specified for the concept of possibility necessary in this language. (shrink)

Based on the notion of time translation, we develop a formalism to deal with the logic of quantum properties at different times. In our formalism it is possible to enlarge the usual notion of context to include composed properties involving properties at different times. We compare our results with the theory of consistent histories.

In the present work are identified the main features of the algebraic structure with respect to the logical operations, of the set of all the quantum mechanical utterances for which can be specified a factual counterpart and factual rules for truth valuation. This structure is found not to be a lattice. It depends crucially on the spacetime features of the operations by which the observer prepares the studied states and performs measurements on them.

The so-called classical limit of quantum mechanics is generally studied in terms of the decoherence of the state operator that characterizes a system. This is not the only possible approach to decoherence. In previous works we have presented the possibility of studying the classical limit in terms of the decoherence of relevant observables of the system. On the basis of this approach, in this paper we introduce the classical limit from a logical perspective, by studying the way in which the (...) logical structure of quantum properties corresponding to relevant observables acquires Boolean characteristics. (shrink)

This article proposes a basic logic for application in physics dispensing with the Principle of Excluded Middle. It is based on the article “Matrix Based Logics for Application in Physics (RMQ) which appeared 2009. In his article with Stachow on the Principle of Excluded Middle in Quantum Logic (QL), Peter Mittelstaedt showed that for some suitable QLs, including their own, the Principle of Excluded Middle can be added without any harm for QL; where ‘without any harm for QL’ means that (...) the basic desiderata and the basic results (theorems) of those QLs remain satised in the sense that they avoid the well known difficulties with commensurability and distributivity.In the following article I want to show that the basic desiderata and results (theorems) of RMQ (of avoiding the well-known difficulties with commensurability, distributivity, fusion and Bell’s inequalities) remain satised if by introducing a strong negation (or strong negation and disjunction) the resulting weak intuitionist system RMQI dispenses with the Principle of Excluded Middle; it becomes either invalid or not strictly valid. (shrink)

Es werden die Veränderungen der Wissenschaftssprache der Physik untersucht, die durch den Übergang von der klassich-relativistichen Physik zur Quantenphysik erfolgt sind. Die neuen und prinzipiellen Beschränkungen der Möglichkeiten der Überprüfung wissenschaftlicher Aussagen führen zu Reduktionen der hypothetischen Annahmen, die der Sprache der klassischen Physik zu Grunde liegen. Diese Reduktionen haben ihrerseits Abschwächungen der syntaktischen Strukturen zur Folge, die besonders in der formalen Logik und der Modallogik deutlich werden. Diese auf schwächeren Prämissen basierenden Strukturen sind die Quanten-Logik und die Quanten-Modallogik, die (...) damit auch einen weiteren Geltungsbereich besitzen als die entsprechenden klassischen formalen Systeme. (shrink)

The hypotheses of weak and strong objectification of quantum mechanical observables, as well as theoretical arguments and experimental evidence against these hypotheses, are systematically reviewed.

In this essay, I offer a critical evaluation of Hilary Putnam's writings on epistemology and philosophy of science, in particular his engagement with interpretative problems in quantum mechanics. I trace the development of his thinking from the late 1960s when he adopted a strong causal-realist position on issues of meaning, reference, and truth, via the "internal realist" approach of his middle-period writings, to the various forms of pragmatist, naturalized, or "commonsense" epistemology proposed in his latest books. My contention is that (...) Putnam's retreat from a full-fledged realist outlook has been prompted in large part by his belief that it cannot possibly be reconciled with the implications of quantum mechanics for our understanding of processes and events in the subatomic domain. However, I suggest, this response should be seen as premature given the range of as-yet unresolved problems with quantum mechanics on the orthodox (Copenhagen) interpretation and also the existence of an alternative account - David Bohm's hidden-variables theory - which perfectly matches the established predictive-observational results while providing a credible realist ontology. I also examine Putnam's case for adopting a nonstandard (three-valued) "quantum logic" in relation to the thinking of other philosophers - Michael Dummett among them - who have espoused a more global or doctrinaire version of anti-realism. I conclude that Putnam's early (causal-realist) position is by no means untenable in light of the various arguments that he now takes as counting decisively against it. (shrink)

This paper addresses the theoretical notion of a game as it arisesacross scientific inquiries, exploring its uses as a technical andformal asset in logic and science versus an explanatory mechanism. Whilegames comprise a widely used method in a broad intellectual realm(including, but not limited to, philosophy, logic, mathematics,cognitive science, artificial intelligence, computation, linguistics,physics, economics), each discipline advocates its own methodology and aunified understanding is lacking. In the first part of this paper, anumber of game theories in formal studies are critically (...) surveyed. Inthe second part, the doctrine of games as explanations for logic isassessed, and the relevance of a conceptual analysis of games tocognition discussed. It is suggested that the notion of evolution playsa part in the game-theoretic concept of meaning. (shrink)

Logic and philosophy of science share a long history, though contacts have gone through ups and downs. This paper is a brief survey of some major themes in logical studies of empirical theories, including links to computer science and current studies of rational agency. The survey has no new results: we just try to make some things into common knowledge.

The paper describes in detail the procedure of identification of the inner language and an inner logico of a physical theory. The procedure is a generalization of the original ideas of J. von Neuman and G. Birkhoff about quantum logic.

The determination of the past and the future of a physical system are complementary aims of measurements. An optimal determination of the past of a system can be achieved by an informationally complete set of physical quantities. Such a set is always strongly noncommutative. An optimal determination of the future of a physical system can be obtained by a Boolean complete set of quantities. The two aims can be reconciled to a reasonable degree with using unsharp measurements.

Quantum mechanics is troubled by the problem of nonlocality inherent in the theory. In a series of papers we explore the possibility of an algebraic formulation of quantum mechanics based on local observables which would incorporate nonlocality when small distances are involved but would be separable at large distances. This paper reviews some of the basic ideas and theories developed recently. These include a unified localization scheme, the introduction of local comoving evolution, local comoving observables, and related conservation laws. Technical (...) considerations and mathematical jargon are kept to a minimum to avoid obscuring physical reasoning. (shrink)

Starting with the Born interpretation of quantum mechanics, we show that the quantum theory of measurement, supplemented by the strong law of large numbers, leads to a measurement statistics interpretation of quantum mechanics. A probabilistic characterization of the spectrum of a physical quantity is given, and an analysis of the notions of possible values and possible measurement results is carried out.

Paraconsistent quantum logics are weak forms of quantum logic, where the noncontradiction and the excluded-middle laws are violated. These logics find interesting applications in the operational approach to quantum mechanics. In this paper, we present an axiomatization, a Kripke-style, and an algebraic semantical characterization for two forms of paraconsistent quantum logic. Further developments are contained in Giuntini and Greuling's paper in this issue.

The purpose of the paper is to show that by cleaning Classical Logic (CL) from redundancies (irrelevances) and uninformative complexities in the consequence class and from too strong assumptions (of CL) one can avoid most of the paradoxes coming up when CL is applied to empirical sciences including physics. This kind of cleaning of CL has been done successfully by distinguishing two types of theorems of CL by two criteria. One criterion (RC) forbids such theorems in which parts of the (...) consequent (conclusion) can be replaced by arbitrary parts salva validitate of the theorem. The other (RD) reduces the consequences to simplest conjunctive consequence elements. Since the application of RC and RD to CL leads to a logic without the usual closure conditions, an approximation to RC and RD has been constructed by a basic logic with the help of finite (6-valued) matrices. This basic logic called RMQ (relevance, matrix, Quantum Physics) is consistent and decidable. It distinguishes two types of validity (strict validity) and classical or material validity. All theorems of CL (here: classical propositional calculus CPC) are classically or materially valid in RMQ. But those theorems of CPC which obey RC and RD and avoid the difficulties in the application to empirical sciences and to Quantum Physics are separated as strictly valid in RMQ. In the application to empirical sciences in general the proposed logic avoids the well known paradoxes in the area of explanation, confirmation, versimilitude and Deontic Logic. Concerning the application to physics it avoids also the difficulties with distributivity, commensurability and with Bell's inequalities. (shrink)

Logic and philosophy of science share a long history, though contacts have gone through ups and downs. This paper is a brief survey of some major themes in logical studies of empirical theories, including links to computer science and current studies of rational agency. The survey has no new results: we just try to make some things into common knowledge.

The paper offers a matrix-based logic (relevant matrix quantum physics) for propositions which seems suitable as an underlying logic for empirical sciences and especially for quantum physics. This logic is motivated by two criteria which serve to clean derivations of classical logic from superfluous redundancies and uninformative complexities. It distinguishes those valid derivations (inferences) of classical logic which contain superfluous redundancies and complexities and are in this sense from those which are or in the sense of allowing only the most (...) informative consequences in the derivations. The latter derivations are strictly valid in RMQ, whereas the former are only materially valid. RMQ is a decidable matrix calculus which possesses a semantics and has the finite model property. It is shown in the paper how RMQ by its strictly valid derivations can avoid the difficulties with commensurability, distributivity, and Bell's inequalities when it is applied to quantum physics. (shrink)

The purpose of this paper is to sketch an attack on the general problem of representing a composite physical system in terms of its constituent parts. For quantum-mechanical systems, this is traditionally accomplished by forming either direct sums or tensor products of the Hilbert spaces corresponding to the component systems. Here, a more general mathematical construction is given which includes the standard quantum-mechanical formalism as a special case.

The possibilities of a realistic interpretation of quantum mechanics are investigated by means of a statistical analysis of experiments performed on the simplest type of quantum systems carrying spin or helicity. To this end, fundamental experiments, some new, for measuring polarization are reviewed and (re)analyzed. Theunsharp reality of spin is essential in the interpretation of some of these experiments and represents a natural motivation for recent generalizations of quantum mechanics to a theory incorporating effect-valued measures as unsharp observables and generalized (...) systems of imprimitivity. (shrink)