We discuss a generalization of the standard notion of probability space and show that the emerging framework, to be called operational probability theory, can be considered as underlying quantal theories. The proposed framework makes special reference to the convex structure of states and to a family of observables which is wider than the familiar set of random variables: it appears as an alternative to the known algebraic approach to quantum probability.

We study the possibility of representing the proposition lattice associated with a quantum system by a linear vector space with coefficients from ap-adic field. We find inconsistencies if the lattice is assumed, as usual, to be irreducible, complete, orthocomplemented, atomic, and weakly modular.

The probability pattern emerging in two-slit experiments is a typical quantum feature whose essential ingredients are examined by translating them into the spin- $ \frac{1}{2} $ formalism. In view of the existence of extensions of quantum theory preserving some classical structure, we discuss how the two-slit probabilities behave under such extensions. We consider a generalization of the standard classical probability theory, to be called operational probability theory, that turns out to host the so called quantum probabilities.

In this paper I shall venture into an area with which I am not very familiar and in which I feel far from confident; namely into phenomenology. My main motive is not to get away from standard, boring, methodological questions like those of induction and demarcation; but the conviction that a phenomenological account of the empirical basis forms a necessary complement to Popper's falsificationism. According to the latter, a scientific theory is a synthetic and universal, hence unverifiable proposition. In fact, (...) in order to be technologically useful, a scientific hypothesis must refer to future states-of-affairs; it ought therefore to remain unverified. But in order to be empirical, a theory must bear some kind of relation to factual statements. According to Popper, such a relation can only be one of potential conflict. Thus a theory T will be termed scientific if and only if T is logically incompatible with a so-called basic statement b, where b is both empirically verifiable and empirically falsifiable. In other words: T is scientific if it entails ¬b; where b, hence also ¬b, is an empirically decidable proposition. (shrink)

It has been maintained, by both philosophers and modern scientists, that the two domains of discourse of science and of philosophy are disjoint Though admitting that many physicists subscribed to metaphysical principles, it was claimed - by Duhem and Reichenbach among others - that the scientist's philosophical convictions play, or should play, no role in his scientific work. The present paper attempts to refute this separatist view by showing that Einstein's metaphysical realism - coupled with his Platonistic panmathematicism - played (...) a crucial role in his construction of the Relativity Programme and in his criticism of Quantum Mechanics. The article also shows that although Einstein was neither a strict Humean nor a strict Machian, his phenomenalist interpretation of the empirical basis proved to be an antidote against both conventionalist scepticism and Neurath's coherence theory of truth. /// Tanto filósofos como cientistas têm defendido a ideia de que os domínios discursivos da Ciência e da Filosofia seguem caminhos separados. Mesmo admitindo que muitos cientistas subscreveram princípios metafísicos, a ideia tem sido defendida - por Duhem e Reichenbach, entre outros - de que as convicções filosóficas do cientista não desempenham, ou deveriam não desempenhar, qualquer papel no seu trabalho científico. O objectivo do presente artigo é refutar esta visão separatista das coisas mostrando de que modo o realismo metafísico de Einstein - associado ao seu panmatematicismo platónico - desempenhou um papel crucial na sua construção do Programa da Relatividade e nas suas críticas à Mecânica Quântica. O artigo mostra igualmente que embora Einstein não fosse nem um Humeano estrito nem um estrito Macheano, a sua interpretação fenomenalista da base empírica demonstrou ser um antídoto quer contra o cepticismo convencionalista quer contra a teoria da coerência da verdade de Neurath. (shrink)

Despite the periodic table having been discovered by chemists half a century before the discovery of electronic structure, modern designs are invariably based on physicists’ definition of periods. This table is a chemists’ table, reverting to the phenomenal periods that led to the table’s discovery. In doing so, the position of hydrogen is clarified.

The Term ‘liberty’ invokes such universal respect that most modern political economists and moralists endeavour to find a conspicuous place for it somewhere in their systems or prescriptions. But in view of the innumerable senses of this term an insistence on some kind of definition prior to any discussion seems to be justified. For our present purposes attention to two particularly conflicting interpretations will be sufficient. These are sometimes called the ‘negative’ and the ‘positive’ notions of Liberty. According to the (...) ‘negative’ notion, my own liberty implies the reduction to a minimum of the deliberate interference of other human beings within the area in which I wish to act. Conversely the absence of liberty, or coercion, is regarded as undesirable because it amounts to the prevention by other persons of my doing what I want. On the other hand, the ‘positive’ sense of the word ‘liberty’ consists in the attainment of self-mastery, or, in other words, the release from the domination of ‘adverse’ influences. This ‘slavery’ from which men ‘liberate’ themselves is variously described to include slavery to ‘nature’, to ‘unbridled passions’, to ‘irrational impulses’, or simply slavery to one's ‘lower nature’. ‘Positive’ liberty is then identified with ‘self-realisation’ or an awakening into a conscious state of rationality. The fact that it is contended that such a state can often be attained only by the interference of other ‘rational’ persons who ‘liberate’ their fellow beings from their ‘irrationality’, brings this interpretation of liberty into open and striking conflict with liberty in the ‘negative’ sense. (shrink)

This article, in the example of the subject of shukr (gratitude), proposes a ‘perspective’ for the instructor who determines the processes of bringing a subject into the learning environment. This perspective is related to the encounter with the knowledge of the subject to be taught. It points to the approach of the instructor to the information he/she will refer to about the subject he/she will teach while preparing in the mental plan. The content of the subject, the objectives, the methods, (...) techniques, and resources to be used to present the subject, and how the output will be measured and evaluated are largely determined by this perspective. In a way, the proposed perspective involves monitoring the change and transformation of life and the contextualization of religious knowledge by paying attention to the methodological functioning. Thus, the way the subject of gratitude presented in the Qur’an and hadith narrations aims to provide the teacher with a ‘perspective’ on what kind of content to prepare. This is a suggestion for the instructor to reveal that while managing the process of religiously understanding/interpreting life as it flows by, the instructor should not ignore the ways in which knowledge appears in the Qur’an and hadith narrations. For example, the first meaning of the word shukr (gratitude) in the Qur’an is “faith in Allah.” However, traditionally, shukr (gratitude) is not taught within the subject area of faith. In this context, the article follows the suggestion that referring to the method and source of the knowledge to be taught can provide the instructor with a holistic and in-depth ‘perspective.’. (shrink)