When adopting a sound logical system, reasonings made within this system are correct. The situation with reasonings expressed, at least in part, with natural language is much more ambiguous. One way to be certain of the correctness of these reasonings is to provide a logical model of them. To conclude that a reasoning process is correct we need the logical model to be faithful to the reasoning. In this case, the reasoning inherits, so to speak, the correctness of the logical (...) model. There is a weak link in this procedure, which we call the faithfulness problem: how do we decide that the logical model is faithful to the reasoning that it is supposed to model? That is an issue external to logic, and we do not have rigorous formal methods to make the decision. The purpose of this paper is to expose the faithfulness problem (not to solve it). For that purpose, we will consider two examples, one from the geometrical reasoning in Euclid’s Elements and the other from a study on deductive reasoning in the psychology of reasoning. (shrink)

The received view in philosophical studies of quantum field theory is that Feynman diagrams are simply calculational devices. Alongside this view we have the one that takes virtual quanta to be also simply formal tools. This received view was developed and consolidated in philosophy of physics by Mario Bunge, Paul Teller, Michael Redhead, Robert Weingard, Brigitte Falkenburg, and others. In this article I present an alternative to the received view.

ABSTRACT In Einstein’s physical geometry, the geometry of space and the uniformity of time are taken to be non-conventional. However, due to the stipulation of the isotropy of the one-way speed of light in the synchronization of clocks, as it stands, Einstein’s views do not seem to apply to the whole of the Minkowski space-time. In this work we will see how Einstein’s views can be applied to the Minkowski space-time. In this way, when adopting Einstein’s views, chronogeometry is a (...) physical chronogeometry. (shrink)

The purpose of this work is to address what notion of geometrical object and geometrical figure we have in different kinds of geometry: practical, pure, and applied. Also, we address the relation between geometrical objects and figures when this is possible, which is the case of pure and applied geometry. In practical geometry it turns out that there is no conception of geometrical object.

Quantum electrodynamics presents intrinsic limitations in the description of physical processes that make it impossible to recover from it the type of description we have in classical electrodynamics. Hence one cannot consider classical electrodynamics as reducing to quantum electrodynamics and being recovered from it by some sort of limiting procedure. Quantum electrodynamics has to be seen not as a more fundamental theory, but as an upgrade of classical electrodynamics, which permits an extension of classical theory to the description of phenomena (...) that, while being related to the conceptual framework of the classical theory, cannot be addressed from the classical theory. (shrink)

In this work we will consider gauge interpretations of the conventionality of simultaneity as developed initially by Anderson and Stedman, and later by Rynasiewicz. We will make a critical reassessment of these interpretations in relation to the “tradition” as developed in particular by Reichenbach, Grünbaum, and Edwards. This paper will address different issues, including: the relation between these two gauge interpretations; what advantages or defects these gauge approaches might have; how “new” Rynasiewicz’s approach in relation to the previous ones is; (...) how much of the gauge interpretation Rynasiewicz actually applies to deal with objections to the conventionality of simultaneity thesis. The conclusion is that the gauge interpretations, in their current formulation, do not provide a better “rationale” of the conventionality of simultaneity thesis that supersedes the “tradition”. (shrink)

In this work, we consider the views of three exponents of major areas of linguistics – Levelt (psycholinguistics), Jackendoff (theoretical linguistics), and Gil (field linguistics) – regarding the issue of the universality or not of the conceptual structure of languages. In Levelt’s view, during language production, the conceptual structure of the preverbal message is language-specific. In Jackendoff’s theoretical approach to language – his parallel architecture –, there is a universal conceptual structure shared by all languages, in contradiction to Levelt’s view. (...) In Gil’s work on Riau Indonesian, he proposes a conceptual structure that is quite different from that of English, adopted by Jackendoff as universal. We find no reason to disagree with Gil’s view. In this way, we take Gil’s work as vindicating Levelt’s view that during language production preverbal messages are encoded with different conceptual structures for different languages. (shrink)

Philosophy of Physics has emerged recently as a scholarly important subfield of philosophy of science. However outside the small community of experts it is not a well-known field. It is not clear even to experts the exact nature of the field: how much philosophical is it? What is its relation to physics? In this work it is presented an overview of philosophy of physics that tries to answer these and other questions.

A re-evaluation of the notion of vacuum in quantum electrodynamics is presented, focusing on the vacuum of the quantized electromagnetic field. In contrast to the ‘nothingness’ associated to the idea of classical vacuum, subtle aspects are found in relation to the vacuum of the quantized electromagnetic field both at theoretical and experimental levels. These are not the usually called vacuum effects. The view defended here is that the so-called vacuum effects are not due to the ground state of the quantized (...) electromagnetic field. Nevertheless it is possible to maintain an empirically demonstrable notion of vacuum state that is consistent with the interpretation of the formalism of the theory. (shrink)

In this paper, we will make explicit the relationship that exists between geometric objects and geometric figures in planar Euclidean geometry. That will enable us to determine basic features regarding the role of geometric figures and diagrams when used in the context of pure and applied planar Euclidean geometry, arising due to this relationship. By taking into account pure geometry, as developed in Euclid’s Elements, and practical geometry, we will establish a relation between geometric objects and figures. Geometric objects are (...) defined in terms of idealizations of the corresponding figures of practical geometry. We name the relationship between them as a relation of idealization. This relation, existing between objects and figures, is what enables figures to have a role in pure and applied geometry. That is, we can use a figure or diagram as a representation of geometric objects or composite geometric objects because the relation of idealization corresponds to a resemblance-like relationship between objects and figures. Moving beyond pure geometry, we will defend that there are two other ‘layers’ of representation at play in applied geometry. To show that, we will consider Euclid’s Optics. (shrink)

When modeling informal proofs like that of Euclid’s Elements using a sound logical system, we go from proofs seen as somewhat unrigorous – even having gaps to be filled – to rigorous proofs. However, metalogic grounds the soundness of our logical system, and proofs in metalogic are not like formal proofs and look suspiciously like the informal proofs. This brings about what I am calling here the groundedness problem: how can we decide with certainty that our metalogical proofs are rigorous (...) and sustain our logical system? In this paper, I will expose this problem. I will not try to solve it here. (shrink)

It has been argued in relation to Old Babylonian mathematical procedure texts that their validity or correctness is self-evident. One “sees” that the procedure is correct without it having, or being accompanied by, any explicit arguments for the correctness of the procedure. Even when agreeing with this view, one might still ask about how is the correctness of a procedure articulated? In this work, we present an articulation of the correctness of ancient Egyptian and Old Babylonian mathematical procedure texts – (...) mathematical texts presenting the solution of problems. We endeavor to make explicit and explain how and why the procedures are reliable over and above the fact that their correctness is intuitive. (shrink)

In a way similar to classical mechanics where we have the concept of inertial time as expressed in the motions of bodies, in the theory of relativity we can regard the inertial time as the only notion of time at play. The inertial time is expressed also in the propagation of light. This gives rise to a notion of clock—the light clock, which we can regard as a notion derived from the inertial time. The light clock can be seen as (...) a solution of the theory, which complies with the requirement that a clock to be so must have a rate that is independent from its past history. Contrary to Einstein’s view, we do not need the concept of “clock” as an independent concept. This implies, in particular, that we do not need to rely on the notions of atomic clock or atomic time in the theory of relativity. (shrink)

The clock hypothesis is taken to be an assumption independent of special relativity necessary to describe accelerated clocks. This enables to equate the time read off by a clock to the proper time. Here, it is considered a physical system–the light clock–proposed by Marzke and Wheeler. Recently, Fletcher proved a theorem that shows that a sufficiently small light clock has a time reading that approximates to an arbitrary degree the proper time. The clock hypothesis is not necessary to arrive at (...) this result. Here, one explores the consequences of this regarding the status of the clock hypothesis. (shrink)