Science, Logic, and Mathematics

Discussive logic was introduced by Jaskowski as a logic of discussion. In this note we show that some natural translation-based formalizations of discussive logic in modal logic do not yield a paraconsistent logic but rather classical logic. Some alternative modal formalizations of discussive logic that avoid the collapse into classical logic are put forward.

Connexive expansions of relevant logics tend to prove every negated implication formula. In this paper I discuss why they tend to satisfy this unsavoury property, and discuss avenues by which it can be avoided, providing logics which stand as proofs of concept that these avenues can be made to work.

The logic subDL and its quantified extension subDLQ were proposed by Badia and Weber (Dialethism and its Applications, 2019: 155-176) as a basis for developing a version of mathematics in which paradoxes are harmless. In the present paper, subDL as defined in the literature is shown to be too strong to support the theories which motivate it. The crucial point is that contraction is derivable in subDL. It follows that the semantic structure used by Badia and Weber to invalidate contraction (...) is not, in fact, a model of subDL. Here we identify the axioms responsible for contraction in subDL and prove that the logic, weakened by removal of these axioms, is contraction-free and paraconsistent. (shrink)

Nilpotent Minimum logic (NML) is a substructural algebraizable logic that is a distinguished member of the family of systems of Mathematical Fuzzy logic, and at the same time it is the axiomatic extension with the prelinearity axiom of Nelson and Markov’s Constructive logic with strong negation. In this paper our main aim is to characterize and axiomatize paraconsistent variants of NML and its extensions defined by (sets of) logical matrices over linearly ordered NM-algebra with lattice filters as designated values, with (...) special emphasis on those that only exclude the falsum truth-value, called non-falsity preserving logics. We also consider turning these non-falsity preserving logics into Logics of Formal Inconsistency by expanding them with a consistency operator, and we axiomatize them as well. Finally, we provide a full description of the logics defined by finite products of matrices over finite NM-chains. (shrink)

COVID-19 did not disappear in the third year (2022) of the global pandemic. On the contrary, the number of infected people several times exceeded the highs of previous years, but the greater morbidity was not accompanied by a relatively comparable number of deaths. Some studies showed that the SARS-CoV-2 virus impact, e.g. in CEE EU countries, characterizes the seasonal intensity as temperatures fall or rise in relative humidity. All researchers agree that the number of COVID-19-infected people is only an estimate (...) based on the volume of tests performed and that the true numbers are usually much higher. The implementation of spatial interaction modeling could potentially aid in the control of the COVID-19 pandemic due to the inherently spatial nature of its diffusion. The gravity models used in this investigation to simulate the regional spread of the COVID-19 epidemic are based methodologically on previous empirical studies. The proposed methodology uses techniques for modeling spatial interactions due to the epidemics described above, which are a direct result of the number of contacts between individuals. The COVID-19 pandemic can be studied regionally using spatial diffusion methods as well as population potential models (spatial interaction models) and visualized using geographic information system software. Empirical verification and geovisualizations are based on available recent population and pandemic statistics that are possible to acquire from national health services. Methodologically, this type of modeling and simulation aimed at reconstructing a factual situation can be defined as abductive chorological inferring. (shrink)

Explainable AI (XAI) provides methods to understand non-interpretable machine learning models. However, we have little knowledge about what legal experts expect from these explanations, including their legal compliance with, and value against European Union legislation. To close this gap, we present the Explanation Dialogues, an expert focus study to uncover the expectations, reasoning, and understanding of legal experts and practitioners towards XAI, with a specific focus on the European General Data Protection Regulation. The study consists of an online questionnaire and (...) follow-up interviews, and is centered around a use-case in the credit domain. We extract both a set of hierarchical and interconnected codes using grounded theory, and present the standpoints of the participating experts towards XAI. We find that the presented explanations are hard to understand and lack information, and discuss issues that can arise from the different interests of the data controller and subject. Finally, we present a set of recommendations for developers of XAI methods, and indications of legal areas of discussion. Among others, recommendations address the presentation, choice, and content of an explanation, technical risks as well as the end-user, while we provide legal pointers to the contestability of explanations, transparency thresholds, intellectual property rights as well as the relationship between involved parties. (shrink)

Paul K Feyerabend’s engagement with physics started before his engagement with philosophy, and he continued to think about new developments in physics until the end. To understand Feyerabend’s philosophy, therefore, it is crucial to understand his views on physics, many of which have remained unpublished until now. Doing so pays off, not only in helping us to understand the history of philosophy of science, but also insofar as it opens up new resources for contemporary philosophy of physics. The papers collected (...) in this special issue demonstrate just how impactful such a project can be. -/- This special issue arrives in two parts, each collecting four papers. The first half was published in 2022. This is the introduction for the second half. (shrink)

This essay offers a discussion and contextualisation of a series of letters exchanged between Jordi Cat and Paul Feyerabend from 1989 to 1994. These letters provide insights into Feyerabend’s later thought on a variety of themes including quantum holism, the disunity of science, the development of logical empiricism, and science activism. In doing so, we provide some original analysis and exegesis of Feyerabend’s evolving views on scientific methodology and quantum mechanics by focusing on Feyerabend’s changing attitudes towards Bohm, Bohr, and (...) his eventual colleague Hans Primas and his later sympathies with the algebraic approach. We also highlight Feyerabend’s role in the growth of the Disunity of Science movement and how he connected disunity to practical considerations in the philosophy of action. (shrink)

In this paper I attempt to broaden Feyerabend scholarship by asking whether and how Feyerabend's philosophy of science, in particular his commitments to realism and pluralism about scientific theories as well as anarchism about scientific methods, is borne out in multidisciplinary research concerning the Leggett–Garg inequalities. These inequalities were derived explicitly to be a temporal analogue to Bell's inequalities: the viability of macroscopic realism is tested against the predictions of quantum mechanics by performing a series measurements on a macroscopic variable (...) of one system at different time intervals, then evaluating correlations among resultant values. In the nearly forty years since Leggett and Garg's paper, questions continue to be raised whether common tests of these inequalities reveal genuine violations or merely experimental disturbances. There is also much debate about what genuine violations in fact signify, if (as most agree) they are not straight-forwardly analogous to Bell tests. Taking this fascinating and as yet largely unsettled episode from physics as a case study, I derive three Feyerabendian lessons that demonstrate the relevance of his views even today. (shrink)

We scan Paul K. Feyerabend's work in philosophy of physics and of science more generally for insights that could be useful for the contemporary debate on the foundations of quantum mechanics. We take as our starting point what Feyerabend has actually written about quantum mechanics, but we extend our analysis to his general views on realism, objectivity, pluralism, and the relation between physics and philosophy, finding that these more general views could in fact offer many interesting insights for physicists and (...) philosophers working on quantum foundations. (shrink)

This paper explores how the epistemic emotions of curiosity, awe, and wonder can motivate us to expand our understanding. Curiosity drives us to fill a local gap in our knowledge. Awe is a mixture of fear and fascination for something so vast and mysterious that it challenges our understanding, thus inciting cognitive accommodation. Wonder is intermediate between curiosity and awe. Awe is commonly understood as a religious emotion, a reverence for the “numinous”—a transcendent reality out of bounds for ordinary humans. (...) Awe has also been conceived as a scientific emotion, a desire to explore an infinite realm of potentiality. The latter defines “raw transcendence”, a willingness to go beyond any boundary imposed by tradition or authority. Newtonian science ignores such emotions, proposing a purely rational, reductionist picture of the world as a clockwork mechanism. However, the new scientific worldview sees the universe as evolving while producing endless novelty. The scientific investigation of this potential can benefit from practices that promote awe and wonder. These include experiencing landscapes, artistic beauty, complex patterns, and mathematical infinity. Awe and wonder thus can help us to realize the Enlightenment's promise of unbounded progress in our understanding of the universe. (shrink)

In this article, which testifies the European dimension of Federigo Enriques, an essential question is raised: is it conceivable to admit a radical antithesis between logical empiricism or neo-empiricism and the Enriquesian view of scientific thought? This paper therefore analyses the relationship between Enriques’ conception of science and that of Otto Neurath, one of the main representatives of neo-empiricism. While the interest towards empiricism in Enriques’ conception of the scientific knowledge is emphasised, it cannot be denied that the relationship of (...) Enriques’ epistemology to the scientific idea of the world appears problematic. However, elements of convergence between Neurath and Enriques are discernible above all in the neo-empiricist principle of verification, in the idea of the unity of science and in the recognition by both of the historical nature of the scientific enterprise. In particular, the comparison is emphasised between Neurath’s idea of the encyclopaedia and Enriques’ rationalism, that highlights how, on closer inspection, Neurath’s critical view is not a true antithesis of the historical perspective of science. (shrink)

This paper aims to analyze a specific way in which a scientific programme or area can, in Lakatosian terms, degenerate: namely, through a developmental process of intellectual inflation. Adopting a pluralist approach to the notion of scientific progress, we propose that the historical development of a particular scientific area can be analyzed as being intellectually inflationary during a bounded period of time if it has considerably increased its productive output (thus displaying productive progress) while the overall semantic or epistemic value (...) of those products have not improved in a significant fashion (thus lacking progress in a semantic or epistemic sense). Then, we apply this concept to thoroughly assess whether there are some intellectually inflationary patterns in the development of two areas of research: (i) information-theoretical evolutionary biology in 1961-2023, and (ii) ensemblist non-equilibrium statistical mechanics in 1938-2023. And finally, we argue that tracking and analyzing intellectually inflationary patterns in the history of sciences might contribute to vindicate a non-productivist picture of current scientific research. (shrink)

Through an examination of Stack Overflow posts, this study explores Docker-related subjects and difficulties in order to pinpoint common problems and patterns in Docker development. We created an extensive dataset of Docker conversations by utilising both tag-based and content-based filtering techniques. These conversations were categorised using Latent Dirichlet Allocation (LDA) topic modelling, which showed that the most common theme is Application Development, which includes topics like Framework Management, Coding Problems, Data Transfer, and Docker-specific frameworks. Because of Docker's strong market presence, (...) developers are very interested in using it to build and manage apps, as evidenced by this dominant category. The study highlights important areas of interest and difficulty within the Docker community and offers insightful information on the many technical and operational problems faced by Docker developers. These findings offer guidance for future research, tool development, and educational resources, aiming to address the evolving needs of Docker practitioners and enhance the overall development experience. (shrink)

This article offers critical analysis of the debate between Karl Popper and Imre Lakatos about distinctive features of empirical science that allow to demarcate it from non-science and especially pseudoscience. Popper's demarcational proposition is explained as involving essentially two requirements, logical (to the theory itself, that it had potential falsifiers) and methodological (to scientists' attitude with respect to the theory, that they were willing to recognise its empirical falsification. Lakatos's criticisms of ‘Popper's basic rule’ that ‘criteria of refutation have to (...) be laid down beforehand’ and Popper's reply to these criticisms, as well as Lakatos's alternative demarcational proposition, are discussed. The argument is made that although Lakatos's criticisms and proposition have considerable merits, he goes too far in claiming that it is OK for scientists to wave away or ignore apparent falsifications of a theory so long as the theory is successful in generating lots of successful unexpectable predictions, and generally understates the importance of the critical attitude for the development of science. On the other hand, Popper's falsificationist approach can be modified so as to accommodate sound points of Lakatos's criticisms and proposition while retaining the basic structure and critical rationalist character of Popper's demarcational proposition. (shrink)

The main drawback of the OFDM system is high Peak to Average Power Ratio (PAPR), which calls for high power amplifiers in the system. This problem can be mitigated by using Block codes that are Non Transparent. We investigated the potential of the Palindromic codes in reducing the PAPR with the proposed biasing method. Using exhaustive search, a bias vector of n bits is chosen and added to all possible codewords (using modulo-2 addition) such that the maximum PAPR of all (...) these codewords is minimized. For making the number of carriers to be a power of two for efficient IFFT/FFT, Redundant Bits are to be added to the biased code word even though there is a slight degradation in PAPR performance. (shrink)

Popper’s (1983, 2002) philosophy of science has enjoyed something of a renaissance in the wake of the replication crisis, offering a philosophical basis for the ensuing science reform movement. However, adherence to Popper’s approach may also be at least partly responsible for the sense of “crisis” that has developed following multiple unexpected replication failures. In this article, I contrast Popper’s approach with that of Lakatos (1978) as well as with a related but problematic approach called naïve methodological falsificationism (NMF; Lakatos, (...) 1978). The Popperian approach is powerful because it is based on logical refutations, but its theories are noncausal and, therefore, potentially lacking in scientific value. In contrast, the Lakatosian approach considers causal theories, but it concedes that these theories are not logically refutable. Finally, NMF represents a hybrid approach that subjects Lakatosian causal theories to Popperian logical refutations. However, its tactic of temporarily accepting a ceteris paribus clause during theory testing may be viewed as scientifically inappropriate, epistemically inconsistent, and “completely redundant” (Lakatos, 1978, p. 40). I conclude that the replication “crisis” makes the most sense in the context of the Popperian and NMF approaches because it is only in these two approaches that the failure to replicate a previously corroborated theory represents a logical refutation of that theory. In contrast, such replication failures are less problematic in the Lakatosian approach because they do not logically refute theories. Indeed, in the Lakatosian approach, replication failures can be temporarily ignored or used to motivate theory development. (shrink)

The proposed system will be implemented as an online website equipped with a user-friendly interface designed to cater to the intuitive navigation needs of undergraduate students. The frontend technologies selected will prioritize usability and responsiveness, ensuring seamless interaction across devices. Meanwhile, robust backend and database technologies will be employed to securely store and efficiently retrieve educational content and user data.

The level of accuracy needed to identify the type of tumor using MRI data is necessary to choose the best method for medical care. The K-Nearest Neighbor approach, a fundamental scientific application and image classification technique, can be used to computationally analyze MRI results. The objective of the tumor classification system is to identify the tumor. The only information used to analyze data for this type of system comes from the MRI's axial portion, which are divided into three categories they (...) are: oligodendroglioma, glioblastoma, and astrocyte. Basic image processing techniques, such as image enhancement, image biniarization, morphological image and watershed are used to identify the tumor region. Tumor categorization achieved findings of 89.5 percent, which may provide more precise and in-depth information about tumor identification. (shrink)