A proof of Fermat’s last theorem is demonstrated. It is very brief, simple, elementary, and absolutely arithmetical. The necessary premises for the proof are only: the three definitive properties of the relation of equality (identity, symmetry, and transitivity), modus tollens, axiom of induction, the proof of Fermat’s last theorem in the case of n = 3 as well as the premises necessary for the formulation of the theorem itself. It involves a modification of Fermat’s approach of infinite descent. The infinite (...) descent is linked to induction starting from n = 3 by modus tollens. An inductive series of modus tollens is constructed. The proof of the series by induction is equivalent to Fermat’s last theorem. As far as Fermat had been proved the theorem for n = 4, one can suggest that the proof for n ≥ 4 was accessible to him. An idea for an elementary arithmetical proof of Fermat’s last theorem (FLT) by induction is suggested. It would be accessible to Fermat unlike Wiles’s proof (1995). (shrink)

The paper continues the consideration of Hilbert mathematics to mathematics itself as an additional “dimension” allowing for the most difficult and fundamental problems to be attacked in a new general and universal way shareable between all of them. That dimension consists in the parameter of the “distance between finiteness and infinity”, particularly able to interpret standard mathematics as a particular case, the basis of which are arithmetic, set theory and propositional logic: that is as a special “flat” case of Hilbert (...) mathematics. The following four essential problems are considered for the idea to be elucidated: Fermat’s last theorem proved by Andrew Wiles; Poincaré’s conjecture proved by Grigori Perelman and the only resolved from the seven Millennium problems offered by the Clay Mathematics Institute (CMI); the four-color theorem proved “machine-likely” by enumerating all cases and the crucial software assistance; the Yang-Mills existence and mass gap problem also suggested by CMI and yet unresolved. They are intentionally chosen to belong to quite different mathematical areas (number theory, topology, mathematical physics) just to demonstrate the power of the approach able to unite and even unify them from the viewpoint of Hilbert mathematics. Also, specific ideas relevant to each of them are considered. Fermat’s last theorem is shown as a Gödel insoluble statement by means of Yablo’s paradox. Thus, Wiles’s proof as a corollary from the modularity theorem and thus needing both arithmetic and set theory involves necessarily an inverse Grothendieck universe. On the contrary, its proof in “Fermat arithmetic” introduced by “epoché to infinity” (following the pattern of Husserl’s original “epoché to reality”) can be suggested by Hilbert arithmetic relevant to Hilbert mathematics, the mediation of which can be removed in the final analysis as a “Wittgenstein ladder”. Poincaré’s conjecture can be reinterpreted physically by Minkowski space and thus reduced to the “nonstandard homeomorphism” of a bit of information mathematically. Perelman’s proof can be accordingly reinterpreted. However, it is valid in Gödel (or Gödelian) mathematics, but not in Hilbert mathematics in general, where the question of whether it holds remains open. The four-color theorem can be also deduced from the nonstandard homeomorphism at issue, but the available proof by enumerating a finite set of all possible cases is more general and relevant to Hilbert mathematics as well, therefore being an indirect argument in favor of the validity of Poincaré’s conjecture in Hilbert mathematics. The Yang-Mills existence and mass gap problem furthermore suggests the most general viewpoint to the relation of Hilbert and Gödel mathematics justifying the qubit Hilbert space as the dual counterpart of Hilbert arithmetic in a narrow sense, in turn being inferable from Hilbert arithmetic in a wide sense. The conjecture that many if not almost all great problems in contemporary mathematics rely on (or at least relate to) the Gödel incompleteness is suggested. It implies that Hilbert mathematics is the natural medium for their discussion or eventual solutions. (shrink)

In this dissertation we present proof systems for several modal logics. These proof systems are based on analytic (or semantic) tableaux. -/- Modal logics are logics for reasoning about possibility, knowledge, beliefs, preferences, and other modalities. Their semantics are almost always based on Saul Kripke’s possible world semantics. In Kripke semantics, models are represented by relational structures or, equivalently, labeled graphs. Syntactic formulas that express statements about knowledge and other modalities are evaluated in terms of such models. -/- This dissertation (...) focuses on modal logics with dynamic operators for public announcements, belief revision, preference upgrades, and so on. These operators are defined in terms of mathematical operations on Kripke models. Thus, for example, a belief revision operator in the syntax would correspond to a belief revision operation on models. -/- The ‘dynamic’ semantics of dynamic modal logics are a clever way of extending languages without compromising on intuitiveness. We present ‘dynamic’ tableau proof systems for these dynamic semantics, with the express aim to make them conceptually simple, easy to use, modular, and extensible. This we do by reflecting the semantics as closely as possible in the components of our tableau system. For instance, dynamic operations on Kripke models have counterpart dynamic relations between tableaux. -/- Soundness, completeness, and decidability are three of the most important properties that a proof system may have. A proof system is sound if and only if any formula for which a proof exists, is true in every model. A proof system is complete if and only if for any formula that is true in all models, a proof exists. A proof system is decidable if and only if any formula can be proved to be a theorem or not a theorem in a finite number of steps. All proof systems in this dissertation are sound, complete, and decidable. -/- Part of our strategy to create modular tableau systems is to delay concerns over decidability until after soundness and completeness have been established. Decidability is attained through the operations of folding and through operations on ‘tableau cascades’, which are graphs of tableaux. -/- Finally, we provide a proof-of-concept implementation of our dynamic tableau system for public announcement logic in the Clojure programming language. (shrink)

Jury theorems are mathematical theorems about the ability of collectives to make correct decisions. Several jury theorems carry the optimistic message that, in suitable circumstances, ‘crowds are wise’: many individuals together (using, for instance, majority voting) tend to make good decisions, outperforming fewer or just one individual. Jury theorems form the technical core of epistemic arguments for democracy, and provide probabilistic tools for reasoning about the epistemic quality of collective decisions. The popularity of jury theorems spans across various disciplines such (...) as economics, political science, philosophy, and computer science. This entry reviews and critically assesses a variety of jury theorems. It first discusses Condorcet's initial jury theorem, and then progressively introduces jury theorems with more appropriate premises and conclusions. It explains the philosophical foundations, and relates jury theorems to diversity, deliberation, shared evidence, shared perspectives, and other phenomena. It finally connects jury theorems to their historical background and to democratic theory, social epistemology, and social choice theory. (shrink)

Empirically-informed approaches to emotion often construe our emotions as modules: systems hardwired into our brains by evolution and purpose-built to generate certain coordinated patterns of expressive, physiological, behavioural and phenomenological responses. In ‘Against Modularity’ (2008), de Sousa argues that we shouldn’t think of our emotions in terms of a limited number of modules because this conflicts with our aspirations for a life of greater emotional richness. My aim in this paper is to defend de Sousa’s critique of modular emotion (...) taxonomies from some obvious rejoinders, and to develop his positive proposal as to how we might reconcile the evidence for emotional modularity with an attitude of disapproval towards rigid emotion taxonomies. (shrink)

In this paper, I make a case for the modularity of the motor system. I start where many do in discussions of modularity, by considering the extent to which the motor system is cognitively penetrable, i.e., the extent to which its processing and outputs are causally influenced, in a semantically coherent way, by states of central cognition. I present some empirical findings from a range of sensorimotor adaptation studies that strongly suggest that there are limits to such influence (...) under certain conditions. These results cry out for an explanation. In the remainder of the paper, I provide one: The motor system is cognitively penetrable, but nonetheless modular along broadly Fodorian lines, insofar as it is informationally encapsulated. This means that its access is limited to its own proprietary database in computing its function from input to output, which does not include the information stored in central cognition. I then offer a model of action control, from distal intention to action outcomes, that further helps to illustrate this picture and can accommodate the target empirical findings. (shrink)

Computer assisted theorem proving is an increasingly important part of mathematical methodology, as well as a long-standing topic in artificial intelligence (AI) research. However, the current generation of theorem proving software have limited functioning in terms of providing new proofs. Importantly, they are not able to discriminate interesting theorems and proofs from trivial ones. In order for computers to develop further in theorem proving, there would need to be a radical change in how the software functions. Recently, machine learning results (...) in solving mathematical tasks have shown early promise that deep artificial neural networks could learn symbolic mathematical processing. In this paper, I analyze the theoretical prospects of such neural networks in proving mathematical theorems. In particular, I focus on the question how such AI systems could be incorporated in practice to theorem proving and what consequences that could have. In the most optimistic scenario, this includes the possibility of autonomous automated theorem provers (AATP). Here I discuss whether such AI systems could, or should, become accepted as active agents in mathematical communities. (shrink)

Learner’s attitude towards modular distance learning catches uncertainties as a world crisis occurs up to this point. As self-learning modules (SLMs) become a supplemental means of learning in new normal education, this study investigated efficiency towards the learners’ attitude and performance. Specifically, the study described the learners’ profile and their attitude and performance towards SLMs. It also ascertained the relationship between the learner’s profile with their attitude and performance, as well as the relationship between attitude and performance relevant to SLMs. (...) A descriptive-correlational research design was employed in the study with 88 non-randomly chosen participants from secondary schools in West Philippines. The learners’ GWA (general weighted average) was used to determine their performance and a survey questionnaire for their profile and attitude. Frequency counts, percentage, and Spearman’s rank correlation coefficient were used to analyze the data gathered with the aid of Jamovi software. Results revealed a strong correlation between attitude and performance, but there was no link between learner’s attitude and performance as to the learner’s profile. It was affirmed that attitude is a compelling factor that is related with performance. Hence, this research has broader ramifications that can direct the Bureau of Learning Delivery to orient the module writers to further contextualize the learning materials that can compound learner’s disposition and academic performance. (shrink)

Amongst philosophers and cognitive scientists, modularity remains a popular choice for an architecture of the human mind, primarily because of the supposed explanatory value of this approach. Modular architectures can vary both with respect to the strength of the notion of modularity and the scope of the modularity of mind. We propose a dilemma for modular architectures, no matter how these architectures vary along these two dimensions. First, if a modular architecture commits to the informational encapsulation of (...) modules, as it is the case for modularity theories of perception, then modules are on this account impenetrable. However, we argue that there are genuine cases of the cognitive penetrability of perception and that these cases challenge any strong, encapsulated modular architecture of perception. Second, many recent massive modularity theories weaken the strength of the notion of module, while broadening the scope of modularity. These theories do not require any robust informational encapsulation, and thus avoid the incompatibility with cognitive penetrability. However, the weakened commitment to informational encapsulation greatly weakens the explanatory force of the theory and, ultimately, is conceptually at odds with the core of modularity. (shrink)

Discussions concerning the modularity of the pain system have been focused on questions regarding the cognitive penetrability of pain mechanisms. It has been claimed that phenomena such as placebo analgesia demonstrate that the pain system is cognitively penetrated; therefore, it is not encapsulated from central cognition. However, important arguments have been formulated which aim to show that cognitive penetrability does not in fact entail a lack of modularity of the pain system. This paper offers an alternative way to (...) reject the modularity of the pain system, which is independent from, but consistent with, the presence of cognitive penetration. It is proposed that, given the current knowledge regarding the functioning and the structure of the pain system, there are good reasons to accept that certain central cognitive mechanisms are part of the pain system. It is argued that such a ‘cognitive constitution’ of the pain system entails that the pain system is not modular. (shrink)

There is a growing consensus that emotions contribute positively to human practical rationality. While arguments that defend this position often appeal to the modularity of emotion-generation mechanisms, these arguments are also susceptible to the criticism, e.g. by Jones (2006), that emotional modularity supports pessimism about the prospects of emotions contributing positively to practical rationality here and now. This paper aims to respond to this criticism by demonstrating how models of emotion processing can accommodate the sorts of cognitive influence (...) required to make the pro-emotion position plausible whilst exhibiting key elements of modularity. (shrink)

Modular approaches to the architecture of the mind claim that some mental mechanisms, such as sensory input processes, operate in special-purpose subsystems that are functionally independent from the rest of the mind. This assumption of modularity seems to be in tension with recent claims that the mind has a predictive architecture. Predictive approaches propose that both sensory processing and higher-level processing are part of the same Bayesian information-processing hierarchy, with no clear boundary between perception and cognition. Furthermore, it is (...) not clear how any part of the predictive architecture could be functionally independent, given that each level of the hierarchy is influenced by the level above. Both the assumption of continuity across the predictive architecture and the seeming non-isolability of parts of the predictive architecture seem to be at odds with the modular approach. I explore and ultimately reject the predictive approach’s apparent commitments to continuity and non-isolation. I argue that predictive architectures can be modular architectures, and that we should in fact expect predictive architectures to exhibit some form of modularity. (shrink)

Structuralism can be defined as an important concept of using “units” as elements of form and space-giving, where the whole form is made not only up of a “texture”, a certain flexible grid, or an algorithm of shape-giving, but it depends also on the relationships created and how people use it. The hypothesis of this study is that “Modular Construction” can also have an aesthetically pleasing outlook and that modular housing can definitely have increasing importance in the future. Modular housing (...) due to its cheap, and manufactural way of construction can be replicable in various locations. Structuralism and Modular Construction have been at the core of the Modernist movement. Although postmodernism marked the decline of modular construction adopting methods known for a more close sense of place, vernacular, and locality, which differs from the ubiquitous model of modernism, it is the universality of space and habitation seen since the times of Hippodamus Grid, Japanese Tattami systems, and rational universal space in housing known in Europe that make grid and modular design an excellent system in obtaining, rationality, functionality, flexibility, and energy efficiency, including quick construction and possibility for replication. In this regard, modular construction has a future, especially in times of crisis and economic instability. (shrink)

Face-to-face learning engagement has been suspended due to the health crisis that affected the whole world. This led to the adaptation of modular distance learning to continue delivering quality education. As the transition continues, its effectiveness has been frequently assessed. The key purpose of this study is to determine the relationship between the level of implementation of modular distance learning and English Writing Proficiency among the senior high school students in Saint Joseph College Maasin City School year 2021-2022. The study (...) employed a descriptive correlational design with 39 purposively chosen respondents. The main tools used in gathering the data were questionnaires, learning modules, and rubrics. Findings revealed that the implementation of modular distance learning (MDL) has an overall very satisfactory rating based on the perception of the students. The student’s perception of the implementation of modular distance learning and their writing proficiency is significantly related. Moreover, it revealed that students had difficulties in finding supplementary learning materials and educational support from home. The researcher recommends a set of guidelines for the successful and effective implementation of modular distance learning as the output of the study. (shrink)

The paper presents an analysis of the current state of administrative modular buildings and co-working spaces in some European countries and Latin America. The study provides an overview of the concept of modular buildings and co-working spaces, including their history and evolution and their energy efficiency. They also examine the benefits and drawbacks of these types of buildings, as well as the factors that contribute to their success. The authors analyze several case studies of administrative modular buildings and co-working spaces (...) in different European countries and Latin America, such as the UK, Germany, Slovakia, and Ukraine ending with Brazil. The paper takes into consideration the design and construction of these buildings, as well as the services and amenities they offer. The paper also considers the impact of administrative modular buildings and co-working spaces on the environment, as well as their potential for promoting sustainable development. The authors discuss the challenges and opportunities associated with the development of administrative modular buildings and co-working spaces and provide recommendations for future research in this area. Energy-efficient modular buildings and co-working spaces have the potential to support organizations in achieving their sustainability goals while also providing a range of benefits for employees and stakeholders. (shrink)

In this introduction, we give a brief overview of the main concepts of modularity that have been offered in recent literature. After this, we turn to a summary of the papers collected in this volume. Our primary aim is to explain how the modularity of emotion question relates to traditional debates in emotion theory.

Representation theorems are often taken to provide the foundations for decision theory. First, they are taken to characterize degrees of belief and utilities. Second, they are taken to justify two fundamental rules of rationality: that we should have probabilistic degrees of belief and that we should act as expected utility maximizers. We argue that representation theorems cannot serve either of these foundational purposes, and that recent attempts to defend the foundational importance of representation theorems are unsuccessful. As a result, we (...) should reject these claims, and lay the foundations of decision theory on firmer ground. (shrink)

Ever since Chomsky, language has become the paradigmatic example of an innate capacity. Infants of only a few months old are aware of the phonetic structure of their mother tongue, such as stress-patterns and phonemes. They can already discriminate words from non-words and acquire a feel for the grammatical structure months before they voice their first word. Language reliably develops not only in the face of poor linguistic input, but even without it. In recent years, several scholars have extended this (...) uncontroversial view into the stronger claim that natural language is a human-specific adaptation. As I shall point out, this position is more problematic because of a lack of conceptual clarity over what human-specific cognitive adaptations are, and how they relate to modularity, the notion that mental phenomena arise from several domain-specific cognitive structures. The main aim of this paper is not to discuss whether or not language is an adaptation, but rather, to examine the concept of modularity with respect to
the evolution and development of natural language.
. (shrink)

After presenting evidence about categorization behavior, this paper argues for the following theses: 1) that there is a border between perception and cognition; 2) that the border is to be characterized by perception being modular (and cognition not being so); 3) that perception outputs conceptualized representations, so views that posit that the output of perception is solely non-conceptual are false; and 4) that perceptual content consists of basic-level categories and not richer contents.

This study focused on the adaptability and attitude of Grade 6 students in the Modular Learning Approach. This study aims to create a comprehensive review of the adaptability and attitude of elementary students in the Modular Learning Approach Especially. It seeks to describe and analyze the following: the profile of the respondents in terms of sex and education of the parents; the adaptability of the respondents toward the relationship between the student's profile in terms of their sex and educational attainment (...) of parents; the attitude of the respondent's significant relationship between sex and educational attainment. The researcher used the quantitative survey questionnaires to gather data from 128 Grade 6 students in five Elementary Schools in Bongabon, Nueva Ecija who enrolled during the School Year 2020-2021. The study revealed that the respondent's demographic profile in sex has no significant relationship to their adaptability and attitude in the modular learning approach. Yet the parents' educational attainment of the respondents has a significant relationship to adaptability in terms of learning assistance and support in the modular learning approach. The results further signified that parents' educational attainment is a basis for adaptability in modular learning. -/- . (shrink)

Cognitive modules are internal mental structures. Some theorists and empirical researchers hypothesise that the human mind is either partially or massively comprised of structures that are modular in nature. Is the massive modularity of mind hypothesis a cogent view about the ontological nature of human mind or is it, rather, an effective/ineffective adaptationist discovery heuristic for generating predictively successful hypotheses about both heretofore unknown psychological traits and unknown properties of already identified psychological traits? Considering the inadequacies of the case (...) in favour of massive modularity as an ontological hypothesis, I suggest approaching and valuing massive modularity as an adaptationist discovery heuristic. (shrink)

According to the `grammatical account', scalar implicatures are triggered by a covert exhaustification operator present in logical form. This account covers considerable empirical ground, but there is a peculiar pattern that resists treatment given its usual implementation. The pattern centers on odd assertions like #"Most lions are mammals" and #"Some Italians come from a beautiful country", which seem to trigger implicatures in contexts where the enriched readings conflict with information in the common ground. Magri (2009, 2011) argues that, to account (...) for these cases, the basic grammatical approach has to be supplemented with the stipulations that exhaustification is obligatory and is based on formal computations which are blind to information in the common ground. In this paper, I argue that accounts of oddness should allow for the possibility of felicitous assertions that call for revision of the common ground, including explicit assertions of unusual beliefs such as "Most but not all lions are mammals" and "Some but not all Italians come from Italy". To adequately cover these and similar cases, I propose that Magri's version of the Grammatical account should be refined with the novel hypothesis that exhaustification triggers a bifurcation between presupposed (the negated relevant alternatives) and at-issue (the prejacent) content. The explanation of the full oddness pattern, including cases of felicitous proposals to revise the common ground, follows from the interaction between presupposed and at-issue content with an independently motivated constraint on accommodation. Finally, I argue that treating the exhaustification operator as a presupposition trigger helps solve various independent puzzles faced by extant grammatical accounts, and motivates a substantial revision of standard accounts of the overt exhaustifier "only". (shrink)

Functional robustness refers to a system’s ability to maintain a function in the face of perturbations to the causal structures that support performance of that function. Modularity, a crucial element of standard methods of causal inference and difference-making accounts of causation, refers to the independent manipulability of causal relationships within a system. Functional robustness appears to be at odds with modularity. If a function is maintained despite manipulation of some causal structure that supports that function, then the relationship (...) between that structure and function fails to be manipulable independent of other causal relationships within the system. Contrary to this line of reasoning, I argue that functional robustness often attends feedback control, rather than failures of modularity. Feedback control poses its own challenges to causal explanation and inference, but those challenges do not undermine modularity—and indeed, modularity is crucial to grappling with them. (shrink)

We suggest that pain processing has a modular architecture. We begin by motivating the (widely assumed but seldom defended) conjecture that pain processing comprises inferential mechanisms. We then note that pain exhibits a characteristic form of judgement independence. On the assumption that pain processing is inferential, we argue that its judgement independence is indicative of modular (encapsulated) mechanisms. Indeed, we go further, suggesting that it renders the modularity of pain mechanisms a default hypothesis to be embraced pending convincing counterevidence. (...) Finally, we consider what a modular pain architecture might look like, and question alleged counterevidence to our proposal. (shrink)

Perceptual processes differ from cognitive, this paper argues, in functioning to be causally controlled by proximal stimuli, and being modular, at least in a modest sense that excludes their being isotropic in Jerry Fodor's sense. This claim agrees with such theorists as Jacob Beck and Ben Phillips that a function of stimulus-control is needed for perceptual status. In support of this necessity claim, I argue, inter alia, that E.J. Green's recent architectural account misclassifies processes deploying knowledge of grammar as perceptual. (...) _Pace_ Beck and Phillips, however, I argue a function of stimulus-control is insufficient for perceptual as opposed to cognitive status. One consideration in favour of such insufficiency, noted but (I argue) not convincingly rebutted by these theorists, concerns perpetually grounded demonstrative thought. Two other considerations trade on the fact that a function of stimulus-control can arise not from blind nature but intentional design or social institutions, where so-functioning processes may but need not be perceptual. I offer two cases where such processes are cognitive, viz. skilful play-by-play announcing of ongoing events, and voluntary visualizing of ongoing events under the guidance of apt play-by-play announcements, dubbed announcement-driven visualizing (ADV). The cognitive status of these three diverse phenomena cannot be explained by an absence of a perception-like representational format or content (for ADV has such) or by a presence of personal-level mental states causally mediating between stimuli and outputs (for perception has such). A bettter explanation invokes, I argue, the non-modular character of the generating process. (shrink)

The premise of biological modularity is an ontological claim that appears to come out of practice. We understand that the biological world is modular because we can manipulate different parts of organisms in ways that would only work if there were discrete parts that were interchangeable. This is the foundation of the BioBrick assembly method widely used in synthetic biology. It is one of a number of methods that allows practitioners to construct and reconstruct biological pathways and devices using (...) DNA libraries of standardized parts with known functions. In this paper, we investigate how the practice of synthetic biology reconfigures biological understanding of the key concepts of modularity and evolvability. We illustrate how this practice approach takes engineering knowledge and uses it to try to understand biological organization by showing how the construction of functional parts and processes can be used in synthetic experimental evolution. We introduce a new approach within synthetic biology that uses the premise of a parts-based ontology together with that of organismal self-organization to optimize orthogonal metabolic pathways in E. coli. We then use this and other examples to help characterize semisynthetic categories of modularity, parthood, and evolvability within the discipline. (shrink)

We give a review and critique of jury theorems from a social-epistemology perspective, covering Condorcet’s (1785) classic theorem and several later refinements and departures. We assess the plausibility of the conclusions and premises featuring in jury theorems and evaluate the potential of such theorems to serve as formal arguments for the ‘wisdom of crowds’. In particular, we argue (i) that there is a fundamental tension between voters’ independence and voters’ competence, hence between the two premises of most jury theorems; (ii) (...) that the (asymptotic) conclusion that ‘huge groups are infallible’, reached by many jury theorems, is an artifact of unjustified premises; and (iii) that the (nonasymptotic) conclusion that ‘larger groups are more reliable’, also reached by many jury theorems, is not an artifact and should be regarded as the more adequate formal rendition of the ‘wisdom of crowds’. (shrink)

This study aimed to examine the challenges encountered by science teachers in implementing modular distance learning and the coping strategies they employed to address these challenges. Using a mixed-method research approach, data were collected through a survey of thirty-eight Junior High School science teachers in Mandaon District in Masbate, Philippines. Findings revealed that the implementation of modular distance learning presented various challenges, including technical problems, distribution and retrieval difficulties, student utilization issues, and unreliable assessment results. To cope with these challenges, (...) teachers employed various strategies, including attending ICT training, asking for technical assistance, developing income-generating projects, and utilizing differentiated instruction and targeted assessments. The study also highlights the need for more parental involvement, adequate funding for schools, clear instructions and guidance to students, and proper monitoring of student performance. Overall, the study suggests that with effective implementation and support, modular distance learning can be an effective mode of instruction, particularly during times of crisis. (shrink)

This paper compares current ways of modeling the inferential structure of practical reasoning arguments, and proposes a new approach in which it is regarded in a modular way. Practical reasoning is not simply seen as reasoning from a goal and a means to an action using the basic argumentation scheme. Instead, it is conceived as a complex structure of classificatory, evaluative, and practical inferences, which is formalized as a cluster of three types of distinct and interlocked argumentation schemes. Using two (...) real examples, we show how applying the three types of schemes to a cluster of practical argumentation allows an argument analyst to reconstruct the tacit premises presupposed and evaluate the argumentative reasoning steps involved. This approach will be shown to overcome the limitations of the existing models of practical reasoning arguments within the BDI and commitment theoretical frameworks, providing a useful tool for discourse analysis and other disciplines. In particular, applying this method brings to light the crucial role of classification in practical argumentation, showing how the ordering of values and preferences is only one of the possible areas of deep disagreement. (shrink)

Der hier vorliegende Text befasst sich mit der Rezeption von Aristoteles’ Metaphysik Λ bei Albertus Magnus und Thomas von Aquin. Er stellt das Material bereit für die Auswertung, die als Band 61 der Bochumer Studien zur Philosophie unter dem Titel Zur mittelalterlichen Herkunft einiger Theoreme in der modernen Aristoteles-Interpretation Eine Fallstudie anhand der Kommentare von Albertus Magnus und Thomas von Aquin zu Aristoteles’ Metaphysik Λ, bei John Benjamins Publishing Company, Amsterdam / Philadelphia 2024, erscheinen wird. **************************** This text deals with (...) the reception of Aristotle's Metaphysics Λ by Albertus Magnus and Thomas Aquinas. It provides the material for the analysis, which will be published as volume 61 of the BochumerStudien zur Philosophie under the title "Zur mittelalterlichenHerkunft einiger Theoreme in der modernenAristoteles-Interpretation. Eine Fallstudie anhand derKommentare von Albertus Magnus und Thomas vonAquin zu Aristoteles' Metaphysik Λ," by John Benjamins Publishing Company, Amsterdam / Philadelphia, 2024. (shrink)

Peer review is often taken to be the main form of quality control on academic research. Usually journals carry this out. However, parts of maths and physics appear to have a parallel, crowd-sourced model of peer review, where papers are posted on the arXiv to be publicly discussed. In this paper we argue that crowd-sourced peer review is likely to do better than journal-solicited peer review at sorting papers by quality. Our argument rests on two key claims. First, crowd-sourced peer (...) review will lead on average to more reviewers per paper than journal-solicited peer review. Second, due to the wisdom of the crowds, more reviewers will tend to make better judgments than fewer. We make the second claim precise by looking at the Condorcet Jury Theorem as well as two related jury theorems developed specifically to apply to peer review. (shrink)

Any intermediate propositional logic can be extended to a calculus with epsilon- and tau-operators and critical formulas. For classical logic, this results in Hilbert’s $\varepsilon $ -calculus. The first and second $\varepsilon $ -theorems for classical logic establish conservativity of the $\varepsilon $ -calculus over its classical base logic. It is well known that the second $\varepsilon $ -theorem fails for the intuitionistic $\varepsilon $ -calculus, as prenexation is impossible. The paper investigates the effect of adding critical $\varepsilon $ - (...) and $\tau $ -formulas and using the translation of quantifiers into $\varepsilon $ - and $\tau $ -terms to intermediate logics. It is shown that conservativity over the propositional base logic also holds for such intermediate ${\varepsilon \tau }$ -calculi. The “extended” first $\varepsilon $ -theorem holds if the base logic is finite-valued Gödel–Dummett logic, and fails otherwise, but holds for certain provable formulas in infinite-valued Gödel logic. The second $\varepsilon $ -theorem also holds for finite-valued first-order Gödel logics. The methods used to prove the extended first $\varepsilon $ -theorem for infinite-valued Gödel logic suggest applications to theories of arithmetic. (shrink)

Introduction to Special Issue of Review of Philosophy and Psychology. Overview of the central issues in cognitive architecture, epistemology, and ethics surrounding cognitive penetrability. Special issue includes papers by philosophers and psychologists: Gary Lupyan, Fiona Macpherson, Reginald Adams, Anya Farennikova, Jona Vance, Francisco Marchi, Robert Cowan.

This paper begins with a puzzle regarding Lewis' theory of radical interpretation. On the one hand, Lewis convincingly argued that the facts about an agent's sensory evidence and choices will always underdetermine the facts about her beliefs and desires. On the other hand, we have several representation theorems—such as those of (Ramsey 1931) and (Savage 1954)—that are widely taken to show that if an agent's choices satisfy certain constraints, then those choices can suffice to determine her beliefs and desires. In (...) this paper, I will argue that Lewis' conclusion is correct: choices radically underdetermine beliefs and desires, and representation theorems provide us with no good reasons to think otherwise. Any tension with those theorems is merely apparent, and relates ultimately to the difference between how 'choices' are understood within Lewis' theory and the problematic way that they're represented in the context of the representation theorems. For the purposes of radical interpretation, representation theorems like Ramsey's and Savage's just aren't very relevant after all. (shrink)

In this short survey article, I discuss Bell’s theorem and some strategies that attempt to avoid the conclusion of non-locality. I focus on two that intersect with the philosophy of probability: (1) quantum probabilities and (2) superdeterminism. The issues they raised not only apply to a wide class of no-go theorems about quantum mechanics but are also of general philosophical interest.

The standard representation theorem for expected utility theory tells us that if a subject’s preferences conform to certain axioms, then she can be represented as maximising her expected utility given a particular set of credences and utilities—and, moreover, that having those credences and utilities is the only way that she could be maximising her expected utility. However, the kinds of agents these theorems seem apt to tell us anything about are highly idealised, being always probabilistically coherent with infinitely precise degrees (...) of belief and full knowledge of all a priori truths. Ordinary subjects do not look very rational when compared to the kinds of agents usually talked about in decision theory. In this paper, I will develop an expected utility representation theorem aimed at the representation of those who are neither probabilistically coherent, logically omniscient, nor expected utility maximisers across the board—that is, agents who are frequently irrational. The agents in question may be deductively fallible, have incoherent credences, limited representational capacities, and fail to maximise expected utility for all but a limited class of gambles. (shrink)

Pettit (2012) presents a model of popular control over government, according to which it consists in the government being subject to those policy-making norms that everyone accepts. In this paper, I provide a formal statement of this interpretation of popular control, which illuminates its relationship to other interpretations of the idea with which it is easily conflated, and which gives rise to a theorem, similar to the famous Gibbard-Satterthwaite theorem. The theorem states that if government policy is subject to popular (...) control, as Pettit interprets it, and policy responds positively to changes in citizens' normative attitudes, then there is a single individual whose normative attitudes unilaterally determine policy. I use the model and theorem as an illustrative example to discuss the role of mathematics in normative political theory. (shrink)

In response to recent work on the aggregation of individual judgments on logically connected propositions into collective judgments, it is often asked whether judgment aggregation is a special case of Arrowian preference aggregation. We argue for the converse claim. After proving two impossibility theorems on judgment aggregation (using "systematicity" and "independence" conditions, respectively), we construct an embedding of preference aggregation into judgment aggregation and prove Arrow’s theorem (stated for strict preferences) as a corollary of our second result. Although we thereby (...) provide a new proof of Arrow’s theorem, our main aim is to identify the analogue of Arrow’s theorem in judgment aggregation, to clarify the relation between judgment and preference aggregation, and to illustrate the generality of the judgment aggregation model. JEL Classi…cation: D70, D71.. (shrink)

The study was conducted to determine the pitfalls encountered by grade five teachers during modular teaching and learning. Specifically, it aimed to find out the pitfalls encountered by teachers along with students’ comprehension, students’ academic behavior, monitoring of students’ education, and physical interaction with the learners. The personal profile of teachers, out of the total respondents (56), most of the teachers are female-dominated. Most of them belong to the age bracket of 34 to 45 and most of the teachers are (...) married. Most of the teachers had attended post-graduate studies. Most respondents are still young in the service, holding Teacher 2 and Teacher 3 positions, and attending local, national, and regional training. On the level of pitfalls encountered by teachers in modular teaching and learning, most respondents experienced a slight gravity level in the four aspects. The computed average weighted mean along comprehension is 2.50, along academic behavior is 2.54, along monitoring of students’ performance is 2.58, and along physical interaction is 2.79. All have an equivalent value of moderately grave. There is a specific profile of teachers that is significantly related. Age is significantly associated with monitoring students’ learning. The computed r value is .270, while the calculated significance level is 0.04. Training attended by the teachers is significantly related to some aspects of students’ comprehension, (computed sig. value is 0.04 and physical interaction is .02), which is lower than the .05 level of significance. The grade five teachers who served as respondents are mostly female dominated; they are in their early forties and married. Most of them are attending post-graduate studies and have attended relevant training. Second, the level of teachers’ pitfalls is mostly moderately grave. In addition, age is significantly related to monitoring, training is significantly associated substantially with physical interaction and comprehension. (shrink)

Amalgamating evidence of different kinds for the same hypothesis into an overall confirmation is analogous, I argue, to amalgamating individuals’ preferences into a group preference. The latter faces well-known impossibility theorems, most famously “Arrow’s Theorem”. Once the analogy between amalgamating evidence and amalgamating preferences is tight, it is obvious that amalgamating evidence might face a theorem similar to Arrow’s. I prove that this is so, and end by discussing the plausibility of the axioms required for the theorem.

Perceptual processes, in particular modular processes, have long been understood as being mandatory. But exactly what mandatoriness amounts to is left to intuition. This paper identifies a crucial ambiguity in the notion of mandatoriness. Discussions of mandatory processes have run together notions of automaticity and ballisticity. Teasing apart these notions creates an important tool for the modularist's toolbox. Different putatively modular processes appear to differ in their kinds of mandatoriness. Separating out the automatic from the ballistic can help the modularist (...) diagnose and explain away some putative counterexamples to multimodal and central modules, thereby helping us to better evaluate the evidentiary status of modularity theory. (shrink)

The use of modular construction technology has emerged as a promising solution to the challenges of the construction industry all over the world. This paper examines the new horizons and opportunities that modular construction technology offers not only in the Albanian context but also in some European countries. The paper provides an overview of the status of Albania's construction market and emphasizes the advantages of modular construction technology, including quicker construction, lower costs, and better quality control. Unfortunately, prefabricated constructions are (...) not very present Albanian construction industry, and it is not given the proper attention due to lack of infrastructure, organizational purposes, and lack of proper experience. The paper also examines the challenges associated with the implementation of modular construction technology in Albania, exploring the history of prefabricated constructions, also including regulatory barriers, lack of awareness, and the need for skilled labor. Finally, the paper concludes by suggesting strategies to overcome these challenges and promote the adoption of modular construction technology in Albania, such as targeted government policies, education and training programs, and partnerships between industry stakeholders. (shrink)

To counter a general belief that all the paradoxes stem from a kind of circularity (or involve some self--reference, or use a diagonal argument) Stephen Yablo designed a paradox in 1993 that seemingly avoided self--reference. We turn Yablo's paradox, the most challenging paradox in the recent years, into a genuine mathematical theorem in Linear Temporal Logic (LTL). Indeed, Yablo's paradox comes in several varieties; and he showed in 2004 that there are other versions that are equally paradoxical. Formalizing these versions (...) of Yablo's paradox, we prove some theorems in LTL. This is the first time that Yablo's paradox(es) become new(ly discovered) theorems in mathematics and logic. (shrink)

This paper is concerned with the construction of theories of software systems yielding adequate predictions of their target systems’ computations. It is first argued that mathematical theories of programs are not able to provide predictions that are consistent with observed executions. Empirical theories of software systems are here introduced semantically, in terms of a hierarchy of computational models that are supplied by formal methods and testing techniques in computer science. Both deductive top-down and inductive bottom-up approaches in the discovery of (...) semantic software theories are refused to argue in favour of the abductive process of hypothesising and refining models at each level in the hierarchy, until they become satisfactorily predictive. Empirical theories of computational systems are required to be modular, as modular are most software verification and testing activities. We argue that logic relations must be thereby defined among models representing different modules in a semantic theory of a modular software system. We exclude that scientific structuralism is able to define module relations needed in software modular theories. The algebraic Theory of Institutions is finally introduced to specify the logic structure of modular semantic theories of computational systems. (shrink)

The purpose of this study is to investigate the pedagogical practices employed by secondary school teachers under the new normal. It also identifies the difficulties teachers face when facilitating modular distant learning. Science high school teacher from North District Butuan City took part in the study. In this study, quantitative methodology was employed. To collect the data for the study, survey questionnaires were distributed. According to the research study's findings, the restricted face-to-face parent orientation is the most used pedagogical practices (...) in the new normal, specifically in modular distance learning is the limited face-to-face parent orientation. Enables teachers to incorporate ICT skills to students’ lessons even in modular distance learning, aids in monitoring students’ learning performance using self- learning modules in modular distance learning. Miscommunication because of the distant mode of instruction and difficulties in reaching students due to pandemic are some of the challenges encountered by the teachers in applying pedagogical practices. To address this issue, the researchers designed a capsule training intervention plan that will help teachers enhance their knowledge in choosing and effective pedagogical practice particularly in modular distance learning. (shrink)

In this paper a symmetry argument against quantity absolutism is amended. Rather than arguing against the fundamentality of intrinsic quantities on the basis of transformations of basic quantities, a class of symmetries defined by the Π-theorem is used. This theorem is a fundamental result of dimensional analysis and shows that all unit-invariant equations which adequately represent physical systems can be put into the form of a function of dimensionless quantities. Quantity transformations that leave those dimensionless quantities invariant are empirical and (...) dynamical symmetries. The proposed symmetries of the original argument fail to be both dynamical and empirical symmetries and are open to counterexamples. The amendment of the original argument requires consideration of the relationships between quantity dimensions. The discussion raises a pertinent issue: what is the modal status of the constants of nature which figure in the laws? Two positions, constant necessitism and constant contingentism, are introduced and their relationships to absolutism and comparativism undergo preliminary investigation. It is argued that the absolutist can only reject the amended symmetry argument by accepting constant necessitism. I argue that the truth of an epistemically open empirical hypothesis would make the acceptance of constant necessitism costly: together they entail that the facts are nomically necessary. (shrink)

This paper deals with, prepositional calculi with strong negation (N-logics) in which the Craig interpolation theorem holds. N-logics are defined to be axiomatic strengthenings of the intuitionistic calculus enriched with a unary connective called strong negation. There exists continuum of N-logics, but the Craig interpolation theorem holds only in 14 of them.