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  Subjects -> PHILOSOPHY (Total: 762 journals)
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Axiomathes
Journal Prestige (SJR): 0.184
Number of Followers: 6  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1122-1151 - ISSN (Online) 1572-8390
Published by Springer-Verlag Homepage  [2467 journals]
  • Deep Disagreement in Mathematics

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      Abstract: Abstract Disagreements that resist rational resolution, often termed “deep disagreements”, have been the focus of much work in epistemology and informal logic. In this paper, I argue that they also deserve the attention of philosophers of mathematics. I link the question of whether there can be deep disagreements in mathematics to a more familiar debate over whether there can be revolutions in mathematics. I propose an affirmative answer to both questions, using the controversy over Shinichi Mochizuki’s work on the abc conjecture as a potential example of both phenomena. I conclude by investigating the prospects for the resolution of mathematical deep disagreements in virtue-theoretic approaches to informal logic and mathematical practice.
      PubDate: 2023-02-01
       
  • On the Foundations of Computing. Computing as the Fourth Great Domain of
           Science

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      Abstract: Abstract This review essay analyzes the book by Giuseppe Primiero, On the foundations of computing. Oxford: Oxford University Press (ISBN 978-0-19-883564-6/hbk; 978-0-19-883565-3/pbk). xix, 296 p. (2020). It gives a critical view from the perspective of physical computing as a foundation of computing and argues that the neglected pillar of material computation (Stepney) should be brought centerstage and computing recognized as the fourth great domain of science (Denning).
      PubDate: 2023-01-31
       
  • On Giving Meanings to Programs

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      Abstract: Abstract In a short section on the semantics of programs within his discussion of program correctness, Primiero seems to endorse the received view on the Scott-Strachey approach to denotational semantics as directly related to correctness. While this is true to some extent, I argue that the mathematical entities associated with programs play a lesser role in reasoning on program correctness, while the mathematical foundations of denotational semantics, namely the theory of domains, have contributed significantly to the conceptual understanding of programming and of computation in general
      PubDate: 2023-01-31
       
  • Domain Restrictions in the Aggregation of Classifications

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      Abstract: Abstract The possibility of domain restrictions that allow the consistent use of majority-based aggregators for rankings of objects has been widely explored. This paper extends this exploration to structures in which equivalence relations or classifications are aggregated, and shows that there is very limited scope for such restrictions in the binary structure of Mirkin and in the unary structure of Maniquet and Mongin. We develop a hybrid structure that combines binary and unary conditions on the aggregator, and that allows the use of a majority-based aggregator if and only if each object is eligible for inclusion in no more than two categories out of some greater number. We also show that in many circumstances, the surjectivity requirement of Maniquet and Mongin implicitly introduces binary conditions on the aggregator, and that their structure is entailed by the hybrid structure introduced here.
      PubDate: 2023-01-31
       
  • Rejection, Disagreement, Controversy and Acceptance in Mathematical
           Practice: Episodes in the Social Construction of Infinity

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      Abstract: Abstract The concept of infinity has a long and troubled history. Thus it is a promising concept with which to explore rejection, disagreement, controversy and acceptance in mathematical practice. This paper briefly considers four cases from the history of infinity, drawing on social constructionism as the background social theory. The unit of analysis of social constructionism is conversation. This is the social mechanism whereby new mathematical claims are proposed, scrutinised and critiqued. Minimally, conversation is based on the two roles of proponent and critic. The proponent puts forward a proposal, which is reacted to and evaluated by those in the role of critic. There is a continuum of contexts in which such conversations take place from inner conversations the mathematician has within themselves, and casual face-to face interactions between mathematicians at the chalkboard, all the way to the formal responses of referees and editors to submitted journal papers. Such responses vary from unconditional acceptance, partial acceptance through to outright rejection. There may be disagreements between proponents and critics, among those in the joint role of critic, and broader, community-wide disagreements and controversies, according to specific mathematical proposal and the critical judgements of it.
      PubDate: 2023-01-31
       
  • Reichenbach’s ‘Causal’ Theory of Time: A Re-assessment

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      Abstract: Abstract The paper proposes a re-assessment of Reichenbach’s ‘causal’ theory of time. Reichenbach’s version of the theory, first proposed in 1921, is interesting because it is one of the first attempts to construct a causal theory as a relational theory of time, which fully takes the results of the Special theory of relativity into account. The theory derives its name from the cone structure of Minkowski space–time, in particular the emission of light signals. At first Reichenbach defines an ‘order’ of time, a ‘before-after’ relationship between mechanical events. In his later work, he comes to the conclusion that the ‘order’ of time needs to be distinguished from the ‘direction’ of time. He therefore abandons the sole focus on light geometry and turns to Boltzmann’s statistical version of thermodynamics. However, as Einstein pointed out, the emission and reception of light signals have thermodynamic aspects. When this is taken into account, Reichenbach’s ‘causal’ theory turns out to be an entropic theory of time. It also emerges that Reichenbach discusses phase space and typicality arguments in support of his dynamic view of time. They provide a better understanding of the notion of entropy. This unifies his approach and helps to answer some of the standard objections against a causal theory of time.
      PubDate: 2023-01-31
       
  • Editorial Preface: Thought Experiments in Mathematics

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      PubDate: 2023-01-24
       
  • Do Imaginings have a Goal'

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      Abstract: Abstract The paper investigates whether imaginative states about propositions can be assessed in terms of fittingness (also known as correctness, appropriateness, aptness). After characterizing propositional imaginings and explaining the idea of fittingness, I present some considerations in favour of the no conditions view: imagining seems to be the sort of action that cannot be done unfittingly, and imaginings have no external cognitive nor conative goals in light of which they could be unfitting. I then examine the local conditions view, that there can be fittingness conditions on imaginings, but that these are inherited from the mental projects in which imaginings can play a role. Given that there are virtues of the imagination such as creativity and spontaneity, and given that imaginings are subject to purposive mechanisms, and given that there are cases in which it is unfitting to fail to imagine, I endorse the general conditions view, on which imaginings have a goal, and therefore fittingness conditions, even outside the context of mental projects. I then examine 4 versions of the general conditions view and argue that imaginings aim to make contents available to mental projects.
      PubDate: 2023-01-24
       
  • Technologies, Inbetweenness and Affordances

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      Abstract: Abstract Categorization of technologies by the order of their inbetweenness is a useful device for parsing complex structures info fundamental parts and understanding the application of a technology. This promises a coherent foundation for explaining how we deploy technologies in design, in particular with respect to the affordances they create. By connecting the categorization of technologies to the matching of user effectivities to features of the environment in affordances, the paper proposes an approach to the transparent description of the assemblages produced by design in terms of which technologies are involved and how they connect to each other, to the wider environment and to users. For affordances, this improves specificity concerning the features of the environment that are directly relevant to an interaction and the connections between these features and the rest of the environment. With respect to technologies, it helps understand not only why a technology may be used under certain circumstances but also abuse and underperformance. Finally, it supports design by providing means for parsing complex situations into chains of technologies between animals and environments. This helps explain how technologies modify effectivities, environments or relations between the two and how this affects design performance.
      PubDate: 2023-01-24
       
  • The Problem of Truth in Quantum Mechanics

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      Abstract: Abstract There is a large literature on the issue of the lack of properties (i.e. accidents) in quantum mechanics (the problem of “hidden variables”) and also on the indistinguishability of particles. Both issues were discussed as far back as the late 1920’s. However, the implications of these challenges to classical ontology were taken up rather late, in part in the ‘quantum set theory’ of Takeuti (Curr Issues Quant Logic 303–322, 1981), Finkelstein (in Beltrametti EG, Van Fraassen BC (eds) Current issues in quantum logic. Plenum, New York, 1981) and the work of Décio Krause (1992)—and subsequent publications). But the problems created by quantum mechanics go far beyond set theory or the identity of indiscernibles (another subject that has been often discussed)—it extends, I argue, to our accounts of truth. To solve this problem, i.e. to have an approach to truth that facilitates a transition from a classical to a quantum ontology one must have a unified framework for them both. This is done within the context of a pluralist view of truthmaking, where the truthmakers are unified in having a monoidal structure. The structure of the paper is as follows. After a brief introduction, the idea of a monoid is outlined (in Sect. 1) followed by a standard set of axioms that govern the truthmaker relation from elements of the monoid to the set of propositions. This is followed, in Sect. 2, by a discussion of how to have truthmakers for two kinds of necessities: tautologies and analytic truths. The next Sect. 3, then applies these ideas to quantum mechanics. It gives an account of quantum states and shows how these form a monoid. The final section then argues that quantum logic does not, despite what one might initially suspect, stand in the way of an account of quantum truth.
      PubDate: 2023-01-24
       
  • Against Phylogenetic Conceptions of Race

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      Abstract: Abstract Biological racial realism (BRR) continues to be a much-discussed topic, with several recent papers presenting arguments for the plausibility of some type of “biological race.” In this paper, the focus will be on the phylogenetic conceptions of race, which is one of the most promising views of BRR, that define races as lineages of reproductively isolated breeding populations. However, I will argue that phylogenetic conceptions of race fail to prove that races are biologically real. I will develop and defend my argument against the phylogenetic views of race by relying on current research in population genetics, human evolution, and social sciences. Ultimately, I will argue that (i) race is not a biologically legitimate category and (ii) philosophers should direct their resources to understand problems that arise due to racialization, and thereby they should find solutions to those problems.
      PubDate: 2023-01-24
       
  • Empirical Concepts: Their Meaning and its Emergence

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      Abstract: This article presents a detailed, novel account of the emergence of (the meaning of) empirical concepts. Acquiring experience and empirical concepts is shown to be the result of multifaceted, cognitive processes, which require both material realization and conceptual interpretation. Generally speaking, the meaning of empirical concepts consists of several distinct components, but it includes at least a structuring and an abstracting component. These two meaning components are abstract entities, which can be justifiably interpreted as real objects. On this basis, I address the subject of emergence. The primary claim is that the abstracting meaning component (but not the structuring one) emerges from its underlying empirical processes: it both depends on and transcends these processes. This claim is expounded by discussing relevant similarities and dissimilarities between the emergence of abstract meanings and a range of central features of emergence prominent in recent debates on this topic. The conception of empirical concepts with emergent abstracting meaning components involves an interpretation that avoids the problematic extremes of both empiricism and Platonism.
      PubDate: 2023-01-24
       
  • Lithbea, a New Domain Outside the Tree of Life

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      Abstract: Abstract At this time when the development of synthetic biology and artificial intelligence are changing the world around us, philosophers and scientists, first of all, must converge to analyze the present and predict the ethical-social consequences and biological dangers associated with new “living entities” that are not the result of the natural evolutionary process. As synthetic/artificial life forms (xenobots, robots, transgenic organisms, etc.) become more and more abundant and sophisticated, it seems first of all necessary to bring some order to all this new biodiversity, establishing what is alive and what is not, and analyzing the consequences of this incessant creative activity. Here I intend to organize all these human-made entities and clarify their status as living beings or artificial elements, leaving the door open to an uncertain future in which we will be able to see how “the artificial” and “the natural” could merge to originate something different from everything known. Accordingly, I propose the creation of a new domain, Lithbea, which includes all synthetic and artificial entities within a new kingdom called Humade (derived from human-made). I have also included viruses in a new realm, the Viral kingdom, because they were excluded from the classical three-domain tree of life despite playing a fundamental role in the evolution of biodiversity on Earth. Finally, I make a brief comment on the unpredictability of the unknown, the implications of this new landscape of biodiversity, and the uncertain future of all these advances.
      PubDate: 2023-01-24
       
  • Primiero on Physical Computation

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      Abstract: Abstract This note discusses the account of physical computation offered in Part II of Primiero’s On the Foundations of Computing. Although there is much to find attractive about the account, I argue that the account is obscure at certain crucial junctures and that it does not supply a wholly satisfactory account of miscomputation. I close by considering whether the engineering foundation of computing requires a theory of physical computation in the first place, suggesting tentatively that it does not.
      PubDate: 2023-01-24
       
  • Temporal Omniscience, Free will, and Their Logic

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      Abstract: Abstract Taking divine omniscience as including temporal omniscience, which means God exists at all times and knows everything, I point out the fallacies in an incompatibilist argument. Syntactically, due to misapplication of the principle of substitutivity, this incompatibilist argument isn’t valid. Semantically, due to cancelation of a supposition on which God’s earlier belief depends, an agent’s alternative action won’t result in falsification of divine belief. Finally, by appealing to an eternalist conception of truth of proposition about the future, I argue that what divine belief entails isn’t the necessity of an agent’s action but the action itself, and put forward a notion of conditional fatalism, which allows for human free will.
      PubDate: 2023-01-24
       
  • The Citadel Itself: Defending Semantic Internalism

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      Abstract: Abstract Semantic internalism is the view that linguistic meaning amounts to forms of conceptual instructions, and that the process of forming linguistic representations does not involve reference to extra-mental entities. Contemporary philosophy of language remains predominantly externalist in focus, having developed systems of extensional reference which depart from classical rationalist assumptions. Semantic internalism is defended here using a broad range of case studies. Particular focus is be placed on exemplar cases such as natural kind and artifactual terms. Typical natural kind terms are shown to have their meaning constructed via a range of cognitive faculties (considerations of material basis being only one of them), and consulting basic properties of language processing and parsing can explain our intuitions about common word use, a major goal of the internalist enterprise. Copredication via inherent polysemy is used as a strong source of evidence for internalism, countering the received view of the externalist character of meaning. Semantic internalism is comprehensively defended against its critics, pushing the exploration of linguistic content and meaning “back into the head”.
      PubDate: 2023-01-24
       
  • Causes Versus Background Conditions: A Double Negation Account

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      Abstract: Abstract I shall present in this article a double negation account of the distinction between causes and background conditions. Such an account will be based on the idea that, unlike causes, background conditions allow for certain effects by way of double prevention. In Sect. 1 I shall introduce objective and non-objective theories of the causes-background conditions distinction and I shall discuss and reject some non-objective theories. In Sect. 2 I shall examine some existing objective theories and argue that they need to be supplemented in two relevant respects. In Sect. 3 I shall present my double negation account. Background conditions will be taken to allow for their effects by acting as early double preventers, late double preventers or effect double preventers. In Sect. 4 I shall deal with two main problems, i.e., the possibility of interpreting background conditions as purely indirect causes and the introduction of negative entities in my account, and with further issues.
      PubDate: 2023-01-14
       
  • Correction: Muslim Philosophers on Affirmative Judgement with Negative
           Predicate

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      PubDate: 2022-12-22
       
  • RETRACTED ARTICLE: Categorial Inference and Convert Realism: Structuring
           Ontology Via Nomological Axiomatics

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      PubDate: 2022-12-01
       
  • That’s Not IBE: Reply to Park

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      Abstract: Abstract Park (Sociologija 28(1):56–64, 2017; Axiomathes 28(4):435–446, 2018;Soc Epistemol 33(1):88–99, 2019) argues that Bas van Fraassen (1980) uses inference to the best explanation (IBE) to defend his contextual theory of explanation. If Park is right, then van Fraassen is in trouble because he rejects IBE as a rational rule of inference. In this reply, I argue that van Fraassen does not use IBE in defending the contextual theory of explanation. I distinguish between several conceptions of IBE: heuristic IBE, objective Bayesian IBE, and ampliative IBE. I argue that van Fraassen holds the ampliative conception of IBE and that his rejection of IBE concerns only ampliative IBE. I also argue that van Fraassen’s defense of the contextual theory of explanation, at best, can be interpreted as an instance of heuristic IBE, but not ampliative IBE. Therefore, I argue, Park’s criticism of van Fraassen misfires.
      PubDate: 2022-12-01
       
 
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