Results for 'infinite domains'

959 found
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  1. Accuracy and Probabilism in Infinite Domains.Michael Nielsen - 2023 - Mind 132 (526):402-427.
    The best accuracy arguments for probabilism apply only to credence functions with finite domains, that is, credence functions that assign credence to at most finitely many propositions. This is a significant limitation. It reveals that the support for the accuracy-first program in epistemology is a lot weaker than it seems at first glance, and it means that accuracy arguments cannot yet accomplish everything that their competitors, the pragmatic (Dutch book) arguments, can. In this paper, I investigate the extent to (...)
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  2. Argument-Forms which Turn Invalid over Infinite Domains: Physicalism as Supertask?Catherine Legg - 2008 - Contemporary Pragmatism 5 (1):1-11.
    Argument-forms exist which are valid over finite but not infinite domains. Despite understanding of this by formal logicians, philosophers can be observed treating as valid arguments which are in fact invalid over infinite domains. In support of this claim I will first present an argument against the classical pragmatist theory of truth by Mark Johnston. Then, more ambitiously, I will suggest the fallacy lurks in certain arguments for physicalism taken for granted by many philosophers today.
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  3. Probability Modals and Infinite Domains.Adam Marushak - 2020 - Journal of Philosophical Logic 49 (5):1041-1055.
    Recent years have witnessed a proliferation of attempts to apply the mathematical theory of probability to the semantics of natural language probability talk. These sorts of “probabilistic” semantics are often motivated by their ability to explain intuitions about inferences involving “likely” and “probably”—intuitions that Angelika Kratzer’s canonical semantics fails to accommodate through a semantics based solely on an ordering of worlds and a qualitative ranking of propositions. However, recent work by Wesley Holliday and Thomas Icard has been widely thought to (...)
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  4. Numerical point of view on Calculus for functions assuming finite, infinite, and infinitesimal values over finite, infinite, and infinitesimal domains.Yaroslav Sergeyev - 2009 - Nonlinear Analysis Series A 71 (12):e1688-e1707.
    The goal of this paper consists of developing a new (more physical and numerical in comparison with standard and non-standard analysis approaches) point of view on Calculus with functions assuming infinite and infinitesimal values. It uses recently introduced infinite and infinitesimal numbers being in accordance with the principle ‘The part is less than the whole’ observed in the physical world around us. These numbers have a strong practical advantage with respect to traditional approaches: they are representable at a (...)
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  5.  32
    "Dark Matter" and “Black holes” in the Infinite Quantum Field.Đulijano Đulić - manuscript
    This paper explores the phenomena of "dark matter" and "black holes" within the framework of infinite quantum field theory, presenting them as interconnected and complementary aspects of cosmic dynamics. "Dark matter" arises from the interference between discrete particle orbits and indiscernible distant energy states, manifesting as a diffuse yet pervasive energetic presence. Its continuous growth reflects the expansive nature of the quantum field's self-modifying processes. Conversely, "black holes" are portrayed as loci of energy concentration and reintegration, counterbalancing the expansive (...)
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  6.  43
    Symbolic AI Over Quantum Tensor Fields in Non-Commutative Domains.Parker Emmerson - 2025 - Journal of Liberated Mathematics 1.
    In this paper, we extend the mathematical framework of **non-commutative scalar fields** and numerical techniques discussed previously to build a foundation for **AI-based reasoning systems**. The goal is to enable AI to operate over **symbolic hierarchies, semantic transformations**, and **large-scale infinite or non-commutative domains**. Inspired by quantum tensor field operations, we integrate reasoning over symbolic, numeric, and approximate representations into machine learning pipelines. This work leverages concepts from numerical techniques for non-commutative mixed derivatives, recur- sive tensor calculus, and (...)
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  7. Presences of the Infinite: J.M. Coetzee and Mathematics.Peter Johnston - 2013 - Dissertation, Royal Holloway, University of London
    This thesis articulates the resonances between J. M. Coetzee's lifelong engagement with mathematics and his practice as a novelist, critic, and poet. Though the critical discourse surrounding Coetzee's literary work continues to flourish, and though the basic details of his background in mathematics are now widely acknowledged, his inheritance from that background has not yet been the subject of a comprehensive and mathematically- literate account. In providing such an account, I propose that these two strands of his intellectual trajectory not (...)
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  8. The entanglement of logic and set theory, constructively.Laura Crosilla - 2022 - Inquiry: An Interdisciplinary Journal of Philosophy 65 (6).
    ABSTRACT Theories of sets such as Zermelo Fraenkel set theory are usually presented as the combination of two distinct kinds of principles: logical and set-theoretic principles. The set-theoretic principles are imposed ‘on top’ of first-order logic. This is in agreement with a traditional view of logic as universally applicable and topic neutral. Such a view of logic has been rejected by the intuitionists, on the ground that quantification over infinite domains requires the use of intuitionistic rather than classical (...)
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  9. Logical reduction of relations: From relational databases to Peirce’s reduction thesis.Sergiy Koshkin - 2023 - Logic Journal of the IGPL 31 (5):779-809.
    We study logical reduction (factorization) of relations into relations of lower arity by Boolean or relative products that come from applying conjunctions and existential quantifiers to predicates, i.e. by primitive positive formulas of predicate calculus. Our algebraic framework unifies natural joins and data dependencies of database theory and relational algebra of clone theory with the bond algebra of C.S. Peirce. We also offer new constructions of reductions, systematically study irreducible relations and reductions to them and introduce a new characteristic of (...)
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  10. Greek and Roman Logic.Robby Finley, Justin Vlasits & Katja Maria Vogt - 2019 - Oxford Bibliographies in Classics.
    In ancient philosophy, there is no discipline called “logic” in the contemporary sense of “the study of formally valid arguments.” Rather, once a subfield of philosophy comes to be called “logic,” namely in Hellenistic philosophy, the field includes (among other things) epistemology, normative epistemology, philosophy of language, the theory of truth, and what we call logic today. This entry aims to examine ancient theorizing that makes contact with the contemporary conception. Thus, we will here emphasize the theories of the “syllogism” (...)
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  11. Pure Logic and Higher-order Metaphysics.Christopher Menzel - 2024 - In Peter Fritz & Nicholas K. Jones (eds.), Higher-Order Metaphysics. Oxford University Press.
    W. V. Quine famously defended two theses that have fallen rather dramatically out of fashion. The first is that intensions are “creatures of darkness” that ultimately have no place in respectable philosophical circles, owing primarily to their lack of rigorous identity conditions. However, although he was thoroughly familiar with Carnap’s foundational studies in what would become known as possible world semantics, it likely wouldn’t yet have been apparent to Quine that he was fighting a losing battle against intensions, due in (...)
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  12. ONE AND THE MULTIPLE ON THE PHILOSOPHY OF MATHEMATICS - ALEXIS KARPOUZOS.Alexis Karpouzos - 2025 - Comsic Spirit 1:6.
    The relationship between the One and the Multiple in mystic philosophy is a profound and central theme that explores the nature of existence, the cosmos, and the divine. This theme is present in various mystical traditions, including those of the East and West, and it addresses the paradoxical coexistence of the unity and multiplicity of all things. -/- In mystic philosophy, the **One** often represents the ultimate reality, the source from which all things emanate and to which all things return. (...)
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  13. Incompleteness of a first-order Gödel logic and some temporal logics of programs.Matthias Baaz, Alexander Leitsch & Richard Zach - 1996 - In Kleine Büning Hans (ed.), Computer Science Logic. CSL 1995. Selected Papers. Springer. pp. 1--15.
    It is shown that the infinite-valued first-order Gödel logic G° based on the set of truth values {1/k: k ε w {0}} U {0} is not r.e. The logic G° is the same as that obtained from the Kripke semantics for first-order intuitionistic logic with constant domains and where the order structure of the model is linear. From this, the unaxiomatizability of Kröger's temporal logic of programs (even of the fragment without the nexttime operator O) and of the (...)
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  14. Does von Neumann Entropy Correspond to Thermodynamic Entropy?Eugene Y. S. Chua - 2021 - Philosophy of Science 88 (1):145-168.
    Conventional wisdom holds that the von Neumann entropy corresponds to thermodynamic entropy, but Hemmo and Shenker (2006) have recently argued against this view by attacking von Neumann's (1955) argument. I argue that Hemmo and Shenker's arguments fail due to several misunderstandings: about statistical-mechanical and thermodynamic domains of applicability, about the nature of mixed states, and about the role of approximations in physics. As a result, their arguments fail in all cases: in the single-particle case, the finite particles case, and (...)
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  15. Complexity Reality and Scientific Realism.Avijit Lahiri - manuscript
    We introduce the notion of complexity, first at an intuitive level and then in relatively more concrete terms, explaining the various characteristic features of complex systems with examples. There exists a vast literature on complexity, and our exposition is intended to be an elementary introduction, meant for a broad audience. -/- Briefly, a complex system is one whose description involves a hierarchy of levels, where each level is made of a large number of components interacting among themselves. The time evolution (...)
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  16. Ranking Multidimensional Alternatives and Uncertain Prospects.Philippe Mongin - 2015 - Journal of Economic Theory 157:146-171.
    We introduce a ranking of multidimensional alternatives, including uncertain prospects as a particular case, when these objects can be given a matrix form. This ranking is separable in terms of rows and columns, and continuous and monotonic in the basic quantities. Owing to the theory of additive separability developed here, we derive very precise numerical representations over a large class of domains (i.e., typically notof the Cartesian product form). We apply these representationsto (1)streams of commodity baskets through time, (2)uncertain (...)
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  17. Computers Aren’t Syntax All the Way Down or Content All the Way Up.Cem Bozşahin - 2018 - Minds and Machines 28 (3):543-567.
    This paper argues that the idea of a computer is unique. Calculators and analog computers are not different ideas about computers, and nature does not compute by itself. Computers, once clearly defined in all their terms and mechanisms, rather than enumerated by behavioral examples, can be more than instrumental tools in science, and more than source of analogies and taxonomies in philosophy. They can help us understand semantic content and its relation to form. This can be achieved because they have (...)
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  18. Cellular Primary Consciousness Theory (CPCT): The Foundation Intelligence of Emergent Phenomena in Closed Systems; in Theory and Practice And Open and Closed Systems Theory (OCST): The Purpose of Meaninglessness.Brian Brown - manuscript
    This paper presents a unified theory of reality, which integrates two interdependent frameworks: Cellular Primary Consciousness Theory (CPCT) and Open and Closed Systems Theory (OCST). Although CPCT and OCST can each stand as individual theories, they are, in this work, combined to form a cohesive explanation of both the mechanics and purpose of the universe. CPCT posits that consciousness is a fundamental aspect of all life, extending to even the simplest cells, rather than being an emergent property exclusive to complex (...)
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  19. Deleuze and the Mathematical Philosophy of Albert Lautman.Simon B. Duffy - 2009 - In Jon Roffe & Graham Jones (eds.), Deleuze’s Philosophical Lineage. Edinburgh University Press.
    In the chapter of Difference and Repetition entitled ‘Ideas and the synthesis of difference,’ Deleuze mobilizes mathematics to develop a ‘calculus of problems’ that is based on the mathematical philosophy of Albert Lautman. Deleuze explicates this process by referring to the operation of certain conceptual couples in the field of contemporary mathematics: most notably the continuous and the discontinuous, the infinite and the finite, and the global and the local. The two mathematical theories that Deleuze draws upon for this (...)
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  20. Quantum Computer: Quantum Model and Reality.Vasil Penchev - 2020 - Epistemology eJournal (Elsevier: SSRN) 13 (17):1-7.
    Any computer can create a model of reality. The hypothesis that quantum computer can generate such a model designated as quantum, which coincides with the modeled reality, is discussed. Its reasons are the theorems about the absence of “hidden variables” in quantum mechanics. The quantum modeling requires the axiom of choice. The following conclusions are deduced from the hypothesis. A quantum model unlike a classical model can coincide with reality. Reality can be interpreted as a quantum computer. The physical processes (...)
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  21. Craig’s Kalam Cosmology.Graham Oppy - 2009 - Philo 12 (2):200-216.
    Hypotheses about the shape of causal reality admit of both theistic and non-theistic interpretations. I argue that, on the simplest hypotheses about the causal shape of reality—infinite regress, contingent initial boundary, necessary initial boundary—there is good reason to suppose that non-theism is always either preferable to, or at least the equal of, theism, at least insofar as we restrict our attention merely to the domain of explanation of existence. Moreover, I suggest that it is perfectly proper for naturalists to (...)
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  22. Ontologie relazionali e metafisica trinitaria. Sussistenze, eventi e gunk.Damiano Migliorini - 2022 - Brescia: Morcelliana.
    The book aims to examine how a Trinitarian Theism can be formulated through the elaboration of a Relational Ontology and a Trinitarian Metaphysics, in the context of a hyperphatic epistemology. This metaphysics has been proposed by some supporters of the so-called Open Theism as a solution to the numerous dilemmas of Classical Theism. The hypothesis they support is that the Trinitarian nature of God, reflected in a world of multiplicity, relationality, substance and relations, demands that we think of God as (...)
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  23. Natural Recursion Doesn’t Work That Way: Automata in Planning and Syntax.Cem Bozsahin - 2016 - In Vincent C. Müller (ed.), Fundamental Issues of Artificial Intelligence. Cham: Springer. pp. 95-112.
    Natural recursion in syntax is recursion by linguistic value, which is not syntactic in nature but semantic. Syntax-specific recursion is not recursion by name as the term is understood in theoretical computer science. Recursion by name is probably not natural because of its infinite typeability. Natural recursion, or recursion by value, is not species-specific. Human recursion is not syntax-specific. The values on which it operates are most likely domain-specific, including those for syntax. Syntax seems to require no more (and (...)
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  24. Occipital and left temporal instantaneous amplitude and frequency oscillations correlated with access and phenomenal consciousness.Vitor Manuel Dinis Pereira - manuscript
    Given the hard problem of consciousness, there are no brain electrophysiological correlates of the subjective experience (the felt quality of redness or the redness of red, the experience of dark and light, the quality of depth in a visual field, the sound of a clarinet, the smell of mothball, bodily sensations from pains to orgasms, mental images that are conjured up internally, the felt quality of emotion, the experience of a stream of conscious thought, or the phenomenology of thought). However, (...)
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  25.  69
    Everything's OK.B. T. Clevenger - manuscript
    "Everything's OK" explores the philosophical and practical dimensions of complexity alignment as a framework for understanding coherence across personal, social, and existential domains. Rooted in lived experience and refined with the assistance of artificial intelligence, this work introduces the OK Model, a triadic lens (S-Φ-P: Singularity, Pharmonic Field, Plane of Incidencion) for navigating infinite possibilities into stable, meaningful outcomes. By examining the role of ethical coherence, trust, and iterative refinement, the manuscript bridges philosophy, complexity science, and ethics to (...)
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  26. Infinite Prospects.Jeffrey Sanford Russell & Yoaav Isaacs - 2021 - Philosophy and Phenomenological Research 103 (1):178-198.
    People with the kind of preferences that give rise to the St. Petersburg paradox are problematic---but not because there is anything wrong with infinite utilities. Rather, such people cannot assign the St. Petersburg gamble any value that any kind of outcome could possibly have. Their preferences also violate an infinitary generalization of Savage's Sure Thing Principle, which we call the *Countable Sure Thing Principle*, as well as an infinitary generalization of von Neumann and Morgenstern's Independence axiom, which we call (...)
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  27. Boring Infinite Descent.Tuomas E. Tahko - 2014 - Metaphilosophy 45 (2):257-269.
    In formal ontology, infinite regresses are generally considered a bad sign. One debate where such regresses come into play is the debate about fundamentality. Arguments in favour of some type of fundamentalism are many, but they generally share the idea that infinite chains of ontological dependence must be ruled out. Some motivations for this view are assessed in this article, with the conclusion that such infinite chains may not always be vicious. Indeed, there may even be room (...)
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  28. Infinite Aggregation and Risk.Hayden Wilkinson - 2023 - Australasian Journal of Philosophy 101 (2):340-359.
    For aggregative theories of moral value, it is a challenge to rank worlds that each contain infinitely many valuable events. And, although there are several existing proposals for doing so, few provide a cardinal measure of each world's value. This raises the even greater challenge of ranking lotteries over such worlds—without a cardinal value for each world, we cannot apply expected value theory. How then can we compare such lotteries? To date, we have just one method for doing so (proposed (...)
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  29. Are infinite explanations self-explanatory?Alexandre Billon - 2021 - Erkenntnis 88 (5):1935-1954.
    Consider an infinite series whose items are each explained by their immediate successor. Does such an infinite explanation explain the whole series or does it leave something to be explained? Hume arguably claimed that it does fully explain the whole series. Leibniz, however, designed a very telling objection against this claim, an objection involving an infinite series of book copies. In this paper, I argue that the Humean claim can, in certain cases, be saved from the Leibnizian (...)
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  30. Explaining Universality: Infinite Limit Systems in the Renormalization Group Method.Jingyi Wu - 2021 - Synthese (5-6):14897-14930.
    I analyze the role of infinite idealizations used in the renormalization group (RG hereafter) method in explaining universality across microscopically different physical systems in critical phenomena. I argue that despite the reference to infinite limit systems such as systems with infinite correlation lengths during the RG process, the key to explaining universality in critical phenomena need not involve infinite limit systems. I develop my argument by introducing what I regard as the explanatorily relevant property in RG (...)
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  31. Infinite Paths to Infinite Reality: Sri Ramakrishna and Cross-Cultural Philosophy of Religion.Ayon Maharaj - 2018 - New York, NY, USA: Oxford University Press.
    This book examines the philosophy of the nineteenth-century Indian mystic Sri Ramakrishna and brings him into dialogue with Western philosophers of religion, primarily in the recent analytic tradition. Sri Ramakrishna’s expansive conception of God as the impersonal-personal Infinite Reality, Maharaj argues, opens up an entirely new paradigm for addressing central topics in the philosophy of religion, including divine infinitude, religious diversity, the nature and epistemology of mystical experience, and the problem of evil.
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  32. Infinite Opinion Sets and Relative Accuracy.Ilho Park & Jaemin Jung - 2023 - Journal of Philosophy 120 (6):285-313.
    We can have credences in an infinite number of propositions—that is, our opinion set can be infinite. Accuracy-first epistemologists have devoted themselves to evaluating credal states with the help of the concept of ‘accuracy’. Unfortunately, under several innocuous assumptions, infinite opinion sets yield several undesirable results, some of which are even fatal, to accuracy-first epistemology. Moreover, accuracy-first epistemologists cannot circumvent these difficulties in any standard way. In this regard, we will suggest a non-standard approach, called a relativistic (...)
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  33. Pareto Principles in Infinite Ethics.Amanda Askell - 2018 - Dissertation, New York University
    It is possible that the world contains infinitely many agents that have positive and negative levels of well-being. Theories have been developed to ethically rank such worlds based on the well-being levels of the agents in those worlds or other qualitative properties of the worlds in question, such as the distribution of agents across spacetime. In this thesis I argue that such ethical rankings ought to be consistent with the Pareto principle, which says that if two worlds contain the same (...)
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  34. Default Domain Restriction Possibilities.Katherine Ritchie & Henry Schiller - forthcoming - Semantics and Pragmatics.
    We start with an observation about implicit quantifier domain restriction: certain implicit restrictions (e.g., restricting objects by location and time) appear to be more natural and widely available than others (e.g., restricting objects by color, aesthetic, or historical properties). Our aim is to explain why this is. That is, we aim to explain why some implicit domain restriction possibilities are available by default. We argue that, regardless of their other explanatory virtues, extant pragmatic and metasemantic frameworks leave this question unanswered. (...)
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  35. Domains, plural truth, and mixed atomic propositions.Jeremy Wyatt - 2013 - Philosophical Studies 166 (S1):225-236.
    In this paper, I discuss two concerns for pluralist truth theories: a concern about a key detail of these theories and a concern about their viability. The detail-related concern is that pluralists have relied heavily upon the notion of a domain, but it is not transparent what they take domains to be. Since the notion of a domain has been present in philosophy for some time, it is important for many theorists, not only truth pluralists, to be clear on (...)
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  36.  49
    Infinite Possibilities Argument: A Rational and Metaphysical Framework for God’s Inevitable Existence.Michael Haimes - manuscript
    This argument demonstrates that within an infinite framework of possibilities, the existence of God—a necessary, omnipotent, omniscient, and perfectly good being—is not only logically possible but metaphysically inevitable. By grounding its premises in logical coherence, probabilistic reasoning, and metaphysical necessity, the argument provides a profound exploration of existence, divinity, and humanity's role in infinite potential. It offers implications for ethical striving, collective responsibility, and the divine foundation of reality. -/- .
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  37. Infinite barbarians.Daniel Nolan - 2019 - Ratio 32 (3):173-181.
    This paper discusses an infinite regress that looms behind a certain kind of historical explanation. The movement of one barbarian group is often explained by the movement of others, but those movements in turn call for an explanation. While their explanation can again be the movement of yet another group of barbarians, if this sort of explanation does not stop somewhere we are left with an infinite regress of barbarians. While that regress would be vicious, it cannot be (...)
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  38. The infinite regress of optimization.Philippe Mongin - 1991 - Behavioral and Brain Sciences 14 (2):229-230.
    A comment on Paul Schoemaker's target article in Behavioral and Brain Sciences, 14 (1991), p. 205-215, "The Quest for Optimality: A Positive Heuristic of Science?" (https://doi.org/10.1017/S0140525X00066140). This comment argues that the optimizing model of decision leads to an infinite regress, once internal costs of decision (i.e., information and computation costs) are duly taken into account.
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  39. The Hypercategorematic Infinite.Maria Rosa Antognazza - 2015 - The Leibniz Review 25:5-30.
    This paper aims to show that a proper understanding of what Leibniz meant by “hypercategorematic infinite” sheds light on some fundamental aspects of his conceptions of God and of the relationship between God and created simple substances or monads. After revisiting Leibniz’s distinction between (i) syncategorematic infinite, (ii) categorematic infinite, and (iii) actual infinite, I examine his claim that the hypercategorematic infinite is “God himself” in conjunction with other key statements about God. I then discuss (...)
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  40. Infinite Regresses of Justification.Oliver Black - 1988 - International Philosophical Quarterly 28 (4):421-437.
    This paper uses a schema for infinite regress arguments to provide a solution to the problem of the infinite regress of justification. The solution turns on the falsity of two claims: that a belief is justified only if some belief is a reason for it, and that the reason relation is transitive.
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  41. Fair infinite lotteries.Sylvia Wenmackers & Leon Horsten - 2013 - Synthese 190 (1):37-61.
    This article discusses how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. Techniques and ideas from non-standard analysis are brought to bear on the problem.
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  42. Infinite Value and the Best of All Possible Worlds.Nevin Climenhaga - 2018 - Philosophy and Phenomenological Research 97 (2):367-392.
    A common argument for atheism runs as follows: God would not create a world worse than other worlds he could have created instead. However, if God exists, he could have created a better world than this one. Therefore, God does not exist. In this paper I challenge the second premise of this argument. I argue that if God exists, our world will continue without end, with God continuing to create value-bearers, and sustaining and perfecting the value-bearers he has already created. (...)
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  43. Domain Extension and Ideal Elements in Mathematics†.Anna Bellomo - 2021 - Philosophia Mathematica 29 (3):366-391.
    Domain extension in mathematics occurs whenever a given mathematical domain is augmented so as to include new elements. Manders argues that the advantages of important cases of domain extension are captured by the model-theoretic notions of existential closure and model completion. In the specific case of domain extension via ideal elements, I argue, Manders’s proposed explanation does not suffice. I then develop and formalize a different approach to domain extension based on Dedekind’s Habilitationsrede, to which Manders’s account is compared. I (...)
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  44. Infinite Descent.T. Scott Dixon - 2020 - In Michael J. Raven (ed.), The Routledge Handbook of Metaphysical Grounding. New York: Routledge. pp. 244-58.
    Once one accepts that certain things metaphysically depend upon, or are metaphysically explained by, other things, it is natural to begin to wonder whether these chains of dependence or explanation must come to an end. This essay surveys the work that has been done on this issue—the issue of grounding and infinite descent. I frame the discussion around two questions: (1) What is infinite descent of ground? and (2) Is infinite descent of ground possible? In addressing the (...)
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  45. Infinite graphs in systematic biology, with an application to the species problem.Samuel A. Alexander - 2013 - Acta Biotheoretica 61 (2):181--201.
    We argue that C. Darwin and more recently W. Hennig worked at times under the simplifying assumption of an eternal biosphere. So motivated, we explicitly consider the consequences which follow mathematically from this assumption, and the infinite graphs it leads to. This assumption admits certain clusters of organisms which have some ideal theoretical properties of species, shining some light onto the species problem. We prove a dualization of a law of T.A. Knight and C. Darwin, and sketch a decomposition (...)
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  46. Infinite Modes.Kristina Meshelski - 2015 - In Andre Santos Campos (ed.), Spinoza: Basic Concepts. Burlington, VT, USA: Imprint Academic. pp. 43-54.
    In this chapter I explain Spinoza's concept of "infinite modes". After some brief background on Spinoza's thoughts on infinity, I provide reasons to think that Immediate Infinite Modes are identical to the attributes, and that Mediate Infinite Modes are merely totalities of finite modes. I conclude with some considerations against the alternative view that infinite modes are laws of nature.
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  47. Infinite numbers are large finite numbers.Jeremy Gwiazda - unknown
    In this paper, I suggest that infinite numbers are large finite numbers, and that infinite numbers, properly understood, are 1) of the structure omega + (omega* + omega)Ө + omega*, and 2) the part is smaller than the whole. I present an explanation of these claims in terms of epistemic limitations. I then consider the importance, part of which is demonstrating the contradiction that lies at the heart of Cantorian set theory: the natural numbers are too large to (...)
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  48. Infinite options, intransitive value, and supererogation.Daniel Muñoz - 2020 - Philosophical Studies 178 (6):2063-2075.
    Supererogatory acts are those that lie “beyond the call of duty.” There are two standard ways to define this idea more precisely. Although the definitions are often seen as equivalent, I argue that they can diverge when options are infinite, or when there are cycles of better options; moreover, each definition is acceptable in only one case. I consider two ways out of this dilemma.
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  49. Complexity, Existence and Infinite Analysis.Giovanni Merlo - 2012 - The Leibniz Review 22:9-36.
    According to Leibniz’s infinite-analysis account of contingency, any derivative truth is contingent if and only if it does not admit of a finite proof. Following a tradition that goes back at least as far as Bertrand Russell, several interpreters have been tempted to explain this biconditional in terms of two other principles: first, that a derivative truth is contingent if and only if it contains infinitely complex concepts and, second, that a derivative truth contains infinitely complex concepts if and (...)
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  50. Spinoza’s ‘Infinite Modes’ Reconsidered.Kristin Primus - 2019 - Journal of Modern Philosophy 1 (1):1-29.
    My two principal aims in this essay are interconnected. One aim is to provide a new interpretation of the ‘infinite modes’ in Spinoza’s Ethics. I argue that for Spinoza, God, conceived as the one infinite and eternal substance, is not to be understood as causing two kinds of modes, some infinite and eternal and the rest finite and non-eternal. That there cannot be such a bifurcation of divine effects is what I take the ‘infinite mode’ propositions, (...)
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