Results for 'Finitism'

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  1. Apophatic Finitism and Infinitism.Jan Heylen - 2019 - Logique Et Analyse 62 (247):319-337.
    This article is about the ontological dispute between finitists, who claim that only finitely many numbers exist, and infinitists, who claim that infinitely many numbers exist. Van Bendegem set out to solve the 'general problem' for finitism: how can one recast finite fragments of classical mathematics in finitist terms? To solve this problem Van Bendegem comes up with a new brand of finitism, namely so-called 'apophatic finitism'. In this article it will be argued that apophatic finitism (...)
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  2. Finitism and the Beginning of the Universe.Stephen Puryear - 2014 - Australasian Journal of Philosophy 92 (4):619-629.
    Many philosophers have argued that the past must be finite in duration because otherwise reaching the present moment would have involved something impossible, namely, the sequential occurrence of an actual infinity of events. In reply, some philosophers have objected that there can be nothing amiss in such an occurrence, since actually infinite sequences are ‘traversed’ all the time in nature, for example, whenever an object moves from one location in space to another. This essay focuses on one of the two (...)
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  3. Aristotelian finitism.Tamer Nawar - 2015 - Synthese 192 (8):2345-2360.
    It is widely known that Aristotle rules out the existence of actual infinities but allows for potential infinities. However, precisely why Aristotle should deny the existence of actual infinities remains somewhat obscure and has received relatively little attention in the secondary literature. In this paper I investigate the motivations of Aristotle’s finitism and offer a careful examination of some of the arguments considered by Aristotle both in favour of and against the existence of actual infinities. I argue that Aristotle (...)
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  4. Finitism, Divisibilty, and the Beginning of the Universe: Replies to Loke and Dumsday.Stephen Puryear - 2016 - Australasian Journal of Philosophy 94 (4):808-813.
    Some philosophers contend that the past must be finite in duration, because otherwise reaching the present would have involved the sequential occurrence of an actual infinity of events, which they regard as impossible. I recently developed a new objection to this finitist argument, to which Andrew Ter Ern Loke and Travis Dumsday have replied. Here I respond to the three main points raised in their replies.
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  5. Benardete Paradoxes, Causal Finitism, and the Unsatisfiable Pair Diagnosis.Joseph C. Schmid & Alex Malpass - forthcoming - Mind.
    We examine two competing solutions to Benardete paradoxes: causal finitism, according to which nothing can have infinitely many causes, and the unsatisfiable pair diagnosis (UPD), according to which such paradoxes are logically impossible and no metaphysical thesis need be adopted to avoid them. We argue that the UPD enjoys notable theoretical advantages over causal finitism. Causal finitists, however, have levelled two main objections to the UPD. First, they urge that the UPD requires positing a ‘mysterious force’ that prevents (...)
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  6. Finitism in the Metaphysical Foundations.Lydia Patton - 2022 - In Michael Bennett McNulty (ed.), Kant's Metaphysical Foundations of Natural Science: A Critical Guide. Cambridge: Cambridge University Press. pp. 119-137.
    In this paper, building on recent and longstanding work (Warren 2001, Friedman 2013, Glezer 2018), I investigate how the account of the essences or natures of material substances in the Metaphysical Foundations is related to Kant’s demand for the completeness of the system of nature. We must ascribe causal powers to material substances for the properties of those substances to be observable and knowable. But defining those causal powers requires admitting laws of nature, taken as axioms or principles of natural (...)
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  7. Strict Finitism's Unrequited Love for Computational Complexity.Noel Arteche - manuscript
    As a philosophy of mathematics, strict finitism has been traditionally concerned with the notion of feasibility, defended mostly by appealing to the physicality of mathematical practice. This has led the strict finitists to influence and be influenced by the field of computational complexity theory, under the widely held belief that this branch of mathematics is concerned with the study of what is “feasible in practice”. In this paper, I survey these ideas and contend that, contrary to popular belief, complexity (...)
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  8. An inexplicably good argument for causal finitism.Ibrahim Dagher - 2023 - International Journal for Philosophy of Religion 94 (2):199-211.
    Causal finitism, the view that the causal history of any event must be finite, has garnered much philosophical interest recently—especially because of its applicability to the Kalām cosmological argument. The most prominent argument for causal finitism is the Grim Reaper argument, which attempts to show that, if infinite causal histories are possible, then other paradoxical states of affairs must also be possible. However, this style of argument has been criticized on the grounds of (i) relying on controversial modal (...)
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  9. On the Coherence of Strict Finitism.Auke Alesander Montesano Montessori - 2019 - Kriterion - Journal of Philosophy 33 (2):1-14.
    Strict finitism is the position that only those natural numbers exist that we can represent in practice. Michael Dummett, in a paper called Wang’s Paradox, famously tried to show that strict finitism is an incoherent position. By using the Sorites paradox, he claimed that certain predicates the strict finitist is committed to are incoherent. More recently, Ofra Magidor objected to Dummett’s claims, arguing that Dummett fails to show the incoherence of strict finitism. In this paper, I shall (...)
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  10. Hilbert’s Finitism: Historical, Philosophical, and Metamathematical Perspectives.Richard Zach - 2001 - Dissertation, University of California, Berkeley
    In the 1920s, David Hilbert proposed a research program with the aim of providing mathematics with a secure foundation. This was to be accomplished by first formalizing logic and mathematics in their entirety, and then showing---using only so-called finitistic principles---that these formalizations are free of contradictions. ;In the area of logic, the Hilbert school accomplished major advances both in introducing new systems of logic, and in developing central metalogical notions, such as completeness and decidability. The analysis of unpublished material presented (...)
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  11. A Step-by-Step Argument for Causal Finitism.Joseph C. Schmid - 2023 - Erkenntnis 88 (5):2097-2122.
    I defend a new argument for causal finitism, the view that nothing can have an infinite causal history. I begin by defending a number of plausible metaphysical principles, after which I explore a host of novel variants of the Littlewood-Ross and Thomson’s Lamp paradoxes that violate such principles. I argue that causal finitism is the best solution to the paradoxes.
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  12. Inconcistency of ℕ from a not-finitist point of view.Enrico Pier Giorgio Cadeddu - 2023 - International Journal of Modern Research in Engineering and Technology 8 (10):2.
    Considering the set of natural numbers ℕ, then in the context of Peano axioms, starting from inequalities between finite sets, we find a fundamental contradiction, about the existence of ℕ, from a not-finitist point of view.
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  13. Grim Reaper Paradoxes and Patchwork Principles: Severing the Case for Finitism.Troy Dana & Joseph C. Schmid - forthcoming - Journal of Philosophy.
    Benardete paradoxes involve infinite collections of Grim Reapers, assassins, demons, deafening peals, or even sentences. These paradoxes have recently been used in arguments for finitist metaphysical theses such as temporal finitism, causal finitism, and discrete views of time. Here we develop a new finite Benardete-like paradox. We then use this paradox to defend a companions in guilt argument that challenges recent applications of patchwork principles on behalf of the aforementioned finitist arguments. Finally, we develop another problem for those (...)
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  14. Numbers and functions in Hilbert's finitism.Richard Zach - 1998 - Taiwanese Journal for History and Philosophy of Science 10:33-60.
    David Hilbert's finitistic standpoint is a conception of elementary number theory designed to answer the intuitionist doubts regarding the security and certainty of mathematics. Hilbert was unfortunately not exact in delineating what that viewpoint was, and Hilbert himself changed his usage of the term through the 1920s and 30s. The purpose of this paper is to outline what the main problems are in understanding Hilbert and Bernays on this issue, based on some publications by them which have so far received (...)
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  15. Takeuti's well-ordering proofs revisited.Andrew Arana & Ryota Akiyoshi - 2021 - Mita Philosophy Society 3 (146):83-110.
    Gaisi Takeuti extended Gentzen's work to higher-order case in 1950's–1960's and proved the consistency of impredicative subsystems of analysis. He has been chiefly known as a successor of Hilbert's school, but we pointed out in the previous paper that Takeuti's aimed to investigate the relationships between "minds" by carrying out his proof-theoretic project rather than proving the "reliability" of such impredicative subsystems of analysis. Moreover, as briefly explained there, his philosophical ideas can be traced back to Nishida's philosophy in Kyoto's (...)
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  16. The End is Near: Grim Reapers and Endless Futures.Joseph C. Schmid - forthcoming - Mind.
    José Benardete developed a famous paradox involving a beginningless set of items each member of which satisfies some predicate just in case no earlier member satisfies it. The Grim Reaper version of this paradox has recently been employed in favor of various finitist metaphysical theses, ranging from temporal finitism to causal finitism to the discrete nature of time. Here, I examine a new challenge to these finitist arguments—namely, the challenge of implying that the future cannot be endless. In (...)
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  17. The Partial Identity Account of Partial Similarity Revisited.Matteo Morganti - 2011 - Philosophia 39 (3):527-546.
    This paper provides a defence of the account of partial resemblances between properties according to which such resemblances are due to partial identities of constituent properties. It is argued, first of all, that the account is not only required by realists about universals à la Armstrong, but also useful (of course, in an appropriately re-formulated form) for those who prefer a nominalistic ontology for material objects. For this reason, the paper only briefly considers the problem of how to conceive of (...)
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  18. Inconsistency of ℕ and the question of infinity.Enrico Pier Giorgio Cadeddu - manuscript
    In the article ”Inconsistency of N from a not-finitist point of view” we have shown the inconsistency of N, going through a denial. Here we delete this indirect step and essentially repeat the same proof. Contextually we find a contradiction about natural number definition. Then we discuss around the rejection of infinity.
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  19. The Quantum Strategy of Completeness: On the Self-Foundation of Mathematics.Vasil Penchev - 2020 - Cultural Anthropology eJournal (Elsevier: SSRN) 5 (136):1-12.
    Gentzen’s approach by transfinite induction and that of intuitionist Heyting arithmetic to completeness and the self-foundation of mathematics are compared and opposed to the Gödel incompleteness results as to Peano arithmetic. Quantum mechanics involves infinity by Hilbert space, but it is finitist as any experimental science. The absence of hidden variables in it interpretable as its completeness should resurrect Hilbert’s finitism at the cost of relevant modification of the latter already hinted by intuitionism and Gentzen’s approaches for completeness. This (...)
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  20. Aristotle's Actual Infinities.Jacob Rosen - 2021 - Oxford Studies in Ancient Philosophy 59.
    Aristotle is said to have held that any kind of actual infinity is impossible. I argue that he was a finitist (or "potentialist") about _magnitude_, but not about _plurality_. He did not deny that there are, or can be, infinitely many things in actuality. If this is right, then it has implications for Aristotle's views about the metaphysics of parts and points.
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  21. The gödel paradox and Wittgenstein's reasons.Francesco Berto - 2009 - Philosophia Mathematica 17 (2):208-219.
    An interpretation of Wittgenstein’s much criticized remarks on Gödel’s First Incompleteness Theorem is provided in the light of paraconsistent arithmetic: in taking Gödel’s proof as a paradoxical derivation, Wittgenstein was drawing the consequences of his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. It is shown that the features of paraconsistent arithmetics match (...)
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  22. Determination Relations and Metaphysical Explanations.Maşuk Şimşek - forthcoming - Dialectica.
    Ross Cameron (2022) argues that metaphysical infinitists should reject the generally accepted idea that metaphysical determination relations back metaphysical explanations. Otherwise it won’t be possible for them to come up with successful explanations for the existence of dependent entities in non-wellfounded chains of dependence. I argue that his argument suffers from what he calls the finitist dogma, although indirectly so. However, there is a better way of motivating Cameron’s conclusion. Assuming Cameron’s principle of Essence, explanations for the existence of dependent (...)
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  23. THE SYNTHETICITY OF TIME: Comments on Fang's Critique of Divine Computers.Stephen R. Palmquist - 1989 - Philosophia Mathematica: 233–235.
    In a recent article in this journal [Phil. Math., II, v.4 (1989), n.2, pp.?- ?] J. Fang argues that we must not be fooled by A.J. Ayer (God rest his soul!) and his cohorts into believing that mathematical knowledge has an analytic a priori status. Even computers, he reminds us, take some amount of time to perform their calculations. The simplicity of Kant's infamous example of a mathematical proposition (7+5=12) is "partly to blame" for "mislead[ing] scholars in the direction of (...)
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  24. Creative reasoning.John Turri - 2014 - In John Turri & Peter D. Klein (eds.), Ad infinitum: new essays on epistemological infinitism. New York, NY: Oxford University Press. pp. 210-226.
    I defend the unpopular view that inference can create justification. I call this view inferential creationism. Inferential creationism has been favored by infinitists, who think that it supports infinitism. But it doesn’t. Finitists can and should accept creationism.
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  25. Can there be a Finite Interpretation of the Kantian Sublime?Sacha Golob - 2019 - Kant Yearbook 11 (1):17-39.
    Kant’s account of the sublime makes frequent appeals to infinity, appeals which have been extensively criticised by commentators such as Budd and Crowther. This paper examines the costs and benefits of reconstructing the account in finitist terms. On the one hand, drawing on a detailed comparison of the first and third Critiques, I argue that the underlying logic of Kant’s position is essentially finitist. I defend the approach against longstanding objections, as well as addressing recent infinitist work by Moore and (...)
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  26. Zeno Beach.Jacob Rosen - 2020 - Phronesis 65 (4):467-500.
    On Zeno Beach there are infinitely many grains of sand, each half the size of the last. Supposing Aristotle denied the possibility of Zeno Beach, did he have a good argument for the denial? Three arguments, each of ancient origin, are examined: the beach would be infinitely large; the beach would be impossible to walk across; the beach would contain a part equal to the whole, whereas parts must be lesser. It is attempted to show that none of these arguments (...)
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  27. On Infinite Number and Distance.Jeremy Gwiazda - 2012 - Constructivist Foundations 7 (2):126-130.
    Context: The infinite has long been an area of philosophical and mathematical investigation. There are many puzzles and paradoxes that involve the infinite. Problem: The goal of this paper is to answer the question: Which objects are the infinite numbers (when order is taken into account)? Though not currently considered a problem, I believe that it is of primary importance to identify properly the infinite numbers. Method: The main method that I employ is conceptual analysis. In particular, I argue that (...)
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  28. More Than a Flesh Wound.Graham Oppy - 2002 - Ars Disputandi 2:214-224.
    In ‘The Kalam Cosmological Argument Neither Bloodied nor Bowed’ , David Oderberg provides four main criticisms of the line of argument which I developed in ‘Time, Successive Addition, and Kalam Cosmological Arguments’ . I argue here that none of these lines of criticism succeeds. Further I re-emphasise the point that those who maintain that the temporal series of past events is formed by ‘successive addition’ are indeed thereby committed to a highly contentious strict finitist metaphysics.
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  29. Tarski's Nominalism.Greg Frost-Arnold - 2008 - In Douglas Patterson (ed.), New essays on Tarski and philosophy. New York: Oxford University Press.
    Alfred Tarski was a nominalist. But he published almost nothing on his nominalist views, and until recently the only sources scholars had for studying Tarski’s nominalism were conversational reports from his friends and colleagues. However, a recently-discovered archival resource provides the most detailed information yet about Tarski’s nominalism. Tarski spent the academic year 1940-41 at Harvard, along with many of the leading lights of scientific philosophy: Carnap, Quine, Hempel, Goodman, and (for the fall semester) Russell. This group met frequently to (...)
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  30. The Physical Foundations of Biology and the Problem of Psychophysics.Alfred Gierer - 1970 - Ratio (Misc.) 12:47-64.
    Full applicability of physics to human biology does not necessarily imply that one can uncover a comprehensive, algorithmic correlation between physical brain states and corresponding mental states. The argument takes into account that information processing is finite in principle in a finite world. Presumbly the brain-mind-relation cannot be resolved in all essential aspects, particularly when high degrees of abstraction or self-analytical processes are involved. Our conjecture plausibly unifies the universal validity of physics and a logical limitation of human thought, and (...)
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  31. Nothing Infinite: A Summary of Forever Finite.Kip Sewell - 2023 - Rond Media Library.
    In 'Forever Finite: The Case Against Infinity' (Rond Books, 2023), the author argues that, despite its cultural popularity, infinity is not a logical concept and consequently cannot be a property of anything that exists in the real world. This article summarizes the main points in 'Forever Finite', including its overview of what debunking infinity entails for conceptual thought in philosophy, mathematics, science, cosmology, and theology.
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  32. Truth and Existence.Jan Heylen & Leon Horsten - 2017 - Thought: A Journal of Philosophy 6 (1):106-114.
    Halbach has argued that Tarski biconditionals are not ontologically conservative over classical logic, but his argument is undermined by the fact that he cannot include a theory of arithmetic, which functions as a theory of syntax. This article is an improvement on Halbach's argument. By adding the Tarski biconditionals to inclusive negative free logic and the universal closure of minimal arithmetic, which is by itself an ontologically neutral combination, one can prove that at least one thing exists. The result can (...)
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  33. Gödel mathematics versus Hilbert mathematics. I. The Gödel incompleteness (1931) statement: axiom or theorem?Vasil Penchev - 2022 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 14 (9):1-56.
    The present first part about the eventual completeness of mathematics (called “Hilbert mathematics”) is concentrated on the Gödel incompleteness (1931) statement: if it is an axiom rather than a theorem inferable from the axioms of (Peano) arithmetic, (ZFC) set theory, and propositional logic, this would pioneer the pathway to Hilbert mathematics. One of the main arguments that it is an axiom consists in the direct contradiction of the axiom of induction in arithmetic and the axiom of infinity in set theory. (...)
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  34. Brain, mind and limitations of a scientific theory of human consciousness.Alfred Gierer - 2008 - Bioessays 30 (5):499-505.
    In biological terms, human consciousness appears as a feature associated with the func- tioning of the human brain. The corresponding activities of the neural network occur strictly in accord with physical laws; however, this fact does not necessarily imply that there can be a comprehensive scientific theory of conscious- ness, despite all the progress in neurobiology, neuropsychology and neurocomputation. Pre- dictions of the extent to which such a theory may become possible vary widely in the scien- tific community. There are (...)
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  35. Hume against the Geometers.Dan Kervick -
    In the Treatise of Human Nature, David Hume mounts a spirited assault on the doctrine of the infinite divisibility of extension, and he defends in its place the contrary claim that extension is everywhere only finitely divisible. Despite this major departure from the more conventional conceptions of space embodied in traditional geometry, Hume does not endorse any radical reform of geometry. Instead Hume espouses a more conservative approach, claiming that geometry fails only “in this single point” – in its purported (...)
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  36. An Eternal Society Paradox.Wade A. Tisthammer - 2020 - Aporia 30 (1):49-58.
    An eternal society with the abilities of ordinary humans in each year of its existence would have had the ability to actualize a logical contradiction. This fact casts doubt on the metaphysical possibility of an infinite past. In addition to using this paradox in an argument against an infinite past, one can also use the paradox mutatis mutandis as a decisive argument against the sempiternality of God.
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  37. Toward a new kalām cosmological argument.Benjamin Victor Waters - 2015 - Cogent Arts and Humanities 2 (1).
    William Lane Craig has revived interest in the medieval kalām argument to the point where it is now one of the most discussed arguments for God’s existence in the secondary literature. Still, the reception of Craig’s argument among philosophers of religion has been mostly critical. In the interest of developing an argument that more philosophers of religion would be inclined to support, I will lay the philosophical groundwork for a new kalām cosmological argument that, in contrast with Craig’s argument, does (...)
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  38. Forever Finite: The Case Against Infinity (Expanded Edition).Kip K. Sewell - 2023 - Alexandria, VA: Rond Books.
    EXPANDED EDITION (eBook): -/- Infinity Is Not What It Seems...Infinity is commonly assumed to be a logical concept, reliable for conducting mathematics, describing the Universe, and understanding the divine. Most of us are educated to take for granted that there exist infinite sets of numbers, that lines contain an infinite number of points, that space is infinite in expanse, that time has an infinite succession of events, that possibilities are infinite in quantity, and over half of the world’s population believes (...)
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  39. Review of Approaches to Wittgenstein: Collected Papers, by Brian McGuinness and Wittgenstein, Rules and Institutions, by David Bloor. [REVIEW]Julian Friedland - 2004 - Essays in Philosophy 5 (1):164-168.
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