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  1. Jeremy Gwiazda, Paradoxes of the Infinite Rest on Conceptual Confusion.
    The purpose of this paper is to dissolve paradoxes of the infinite by correctly identifying the infinite natural numbers.
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  2. Jeremy Gwiazda (2014). Orderly Expectations. Mind 123 (490):503-516.
    In some games, the products of the probabilities times the payouts result in a series that is conditionally convergent, which means that the sum can vary based on the order in which the products are summed. The purpose of this paper is to address the question: How should such games be valued? We first show that, contrary to widespread belief, summing in the order determined by the mechanism of the game does not lead to the correct value. We then consider (...)
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  3. Jeremy Gwiazda (2014). On Multiverses and Infinite Numbers. In Klaas Kraay (ed.), God and the Multiverse. Routledge. 162-173.
    A multiverse is comprised of many universes, which quickly leads to the question: How many universes? There are either finitely many or infinitely many universes. The purpose of this paper is to discuss two conceptions of infinite number and their relationship to multiverses. The first conception is the standard Cantorian view. But recent work has suggested a second conception of infinite number, on which infinite numbers behave very much like finite numbers. I will argue that that this second conception of (...)
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  4. Jeremy Gwiazda (2013). Two Concepts of Completing an Infinite Number of Tasks. The Reasoner 7 (6):69-70.
     
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  5. Jeremy Gwiazda (2013). Throwing Darts, Time, and the Infinite. Erkenntnis 78 (5):971-975.
    In this paper, I present a puzzle involving special relativity and the random selection of real numbers. In a manner to be specified, darts thrown later hit reals further into a fixed well-ordering than darts thrown earlier. Special relativity is then invoked to create a puzzle. I consider four ways of responding to this puzzle which, I suggest, fail. I then propose a resolution to the puzzle, which relies on the distinction between the potential infinite and the actual infinite. I (...)
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  6. Jeremy Gwiazda (2012). A Proof of the Impossibility of Completing Infinitely Many Tasks. Pacific Philosophical Quarterly 93 (1):1-7.
    In this article, I argue that it is impossible to complete infinitely many tasks in a finite time. A key premise in my argument is that the only way to get to 0 tasks remaining is from 1 task remaining, when tasks are done 1-by-1. I suggest that the only way to deny this premise is by begging the question, that is, by assuming that supertasks are possible. I go on to present one reason why this conclusion (that supertasks are (...)
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  7. Jeremy Gwiazda (2012). On Infinite Number and Distance. 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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  8. Jeremy Gwiazda (2012). Repeated St Petersburg Two-Envelope Trials and Expected Value. The Reasoner 6 (3).
    It is commonly believed that when a finite value is received in a game that has an infinite expected value, it is in one’s interest to redo the game. We have argued against this belief, at least in the repeated St Petersburg two-envelope case. We also show a case where repeatedly opting for a higher expected value leads to a worse outcome.
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  9. Jeremy Gwiazda (2011). Infinitism, Completability, and Computability: Reply to Peijnenburg. Mind 119 (476):1123-1124.
    In ‘Infinitism Regained’, Jeanne Peijnenburg argues for a version of infinitism wherein ‘beliefs may be justified by an infinite chain of reasons that can be actually completed’. I argue that Peijnenburg has not successfully argued for this claim, but rather has shown that certain infinite series can be computed.
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  10. Jeremy Gwiazda (2011). On Making the Same Choice Eternally: A Reply to Davis. Sophia 50 (4):693-696.
    In this brief reply to Stephen Davis, I argue that Davis’s separationist position, wherein those who remain eternally apart from God do so by choice, is internally contradictory in that it leads to universalism.
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  11. Jeremy Gwiazda (2011). Worship and Threshold Obligations. Religious Studies 47 (4):521 - 525.
    In this reply to Tim Bayne and Yujin Nagasawa, I defend the possibility of a maximal-excellence account of the grounding of the obligation to worship God.I do not offer my own account of the obligation to worship God; rather I argue that the major criticism (that is raised against maximal-excellence accounts) fails. Thus maximal-excellence can ground an obligation to worship God.
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  12. Jeremy Gwiazda (2010). God's Random Selection: Reply to Steinberg. Sophia 49 (1):141-143.
    In this reply to Jesse Steinberg’s ‘God and the possibility of random creation’, I suggest a procedure whereby a being such as God could randomly select a number from an infinite set.
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  13. Jeremy Gwiazda, Probability, Hyperreals, Asymptotic Density, and God's Lottery.
    Consider a subset, S, of the positive integers. What is the probability of selecting a number in S, assuming that each positive integer has an equal chance of selection? The purpose of this short paper is to provide an answer to this question. I also suggest that the answer allows us to determine the relative sizes of two subsets of the positive integers.
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  14. Jeremy Gwiazda (2010). Richard Swinburne, the Existence of God, and Exact Numerical Values. Philosophia 38 (2):357-363.
    Richard Swinburne’s argument in The Existence of God discusses many probabilities, ultimately concluding that God probably exists. Swinburne gives exact values to almost none of these probabilities. I attempted to assign values to the probabilities that met that weak condition that they could be correct. In this paper, I first present a brief outline of Swinburne’s argument in The Existence of God. I then present the problems I encountered in Swinburne’s argument, specifically problems that interfered with my attempt to arrive (...)
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  15. Jeremy Gwiazda (2010). The Lawn Mowing Puzzle. Philosophia 38 (3):629-629.
    In this brief paper, I present a puzzle for consideration.
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  16. Jeremy Gwiazda (2009). Richard Swinburne's Argument to the Simplicity of God Via the Infinite. Religious Studies 45 (4):487-493.
    In ’The Coherence of Theism’ Richard Swinburne writes that a person cannot be omniscient and perfectly free. In ’The Existence of God’ Swinburne writes that God is a person who is omniscient and perfectly free. There is a straightforward reason why the two passages are not in tension, but recognition of this reason raises a problem for Swinburne’s argument in ’The Existence of God’ (the conclusion of which is that God likely exists). In this paper I present the problem for (...)
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  17. Jeremy Gwiazda (2009). Richard Swinburne, the Existence of God, and Principle P. Sophia 48 (4):393-398.
    Swinburne relies on principle P in The Existence of God to argue that God is simple and thus likely to exist. In this paper, I argue that Swinburne does not support P. In particular, his arguments from mathematical simplicity and scientists’ preferences both fail. Given the central role P plays in Swinburne’s overall argument in The Existence of God , I conclude that Swinburne should further support P if his argument that God likely exists is to be persuasive.
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  18. Jeremy Gwiazda (2009). Richard Swinburne, 'The Existence of God'. Sophia 48 (4):393 - 398.
    Swinburne relies on principle P in ’The Existence of God’ to argue that God is simple and thus likely to exist. In this paper, I argue that Swinburne does not support P. In particular, his arguments from mathematical simplicity and scientists’ preferences both fail. Given the central role P plays in Swinburne’s overall argument in ’The Existence of God’, I conclude that Swinburne should further support P if his argument that God likely exists is to be persuasive.
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  19. Jeremy Gwiazda (2008). Remarks on Jove and Thor. Faith and Philosophy 25 (1):79-86.
    In “How an Unsurpassable Being can Create a Surpassable World,” Daniel and Frances Howard-Snyder employ a fascinating thought experiment in anattempt to show that a morally unsurpassable being can create a surpassable world. Imagine that for each positive integer there is a world that a good,omnipotent, omniscient being can create. Jove randomly selects a number and creates the corresponding world; Thor simply creates world 888. The Howard-Snyders argue that it is logically possible that Jove is morally unsurpassable. William Rowe counters (...)
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  20. Jeremy Gwiazda, The Probability of an Infinite Sequence of Heads.
    Recently Timothy Williamson asked ‘How probable is an infinite sequence of heads?’ In this paper, I suggest the probability of an infinite sequence of heads.
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  21. Jeremy Gwiazda (2007). A Reply to Schlesinger's Theodicy. Religious Studies 43 (4):481-486.
    In "Religion and Scientific Method," George Schlesinger presented a strikingly original theodicy. In this paper, I explain the strategy underlying Schlesinger's argument. I then present a parallel argument to indicate the weakness of Schlesinger's theodicy. Finally, I show that Schlesinger's theodicy assumes a false principle, and therefore fails.
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  22. Jeremy Gwiazda (2006). The Train Paradox. Philosophia 34 (4):437-438.
    When two omnipotent beings are randomly and sequentially selecting positive integers, the being who selects second is almost certain to select a larger number. I then use the relativity of simultaneity to create a paradox by having omnipotent beings select positive integers in different orders for different observers.
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  23. Jeremy Gwiazda, Infinite Numbers Are Large Finite Numbers.
    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 be counted (...)
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