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A course of dialogical reasoning involving the atheist and the theist reveals a connection between the Curry phenomenon and the step‐wise construction of a sound version of the modal ontological argument. The exercise is both adversarial and cooperative as the participants are committed to the norms of shared truth‐seeking, respect for one's opponents and a desire to continue the dialectic for as long as possible. The theist relies on the interaction between the properties of a Curry‐style sentence and the structure of implication in order to show that the atheist's own commitments imply Anselm's principle (God necessarily exists if He actually exists at all). As Anselm's principle and the possibility premise are the only assumptions required for the modal ontological argument it follows that the theist has, given the norms of the dialogue, a winning strategy against the atheist. This follows since the possibility premise is granted by the atheist as part of their commitment to the norms governing the dialectic though the theist in virtue of those same norms must accept that God is at best maximally perfect in the light of the argument from evil and the Stone paradox.
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En este artículo discutiré algunos problemas lógicos de la omnipotencia que van más allá de las clásicas paradojas ligadas a esta noción. Presentaré una versión refinada de la paradoja de Fitch sobre la omnipotencia que tiene en cuenta la distinción entre acciones básicas y derivadas, así como la distinción entre la capacidad de hacer algo y la mera posibilidad metafísica de hacerlo. También explico cómo esta paradoja puede reformularse para obtener una versión afín a la paradoja del mentiroso que afecta a la consistencia de ciertas nociones de omnipotencia. Por último, evalúo algunas posibles respuestas disponibles para el teísta y un intento de usar la paradoja de Fitch como argumento a favor de la existencia de Dios.
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Humberstone has shown that if some set of agents is collectively omniscient (every true proposition is known by at least one agent) then one of them alone must be omniscient. The result is paradoxical as it seems possible for a set of agents to partition resources whereby at the level of the whole community they enjoy eventual omniscience. The Humberstone paradox only requires the assumption that knowledge distributes over conjunction and as such can be viewed as a reductio against the universal validity of that principle. A new route to this paradox is presented which does not require the distribution principle, building on earlier work of Jago and Williamson on Fitch’s paradox. The result relies on an axiom strictly weaker than one necessary for the Jago-Fitch variant. It is shown that the same reasoning behind the variant form of Humberstone’s paradox can recover Bigelow’s results in action theory in a way that is immune to an objection brought against it by Guigon and Humberstone.
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Two proofs are given which show that if some set of truths fall under finitely many concepts (so‐called ), then they all fall under at least one of them even if we do not know which one. Examples are given in which the result seems paradoxical. The first proof crucially involves Moorean propositions while the second is a reconstruction and generalization of a proof due to Humberstone free from any reference to such propositions. We survey a few solution routes including Tennant‐style restriction strategies. It is concluded that accepting for some set of truths while also denying that any of the involved concepts in isolation capture all of them requires that one of these concepts cannot be closed under conjunction elimination. This is surprising since the paper surveys several applications in which and the latter closure condition seemed jointly satisfiable for concepts of actual philosophical interest.
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In virtue of Fitch-Church proof, also known as the knowability paradox, we are able to prove that if everything is knowable, then everything is known. I present two ‘onto-theological’ versions of the proof, one concerning collective omniscience and another concerning omnificence. I claim these arguments suggest new ways of exploring the intersection between logical and ontological givens that is a grounding theme of religious thought. What is more, they are good examples of what I call semi-paradoxes: apparently sound arguments whose conclusion is not properly unacceptable, but simply arguable.
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I propose a taxonomy of arguments for the existence of God and survey those categories of arguments I identify as nontraditional. I conclude with two general observations about theistic arguments, followed by suggestions for going forward.
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In 1945, Alonzo Church issued a pair of referee reports in which he anonymously conveyed to Frederic Fitch a surprising proof showing that wherever there is (empirical) ignorance there is also logically unknowable truth. Fitch published this and a generalization of the result in 1963. Ever since, philosophers have been attempting to understand the significance and address the counter-intuitiveness of this, the so-called paradox of knowability. This book assembles Church's referee reports, Fitch's 1963 paper, and nineteen new papers on the knowability paradox. The book contains a general introduction to the paradox and the background literature, and is divided into seven sections that roughly mark the central points of debate. The sections include the history of the paradox, Michael Dummett's constructivism, issues of paraconsistency, developments of modal and temporal logics, Cartesian restricted theories of truth, modal and mathematical fictionalism, and reconsiderations about how, and whether, we ought to construe an anti-realist theory of truth.
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Frederic Fitch, in a fascinating article, most regrettably ignorod by philosophers of religion, proves the following theorem on omnipotence: If for each situation that is the case it is logically possible that that situation was brought about by some agent, then whatever is the case was personally brought about by that agent. This is a mightily perplexing result. It seems to say that an omnipotent agent, in this sense, must personally have brought about every actual state of affairs that obtains. Yet many theologians have held that God is omnipotent while not being a universal agent. The free will defense, ~ for example, seems to require that there should be some actual states of affairs not (personally, at any rate) brought about by God. Whether and how God acts is puzzling in its own right. But in any case it has often been assumed that God is omnipotent, at least minimally in Fiteh's sense, without being a universal personal agent.
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The purpose of this paper is to provide a partial logical analysis of a few concepts that may be classified as value concepts or as concepts that are closely related to value concepts. Among the concepts that will be considered are striving for, doing, believing, knowing, desiring, ability to do, obligation to do , and value for . Familiarity will be assumed with the concepts of logical necessity, logical possibility, and strict implication as formalized in standard systems of modal logic (such as S4), and with the concepts of obligation and permission as formalized in systems of deontic logic. It will also be assumed that quantifiers over propositions have been included in extensions of these systems.