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The Paradox of the Stone
... Thanks to the word taken in the first meaning the sentence ''Electra knows that Orestes is her brother'' stands, more or less, for ''Electra knows her brother Orestes''. The other sentence from the analyzed story, ''Electra 11 Kotarbiński [5], p. 187. 12 This definition was ridiculed by Diogenes of Sinope (ca. ...
... Since the task of creating a stone that being X cannot lift is internally contradictory if and only if X is an omnipotent being, the 36 Mayo [10], p. 250. 37 Savage [11]. 38 Savage [11], p. 74. ...
... 37 Savage [11]. 38 Savage [11], p. 74. 39 Keene's error concerning the expression ''can'' is clearly repeated here. ...
Language is a tool, which we use every time we want to say something about reality, one or another. Because reality transcends
the limits of language, we are bound to use the same terms in meanings that can vary, from similar to completely different.
Ambiguity of natural language expressions is thus a phenomenon both natural and very common. Unfortunately, we tend to forget
about it. Even scientific discourse is sometimes poisoned by the error of ambiguity. In this chapter, we shall focus on the
most important problems, which have their source in ambiguity.
... Example: If S consists of the single wff AA(q v ~q, p & BU{p 9 q)) 9 a skeleton of S consists of the following ten wffs: p; q\ BU{p 9 q) AA(qv~q 9 p&BU(p 9 q)) BA(p 9 q) AU(qv~q 9 p&BIl(p 9 q)) BU(p& (qv~q), qy(p&BU(p 9 q))) BA(p &(qv ~q) 9 ...
... Example: If S consists of the single wff AA(q v ~q, p & BU{p 9 q)) 9 a skeleton of S consists of the following ten wffs: p; q\ BU{p 9 q) AA(qv~q 9 p&BU(p 9 q)) BA(p 9 q) AU(qv~q 9 p&BIl(p 9 q)) BU(p& (qv~q), qy(p&BU(p 9 q))) BA(p &(qv ~q) 9 ...
... Part 4 is a lemma for Part 5. In Part 5, I show that by using the rule stated in Part 3 one obtains models for LA(S X ) 9 LA(S 2 ), etc. Since the valuation V k+ι for LA(S k+{ ) agrees with the valuation V k for LA(S k ) on 5*, one can then define F f by: F 1 " assigns the same truth-values as V k to members of S k . ...
... Esta paradoja, que tiene raíces medievales, pero aparece en Savage (1967), podría enseñarse en el curso de filosofía de la religión o incluso podría plantearse como desafío para estudiantes de teología. ¿Puede Dios crear una piedra tan grande que él mismo no sea capaz de levantar? ...
Últimamente, la educación se ha visto desafiada por el contexto digital que beneficia a las plataformas virtuales
que contienen creaciones de youtubers o influencers, los cuales se enfocan en entretener más que en formar integralmente al estudiante. En este sentido, este artículo considera a las paradojas como recursos didácticos que pueden ayudar al desarrollo del pensamiento crítico del estudiante durante su formación. Esta investigación es documental y se basa en la consulta de fuentes escritas y de internet. Comienza aclarando los conceptos de falacia y reducción al absurdo, pues las paradojas han sido vistas como falacias muy sutiles por algunos estudiosos como Bertrand Russell y, además, hay quienes utilizan las paradojas para realizar deducciones, como ocurre en la reducción al absurdo que se aplica en el argumento ontológico de San Anselmo de Canterbury. Enseguida, se analiza una lista de paradojas, pero con el objetivo de que puedan ser utilizadas en un aula de clase. Así, se trata sobre algunas paradojas como la paradoja de Aquiles y la Tortuga, la de Galileo, la del hotel de Hilbert, la de Tristam Shandy, la de Protágoras, etc. Este trabajo se cierra tratando de explicitar el aspecto afectivo y emocional que un estudiante experimenta cuando trata con esta clase de problemas.
... It pleads with God to play the fool. None of Mavrodes' (1963) solutions concerning omnipotence, Geach's (1973) four restrictions, Wade's (1967) attempted solutions to the paradox of the Stone, Aquinas triangle, or Descartes' indivisible things, and so on, say anything about God's logical insulation from stupidity. The only true solution is to highlight the dununu principle: that account of the things that God, being God, would rather not do and would rather not be seen doing. ...
... 17 Diğerleri ise paradoksun bir ikilemin ikinci ucunun yanlışa yönlendiren bir yorumuna bağlı olduğunu göstermeye çalıştılar. 18 Grim'in her şeyi bilme (Omniscience)'ye karşı olan argümanına cevaben, bazıları bizim alternatif bir küme teorisini benimsememiz durumunda bu argümanın işlemeyeceğini savunurken, 19 diğerleri bu argümanın kendi kendisini çürüttüğünü iddia etmişlerdir. 20 Tanrı'nın günah işleyememe argümanına cevaben bazıları ahlaken yanlış olan filleri yapamamanın, güçte bir sınırlama olmadığını göstermeye çalışırken, 21 diğerleri ise güçlü gerçekleştirme ile zayıf gerçekleştirme arasındaki ayırımın sunulması ile bu argümanın başarısız olacağını iddia ederler. ...
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Tanrı’nın kendisinden daha büyüğü düşünülemeyen varlık olduğunu savunan Anselmci teistler, genel olarak Tanrı’nın her şeyi bilen, her şeye gücü yeten ve mutlak iyi olan bir varlık olduğu çıkarımında bulunurlar. Eleştirmenler bu iddialara sayısız farklı argümanlar ile saldırıda bulundular, örneğin, taş paradoksu, Tanrı’nın günah işleyememe argümanı ve kötülük problemi. Anselmci teistler bu argümanların her birine birbirinden bağımsız cevaplar inşa ederek cevapladılar. Anselmci teizmi bu yolla savunmak ihtiyatsızdır/boşyeredir. Ben Anselmci teizme karşı var olan hemen hemen bütün argümanları bir seferde geçersiz kılacak yeni bir savunu kurmaya çalışacağım. Bu savunuyu geliştirirken, Anselmci Tanrı’nın her şeyi bilen, her şeye gücü yeten ve mutlak iyi olan bir varlık olmadığı ihtimalini göz önünde bulunduracağım.
nselmian theists, for whom God is the being than which no greater can be thought, usually infer that he is an omniscient, omnipotent and omnibenevolent being. Critics have attacked these claims by numerous distinct arguments, such as the paradox of the stone, the argument from God's inability to sin, and the argument from evil. Anselmian theists have responded to these arguments by constructing an independent response to each. This way of defending Anselmian theism is uneconomical. I seek to establish a new defence which undercuts almost all the existing arguments against Anselmian theism at once. In developing this defence, I consider the possibility that the Anselmian God is not an omniscient, omnipotent and omnibenevolent being.
nselmian theists, for whom God is the being than which no greater can be thought, usually infer that he is an omniscient, omnipotent and omnibenevolent being. Critics have attacked these claims by numerous distinct arguments, such as the paradox of the stone, the argument from God's inability to sin, and the argument from evil. Anselmian theists have responded to these arguments by constructing an independent response to each. This way of defending Anselmian theism is uneconomical. I seek to establish a new defence which undercuts almost all the existing arguments against Anselmian theism at once. In developing this defence, I consider the possibility that the Anselmian God is not an omniscient, omnipotent and omnibenevolent being.
As shown in (Łukowski, Gensler, 2013), the paradox of the stone is a failed attempt to show that “omnipotence” is a contradictory concept. An element of the argument presented there is that God, while unable to lift the stone, can nevertheless annihilate it. This work considers the amplification of the paradox of the stone to the form generated by the question: can God create a stone which He will not be able to lift, nor, once created, will He be able to destroy.
Classical theists hold that God is omnipotent. But now suppose a critical atheologian were to ask: Can God create a stone so heavy that even he cannot lift it? This is the dilemma of the stone paradox. God either can or cannot create such a stone. Suppose that God can create it. Then there's something he cannot do – namely, lift the stone. Suppose that God cannot create the stone. Then, again, there's something he cannot do – namely, create it. Either way, God cannot be omnipotent. Among the variety of known theological paradoxes, the paradox of the stone is especially troubling because of its logical purity. It purports to show that one cannot believe in both God and the laws of logic. In the face of the stone paradox, how should the contemporary analytic theist respond? Ought they to revise their belief in theology or their belief in logic? Ought they to lose their religion or lose their mind?
In “God of the Gaps: A Neglected Reply to God’s Stone Problem”, Jc Beall and A. J. Cotnoir offer a gappy solution to the paradox of (unrestricted) omnipotence that is typified by the classic stone problem. Andrew Tedder and Guillermo Badia, however, have recently argued that this solution could not be extended to a more serious Curry-like version of the paradox. In this paper, we show that such a gappy solution does extend to it
Artificial intelligence (AI) is a young scientific field, which like other domains of information processing sciences, was born in the middle of the XXth century, with the arrival of the first computers. However, much more long-standing concerns have contributed to its final emergence. They can be broadly articulated around two main issues: the formalization of reasoning and learning mechanisms and the design of machines having autonomous capabilities in terms of computation and action. Over time, such machines have been first dreamed, before being designed and made real. The progressive achievements have fed the imagination of philosophers, but also writers, movie makers, and other artists. This is the reason why in the few elements of the great historical epic that we sketch here, references to all sectors of human creativity are involved.
I discuss Thomas Aquinas’ views on being, power, and logic, and show how together they provide rebuttals against certain principal objections to the notion of divine omnipotence. The objections I have in mind can be divided into the two classes. One says that the notion of omnipotence ends up in self-contradiction. The other says that it ends up contradicting certain doctrines of traditional theism. Thomas’ account is frequently misunderstood to be a version of what I call a ‘consistent description’ account of omnipotence, which is a standard contemporary account. That account of omnipotence, however, succumbs to certain contemporary objections. Thomas’ account withstands those objections because of his view of logic and, specifically self-contradiction. Moreover, a certain thesis found in Thomas’ understanding of God, but almost entirely absent from contemporary debates about omnipotence, is that God is not just a being, but the source of being. This thesis, I argue, puts Thomas’ account in a position that differs greatly from many contemporary accounts since the scope of possibility, and specifically the scope of what possible powers there are, is ultimately grounded in God’s being. Further still, many contemporary accounts of omnipotence do not seek to establish substantive account of power itself. Thomas, by contrast, has a robust and independent account of what power is. And that account informs his account of what it is to have all powers, or to be omnipotent, in a way that makes his account resistant to contemporary objections. Against contemporary objections, Thomas’ account of omnipotence can sustain the claim that God can do all things.
Theism is characterized by belief in a God that possesses a unique set of characteristics or attributes. The theistic conception of God that is formed by the combination of these attributes has been troublesome through the centuries and has given rise to many questions and criticisms — by theists and nontheists alike — both of the individual attributes and the collective set of attributes. These problems persisted throughout the twentieth century and intensified in the last few decades. Some of the issues concerning the attributes are old ones revisited in light of our changing knowledge of the natural world as a result of the development of science. Others are logical issues that have been given new “twists” by contemporary scholars, quite independently of contingent matters. The coherence of the attributes that comprise the concept of God is fundamental to theism since the viability of theism must begin with the viability of the concept of God. Sorting through the difficulties surrounding the traditional attributes of the theistic deity is such a fundamental problem that Richard Swinburne devotes approximately two-thirds of what many consider his seminal work, The Coherence of Theism, to an explanation and defense of the coherence of these attributes. Although there are many disagreements among theists that need to be explored, I shall take Swinburne’s view as typical of the traditional theistic concept of God: namely, “that there exists eternally an omnipresent spirit, free, creator of the universe, omnipotent, omniscient, perfectly good, and a source of moral obligation.”1
La philosophie analytique a repris le flambeau de la théologie naturelle que l’on croyait éteint depuis Pascal, Hume, Kant, Kierkegaard, Schleiermacher. Il s’est produit un curieux chassé-croisé : la philosophie analytique a fini par se réconcilier avec l’enquête métaphysique, alors que la théologie continentale a pour une bonne part accompagné voire encouragé la déconstruction de la métaphysique théiste. On présente ici en particulier comment la philosophie analytique permet de renouveler l’approche du concept de création ex nihilo.
Focusing on God’s essential attributes of omnipotence, omniscience, being eternal and omnipresent, being a creator and sustainer, and being a person, I examine how far recent discussion has been able to provide for each of these divine attributes a consistent interpretation. I also consider briefly whether the attributes are compatible with each other.
I begin with some remarks on Christian Atheism and the Death of God Theology. These are not, as might be thought, identical movements. Rather, as I shall try to make clear, Christian Atheism is one form that the Death of God theology has assumed.
Anselmian theists, for whom God is the being than which no greater can be thought, usually infer that he is an omniscient, omnipotent and omnibenevolent being. Critics have attacked these claims by numerous distinct arguments, such as the paradox of the stone, the argument from God's inability to sin, and the argument from evil. Anselmian theists have responded to these arguments by constructing an independent response to each. This way of defending Anselmian theism is uneconomical. I seek to establish a new defence which undercuts almost all the existing arguments against Anselmian theism at once. In developing this defence, I consider the possibility that the Anselmian God is not an omniscient, omnipotent and omnibenevolent being.
Atheists are frequently content to argue God's nonexistence using contingent premises concerning the existence of evil or, more plausibly, concerning the enormous quantity of evil in the world. But sometimes they are more aggressive. They may try to argue that God cannot exist because the very concept God (taken here as including the properties of being omnipotent, omniscient, and perfectly good) is logically self-contradictory or inconsistent. This takes some doing since the conception is certainly not obviously inconsistent. One collection of arguments in this vein focuses on the concept of omnipotence and attempts to show that it is incoherent to suppose the conception actually applies to something. A typical example of this sort is the "Paradox of the Stone." Can God make a stone which even He cannot lift? Yes? Then there is something which He cannot do, viz., lift said stone. No? Then there is something which He cannot do: make such a stone. In either case, God is not omnipotent. Hence, of necessity, God cannot be omnipotent. Hence, He cannot exist. Well, what is or at least should be the standard reply is that omnipotence does not require the impossible and creating a stone which an omnipotent being cannot lift is impossible. This is pretty much the answer given by St. Thomas Aquinas ([26], Question 25, Article 3), George Mavrodes ([13]), Alvin, Plantinga ([19]) and others. Actually the argument as stated contains a logical gap (see Section I below), so that if the theist wanted to be strict about it, he could reject the thing after pointing out its invalidity. However, it is relatively easy to fill the lacuna and give the atheist his due. But when this is done, the reasoning is still subject to the objection just explained.
No matter how much controversy and debate may currently surround the extraordinary attribute of divine omnipotence, there is a virtually complete consensus amongst philosophers and theologians that Aquinas is correct in saying that 'anything that implies a contradiction does not fall under God's omnipotence, 't and that Descartes, in maintaining that God can arrange that a mountain should exist without a valley or that one and two should not make three, 2 in effect fulfilled his own dictum that nothing is too absurd for some philosopher to have said it at some time. This provocative but forever unpopular thesis, called the absolutist theory of omnipotence (hereafter ATO), can be stated as follows: The theistic God is omnipotent in the sense that he is able to bring about absolutely any state of affairs, including those states of affairs which are logically impossible to bring about and those which are inconsistent with any of his attributes. I hope to show, first of all, that two sets of objections that are often raised against ATO are wanting in validity or soundness. Interestingly, clear and elaborate arguments against ATO are difficult to come by in the literature on omnipotence. Unfortunately, ATO is often quickly dismissed as something that no philosopher or theologian of repute (with the exception of Descartes) has taken seriously)
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.
“Reflexivity” is the generic name for all kinds and species of circularity. It includes the self-reference of signs, the self-appplication of principles and predicates, the self-justification and self-refutation of propositions and inferences, the self-fulfillment and self-falsification of predictions, the self-creation and self-destruction of logical and legal entities, the self-augmentation and self-limitation of powers, circular reasoning, circular causation, cyclic and spiral recurrence, feedback systems, mutuality, reciprocity, and organic form. It includes the fallacious, the vicious, the trivial, and the question begging, but also the sound, the benign, the useful, and the inescapable. It ranges from the prosaic to the numinous, from the paradoxical to the self-evident, from science to religion. It is reality and appearance, native to the processes of the world and to our knowledge and discourse about them.
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