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Incompleteness and inconsistency

Mind 111 (444):817-832 (2002)

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  1. Is there an inconsistent primitive recursive relation?Seungrak Choi - 2022 - Synthese 200 (5):1-12.
    The present paper focuses on Graham Priest’s claim that even primitive recursive relations may be inconsistent. Although he carefully presented his claim using the expression “may be,” Priest made a definite claim that even numerical equations can be inconsistent. His argument relies heavily on the fact that there is an inconsistent model for arithmetic. After summarizing Priest’s argument for the inconsistent primitive recursive relation, I first discuss the fact that his argument has a weak foundation to explain that the existence (...)
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  • A Note on Gödel, Priest and Naïve Proof.Massimiliano Carrara - forthcoming - Logic and Logical Philosophy:1.
    In the 1951 Gibbs lecture, Gödel asserted his famous dichotomy, where the notion of informal proof is at work. G. Priest developed an argument, grounded on the notion of naïve proof, to the effect that Gödel’s first incompleteness theorem suggests the presence of dialetheias. In this paper, we adopt a plausible ideal notion of naïve proof, in agreement with Gödel’s conception, superseding the criticisms against the usual notion of naïve proof used by real working mathematicians. We explore the connection between (...)
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  • La dualité de Lautman contre la négativité de Hegel, et le paradoxe de leurs formalisations : Contribution à une enquête sur les formalisations de la dialectique.Emmanuel Barot - 2010 - Philosophiques 37 (1):111-148.
    L’article montre d’abord jusqu’où convergent la dialectique hégélienne de l’Idée et la dialectique lautmanienne des Idées, et ce sur quoi elles se séparent en profondeur : sur la négativité et le statut de la contradiction. Il s’intéresse ensuite à certaines formalisations qui ont été proposées de ces deux dialectiques : celle de Doz et Dubarle pour Hegel dans une extension de la logique booléenne, et celle, récemment esquissée par F. Zalamea en théorie des catégories, pour Lautman. Est montré dans ses (...)
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  • الهیات تمثیلی یا الهیات تشکیکی.محمد بهرامی - 2016 - پژوهشنامه فلسفه دین 14 (1):69-89.
    در زبان بشری الفاظی وجود دارد که در زبان دینی به نحو مشترک به خدا و مخلوقات نسبت داده می‌شود. نسبت این الفاظ به خدا و انسان به نحو مشترک لفظی و مشترک معنوی منجر به دیدگاه تشبیه و تعطیل می‌شود که از چالش‌های الهیاتی است. اندیشمندان اسلامی برای حل این چالش به معنا و مفاهیم تشکیکی این الفاظ متوسل شده‌اند. ملاصدرا، با مبانی فلسفی خود، برای حل این مسئله نظری را طرح کرده که می‌توان آن را الهیات تشکیکی نامید. (...)
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  • جعل معنا از نگاه سارتر و نقد و بررسی آن بر اساس مبانی شناخت‌گرایی.داود صدیقی & امیر عباس علیزمانی - 2016 - پژوهشنامه فلسفه دین 14 (1):119-142.
    جعل و کشف معنا دو دیدگاه بنیادین در معنای زندگی هستند که هر کدام موافقان و مخالفانی را به خود اختصاص داده‌اند. سارتر با تبیین وجودِ فی‌نفسه و وجودِ‌ لنفسه، و همچنین مفاهیمی همچون امکان ناضرور، آزادی و فردیت، ابتدا جهان را از هر معنایی تهی می‌کند و سپس برای استعلای خویش و همچنین عدم انفعال، در پی جعل معناست. بنابراین، در این حوزه، سارتر را می‌توان یک ناشناخت‌گرا و سوبژکتیویست خواند و از این رو انتقادات مربوط به این دو (...)
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  • What Is an Inconsistent Truth Table?Zach Weber, Guillermo Badia & Patrick Girard - 2016 - Australasian Journal of Philosophy 94 (3):533-548.
    ABSTRACTDo truth tables—the ordinary sort that we use in teaching and explaining basic propositional logic—require an assumption of consistency for their construction? In this essay we show that truth tables can be built in a consistency-independent paraconsistent setting, without any appeal to classical logic. This is evidence for a more general claim—that when we write down the orthodox semantic clauses for a logic, whatever logic we presuppose in the background will be the logic that appears in the foreground. Rather than (...)
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  • Dialetheias and Numbers Distinct from Themselves.Uwe Petersen - 2023 - Notre Dame Journal of Formal Logic 64 (2):239-246.
    According to Priest, a proof can be distinct from itself in the same way that a number can. Priest does not specify any such number, so the present little note aims at filling this lacuna by providing a plain arithmetical code of a dialetheia similar to but simpler than the one presented in our recent work and thereby a natural number distinct from itself.
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  • Truth and the Unprovability of Consistency.H. Field - 2006 - Mind 115 (459):567-606.
    It might be thought that we could argue for the consistency of a mathematical theory T within T, by giving an inductive argument that all theorems of T are true and inferring consistency. By Gödel's second incompleteness theorem any such argument must break down, but just how it breaks down depends on the kind of theory of truth that is built into T. The paper surveys the possibilities, and suggests that some theories of truth give far more intuitive diagnoses of (...)
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  • The importance of being Ernesto: Reference, truth and logical form.A. Bianchi, V. Morato & G. Spolaore (eds.) - 2016 - Padova: Padova University Press.
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  • Dialetheism.Graham Priest - 2008 - Stanford Encyclopedia of Philosophy.
    A dialetheia is a sentence, A, such that both it and its negation, A, are true (we shall talk of sentences throughout this entry; but one could run the definition in terms of propositions, statements, or whatever one takes as her favourite truth bearer: this would make little difference in the context). Assuming the fairly uncontroversial view that falsity just is the truth of negation, it can equally be claimed that a dialetheia is a sentence which is both true and (...)
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  • Dialetheism.Francesco Berto, Graham Priest & Zach Weber - 2008 - Stanford Encyclopedia of Philosophy 2018 (2018).
    A dialetheia is a sentence, A, such that both it and its negation, ¬A, are true (we shall talk of sentences throughout this entry; but one could run the definition in terms of propositions, statements, or whatever one takes as her favourite truth-bearer: this would make little difference in the context). Assuming the fairly uncontroversial view that falsity just is the truth of negation, it can equally be claimed that a dialetheia is a sentence which is both true and false.
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  • A Critical Analysis of J.L. Schellenberg's Views on the Problem of Divine Hiddenness تحلیل انتقادی دیدگاه جان شلنبرگ در باب مسأله خفای الاهی.Sayyed Nasirahmad Hossaini - 2014 - پژوهشنامه فلسفه دین 12 (2):133-157.
    In 1993, for the first time, John L. Schellenberg, the contemporary philosopher of religion, proposed the “Hiddenness Argument’’. According to this argument, as God doesn’t provide for many people sufficient evidence for His existence, He is Hidden. In the other words, that many people inculpably fail to find sufficient evidence for the existence of God constitutes evidence for atheism. Schellenberg argues that since a loving God would not withhold the benefits of belief, the lack of evidence for God’s existence is (...)
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  • John Hick on the Role of Cosmic Optimism and Culture in the Meaning of Life.Ahmad Pourghasem, Reyhane Sadat Azimi & Amir Abbas Alizamani - 2016 - پژوهشنامه فلسفه دین 13 (2):73-90.
    The question of the “meaning of life” has always studied by philosophers like John Hick and led them to make an explanation regarding their philosophical bases about it. John Hick mentions “the meaning of life” in his work based on the concepts he borrows from Wittgenstein and Kant and states that the meaning of life depends on an interrelation between the human and the world. Thus, he inevitably talks about the world as a place in which the human experiences his (...)
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  • Stace on Religious Language: The Epistemological Foundations.Mohammad Hosein Mahdavinejad & Maasome Salari - 2016 - پژوهشنامه فلسفه دین 13 (2):199-219.
    As an English analytic philosopher, Stace considers religion to be identical with mysticism and mystical experience to be its core. According to him, mystical experiences and thus religious propositions are ineffable. Existence consists of temporal and eternal realms each of which has its special language. While the temporal world is the realm of finite reason, religion belongs to the eternal level that can be perceived only by intuition. Religious language is symbolic. Symbolic proposition is not a report of reality, but (...)
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  • Wainwright on Drug-induced Religious Experience.Hossein Tousi - 2016 - پژوهشنامه فلسفه دین 13 (2):155-176.
    Conducting experiments and investigations, some researchers have tried to prove that mystical and religious experiences can be created through drug injection. W. J. Wainwright distinguishes between theistic and monistic mystical experiences. Assessing research done by Clark, Pahnke-Houston and Masters, he believes that although psychedelic drugs can induce some kind of monistic mystical experience, they cannot produce theistic mystical experiences. There is no significant evidence in the research based on which one can attribute theistic mystical experience to drug injection. Analysis of (...)
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  • Convention-Interpretation Theory of Tabatabaei: An Introduction to Divine Philosophy of Islam.Zoheir Ansarian - 2015 - پژوهشنامه فلسفه دین 13 (1):1-24.
    Tabatabaei’s view about the relationship between religion and philosophy can be considered in two stages: formation and understanding. He introduces revelation as an unknown method. Therefore, the methodological relation between religion and philosophy cannot be explained well. To provide its content, scripture uses a common language which is conventional. Besides, religion has reached its summit later than philosophy. The relationship between religion and philosophy in the understanding stage in Tabatabaei’s view is based on interpretation of Quran by Quran. This method (...)
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  • From Inconsistency to Consistency of Theism and Darwinian Evolution: A Critical Approach to Four Perspectives.Seyed Hassan Hosseini - 2015 - پژوهشنامه فلسفه دین 13 (1):71-88.
    In this paper, we present four philosophical approaches and their prominent advocates toward the problem of relationship between Darwinian evolution and theistic beliefs: Atheistic Inconsistency: there is a deep conflict between Darwinian evolution and theism; among atheists, Richard Dawkins and Daniel Dennett could be regarded as the best representatives in this branch. Theistic Inconsistency: A deep conflict could also be seen among theists, M.H. Tabātabā’ī’s Quranic exegesis is one of the most significant sources in this regard from Islamic side, correspondent (...)
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  • Realism in William James’s Philosophy of Religion.Abbas Haj Zeinolabedini & Mohsen Javadi - 2015 - پژوهشنامه فلسفه دین 13 (1):47-70.
    James’s primary interest in religion was directed to practical consequences of religious belief in believer’s real life. His general approach to justify the truth of religious belief is resorting to these same consequences. Due to this background and due to some of James’s own statements regarding his theory of truth according to which he identifies the truth of a belief with its practical utility, some interpreters have interpreted him as a philosopher who attempted to present pragmatism as an alternative to (...)
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  • Ibn Sina’s Difficulties on the Adoption or Rejection of Bodily Resurrection.Fatemeh Sadeqzadeh - 2015 - پژوهشنامه فلسفه دین 13 (1):89-110.
    Ibn Sina has had two completely different positions on bodily resurrection. At times, after rational demonstration of spiritual resurrection, he declared that he merely accepts bodily resurrection by trusting the saying of Prophet and sometimes by criticizing those who believe in the resurrection of body and soul, he only accepts the resurrection of souls. The problem here is that he can believe in the corporeality of resurrection in this way only if he regards it possible and already has shown its (...)
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  • Allameh Hilli and Thomas Aquinas on semantics of divine attributes.Hasan Abasi Hossein Abadi - 2015 - پژوهشنامه فلسفه دین 12 (2):91-108.
    One of the major issues in the names and attributes of God, is the semantic interpretation of how to interpret and apply the concepts and predicates that talk about God. A historical survey proves that Imami theologians’ theological views are derived from the Qur'an and hadith. The Quran ascribed some attributes to God that prompted scholars to discuss and analyze the applicability of these concepts to God; accordingly, different views emerged Including Allameh Hilli’s apophaticism which is similar to the apophatic–cataphatic (...)
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  • The Hermeneutic Dialectical between Reason and Religion: A New Approach to Their Relation.Jahangir Masoudi - 2016 - پژوهشنامه فلسفه دین 13 (2):177-198.
    There are four main theories concerning the explanation of the relation between “reason and religion” including rationalism, traditionalism, primacy of reason, and primacy of revelation. In this article, after a review of these theories, I shall argue that none of them is satisfactory and thus, we should look for an alternative theory. I suggest that the dialectical hermeneutical approach to the relation between reason and religion can be such a satisfactory theory which avoids the difficulties with the aforementioned theories. I (...)
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  • Transcendent Philosophy, Na’eeni School, and Muhammad Taghi Ja’fari on Free will and Necessity.Abdollah Nasri - 2015 - پژوهشنامه فلسفه دین 12 (2):159-184.
    The relation between free will and necessity is one of the most important issues regarding the problem of “free will”. This is because of the rule which indicates that “being not necessary, an event would not be came off”. There has been an ongoing debate among theologians, philosophers and Jurists on whether this rule includes free actions. Sadrain Philosophers believe that this rule is inclusive of human free actions, while followers of the Na’eeni school endorse the opposite. In this article, (...)
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  • Revisiting the Logical Problem of Evil and Swinburne’s Greater Goods Theodicy.Tavakkol Kouhi Giglou & Javad Danesh - 2015 - پژوهشنامه فلسفه دین 13 (1):149-164.
    The problem of evil is challenging the belief in the omniscient, omnipotent, and wholly good God. In its logical sense and deductive form, it claims that there are some pointless evils and myriads of life disorderliness with the existence of which God’s existence and his positive attributions are inconsistent. Needless to say, the reliability of this argument is based on the trueness or at least probable trueness of the concrete statement. Nevertheless, some philosophers like Swinburne have tried to deny the (...)
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  • Ashtiani’s Objections to Mudarres’s Theory of “Bodily Resurrection”.Mohammad Reza Ershadinia - 2016 - پژوهشنامه فلسفه دین 13 (2):1-27.
    Relying on the applicability of principles of Transcendent Philosophy for reconstructing religious beliefs, Aqa Ali Mudarres has tried to give a new explanation of “bodily resurrection”. He does this by appealing to the purely Sadraian philosophical principles as well as his method in which he begins by agreeing with popular beliefs and ends with a departure from them. Appealing to some Sadraian ontological principles as “substantial motion” as well as his principles of self-knowledge, Mudarres explains bodily resurrection to be the (...)
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  • Zagzebski’s Theory of Divine Motivation about the Relation of Religion and Morality.Mohsen Javady & Shima Shahriyari - 2015 - پژوهشنامه فلسفه دین 12 (2):25-51.
    Divine Motivation theory is an ethical theory with a theological foundation, attempting to explain the relation between religion and morality in the context of Christian theology with emphasizing on neo-Aristotelian and motivation-based ethics. This theory that is presented by Linda Zagzebski, provides a new form of virtue ethics that God's motives, especially that of love, are foundations of moral life and these motivational states are considered ontologically and explanatorily the basis for all moral properties and values. This theory uses five (...)
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  • Fakhr al-Din al-Razi on the Extent of Prophets’ Innocence.Alireza Parsa & Ali Parimi - 2016 - پژوهشنامه فلسفه دین 13 (2):27-52.
    According to Fakhr al-Din al-Razi, it is essential for the prophets to be infallible after the beginning of their prophetic mission. Yet he doesn’t authorize chastity before mission for the prophets and believes that although prophets do not commit sins intentionally, they may do unintentionally. In his view, the extent of prophets’ innocence includes four domains of belief, propagation and mission, laws and judgments as well as actions and behaviors. On the basis of some foundations such as determinism implied by (...)
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  • A Meditation in Internal Coherency of Mulla Sadra’s Philosophical Thought Concerning Human Knowledge of God.Mohammad Kazem Forghani & Ali Ghazali Far - 2015 - پژوهشنامه فلسفه دین 13 (1):131-148.
    Mulla Sadra believes that only possible true and authentic way to know God is presented knowledge. It seems that the human presented knowledge of God is not free from difficulty and ambiguity. According to the other principles of Mulla Sadra’s transcendental philosophy, someone can say that the human presented knowledge of God is incoherent with other parts of his philosophy. In this paper, six conflicts, named meditations, are discussed. They are as follows: The problem of the true presented knowledge of (...)
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  • Religious Belief and Intellectual Autonomy.Amirhossein Khodaparast - 2016 - پژوهشنامه فلسفه دین 13 (2):91-112.
    Intellectual autonomy indicates how human being can preserve her epistemic agency and intellectually manage and regulate herself. This epistemic value is commonly proposed against intellectual heteronomy according to which the believer is not capable of applying her epistemic agency because of internal or external impediments. Since the early modern era, some philosophers and intellectuals have supposed, implicitly or explicitly, that religious belief violates intellectual autonomy. However, the responsibilist version of virtue epistemology shows that autonomy, as an intellectual virtue, is not (...)
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  • فهم دینی کرکگور از «سوبژکتیویته».محمد اصغری & ندا محجل - 2016 - پژوهشنامه فلسفه دین 14 (1):1-21.
    در این مقاله سعی شده است فهم دینی کرکگور از «سوبژکتیویته» با استناد به گفته‌های او به ویژه در دست‌نوشته‌ها و سایر نوشته‌هایش تبیین شود. او مفاهیم کلیدی نظیر «مسیحیت»، «حقیقت»، «شور»، «خدا»، و «ایمان» را برای توصیف و تبیین «سوبژکتیویته» به کار می‌برد. برای مثال تلقی وی از مسیحیت به مثابۀ «سوبژکتیویته» با تلقی رایج و عمدتاً تاریخی از مسیحیت که عمدتاً درک ابژکتیو از آن دارند کاملاً متفاوت است. مسیحیت از نظر این متفکر عمدتاً در قالب آموزه‌ها مطرح (...)
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  • طبیعت‌گرایی خوش‌بینانه و معناداری زندگی.سیدمصطفی میرباباپور & یوسف دانشور نیلو - 2016 - پژوهشنامه فلسفه دین 14 (1):143-164.
    نظریه‌های معنای زندگی را در یک تقسیم‌بندی کلان و اجمالی می‌توان به دو دستۀ دیدگاه‌های طبیعت‌گرا و غیرطبیعت‌گرا افراز کرد. یکی از اشکالات همیشگی وارد بر دیدگاه‌های طبیعت‌گرا ناتوانی آنها در حل معضل پوچی است؛ طبیعت‌گرایی خوش‌بینانه عنوان ایده‌ای است که مدعی شده بر مبنای پیشرفت‌های علمی و دستاوردهای فناورانه می‌توان، در عین پای‌بندی به طبیعت‌گرایی، از معضل پوچی رهایی یافت. در این مقاله، با تأکید بر دیدگاه‌های لئو تولستوی و تامس نیگل دربارۀ معضل پوچی، طبیعت‌گرایی خوش‌بینانه، بر مبنای دیدگاه (...)
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  • نقش تربیتی انبیا در سیر معرفتی انسان‌ها از دیدگاه غزالی.میترا پورسینا - 2016 - پژوهشنامه فلسفه دین 14 (1):23-45.
    از دید غزالی، انبیا تأثیری بنیادین در رساندن سایر انسان‌ها به عالی‌ترین مرتبۀ معرفتی دارند. این تأثیر، علاوه بر این که در حوزۀ تعلیم حقایق به انجام می‌رسد، تأثیری تربیتی است که با ایجاد تغییر در ساحت‌های عاطفی‌ـ‌ارادی انسان‌ها ساحت معرفت را به مرتبۀ یقین و به سطح مکاشفه می‌رساند. نقش تربیتی انبیا هدایتگری «سفری» است که انسان در نفس خود به سوی حقیقت در پیش می‌گیرد تا «قابلیت» دریافت حقایق را بیابد. رسیدن به این قابلیت مستلزم «تسویه» و «اعتدال» (...)
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  • Can Gödel's Incompleteness Theorem be a Ground for Dialetheism?Seungrak Choi - 2017 - Korean Journal of Logic 20 (2):241-271.
    Dialetheism is the view that there exists a true contradiction. This paper ventures to suggest that Priest’s argument for Dialetheism from Gödel’s theorem is unconvincing as the lesson of Gödel’s proof (or Rosser’s proof) is that any sufficiently strong theories of arithmetic cannot be both complete and consistent. In addition, a contradiction is derivable in Priest’s inconsistent and complete arithmetic. An alternative argument for Dialetheism is given by applying Gödel sentence to the inconsistent and complete theory of arithmetic. We argue, (...)
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