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- Metaphysics (23)
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- Epistemology (15)
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- Philosophy of Science (15)
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- Catuṣkoṭi (4)
- Graham Priest (3)
- Nāgārjuna (3)
- Philosophy of logic (3)
- Buddhism (2)
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- Buddhist logic (2)
- Catuskoti (2)
- Comparative philosophy (2)
- Ineffability (2)
- Many-valued logic (2)
- Nagarjuna (2)
- Advaita (1)
- Aesthetics (1)
- Andi Kapsner (1)
- Antirealism (1)
- Axiom of regularity (1)
- Buddhist philosophy (1)
- Clausewitz’s absolute war and real war (1)
- Context-sensitive universality (1)
- Critical Buddhism (1)
- Critiques of logic (1)
- Cross-cultural philosophy (1)
- Definite description (1)
- Dialetheism (1)
- Doubly negated propositions (1)
- Eastern logic as a problem (1)
- Emptiness (1)
- Empty name (1)
- Epistemic pluralism (1)
- Fa Zang (1)
Articles 1 - 27 of 27
Full-Text Articles in Logic and Foundations of Mathematics
The Limits Of Universal Logic: A Cross-Cultural Archaeology Of Logical Critique, Murat Kelikli
The Limits Of Universal Logic: A Cross-Cultural Archaeology Of Logical Critique, Murat Kelikli
Comparative Philosophy
This study examines critiques of logic articulated across diverse historical and cultural traditions within a comparative framework. The critiques developed in Islamic, Buddhist, Chinese, Indian, Zen, and modern Western philosophy do not, in the main, reject logic or reasoning as such; rather, they target the conceptualization of logic as a universal, context-independent, and singular normative standard. The analysis shows that objections raised at ontological, epistemic, linguistic, methodological, and political levels converge on a set of shared concerns rooted in the structural features of logic itself, most notably categorical determinacy, universalist assumptions, and claims of context-independence. At the same time, these …
The Modal Catuṣkoṭi: Formalizing Emptiness In Classical Modal Logic, Chance Chapman
The Modal Catuṣkoṭi: Formalizing Emptiness In Classical Modal Logic, Chance Chapman
Comparative Philosophy
Nāgārjuna’s arguments in the Mūlamadhyamakakārikā rely extensively on modus tollens, yet this inference is invalid in the paraconsistent frameworks typically used to formalize the catuṣkoṭi. We develop a modal extension of Belnap-Dunn semantics to address this, expressed as: ¬□(v(P) = t) ∧ ¬□(v(P) = f) ∧ ¬□(v(P) = b) ∧ ¬□(v(P) = n). This formula applies self-reflexively, resolves longstanding interpretive debates regarding verses within Nāgārjuna’s Mūlamadhyamakakārikā and Vigrahavyāvartanī such as his “no thesis” defense, and bridges interpretive gaps between traditionally designated Eastern and Western logical traditions, providing a Western analytical translation of Indian dialectic into symbolic modal logic that …
A Cross-System Analysis Of Structural Commensurability Between Axiomatic Foundations Of Set Theory (Zfc) And The Principles Of Transcendent Wisdom, Mohammadjavad Maarefvand
A Cross-System Analysis Of Structural Commensurability Between Axiomatic Foundations Of Set Theory (Zfc) And The Principles Of Transcendent Wisdom, Mohammadjavad Maarefvand
Comparative Philosophy
Building on observed similarities in uniqueness proofs for the empty set and the Necessary Existent (Wājib al-Wujūd), this study engages the meta-methodological issue of cross-system commensurability. It identifies four instances of structural commensurability between Zermelo-Fraenkel set theory with Choice (ZFC) and Mulla Sadra's Transcendent Wisdom (Ḥikmat al-Muta'āliyah). First, identity principles: the Axiom of Extensionality provides a formal operational criterion analogous to the philosophical principle of identity through absence of distinguishing features. Second, multiplicity mechanisms: ZFC's constructor axioms (bottom-up construction) and emanation principles (top-down explanation) address analogous problems with inverse orientations. Third, transcending limitation: the Axiom of Infinity ensuring quantitative extensional …
Challenging The Double-Negation Principle: An Analysis Of Strategic Theories Of Sun Zi, Carnot, And Clausewitz Through Intuitionist Logic, Antonino Drago
Challenging The Double-Negation Principle: An Analysis Of Strategic Theories Of Sun Zi, Carnot, And Clausewitz Through Intuitionist Logic, Antonino Drago
Comparative Philosophy
To study a subject similarly represented in Eastern and Western cultures, I examine some classical theories of war strategy according to a new analytical method. This method is based on the recognition that the most important strategic theories are organized as theories essentially not deduced from axioms according to classical logic. Such theories reason through doubly negated propositions (DNPs), whose meanings differ from those of their affirmative counterparts. This corresponds to the use of intuitionist logic instead of classical logic. An inspection of the works of the texts of Sun Zi, Lazare Carnot, and Clausewitz reveals many such propositions, and …
Zero, Śūnya And Pūrṇa: A Comparative Analysis, Animisha Tewari
Zero, Śūnya And Pūrṇa: A Comparative Analysis, Animisha Tewari
Comparative Philosophy
Due to apparent duality in this world, one has to face a lot of difficulties while searching for the Truth. Our ego is the root cause for perception of duality and this in turn leads to suffering. This suffering can only be extinguished by attainment of the Truth, i.e, non-duality. However, in order to enable the finite intellect to comprehend the incomprehensible non-duality, this undifferentiated whole is sometimes denoted by nothingness (śūnya) or fullness (pūrṇa). Non-duality is usually understood by the numeral ‘1’ which stands for unity or oneness. The main aim of this paper is …
Ineffability, Emptiness And The Aesthetics Of Logic, Andreas Kapsner
Ineffability, Emptiness And The Aesthetics Of Logic, Andreas Kapsner
Comparative Philosophy
In this essay, I explore the nature of the logical analysis of Buddhist thought that Graham Priest has offered in his book The Fifth Corner of Four (5of4). The paper traces the development of a logical value in- troduced in 5of4, which Priest has called e. The paper points out that certain criticisms I have made earlier still stand, but focuses on a recon- ceptualization of 5of4 in which these arguments carry less weight. This new perspective on the book, inspired by a response to my arguments by Priest himself, sees the logical analysis of Buddhism …
Don’T Be So Fast With The Knife: A Reply To Kapsner, Graham Priest
Don’T Be So Fast With The Knife: A Reply To Kapsner, Graham Priest
Comparative Philosophy
The is a brief reply to the central objection against the construction of my The Fifth Corner of Four by Andi Kapsner in his “Cutting Corners: A Critical Note on Priest’s Five-Valued Catuṣkoṭi. This concerns the desirability of adding a fifth corner (ineffability) to the four of the catuṣkoṭi.
Cutting Corners: A Critical Note On Priest’S Five-Valued Catuṣkoṭi, Andreas Kapsner
Cutting Corners: A Critical Note On Priest’S Five-Valued Catuṣkoṭi, Andreas Kapsner
Comparative Philosophy
Graham Priest has offered a rational reconstruction of Buddhist thought that involves, first, modeling the Catuṣkoṭi by a four valued logic, and then later adding a fifth value, read as “ineffability”. This note examines that fifth value and raises some concerns about it that seem grave enough to reject it. It then sketches an alternative to Priest’s account that has no need for the fifth value.
A Russellian Analysis Of Buddhist Catuskoti, Nicholaos Jones
A Russellian Analysis Of Buddhist Catuskoti, Nicholaos Jones
Comparative Philosophy
Names name, but there are no individuals who are named by names. This is the key to an elegant and ideologically parsimonious strategy for analyzing the Buddhist catuṣkoṭi. The strategy is ideologically parsimonious, because it appeals to no analytic resources beyond those of standard predicate logic. The strategy is elegant, because it is, in effect, an application of Bertrand Russell's theory of definite descriptions to Buddhist contexts. The strategy imposes some minor adjustments upon Russell's theory. Attention to familiar catuṣkoṭi from Vacchagotta and Nagarjuna as well as more obscure catuṣkoṭi from Khema, Zhi Yi, and Fa Zang motivates the …
Recapture, Transparency, Negation And A Logic For The Catuṣkoṭi, Adrian Kreutz
Recapture, Transparency, Negation And A Logic For The Catuṣkoṭi, Adrian Kreutz
Comparative Philosophy
The recent literature on Nāgārjuna’s catuṣkoṭi centres around Jay Garfield’s (2009) and Graham Priest’s (2010) interpretation. It is an open discussion to what extent their interpretation is an adequate model of the logic for the catuskoti, and the Mūla-madhyamaka-kārikā. Priest and Garfield try to make sense of the contradictions within the catuskoti by appeal to a series of lattices – orderings of truth-values, supposed to model the path to enlightenment. They use Anderson & Belnaps's (1975) framework of First Degree Entailment. Cotnoir (2015) has argued that the lattices of Priest and Garfield …
Dialetheism, Paradox, And Nāgārjuna’S Way Of Thinking, Richard H. Jones
Dialetheism, Paradox, And Nāgārjuna’S Way Of Thinking, Richard H. Jones
Comparative Philosophy
Nāgārjuna’s doctrine of emptiness, his ideas on “two truths” and language, and his general method of arguing are presented clearly by him and can be stated without paradox. That the dialetheists today can restate his beliefs in paradoxical ways does not mean that Nāgārjuna argued that way; in fact, their restatements misrepresent and undercut his arguments.
In Memoriam: Richard Lane Tieszen (1951-2017)
In Memoriam: Richard Lane Tieszen (1951-2017)
Comparative Philosophy
No abstract provided.
Moving, Moved And Will Be Moving: Zeno And Nāgārjuna On Motion From Mahāmudrā, Koan And Mathematical Physics Perspectives, Robert Alan Paul
Moving, Moved And Will Be Moving: Zeno And Nāgārjuna On Motion From Mahāmudrā, Koan And Mathematical Physics Perspectives, Robert Alan Paul
Comparative Philosophy
Zeno’s Arrow and Nāgārjuna’s Fundamental Wisdom of the Middle Way (Mūlamādhyamakakārikā, MMK) Chapter 2 (MMK/2) contain paradoxical, dialectic arguments thought to indicate that there is no valid explanation of motion, hence there is no physical or generic motion. There are, however, diverse interpretations of the latter text, and I argue they apply to Zeno’s Arrow as well. I also find that many of the interpretations are dependent on a mathematical analysis of material motion through space and time. However, with modern philosophy and physics we find that the link from no explanation to no phenomena is invalid and …
Vol 8 No 2 Editor's Words, Bo Mou
Editor's Words, Bo Mou