‘Ju Mipham Rinpoche, (1846-1912) an important figure in the _Ris med_, or non- sectarian movement influential in Tibet in the late 19th and early 20th Centuries, was an unusual scholar in that he was a prominent _Nying ma_ scholar and _rDzog_ _chen_ practitioner with a solid dGe lugs education. He took dGe lugs scholars like Tsong khapa and his followers seriously, appreciated their arguments and positions, but also sometimes took issue with them directly. In his commentary to Candrak¥rti’s _Madhyamakåvatåra, (...) _Mi pham argues that Tsong khapa is wrong to take Candrak¥rti’s rejection of the reflexive character of consciousness to be a rejection of the _conventional _existence of reflexive awareness. Instead, he argues, Candrak¥rti only intends to reject the reflexivity of awareness _ultimately_, and, indeed, Mipham argues, it is simply _obvious _that conventionally, consciousness is reflexive. (shrink)
In this paper, I discuss the problem of how empty persons can make distinctions between right and wrong within the two-truths doctrine of the Buddhist tradition. To do so, I rely on the teachings of the fifteenth- century founder of Tibetan Buddhism, Tsong kha pa Lo sang drak pa. I summarize Tsong kha pa’s exposition of the Buddhist tradition on this question, and then show how he held that profound emptiness, the ultimate truth found under scrupulous analysis of (...) how things exist, must be understood as complementing and fulfilling, rather than canceling, the principles of moral action, based as they are, primarily, on valid conventional distinctions. Along the way, I highlight Tsong kha pa’s major contribution to the history of Tibetan philosophy, namely, that conventional realities are not obviated by their profound emptiness of essence but have their own kind of validity; I then outline his criteria for saying that something exists conventionally. (shrink)
This paper delves into one particular topic within this Buddhist theory of cognition. I examine a single argument by Phywa pa Chos kyi seṅ ge (1109–1169) contained within his famous epistemology text, the Tshad ma yid kyi mun sel, drawing out the philosophical implications that this argument has on his theory of cognition and his account of ontological dependence. I make the case that Phywa pa’s argument fails to explain adequately the nature of the relation between certain cognitive episodes and (...) the contents of those episodes. In addition, I will show that Phywa pa is forced to accept an arguably dubious version of externalism about mental content. (shrink)
At least in as much as it is accessible to ?transcendental wisdom?, Tsong khapa and Go rampa both maintain that ultimate truth is an object of knowledge. So granting that ultimate truth is an object of knowledge and that transcendental wisdom its knowing subject, this paper attempts to address one key epistemological problem: how does transcendental wisdom know or realise ultimate truth? The responses from the Tibetan Mådhyamikas entail that transcendental wisdom knows ultimate truth in at least two different (...) ways: firstly, ?by way of not seeing it? (ma gzigs pa'i tshul gyis gzigs); and, secondly, ?by way of transcending the conceptual elaborations? (spros bral gyis sgo nas gzigs tshul), therefore by way of the non-dual engagement (gnyis snang dral ba'i sgo nas gzigs tshul). Although the emphasis is slightly different in each of the two modes of engagement, they are nevertheless alike in that both represent epistemic pathways geared towards the same non-conceptual realisation of ultimate truth. So what does each of these epistemic modes really mean in relation to ultimate truth? This paper addresses this question at issue by means of undertaking a comparative analysis of Tsong khapa's and Go rampa's epistemological traditions regarding the matters at question. (shrink)
We give a self-contained and streamlined version of the classification of the provably computable functions of PA. The emphasis is put on illuminating as well as seems possible the intrinsic computational character of the standard cut elimination process. The article is intended to be suitable for teaching purposes and just requires basic familiarity with PA and the ordinals below ε0. (Familiarity with a cut elimination theorem for a Gentzen or Tait calculus is helpful but not presupposed).
Introduction Na?ga?rjuna, the most well-known Buddhist thinker after the Buddha himself, points out in his famous Mu?lamadhyamakaka?rika? that ?The Buddha's teachings of the Dharma is based on the two truths: a truth of worldly conventions and an ultimate truth? (XXIV:8). This doctrine of the two truths does indeed lie at the very heart of Buddhism. More particularly, the phenomenological and soteriological discourses in the Ma?dhyamika tradition revolve around ideas concerning the two truths. Central to the doctrine is the concept that (...) all phenomena possess dual characteristics?conventional and ultimate. The former, defined as the mode of phenomenal appearance, is the conventional truth; while the latter, defined as the ultimate mode of being, is the ultimate truth. This paper examines the ways in which these two truths are related from the Tibetan Pra?sangika Ma?dhyamika perspective, and argues that there are two radically distinct Tibetan ways of reading and interpreting the issues surrounding them. It does so by comparing the ccounts of Tsong khapa Blo bzang Grags pa (hereafter Tsong khapa, 1357?1423 A.D.) and Go rampa bSod nams Senge's (hereafter Go rampa 1429-1489 A.D.), and focuses on the way in which the two truths are related. It will be argued that, for Tsong khapa, the two truths constitute a ?single ontological identity? (ngo bo gcig) with ?different conceptual identities? (ldog pa tha dad), whereas for Go rampa, the truths are separate in a way that is ?incompatible with their unity? (gcig pa bkag pa'i tha dad) or identity. (shrink)
This paper is the first of a series of three articles that present the syntactic proof of the PA-completeness of the modal system G, by introducing suitable proof-theoretic objects, which also have an independent interest. We start from the syntactic PA-completeness of modal system GL-LIN, previously obtained in [7], [8], and so we assume to be working on modal sequents S which are GL-LIN-theorems. If S is not a G-theorem we define here a notion of syntactic metric d(S, G): we (...) calculate a canonical characteristic fomula H of S (char(S)) so that G H (S) and GL-LIN H, and the complexity of H gives the distance d(S, G) of S from G. Then, in order to produce the whole completeness proof as an induction on this d(S, G), we introduce the tree-interpretation of a modal sequent Q into PA, that sends the letters of Q into PA-formulas describing the properties of a GL-LIN-proof P of Q: It is also a d(*, G)-metric linked interpretation, since it will be applied to a proof-tree T of H with H = char(S) and ( H) = d(S, G). (shrink)
This paper has attempted to present Wonch'uk's Ban-ya pa-ra-mil-da sim gyeong chan (般若波羅蜜多心經贊) or Commentary on the Heart Sūtra which was written in classical Chinese in the 7th century. As an example of the intellectual analysis of a sūtra, Wonch'uk's Commentary is an important text that has exerted asignificant influence on East Asian Buddhist thought. A prominent Korean Yogācāra scholar, Wonch'uk authored twenty-three works during his lifetime; unfortunately, all but three have been lost. The Commentary on the Heart Sūtra is (...) the shortest among his extant writings, yet it clearly reflects his incomparable erudition. To date, there has been very limited research on Wonch'uk and his thought in both the East and West. Utilizing Wonch'uk's original Chinese text,this paper will examine the distinctive features of Wonch'uk's Commentary which may offer the contemporary readers an opportunity to remind the importance of sūtra study and the engagement in sūtra exegesis. (shrink)
This paper is the final part of the syntactic demonstration of the Arithmetical Completeness of the modal system G; in the preceding parts [9] and [10] the tools for the proof were defined, in particular the notion of syntactic countermodel. Our strategy is: PA-completeness of G as a search for interpretations which force the distance between G and a GL-LIN-theorem to zero. If the GL-LIN-theorem S is not a G-theorem, we construct a formula H expressing the non G-provability of S, (...) so that ⊢GL-LIN ∼ H and so that a canonical proof T of ∼ H in GL-LIN is a syntactic countermodel for S with respect to G, which has the height θ(T) equal to the distance d(S, G) of S from G. Then we define the interpretation ξ of S which represents the proof-tree T in PA. By induction on θ(T), we prove that ⊢PA Sξ and d(S, G) > 0 imply the inconsistency of PA. (shrink)
We generalize a result on True Arithmetic (TA) by Lachlan and Soare to certain other completions of Peano Arithmetic (PA). If T is a completion of PA, then Rep(T) denotes the family of sets $X \subseteq \omega$ for which there exists a formula φ(x) such that for all n ∈ ω, if n ∈ X, then $\mathscr{T} \vdash \varphi(S^{(n)})$ (0)) and if $n \not\in X$ , then $\mathscr{T} \vdash \neg\varphi(S^{(n)}(0))$ . We show that if $\mathscr{S,J} \subseteq \mathscr{P}(\omega)$ such that S (...) is a Scott set, J is a jump ideal, $\mathscr{S} \subset \mathscr{J}$ and for all X ∈ J, there exists C ∈ S such that C is a "coding" set for the family of subtrees of 2 $^{ computable in X, and if T is a completion of PA such that Rep(T) = S, then there exists a model A of T such that J is the Scott set of A and no enumeration of Rep(T) is computable in A. The model A of T is obtained via a new notion of forcing. Before proving our main result, we demonstrate the existence of uncountably many different pairs (S,J) satisfying the conditions of our theorem. This involves a new characterization of 1-generic sets as coding sets for the computable subtrees of 2 $^{ . In particular, $C \subseteq \omega$ is a coding set for the family of subtrees of 2 $^{ computable in X if and only if for all trees T $\subseteq 2^{ computable in X, if χ C is a path through T, then there exists σ ∈ T such that $\sigma \subset \chi_C$ and every extension of σ is in T. Jockusch noted a connection between 1-generic sets and coding sets for computable subtrees of 2 $^{ . We show they are identical. (shrink)
For α less than ε0 let $N\alpha$ be the number of occurrences of ω in the Cantor normal form of α. Further let $\mid n \mid$ denote the binary length of a natural number n, let $\mid n\mid_h$ denote the h-times iterated binary length of n and let inv(n) be the least h such that $\mid n\mid_h \leq 2$ . We show that for any natural number h first order Peano arithmetic, PA, does not prove the following sentence: For all (...) K there exists an M which bounds the lengths n of all strictly descending sequences $\langle \alpha_0, ..., \alpha_n\rangle$ of ordinals less than ε0 which satisfy the condition that the Norm $N\alpha_i$ of the i-th term αi is bounded by $K + \mid i \mid \cdot \mid i\mid_h$ . As a supplement to this (refined Friedman style) independence result we further show that e.g., primitive recursive arithmetic, PRA, proves that for all K there is an M which bounds the length n of any strictly descending sequence $\langle \alpha_0,..., \alpha_n\rangle$ of ordinals less than ε0 which satisfies the condition that the Norm $N\alpha_i$ of the i-th term αi is bounded by $K + \mid i \mid\cdot inv(i)$ . The proofs are based on results from proof theory and techniques from asymptotic analysis of Polya-style enumerations. Using results from Otter and from Matou $\breve$ ek and Loebl we obtain similar characterizations for finite bad sequences of finite trees in terms of Otter's tree constant 2.9557652856... (shrink)
Jacques Arènes | : Marie de la Trinité est une mystique contemporaine dont Jacques Lacan fut l’analyste. Cette trajectoire est paradigmatique de la manière dont une mystique rencontre la souffrance psychique dans le paysage culturel du milieu du xxe siècle. La pensée de Jacques Lacan concernant la mystique, ainsi que des considérations psychanalytiques plus générales à propos de la paternité, sont mises en relation avec la logique apophatique de cette spirituelle. Cette mystique « antinaturelle » se déploie en une sécheresse (...) vertigineuse, à la lisière du Symbolique, et dans une fascination vis-à-vis de l’attraction du Père, impérieuse et contrariée. L’article analyse en particulier, à travers la figure de Marie de la Trinité, la manière dont la mystique contemporaine se confronte, dans le champ chrétien, à la question de la mort de Dieu, et du déclin du Père. | : Marie de la Trinité was a contemporary mystic who was analyzed by Jacques Lacan. The trajectory of her life is a paradigmatic example of the way in which a mystic encountered psychic suffering in the cultural landscape of the mid-20th century. Jacques Lacan’s thinking about mysticism, as well as broader psychoanalytical considerations about fatherhood, are associated here with the apophatic path of Marie. As her counter-natural mysticism unfolds she draws ever closer to the symbolic, fascinated by the dual nature of the attraction, at once imperious and impeded, exerted by the Father. This article uses the figure of Marie de la Trinité as the specific vantage point to examine how contemporary Christian mysticism is faced with the question of the death of God and the decline of the Father. (shrink)
A considerable literature exists regard-ing the moral obligation to keep one's promises. Several authors have focused on the exceptional circumstances which may or should excuse this moral duty. Less frequently discussed is the question of how this general moral obligation and its possible exceptions play out in the context of negotiable written promises to pay money, i.e., so-called "commercial paper."This paper focuses on the application of the legal rules governing commercial paper, and on the ethical implications involved in the application (...) of those rules. More specifically, it asks whether the assertion of the technical doctrine known as "holder in due course," and the denial of that status in some cases, promotes ethical behavior in the marketplace. By examining the circumstances of one case, involving a substantial investment and a large bank, I hope to shed some light on how the legal and ethical rules do in fact "intersect.". (shrink)
This paper is the second part of the syntactic demonstration of the Arithmetical Completeness of the modal system G, the first part of which is presented in [9]. Given a sequent S so that ⊢GL-LIN S, ⊬G S, and given its characteristic formula H = char(S), which expresses the non G-provability of S, we construct a canonical proof-tree T of ~ H in GL-LIN, the height of which is the distance d(S, G) of S from G. T is the syntactic (...) countermodel of S with respect to Gand is a tool of general interest in Provability Logic, that allows some classification in the set of the arithmetical interpretations. (shrink)
