The first degree entailment (FDE) family is a group of logics, a many-valued semantics for each system of which is obtained from classical logic by adding to the classical truth-values true and false any subset of {both, neither, indeterminate}, where indeterminate is an infectious value (any formula containing a subformula with the value indeterminate itself has the value indeterminate). In this paper, we see how to extend a version of star semantics for the logics whose many-valued semantics lack indeterminate to (...) star semantics for logics whose many-valued semantics include indeterminate. The equivalence of the many-valued semantics and star semantics is established by way of a soundness and completeness proof. The upshot of the novel semantics in terms of the applied semantics of these logics, and specifically infectiousness, is explored, settling on the idea that infectiousness concerns ineffability. (shrink)

In early Buddhist logic, it was standard to assume that for any state of a ff airs there were four possibilities: that it held, that it did not, both, or neither. This is the catuskoti (or tetralemma). Classical logicians have had a hard time mak­ing sense of this, but it makes perfectly good sense in the se­mantics of various paraconsistent logics, such as First Degree Entailment. Matters are more complicated for later Buddhist thinkers, such as Nagarjuna, who appear to suggest (...) that none of these options , or more than one, may hold. The point of this paper is to examine the matter, including the formal logical machinery that may be appropriate. (shrink)

Nāgārjuna, the famous founder of the Madhyamika School, proposed the positive catuṣkoṭi in his seminal work, Mūlamadhyamakakārikā: ‘All is real, or all is unreal, all is both real and unreal, all is neither unreal nor real; this is the graded teaching of the Buddha’. He also proposed the negative catuṣkoṭi: ‘“It is empty” is not to be said, nor “It is non-empty,” nor that it is both, nor that it is neither; [“empty”] is said only for the sake of instruction’ (...) and the no-thesis view: ‘No dharma whatsoever was ever taught by the Buddha to anyone’. In this essay, I adopt Gricean pragmatics to explain the positive and negative catuṣkoṭi and the no-thesis view proposed by Nāgārjuna in a way that does not violate classical logic. For Nāgārjuna, all statements are false as long as the hearer understands them within a reified conceptual scheme, according to which substance is a basic categorical concept; substances have svabhāva, and names and sentences have svabhāva. (shrink)

The logical analysis of Nāgārjuna’s catuṣkoṭi has remained a heated topic for logicians in Western academia for nearly a century. At the heart of the catuṣkoṭi, the four corners’ formalization typically appears as: A, Not A, Both, and Neither. The pulse of the controversy is the repetition of negations in the catuṣkoṭi. Westerhoff argues that Nāgārjuna in the Mūlamadhyamakakārikā uses two different negations: paryudāsa and prasajya-pratiṣedha. This paper builds off Westerhoff’s account and presents some subtleties of Nāgārjuna’s use of these (...) negations regarding their scope. This is achieved through an analysis of the Sanskrit and Tibetan Madhyamaka commentarial tradition and through a grammatical analysis of Nāgārjuna’s use of na and a- within a diverse variety of the catuṣkoṭi within the Mūlamadhyamakakārikā. (shrink)

This article is about a pedagogical movement I discern in Quentin Meillassoux’s ontology. The goal of the essay is to introduce his approach to reality in outline form and offer it as a possible route to conceptualize education as the practice of keeping the bodymind attentive and agile against its unsound ossification by way of providing a unified heightened sense of meaning, that is, consummatory experience, in a radically open and contingent world. Meillassoux offers a new conception of necessity and (...) contingency based on the Badioun principle that ‘nothing is inaccessible to reason.’ This move helps Meillassoux to claim that reason can access the absolute for there is no inaccessible necessary transcendence by providing an intriguing critique of the principle of sufficient reason. As a result, Meillassoux’s argument leads to the conclusion that the only necessity is contingency itself. By excluding any necessary being, but also maintaining the absolute necessity of contingency itself, Meillassoux establishes what he calls the “factial.” Meillassoux’s factiality induce pedagogical interventions that lead to acquiring a new point of view whereby ossification of bodymind is staved off and a state of mind that is endlessly fascinated by the immanence, or the most radical becoming, of the world is achieved. (shrink)

This paper attempts to provide a defence for a narrative theory of the self in the face of criticisms from the anti‐narrative camp. It begins by addressing certain uncontroversial premises that both pro‐ and the anti‐narrative camps might be thought to agree on: the status of humans as homo significans or meaning‐makers, the natural form‐finding tendency and certain desiderata for significance and value that we possess, and the raw material of life and its constituents that we proceed from. Whereas the (...) pro‐narrative camp seeks to provide the narrative theory of the self as a valid argument for how we proceed from the raw material of life and undifferentiated experience and these desiderata and tendencies (i.e.: the premises) to a conception of both selfhood and moral responsibility (i.e.: the conclusion), the anti‐narrative camp holds the conclusion to be false and the narrative theory of the self to be invalid. The Parfitian view holds the conception of the self to be ultimately false, whereas the Strawsonian view holds both the conception of the self and the conception of moral responsibility to be ultimately false. The grounds they provide, however, tend to be metaphysical in nature, demonstrating that they have fundamentally misunderstood how the narrative theory of the self functions as a semantic thesis. I will demonstrate certain defects in the metaphysical arguments that anti‐narrativists like Parfit and Strawson have made against what is essentially a semantic thesis about how we make sense of our lives. I will also attempt to shore up the semantic thesis in other relevant aspects. (shrink)

This thesis is the attempt to find a logical model for, and trace the history of, the catuṣkoṭi as it developed in the Indo-Tibetan milieu and spread, via China, to Japan. After an introduction to the history and key-concepts of Buddhist philosophy, I will finish the first chapter with some methodological considerations about the general viability of comparative philosophy. Chapter §2 is devoted to a logical analysis of the catuṣkoṭi. Several attempts to model this fascinating piece of Buddhist philosophy with (...) the tools of classical logic shall be debunked. A paraconsistent alternative will be discussed but eventually dismissed. As a rejoinder, I shall propose a model for the catuṣkoṭi with the help of speech-acts. The remainder of this chapter will look at Chinese and Japanese forms of the catuṣkoṭi which I shall model in a quasi-recursive system. The third and final chapter will look at the Kyoto School's soku-hi dialectics which ties together the different threads of this essay. I will criticise an established, classical model of the soku-hi dialectics and offer an alternative with a second-order paraconsistent semantics. (shrink)