Questions and Answers about Oppositions

A general characterization of logical opposition is given in the present paper, where oppositions are defined by specific answers in an algebraic question-answer game. It is shown that opposition is essentially a semantic relation of truth values between syntactic opposites, before generalizing the theory of opposition from the initial Apuleian square to a variety of alter- native geometrical representations. In the light of this generalization, the famous problem of existential import is traced back to an ambiguous interpretation of assertoric sentences in Aristotle's traditional logic. Following Abelard’s distinction between two alternative readings of the O-vertex: Non omnis and Quidam non, a logical difference is made between negation and denial by means of a more fine- grained modal analysis. A consistent treatment of assertoric oppositions is thus made possible by an underlying abstract theory of logical opposition, where the central concept is negation. A parallel is finally drawn between opposition and consequence, laying the ground for future works on an abstract operator of opposition that would characterize logical negation just as does Tarski’s operator of consequence for logical truth

Epistemic Pluralism

The present paper wants to promote epistemic pluralism as an alternative view of non-classical logics. For this purpose, a bilateralist logic of acceptance and rejection is developed in order to make an important di erence between several concepts of epistemology, including information and justi cation. Moreover, the notion of disagreement corresponds to a set of epistemic oppositions between agents. The result is a non-standard theory of opposition for many-valued logics, rendering total and partial disagreement in terms of epistemic negation and semi-negations

Negation and Dichotomy

The present contribution might be regarded as a kind of defense of the common sense in logic. It is demonstrated that if the classical negation is interpreted as the minimal negation with n = 2 truth values, then deviant logics can be conceived as extension of the classical bivalent frame. Such classical apprehension of negation is possible in non- classical logics as well, if truth value is internalized and bivalence is replaced by bipartition

Wittgenstein on rules and practices

Some readers of Wittgenstein---I discuss Robert Brandom---think that his writings contain a regress argument showing that the notion of participating in a practice is more basic than the notion of following a rule, in explanations of linguistic correctness. But the regress argument bears equally on both these notions: if there is an explanatory regress of rules, then there is an explanatory regress of practices as well. Why then does Wittgenstein invoke the notion of a practice, apparently by way of diagnosing the error on which the regress argument rests? I suggest that he invokes that notion to emphasize certain aspects of rule-following which we are apt to neglect, when we forget that rule-following is---not, rests upon---participating in a practice. When we appreciate those aspects of rule/practice-following we see the flaw in both regress arguments

Against Explanatory Minimalism in Psychiatry

The idea that psychiatry contains, in principle, a series of levels of explanation has been criticised both as empirically false but also, by Campbell, as unintelligible because it presupposes a discredited pre-Humean view of causation. Campbell’s criticism is based on an interventionist-inspired denial that mechanisms and rational connections underpin physical and mental causation respectively and hence underpin levels of explanation. These claims echo some superficially similar remarks in Wittgenstein’s Zettel. But attention to the context of Wittgenstein’s remarks suggests a reason to reject explanatory minimalism in psychiatry and reinstate a Wittgensteinian notion of level of explanation. Only in a context broader than the one provided by interventionism is the ascription of propositional attitudes, even in the puzzling case of delusions, justified. Such a view, informed by Wittgenstein, can reconcile the idea that the ascription mental phenomena presupposes a particular level of explanation with the rejection of an a priori claim about its connection to a neurological level of explanation

Virtual Evidence: A Constructive Semantics for Classical Logics

This article presents a computational semantics for classical logic using constructive type theory. Such semantics seems impossible because classical logic allows the Law of Excluded Middle (LEM), not accepted in constructive logic since it does not have computational meaning. However, the apparently oracular powers expressed in the LEM, that for any proposition P either it or its negation, not P, is true can also be explained in terms of constructive evidence that does not refer to "oracles for truth." Types with virtual evidence and the constructive impossibility of negative evidence provide sufficient semantic grounds for classical truth and have a simple computational meaning. This idea is formalized using refinement types, a concept of constructive type theory used since 1984 and explained here. A new axiom creating virtual evidence fully retains the constructive meaning of the logical operators in classical contexts. Key Words: classical logic, constructive logic, intuitionistic logic, propositions-as-types, constructive type theory, refinement types, double negation translation, computational content, virtual evidenc

A Gesture of Understanding: Wittgenstein, Moore, and "Therapy�

Wittgenstein scholarship appears currently to be engaging\ud in a deepening debate over the role of nonsense in\ud Wittgenstein"s later philosophical work. For one party to\ud this engagement, Wittgenstein"s later work pursues the\ud project of exposing nonsense when it emerges during the\ud course of philosophical discussions, and thereby provides\ud a kind of therapeutic assistance to those philosophers who\ud might otherwise have defended positions whose tenets\ud include nonsensical remarks that "do not say anything�\ud (Crary 5). This therapeutic reading argues in The New\ud Wittgenstein and Wittgenstein in America particularly in the\ud hands of James Conant that an austere interpretation of\ud the role of nonsense in the Tractatus can be successfully\ud extended to account for the project of Wittgenstein"s later\ud writings as well. Opposing this therapeutic reading of\ud Wittgenstein, P.M.S. Hacker has argued that Wittgenstein\ud sees nonsense as arising from our attempts to deny\ud grammatical rules by forming "nonsense which violates the\ud grammar� (Baker 279)

Derrida's Open and Its Closure: The Aporia of Différance and the Only Logic of Thinking

Derrida’s thought on “trace,” “différance,” “writing,” and “supplement” is always thought the breaking of logocentrism, the essence, the positive meaning, and the closure of the metaphysics of presence; this thinking is accordingly regarded the thinking with the fundamental structure of difference and openness. By tracking back to Saussure, Husserl and Levinas, this fundamental difference breaks the myth of ideal meaning as well as the illusion of the absolute open; its lack of ideality and absoluteness contains the fundamental difference within itself and thus has the structure of open. However, from a broader perspective, I will re-ask the question “Whether or not Derrida’s ‘trace,’ ‘différance,’ ‘writing,’ and ‘supplement’ have a structure of open.” When the web of differences encompasses everything even its own “exit,” this “open” thus conceals and denies other modes of thinking. With the impossibility of going out of this mode of thinking, the structure of différance is closed