A rational interpretation is proposed for two ancient Indian logics: the Jaina saptabhaṅgī, and the Mādhyamika catuṣkoṭi. It is argued that the irrationality currently imputed to these logics relies upon some philosophical preconceptions inherited from Aristotelian metaphysics. This misunderstanding can be corrected in two steps: by recalling their assumptions about truth; by reconstructing their ensuing theory of judgment within a common conceptual framework.

This paper concerns Bertrand Russell’s changing views on negative judgement. ‘Negative judgement’ is considered in the context of three theories of judgement that Russell put forth at different times: a dual relation theory ; a multiple relation theory ; a psychological theory of judgement. Four issues are singled out for a more detailed discussion: quality dualism versus quality monism, that is, the question whether judgement comes in two kinds, acceptance and rejection, or whether there is only one judgement-quality ; the (...) structure of negative judging; the problem of truth-making for negative facts; the different roles of ‘fact’ in Russell’s theories of truth. What emerges from the discussion is a rough chronology of Russell’s views on negative judgement during the period from 1903 to 1948. (shrink)

A substitutional account of logical validity for formal first‐order languages is developed and defended against competing accounts such as the model‐theoretic definition of validity. Roughly, a substitution instance of a sentence is defined as the result of uniformly substituting nonlogical expressions in the sentence with expressions of the same grammatical category and possibly relativizing quantifiers. In particular, predicate symbols can be replaced with formulae possibly containing additional free variables. A sentence is defined to be logically true iff all its substitution (...) instances are satisfied by all variable assignments. Logical consequence is defined analogously. Satisfaction is taken to be a primitive notion and axiomatized.For every set‐theoretic model in the sense of model theory there exists a corresponding substitutional interpretation in a sense to be specified. Conversely, however, there are substitutional interpretations – in particular the ‘intended’ interpretation – that lack a model‐theoretic counterpart. The substitutional definition of logical validity overcomes the weaknesses of more restrictive accounts of substitutional validity; unlike model‐theoretic logical consequence, the substitutional notion is trivially and provably truth preserving. In Kreisel's squeezing argument the formal notion of substitutional validity naturally slots into the place of intuitive validity. (shrink)