Online research in philosophy

I introduce a formal language called the language of informational independence (IL-language, for short) that extends an ordinary first-order language in a natural way. This language is interpreted in terms of semantical games of imperfect information. In this language, one can define two negations: (i) strong or dual negation, and (ii) weak or contradictory negation. The latter negation, unlike the former, can occur only sentence-initially. Then I argue that, to a certain extent, the two negations match the distinction existing in natural languages between sentential and constituent negation. As a corollary, I derive the fact that there are no mechanical rules for forming the contradictory negation of an English sentence.

The paper is devoted to the contributions of Helena Rasiowa to the theory of non-classical negation. The main results of Rasiowa in this area concerns–constructive logic with strong (Nelson) negation.

What I hope to achieve in this paper is some rather deeper understanding of the semantic and pragmatic properties of utterances which are said to involve the phenomenon of metalinguistic negation[FN1]. According to Laurence Horn, who has been primarily responsible for drawing our attention to it, this is a special non-truthfunctional use of the negation operator, which can be glossed as 'I object to U' where U is a linguistic utterance. This is to be distinguished from descriptive truthfunctional negation which operates over a proposition.

At least since [Frege, 1960] and [Geach, 1965], there has been some consensus about the relation between negation, the speech act of denial, and the attitude of rejection: a denial, the consensus has had it, is the assertion of a negation, and a rejection is a belief in a negation. Recently, though, there have been notable deviations from this orthodox view. Rejectivists have maintained that negation is to be explained in terms of denial or rejection, rather than vice versa. Some other theorists have maintained that negation is a separate phenomenon from denial, and that neither is to be explained in terms of the other. In this paper, I present and consider these heterodox theories of the relation between negation, denial, and rejection.

I think that one of the main objections to be made to Ayer's verifiability criterion is simply the mechanical way in which it is designed to work: supposedly, a philosopher need not study, for example, how religious assertions are used, nor what sorts of illumination their users take themselves to be shedding on the human condition; instead, Ayer imagines that we can test them in a simple way that requires us to do no exploration whatever. This, surely, is hubris; and that accounts for much of the very angry and passionate reaction which Ayer's criterion provoked.