Online research in philosophy

This paper explores the question of what logic is not. It argues against the wide spread assumptions that logic is: a model of reason; a model of correct reason; the laws of thought, or indeed is related to reason at all such that the essential nature of the two are crucially or essentially co-illustrative. I note that due to such assumptions, our current understanding of the nature of logic itself is thoroughly entangled with the nature of reason. I show that (...) most arguments for the presence of any sort of essential re- lationship between logic and reason face intractable problems and demands, and fall well short of addressing them. These arguments include those for the notion that logic is normative for reason (or that logic and correct reason are in some way the same thing), that logic is some sort of description of correct reason and that logic is an abstracted or idealised version of correct reason. A strong version of logical realism is put forward as an alternative view, and is briefly explored. (shrink)

I argue that one in particular of CrispinWright’s attempts to capture our common or intuitive concepts of objectivity, warrant, and other associated notions, relies on an ambiguity between a given constructivist reading of the concepts and at least one other, arguablymore ‘ordinary’, version of the notions he tries to accommodate. I do this by focusing on one case in point, and concluding with a brief argument showing how this case generalises. I demonstrate why this ambiguity is unacceptable and also that (...) its resolution undermines the aim it serves: to account for and accommodate our ordinary conception of (at least) objectivity, warrant (or justication) and truth. (shrink)

In an attempt to find some new ways of tackling old problems about meaning, I explore some possible models in which meaning may be conceptually situated. I take a close look at a traditional realist conception of meaning and give some reasons as to why we may have more room to move within this than is immediately apparent. Alternative frameworks are explored along the way. The approach of thus situating meaning is an ontological one, but it is also an epistemological, (...) as well as a hermeneutical one; in that the models put forward illuminate central issues and offer potential solutions to outstanding puzzles ranging across (at least) all of these broad realms of enquiry. Such solutions give a set of initial conceptualizations of the potential role meaning can play across broader frameworks of enquiry. As such they offer fresh inroads into otherwise deadlocked debates over the nature and place of meaning across philosophical enquiry in general. (shrink)

We first consider the entailment logic MC, based on meaning containment, which contains neither the Law of Excluded Middle (LEM) nor the Disjunctive Syllogism (DS). We then argue that the DS may be assumed at least on a similar basis as the assumption of the LEM, which is then justified over a finite domain or for a recursive property over an infinite domain. In the latter case, use is made of Mathematical Induction. We then show that an instance of the (...) LEM is intrumental in the proof of Cantor's Theorem, and we then argue that this is based on a more general form than can be reasonably justified. We briefly consider the impact of our approach on arithmetic and naive set theory, and compare it with intuitionist mathematics and briefly with recursive mathematics. Our "Four Basic Logical Issues" paper would provide useful background, the current paper being an application of the some of the ideas in it. (shrink)