Basic Laws of Logic

Ross Brady

La Trobe University - Australia

The basic laws of logic are those that hold purely as a result of the meanings of the logical terms in them and are thus independent of the way the world is. By examining the definition and role of deductive logic, we make out the basic concepts upon which logic rests: meaning containment and a 4-valued (De Morgan) negation. From these, we determine a specific logic called MC (previously DJd) and also determine the role of the Law of Excluded Middle (LEM) and the Disjunctive Syllogism (DS), the key constituents of classical logic. We will argue that these two are contingent and not basic laws of logic.
In the first session we will introduce MC and its quantificational extension QMC. We will also argue for the rational assumption of the DS and introduce the three levels of involvement of the LEM.
The second session will examine the properties of MC and place it within the following classes of logics: M1-metacomplete, depth relevant and paraconsistent. 
The third session will introduce a Fitch-style natural deduction system for MC and QMC and a Routley-Meyer semantics for MC.

Bibliography:

R.T. Brady, "The Simple Consistency of a Set Theory Based on the Logic CSQ", Notre Dame Journal of Formal Logic, Vol.24 (1983), pp.431-449.
R.T. Brady, "Depth Relevance of Some Paraconsistent Logics", Studia Logica, Vol.43 (1984), pp.63-73.
R.T. Brady, "Natural Deduction Systems for Some Quantified Relevant Logics", Logique et Analyse, Vol.27 (1984), pp.355-377.
R.T. Brady, "Relevant Implication and the Case for a Weaker Logic",  Journal of Philosophical Logic, Vol.25 (1996), pp.151-183.
R.T. Brady, "Entailment, Negation and Paradox Solution", in D. Batens, C. Mortensen, G. Priest, J.-P. van Bendegem (eds.), Frontiers of Paraconsistent Logic, Research Studies Press, Baldock, 2000, pp.113-135.
R.T. Brady, "Normalized Natural Deduction Systems for Some Relevant Logics I: The Logic DW", The Journal of Symbolic Logic, Vol.71 (2006), pp.35-66.
R.T. Brady, "Entailment Logic - A Blueprint", in J-Y. Beziau and W. Carnielli (eds.) Paraconsistency with No Frontiers, Elsevier Science, pp.109-131, 2006.
R.T. Brady, Universal Logic, CSLI Publs, Stanford, 2006.