Mathematical Rationality And Reality Metaphysical And Theological Consequences

Abstract

Is formal mathematics a precise and objective instrument in order to express with objectivity our knowledge of the real world? The reduction of deductive reasoning to formal rules is a challenge which underlies the mechanicist ideal. Formal languages convert propositions into objects which can be handled by computers and have approximated human thought to that of computers. The results of formal mathematics cannot be complete and, therefore, they are open to several possibilities which cannot be predetermined in all cases. Another source of indeterminacy lies in the probabilistic and chaotic nature of the real world laws. This means that mathematical activity is, of necessity, faced with the risk of choosing from several possibilities. The opening up of mathematics to risk is not an opening up to irrationality. On asking meta-rationally for the permanence of global rationality, we verify that the consistency of the systems and the exclusion of mutual contradiction in their co-existence, is a meta-rational value, with metaphysical and theological consequences.