Chapter 8 Remarks on the Origin and Foundations of Formalisation
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Abstract
The Aristotelian origins of formal systems are outlined, together with Aristotle’s use of causal terms in describing a syllogism. The precision and exactness of a formalism being based on the projection of logical forms to perceptive signs is contrasted with foundational, abstract concepts, independent of any formalism, which are presupposed for the understanding of a formal language. The definition of a formal system by means of a Turing machine is put in the context of Wittgenstein’s general considerations of a machine understood as a sign. A modification of Łukasiewicz’s logic Ł3 with the inclusion of justification terms is proposed in order to formally analyze some features of formalistic reasoning as a mechanical, causal affair within a wider context of “indeterminacy.”