ABSTRACT
Presuppositions of Aristotle's Logic are easy to describe logic by extension, i.e. listing the logical constants and giving an axiom system. Bolzano's anticipation of the current definitions of completeness, validity, and logical truth goes back to 1837. The problem of logical constants is the central concern of what has been called 'philosophical logic'. Another advantage of the modal approach is that possibility and necessity are natural concepts unlike philosophers' inventions such as subsistence and analyticity. A related virtue is that they are not only relevant to mathematics but also to general metaphysics. The two pillars of Aristotle's philosophy may be said to be his logic and his system of development. The completeness theorem actually shows more than the derivability of? A from Vs (A). It shows that validity in a weaker sense, viz. validity over the domain of natural numbers, is sufficient to assure derivability in standard systems of predicate logic.
