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Second post in the series on important innovations in logic theory to be found in my works.
In my previous post I highlighted two important innovations in formal deductive logic, presented in Future Logic, chapters 15 and 17, namely: a) a first figure syllogism consisting of attributive propositions (of the form “S is P”) that draws a possible conclusion from a possible major premise is invalid, but (b) we can however from such premises (and others like them) draw a disjunctive conclusion of the form “S can get to be or become P” (i.e. a disjunction of alterative and mutative propositions). In the present post, I wish to explain the larger significance of these two related findings.
The first finding is of course significant in itself in that wrong reasoning has wide repercussions on all knowledge, and past logicians of the highest caliber have till now (so far as I know) failed to notice the error made by Aristotle and his successors. Aristotle may be excused somewhat because in his mind “possibility” here meant uncertainty one way or the other; thus, he reasoned: if the major and minor premises are both uncertain, so must the conclusion be. But of course, even this intuitive argument is upon reflection untenable, for the two premises may well be uncertain while the conclusion is quite certain for other reasons – so one cannot infer uncertainty for it from the premises, i.e. the syllogism adds nothing to the status of the conclusion.
The second finding is of course significant in itself in that it opens the door to a formal logic concerning change, which here again (to my knowledge) has received no systematic treatment till now. Aristotle’s deductive logic dealt with attributive propositions, but virtually ignored transitive (alterative or mutative) ones, even though in his general discussions concerning nature and knowledge he was very conscious of the fact of change and had many important insights concerning it. This second finding is also significant in that it was not made independently of the first, but from the beginning was closely tied with it, constituting a solution to the problem it raised.
This brings us to the combined significance of these findings. It is this: whereas till now formal deductive logic has seemed to be a description of essentially static interrelations between individual objects and concepts about them and between concepts, it can henceforth be viewed in a much more dynamic light. This concerns specifically the logic of classification, or class logic. Till now, based on Aristotle’s syllogistic theory, which encompassed only attributive propositions, we could only tell us how things are classified in our minds at a specific time. This expansion of syllogistic theory to include propositions about change allows us at last to see our knowledge in motion, with things changing classes over time. Till now, such changes in classification were intuitively obvious enough, but they were not formally taken into account.
More broadly still, this expanded view of the possibilities of syllogistic reasoning was made possible through the full integration of natural modality in the Aristotelian scheme. Whereas Aristotle had developed modal syllogism rather intuitively in relation to what seems to be an epistemic type of modality, in Future Logic I have managed to systematically insert natural modality and show that its behavior is similar to Aristotle’s quantity (i.e. to extensional modality). Natural modality being inherently a reflection of natural change, this study was bound to lead to a consideration of transitive propositions and of their relations to attributive ones.
Furthermore, the discovery of dynamic formal deductive logic opened the door to my later treatment of the dynamics of induction, i.e. to formal inductive logic, including factorial analysis, factor selection and formula revision. More will be said on this and other consequences in later posts.
All these developments hugely enlarge the scope of formal logic. And of course they reflect more precisely the actual ways human thought is formed and progresses. They are not artificial contraptions externally imposed on people by narrow-minded logicians.