Original writings by Avi Sion on the theory and practice of inductive and deductive LOGIC  

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© Avi Sion, 2005. All rights reserved.



R. Ishmael’s Rule No. 13, the last in his list, covers many different cases, most of which cannot readily be illustrated. However, the following diagram illustrates one example of the dialectic often involved, where thesis and antithesis are both narrowed, and replaced by their synthesis or common ground.


Diagram 10


This illustration is symbolic, note well, because strictly speaking (in class logic) the propositions “All S are P” and “Only some S are P” should overlap – and their common ground, the indefinite “Some S are P”, would be their area of overlap.

This is just one example – the most ‘deductive’ – of how these conflicting theses might be reconciled. Other inductive possibilities would be to asymmetrically favor one or the other given theses – in which case, the selected one would constitute our synthesis.

In some (other) cases, too, it is possible to argue that the theses are not in as real a conflict as at first appears.



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