Epistle 1. Posted on 2019-01-21. Edited on 2019-05-06.
Normally, discussions about logic itself do not arise. Nonetheless, analytic logic is central to my practice, and I am always glad to discuss it upon request.
Analytic logic is a class of logic that differs substantially from mathematical logic. With few exceptions, most modern logic is mathematical logic, and is often referred to as classical logic, first-order logic, and so on. Mathematical logic has numerous shortcomings that are known widely. For an extensive presentation of these shortcomings, see Angell (2002).
The foundations of mathematical logic are mathematics, not surprisingly, rather than formal reason. For example, logical operators were defined with Boolean algebra. In contrast, analytic logic is defined with formal reason, to which I will return.
I refer to analytic logic as a class of logic that includes A-Logic (Angell, 2002), as well as many systems of connexive logic, and the ancient system of Stoic logic. I am currently writing a book about my interpretation of Stoic logic, which differs slightly from Angell’s A-Logic. Until my work is published, any formal discussions about logic will be expressed in A-Logic, so that a common ground is available. But I do prefer Stoic logic.
Analytic logic is defined here as a class of logic that is itself defined with respect to contradiction. Operators, modality, validity, rules of inference, and so on, are all defined here with respect to one first principle which is expressed as a proposition:
~(p & ~p).
That is to say that formal reason is defined with consistency, against contradiction.
As it turns out, analytic logic is a class of intensional logic; intensional logic does not necessarily have to be analytic logic. Extensional-only logic is regarded as incoherent, and is incompatible with analytic logic, logic based on formal reason. Meaning is required to correctly evaluate anything.
Vale (pronounced WAH-lay is Latin for “Farewell”),
Angell, R.B. (2002). A-Logic. University Press of America: New York, NY. URL: http://www.amazon.com/Logic-Richard-Bradshaw-Angell/dp/0761822356/.