02. Systematic Ambiguity

Script: Stan Lee  Pencils and Inks: Steve Ditko 

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(Systematic ambiguity)

The Contradictory Function: with argument p (any proposition) is the       proposition which is contradictory of p, asserting p is not p.

~p = not p or the negation of the proposition p.

The Logical Sum: is a propositional function with two arguments p and q and the proposition asserting p and q disjunctively, asserting that at least one of the two p and q is true.

p v q is the logical sum of p and q.

p v q means at least p or q is true, not exclusive of the case that both are true.

The Logical Pretext: asserts both p and q conjunctively, therefore both p and q are true, denoted p `q or p:q or p:.q or p::q all mean both p and q are true.

Also true for ~p or ~q must be false:

p . q = ~(~p v ~q)

The Implicative Function: is a proposition with two arguments p and q, and that either ‘not p’ or q is true or

~p v q. Thus if p is true, ~p is false, and accordingly the only alternative left by the proposition ~p v q is that q is true. In other words if p and ~p v q are both true, then q is true. In this sense the proposition ~p v q will be quoted as p implies q.

The symbol employed for p implies q or “~p v q” is p É q

p É q may also be read “if p, then q.”

The association of implication with the use of an apparent variable produces an extension called “formal implication.” (explained later) It is an idea derived from “implication” as defined above.

When it is necessary explicitly to discriminate “implication” from “formal implication,” it is called “material implication.”

These four functions of propositions are the fundamental constant (i.e. definite) propositional functions with propositions as arguments, and all other constant propositions as arguments in the present work, are formed out of them by successive steps. No variable propositional functions of this kind occur in this work.



Dan DeCarlo The greatest of all time comic book artist!  Archie Andrews and Betty Cooper  

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In approaching this subject I urge you to see it as a work of metaphysics rather than mathematics. Memorization is not necessary or particularly useful in understanding it. Following posts will contain thousands of words expressing very concise and useful information, but all without a single subject to serve as glue to hold it together. This “glue” is to be your mind and your thought process. All of the material to come must be processed into our consciousness, and the device to make this happen is the work, Principia Mathematica, itself.

The authors carefully point out that the reason for this work is to train the mind to function without rules. They describe rules for various purposes of learning the material, but are clear that these can and must be left behind as the dharma takes hold and is put to practice. As the heading Systematic Ambiguity implies the purpose of dealing with any complex problem begins with establishing propositions of various functions and their relations. It is the essential function of this work to set out a clear vocabulary and hierarchy we may use to think of and communicate complexity in a manageable and intelligible manner.

*Note* Please be patient, the Indian connection will become apparent eventually if it is to clear already.

Script Pencils and Inks: The Venerable George Herriman  © Respective copyright/trademark holders