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==Case analysis-synthesis theorem==

==Case analysis-synthesis theorem==

The task at hand is to lay out what I think of as the pontoon bridge between the model-theoretic and the proof-theoretic shores, and thus between their diverging perspectives on logical procedure, even if I can construct it at a point but so close to their common source that it may not seem like it's worth the candle.

 

The task at hand is to build a bridge between model-theoretic and proof-theoretic perspectives on logical procedure, even if we can but construct it at a point so close to their common source that it may not seem worth the candle at all.

The substance of this principle was known to Boole in the 1850's, tantamount to what we now call the ''boolean expansion'' of a propositional expression.  The only novelty here resides in a certain manner of presentation, in which we will prove the basic principle from the axioms given before.  One name for this rule is the ''Case Analysis-Synthesis Theorem'' (CAST).

The substance of this principle was known to Boole in the 1850's, tantamount to what we now call the ''boolean expansion'' of a propositional expression.  The only novelty here resides in a certain manner of presentation, in which we will prove the basic principle from the axioms given before.  One name for this rule is the ''Case Analysis-Synthesis Theorem'' (CAST).

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NB.  QES = "Quod Erat Sketchiendum".

===Example===

Some of the jobs that the CAST can be usefully put to work on are proving propositional theorems and establishing equations between propositions.  Once again, let us turn to the example of Leibniz's ''Praeclarum Theorema'' as a way of illustrating how.

Some of the jobs that the CAST can be usefully put to work on are proving propositional theorems and establishing equations between propositions.  Once again, let us turn to the example of Leibniz's ''Praeclarum Theorema'' as a way of illustrating how.