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====2.5.2.  Prospects for a Differential Logic====

====2.5.2.  Prospects for a Differential Logic====

Pragmatically, the "proper" form of a differential logic is likely to be regulated by the purposes to which it is intended to be put, or determined by the uses to which it is actually, eventually, and suitably put.  With my current level of uncertainty about what will eventually work out, I have to be guided by my general intention of using this logic to describe the dynamics of inquiry and intelligence in systematic terms.  For this purpose it seems only that many different types of "fiber bundles" or systems of "spaces at points" will have to be contemplated.

Pragmatically speaking, the ''proper'' form of a differential logic is likely to be regulated by the purposes to which it is intended to be put, or determined by the uses to which it is actually, eventually, and suitably put.  With my current level of uncertainty about what will eventually work out, I have to be guided by my general intention of using this logic to describe the dynamics of inquiry and intelligence in systematic terms.  For this purpose it seems only that many different types of ''fiber bundles'' or systems of ''spaces at points'' will have to be contemplated.

Although the limited framework of propositional calculus seems to rule out this higher level of generality, the exigencies of computation on symbolic expressions have the effect of bringing in this level of arbitration by another route.  Even though we use the same alphabet for the joint basis of coordinates and differentials at each point of the manifold, one of our intended applications is to the states of interpreting systems, and there is nothing a priori to determine such a program to interpret these symbols in the same way at every moment.  Thus, the arbitrariness of local reference frames that concerns us in physical dynamics, that makes the arbitrage or negotiation of transition maps between charts (qua markets) such a profitable enterprise, raises its head again in computational dynamics as a relativity of interpretation to the actual state of a running interpretive program.

Although the limited framework of propositional calculus seems to rule out this higher level of generality, the exigencies of computation on symbolic expressions have the effect of bringing in this level of arbitration by another route.  Even though we use the same alphabet for the joint basis of coordinates and differentials at each point of the manifold, one of our intended applications is to the states of interpreting systems, and there is nothing a priori to determine such a program to interpret these symbols in the same way at every moment.  Thus, the arbitrariness of local reference frames that concerns us in physical dynamics, that makes the arbitrage or negotiation of transition maps between charts (qua markets) such a profitable enterprise, raises its head again in computational dynamics as a relativity of interpretation to the actual state of a running interpretive program.