Differential Propositional Calculus • 5

Casual Introduction (concl.)

Table 5 exhibits the rules of inference responsible for giving the differential proposition \mathrm{d}q its meaning in practice.

\text{Table 5. Differential Inference Rules}
Differential Inference Rules / From ¬q and ¬dq infer ¬q next / From ¬q and  dq infer  q next / From  q and ¬dq infer  q next / From  q and  dq infer ¬q next /

If the feature q is interpreted as applying to an object in the universe of discourse X then the differential feature \mathrm{d}q may be taken as an attribute of the same object which tells it is changing significantly with respect to the property q — as if the object bore an “escape velocity” with respect to the condition q.

For example, relative to a frame of observation to be made more explicit later on, if q and \mathrm{d}q are true at a given moment, it would be reasonable to assume \lnot q will be true in the next moment of observation.  Taken all together we have the fourfold scheme of inference shown above.

Resources

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