Tacit Extensions

Returning to the Table of Differential Propositions, let’s examine how the general concept of a tacit extension applies to the differential extension of a one‑dimensional universe of discourse, where and

Each proposition has a canonical expression in the set   The tacit extension may then be expressed as a logical conjunction where is a logical tautology using all the variables in   The following Table shows how the tacit extensions of the propositions may be expressed in terms of the extended basis

In its bearing on the singular propositions over a universe of discourse the above analysis has an interesting interpretation.  The tacit extension takes us from thinking about a particular state, like or to considering the collection of outcomes, the outgoing changes or singular dispositions springing or stemming from that state.

Resources

• Differential Logic and Dynamic Systems
• Differential Logic • Tacit Extensions

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