Category Archives: Topology

Special Classes of Propositions (cont.) Next we take up the family of positive propositions and follow the same plan as before, tracing the rule of their formation in the case of a 3‑dimensional universe of discourse. Positive Propositions The positive … Continue reading →

Special Classes of Propositions (cont.) Let’s pause at this point and get a better sense of how our special classes of propositions are structured and how they relate to propositions in general.  We can do this by recruiting our visual … Continue reading →

Special Classes of Propositions The full set of propositions contains a number of smaller classes deserving of special attention. A basic proposition in the universe of discourse is one of the propositions in the set   There are of course … Continue reading →

Formal Development (cont.) Before moving on, let’s unpack some of the assumptions, conventions, and implications involved in the array of concepts and notations introduced above. A universe of discourse qualified by the logical features is a set plus the set of … Continue reading →

Formal Development The preceding discussion outlined the ideas leading to the differential extension of propositional logic.  The next task is to lay out the concepts and terminology needed to describe various orders of differential propositional calculi. Elementary Notions Logical description … Continue reading →

Cactus Calculus Table 6 outlines a syntax for propositional calculus based on two types of logical connectives, both of variable -ary scope. A bracketed sequence of propositional expressions is taken to mean exactly one of the propositions is false, in … Continue reading →

Casual Introduction (concl.) Table 5 exhibits the rules of inference responsible for giving the differential proposition its meaning in practice. If the feature is interpreted as applying to an object in the universe of discourse then the differential feature may … Continue reading →

Casual Introduction (cont.) In Figure 3 we saw how the basis of description for the universe of discourse could be extended to a set of two qualities while the corresponding terms of description could be extended to an alphabet of … Continue reading →

Casual Introduction (cont.) Figure 3 returns to the situation in Figure 1, but this time interpolates a new quality specifically tailored to account for the relation between Figure 1 and Figure 2. The new quality, is marked as a differential quality on account of … Continue reading →

Casual Introduction (cont.) Now consider the situation represented by the venn diagram in Figure 2. Figure 2 differs from Figure 1 solely in the circumstance that the object is outside the region while the object is inside the region Nothing says our encountering … Continue reading →