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 its absence or presence qualifying the absence or presence of change occurring in another quality.  As with any quality, it is represented in the venn diagram by means of a “circle” distinguishing two halves of the universe of discourse, in this case, the portions of outside and inside the region

Figure 1 represents a universe of discourse together with a basis of discussion for expressing propositions about the contents of that universe.  Once the quality is given a name, say, the symbol we have the basis for a formal language specifically cut out for discussing in terms of   That language is more formally known as the propositional calculus with alphabet

In the context marked by and there are just four distinct pieces of information which can be expressed in the corresponding propositional calculus, namely, the constant proposition the negative proposition the positive proposition and the constant proposition

For example, referring to the points in Figure 1, the constant proposition holds of no points, the negative proposition holds of and the positive proposition holds of and and the constant proposition holds of all points in the sample.

Figure 3 preserves the same universe of discourse and extends the basis of discussion to a set of two qualities,   In corresponding fashion, the initial propositional calculus is extended by means of the enlarged alphabet,

Resources

• Logic Syllabus
• Survey of Differential Logic

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