Changes

Figure 2 differs from Figure 1 solely in the circumstance that the object <math>j\!</math> is outside the region <math>Q\!</math> while the object <math>k\!</math> is inside the region <math>Q.\!</math>  So far, there is nothing that says that our encountering these Figures in this order is other than purely accidental, but if we interpret the present sequence of frames as a "moving picture" representation of their natural order in a temporal process, then it would be natural to say that <math>h\!</math> and <math>i\!</math> have remained as they were with regard to quality <math>q\!</math> while <math>j\!</math> and <math>k\!</math> have changed their standings in that respect.  In particular, <math>j\!</math> has moved from the region where <math>q\!</math> is <math>\operatorname{true}\!</math> to the region where <math>q\!</math> is <math>\operatorname{false}\!</math> while <math>k\!</math> has moved from the region where <math>q\!</math> is <math>\operatorname{false}\!</math> to the region where <math>q\!</math> is <math>\operatorname{true}.\!</math>

Figure 2 differs from Figure 1 solely in the circumstance that the object <math>j\!</math> is outside the region <math>Q\!</math> while the object <math>k\!</math> is inside the region <math>Q.\!</math>  So far, there is nothing that says that our encountering these Figures in this order is other than purely accidental, but if we interpret the present sequence of frames as a "moving picture" representation of their natural order in a temporal process, then it would be natural to say that <math>h\!</math> and <math>i\!</math> have remained as they were with regard to quality <math>q\!</math> while <math>j\!</math> and <math>k\!</math> have changed their standings in that respect.  In particular, <math>j\!</math> has moved from the region where <math>q\!</math> is <math>\operatorname{true}\!</math> to the region where <math>q\!</math> is <math>\operatorname{false}\!</math> while <math>k\!</math> has moved from the region where <math>q\!</math> is <math>\operatorname{false}\!</math> to the region where <math>q\!</math> is <math>\operatorname{true}.\!</math>

Figure&nbsp;1&prime; reprises the situation shown in Figure&nbsp;1, but adduces a new quality for the purpose of explaining what we know &mdash; now &mdash; we'll see in Figure&nbsp;2.

Figure&nbsp;1&prime; reprises the situation shown in Figure&nbsp;1, but adduces a new quality for the purpose of explaining what we now know we'll see in Figure&nbsp;2.

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This new quality, <math>\operatorname{d}q,\!</math> is an example of a ''differential quality'', since its absence or presence qualifies the absence or presence of change occurring in another quality.  As with any other quality, it is represented in the venn diagram by means of a "circle" that distinguishes two halves of the universe of discourse, in this case, outside and inside the region <math>\operatorname{d}Q.\!</math>

This new quality, <math>\operatorname{d}q,\!</math> is an example of a ''differential quality'', since its absence or presence qualifies the absence or presence of change occurring in another quality.  As with any other quality, it is represented in the venn diagram by means of a "circle" that distinguishes two halves of the universe of discourse, in this case, the portions of <math>X\!</math> outside and inside the region <math>\operatorname{d}Q.\!</math>

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