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Directory talk:Jon Awbrey/Papers/Differential Propositional Calculus (view source)
Revision as of 01:40, 30 June 2008
, 01:40, 30 June 2008→Tacit Extensions: HTML → TeX
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|+ '''Table 15. Tacit Extension of [''A''] to [''A'', d''A'']'''
|+ '''Table 15. Tacit Extension of <math>[A]\!</math> to <math>[A, \operatorname{d}A]</math>'''
|
|
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|
|
| 0
| <math>0\!</math>
| =
| <math>=\!</math>
| 0
| <math>0\!</math>
| ·
| <math>\cdot\!</math>
| ((d''A''), d''A'')
| <math>((\operatorname{d}A),\ \operatorname{d}A)\!</math>
| =
| <math>=\!</math>
| 0
| <math>0\!</math>
|
|
|-
|-
|
|
| (''A'')
| <math>(A)\!</math>
| =
| <math>=\!</math>
| (''A'')
| <math>(A)\!</math>
| ·
| <math>\cdot\!</math>
| ((d''A''), d''A'')
| <math>((\operatorname{d}A),\ \operatorname{d}A)\!</math>
| =
| <math>=\!</math>
| (''A'')(d''A'') + (''A'') d''A''
| <math>(A)(\operatorname{d}A)\ +\ (A)\ \operatorname{d}A\!</math>
|
|
|-
|-
|
|
| ''A''
| <math>A\!</math>
| =
| <math>=\!</math>
| ''A''
| <math>A\!</math>
| ·
| <math>\cdot\!</math>
| ((d''A''), d''A'')
| <math>((\operatorname{d}A),\ \operatorname{d}A)\!</math>
| =
| <math>=\!</math>
| ''A'' (d''A'') + ''A'' d''A''
| <math>A\ (\operatorname{d}A)\ +\ A\ \operatorname{d}A\!</math>
|
|
|-
|-
|
|
| 1
| <math>1\!</math>
| =
| <math>=\!</math>
| 1
| <math>1\!</math>
| ·
| <math>\cdot\!</math>
| ((d''A''), d''A'')
| <math>((\operatorname{d}A),\ \operatorname{d}A)\!</math>
| =
| <math>=\!</math>
| 1
| <math>1\!</math>
|}
|}
|}
|}
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In its effect on the singular propositions over ''X'', this analysis has an interesting interpretation. The tacit extension takes us from thinking about a particular state, like ''A'' or (''A''), to considering the collection of outcomes, the outgoing changes or the singular dispositions, that spring from that state.
In its effect on the singular propositions over <math>X,\!</math> this analysis has an interesting interpretation. The tacit extension takes us from thinking about a particular state, like <math>A\!</math> or <math>(A),\!</math> to considering the collection of outcomes, the outgoing changes or the singular dispositions, that spring from that state.
===Example 2. Drives and Their Vicissitudes===
===Example 2. Drives and Their Vicissitudes===