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Directory:Jon Awbrey/Papers/Differential Propositional Calculus (view source)
Revision as of 02:52, 5 May 2008
, 02:52, 5 May 2008→Note 7: edit & markup
<1, 1, 1, 1, 1, 1>.
<1, 1, 1, 1, 1, 1>.
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</pre>
*<p>Working in the ''conjunctive product'' form of representation, if the conjunctive proposition <math>x\!</math> is a model of <math>q\!</math> in <math>X,\!</math> then one can construct a conjunctive proposition <math>\operatorname{e}x\!</math> as a model for <math>\operatorname{e}q\!</math> in <math>\operatorname{E}X\!</math> just by appending any combination of values for the differential variables in <math>\operatorname{d}\mathcal{X}.</math></p><p>The tacit extensions of <math>c\!</math> that are models of <math>\operatorname{e}q\!</math> in <math>\operatorname{E}X\!</math> are as follows:</p>
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<pre>
u v w (du)(dv)(dw),
u v w (du)(dv)(dw),
u v w (du)(dv) dw ,
u v w (du)(dv) dw ,
u v w du dv (dw),
u v w du dv (dw),
u v w du dv dw .
u v w du dv dw .
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In short, eq.c just enumerates all of the possible changes in EX
In short, <math>\operatorname{e}q \cdot c</math> just enumerates all of the possible changes in <math>\operatorname{E}X\!</math> that ''derive from'', ''issue from'', or ''stem from'' the cell <math>c\!</math> in <math>X.\!</math>
that "derive from", "issue from", or "stem from" the cell c in X.
That was pretty tedious, and I know that it all appears to be totally trivial, which is precisely why we usually just leave it "tacit" in the first place, but hard experience, and a real acquaintance with the confusion that can beset us when we do not render these implicit grounds explicit, have taught me that it will ultimately be necessary to get clear about it, and by this ''clear'' to say ''marked'', not merely ''transparent''.
to be totally trivial, which is precisely why we usually just
leave it "tacit" in the first place, but hard experience, and
a real acquaintance with the confusion that can beset us when
we do not render these implicit grounds explicit, have taught
me that it will ultimately be necessary to get clear about it,
and by this "clear" to say "marked", not merely "transparent".
===Note 8===
===Note 8===