12,089
edits
Changes
Directory:Jon Awbrey/Papers/Differential Propositional Calculus (view source)
Revision as of 17:40, 6 May 2008
, 17:40, 6 May 2008→Note 15: markup
Given <math>\mathbb{B} = \{ \mathrm{charged}, \mathrm{resting} \},</math> the Table presents the appearance of a function <math>f : \mathbb{B} \times \mathbb{B} \times \mathbb{B} \to \mathbb{B},</math> where <math>f(x, y, z) = (x, y, z).\!</math>
Given <math>\mathbb{B} = \{ \mathrm{charged}, \mathrm{resting} \},</math> the Table presents the appearance of a function <math>f : \mathbb{B} \times \mathbb{B} \times \mathbb{B} \to \mathbb{B},</math> where <math>f(x, y, z) = (x, y, z).\!</math>
If we make the identifications, <math>\mathrm{charged} = \mathrm{false},\ \mathrm{resting} = \mathrm{true},\!</math> in accord with the so-called ''existential interpretation'', then the physical function <math>f : \mathbb{B}^3 \to \mathbb{B}\!</math> is tantamount to the logical function that is suggested by the phrase "just 1 of 3 is false". Table 9 is the truth table for the logical function that we get, this time using 0 for false and 1 for true in the customary way.
<pre>
<pre>
Table 9. Existential Interpretation of (x, y, z)
Table 9. Existential Interpretation of (x, y, z)
o-----------o-----------o-----------o-----------o
o-----------o-----------o-----------o-----------o