*22. CALCULUS OF CLASSES.
Project Gutenberg EPUB3 edition
Whitehead, Alfred North and Russell, Bertrand
*22·57.
These embody the commutative law.
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These embody the associative law.
*22·5.
*22·56.
These embody the law of tautology.
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These embody the distributive law. It will be seen that the second results from the first by everywhere interchanging the signs of addition and multiplication.
*22·8.
This is the principle of double negation.
*22·81.
This is the principle of transposition.
(2) Other useful propositions:
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*22·441.
These embody the two forms of the syllogism in Barbara.
*22·62.
*22·621.
These two propositions enable us to transform any inclusion ( into an equation.
*22·91.
I.e. " or " is identical with " or the part of which is excluded from ."
*22·01.
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Dem.
This proposition is used in proving that the null-class is not identical with the class containing everything (*24·1), which is used to show that at least two classes exist. Our axioms do not suffice to prove that more than one individual exists, but they prove the existence of at least two classes and at least two relations.