*14. DESCRIPTIONS.
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Whitehead, Alfred North and Russell, Bertrand
*14·111.
Dem.
*14·112.
In the above proposition, we assume the convention explained on p. 182, after the statement of *14·03.
*14·113.
This proposition shows that when two descriptions occur in the same proposition, the truth-value of the proposition is unaffected by the question which has the larger scope.
*14·12.
Dem.
*14·121.
Dem.
*14·122.
Dem.
The two following propositions (*14·123·124) are placed here because of the analogy with *14·122, but they are not used until we come to the theory of couples (*55 and *56).
*14·123.
Dem.
*14·124.
Dem.
*14·13.
Dem.
This proposition is not an immediate consequence of *13·16, because "" is not a value of the function "." Similar remarks apply to the following propositions.
*14·131.
Dem.
In the above proposition, in accordance with our convention, the descriptive expression ( is eliminated before (, because it occurs first in "("; but in "(," ( is to be first eliminated. The order of elimination makes no difference to the truth-value, as was proved in *14·113.
The above proposition may also be proved as follows:
*14·14.
*14·142.
Dem.
*14·144.
Dem.
*14·145.
Dem.
*14·15.
Dem.
*14·16.
Dem.
*14·17.
Dem.
It should be observed that we do not have for, if is always false, and therefore holds for all values of . But we do have
*14·171.
Dem.