*37. PLURAL DESCRIPTIVE FUNCTIONS.
Project Gutenberg EPUB3 edition
Whitehead, Alfred North and Russell, Bertrand
*37·212.
*37·22.
This proposition is very frequently used. The fact that here we have identity, while in *37·21 we only have inclusion, is due to the fact that *10·42 states an equivalence, while *10·5 only states an implication.
Dem.
*37·221.
*37·222.
*37·23.
*37·231.
The type of "" here is that type whose members are of the same type as . In the proof, use is made of the convention that a Greek letter always stands for an expression of the form .
Dem.
As appears in the above proof, it is necessary, when a proposition containing "" is to be proved, to abandon the notation with Greek letters, and revert to the explicit functional notation.
*37·24.
Dem.
*37·25.
Dem.
*37·26.
Dem.
*37·261.
*37·262.
*37·263.
*37·264.
Dem.
*37·265.
Dem.
*37·27.
*37·271.
*37·28.
*37·29.
Dem.
*37·3.
Dem.
*37·301.
*37·302.
*37·31.
Dem.
*37·311.
*37·32.
Dem.
*37·321.
*37·322.