*10. THEORY OF PROPOSITIONS CONTAINING ONE APPARENT VARIABLE.
Project Gutenberg EPUB3 edition
Whitehead, Alfred North and Russell, Bertrand
"If all men are mortal, and Socrates is a man, then Socrates is mortal."
Another form of the syllogism in Barbara is given in *10·3. The two forms, formerly wrongly identified, were first distinguished by Peano and Frege.
*10·27.
This is *9·21. In the alternative method, the proof is as follows.
Dem.
*10·271.
Dem.
*10·28.
This is *9·22. In the alternative method, the proof is as follows.
Dem.
*10·281.
*10·29.
Dem.
This is an extension of the principle of composition.
*10·3.
This is the second form of the syllogism in Barbara.
Dem.
*10·301.
Dem.
In the second line of the proofs of *10·3 and *10·301, we abbreviate the process of proof in a way which is often convenient. In *10·3, the full process would be as follows:
The above two propositions show that formal implication and formal equivalence are transitive relations between functions.
*10·31.
Dem.
*10·311.
Dem.
The above two propositions are extensions of the principle of the factor.
*10·32.
Dem.
This proposition shows that formal equivalence is symmetrical.
*10·321.
Dem.
*10·322.
Dem.
*10·33.
Dem.
*10·34.
This follows immediately from *9·05·01 and *1·01. In the alternative method, the proof is as follows.
Dem.
*10·35.
Dem.