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| Today: colourized to make April look August |
LANGER, SUSANNE K (1953)(1967) An Introduction to Symbolic Logic, Dover Publications, New York.
In symbolic logic, the word 'the' means more than 'all'. (122).
'The' expresses the fact that there is at least one element in a certain class. (122).
Class in review:
A class is a class of so and so's, as in each member of the class has a certain character. (115). Langer uses the following example, bear in mind this was written in the 1950s and 1960s: A man belongs in the class of politicians, only if he is a politician. Being a politician equals being in the class of politician. (115).
Langer uses the example of the wife of King Arthur (122) as in there is at least one element under this concept. (122). One element is within this class. Class is also defined as 'sort'. (122). If there is no wife of King Arthur, then there is nothing of the sort. (122).
This is null class.
'Null' class means that means 'all its members' equals none at all. This null class could be 'No wives of King Arthur'. (123).
Possible equations:
∃=There exists
∃!=There exists
˜=Not
∃ ˜ W
There exists not King Arthur's wife (W).
∃! ˜ W
There exists not King Arthur's wife (W).
˜ (∃! x)
x (King Arthur's wife) does not exist.
ε is epsilon from the Greek alphabet meaning is, a. The ε symbol, according to Langer is specifically meant as a symbol for is, a, in contrast with any symbol for is.
(x) : x ε B
(x King Arthur) is a B: Bachelor).
(x) : x ε U
(x King Arthur) is U: Unmarried).
(x) : x = ∃!
(x Arthur's wife) does not exist.
⊨ is entails
Biblically and theologically another true god/God would be a null class.
(x) : x ⊨ ˜ og
(x Trinitarian God) entails not or no other god/God.
or
T ⊨ ˜ OG
t ⊨ ˜ og
