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Edited for reference for an entry on academia.edu, 20240316
LANGER, SUSANNE K (1953)(1967) An Introduction to Symbolic Logic, Dover Publications, New York. The Langer philosophy text review, continues. Some key symbols from the textbook:
≡df = Equivalence by definition
: = Equal (s)
ε = Epsilon and means is
⊃ = Is the same as
⊨ is Entails
˜ = Not
∃ = There exists
∃! = There exists
∴ = Therefore
· = Therefore
<= Is included
v = a logical inclusive disjunction (disjunction is the relationship between two distinct alternatives).
x = variable
· = Conjunction meaning And
0= Null class
---
Philosopher Langer next deals with the concept of Equivalent Expressions. This is complex and will be reviewed, bit by bit.
K= int (interpreted as) 'houses'.
nt = int (interpreted as) 'north of'.
She provides an example basically stating that if (149):
(a nt b) . (b nt c) ⊃ (a nt c)
House A is north of House B and House B is north of House C, is the same as House A is north of House C.
(y) Means no house is north of itself. This concept explained earlier in the text and in my website archives. No two houses are to the north of each other. (150)
(∃x)(∃y): y nt x (150).
X house exists, and Y house exists, equals Y house is north of X house.
The condition of being north of x may apply to any number of K=interpreted as houses. (150).
Langer then explains that for the purposes of the text, henceforth, y nt x shall be equivalent to y ε Ax. (150). Therefore it could be stated that (z) : (z nt y) ⊃ (z nt x) meaning z is north of y is the equivalent expression of z is north of x.
Updated November 7, 2020
LANGER, SUSANNE K (1953)(1967) An Introduction to Symbolic Logic, Dover Publications, New York. The Langer philosophy text review, continues. Some key symbols from the textbook:
≡df = Equivalence by definition
: = Equal (s)
ε = Epsilon and means is
⊃ = Is the same as
⊨ is Entails
˜ = Not
∃ = There exists
∃! = There exists
∴ = Therefore
· = Therefore
<= Is included
v = a logical inclusive disjunction (disjunction is the relationship between two distinct alternatives).
x = variable
· = Conjunction meaning And
0= Null class
---
Philosopher Langer next deals with the concept of Equivalent Expressions. This is complex and will be reviewed, bit by bit.
K= int (interpreted as) 'houses'.
nt = int (interpreted as) 'north of'.
She provides an example basically stating that if (149):
(a nt b) . (b nt c) ⊃ (a nt c)
House A is north of House B and House B is north of House C, is the same as House A is north of House C.
(y) Means no house is north of itself. This concept explained earlier in the text and in my website archives. No two houses are to the north of each other. (150)
(∃x)(∃y): y nt x (150).
X house exists, and Y house exists, equals Y house is north of X house.
The condition of being north of x may apply to any number of K=interpreted as houses. (150).
Langer then explains that for the purposes of the text, henceforth, y nt x shall be equivalent to y ε Ax. (150). Therefore it could be stated that (z) : (z nt y) ⊃ (z nt x) meaning z is north of y is the equivalent expression of z is north of x.
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Necessary v. Contingent
1. The necessary must exist.
2. God is necessary.
3. God's plans are necessary.
4. The contingent exist.
5. The necessary supersedes the contingent.
6. Human beings are contingent.
7. Human being's plans are contingent.
8. Human being's needs are contingent.
Therefore, the suffering of the contingent is permissible.
I am not stating that God by nature had to create anything, or anything finite. God does have significant free will within divine nature. His plans reflect nature. I am stating that God's plans must occur and therefore are necessary. It could be stated that it is a weaker sense of necessity in point 3 than points 1 and 2. Some may view God’s plans as contingent as opposed to necessary.
If God’s plans for humanity are contingent, because he could have done otherwise, the fact these contingent plans come from a necessary being would still have them supersede the plans and needs of the contingent.
1. The necessary must exist.
2. God is necessary.
3. God's plans are necessary.
4. The contingent exist.
5. The necessary supersedes the contingent.
6. Human beings are contingent.
7. Human being's plans are contingent.
8. Human being's needs are contingent.
Therefore, the suffering of the contingent is permissible.
I am not stating that God by nature had to create anything, or anything finite. God does have significant free will within divine nature. His plans reflect nature. I am stating that God's plans must occur and therefore are necessary. It could be stated that it is a weaker sense of necessity in point 3 than points 1 and 2. Some may view God’s plans as contingent as opposed to necessary.
If God’s plans for humanity are contingent, because he could have done otherwise, the fact these contingent plans come from a necessary being would still have them supersede the plans and needs of the contingent.
However...
Open Edition Journals: Philosophia Scientia What is Absolute Necessity? Bob Hale 16/2/2012
Cited
Absolute necessity might be defined as truth at absolutely all possible worlds without restriction. But we should be able to explain it without invoking possible worlds.
By my definition 1,2 are absolutely necessary in all possible worlds, in other words, of absolute necessity.
3. God's plans are necessary.
This could be explained as relative necessity.
Cited
The standard account defines each kind of relative necessity by means of a necessitated or strict conditional, whose antecedent is a propositional constant for the body of assumptions relative to which the consequent is asserted to be necessary.
The relative necessity of (3) has as antecedent the absolute necessity of (1,2).
Further, God, within his infinite, eternal nature, would only be morally obligated to keep his revealed word, as in promises, in regard to contingent, human beings. These are documented in the Hebrew Bible and New Testament within a theistic, Christian worldview.
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