Granting the other side logic

Granting the other side logic

March 26 2018 article, revised and improved for an entry on academia.edu on July 16 2023

LANGER, SUSANNE K (1953)(1967) An Introduction to Symbolic Logic, Dover Publications, New York. (Philosophy)

The continuation of text review:

Key symbols

≡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
cls = Class
int = Interpretation
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Granting the other side logic

Philosopher Langer, explains that within the nature of a logical deductive system (190), there is a best means for description and there is a character of 'granted' propositions. (190).

By granted propositions, this is logically granted. For examples: A theistic approach may not accept an atheistic, logical argument as true, but grant it as valid. An atheist approach may not accept a theistic, logical argument as true, but grant it as valid. Langer explains there needs to be a systematic construction that is a logical edifice. (190) An argument can be deduced within a system via propositions/premises leading to conclusion (s).
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A=Atheism

E=Evil

G=God

N=Necessary

P=The problem of evil

S=Suffering

(E ⊨ S) ∴ (P ⊨ A)

Evil entails suffering, therefore the problem of evil entails atheism  A classic atheistic equation.

(Logical, but the second bracketed equation is unreasonable and false, in my view)

(E ∃!) ∴ (S ∃!) ⊃ (P)

Evil exists therefore suffering exists, is the same as the problem of evil.

(Logical, reasonable and true, in my view)

(N ∃!) ∴ (G ∃!)

The necessary exists, therefore God exists.

(Logical, reasonable and true, in my view)

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Practical

Granting the other side logic means the other side, or other world view, for example, may present logical premises and conclusion (s) which are not necessarily true. An argument that is logical, must importantly be reasonable and sound. Soundness means that all the premises and conclusion are true. Pire writes that a sound (true) argument has all true premises. (69). 

 
BLACKBURN, SIMON (1996) Oxford Dictionary of Philosophy, Oxford, Oxford University Press. 

LANGER, SUSANNE K (1953)(1967) An Introduction to Symbolic Logic, Dover Publications, New York. (Philosophy) 

PIRIE, MADSEN (2006)(2015) How To Win Every Argument, Bloomsbury, London.

PLANTINGA, ALVIN C. (1977)(2002) God, Freedom, and Evil, Grand Rapids, Wm. B. Eerdmans Publishing Company. 

PLANTINGA, ALVIN C. (1982) The Nature of Necessity, Oxford, Clarendon Press. 

PLANTINGA, ALVIN C. (2000) Warranted Christian Belief, Oxford, Oxford University Press.