Deductive Arguments for God’s Existence.
An argument is a series of statements leading to a conclusion, in which the premises are presented
as providing evidential support for the conclusion.
A deductive argument is an argument in which the premises are intended to establish
conclusively (to entail) the conclusion.
A deductive argument form is valid if and only if it is such that it is logically impossible for the
premises all to be true and the conclusion to be false. (The set consisting of the premises and the
negation of the conclusion is inconsistent.)
A deductive argument is sound if and only if (1) its argument form is valid; and (2) all of the
premises are true.
1.) A valid argument form (modus ponens):
A valid, but not sound, argument:
If P then Q
P
Therefore, Q
If today is Wednesday, then it is raining.
Today is Wednesday.
Therefore, today it is raining.
A sound argument:
If Bill is a man then he is a human being.
Bill is a man.
Therefore, Bill is a human being.
2.) Some fallacies in deductive argument form:
a.) Fallacy of affirming the consequent.
If P then Q
Q
Therefore, P
If Roger lied on his tax return, he is a bad man.
Roger is a bad man.
Therefore, Roger lied on his tax return.
b.) Fallacy of denying the antecedent:
If P then Q
-P
Therefore, -Q
If Tom admitted doing the crime, then he is guilty.
Tom did not admit doing the crime.
Therefore, Tom is not guilty.
What is desired in a deductive argument for God’s existence is an argument in which:
(1)
The argument form is valid;
(2)
The premises are all true;
(3)
The premises are known (or can be shown) to be true;
(4)
We initially have greater confidence in the truth of the premises than in the truth of
the conclusion;
(5)
There is a clear and relevant connection between the premises and the conclusion.
Condition (5) is necessary because, given the rules of correct inference, trivial proofs of God’s
existence are easy to construct. Consider the following two arguments:
Argument A
1a
2a
Concl
Either God exists or nothing exists.
Something exists.
God exists.
Argument B
1b
2b
Concl
Either God does not exist or nothing exists.
Something exists.
God does not exist.
[From George Mavrodes and Keith Yandell]
Since a disjunction (premisses 1a and 1b) is true if one of its members (disjuncts) is true, either
Argument A or Argument B is a sound deductive argument. But unless we know independently
of the proofs whether God exists we do not know which argument is sound.
Moreover, the connection between the first premise and the conclusion in each argument is not
clear. Thus, even if we knew which argument is sound, the argument would not be persuasive to
anyone who did not already accept the conclusion.