My only concern is that calling circular arguments valid proofs will only lead to confusion.
I can only hope that the following is read in a spirit of fair play.
The formal argument affords a point of discussion at the points of the premises. No one is expecting anyone to roll over and accept any deductive argument, for if the premises were embraced, the argument would most likely not have been needed in the first place.
A sound argument that all men are mortal is:
Whatever Scripture teaches is true
Scripture teaches that all men are mortal
Therefore, it is true that all men are mortal
The premises are true and the form valid, so the conclusion is reliable and true.
NOTE:
The "demonstration" that all men are mortal is not to be found in the proof. Demonstration, which is most appropriate, is accomplished through witnessing one death after another, which
supports but does not
establish as sound the argument for all men being mortal. If that is not grasped, the rest will be lost. Induction is impotent to establish the absolute truth of any premise, but it is most useful in corroborating what the Scriptures teach as true.
Now consider TAG:
Prove A: The Christian God exists.
Step 1 ~A: (Assume the opposite of what we are trying to prove): The Christian God does not exist.
Step 2 (~A--> B): If God does not exist, then there is no intelligible experience since God is the precondition of intelligibility
Step 3 (~B): There is intelligible experience (Contradiction!)
Step 4 (~ ~A): It is not the case that God does not exist (
Modus Tollens on 2 and 3)
Step 5 (A):= God does exist (Law of negation.)
The veracity of step 2 can be
demonstrated by refuting all would-be competitors to the Christian worldview but the inductive demonstration of what step 2 states is not itself a "sound" proof. For how can the
truth value of a premise for a deductive argument be deduced as true on inductive grounds? If we are left to establish step-2 by induction, then we don't have a deduced or revealed truth value for the premise in question, which means that the conclusion that it is
true that God exists goes beyond the scope of the premises. Moreover, we know that induction is only possible given God's existence. Therefore, the inductive principle used to establish step-2 would be unjustified and would, therefore, entail question begging over the necessary preconditions for induction. I would think that the non-Van Tillians on this site would join me in arguing that induction cannot properly justify step 2.
I know - faith is a dirty world. Aquinas gave up the field of reason when he declared that Christian faith was separate from reason.
I don´t think faith is a dirty word in the least. Fideism is though. Faith saves our reasoning; faith being a justified belief in God granted by God. That all men have an
a priori knowledge of God does not imply that a sound proof for God´s existence cannot or should not be constructed as a point of engagement. We don´t put forth an argument such as I have and leave it there. That would be fideism. We should engage the atheist in order to demonstrate before God and a watching world that God is the precondition for all intelligible experience. We engage him on step 2 by refuting, one by one, all his arguments.
By doing so we are not providing a sound argument through the inductive elimination of a finite number of hypothetical worldviews; rather we're corroborating by induction the sound, deductive argument we've posited.
You can not logical prove axioms.
Not to take away from what I just wrote, what is below is most worthy of serious consideration. I don´t know that I can improve upon it.
One cannot prove as true those axioms that are inductively inferred because there´s nothing that can be appealed to as proving the truth value of the axiom apart from finite observations, yet to do so in an effort to establish an absolute truth proposition is to commit the fallacy of asserting the consequent. Accordingly, what does one "œdeductively" prove when the premises of the proof are based upon inductively assumed axioms? That is something worthy wrestling with I would think.
Now let´s shift gears. The "œaxiom" of Scriptural revelation is
not an inductively inferred axiom but an actual truth that we know, not by inference but upon God´s self-attesting say so. Accordingly, being absolute truth it can properly be appealed to in order to establish true premises that fit into a valid argument.
At the very least, what I find terribly ironic in all of this is that so many are willing to base the premises of deductive arguments on inductively inferred axioms, but they are unwilling to base premises on God´s revealed axiom. They call the latter "œbegging the question" and the former "œlogic!" It hardly needs to be said that nobody has experienced every instance of the law of non-contradiction; so to appeal to the axiom of logic apart from God´s unchanging character as revealed in Scripture is to reduce any appeal to logic to an appeal to an inductively inferred axiom, which is to make the conclusion of any deductive argument no more grounded than it´s foundational axiom, which is being defended on inductive grounds, not revelation.
Accordingly, I see two problems. 1) It has been asserted that a sound, deductive argument needs more than a valid form and true premises. 2) If one denies the validity of appealing to Scripture to justify premises in deductive arguments, then all deductive arguments must be philosophically based on inferred or arbitrary axioms. 2 leaves us with no defense of the faith.
Now I trust that my opponents will say that they know their axioms based upon God´s revelation. That much is good. Notwithstanding, their views on sound argumentation and "œquestion begging" do not allow them to prove anything, simply because they will not put forth any justification for their axioms other than inductive inference or arbitrariness.
Ron