Deduction as a construct does not bring forth certainty any more than induction. Inductivists try to move from what might be thought to be known, or considered most probably the case, to what is not yet believed with the same veracity. Induction is “open ended” we might say, because induction as a process is never fully exhaustive. Rather, it comes to an end once one is satisfied with his personal pursuit. To put it another way, once cognitive satisfaction has been achieved the inductive pursuit is over, but it always stops short of philosophical certainty due to the nature of induction.
The deductive process on the other hand often leaves people with the impression that as a construct deduction brings forth knowledge. This would only be true, that deduction yields knowledge, if epistemic certainly was only a matter of construct, which it is not. Indeed, if the deductive process is valid, then the conclusion certainly follows from the premises. Whether the premises are reliable, however, is another matter altogether that requires further investigation having nothing to do with the deduction at hand. Deduction itself does not bring forth knowledge because for one to know the conclusion for what it truly is, he would first have to justify the premises that lead to the conclusion, which the immediate deduction in view does not achieve. That does not mean that deduction cannot aid in obtaining knowledge. The justification of many propositions that can be known comes by way of deduction.
Akin to those common errors, people often require a "philosophically certain" proof. I understand what epistemic certainty is, and appreciate what people mean by psychological certainty. I also understand what constitutes a valid and invalid argument, and what distinguishes those types of arguments from sound and unsound arguments. But what is a “philosophically certain argument”? People are certain, not arguments. Whether sound arguments will persuade someone to any degree of certainty is the job of the Holy Spirit, not the apologist.
Deduction is not a sufficient condition for knowledge. First, there is the "garbage in garbage out" consideration. The conclusion of a valid deduction need not be true; it only needs to follow from the premises. Accordingly, further investigation into the truth of the premises must occur for there to be the possibility of knowledge; yet that lies beyond the scope of the deduction at hand. Added to that, the Holy Spirit must grant justification for beliefs, which truth and structure alone cannot produce. Finally, the Holy Spirit must grant the knowledge that a valid deduction is reliable given true premises, which deduction cannot do. In short, God produces knowledge. He might even use weak inductive inferences in the process, but when knowledge is attained, the justification for what is believed to be true is through the illuminating power of God. Knowledge does not rely upon the induction or deduction that might have been employed in the process, but rather when one knows he has been taught by God.
A word or two might be in order regarding transcendental arguments (TAG in particular). TAG has a distinctly inductive aspect to it because with TAG the Christian investigates what must be true in order for some experience to be intelligible. Such explorations are inductive in emphasis. Notwithstanding, the manner of the investigation is not "open ended" because the premises within TAG do not merely support the conclusion, they ensure it. That point is missed by those who think TAG is inductive: http://reformedapologist.blogspot.com/2006/03/impropriety-of-trying-to-prove.html The aspect of "closure", where the premises ensure the conclusion, is unique to deduction, not induction. Moreover, the conclusion from TAG is not a mere hypothesis, but rather a sound conclusion derived through a deductive process that justifies its premises authoritatively. Finally, TAG falls short of being fully inductive because there is no asserting the consequent with TAG, as there is with all scientific inference, the playground for induction. Nonetheless, TAG has an inductive aspect to it because of the exploratory nature of TAG.
Of course TAG is deductive, but it is unlike all other deductive arguments. What sets TAG apart from garden variety deduction is that with the latter we begin with some truths (or inferences) and reason to others - but that to which we reason is not presupposed as a necessary precondition for the intelligible experience of the original fact of experience. More on that here: http://reformedapologist.blogspot.com/2010/03/to-us-only-thing-of-great-significance.html
As Bahnsen often quipped, "The proof of God's existence is that without Him one could not prove anything." That is nothing other than "Proof presupposes God" (or "If Proof, then God" since God is a necessary precondition for proof). Bahnsen's deduction and a defense of it can be found here:http://reformedapologist.blogspot.com/2010/04/bahnsen-misunderstood-servant-of-lord.html
(Given the inductive and deductive aspects of TAG, we shouldn't find it at all strange that Van Til said that in what he called the "Christian method" of apologetics, we find "elements of both induction and of deduction in it, if these terms are understood in a Christian sense.”)
Pastorally it should be said that we do not come to know the truth through cleverly devised proofs. Nothing could be further from the truth. We know God by nature (through revelation and conscience), and we must justify that knowledge by Scripture, the Christian's ultimate authority. I know my Savior lives because God has revealed that to me in His word. That is not my defense of the Christian worldview, but it's certainly a defensible fact. In other words, we don't "reason" ourselves to God, but our belief in God is indeed reasonable. In fact, it is not just reasonable; it is justifiable and true, which is to say it constitutes as knowledge.
Apologetically speaking, belief in God is the only reasonable position to hold if for no other reason, it is unreasonable to argue against God's existence because to do so one must first presuppose those tools of argumentation that only are defensible given God's existence. The precondition of intelligible experience is God. The justification for the precondition of intelligible experience is God’s word. An elaboration of that distinction is for another day.
Ron
