Deduction, Induction, TAG and Certainty

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

A Christian Reason for Celebrating Easter

Induction, the basis for all scientific inference, presupposes the uniformity of nature, which is to say it operates under the principle of the future being like the past; yet the resurrection of Christ from the dead is contra-uniform since it does not comport with past experience. Our experience is that people die and are not raised three days later. Also, we’ve all met plenty of liars and those deceived into embracing false beliefs (even dying for false beliefs!) but we have never observed a single resurrection of the body. Accordingly, the lives and martyrdom of zealots need not lead us to conclude that Christ has risen. Consequently, drawing an inference based upon past experience as it pertains to the question of the empty tomb is not very useful. Evidentialism indeed fails as an apologetic. After all, given only the uniformity of nature coupled with personal experience, a more probable explanation for the empty tomb is a hoax put on by liars rather than a miracle put on by God. The same reasoning applies all the more to the virgin birth I would think.

The fact of the matter is that we do not come to know that our Savior lives by examining the evidence according to some alleged neutral posture, for the facts do not demand the conclusion that Christ has risen. The facts are indeed consistent with the resurrection but the facts do not speak for themselves let alone lead us to the Christian conclusion, which is no conclusion at all but rather a starting point for apologetical discourse and belief. God speaks in order that we might interpret the facts aright. The fact of the empty tomb, therefore, is not what leads us to the "conclusion" of the resurrection but rather the empty tomb corroborates what we already know from God, that Christ is resurrected.

Similarly, we read in Scripture that a man named Saul who once opposed Christ became the chief apologist for the Christian faith. The way in which one will interpret the transformation of Saul to Paul will be consistent with one’s pre-commitment(s). Christians take the fanaticism of the apostle as corroborating what they already know to be true about the resurrection. The fanaticism of the apostle no more “proves” the resurrection of Christ than does the empty tomb. Moreover, neither the empty tomb nor the life of Paul proves the resurrection any more than it can disprove it by proving that a conspiracy to overthrow ancient Judaism took place evidenced by the hoax of the resurrection. The point is simply this. Naturalists will find their explanation for the apostle’s transformation and the empty tomb elsewhere, outside of the Christian resurrection interpretation. Similarly, the way in which one interprets the facts surrounding Joseph Smith will be according to one’s pre-commitment(s). If one is committed to a closed canon, then the claims of Mormonism will be deemed false.

Of course the tomb is empty, for Christ has risen. Of course the apostle Paul preached the resurrection of Christ with all his heart, soul and strength, for Christ has risen. Of course the Mormon religion is a cult, for Jesus is God and the canon is closed. Do we come to believe these things by evaluating supposed brute particulars in an alleged neutral fashion or are our beliefs already marshaled according to our pre-commitment to God’s word in general and the resurrection in particular? Do the “facts” speak for themselves or has God already exegeted the facts for us?

The reason one believes that Christ has risen from the grave is because God has revealed the truth of the resurrection. In fact, we don’t just believe God’s word on the matter, we actually know God is telling the truth. Yet, unwittingly, often times Christians do not speak the truth with respect to why they believe in the resurrection. Too often Christians will say that they believe in the resurrection because of such evidence, which if true would reduce one’s confidence in God’s say-so to speculation based upon supposed brute facts that (would) readily lend themselves to suspicion (when God’s word is not presupposed as reliable, true and one's ultimate authority). Christians need to lay hold of the fact that the “Word of God” is God’s word, and God cannot lie.

With the resurrection the former days of ignorance are gone (Acts 17:30); so our belief in the truth couldn’t be more justified since our justification comes from the self-attesting Christ of Scripture working in accordance with the internal witness of the Holy Ghost. We do not come to know Jesus lives by drawing inferences from uninterpreted facts in the light of past experiences but rather by believing with maximal warrant the word of truth. Indeed, we have a more sure word of knowledge. (2 Peter 1:19)

The Westminster Confession of Faith (chapter 1 paragraph 5) could not have been more on target in its reason for why Scripture's testimony should be believed:

"We may be moved and induced by the testimony of the Church to an high and reverent esteem of the Holy Scripture. And the heavenliness of the matter, the efficacy of the doctrine, the majesty of the style, the consent of all the parts, the scope of the whole (which is, to give all glory to God), the full discovery it makes of the only way of man's salvation, the many other incomparable excellencies, and the entire perfection thereof, are arguments whereby it does abundantly evidence itself to be the Word of God: yet notwithstanding, our full persuasion and assurance of the infallible truth and divine authority thereof, is from the inward work of the Holy Spirit bearing witness by and with the Word in our hearts."

Ron

Confusion Over The Transcendental Argument For The Existence Of God

Generally speaking TAG is a deductive argument, 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 unlike transcendental arguments that to which we reason is not presupposed as a necessary precondition for the intelligible experience of the original fact of experience (or its denial). For instance, “If causality then God” merely means that causality is a sufficient condition for God and that God is a necessary condition for causality. Which is to say: if causality exists then it is logically necessary that God exists. However, such a premise does not delve into the question of how God and causality relate to each other. It does not tell us whether God exists because of causality or whether causality exists because of God. Causality presupposes God says more than causality is a sufficient condition for God and that God is a necessary condition for causality. If causality presupposes God then God must be logically prior to causality.

The transcendental argument for the existence of God is an argument that has as its conclusion God exists.

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.)
Q.E.D.

Whereas professing atheists are willing to concede the validity of the above argument Christians should happily concede that the argument is not only not fallacious (i.e. valid) but also sound. In other words, although professing atheists and Christians alike agree that the above argument has a valid form – i.e. the conclusion follows from the premises – Christians should agree that since the premises are all true and the form is valid the conclusion is true. But unfortunately Christians don't always grasp this point.

Christians often say that TAG does not achieve its goal because not every worldview is refuted in the argument. Such a claim simply demonstrates a fundamental misunderstanding of the scope of TAG. The above argument is aimed to prove that God exists, which it does. To deny that it does is to reject logic and / or biblical truths. Again, the argument above has a specific conclusion, God exists. The conclusion of the argument is not that if God does not exist, then there could be no intelligible experience. In other words, the above transcendental argument does not aim to prove that God is the precondition for intelligible experience, though that is a premise used in the argument which is why the argument is transcendental. That is where Christians who oppose TAG get tripped up. They don’t appreciate what is being argued.

So what about step 2 of the argument? We can defend the premise of step 2 deductively by appealing to the absolute authority of Scripture. Of course the unbeliever rejects that authority; nonetheless that the unbeliever is dysfunctional does not mean that an appeal to Scripture is fallacious! After all, if a skeptic rejects logic should we then argue apart from logic? Since when does the dullness of an opponent dictate which tools of argumentation may be used? Of course, given the unbeliever’s suppression of the truth the Christian does well to defend step 2 inductively by performing internal critiques of opposing worldviews, which of course can only corroborate the veracity of step 2. It would be fallacious, however, to conclude because of such condescension toward the unbeliever that the conclusion of TAG (God exists) and the justification for its step 2 (God is the precondition of intelligibility) rest upon inductive inference. By the use of induction the Christian is merely acknowledging that the unbeliever refuses to bend the knee to the self-attesting Word from which step 2 can be deduced by sound argumentation. Since unbelievers will not accept the truth claims of the Bible and, therefore, a deductive defense of step 2 the only thing the Christian can do is refute the hypothetical competitors, but that hardly implies that step 2 cannot be proved by deduction.

Finally, it has been noted by some and popularized by Don Collet in the Westminster Theological Journal that the only way a transcendental argument may be formalized is thusly (TAG*):

C presupposes G if and only if both 1 & 2:
1. If C then God exists
2. If ~C then God exists

Given such a construct, we are no longer negating the metaphysicality of causality but rather the truth value of the predication of the metaphysicality of causality. In other words: ~causality (which is chaos) does not presuppose God so for the construct to make sense it must pertain only to prediction about causality. In other words, since non-causality is an impossible entity that defies creation, providence and intelligibility, such a formulation of TAG (TAG*) limits itself to predication only. Does the apologist really want to do that? Do we want to give up arguing that God is the precondition for the intelligible experience of actual causality? I think not. TAG* (as opposed to TAG) is indeed powerful but it does not pertain to anything other than predication; whereas TAG may pertain to predication and the reality that the predication contemplates.

Ron

A Couple of Oldies But Goodies by Michael Butler

Here is a very accessible introduction to Presuppostional Apologetics, written by Michael Butler (Greg Bahnsen's protégé).
 
Also, here is a more detailed explication of the Transcendental Argument for God's Existence, also by Michael Butler.

More on Paradox

If God is good, then he cannot ordain evil. God ordains evil and is good. Therefore, I have to accept "by faith" that although what appears contradictory is not. I'm to believe what appears to me to be defeated. Some Reformed Christians actually say that we are to think that way. We are to believe what we think looks false.

Greg Bahnsen had a response to that problem had by so many, which is commonly called the problem of evil. His answer was simply that God has a morally sufficient reason for the evil he ordains. With Bahnsen, I find that response sufficient to remedy any apparent contradiction between God’s goodness and his determination of all things including evil, but I don’t find the additional premise to be a stroke of genius by any stretch. The apparent problem had by so many is that they judge goodness by carnal standards, forgetting that God defines goodness and what is acceptable behavior for himself. (Note: That God defines goodness does not imply that goodness is arbitrary.)

That God’s goodness and his sovereign determination of evil appears contradictory to some hardly implies that it should appear contradictory to all. It’s simply too grand a claim to suggest that if some perceive contradictions then others should.

One might even expect to have a better chance of alleviating apparent contradictions by beginning with a simple presupposition that says there need not be any apparent contradictions. The belief in apparent contradiction can make one not only lazy but also very unjustified in his theology, just like by not believing that the inverse operation of subtraction is always addition can make a child think his wrong answers could be correct though they don't check out just right by performing the inverse operation. The less partisan will find the analogy acceptable, whereas those who blindly follow Van Til will no doubt throw the rationalistic flag at this juncture. Notwithstanding, the point that can be received by the less fearful who are brave enough to be their own man is simply that once we become committed to our ability by grace to alleviate apparent contradictions within God’s word, we might end up working a bit harder at resolving them rather than letting the axiom of apparent contradiction cause us to accept things as true that really appear false to us.  Now of course this comes at a price. There must be a willingness to accept the label rationalistic, but what’s the alternative, believing in something that appears false yet while hoping it is not?

Now some might say that we have reason to believe what appears false and that reason is the church teaches it, which reduces the belief to an inference short of knowledge if that's all the belief is based upon. There is a subtle distinction that must be teased out from such a theory. It pertains to the difference between a justification for believing something is true and a justification of the facts themselves that are believed to be true. I can believe a doctrine is true because the church teaches it, but it’s quite another thing to know those teachings are true. Such a justification of the truth of the church's teachings can only come from God. This is not to say that the God does not speak through the church, for he does. Notwithstanding, if one is basing a theological propositional belief on something other than God's testimony, then such a belief can hardly account as knowledge of the truth.

How can we know truth while it appears false? What would be the warrant for believing what appears to be a defeated proposition? If one says God's say-so, then why if I'm to believe what appears false ought I not disbelieve what appears true?

Not only do the following passages teach that we’re to hear from God and not men on these matters, the Confession's addresses cited below, in concert with Scripture, commend such a practice. (Matt. 16:13-17; John 4:39-42; Galatians 1:11, 12; I Thess. 2:13;  WCF 1.5 and 1.10; WCF 14.2) Note well that Paul when battling the Judaizers did not even cite the apostles but rather Christ alone in his defense of the gospel he knew to be true, for he did not receive it by man but from God.

In a nutshell, contradictions take the form of p = ~p, so if a doctrine is to appear contradictory it must appear to take that form. Until one shows how any Christian doctrine appears to take that form, he fails to show that any doctrine actually appears contradictory. But it gets much worse than that. Until one shows that any doctrine takes a contradictory form, he fails to show how it appears contradictory even to himself! Consequently, not only have these people failed to show that Christian doctrines are apparently contradictory, a universal claim of theirs that applies to every person – they even fail to show that they appear contradictory to them personally.

The only contradictions I’m finding are in their reasoning. They assert apparent contradiction and fail to demonstrate any.

Evidence, Apologetics & the Resurrection

Induction, the basis for all scientific inference, presupposes the uniformity of nature, which is to say it operates under the principle of the future being like the past; yet the resurrection of Christ from the dead is contra-uniform since it does not comport with past experience. Our experience is that people die and are not raised three days later. Also, we’ve all met plenty of liars and those deceived into embracing false beliefs (even dying for false beliefs!) but we have never observed a single resurrection of the body. Accordingly, the lives and martyrdom of zealots need not lead us to conclude that Christ has risen. Consequently, drawing an inference based upon past experience as it pertains to the question of the empty tomb is not very useful. Evidentialism indeed fails as an apologetic. After all, given only the uniformity of nature coupled with personal experience, a more probable explanation for the empty tomb is a hoax put on by liars rather than a miracle put on by God. The same reasoning applies all the more to the virgin birth I would think.

The fact of the matter is that we do not come to know that our Savior lives by examining the evidence according to some alleged neutral posture, for the facts do not demand the conclusion that Christ has risen. The facts are indeed consistent with the resurrection but the facts do not speak for themselves let alone lead us to the Christian conclusion, which is no conclusion at all but rather a starting point! God speaks in order that we might interpret the facts aright. The fact of the empty tomb, therefore, is not what leads us to the "conclusion" of the resurrection but rather the empty tomb corroborates what we already know from God, that Christ is resurrected.

Similarly, we read in Scripture that a man named Saul who once opposed Christ became the chief apologist for the Christian faith. The way in which one will interpret the transformation of Saul to Paul will be consistent with one’s pre-commitment(s). Christians take the fanaticism of the apostle as corroborating what they already know to be true about the resurrection. The fanaticism of the apostle no more “proves” the resurrection of Christ than does the empty tomb. Moreover, neither the empty tomb nor the life of Paul proves the resurrection any more than it can disprove it by proving that a conspiracy to overthrow ancient Judaism took place evidenced by the hoax of the resurrection. The point is simply this. Naturalists will find their explanation for the apostle’s transformation and the empty tomb elsewhere, outside of the Christian resurrection interpretation. Similarly, the way in which one interprets the facts surrounding Joseph Smith will be according to one’s pre-commitment(s). If one is committed to a closed canon, then the claims of Mormonism will be deemed false.

Of course the tomb is empty, for Christ has risen. Of course the apostle Paul preached the resurrection of Christ with all his heart, soul and strength, for Christ has risen. Of course the Mormon religion is a cult, for Jesus is God and the canon is closed. Do we come to believe these things by evaluating supposed brute particulars in an alleged neutral fashion or are our beliefs already marshaled according to our pre-commitment to God’s word in general and the resurrection in particular? Do the “facts” speak for themselves or has God already exegeted the facts for us?

The reason one believes that Christ has risen from the grave is because God has revealed the truth of the resurrection. In fact, we don’t just believe God’s word on the matter, we actually know God is telling the truth. Yet, unwittingly, often times Christians do not speak the truth with respect to why they believe in the resurrection. Too often Christians will say that they believe in the resurrection because of such evidence, which if true would reduce one’s confidence in God’s say-so to speculation based upon supposed brute facts that (would) readily lend themselves to suspicion (when God’s word is not presupposed as reliable, true and one's ultimate authority). Christians need to lay hold of the fact that the “Word of God” is God’s word, and God cannot lie.

The former days of ignorance are gone; so our belief in the truth couldn’t be more justified since our justification comes from the self-attesting Christ of Scripture working in accordance with the internal witness of the Holy Ghost. We do not come to know Jesus lives by drawing inferences from uninterpreted facts in the light of past experiences but rather by believing with maximal warrant the word of truth. Indeed, we have a more sure word of knowledge.

Ron

Counter since: 9/6/2006

More on Induction and Knowledge

If knowledge is so broad as to include things believed by inductive inference, then either one can know something on faulty justification (e.g., my clock scenario in the previous blog-entry), or one cannot be 100% certain of the truth of that which is alleged to be "known" by way of induction. In other words, since inductive inference can be based upon rational yet faulty justification, then it follows that one cannot be 100% certain of what he “knows" by induction even if what is believed were true. Accordingly, in common parlance we’d have to distinguish between knowing something “for sure” and knowing something that we’re not 100% sure about. Why not then define "knowledge" as including only that which we can be 100% sure about? Imagine the judge saying: “Do you know that Mr. Smith killed his wife?” “Yes” says Mr. Jones, "I’m nearly 90% certain that it is true!" What is it to “know” something without certainty after all? At what point does one truly “know” anything through induction?

Given inductive-knowledge, either we can know things that are false, or else we can know things that we cannot be 100% certain about. If the latter is true – that we can know things that we cannot be 100% certain about - then we cannot know for certain that which we "know" when that which we "know" comes by way of induction. If that is true, then what does it really mean that we “know” things by way of induction?!

I often hear people say that they appreciate the limitations of induction as it stands in contrast to revelation and deduction, which would suggest that the only difference between philosophers is simply the semantic tagging of words. However, there is better reason to believe that this is not the case and that these people do not grasp the limits of induction. These misguided fellows are quick to argue that one could not even know he is saved apart from induction. They reason thereby that since they can know they are saved that, therefore, induction must be able to yield absolute knowledge. What they acknowledge with one hand they take away with the other! A recent response on this site stated this very sentiment with even a broader brush: “So my point is that if you are going to claim we can't know we know anything through induction, you then have to say the same thing about language and therefore God's Word. And thus knowledge is demolished.”

It is remarkable that so many Reformed thinkers are willing to redefine knowledge so as to include inductive inference in order that they can “know” more things, such as that they are saved! If it is true that induction cannot yield absolute certainty and if it, also, true (as some would have us believe) that we come to embrace God’s word through induction, then we must concede that we cannot know with absolute certainty the truth of the gospel! Yet we can know with 100% certainty the truth of the gospel. Accordingly, either induction can yield 100% certainty or else understanding God’s word is not based on induction. Thankfully, the latter is true. Induction cannot yield 100% certainty, but it is also false that we know the gospel by way of induction. {To introduce “psychological” certainty is simply to muddy the waters. The question is not whether I have a feeling of certainty, but what degree of warrant I have for my beliefs.} A belief in my existence or that Jesus died for me is not obtained through induction, which is precisely why one can know with infallible certainty he has eternal life.

A word or two about Clarkian axioms might be in order at this time. Axioms in geometry cannot be proved as long as they are not deducible or revealed by God. What can one appeal to after all to justify such an axiom? They’re not known as true-transcendentals for they are only posited in order to maintain a rational conceptual scheme. In other words, they are not revealed to men as ontological necessities but rather assumed by men for conceptual necessity. However, the axiom of God’s revelation can be proved since a sound deductive argument can be constructed based upon God’s say so.

What needs to be appreciated is that an argument is sound given true premises and a valid form, which is available to us in Scripture. Even the following is a sound proof for God's existence:

p1. God exists or nothing exists

p.2 Not nothing exists (something exists)

C. Therefore, God exists.

The above proof is not transcendental in nature because it is not concerned with what must be true in order for some other human experience to be intelligible. Notwithstanding, it does demonstrate that proof is child's play since sound arguments are concerned with truth and form, not persuasion. {Such proofs of mathematical axioms cannot be derived since there can be only an inductive appeal for the truth value of any such axiom.}

What is Clark's axiom – but that God exists! Well, I just proved that axiom with a valid form and true premises. Since Clarkians must affirm the form and the premises of the above argument, then why not the proof? The problem is that most Clarkians do not know what is entailed by a sound argument. Accordingly, they typically reduce themselves to skepticism since they can never justify any ultimate truth claim. Without a justification for their truth claims, their arguments are equally unjustified and arbitrary. Now if more Van Tillians would appreciate that TAG is a type of deductive argument http://reformedapologist.blogspot.com/2006/03/formal-blunder-on-van-til-by-wtj-no.html and that induction can NEVER prove an absolute truth value, I might sleep better…


Ron

Counter since: 9/6/2006





Hit Counters

Induction and Knowledge

Does one know that the President of the United States in the 1980’s had the initials R.R. if he thinks that Roy Rogers was President then?
Let’s talk about time.

1. Justification: Inductive inference that the clock is working based upon history

2. Belief: Believe as true the time the clock indicates, which is 12:00

3. Truth: It is 12:00

Someone might say that since all the criteria for knowledege have been met, one can know it is 12:00 given inductive-knowledge. However, the 3 criteria justify the belief that it is 12:00 even when relying upon a broken clock! Shouldn't this intuitively bother us? Can we "know" things based upon false information? The problem with induction is that inferences that are rational to maintain can always be false. Let me try to make this even more glaring. Let’s say there is another man in the room who has strong reason to believe that the clock is broken. Accordingly, this man will not rely upon the clock. In fact, this man believes that any justification of the time based upon the clock will be unwarranted. The point should be obvious. The man who is most informed about the clock is not able to know the time, whereas the man with less information about the clock would be able to “know” the time if inductive inference allows for knowledge! If anyone is looking for a reductio, then here it is. Given and inductive-knowledge, having less information can be the source of more knowledge, and having more information can cause one to rationally lose the knowledge he once had. Ignorance truly would be bliss! It is one thing to have a justification for a belief and quite another thing to justify the truth value of what is believed. The latter can only come through revelation and deduction.

Now let me sum this up. The first man’s inference about the clock was rational because based upon history the clock had an extremely high probability of working; say 99.9%. The second man had an entirely different rational inference based upon his history with broken clocks. He believed that there was less than 1% chance of the clock working the day after he observed it not working. Both men were making rational inferences based upon their finite perspectives and information. At the very least, given inductive-knowledge, deductive or revelatory knowledge becomes something of a different order and not merely a difference of degree. We need to distinguish the two. I prefer applying the term knowledge to more than inductive inference.

Does anybody really know what time it is? Does anybody really care?

Let’s say that there is one clock in the world that is the standard of time. In other words, let’s assume that it indicates the “true time.” Now let’s say we were to hook up a digital transmitter to the clock that would output the time to a series of data acquisition systems all running in parallel. Would all of the systems record the same time at any exact instance? No. How can we arrive at the true time then? Some might take the median time of all the times recorded and call it the true time. Someone else might take the arithmetic mean, whereas someone else the mode. Let’s say we were to conclude that at a particular instance the true time was 12:00 noon +/.000000000000000000000000001 milliseconds. How many points of time can fit between the variance? Well an infinite number of course. Accordingly, what is the probability of one knowing the true time? Well 1/infinity of course. Well, what is 1/infinity? Well zero of course. Consequently, no matter what the time is, nobody knows it!

Finally, induction always operates under the formal fallacy of asserting the consequent. It would be misleading, however, to say that inductive reasoning is always fallacious. Rather, by repeated tests through asserting the consequent a veracity of belief can be obtained. “If A, then B; B therefore, A” is of course fallacious. However: “If A, then B; B therefore, A would appear to have more veracity...” is of course the basis for science and indeed valid. To say that science cannot yield specific truth has great shock value but all such a statement really reduces to is that induction is not deduction, which is no great discovery - or at least it ought not be. Some have argued that induction can "prove" a truth value of a projection with some true degree of variance. This however is false, since to "prove" the truth value of any variance would require one to first "assert the consequent!" For instance: "If the variance of any projection has been proved by certain means, then by implementing those means to this set of circumstances I prove the truth of the variance. I have implemented those means to this set of circumstances, therefore, I have proved the truth of the variance." The fallacy is obvious. Again, science can only show how things might appear; we may not say that it is "true" that things will appear as they have in the past. And to say that it is true that things "might" appear a certain way, is to say that it is true that they might not. As for variances, all we can say is that it would appear, based upon the past, that variances are rational to maintain when arrived at inductively. However, we cannot even arrive at a truth value for the variance without asserting the consequent. Nonetheless, a variance can have veracity just as that which it surrounds can have veracity.

I’m sympathetic to the idea that we might actually know things through induction. However, I would say that we cannot know that we know things through induction. If we do know things through induction it is because God has granted a necessary, causal relationship to those things that appear to us as necessary. God would also have to grant us some warrant to believe that things must be the way they are. Does He do this? I don’t know nor do I think we can know.

What’s the beauty in all of this? Well, for one thing - I am more certain that Jesus lives than I am that toothpaste will squirt out of the tube in the morning!

Ron

Counter since: 9/6/2006




Hit Counters