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Friday, May 12, 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 and that induction can NEVER prove an absolute truth value, I might sleep better…


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Anonymous said...

Hey Ron,

I was just thinking about deduction today and I really don't see how (outside of revelation) it escapes the problem of induction.

For example:

p1: All men are mortal
p2: Socrates is a man
c: Socrates is mortal.

The above argument is true as far as its premises are true but without revelation p1 cannot be justified without faulty appeal to induction as far as I can see.

I might be missing something but this leads me to think that deductive arguments are no 'surer' than induction outside of revelation.

Mr. Anonymous

Ronald W. Di Giacomo said...

"I was just thinking about deduction today and I really don't see how (outside of revelation) it escapes the problem of induction.

For example:

p1: All men are mortal
p2: Socrates is a man
c: Socrates is mortal.

The above argument is true as far as its premises are true but without revelation p1 cannot be justified without faulty appeal to induction as far as I can see."

You are correct. Christians know that all men are mortal because we have it on God’s authority. For instance we know by revelation that “it’s appointed for a man once to die and then the judgment.” The unsaved infer it by way of inductive inference.

The above argument, however, is an inference for the Christian as well, since p2 is not deducible or revealed by God. However, we can deduce that Alexander the Coppersmith is a mortal since we know it is true that he existed, whereas it is only a most rational inference that Socrates existed.

"I might be missing something but this leads me to think that deductive arguments are no 'surer' than induction outside of revelation.

Mr. Anonymous"

I don't think you are missing a thing...


Ronald W. Di Giacomo said...

Raz wrote the following to me:

"…why not:

p1: Allah reveals Islam
p2: What Allah reveals is true
c: Islam is true

You argue that p1 and p2 are false. But how do you know? Through an internal critique."

Raz, you are failing to distinguish the difference between knowledge and a justification for knowledge - and secondly proof as it stands over against persuasion.

I *know* through Scripture that the premises are false and I can *demonstrate* that the premises are false through an internal critique of the Muslim worldview. Consequently, I *know* because Islam contradicts the truth of the Bible and I can *deduce* the same conclusion with an internal critique of Islam.

With respect to:

p1: God reveals Christianity
p2: What God reveals is true
c: Christianity is true?

I know the premises are true through Scripture. They are not arbitrary in the least (as you suggested they were) because they are grounded in God’s word. Such an argument may not be very useful, however, because it doesn’t deal with preconditions of intelligible experience. Nonetheless, the premises are not mere inductive inferences, as is the case with “Socrates existed in the past…” The point, which is clear, is that such an argument is sound, as is TAG; whether they persuade another person or not is not a necessary condition for sound argumentation. Needless to say, the above deductive argument for the truth of Christianity will not be very useful, though TAG can be.


Joshua said...

Ron, could you do a post on whether one can know (certainly) that one is elect?

Is one's individual election deducible from Scripture?

Ronald W. Di Giacomo said...


The quick answer is that our assurance is a matter of revelation but the proposition that Ron D. is saved is not found in Scripture. Scripture tells us that one can *know* he's a son by the internal witness of the Spirit bearing witness with our spirit that we are sons. Often times "Clarkians" have a hard time with this. Whether Clark did, I'll let you decide! :)



Joshua said...


My thoughts are that this Clarkian (me) was having trouble with this, as you can witness over at Bret's blog ( -- the entry on Contra Realist Philosophies).

Having hashed it out (and being made into hash) with Bret and Mark and Clark (in What Do Presbyterians Believe) I realize how elementary my mistake was.

I need to reread De Maegistro, where Augustine brilliantly shows that ALL truth (even knowledge not deduced from Scripture) is revealed by the illumination of Christ, the Teacher.

It is humbling to forget what one ought to have known already. Perhaps the Lord saw that I was enjoying myself in a way I ought not to have been doing?

Nonetheless, my latest moment of stupidity has subsided until the next time I decide to bang my head into bricks, metaphorically speaking of course.

Ronald W. Di Giacomo said...

Don't be too hard on yourself! :)

I didn't know that Augustine thought as he did on this matter until Mark told me that a few weeks ago. I actually came to those conclusions on my own but was delighted to know I was in good company. Obviously my justification of those things I know that are not propositions found in Scripture must be undergirded by Scripture. For instance, that I know that I am saved presupposes that I exist. My justification for my existence is that the God who has revealed himself in Scripture has revealed himself to me, which presupposes that I exist.


Joshua said...

It is good to know that while my fallen mind may play tricks on me, the Lord God of Truth never will.

Ronald W. Di Giacomo said...



Anonymous said...

Can we really know the probability without having omniscience? We know observed instances but can we really say that the probability without knowing the denominator? If we only have 1/2 probability presupposes we know all instances. So, do probability presuppose infallibility?

Reformed Apologist said...

We can know probability of outcome. We can know denominator too. Two is the denominator for a discrete coin flip. A head should obtain 1/2 the time. If we flip it twice, the probability for having at least one head is 1.5 / 2 or 75%.

Of course God knows the outcome because he knows what he ensures. In that sense we're no longer talking about probability. Not knowing you, the probability of you being male is something over 2. Probably a number greater than 1 over 2 since more males attend my site. Yet probability of your gender really wouldn't apply to anyone who knows you posted. It's not so much a matter of omniscience but rather reliable information. For instance, one who knows the game is rigged doesn't work under the probability constraints as the less informed.

Anonymous said...

The example on my mind was something that was more universal. Like say that 20 out of 20 instances we see the swans are white. But in a universal sense we couldn't say that we know the probability because maybe there exist an alien world with only green swan. So, is this where it becomes a matter of information?

Reformed Apologist said...

Probability is a matter of the past and uniformity. It's largely experiential. Even if there were more green swans, the probability of seeing a white one is still greater based upon experience.

I think you're conflating concepts.

Robert Anthony Perez said...

"God exists"is not Clark's axiom.
Can you site where you got your information from?

Reformed Apologist said...

Maybe you would have preferred I *cite* where Clark spoke of his axiom as being God's word. But doesn't God's word presuppose His very existence?

Clark had many axioms, though he failed to recognize he did.

Robert Anthony Perez said...

Whoops I misspelled it. Thanks brother in Christ.

Clark and Robbins had a lot to say about the problems with the proposition "God exists" and trying to prove it as Van Til and Bahnsen attempted through the methods of Thomas Aquinas. God's word does not presuppose the proposition "God exists".

Do you remember where you read about "God exists" being the axiom of the presuppositionalist?

Reformed Apologist said...

Not tracking. Bahnsen and Van Til rejected the "angelic doctor" with respect to apologetics. Clark too was no fan of Aquinas. He was more Augustinian.

Anonymous said...


You seem very tangled up in your understanding of Clark and Van Til.

TheSire said...

The point isn't where Clark or Robbins discussed that proposition(God exist).The point is the Bible(supposed Clarkian axiom) affirms the existence of God.

Reformed Apologist said...

"Do you remember where you read about "God exists" being the axiom of the presuppositionalist?"

Clark was a dogmatist. Clark didn't appreciate that his axiom of the Word reduced to several axioms including the axiom God exists.