A Question on Induction from Ben Wallis (Updated)

Now that Ben has clarified his answer to the problem of induction as being one largely similar to the one provided by P.F. Strawson, and now that I have pointed out the many problems with that solution in this post, I can move on to quote a question from Ben that was asked in his last comment.

Suppose we can’t ground induction in deduction. In that case, why should we refrain from taking inductive inferences to be rational? Why is it that you think justification for a position on, say, the force of gravity on earth, cannot consist of a strong inductive argument? I just don’t see how you could possibly defend that kind of position.

As I’ve already mentioned (in the post linked to above), I don’t care to “ground induction in deduction.” I am not faulting induction for not being deduction. I am, however, posing the age-old problem of induction to Ben in light of his rejection of the Christian worldview. He asks, “why should we refrain from taking inductive inferences to be rational?” My answer is simple, and it was expressed early on in the history of philosophy prior to being popularized by philosophers David Hume and later Bertrand Russell.  

We should “refrain” from taking inductive inferences to be rational upon the basis that even granting that the premises of an inductive argument are true, it does not follow that the conclusion will be true. This statement allows plenty of room for Ben or anyone else to propose their own “standards” of induction that are not deductive. I simply want to know why we should ever take the premises of such an argument, once stated as Ben would want to state it, to provide any support at all for the conclusion of that argument. Thankfully, Ben gets more specific.

Ben asks, “Why is it that you think justification for a position on, say, the force of gravity on earth, cannot consist of a strong inductive argument?” Let me see if I can help Ben out. Does Ben currently experience the force of gravity on earth? Yes. We will grant him this much. Now let’s probe a bit deeper. Does Ben currently experience the force of gravity on earth in the very next second? No. Does Ben currently experience of the force of gravity on earth in its entirety? No. Does Ben currently have universal experience of the force of gravity on earth? No. Could Ben ever have such experience? No. Indeed:

Ben experienced the force of gravity on earth on Monday.

Ben experienced the force of gravity on earth on Tuesday.

Ben experienced the force of gravity on earth on Wednesday.

Ben experienced the force of gravity on earth on Thursday.

Does it follow that Ben will experience the force of gravity on earth on Friday?

Of course not, for the particular experiences listed in the premises of this argument are independent of one another. Now if Ben had some sort of extra premise that told him that his future experience of the force of gravity on earth will resemble his past experience, then we might have something to support his expectations concerning Friday, but as it is, we do not. Or:

Ben experienced the force of gravity on earth in Illinois.

Ben experienced the force of gravity on earth in Iowa.

Ben experienced the force of gravity on earth in Indiana.

Ben experienced the force of gravity on earth in Kentucky.

Does it follow that Ben will experience the force of gravity on earth in Virginia?

Of course not, for the particular experiences listed in the premises of this argument are independent of one another. Now if Ben had some sort of extra premise that told him that nature exhibits regularities including the force of gravity on earth, then we might have something to support his expectations concerning Virginia, but as it is, we do not. In fact, even if Ben experiences the force of gravity on earth in all of the other states, as soon as he goes to Virginia he cannot know that the force of gravity on earth has remained as he previously experienced it in those other states.

So I do not really see that Ben can take a position with respect to the force of gravity on earth beyond whatever experience is present to him unless he wants to do so without any support for doing so. Thus Ben has a problem of justification, knowledge, and rationality with respect to induction as illustrated in the example of gravity.

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EDIT: 

Chris,

I really don’t know what you’re getting at, here. You deny that you are seeking deductive support for induction, but then you turn around and say that you want an inductive conclusion (that is, a conclusion to a cogent inductive argument) to “follow” from the premises. But follow how? An inductive conclusion already DOES follow inductively from the premises. The only other kind of “follow” I know is the deductive kind.

It does not follow from the facts that Ben experienced the force of gravity on earth in Illinois, Iowa, Indiana, and Kentucky that Ben will experience the force of gravity on earth in Virginia. Ben has not provided any reason whatsoever to think that these premises have anything to do with the conclusion.

In other words, it sounds like you want true premises of an inductive argument to guarantee that the conclusion is true. But that is precisely what deduction IS. It’s as if you’ve denied you are seeking water, while simultaneously insisting that you want a liquid with the chemical structure H2O.

Maybe instead you just want the premises of an inductive argument to guarantee that the conclusion is PROBABLY true. But probability is about norms of expectation (i.e. what we should vs should not expect given certain conditions),

And like I have (surely?) pointed out many times by now (at least in other contexts), Ben has not provided any reason whatsoever to think that these premises even probably have anything to do with the conclusion. Why, why, why should we expect to experience the force of gravity on earth a second from now? Ben has no answer to this question. He just arbitrarily, and hence irrationally, does so. The probability that Ben will experience the force of gravity on earth a second from now is equivalent to the probability that he will not, at least given Ben’s worldview.

and so this is why I talked about taking induction as justified by part of what it means for something to be justified. It is part of our epistemic standards that a strong inductive argument constitutes justification for belief. Just like we have moral standards for how we should vs should not behave, so too we have epistemic standards for what we should vs should not believe. These epistemic standards define what it is for something to be “justified,” or “rational,” etc. So, if you want something to be “probably” true, that demand only makes sense in the context of such standards—after we have defined rational justification using induction.

I have already addressed the appeal to Strawson’s argument. Interestingly, Ben proposes that he has moral and epistemic standards within his worldview as well. I would like to know how. But that massive problem aside, Ben is not actually answering the specific questions concerning induction such as why should we expect to experience the force of gravity on earth a second from now. Why should we believe that we will experience the force of gravity on earth a second from now? Stating that there are things we should and should not believe does not answer the question of how we determine what such things are.

On a related note, is this what you mean by “epistemic justification” for induction—having the truth of a conclusion “follow” from the truth of the premises—? Because if that’s it, then I don’t see how your problem with induction hasn’t been answered already. If not, then what DO you mean by “epistemic justification”?

Thanks,
–Ben

This is not difficult, but it may just be that I am a poor communicator. I want to know what reason or evidence Ben has for moving from the premises of an inductive argument like either of the two examples above to the conclusion of such an argument. I want to know this regardless of what we say regarding the probable or expected nature of the conclusion. If Ben wants to represent a piece of inductive reasoning in a different manner then I am fine with that as well, but the same questions will apply. What is it that connects the premises together with the conclusion? How does Ben reason beyond the present testimony of his memory and senses?


25 Comments

Agreus

Mr. Bolt,

What does the problem of induction have to do with existence of God? Even if Mr. Wallis never sufficiently answers your line of questioning regarding induction, how does this constitute an argument for the existence of God? It would be nice for you to state your case for God in clear terms if that is possible. Thank you.

C.L. Bolt

“What does the problem of induction have to do with existence of God?”

In this instance the problem of induction is the particular skeptical argument being answered through a transcendental argument with God as the alleged precondition in that argument.

“Even if Mr. Wallis never sufficiently answers your line of questioning regarding induction, how does this constitute an argument for the existence of God?”

It does not in and of itself constitute an argument for the existence of God. See above.

“It would be nice for you to state your case for God in clear terms if that is possible.”

I did so in my debate with Ben Wallis, which you commented on, and so I am assuming you listened to it. If you have some particular question about my case for God then feel free to ask it, but otherwise you may just need to acquaint yourself with skepticism and transcendental arguments as presented by some source other than me.

Agreus

I’ve listened to your debate with Mr. Wallis and unfortunately I have not heard your case for God clearly stated throughout the debate.

It would appear that Mr. Wallis will never be able to provide a satisfactory explanation to you concerning the problem of induction as it does not entail the existence of God. Likewise, Mr. Wallis doesn’t seem to think your explanation is satisfactory.

So again, what does this have to do with the existence of God? Where is the argument? Thanks.

C.L. Bolt

Well, I did clearly state my case, so you may want to go back and listen again. I stated it at least three different ways, one of which was in the form of a syllogism.

I’m not looking for an explanation of induction from Mr. Wallis that entails the existence of God, since he claims he does not believe in God. As far as satisfaction on one side or another, persuasion is irrelevant to the validity or soundness of an argument.

I already explained what this has to do with the existence of God.

I already explained what type of argument I used.

Again, since you seem determined to ignore the substance of everything I am answering you with, I would encourage you to look at other sources on skepticism and transcendental arguments. It is clear from what you have said that you are ignorant of both, and you seem unwilling to listen to me concerning them.

Agreus

If you are consistently using the definition of “rational justification”, then both yourself and Mr. Wallis have “rational justifications” of induction. Upon scrutiny though, circularity can be found in both of your justifications, so I doubt Hume would find either of your answers satisfactory.

You have criticized your opponent’s views on induction, however you have not solved Hume’s problem yourself. You still have not established the relevance of induction to the existence of God.

C.L. Bolt

I am consistently using the definition of “rational justification”, and Mr. Wallis does not have “rational justification” of induction while I do. Upon scrutiny, circularity can be found in his justification, so I doubt Hume would find his answer satisfactory.

I have criticized my opponent’s view on induction, however I have solved Hume’s problem. I have established the relevance of induction to the existence of God.

Thanks for the unhelpful assertions.

Agreus

Reading your solution for the problem of induction from a transcript of your debate with Wallis, I don’t believe you’ve solved the problem of induction. Suppose one were to substitute “God” with “the universe” in your solution. Would you consider the following to be a solution to the problem of induction: The universe exists such that the future will resemble the past and as our noetic capacities are adapted to the universe, perhaps we know a priori that the future will resemble the future. I’m not really trying to be argumentative, I just don’t think you’ve solved the problem of induction.

C.L. Bolt

There’s a transcript?

The question is how we know that the universe exists such that the future will resemble the past and how we know that our noetic capacities are adapted to the universe. The universe is a contingent, ever changing entity.

God is not a contingent or changing entity, and we know that the universe exists such that the future will resemble the past and our noetic capacities are adapted to the universe because God has “told us so.”

Agreus

Yes there is a transcript. If you google Wallis and Bolt, you will find it.

The problem with your justification is that God’s existence has not been established and hence the inductive principle remains unjustified. What you stated may serve as a great personal justification for you as a theist, but it does not solve Hume’s problem of induction. Do you perhaps have a non-circular argument to justify inductive reasoning? Thanks.

C.L. Bolt

The argument proceeds by taking some proposition to be true *for the sake of argument*. Hence within the Christian worldview, where God is taken to exist, there is a justification for induction. *If* Christian theism were true, *then* induction would thereby be justified. You seem to concede this when you write that this serves as a great personal justification for me as a theist. So then, I have no problem of induction, because I believe in God.

The non-theist cannot say the same, and there are some problems with that.

Agreus

Even for the dubious “sake of argument”, your premise is a conditional that requires support. Until God’s existence is established, the argument is circular and Hume’s problem remains. For someone who does not question the premise, it may serve as some sort of vague explanation or “justification” for the principle of induction, however it does not solve the logical problem of induction as framed by Hume.

Agreus

In order to understand how you have not solved the problem of induction, I think it might be helpful to briefly summarize Hume’s analysis of human beliefs.

Beliefs that are grounded wholly on associations formed within the mind are “relations of ideas”. They are demonstratively true solely by virtue of the concepts contained within them (true by definition). If one accepts the definition of God as being a necessary being, then God would be an example of a “relation of ideas”. Reasoning concerning relations of ideas is deductive reasoning.

Beliefs that are formed based on experience are “matters of fact”. They are substative beliefs, true by virtue of the way the world is. There is no certainty associated with these beliefs as the contrary of the belief can never imply a contradiction. An example of a “matter of fact” would be your revelatory, “God told us so” experience. Reasoning concerning “matters of fact” is inductive reasoning. In inductive reasoning the truth of the premises makes the conclusion more probable.

So the question Hume is concerned with is how do we know that the future will resemble the past? Your answer is, in essence, because “God told us so”. Does this solve the problem for the theist? Unfortunately, even if one presupposes Christian theism, it does not and I think the reason is obvious.

Your revelation falls under the category of “matter of fact” beliefs and one cannot prove the principle of induction from this. As such, the problem of induction remains a logical quagmire for the Christian theist. Furthermore, as I have said ad nauseam, it is completely irrelevant to the question of whether or not God exists. Though your answer may serve as a justification in a different sense, it does not overcome Hume’s logical problem of induction.

C.L. Bolt

Yeah, I’ve studied Hume, but you summarized that well. 🙂

There are at least three problems with your response.

1. If we speak in terms of the traditional categories then God is known a priori.

2. I suggested per Plantinga that the inductive principle is likewise known a priori in accordance with theistic belief.

3. There is a distinction to be made between practice and principle. The theist may practice induction while knowing that it is justified in principle.

C.L. Bolt

One does not have to claim that God exists in order to accept any conditional of the form, “If God exists then…”

You kept requesting that I state my argument clearly, asked where the argument is, and implied that there is not an actual argument being made. Now you are claiming that the argument is circular. Both cannot be the case.

You are also not being clear about whether or not you think there is a justification for induction *if God exists*. Your more recent comment appears to reject it while your previous comments seem to concede that the theist does have such justification.

Agreus

“1. If we speak in terms of the traditional categories then God is known a priori.”

Relations of ideas *are* a priori so if one accepts the notion of a necessary God, then this is not in disagreement with what I wrote previously.

“2. I suggested per Plantinga that the inductive principle is likewise known a priori in accordance with theistic belief.”

This of course cannot be the case as the knowledge comes through revelation. You cannot know something a priori from a posteriori knowledge (based on experience).

“3. There is a distinction to be made between practice and principle. The theist may practice induction while knowing that it is justified in principle.”

I’m unclear as to how this relates to solving Hume’s problem of induction.

“One does not have to claim that God exists in order to accept any conditional of the form, “If God exists then…”

One may be easily tricked into accepting God’s existence if one defines God as a necessarily existing being, which is how you define God. The idea is to define God as a necessarily existing being and then to slip this into the conditional premise.

“You kept requesting that I state my argument clearly, asked where the argument is, and implied that there is not an actual argument being made. Now you are claiming that the argument is circular. Both cannot be the case.”

Actually, when I said it was circular, I was referring to the definition of God as a necessarily existing being, which is essentially the ontological argument.

“You are also not being clear about whether or not you think there is a justification for induction *if God exists*. Your more recent comment appears to reject it while your previous comments seem to concede that the theist does have such justification.”

Justification is not a precise philosophical term and one should always be weary when arguments are based upon this word. When I say you have a different sort of justification for induction, I mean it more in terms of your belief that God created a universe such that the future will resemble the past and that he revealed this knowledge to you. Your justification is more a statement of your faith, then a solution to the problem of induction.

C.L. Bolt

1. Yes, in Hume’s categories relations of ideas are a priori. Whether or not God is a necessary being is irrelevant to the question of whether or not God is known a priori. You have not made any new point here. Since God is known a priori your previous concern is moot, and that was why I mentioned it.

2. Again I have suggested per Plantinga that the inductive principle is known a priori in accordance with theistic belief. You state that this cannot be the case since “the knowledge comes through revelation.” The knowledge of what? I’ve already noted that the knowledge of God is a priori, if we want to use that category of knowledge, and now I am suggesting as well that the inductive principle is a priori. It is known prior to experience of the contingent or empirical realm. So you have not addressed the point here either.

3. My third point is that there is a distinction to be made between practice and principle, and that the theist may practice induction while knowing that it is justified in principle. This point is not set forth in an attempt to solve Hume’s problem of induction, but rather to address your concern that the inductive principle can only be known through revelation that is restricted to the category of “matter of fact.” Again the theist may practice induction in interpreting revelation while knowing that he is principally justified in doing so. There is also something to be said concerning the distinction between broad and narrow uses of induction, but I did not previously bring that point in. So you have not addressed my third point as it relates to the concerns you previously expressed.

Regardless of how God or any other entity is defined, one can accept the conditional “If x exists then…” without accepting that entity as actually existing. Your response about defining God as necessarily existing has nothing to do with the point.

You kept requesting that I state my argument clearly, asked where the argument is, and implied that there is not an actual argument being made. Then you claimed that the argument is circular. Both cannot be the case. Now you are saying that you were referring to my definition of God as a necessarily existing being, but you are creating a lot more problems for yourself in this ad hoc response. First, defining God as a necessarily existing being is not a circular definition anyway since something is predicated of God which is not necessarily contained in the subject. Second, I have not explicitly defined God this way in the discussion. Third, it is irrelevant to the discussion. Fourth, you wrote, “Until God’s existence is established, *the argument* is circular and Hume’s problem remains.” So you were not referring to my definition of God being circular, but *the argument*, which is referring to the argument I used but that elsewhere you have claimed you cannot find. Fifth, now you are identifying my argument as the ontological argument even though I am not using the ontological argument. Sixth, if you are identifying my argument as the ontological argument then you cannot complain as you did before that you cannot find my argument. So something has to give here in your ad hoc response, because it is likewise inconsistent with what you have previously stated.

You are still not being clear as to whether or not you think that my belief that God created the universe such that the future will resemble the past and that He revealed this knowledge to me serves as a justification for induction. I am speaking here of an epistemic justification for induction as you should be able to know if you have followed the discussion. You are not in a position to equivocate on the term just now. If my aforementioned belief does not provide justification of induction, then you need to plainly say so and tell me why it does not. If it does, then you have conceded the argument, and we can move on to talking more about your need for repentance.

Agreus

Let’s set aside questions of circularity as I believe this will come up again in due course. For now rather than engage in nitpicking, we should focus on the question at hand. I’m not interested in scoring debate points, rather I’m genuinely interested in how theism solves the problem of induction.

How do you justify making inductive inferences from the observed to the unobserved? You attempt to ground induction in God, which you claim to know a priori, however I don’t understand how this gets around the problem. How can you rationally justify the principle of induction based on an a priori assumption? Thanks.

C.L. Bolt

Let me remind you that you are the one who raised the “questions of circularity” by asserting that the argument I presented is circular. Now you want to set this issue aside because I have pointed out an inconsistency on your part in asserting on the one hand that you do not recognize that I have an argument and on the other hand that it is circular. I am not engaging in “nitpicking.” You have been asking where my argument is, and then you asserted that my argument is circular. That is inconsistent, and it is easy enough for anyone to see that without “nitpicking.” Pointing out the obvious fact that you are being inconsistent has nothing to do with “scoring debate points.” This is not a formal debate, and there is nothing underhanded in my pointing out the problems with your arguments. If you want to argue a point then do so, but I will attack those arguments and assertions that do not support my position. That should be expected.

I justify making inductive inferences from the observed to the unobserved by virtue of the premise that there are regularities in nature. I know that there are regularities in nature because I know God as the intelligent, revelatory, ordered Creator and Sustainer of the universe, and I know Him “prior” to experience in terms of the traditional categories of a priori and a posteriori knowledge.

Agreus

You claim an a priori knowledge of God and attempt to ground induction in this assumption. However, how can this unjustified assumption (God) serve as a rational justification for induction? I’m not seeing your argument here. Perhaps you could lay it out in the form of a syllogism? It is easy to state that your knowledge of induction is a priori, however I don’t see how this solves the problem of induction.

Recall Hume’s Argument:

1) Matters of fact can only be known “a posteriori” through experience.
2) Therefore matters of fact can only be justified by recourse to experience.
3) But any attempt to do so is circular.

Therefore there is no justification for inductive inferences.

So far, all you have provided are unjustified a priori assumptions.

C.L. Bolt

I presuppose that God exists just as you presuppose that God does not exist. My presupposition is justified through a transcendental argument. God created the universe such that the future will resemble the past and He revealed this knowledge to me. That is how my presupposition serves as a rational justification for induction. Your presupposition, on the other hand, does not serve as a rational justification for induction. So you are mistaken to speak of the existence of God as an “unjustified assumption.” The existence of God is not merely an assumption, but a presupposition, and hence is justified differently than other propositions. It is justified through a transcendental argument. I would recommend that you review transcendental arguments.

You claim yet again that you are not seeing my argument, but you had no problem asserting without any support at all that my argument is circular and asserting that I am using the ontological argument. So you are being inconsistent. As already alluded to, the argument was set forth in a syllogism in my debate with Ben Wallis.

Although you quote your understanding of Hume’s argument from another source there are a number of problems with it. You can consult my debate and other places on this site for several different ways that I have sought to spell out the problem of induction. In any event, premise 2 is false if we follow the way you have stated the argument. Matters of fact can be justified by recourse to transcendental reasoning, and so it is false that they can only be justified by recourse to experience.

Agreus

You should know that you cannot use anything based upon experience as rational justification for induction. To base your knowledge of induction on revelatory experience and use this as rational justification for induction is circular reasoning.

If it is your belief that your worldivew is the only possible worldview that can provide the necessary preconditions for the principle of induction, then feel free to argue your case. However understand that you are not addressing Hume’s problem of induction and this is an entirely different type of justification (as you stated yourself). Hume’s problem is not about identifying the necessary preconditions for inductive reasoning. This is an entirely different question. Hume’s concern is with providing a logical justification for inductive reasoning.

So it would appear that you are equivocating on the term “justification”. Unfortunately, I don’t feel we are making much progress here. If you can concede that theism does not solve the logical problem of induction, then perhaps we can explore modal justifications for the inductive principle.

C.L. Bolt

I am not using something based upon experience as rational justification for induction. My knowledge of God is a priori knowledge. I have repeatedly said this, and you failed in objecting to it the last time you commented, so I do not know why you are pretending as though I am attempting to posit something based upon experience as rational justification for induction. You seem to be forgetting what we have already been over.

You also appear to be confused about what a priori knowledge is. If you want to deny that there is such a thing then that is a wholly different matter. For example, one might argue that even relations of ideas like mathematical propositions, typically considered a priori, are experienced as soon as they are known. This was a concern that Van Til had, and it is the reason that I was careful before to make the qualification, “If we speak in terms of the traditional categories.” This would lead into a discussion of what is meant by a priori, but you have not raised the concern. Perhaps it will help to state that God is known without experiencing the contingent realm. So again, I am not using something based upon experience (in an a posteriori fashion) as rational justification for induction, and you have not raised a successful objection to my using something based upon a priori knowledge (or a presupposition) as rational justification for induction.

I am not equivocating on the term “justification,” though you may be equivocating on the term “experience.” You do not have to tell me what Hume’s problem is about. I know what Hume’s problem is about. I also know what transcendental arguments are about, and how they are related to Hume’s problem. However, you are still avoiding the area of transcendental argument, and I am not sure why unless you just do not understand it. That is fine, except that I keep recommending that you read up on it.

I am addressing your concerns as you raise them, but you keep moving on to other worries, and then when I address those you merely repeat your concerns from before. Try to stick with one objection at a time, and if my answer is not persuasive to you, then let me know why it is not persuasive to you.

Agreus

On 16th Mar, 2011 you state, “My knowledge of God is a priori knowledge. I have repeatedly said this, and you failed in objecting to it the last time you commented, so I do not know why you are pretending as though I am attempting to posit something based upon experience as rational justification for induction. You seem to be forgetting what we have already been over.”

Yet on 15th Mar, 2011 you state, “God created the universe such that the future will resemble the past and He revealed this knowledge to me.”

What are you basing *your* knowledge upon? Your knowledge that God created the universe such that the future will resemble the past is based upon revelation, which is “a posteriori” knowledge dependent on experience. If you are claiming that your knowledge based upon revelation is “a priori”, then I would suggest that perhaps you are the one confused about the meaning of “a priori”.

Even if you really mean that you have an “a priori” knowledge of induction, that doesn’t get you around the problem of induction. As stated earlier, “matters of fact” can only be known through experience. So you still are in a logical quagmire and I’m afraid no amount of handwaving will get you out of it.

C.L. Bolt

My knowledge that God created the universe such that the future will resemble the past is something I know to be the case because of the nature of the God who is known apart from experience of the contingent, empirical realm. If you want to argue (rather than merely assert) that the inductive principle is itself restricted to the category of matters of fact then you would need to produce that argument, but I can’t imagine what it would look like.

You also have not addressed my third point from above which was drawing the distinction between practice and principle. This also speaks to your common objection.

Agreus

Thanks for the discussion Chris. I still am not clear regarding your solution to the problem of induction. Even if I presuppose God’s existence, I cannot see how this solves the problem of induction. Perhaps you need to clearly define “justification”.

It does not matter whether or not the inductive principle is restricted to the category of matters of fact, you still do not have rational justification for the inductive principle.

Regarding the distinction between practice and principle, you stated earlier that the theist can practice induction while knowing it is justified in principle. Before I can address this, you need to clearly define what you mean by justification.


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