Charles Jackson, M.S.
I. Introduction
My purpose in writing is to deliver the foundation for the philosophy of mathematics. That is an offensive thing to write. If it be offensive to you, then you are making an assumption about philosophy which is itself a philosophical judgment. It is therefore open to philosophical refutation, and would be refuted, I maintain. It should also be noted that I am not a foundationalist in the traditional sense.
I believe that I am delivering the very answer to the problems of philosophy of math which is so sorely lacking. The idea is that after philosophers of math have sampled naturalism in mathematics, related theories from cognitive science, indispensability, the sociological attempt, constructivism, formalism, nominalism, fictionalism, structuralism, intuitionism, platonism, and isms ad nauseum, and recognized the ultimate futility of each, they would find MIC and develop a Christian philosophy of math. I will not address these isms here, except to say that they all arbitrarily (i.e. without warrant) and/or self-contradictorily assume the Inductive Principle.
It is not my purpose to impress anyone with my knowledge of philosophy, philosophy of math, history of math, or math. The absence of mathematical notation here will seem very strange. But it only seems to be a requirement that any writer on philosophy of math throw around some mathematical notation. Okay, that’s enough intro.
II. The Necessity of the Concept of the Christian God for the Intelligibility of Human Experience
The concept of the Christian God is the necessary condition for the intelligibility of human experience; therefore, the concept of the Christian God is the necessary condition for the intelligibility of mathematical human experience.
First, the former claim. Reformulating Cornelius Van Til’s Transcendental Argument for the Existence of God,
The proof of the truth of Christianity is that unless its truth be presupposed, human experience could not be intelligible.
This is only one of any number of ways to state the proof. I might have offered an induction-focused proof.
The proof is valid. Let
p = Christianity is true = The Christian God exists
q = human experience is intelligible
Claim
p
Proof
If not p, then not q.
If not not q, then not not p; therefore, p.
The opponent of the Christian apologist immediately seeks to produce another worldview which is sufficient to account for human experience. But any proposal he can produce, being expressed in human language, arbitrarily assumes the Inductive Principle (here I am not referring to the Principle of Mathematical Induction) without providing any warrant for it. According to the Christian worldview, the God Who controls every detail of creation and history reveals that He uses means according to the Inductive Principle.
According to the Christian apologist, God in His Word the Bible breathes out a comprehensive worldview sufficient for human experience. We either take it as it is revealed, or we don’t. If we don’t, then we must deviate from it on the basis of some independent worldview, the sufficiency of which (including but not nearly limited to a foundation for Induction) we must establish. But, given any belief which might be encompassed by such a worldview, we finite humans (as unaided with respect to our finitude) cannot account for any fact outside our limited sphere of knowledge and control, which fact may represent a defeater for that belief. So, on the assumption of the denial of the Christian worldview, which encompasses an exclusivity clause with respect to sufficiency for human experience, knowledge of any kind is unwarranted. Any objection to the Christian worldview is a non-starter. Christianity, with its Omniscient, self-revelatory God, is the only worldview with a chance to be sufficient. And it is.
III. The Necessity of the Concept of the Christian God for the Intelligibility of Human Mathematical Experience
The necessity of the concept of the Christian God for the intelligibility of human mathematical experience follows directly from the necessity of the concept of the Christian God for the intelligibility of human experience.
The concept of the Christian God is the precondition for the intelligibility of human mathematical experience: mathematical knowledge, mathematical practice, etc.
IV. Conclusion
So the concept of the Christian God is the precondition for the intelligibility of human mathematical experience. The foundation of the philosophy of math has been delivered. To Him be all glory.
Math Is Christian 
I am likely to tinker with this. I want to go ahead and use an induction-based proof.
Argue away.
Your proof is invalid. It does not follow from
(1) ~P => ~Q
(2) ~~Q => ~~P
that therefore
(3) P
In fact, (2) is superfluous since it is just the contrapositive of (1). You probably want to use this in its place:
(2′) Q
In other words:
(1) If the Christian God doesn’t exist, then human experience isn’t intelligible.
(2′) Human experience is intelligible.
(3) Therefore, the Christian God exists.
That argument is valid, at least. But there are two problems.
First, it’s not clear what you mean by the predicate is intelligible. Let’s call this predicate Int(x). Considering your comments about knowledge and warrant, maybe you want to say that Int(x) just in case knowledge about x is possible. But whatever you mean, you will need to explain it.
Second, you offer no arguments for (1) and (2′). So once you get clear about what you mean by the predicate Int(x), it will remain to show that those premises are true.
Thanks again, Ben.
“Your proof is invalid. It does not follow from
(1) ~P => ~Q
(2) ~~Q => ~~P
that therefore
(3) P”
That’s not what I’m saying. I didn’t number premises and conclusion the way you did. I’m saying “…and ~~P => P.” Simple deduction.
Your IOW is correct.
“First, it’s not clear what you mean by the predicate is intelligible. Let’s call this predicate Int(x). Considering your comments about knowledge and warrant, maybe you want to say that Int(x) just in case knowledge about x is possible. But whatever you mean, you will need to explain it.”
Int (x) in case x can be accounted for; x can be put into a broader context; x is encompassed by a worldview which is sufficient for x.
“Second, you offer no arguments for (1) and (2′). So once you get clear about what you mean by the predicate Int(x), it will remain to show that those premises are true.”
(1) can be demonstrated in many ways (use of logic, morality, etc.), but one way which I have used, is to argue for Christianity’s ability to account for Induction, as opposed to non-Christianity’s inability.
(2’) is presupposed by this whole discussion or any discussion.
Thanks much, Ben.
I don’t mind defending a proof for the necessity of the concept of an infinite, personal, all-knowing, all-controlling, self-attesting, self-revelatory God. Because of the Fristianity argument(s), I am not as interested in defending a proof for the necessity of the concept of THE Christian God as I was when I made my original post, although I think the concept of Him is necessary. Notice that proof is absent from my second post. I am happy to argue for the necessity of the concept of Him, or–with respect to THE Christian God–to defend my second post “THE FUTILITY OF ALL NON-CHRISTIAN APPROACHES TO THE PHILOSOPHY OF MATHEMATICS.”
Today is the Lord’s Day. Tomorrow and the days following, I will be very busy with work. I may not be able to reply to your replies right away.
Charles,
Well, assuming for the sake of argument that we can even have a concept of causation apart from induction, then I only see that Christianity can “account for” induction in the sense of telling a causal story about induction. That is, Christianity can tell us about an external cause to the fact that induction works. But I don’t see how the existence of a causal story about induction is presupposed by ordinary discussion. I agree that we must assume induction works. But I disagree that, in addition to assuming induction works, we must ALSO assume that there exists an external cause for the workings of induction.
Do you maybe have something else in mind when you talk about Christianity accounting for induction?
Feel free to take your time with replies.
Yes, “Int (x) in case x can be accounted for; x can be put into a broader context; x is encompassed by a worldview which is sufficient for x.”
Induction is encompassed by the Christian worldview which is sufficient for it.
I’m not trying to be difficult here, but I just don’t know what you mean by any of those things. What do you mean when you say that Christianity accounts for induction? Or that it encompasses induction? Or that it is sufficient for induction? When I asked you before what you meant by human experience being intelligible, I was hoping you would give an answer I could understand. But your new terminology is just as mysterious to me as your earlier terminology.
In the comment before last, you seemed to be suggesting that Christianity is able to tell a causal story about the workings of induction, but as explained previously this is unhelpful since we require no such causal story. And if causation is tied up with induction as I suspect, then Christianity won’t even give you that much. But beyond that, I don’t see what you think Christianity has to offer with respect to induction.
“What do you mean when you say that Christianity accounts for induction? Or that it encompasses induction? Or that it is sufficient for induction?”
AT LEAST that some subset of beliefs in Christianity’s web of beliefs, conjoined, entail the Principle of Induction.
Okay, thanks. That does help clarify some of what you mean, and it’s good that you aren’t (explicitly) depending on some kind of causal principle, since causal principles are notoriously indefensible.
However there are a couple of serious problems with your response. First, it doesn’t help your original argument. Remember, you must defend both (1) and (2′) in order to make your argument work. But so far, only the following has been adequately defended:
(4) Christianity entails that induction works.
It hardly follows from this that therefore (1) and (2′) are true.
Second, you appear to want to assert that Christianity is the only belief system which entails induction working, but clearly that is false. Remember that one of my beliefs is that induction works, and this trivially entails itself. It’s easy to cook up a nontrivial entailment too.
Do you have another strategy for defending your argument?
(1) If the Christian God doesn’t exist, then human experience isn’t intelligible. Argument: There are many, maybe as many as there are aspects of human experience. I’ve heard a LOT of moral theories from those who start without God, and none of them can answer the question (from the “futility” post), “’Why should I be moral?’ And in Christian epistemology the warrant can be found which is necessary for knowledge given the nature of the Problem of Induction, which comes into play whenever language is used, such as when God’s existence is debated.” But approaches to the problem of induction by those who start without God have been famously unsuccessful.
(2′) Human experience is intelligible. Argument: You and I have already assumed this; without it, we wouldn’t be having this discussion (nor could we).
As far as other worldviews’ entailing induction working, you like all humans ever believe that it does, but this belief doesn’t comport with your agnosticism/atheism or what I take to be your macro-evolutionism. Why *should* the future be like the past?
Your worldview doesn’t entail “induction working.” Do you know a non-Christian worldview that does?
Charles,
I’m not sure why you would insist that my view doesn’t entail that induction works when I have told you quite plainly that part of my view is that induction works. And it’s easy to cook up a nontrivial entailment too.
You claim that my belief “doesn’t comport” with agnosticism or atheism. Do you mean it is inconsistent with agnosticism and atheism? How so? If agnosticism and believing induction works are somehow inconsistent, then that will give you a powerful argument against agnosticism. But I have yet to discover (or be shown) any such inconsistency.
Regarding your defenses of (1) and (2′), well, it’s still not entirely clear what you mean by human experience being intelligible, but it seems like you want to say that human experience is only intelligible if some true view of the world entails that induction works. And I am willing to grant that whichever sufficiently robust view of the world happens to be true, it entails induction works. In other words, I am willing to grant at least something a bit like (2′).
But then you also claim that human experience is only intelligible if the Christian God exists. In particular, you claim that the only view (true or not) which entails induction works is the Christian one. But this claim is clearly false, as has been shown with the counterexample of my own view (which includes the belief that induction works, and hence trivially entails that induction works).
You also try to support (1) by appealing to morality. But I’m a moral skeptic—I can’t find any coherent meaning behind our moral language. You are free to stipulate definitions for moral terms, but then we will evaluate the truth or falsity of the resulting moral claims by referring to those definitions. And what we find in doing so may not comport very well with our dispositions to use that language.
Ben, I continue to indulge you (for now) even though you rightly admit that you don’t have warrant for the induction you use to write your posts.
Here we are talking about whether your worldview entail that induction works. As we do, each of us presupposes that he has a unified worldview from which to talk about whether your worldview entail that induction works. If it were not so he wouldn’t be able to talk about the different “parts” of his worldview as such (which we are doing right now), and would just be selecting tenets arbitrarily. His worldview *as a whole* wouldn’t entail any of his tenets. Only the individual tenets as such would entail themselves.
(Furthermore, we see that induction entails language which entails (where applied to worldview) unity of worldview.)
And of course I am saying you don’t have unity in your worldview. According to your agnosticism and macro-evolutionism, there isn’t any ultimate force regulating events in the world. According to your induction, there is an ultimate force regulating events in the world. They are inconsistent.
(Re your moral skepticism, you can’t live consistently with it. Also, what’s to keep you playing fair in our little debate here?)
Chuck
Chuck,
What does it mean for a worldview “as a whole” to entail this or that, as opposed to it entailing something not as a whole? That doesn’t seem to make sense. At least, I’m not able to make sense of it.
We believe induction works, and indeed induction really does work. You might complain that I don’t have warrant for my belief, but that complaint would go over a lot better if you weren’t in the same boat! If you can produce warrant for induction, that will be well. But so far you haven’t done so, and I think it’s clear that this is because you don’t have it.
In the mean time, we can get by simply believing that induction works, without warrant. It might be nice to have warrant, but it is by no means necessary.
You write: “According to your agnosticism and macro-evolutionism, there isn’t any ultimate force regulating events in the world.”
It is quite true that there is no ultimate force regulating events in the world on my view. After all, why should there be? But then you continue:
“According to your induction, there is an ultimate force regulating events in the world.”
What? How do you infer from induction that there is an “ultimate force” regulating events?
You also write: “Re your moral skepticism, you can’t live consistently with it.”
How not? This claim appears to me to be entirely baseless.
You also ask: “Also, what’s to keep you playing fair in our little debate here?”
Is this a genuine concern, or is it some kind of rhetorical prelude to a criticism about moral skepticism? You don’t have to respond if you think I’m being rude or uncooperative. But hopefully you do not think that.
BW: Chuck,
What does it mean for a worldview “as a whole” to entail this or that, as opposed to it entailing something not as a whole? That doesn’t seem to make sense. At least, I’m not able to make sense of it.
CJ: It means at least that the conjunction of all beliefs of a worldview’s web of beliefs entails this or that, as opposed to some proper subset of those beliefs’ entailing something.
BW: We believe induction works, and indeed induction really does work. You might complain that I don’t have warrant for my belief,
CJ: Yes, and so your arguments have the nature of, “OK, my worldview’s futile, and I have no right to complain about yours, but these things about your worldview bother me.”
BW: …but that complaint would go over a lot better if you weren’t in the same boat! If you can produce warrant for induction, that will be well. But so far you haven’t done so, and I think it’s clear that this is because you don’t have it.
CJ: No. (I have and will continue to deal with this in the “Futility” thread.)
BW: In the mean time, we can get by simply believing that induction works,
CJ: “Get by”? If that means using induction every minute of your life without warrant, that means you don’t have an argument, which is supposed to be what this exchange is all about.
BW: You write: “According to your agnosticism and macro-evolutionism, there isn’t any ultimate force regulating events in the world.”
It is quite true that there is no ultimate force regulating events in the world on my view. After all, why should there be? But then you continue:
“According to your induction, there is an ultimate force regulating events in the world.”
What? How do you infer from induction that there is an “ultimate force” regulating events?
CJ: Without the ultimate force, there is no regulation, and that is essential to induction. It’s not by or because of chance that we all experience this world such that whenever we squeeze the tooth paste tube, we believe tooth paste will come out, or that our memory of past events can have a bearing on future events, or that when we sit down to write a blog post, words which will continue to be useful for communication will be there. If whatever happens, happen by chance there’s no reason to think that at any time the opposite outcome won’t occur.
BW: You also write: “Re your moral skepticism, you can’t live consistently with it.”
How not? This claim appears to me to be entirely baseless.
CJ: You never express moral approval or disapproval, such as with the Newtown shootings, or when someone cuts you off in traffic?
BW: You also ask: “Also, what’s to keep you playing fair in our little debate here?”
Is this a genuine concern, or is it some kind of rhetorical prelude to a criticism about moral skepticism? You don’t have to respond if you think I’m being rude or uncooperative. But hopefully you do not think that
CJ: In debates in good faith, it is assumed that states of affairs will be represented honestly and morally, such as when I asked that last question. But you’re denying moral categories.
CJ: “It means at least that the conjunction of all beliefs of a worldview’s web of beliefs entails this or that, as opposed to some proper subset of those beliefs’ entailing something.”
Hmm. I don’t know where you’re going with this. Why does it matter if we look to the conjunction of all beliefs instead of a proper subset of them? How is that helpful?
In any case, it’s trivially true that if a proper subset of a set of beliefs entails that induction works then so does the conjection of the whole set. In particular, the conjunction of all the beliefs constituting my view of the world entails that induction holds. So your view doesn’t have any advantage (so to speak) here over mine.
CJ: “Yes, and so your arguments have the nature of, ‘OK, my worldview’s futile, and I have no right to complain about yours, but these things about your worldview bother me.'”
Futile? How so? And why haven’t I any right to complain about your view?
In any case, even if my view is hopelessly flawed, that doesn’t undercut my complaints against yours. For you don’t have any J-warrant for induction either. At best you have Plantinga-warrant. But don’t you want J-warrant?
For my own part, I care nothing for Plantinga-warrant, and I think if folks really appreciated what Plantinga-warrant is then they wouldn’t care about it either.
I guess you want to reserve this part of the argument for the other thread, so forgive my digression. I just want to remind you here that even if you show my view is wrong, you still have a ways to go before you get to conclude that Christianity is true. A long ways.
CJ: “‘Get by’? If that means using induction every minute of your life without warrant, that means you don’t have an argument, which is supposed to be what this exchange is all about.”
Oh but that’s not true though. Remember, you’ve made the argument that since human experience is intelligible, and human experience is only intelligible if God exists, it follows immediately that God exists. By human experience being “intelligible” you evidently mean, at least in part, that some true view of the world entails that induction works.
My objection to this argument consists in pointing out the myriad of non-Christian views which all entail that induction works, leading with the example of my own view. It entails that induction works, and so unless you can show (on independent grounds) that my view is false then you will need some other justification for the premise that human experience is only intelligible if God exists. But notice that it’s not enough to show that my view is unwarranted or unjustified. You need to show that it is false, which you have not done.
And it gets worse too. Once you are done with my view, you need to rule out all the other non-Christian views too! How on earth do you hope to accomplish that incredible task?
Anyway, my point is that none of this depends on induction being warranted. It’s all about truth, not warrant.
CJ: “Without the ultimate force, there is no regulation, and that is essential to induction. It’s not by or because of chance that we all experience this world such that whenever we squeeze the tooth paste tube, we believe tooth paste will come out, or that our memory of past events can have a bearing on future events, or that when we sit down to write a blog post, words which will continue to be useful for communication will be there. If whatever happens, happen by chance there’s no reason to think that at any time the opposite outcome won’t occur.”
Let’s go ahead and assume for the sake of argument that we can even make sense of regulation (and hence causation) apart from induction. I don’t think we really can, but for now I’ll put my doubts aside and go with it. Well, even granting that much, I still disagree that regulation is essential to induction.
You have tried to argue that if induction is not regulated by some external force then we have no reason to think induction will hold. But you need to show more than that. After all, I already grant that neither of us has any reason to think induction will hold! But you seem to overlook the fact that we have no reason to think it will fail to hold either, and that’s what you need to show. Maybe induction will fail and maybe not. But even apart from a regulating force, we have no reason to think that it really will fail.
To put it another way, there is nothing incoherent about the suggestion that induction holds without a regulating external force. So it does not follow that if induction holds then there exists such a regulating force. So if you want to show my view is inconsistent, you will have to find another way.
CJ: “You never express moral approval or disapproval, such as with the Newtown shootings, or when someone cuts you off in traffic?”
I express heartfelt approval and disapproval. But I don’t know what it means to express moral approval/disapproval.
BW: CJ: “Yes, and so your arguments have the nature of, ‘OK, my worldview’s futile, and I have no right to complain about yours, but these things about your worldview bother me.’” Futile? How so? And why haven’t I any right to complain about your view? In any case, even if my view is hopelessly flawed, that doesn’t undercut my complaints against yours.
CJ: Since your view is hopelessly flawed, you can make no complaint. You can’t induce, you can’t predicate, you can’t use language. It’s time to stop complaining.
BW: For you don’t have any J-warrant for induction either. At best you have Plantinga-warrant. But don’t you want J-warrant?
CJ: Plantinga defined “warrant” because justification was not sufficient for knowledge. “J-warrant” seems to represent an attempt to borrow warrant’s sufficiency for knowledge and give it to justification. I have both anyway, as I have written.
BW: CJ: “Without the ultimate force, there is no regulation, and that is essential to induction. It’s not by or because of chance that we all experience this world such that whenever we squeeze the tooth paste tube, we believe tooth paste will come out, or that our memory of past events can have a bearing on future events, or that when we sit down to write a blog post, words which will continue to be useful for communication will be there. If whatever happens, happen by chance there’s no reason to think that at any time the opposite outcome won’t occur.” Let’s go ahead and assume for the sake of argument that we can even make sense of regulation (and hence causation) apart from induction. I don’t think we really can,…
CJ: I don’t either.
BW: …but for now I’ll put my doubts aside and go with it. Well, even granting that much, I still disagree that regulation is essential to induction.
You have tried to argue that if induction is not regulated by some external force then we have no reason to think induction will hold. But you need to show more than that. After all, I already grant that neither of us has any reason to think induction will hold!
CJ: I do. God controls the world and reveals that we are to use induction.
BW: …But you seem to overlook the fact that we have no reason to think it will fail to hold either, and that’s what you need to show. Maybe induction will fail and maybe not. But even apart from a regulating force, we have no reason to think that it really will fail.
CJ: Right. Again, you don’t have a reason for thinking it will hold or fail. You don’t have a reason for believing anything on your worldview. IOW not having warrant for a belief doesn’t give you warrant for the contrary.
BW: To put it another way, there is nothing incoherent about the suggestion that induction holds without a regulating external force.
CJ: If there were nothing to make the future be like the past, why believe the future will be like the past?
BW: CJ: “You never express moral approval or disapproval, such as with the Newtown shootings, or when someone cuts you off in traffic?” I express heartfelt approval and disapproval. But I don’t know what it means to express moral approval/disapproval.
CJ: You never say or think, “That’s not right”?