THE FUTILITY OF ALL NON-CHRISTIAN APPROACHES TO THE PHILOSOPHY OF MATHEMATICS

MATH IS CHRISTIAN

 Charles Jackson, M.S.

THE FUTILITY OF ALL NON-CHRISTIAN APPROACHES TO THE PHILOSOPHY OF MATHEMATICS

The approach given here represents the salvation of the philosophy of math, for which the need is great. My desire 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) assume the Inductive Principle (here I am not referring to the Principle of Mathematical Induction), since they are expressed in human language. Whenever one uses human language, he or she reasons from particulars to universals or generalities (i.e. uses induction); he or she assumes or exhibits belief in the Inductive Principle. But no one can warrant the use of Induction on a non-Christian basis. (See James Anderson, “Secular Responses to the Problem of Induction.”)

By the way, 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.

So, with the failure of all non-Christian attempts at philosophy of math, it remains to consider the Christian alternative.

THE SUFFICENCY OF THE CONCEPT OF THE CHRISTIAN GOD FOR THE INTELLIGIBILITY OF HUMAN EXPERIENCE

The truth of Christianity (i.e. that the Christian God exists) is a sufficient condition for the intelligibility of human experience; therefore, the truth of Christianity is a sufficient condition for the intelligibility of mathematical human experience.

First, the former claim. The Christian God, being, as He is, infinite, personal, all-knowing, all-powerful, all-controlling, self-attesting, and self-revelatory, provides what is necessary for a successful philosophy of anything. To summarize, a successful ontology (and metaphysic), a successful ethical theory, and a successful epistemology are gained. The ontology offered by Christianity is sufficiently rich and explained by reference to the Creator and Sustainer God Who is all-controlling. For example, mind/body is not a problem for Him; He governs the effects of actions in the non-material realm on those in the material realm, and vice versa, and reveals in the Bible that He does so. Christian ethical theory has an answer to the crucial question “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. 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.

THE SUFFICIENCY OF THE CONCEPT OF THE CHRISTIAN GOD FOR THE INTELLIGIBILITY OF HUMAN MATHEMATICAL EXPERIENCE

The sufficiency of the concept of the Christian God for the intelligibility of human mathematical experience follows directly from the sufficiency of the concept of the Christian God for the intelligibility of human experience, simpliciter.

The concept of the Christian God is a sufficient condition for the intelligibility of human mathematical experience:  mathematical knowledge, mathematical practice, etc.

OBJECTION

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, 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.

CONCLUSION

While non-Christian philosophies all fail because of their total inability to warrant their claims (since, for them, Induction lacks a foundation) the Christian one is successful. Furthermore, it encompasses an exclusivity clause with respect to sufficiency for human experience:  its God claims to give the only sufficient basis. So, since the Christian worldview is successful, it is uniquely successful. I actually don’t believe that there is a possible world in which any other worldview is sufficient for human experience. I believe that the truth of Christianity will be shown to be a necessary condition for the intelligibility of human experience. Without the Christian God, we are left with nothing but skepticism.

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43 thoughts on “THE FUTILITY OF ALL NON-CHRISTIAN APPROACHES TO THE PHILOSOPHY OF MATHEMATICS”

  1. I do not understand why non-Chirstian approaches to a philosophy of math would be futile. For one, math has never been distinctively Christian. The bible does not describe any philosophical foundation for math either. There’s a reason that we call numerical methods algorithms, not jesus-christms, or bibleims. Finally, if that allusion to induction refers to Hume’s problems with induction, well, math induction is not the same as Hume’s. That leaving aside that Hume’s problem of induction has its own problems.

    So this seems like a cheap attempt at stealing math from its real founders by some cheap philosophical acrobatics and circular reasoning about the sufficiency of “God” as foundation because a book said that “God” said so.

    Very poor philosophy mixed with very poor thinking and equivocation fallacies. Mistaking mathematical induction with inductive reasoning is not that justifiable when the author claims to be a mathematician.

    1. Thanks for your input, physics.

      “…math has never been distinctively Christian….”

      According to the Christian worldview, every mathematical belief ever expressed has assumed the existence of the Christian God. All men know God (Romans 1.21), but some “by their unrighteousness have suppressed the truth.” (v. 18.)

      “The bible does not describe any philosophical foundation for math either.”

      In the context of a passage on wisdom (*sophia*) the Bible says, “The fear of the Lord is the beginning of knowledge.” Any knowledge, including mathematical knowledge. Hence Paul in Romans 1.21-22, on those who don’t start with the fear of the Lord: “For although they knew God, they did not honor him as God or give thanks to him, but they became futile in their thinking, and their foolish hearts were darkened. Claiming to be wise, they became fools….” 1 Cor 1.20: “Has not God made foolish the wisdom of this world?” In Eph 4.18 Paul says that “they are darkened in their understanding, alienated from the life of God because of the ignorance that is in them, due to their hardness of heart.” It’s not hard to see why. They have given up their only hope of a basis for Induction the infinite, personal, all-knowing, all-powerful, all-controlling, self-attesting, and self-revelatory God, because of their moral situation.

      “There’s a reason that we call numerical methods algorithms, not jesus-christms, or bibleims.”

      You presuppose that the naming of algorithms doesn’t assume the truth of Christianity. But it does, as described above. Unbelievers, whether they use algorithms, name algorithms, or argue against the existence of the Christian God, assume that He exists the moment they open their mouths and expect any kind of result. In using language, they are using Induction, which requires God.

      “Finally, if that allusion to induction refers to Hume’s problems with induction, well, math induction is not the same as Hume’s.”

      Yes, I distinguished the two in my first post: “But any proposal [the non-Christian] 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.”

      “That leaving aside that Hume’s problem of induction has its own problems.”

      Yes, on his basis of empiricism, the very Problem of Induction he put forward cannot be surmounted.

      “So this seems like a cheap attempt at stealing math from its real founders by some cheap philosophical acrobatics and circular reasoning about the sufficiency of “God” as foundation because a book said that “God” said so.”

      God’s self-attestation is a strength of the Christian worldview. If there were a book that described this kind of God, and yet He Himself didn’t call us to believe in Him, there’d be no reason to. Someone beyond the naturalistic realm must tell us what it means. We can’t know from within it.

      “Very poor philosophy mixed with very poor thinking and equivocation fallacies. Mistaking mathematical induction with inductive reasoning is not that justifiable when the author claims to be a mathematician.”

      Mistaking mathematical induction with inductive reasoning would be an equivocation fallacy if I had made it; but again, I distinguished the two in my first post.

      What other “equivocation fallacy” did you have in mind?

      BTW what worldview do you espouse? From what foundation do you implicitly claim answers to the problems of language and induction as you use them to argue against the very One who makes argumentation possible?

  2. How could people who were born before Christianity deny the Christian god? How can fear for a being, even if the being in question were real, be the beginning of knowledge? Fear is an emotion. An emotion is far from being a foundation for knowledge. Sure you can do better than that. Can’t you? I do not remember being afraid of any gods when I learned my first principles of math. I remember starting with addition, not with you shall be afraid of some god! Therefore fear is not the foundation of knowledge. If anything, specially in math, it seems to be a deterrent, rather than a way towards knowledge. Please.

    I had not seen your first post about differentiating mathematical induction from Hume’s. So my mistake and apologies for the fallacy of equivocation claim. However, this makes your case much more difficult, because you are giving it many more steps before you claim that math is Christian. You want to justify induction by your god, therefore language (seriously?), therefore math because you have to use language to develop math, therefore math is Christian? So awfully convoluted. Makes your case worse than the equivocation.

    Then again, you are basically saying that there’s a philosophical problem. Then that if you can imagine a god who could “solve” the problem, then this imaginary being has to be true. But, to imagine this being you have to assume a lot about reality already. You have to have formed concepts and assumed identity all along based on the very reality you want to justify. You are therefore engaging in circular reasoning to justify your god to justify your trusting reality, which you had to trust before you could imagine this god. Do you really not see any problem with this approach? Just to read the Bible you need that language that you so happily deny. Your whole construct depends on induction to the nth power.

    Hume’s problem of induction is much more specific that the problem of language. Language does not assume, nor does it need, for you to know every specimen of, say, a human, before you can form the concept of a human. Or every specimen of chairs before you can form the concept of a chair. Thus, language is far from being Hume-induction problem-like. You do not need all the specifics for every existent in the universe before you can have a useful language to deal with every day events. Thus, the presuppositionalist claim that you have to know everything before you can know anything is beyond … nonsensical. Specially if you want to apply this idea to language.

    As per Hume’s problem, it is wrong because it forgets identity as a foundation. As soon as we recognize that any induction assumes identity we can recognize that it is not circular. Induction assumes that things are what they are. Thus that things do what they do. That they behave according to their identity or nature (recognize this from your own apologetics when referring to God’s nature?). Now try and talk against identity without assuming it. Or try to talk about your god giving you anything, revelation, truth, anything, without identity, and you will see that identity is so foundational that your god as explanation for anything is, not only unnecessary, but excessive, abusive, and frankly, makes your god into a nonsensical cartoon. Because if you wanted to deny identity as foundational you would be denying your own god. No identify, no gods to talk about, no revelations to talk about. All nonsense. Therefore you rely on something much more foundational in order to justify your god as foundational for anything.

    But I will be happy to change my position should you be able to show me exactly how would your god communicate anything, be the foundation of anything, without identity.

    Finally, I have lots of Christian friends, and most of them reject presuppositional apologetics (they understand the circularity). Therefore, you can’t say that what you espouse here is “The Christian Position[TM].” It is your particular apologetic school’s position, but nothing more. Other Christians are smart enough not to engage in this kind of rhetoric.

    I do not think that I espouse a specific worldview. I find it hard to define me as following any specific school. I do not believe in any gods, let alone yours, though. Yours is particularly nonsensical for reasons other than your kind of apologetics.

    1. Will reply as soon as I can…a million papers to grade, semester grades crunch, major complicating factors, and let’s just say that
      Dec. 17, 2012 is one of the most important days of my life!

      1. I expect that you enjoyed your day and that you might add this one to your celebrations at the very least. Comments by some random guy on the web is the least thing you should worry about.

        Marking? I can hear you.

  3. Thanks for your patience. Do you teach?
    Yes, I became a grandfather this week for the first time!

    “How could people who were born before Christianity deny the Christian god?”

    The God of the OT is the same as the God of the NT. “Messiah” (Hebrew) = *Christos* (Greek)

    “How can fear for a being, even if the being in question were real, be the beginning of knowledge? Fear is an emotion. An emotion is far from being a foundation for knowledge. Sure you can do better than that. Can’t you? I do not remember being afraid of any gods when I learned my first principles of math. I remember starting with addition, not with you shall be afraid of some god! Therefore fear is not the foundation of knowledge. If anything, specially in math, it seems to be a deterrent, rather than a way towards knowledge. Please.”

    THIS “fear” entails belief in this God, which is the beginning of knowledge. You had it when you first started doing math, even though you deny it. You believe in God, even though you don’t believe that you believe in God. You “suppress [this] truth.” Romans 1.18

    “I had not seen your first post about differentiating mathematical induction from Hume’s. So my mistake and apologies for the fallacy of equivocation claim. However, this makes your case much more difficult, because you are giving it many more steps before you claim that math is Christian. You want to justify induction by your god, therefore language (seriously?),”

    You don’t think you have to assume particulars based on universals whenever you use language?

    “therefore math”

    I wouldn’t say “therefore math”; the practice of mathematics depends on language, but math more directly depends on God because without His being in control, there’s no reason to think e.g. theorems will continue to be true 10 minutes from now. Why believe so in a chance universe?

    “because you have to use language to develop math, therefore math is Christian? So awfully convoluted. Makes your case worse than the equivocation.”

    You’ve yet to show any inconsistency or contradiction.

    “Then again, you are basically saying that there’s a philosophical problem. Then that if you can imagine a god who could “solve” the problem, then this imaginary being has to be true. But, to imagine this being you have to assume a lot about reality already. You have to have formed concepts and assumed identity all along based on the very reality you want to justify. You are therefore engaging in circular reasoning to justify your god to justify your trusting reality, which you had to trust before you could imagine this god. Do you really not see any problem with this approach? “

    Christianity explains the entire process. Yes, I believe in God even as I reason about Him. Logicians use logic even as they argue about logic. God is in control and has revealed that he orders the world which includes my and your reasoning about Him. No contradiction.

    “Just to read the Bible you need that language that you so happily deny. “

    When did I ever deny language?

    “Your whole construct depends on induction to the nth power.”

    Of course it does.

    “Hume’s problem of induction is much more specific that the problem of language. Language does not assume, nor does it need, for you to know every specimen of, say, a human, before you can form the concept of a human.”

    If it did, you wouldn’t need induction. You’d be God.

    “Or every specimen of chairs before you can form the concept of a chair. Thus, language is far from being Hume-induction problem-like. You do not need all the specifics for every existent in the universe before you can have a useful language to deal with every day events. Thus, the presuppositionalist claim that you have to know everything before you can know anything is beyond … nonsensical. Specially if you want to apply this idea to language.”

    Unless you know everything, or have One Who does know everything reveal Himself, you can never warrant your use of induction. You can’t warrant your belief that any particular is of some universal, or that the future will be like the past, e.g. that the language that you are about to use with someone will work as it has in the past.

    “As per Hume’s problem, it is wrong because it forgets identity as a foundation. As soon as we recognize that any induction assumes identity we can recognize that it is not circular. Induction assumes that things are what they are. Thus that things do what they do. That they behave according to their identity or nature (recognize this from your own apologetics when referring to God’s nature?). Now try and talk against identity without assuming it. Or try to talk about your god giving you anything, revelation, truth, anything, without identity, and you will see that identity is so foundational that your god as explanation for anything is, not only unnecessary, but excessive, abusive, and frankly, makes your god into a nonsensical cartoon. Because if you wanted to deny identity as foundational you would be denying your own god. No identify, no gods to talk about, no revelations to talk about. All nonsense. Therefore you rely on something much more foundational in order to justify your god as foundational for anything.

    But I will be happy to change my position should you be able to show me exactly how would your god communicate anything, be the foundation of anything, without identity.”

    I don’t deny identity. Your problem is that you can’t back up any predication about indentity.

    “Finally, I have lots of Christian friends, and most of them reject presuppositional apologetics (they understand the circularity).”

    Yes, my presuppositions determine my conclusions, just as it is with every other human being in the history of the world. Everyone has ultimate commitments; the issue concerns the contents of those commitments.

    “Therefore, you can’t say that what you espouse here is “The Christian Position[TM].” It is your particular apologetic school’s position, but nothing more. Other Christians are smart enough not to engage in this kind of rhetoric.”

    There can only be one Christian worldview. It defines itself as exclusive. All true Christians are trying to understand that worldview more accurately. Whatever the accurate picture is, it has to include certain things that I have included in my apologetic.

    “I do not think that I espouse a specific worldview. I find it hard to define me as following any specific school. I do not believe in any gods, let alone yours, though. Yours is particularly nonsensical for reasons other than your kind of apologetics.”

    If you view the world, you have a world view. (I expect that you are some kind of evolutionistic physicalist, physics.) You have beliefs in terms of which you say everything you have said in your posts.

    Now, warrant your beliefs, or you are disqualified from rational discussion.

  4. Charles,

    I’m not sure what you think Christianity has to offer here. You appear to be simply assuming that induction works AND that God exists and wants induction to work. Or if you think you can make sense of causation apart from induction, perhaps you want to say that induction works and God exists and causes induction to work. Either way, why not simply assume that induction works, without assuming all the extra stuff about God and Christianity? It is true that we will end up assuming something without warrant, but that’s going to happen any way you cut it. Only with Christianity the problem is worsened since you end up just assuming extra stuff on top of what you really do need to assume (i.e., induction).

    1. Thanks for chiming in, Ben.

      “…why not simply assume that induction works…?”

      Firstly, it’s not a question of whether we will assume induction. We all must do so, just because we are human. We must do so in order to be having this discussion. I think you’re aware of that already. (BTW your statement that “it is true that we will end up assuming something without warrant” might mean that you think that I admit this about myself; I don’t.)

      Secondly, it’s an issue of having universal belief in induction, and then enquiring what worldview can make sense of our belief in induction. Why believe in any universal just because of some particulars? Why believe the future will be like the past? (Or why assume that events have causes?) If one be an empiricist like Hume or an evolutionistic believer in a chance universe, there’s no reason to believe in induction. There’s no connection between facts. Your post seems to acknowledge that.

      The relationship between induction and Christianity is not conjunction, it’s presupposition. To believe in induction (which we do), we must as a condition believe in a Superintendent of the universe whose plan is such that the future IS like the past. (There are other reasons why this God must be the infinite, personal, all-knowing, all-controlling, self-attesting, self-revelatory God of Christianity.)

      You may object that you don’t believe in this God, and yet you believe in Induction. But Christianity can account for this too. The truth of the matter is that you really do believe in this God, but “suppress the truth.” Romans 1.18.

      Again, thanks for your thoughtful input.

  5. Charles,

    Yes, I agree that, at least for the most part, we are stuck using induction, and hence committed to believing that induction works. What I’m trying to get at is this: How is it any better to believe that induction works AND that God exists and wants induction to work? If we don’t have warrant for the first belief, how does it help to stack more beliefs on top of it?

    To put it another way, let me list some of our assumptions/presuppositions (obviously, these lists are not complete):

    Some of my assumptions/presuppositions:
    1. Induction works.

    Some of your assumptions/presuppositions:
    1. Induction works.
    2. God exists.
    3. God wants (or plans for, or causes, etc.) induction to work.

    What sort of warrant do you have in mind here, that your assumptions should be warranted and mine not? In other words, why do you think it helps to assume a bunch of extra stuff in addition to our assumption that induction works?

    1. Ben, I’m saying that you also have all three assumptions/presuppositions, (and more). You know God, but have suppressed the truth. Ro 1.18.

      My belief in induction is warranted because of my belief in the infinite, personal, all-knowing, all-powerful, all-controlling, self-attesting, self-revelatory God, without Whom the Problem of Induction and many other problems are insurmountable. Because you also believe in this God (even though you deny it), you have warranted true belief (knowledge) in many cases. However, on your espoused presuppositions, there’s no reason to believe the things you do. In the case of induction, your belief is arbitrary. BTW what are your presuppositions, Ben?

      1. Charles,

        Thanks for the response, but I don’t see how you really answered my question, so permit me to rephrase it. Let W denote the proposition that induction works, or tends to work. I’m asking, what reason have you for thinking your belief in W is warranted? You wrote, perhaps in answer:

        “My belief in induction is warranted because of my belief in the infinite, personal, all-knowing, all-powerful, all-controlling, self-attesting, self-revelatory God, without Whom the Problem of Induction and many other problems are insurmountable.”

        So you think your belief in W is warranted because you believe the Christian God exists, whereas if the Christian God did not exist then the problem of induction would be insurmountable, i.e. belief in W would not be warranted. But it does not follow from these two premises that therefore your belief in W is warranted.

        In other words, you appear to be arguing as follows:

        (1) Charles believes the Christian God exists.

        (2) If the Christian God did not exist then belief in W would not be warranted.

        (3) Therefore Charles’ belief in W is warranted.

        I’m sure I don’t have to tell you that such reasoning is invalid.

        Also, you ask: “BTW what are your presuppositions, Ben?”

        By “presuppositions,” do you mean beliefs I take for granted without warrant? I don’t know. I imagine I have quite a few such beliefs, W among them. I also believe without warrant in the existence of other minds, apart from my own. Those are the only two unwarranted beliefs I have positively identified. I’m sure there are others, but it’s no small task to unearth them.

      2. Ben, thanks again for writing.

        What I am saying in the sentence you quoted is

        “If Charles’ belief in the Christian God be warranted, then his belief in W is warranted.

        AND

        If one didn’t believe in the Christian God, then his belief in W is not warranted.”

        But now you are using induction even as your warrant for it is being questioned. With what materials are you working, if not those of the Christian worldview?
        In other words, what is your worldview? Macro-evolutionism? Deism? Buddhism?

      3. Charles,

        Thanks for the clarification. You wrote:

        “If Charles’ belief in the Christian God be warranted, then his belief in W is warranted.”

        This might be true if you bundle up induction with the Christian God. For instance you could say that the Christian God wants induction to work, and that the Christian God always gets what it wants (from which W will follow). And I suppose you are free to do that if you like.

        Please note that if you want to conclude further that belief in W is warranted, it remains to show that belief in the Christian God is warranted.

        You continue: “But now you are using induction even as your warrant for it is being questioned. With what materials are you working, if not those of the Christian worldview?
        In other words, what is your worldview? Macro-evolutionism? Deism? Buddhism?”

        I don’t believe in God. In particular, I am an agnostic, but for the most part I operate under the assumption that God does not exist.

        I do accept common descent, yes.

        And of course, I use induction. I don’t claim warrant for my belief that induction works, but neither do I have any reason to stop using induction. I am quite satisfied with it, and will keep on using it as long as it continues to work. And if ever it stops working, well, I may keep using it anyway. After all, what else is there to do?

      4. “I don’t claim warrant for my belief that induction works, but neither do I have any reason to stop using induction. I am quite satisfied with it, and will keep on using it as long as it continues to work. And if ever it stops working, well, I may keep using it anyway. After all, what else is there to do?”

        Exactly. You don’t have a reason for doing anything, or a reason not to do anything.

    1. You’re welcome, RubeRad.

      Yes, I had seen those resources, but forgotten about all but the one in *Foundations of Christian Scholarship*; thanks.

      Sorry, I will get to your other post when I can; until now, I haven’t even had time to read it.

      CJ

  6. I’m a Christian — a Presbyterian like yerself even, but I’m with Mr. ‘physics’ here; I don’t see how math is futile without Christianity. Does it not still balance the checkbook of the infidel, and build the bridges that don’t collapse, regardless of the faith of the civil engineer? To quote Calvin,

    to perceive more clearly how far the mind can proceed in any matter according to the degree of its ability, we must here set forth a distinction: that there is one kind of understanding of earthly things; another of heavenly. I call “earthly things” those which do not pertain to God or his Kingdom, to true justice, or to the blessedness of the future life; but which have their significance and relationship with regard to the present life and are, in a sense, confined within its bounds. I call “heavenly things” the pure knowledge of God, the nature of true righteousness, and the mysteries of the Heavenly Kingdom. The first class includes government, household management, all mechanical skills, and the liberal arts. In the second are the knowledge of God and of his will, and the rule by which we conform our lives to it.

    …What then? Shall we deny that the truth shone upon the ancient jurists who established civic order and discipline with such great equity? Shall we say that the philosophers were blind in their fine observation and artful description of nature? Shall we say that those men were devoid of understanding who conceived the art of disputation and taught us to speak reasonably? Shall we say that they are insane who developed medicine, devoting their labor to our benefit? What shall we say of the mathematical sciences? Shall we consider them the ravings of madmen? No, we cannot read the writings of the ancients on these subjects without great admiration. We marvel at them because we are compelled to recognize how preeminent they are.

    The “knowledge” that begins in the fear of God is the second, heavenly kind of understanding, but math belongs within the realm of “earthly things”.

    I’ve never gotten this need to warrant Induction; if you really feel that strongly about it, it seems to me you would also fall prey to Roman arguments about apostolic succession and a need for infallible papal authority. To both of those issues, I feel the same kind of “so what?”

    And actually, it seems to make more sense to me to assume Induction than otherwise. It makes more sense that stuff would keep working the way it always has, than that it would change. Change would require an external agent, which atheists don’t want anyways. The problem then becomes however (as Christians well know), how do we then get something from nothing (big bang), or life from nonlife, if there is no external agent of change (God) causing these things to happen? (Here are some fantastic quotes from Chesterton on that subject; “broken trail of stones and bones” — that man knew how to turn a phrase!)

    1. Thanks for writing, RubeRad.

      “Does it not still balance the checkbook of the infidel, and build the bridges that don’t collapse, regardless of the faith of the civil engineer?”
      Absolutely, math done by non-Christians accomplishes many things successfully. It is because of the unacknowledged assumption of God’s existence. As I wrote to “physics”, “every mathematical belief ever expressed has assumed the existence of the Christian God. All men know God (Romans 1.21), but some ‘by their unrighteousness have suppressed the truth.’” (v. 18.)

      “The “knowledge” that begins in the fear of God is the second, heavenly kind of understanding, but math belongs within the realm of “earthly things”.”
      It is you, my brother, not the Scripture I cited, who draw that distinction. The burden of proof is on you to show that it was intended.

      “I’ve never gotten this need to warrant Induction.”
      Supplying warrant for central beliefs (if one be able) is appropriate in philosophy and apologetics.

      “If you really feel that strongly about it, it seems to me you would also fall prey to Roman arguments about apostolic succession and a need for infallible papal authority.”
      No, the God of the Scriptures reveals his Lordship over Induction and the principles of the Protestant Reformation.

      “And actually, it seems to make more sense to me to assume Induction than otherwise. It makes more sense that stuff would keep working the way it always has, than that it would change.”
      Are you saying that it makes sense to believe that the future will be like the past, because, in the past, the future proved to be like the past?

      Thanks again,
      CJ

      1. It is you, my brother, not the Scripture I cited, who draw that distinction

        It is Calvin who I cited, that drew that distinction. Sorry it was not very clear, what was quote and what was me, this blog theme you have chosen doesn’t seem to do well with the ‘blockquote’ tag.

        Supplying warrant for central beliefs (if one be able) is appropriate in philosophy and apologetics.

        Probably why I’m not a philsopher or apologist. But is “lack of warrant” the same as “futile”? Every definition of futile I can find online centers on the concept of “ineffective”

        Are you saying that it makes sense to believe that the future will be like the past, because, in the past, the future proved to be like the past?

        No, I’m saying that, just as with Newton’s (1st?) law, acceleration requires an external force, and motion requires a mover, change requires a changer.

        Granted that atheists have no cosmology (and that they consider it equivalent to theists having no explanation for “what created God”) — within an atheist worldview, given that this material universe full of energy and matter with directed momentum does indeed exist, and (wrongly) assuming no personal God to interfere, it makes sense that impersonal matter and energy will keep doing what it has always been doing, since (by assumption) there is nothing that would cause it to do otherwise. It seems to me to be an internally consistent worldview for the most part, although it cannot account for existence (but I don’t think it really cares to), nor can it account for miracles, most importantly the historically attested virgin birth and resurrection.

        For your enjoyment, two webcomics published just today, that touch somewhat on the subject of presuppositions; I hope you enjoy them as much as I did!

        http://xkcd.com/1163/
        http://wondermark.com/907/

      2. “It is Calvin who I cited, that drew that distinction. Sorry it was not very clear, what was quote and what was me, this blog theme you have chosen doesn’t seem to do well with the ‘blockquote’ tag.”
        Looking for another theme…
        Whatever non-Biblical writer it was who drew that distinction, the burden of proof is on him to show that it was intended by God. In Christ are “hidden all the treasures of wisdom and knowledge” (Col. 2:3).

        “…is ‘lack of warrant’ the same as ‘futile’? Every definition of futile I can find online centers on the concept of ‘ineffective.’”
        Argument without warrant is ineffective because it is argument without giving reasons why one should be considered right and his opponent wrong. As you know, in philosophy and apologetics this is called “arbitrariness.” One who is arbitrary is missing the point of the exercise, or worse, pretending that it’s not the point.

        “…within an atheist worldview, given that this material universe full of energy and matter with directed momentum does indeed exist,…”
        “Directed?” It is arbitrary to treat all this as given. “What accounts for all this?” asks the theist. It is now a philosophical issue, requiring argument. The “given” is destroyed.

        “…and (wrongly) assuming no personal God to interfere, it makes sense that impersonal matter and energy will keep doing what it has always been doing, since (by assumption) there is nothing that would cause it to do otherwise.”
        No it doesn’t make sense. In a Godless, chance universe, there is no reason why matter and energy will do anything at all. There’s no reason why hockey pucks wouldn’t go up or at any other angle when dropped. In their worldview, there is nothing that would cause matter to do as it does, OR otherwise. There’s no reason why the future should be like the past. To believe and act as if it should is arbitrary. As I just wrote to Ben above, such a person doesn’t have a reason for doing anything, or a reason not to do anything.

        “It seems to me to be an internally consistent worldview for the most part, although it cannot account for existence (but I don’t think it really cares to).”
        Yes, atheists (in general) don’t want to account for existence, induction, or for the most part anything nonphysical as such. But “atheism” itself is nonphysical. How does the notion of “atheism” emerge from matter + chance? The same can be said of “consciousness”, “macro-evolution”, “induction”, and “consistency.”
        It is not a consistent worldview. Their use of laws of morality, laws of logic, and laws of science is inconsistent with their denial of God. What is “denial”? What are laws, for an atheist? How do they emerge from matter + chance?

        Thanks for the entertaining comics!

      3. Whatever non-Biblical writer it was who drew that distinction, the burden of proof is on him…

        Well all I can say to that is, go read more Calvin.

        “Directed?” It is arbitrary to treat all this as given. “What accounts for all this?” asks the theist. It is now a philosophical issue, requiring argument. The “given” is destroyed.

        I’m not sure if you misinterpreted me there; I didn’t mean “purposed”, I just meant particles of matter moving in certain directions with certain velocities. And I don’t think merely asking “what accounts?” makes matter and energy not exist. In fact, asking the question “What accounts for all this?” indeed presupposes (“given”) “all this”.

        In a Godless, chance universe, there is no reason why matter and energy will do anything at all.

        I think it is arbitrary that you link “Godless”, therefore “chance”. Why not “Godless”, therefore “mechanical, impersonal.” That still leaves you with the arguments below, such as ‘“atheism” itself is nonphysical. How does the notion of “atheism” emerge from matter + chance? The same can be said of “consciousness”, “macro-evolution”, “induction”, and “consistency.”’ The atheist still has no path from impersonal matter to person; from meaningless particles banging into each other, to meaning.

        What are laws, for an atheist? How do they emerge from matter + chance?

        See, I don’t think an atheist would say that laws “emerge”, which would imply that at some point, they didn’t exist. I think actually physical, mathematical, and logical Laws are like God to the atheist. They just are, they always have been, and always will be. There is no accounting for them, and since this god (these gods?) are utterly impersonal, they can’t account for themselves as our true God does; nor are they self-determining as our God is, because that involves Will.

        It is not a consistent worldview. Their use of laws of morality, laws of logic, and laws of science is inconsistent with their denial of God.
        I think it can be consistent. It has to be small, because it has to honestly admit it cannot account for Laws, matter, energy. It would not attempt to account for person, mind, consciousness, emotion, etc., because it would be forced to view them as illusory, just the complex interaction of particles. It would have to deny that any morality is absolute, but is all merely convention, in the end imposed and enforced by power (might makes right (but see here for another twist on that). The fact that he appears to affirm a moral code, to ascribe dignity to fellow men, he would have to write of as ultimately meaningless, a fiction shared amongst ourselves that makes our particles feel good, helps us get along and survive. If an atheist were to be that honest, I don’t see any self-contradiction within that worldview. But like I said, it’s not very big. It’s not a view of the entire world, really it’s just a view of the material world. Which is not all that surprising for a materialist.

      4. RubeRad, why would I “go read more Calvin”, when you’re the one using him to try to make your case?…
        Of course I agree that a “material universe full of energy and matter with directed momentum” exists…
        “Godless universe, therefore chance universe” holds unless one reach for materialistic determinism, which is a non-starter (why argue then?)…
        An atheist can’t arbitrarily have the physical universe and non-physical laws as equally ultimate. One must emerge from the other. Generally for the atheist, laws emerge from matter in some mysterious way…
        RubeRad, do you believe that God has “made foolish the wisdom of this world” (1 Cor 1.20)?

      5. why would I “go read more Calvin”

        You said the burden of proof is on Calvin. Calvin is not going to return from the grave to argue with you, so if you’re going to claim that Calvin had no biblical basis for his statement, the burden falls on you to read Calvin rather than to dismiss him; especially as you are Reformed, and your entire theology is rooted in (presupposes?) his exegeses (exegesises?).

        do you believe that God has “made foolish the wisdom of this world” (1 Cor 1.20)?

        Yes, as worldly attempts to be “saved” (v18) and “know God” (v22) through man-devised wisdom are failures (“futile” even!), but the folly of what Paul preaches has trumped it. And what Paul preaches is nothing but Christ, and him crucified.

        So now that we’re done discussing soteriology and homiletics, how about we return to the topic at hand, mathematics? “What shall we say of the mathematical sciences? Shall we consider them the ravings of madmen?”

        “Godless universe, therefore chance universe” holds unless one reach for materialistic determinism, which is a non-starter (why argue then?)…

        I agree, materialistic determinism plus argument, will, person, etc, is self-contradictory. But it’s a lot more likely you’ll get an atheist to confront his self-contradiction with this route, than with
        presuppositional arguments. I’ve never seen them have any effect, anyways. Is it supposed to be presuppositional apologetics, or presuppositional antagonistics?

      6. RubeRad,

        Calvin entered the discussion *as channeled by you*. The burden of proof is on Calvin as channeled by you.

        Calvin is a great man and a hero of mine, but apologetics is one area in which great advances have been made since Calvin’s time.

        As for 1 Cor 1.20, the even-more-immediate context is about “debate” with “the wise” and “the scribe.” This is not in contrast to the context you referenced. The presuppositional challenge is the challenge of the gospel.

        As for the effects of presuppositional apologetics, one should be, according to Calvin (as channeled by Sproul, Sr.), “to shut the mouths of the obstreperous.”

        Chuck

  7. Charles,

    You wrote: “Exactly. You don’t have a reason for doing anything, or a reason not to do anything.”

    Whoa, how did you get that idea? All I said is that we have no warrant for W, and no reason to stop using induction. But given W (as we all believe), we have plenty of reason to do this or that.

    Maybe you want to argue that in order for us to reason from W, we must first have warrant for W. But since none of us have warrant for W, it’s hard to see how that will be helpful to you.

  8. Ben, I got that idea from your admission that “I don’t claim warrant for my belief that induction works, but neither do I have any reason to stop using induction.”

    “Given W?” W isn’t given; it’s what’s in dispute: What worldview can provide warrant for it?

    Contrary to your last sentence, I do have warrant for W. Christianity (warranted because its infinite, personal, all-knowing, all-controlling, self-attesting, self-revelatory God makes sense of everything: ethics, metaphysics, epistemology, etc. etc. etc.) entails induction.

  9. Charles,

    I am quite sure you will not want to dispute W. Instead, you want to dispute whether you have warrant for W.

    If your belief in Christianity is warranted, say you, then your belief in W is warranted too. So long as you bundle up induction or something like it with Christianity, I’m fine with that. But as I mentioned before, it remains to show that Christianity is warranted. This you have attempted to do.

    In arguing that Christianity is warranted, you claim:

    “…its infinite, personal, all-knowing, all-controlling, self-attesting, self-revelatory God makes sense of everything: ethics, metaphysics, epistemology, etc. etc. etc.”

    But there are two great problems with this argument. First and foremost, what you have claimed does not actually constitute warrant. So what if you think Christianity makes sense of these things? Maybe the truth is unknown to us, still waiting to be discovered. Or maybe our minds are too limited to make sense of everything so that we can never discover the whole truth no matter how hard we look. If you manage to lay out a view (Christianity) which explains or makes sense of the world, that hardly gives you a reason to think your view is true.

    Second, it’s incredible to me that anyone would find Christianity a satisfactory stepping stone for making sense of ethics or epistemology, or even so-called metaphysics. That is, I deny that Christianity actually does the explanatory work you think it does. For instance, I’ve never heard a compelling response to Euthyphro, despite the fact that theologians have had literally thousands of years to produce one. And of course you already know my views on Christian epistemology. As for metaphysics, well, Berkeley came very close but he never needed God except perhaps for inspiration.

    But the second problem is a huge can of worms, I grant. I don’t expect you to deal with it here on this blog. Instead, let’s focus on the first problem, and ignore the second by supposing for the sake of argument that Christianity really does make sense of things, as you dubiously claim. Okay. Now, how does that give you warrant for Christian belief?

    1. BW: “If you manage to lay out a view (Christianity) which explains or makes sense of the world, that hardly gives you a reason to think your view is true.”

      That statement presupposes the falsity of Christianity. Of course, the truth or falsity of Christianity is the matter in question. I presuppose the truth of Christianity: God speaks, I believe. His Word makes sense of everything, including induction. You reject God’s Word, and are therefore responsible to construct a coherent worldview on your own. The induction piece had to be added arbitrarily.

      Euthyphro: Just because you haven’t heard it doesn’t mean that theologians haven’t solved the Euthyphro dilemma. A thing is good if it corresponds to God’s good character. There is no principle above God, and yet God can’t arbitrarily change what it is to be good. He can’t change His own character; as the Bible says, “He cannot deny Himself.”

      The Christian metaphysic explains what is, consistently and with the necessary richness. It avoids the problems associated with saying that everything that is ultimately emerges from what is physical (i.e. is physical or supervenes on what is physical) e.g. laws of logic, language, “physicalism” itself, “materialism”, “naturalism”, consciousness.

      1. No, the good is what it is because it conforms to God’s goodness, and no, God is not arbitrary, and no, God can’t change; He is not going to say that [pick your favorite evil behavior] is good. No, there is no princple of good higher than God.
        Why is his character this way in the first place? We don’t have to know that for the Euthyphro “dilemma” not to be a dilemma for us. God does not reveal everything. Still, there is an answer, a reason, so our faith is rational. It would be a dilemma if God were subject to a principle of the good higher than Himself, or if we wanted to say that God can do absolutely everything, like Allah. The Euthyphro dilemma is aimed at those who want to say that God can do absolutely everything. That is not the Christian God. The Christian God cannot lie, cannot sin, etc. The Christian God is a covenant-keeping God who has revealed Himself.
        But now let me ask you, Tony, what is “good”, and in virtue of what is good good?

  10. Thank you for the response, Charles. Let’s take a look back at one line of argument in particular. You tried to sketch a case for Christianity being warranted, and I objected that even if your claims were true (and they aren’t), they don’t constitute warrant for Christianity. You then counter-objected by saying I was somehow presupposing the falsity of Christianity. Recall:

    CHARLES: “Christianity (warranted because is infinite, personal, all-knowing, all-controlling, self-attesting, self-revelatory God makes sense of everything: ethics, metaphysics, epistemology, etc. etc. etc.)…”

    BEN: “…what you have claimed does not actually constitute warrant. … If you manage to lay out a view (Christianity) which explains or makes sense of the world, that hardly gives you a reason to think your view is true.”

    CHARLES: “That statement presupposes the falsity of Christianity.”

    How so? Unless you want to try turning to externalism, you will surely not disagree that justification is required for warrant. And justification must take the form of some kind of strong inductive or deductive case made from an agreeably true basis. But you have presented no such argument for Christianity. Even if your sweeping claims about God explaining ethics, metaphysics and epistemology were true—and they aren’t—but even if they were, that still would not warrant believing that God exists, because it doesn’t show us how to infer God’s existence deductively or inductively from what we already agree to be true.

    It seems to me that the only thing you can do is characterize warrant to include such externalist concerns as, say, Plantinga’s infamous “proper function.” But then the case for Christianity being Plantinga-warranted depends on Christianity being true. Clearly, though, that’s not the sort of “warrant” most of us care about. It’s not even appropriate, I shouldn’t say, to call it warrant. That’s why I qualify it by calling it Plantinga-warrant.

    So let me ask you straight out, do you think your belief in Christianity is justified in the sense described above? That is, do you think you have a strong inductive or valid deductive argument for Christianity from agreeably true premises? If so, I would be very curious to hear that argument so that we can discuss it. If not, then I would like you to be clear about the fact that you have no such argument.

    In any case, you can insist on calling your claims a kind of “warrant” if you like. But let’s just remember what your claims actually are. You’re not producing any justification here, maybe because you don’t care about justification. Instead, you think Christianity explains or “makes sense” of ethics, metaphysics and epistemology, among other things. Aside from these claims being false (more on that later), they simply are not convincing. So what if Christianity explains ethics? Why should we think this Christian explanation is the true explanation?

    Perhaps you could expand your claims to construct an actual argument. For instance, you might also claim that

    (*) Nothing else explains ethics/metaphysics/epistemology; and

    (**) These things really do have explanations.

    Then it would follow that Christianity is true. But unfortunately, each of these additional premises is just as dubious as your starting premise that Christianity explains ethics, metaphysics and epistemology.

    Anyway, let’s look at a few more of your comments.

    CHARLES: “I presuppose the truth of Christianity: God speaks, I believe.”

    That’s fine as far as it goes, but I’ve been asking about your supposed warrant for Christianity. If you just presuppose that Christianity is true, that’s all well and good, but it doesn’t get you warrant. And it certainly doesn’t get you justification.

    CHARLES: “His Word makes sense of everything, including induction.”

    How so? All you can do is bundle up induction with your religious beliefs and call them, collectively, “Christianity.” But this is just relabeling. You aren’t actually resolving any epistemic problems by doing that. In the end, you still have to assume that induction works. Only on your view, you have a bunch of additional assumptions too! Recall from before:

    BEN: “Some of my assumptions/presuppositions:
    1. Induction works.

    Some of your assumptions/presuppositions:
    1. Induction works.
    2. God exists.
    3. God wants (or plans for, or causes, etc.) induction to work.”

    How is it helpful to tack on that extra stuff?

    CHARLES: “The Christian metaphysic explains what is, consistently and with the necessary richness. It avoids the problems associated with saying that everything that is ultimately emerges from what is physical…”

    Well I’m not a physicalist though (remember I said that Berkeley had it right?). I agree that physicalism is false, but Christianity is hardly the only alternative.

    I should warn you though, it’s lucky that I just so happen to agree that physicalism is false, because what you have outlined above by no means constitutes an argument against physicalism. In particular, physicalists are by no means committed to explaining how consciousness comes about from physical systems. As an analogy, I don’t have to understand the law of gravity to know that a stone will fall if I drop it; if I lived before Newton, I would not be committed to explaining why the stone falls just by believing it does. Similarly, the physicalist is committed to believing that consciousness (if it exists) is physical, but he is not committed to discovering exactly how one reduces to the other.

    Lucky for us, though, we agree on the what, if not the why. Physicalism is false. Moving on.

    You claim that Christianity explains what exists. But this is not so. It does not explain why God himself exists. And it only explains in a very loose sense why particular objects in our universe exist. For example, why does Pluto exist? I suppose you could say, “because God wants Pluto to exist,” but that doesn’t really get at the heart of our curiosity. Why does God want Pluto to exist? Christianity provides no answer.

    Anyway, I’m enjoying our conversation despite the fact that it takes me a long time to type up each response. I’m not sure if you noticed, but I too am a mathematician, and I find it interesting to talk to a fellow mathematician about these topics. If you ever feel like voice chatting via Skype, feel free to hit me up. If you email me (hurtstotalktoyou [at] yahoo [doot] com) I will send you my skype name and we can set something up. I’m also available on Paltalk under the name “hatsoff”. If you want, we could also do something a bit more public. I co-host an increasingly-intermittent podcast called Goodness Over God. Whether private or public, I would enjoy continuing our conversation in voice, where it would probably go a lot faster!

    Or we could just stick to text. Your call.

    1. BW: CHARLES: “Christianity (warranted because is infinite, personal, all-knowing, all-controlling, self-attesting, self-revelatory God makes sense of everything: ethics, metaphysics, epistemology, etc. etc. etc.)…”
      BEN: “…what you have claimed does not actually constitute warrant. … If you manage to lay out a view (Christianity) which explains or makes sense of the world, that hardly gives you a reason to think your view is true.”
      CHARLES: “That statement presupposes the falsity of Christianity.”
      How so? Unless you want to try turning to externalism, you will surely not disagree that justification is required for warrant. And justification must take the form of some kind of strong inductive or deductive case made from an agreeably true basis. But you have presented no such argument for Christianity. Even if your sweeping claims about God explaining ethics, metaphysics and epistemology were true—and they aren’t—but even if they were, that still would not warrant believing that God exists, because it doesn’t show us how to infer God’s existence deductively or inductively from what we already agree to be true.
      It seems to me that the only thing you can do

      CJ: Not the only thing.

      BW: is characterize warrant to include such externalist concerns as, say, Plantinga’s infamous “proper function.” But then the case for Christianity being Plantinga-warranted depends on Christianity being true.

      CJ: Of course. And the case for its not being warranted depends on its being false. But if you go there (and you have), you end up losing warrant for induction therefore language therefore arguing against Christianity’s warrant and truth.

      BW: Clearly, though, that’s not the sort of “warrant” most of us care about.

      CJ: “Most of us?”

      BW: It’s not even appropriate, I shouldn’t say, to call it warrant.

      CJ: Did Plantinga make a mistake somewhere in his analysis of the old “justification”?

      BW: That’s why I qualify it by calling it Plantinga-warrant.
      So let me ask you straight out, do you think your belief in Christianity is justified in the sense described above? That is, do you think you have a strong inductive or valid deductive argument for Christianity from agreeably true premises?

      CJ: “Agreeably”? No. What agreement can there be between those whose God conditions everything else they believe, and those whose denial of God conditions everything else they believe?

      BW: If so, I would be very curious to hear that argument so that we can discuss it. If not, then I would like you to be clear about the fact that you have no such argument.
      In any case, you can insist on calling your claims a kind of “warrant” if you like.

      CJ: I do.

      BW: But let’s just remember what your claims actually are. You’re not producing any justification here,

      CJ: Standing within the Christian worldview, there is every kind of justification you could want: coherence, consistency, explanation of everything, hard evidences, “the starry heavens above and the moral law within.” Standing in a worldview that presupposes that Christianity is false (which is every other worldview), those things are unconvincing as evidence or justification.

      BW: maybe because you don’t care about justification. Instead, you think Christianity explains or “makes sense” of ethics, metaphysics and epistemology, among other things. Aside from these claims being false (more on that later), they simply are not convincing. So what if Christianity explains ethics? Why should we think this Christian explanation is the true explanation?
      Perhaps you could expand your claims to construct an actual argument. For instance, you might also claim that
      (*) Nothing else explains ethics/metaphysics/epistemology; and
      (**) These things really do have explanations.

      CJ: OK. That’s my argument.

      BW: Then it would follow that Christianity is true. But unfortunately, each of these additional premises is just as dubious as your starting premise that Christianity explains ethics, metaphysics and epistemology.

      CJ: (Leaving alone the fact that we assume ** in order to have this conversation in the way that we do,…) Of course you find all these claims dubious. Plantinga: Christianity, if false, is probably not warranted. And you presuppose that Christianity is false.

      BW: Anyway, let’s look at a few more of your comments.
      CHARLES: “I presuppose the truth of Christianity: God speaks, I believe.”
      That’s fine as far as it goes, but I’ve been asking about your supposed warrant for Christianity. If you just presuppose that Christianity is true, that’s all well and good, but it doesn’t get you warrant. And it certainly doesn’t get you justification.

      CJ: Christianity, if true, is warranted. And didn’t you say that justification is required for warrant?

      BW: CHARLES: “His Word makes sense of everything, including induction.”
      How so?

      CJ: Perhaps most pertinently, the Noahic covenant Genesis 8-9. In it, the God of preservation promises among other things that we can continue to live in this world in a way like we have in the past. And there are many other passages that could be cited.

      BW: All you can do is bundle up induction with your religious beliefs and call them, collectively, “Christianity.”

      CJ: No.

      BW: But this is just relabeling…
      CHARLES: “The Christian metaphysic explains what is, consistently and with the necessary richness. It avoids the problems associated with saying that everything that is ultimately emerges from what is physical…”
      Well I’m not a physicalist though (remember I said that Berkeley had it right?).

      CJ: Are you an empiricist and an idealist?

      BW: I agree that physicalism is false, but Christianity is hardly the only alternative.
      I should warn you though, it’s lucky that I just so happen to agree that physicalism is false, because what you have outlined above by no means constitutes an argument against physicalism. In particular, physicalists are by no means committed to explaining how consciousness comes about from physical systems. As an analogy, I don’t have to understand the law of gravity to know that a stone will fall if I drop it; if I lived before Newton, I would not be committed to explaining why the stone falls just by believing it does. Similarly, the physicalist is committed to believing that consciousness (if it exists) is physical, but he is not committed to discovering exactly how one reduces to the other.

      CJ: Metaphysical physicalists as philosophers and defenders of their position are committed to explaining the emergence of consciousness.

      BW: Lucky for us, though, we agree on the what, if not the why. Physicalism is false. Moving on.
      You claim that Christianity explains what exists. But this is not so. It does not explain why God himself exists.

      CJ: On the Christian position, explaining why God exists would be putting explanation and ourselves above God. God knows why He exists. God reveals what we need to know. He doesn’t reveal everything.

      BW: And it only explains in a very loose sense why particular objects in our universe exist. For example, why does Pluto exist? I suppose you could say, “because God wants Pluto to exist,”

      CJ: …and that His glory is revealed in Pluto…

      BW: but that doesn’t really get at the heart of our curiosity. Why does God want Pluto to exist? Christianity provides no answer.

      CJ: God may not reveal what we don’t need to know. What do we need to know? The answer to that will depend on the worldview in which you’re standing. In the Christian worldview, ““The secret things belong to the Lord our God, but those things which are revealed belong to us and to our children forever, that we may do all the words of this law.” Dt 29.29

      BW: Anyway, I’m enjoying our conversation despite the fact that it takes me a long time to type up each response. I’m not sure if you noticed, but I too am a mathematician, and I find it interesting to talk to a fellow mathematician about these topics. If you ever feel like voice chatting via Skype, feel free to hit me up. If you email me (hurtstotalktoyou [at] yahoo [doot] com) I will send you my skype name and we can set something up. I’m also available on Paltalk under the name “hatsoff”. If you want, we could also do something a bit more public. I co-host an increasingly-intermittent podcast called Goodness Over God. Whether private or public, I would enjoy continuing our conversation in voice, where it would probably go a lot faster!
      Or we could just stick to text. Your call.

      CJ: I don’t skype or paltalk; maybe the podcast. Time is a problem…thanks.

      1. The thing is, from a Christian standpoint, Christianity is an explanatory and consistent worldview, but other worldviews aren’t.

        From the standpoint of a worldview which holds to the falsity of Christianity, no worldview is explanatory or consistent.

  11. Charles,

    I am defining justification to be, roughly, an available inference from agreeably true premises which require only valid deductive and/or cogent inductive reasoning. When I speak of justification, that is what I have in mind.

    What do I mean by “agreeably true”? Well, I want to emphasize the fact that justification is context-dependent. But if you object to that part of my definition, then you are free to suggest an alternative. What sort of premises do we need in order for our inferences from them to be justified?

    It seems to me that you cannot infer the existence of the Christian God from premises which are not highly controversial. For instance, a self-styled “professor” of theology over at AOMin once argued, quite seriously, that

    The existence of creation presupposes that God (the Creator) exists. Creation exists. Therefore, God exists.

    This argument is surely valid, yet who would affirm either premise who was not already convinced that God exists? Indeed there must be limiting criteria for what sort of premises we permit to contribute to justification. If we restrict our attention to agreeably true premises, that seems to me to solve the problem. But as I said, you are free to propose different criteria if you want. But we will need something. It won’t do to allow any ol’ set of premises at all.

    In any case, you seem to acknowledge that you have not—perhaps cannot—construct an argument from agreeably true premises which moves via valid deductive and cogent inductive reasoning to the conclusion that the Christian God exists. The premises you have appealed to so far seem to me highly controversial—e.g. (*) and (**) from above.

    This is a problem for you, I think. At best it means that you cannot offer anyone a reason to convert unless they already agree with certain highly controversial premises, like (*) and (**). It also means that your view is nonrational in the sense of not being inferred from uncontroversial premises. It is an open question whether your view is irrational (as opposed to merely nonrational).

    Now let me address some of your comments more directly.

    CJ: “And the case for its [Christianity] not being warranted depends on its being false.”

    This is only true for Plantinga-warrant. But consider a different kind of warrant. Suppose we say that a belief is warranted only if it is justified in the sense described above. Call this J-warrant. Well, clearly you do not have J-warrant for Christianity, regardless of whether or not Christianity happens to be true.

    So the question is, what type of warrant do you want? Do you just want Plantinga-warrant? Then as long as Christianity is true, you have it. But if you want J-warrant then you’re plum out of luck.

    CJ: “Did Plantinga make a mistake somewhere in his analysis of the old ‘justification’?”

    I don’t know how Plantinga defines justification, but certainly his “proper function” account of warrant does not require justification in the sense I have defined above.

    CJ: “Standing within the Christian worldview, there is every kind of justification you could want: coherence, consistency, explanation of everything, hard evidences, ‘the starry heavens above and the moral law within.’ Standing in a worldview that presupposes that Christianity is false (which is every other worldview), those things are unconvincing as evidence or justification.”

    I disagree that Christianity as you envision it is coherent. However let’s leave that aside for now. Suppose for the sake of argument that Christianity is indeed coherent, consistent, and offers the so-called explanations you claim it offers. Nevertheless, that is no reason to think your view is true. So what if your view happens to be consistent and coherent, and offer certain explanations for a variety of observations? Why think those explanations are true?

    On the other hand, you also claim to have evidence for Christianity. This might actually get you some justification—except you have not presented any of this evidence, and you seem to admit that even if you did, non-Christians would not find it convincing. But it’s hard to see how anything could be called “evidence” which only convinces those who are already convinced.

    CJ: “Perhaps most pertinently, the Noahic covenant Genesis 8-9. In it, the God of preservation promises among other things that we can continue to live in this world in a way like we have in the past. And there are many other passages that could be cited.”

    The above quote is your response to my question of how you think Christianity “makes sense” of induction. But I just don’t see how you think these beliefs are supposed to help you. We both believe that induction holds. You have the additional beliefs that God exists, he promised induction will hold, and his promises always come true. How is this helpful at all?

    CJ: “Are you an empiricist and an idealist?”

    I am a Berkeleyan idealist. I’m not sure whether or not I qualify as an empiricist, though. Probably I am an empiricist, but it depends on what counts as sense experience. At the very least, I am quite sympathetic towards empiricism.

    CJ: “On the Christian position, explaining why God exists would be putting explanation and ourselves above God. God knows why He exists. God reveals what we need to know. He doesn’t reveal everything.”

    That’s fine as far as it goes, but it doesn’t change the fact that Christianity does not offer an explanation for everything that exists. So you are left with the claim that Christianity explains some but not all things that exist. And for those things, it only explains them in a very weak sense, along the lines of explaining the existence of Pluto by positing that God wants Pluto to exist and “that his glory is revealed in Pluto.” But why does God want Pluto to exist? How is his glory revealed in the existence of Pluto, whereas it would not be revealed in the nonexistence of Pluto? Christianity offers no answers to these questions.

    And that’s okay. A view of the world need not explain everything to be coherent or rational. It’s perfectly fine to say, for instance, that induction holds, period—i.e. without attempting to offer an explanation. And it’s not the least bit helpful to claim instead that induction holds AND that God exists AND that he wants or promises induction to hold AND that everything he wants or promises always comes true. That’s just adding a bunch of extra stuff on top of what we already assume.

    1.  Charles,
      BW: I am defining justification

      CJ: How did we shift from warrant to justification? Justification—even with true belief–isn’t sufficient for knowledge, anyway.

      BW: to be, roughly, an available inference from agreeably true premises which require only valid deductive and/or cogent inductive reasoning. When I speak of justification, that is what I have in mind.

      CJ: That “agreeably” in there: that’s unusual. Unnecessary, too, since we had been talking about warrant.

      BW: What do I mean by “agreeably true”? Well, I want to emphasize the fact that justification is context-dependent. But if you object to that part of my definition, then you are free to suggest an alternative. What sort of premises do we need in order for our inferences from them to be justified?

      CJ: One definition from the Cambridge Dictionary of Philosophy: “X is justified only if X has been or at least can be justified through adducing reasons.”

      BW: It seems to me that you cannot infer the existence of the Christian God from premises which are not highly controversial. For instance, a self-styled “professor” of theology over at AOMin once argued, quite seriously, that
      The existence of creation presupposes that God (the Creator) exists. Creation exists. Therefore, God exists.
      This argument is surely valid, yet who would affirm either premise who was not already convinced that God exists?

      CJ: Maybe no one. But their rejection could only be by those who hadn’t already rejected that the infinite, personal, all-knowing, all-powerful, all-conditioning, self-attesting, self-contained, self-revelatory Creator God exists.

      BW: Indeed there must be limiting criteria for what sort of premises we permit to contribute to justification.

      CJ: On how are those to be decided before deciding the issue of God’s existence? Can’t be done.

      BW: If we restrict our attention to agreeably true premises, that seems to me to solve the problem. But as I said, you are free to propose different criteria if you want. But we will need something. It won’t do to allow any ol’ set of premises at all.
      In any case, you seem to acknowledge that you have not—perhaps cannot—construct an argument from agreeably true premises which moves via valid deductive and cogent inductive reasoning to the conclusion that the Christian God exists.

      CJ: What’s this “…you seem to acknowledge that you have not—perhaps cannot—…”?! I said flat out, “’Agreeably’? *No.*”!

      BW: The premises you have appealed to so far seem to me highly controversial—e.g. (*) and (**) from above.

      CJ: Of course.

      BW: This is a problem for you, I think. At best it means that you cannot offer anyone a reason to convert unless they already agree with certain highly controversial premises, like (*) and (**).

      CJ: “Convert” was a well-chosen word. A total and complete conversion is necessary for one to have his soul and philosophy saved. 1 Cor 1.18-20

      BW: It also means that your view is nonrational in the sense of not being inferred from uncontroversial premises.

      CJ: There’s that “agreeably” sneaking in there again…On the contrary, any view not based on the infinite, personal, all-knowing, all-powerful, all-conditioning, self-attesting, self-contained, self-revelatory God, i.e., one that lacks any hope of an answer to the problem of induction, and therefore the problem of how we can expect to say anything at all and back it up, is nonrational. He is acting in a certain way against all reason to do so.
      So why are you still here arguing when you admit you have no foundation for induction? Your worldview is unsuccessful; what could be gained by trying to use a futile basis to do damage to another worldview?

      BW: It is an open question whether your view is irrational (as opposed to merely nonrational).

      CJ: If arguing on the foundation of the God I’ve described is nonrational or irrational, then “rational” has no meaning.

      BW: Now let me address some of your comments more directly. CJ: “And the case for its [Christianity] not being warranted depends on its being false.” This is only true for Plantinga-warrant. But consider a different kind of warrant. Suppose we say that a belief is warranted only if it is justified in the sense described above. Call this J-warrant. Well, clearly you do not have J-warrant for Christianity, regardless of whether or not Christianity happens to be true. So the question is, what type of warrant do you want? Do you just want Plantinga-warrant? Then as long as Christianity is true, you have it. But if you want J-warrant then you’re plum out of luck.

      CJ: Is “J-warrant” different than justification? “J-warrant”: “Justification-warrant.” A not-sufficient-for-knowledge kind of sufficiency for knowledge.

      BW: CJ: “Standing within the Christian worldview, there is every kind of justification you could want: coherence, consistency, explanation of everything, hard evidences, ‘the starry heavens above and the moral law within.’ Standing in a worldview that presupposes that Christianity is false (which is every other worldview), those things are unconvincing as evidence or justification.”

      I disagree that Christianity as you envision it is coherent.

      CJ: Of course you do. I just said you would. One’s presuppositions determine the way he interprets evidence.

      BW: However let’s leave that aside for now. Suppose for the sake of argument that Christianity is indeed coherent, consistent, and offers the so-called explanations you claim it offers. Nevertheless, that is no reason to think your view is true. So what if your view happens to be consistent and coherent, and offer certain explanations for a variety of observations? Why think those explanations are true?

      CJ: Didn’t you say that before?! Yes: BW: “If you manage to lay out a view (Christianity) which explains or makes sense of the world, that hardly gives you a reason to think your view is true.” CJ: That statement presupposes the falsity of Christianity…
      You have not shown any problem with my worldview, nor can you.
      .
      BW: On the other hand, you also claim to have evidence for Christianity. This might actually get you some justification—except you have not presented any of this evidence,

      CJ: What was it that I gave above? Do you want me to spell out the evidentialist argument for the resurrection?

      BW: …and you seem to admit that even if you did, non-Christians would not find it convincing.

      CJ: Might not, even though they should.

      BW: But it’s hard to see how anything could be called “evidence” which only convinces those who are already convinced….

      CJ: It’s hard to see how anything could count as “evidence” against Christianity, which would-be evidence only convinces those who are already convinced.

      BW: CJ: “Perhaps most pertinently, the Noahic covenant Genesis 8-9. In it, the God of preservation promises among other things that we can continue to live in this world in a way like we have in the past. And there are many other passages that could be cited.” The above quote is your response to my question of how you think Christianity “makes sense” of induction…

      CJ: God says to live as though he will continue to sustain the world, that the future will be like the past in the relevant way.

      BW: But I just don’t see how you think these beliefs are supposed to help you. We both believe that induction holds. You have the additional beliefs that God exists, he promised induction will hold, and his promises always come true. How is this helpful at all?

      CJ: Right. We both believe that induction holds. I have a worldview that makes sense of that belief. You don’t.

      CJ: “Are you an empiricist and an idealist?”
      I am a Berkeleyan idealist. I’m not sure whether or not I qualify as an empiricist, though. Probably I am an empiricist, but it depends on what counts as sense experience. At the very least, I am quite sympathetic towards empiricism.

      CJ: I understand the attraction of idealism.

      BW: CJ: “On the Christian position, explaining why God exists would be putting explanation and ourselves above God. God knows why He exists. God reveals what we need to know. He doesn’t reveal everything.” That’s fine as far as it goes, but it doesn’t change the fact that Christianity does not offer an explanation for everything that exists. So you are left with the claim that Christianity explains some but not all things that exist.

      CJ: Christianity explains all things that exist. They are what they are because of the plan of God with respect to them. Not all these plans are revealed. Christianity draws these limits.

      BW: And for those things, it only explains them in a very weak sense, along the lines of explaining the existence of Pluto by positing that God wants Pluto to exist and “that his glory is revealed in Pluto.” But why does God want Pluto to exist?

      CJ: Well, what is true about Pluto, known truths and unknown (by man) truths? Evidently, these things were part of the plan of God with respect to it.

      BW: How is his glory revealed in the existence of Pluto, whereas it would not be revealed in the nonexistence of Pluto? Christianity offers no answers to these questions.

      CJ: His glory is revealed in whatever is true about Pluto.

      BW: And that’s okay. A view of the world need not explain everything to be coherent or rational. It’s perfectly fine to say, for instance, that induction holds, period—i.e. without attempting to offer an explanation.

      CJ: It’s fine to say it, but not if you’re saying it as a component of a worldview or philosophy. Arbitrariness is not acceptable there.

      BW: And it’s not the least bit helpful to claim instead that induction holds AND that God exists AND that he wants or promises induction to hold AND that everything he wants or promises always comes true. That’s just adding a bunch of extra stuff on top of what we already assume

      CJ: You also presuppose all those things when you claim that induction holds, as I have explained before.

      Again, The thing is, from the standpoint of the worldview which holds to the truth of Christianity, Christianity is an explanatory and consistent worldview, but other worldviews aren’t.
      From the standpoint of a worldview which holds to the falsity of Christianity, no worldview is explanatory or consistent.

      And “every worldview presupposes either the truth or falsity of Christian theism.”

  12. Charles,

    Let me try to further focus this conversation. I see two (related) main tracks, so permit me to deal with them one at a time.

    First, we have been discussing whether your view is warranted and/or justified. Recall that warrant has been defined as “that extra something” which turns true belief into knowledge. We disagree on whether justification is a sufficient condition for warrant, but that disagreement is unimportant here. Instead, I want us to consider whether justification is a necessary condition for warrant. I think it is, and apparently you agree based on a comment you made earlier.

    So in order to show that your view is unwarranted, it is sufficient to show that it is unjustified. That is what I aim to do. And if it turns out that you don’t think justification is necessary for warrant after all, well, it’s still an interesting question whether your view is justified, and certainly worth pursuing IMO. I think if you really appreciated the fact that your view is not the least bit justified, you would begin to change it accordingly. And if you can show me that your view is justified, then that will be sufficient to persuade me.

    Clearly, though, you don’t approve of my characterization of justification. Recall that I define justification to be, “roughly, an available inference from agreeably true premises which require only valid deductive and/or cogent inductive reasoning.” You have objected to this characterization insofar as it involves agreement between parties on the truth of the premises. But despite my request for you to do so, you haven’t offered an alternative. What sort of justification do you think your view has that is so desirable?

    Instead, you glibly affirm that “of course” the only arguments you have given for the truth of Christianity involve premises which are highly controversial. But don’t you see the problem with that? How do you know those controversial premises are true? Do you have arguments for them too? Arguments which do not depend in turn on premises which are just as controversial? Feel free to surprise me, but I don’t think you can offer anything better than you have so far. All you can do is throw up arguments whose premises are just as dubious than the conclusion you are trying to draw!

    To be fair, you did suggest one characterization for justification, from the Cambridge Dictionary of Philosophy: “X is justified only if X has been or at least can be justified through adducing reasons.” This is actually quite compatible with my view. I too require reasons for justification, and I was even explicit about the sort of reasons I demand: they must be composed of valid deductive and/or cogent inductive inferences from agreeably true premises. This, of course, puts us right back where we started. You reject the “agreeably” part of my definition. That’s fine as far as it goes, but then what would you put in its place? Apparently nothing. You seem undisturbed by the prospect that the only premises you can marshal in your arguments for Christianity are highly controversial and have in turn no good supporting arguments.

    The second track of our discussion involves how our respective views deal with induction. On my view, I simply assume that induction works, without justification—by which I mean that I cannot support it with a (noncircular) valid deductive and/or cogent inductive argument from agreeably true premises. Of course, you can’t do that either, as you have admitted. (Recall that when I remarked about your premises being highly controversial, you responded, “Of course.”)

    So how do you think your view gives us a better account of induction? Well, you claim that there exists a being (God) whose wishes/promises always come true, and who wishes/promises for induction to hold. It follows immediately from these premises that indeed induction does hold. I asked you how you think this is better than simply assuming that induction holds, without adding all that extra stuff. In response, you claimed that my assumption is “arbitrary,” whereas presumably you think yours is not. But do you really think induction is an arbitrary assumption? It seems to me that your belief in a wishes-come-true deity is a lot more arbitrary than my assumption that induction holds.

    So maybe you had better explain what you mean by “arbitrary,” and why you think it is arbitrary to assume induction holds, but not arbitrary to believe in an unembodied mind whose wishes always come true and who wishes for induction to hold!

    1. BW: Charles, Let me try to further focus this conversation. I see two (related) main tracks, so permit me to deal with them one at a time.

      CJ: You continue to write, even though you admit that on your worldview you have no reason to believe in the induction by which you use language as you continue to write. In principle, you produce sound and fury signifying nothing. For now I indulge you as by your belief in God (which you “suppress” Ro 1.18) you write meaningful sentences, even though you aren’t “thankful” (verse 21) for His grace in this matter.

      BW: First, we have been discussing whether your view is warranted and/or justified. Recall that warrant has been defined as “that extra something” which turns true belief into knowledge. We disagree on whether justification is a sufficient condition for warrant, but that disagreement is unimportant here. Instead, I want us to consider whether justification is a necessary condition for warrant. I think it is, and apparently you agree based on a comment you made earlier.
      So in order to show that your view is unwarranted, it is sufficient to show that it is unjustified. That is what I aim to do. And if it turns out that you don’t think justification is necessary for warrant after all, well, it’s still an interesting question whether your view is justified, and certainly worth pursuing IMO. I think if you really appreciated the fact that your view is not the least bit justified, you would begin to change it accordingly. And if you can show me that your view is justified, then that will be sufficient to persuade me.

      CJ: No, it won’t, as long as you’re standing within a worldview which presupposes the falsehood of Christianity.

      BW: Clearly, though, you don’t approve of my characterization of justification. Recall that I define justification to be, “roughly, an available inference from agreeably true premises which require only valid deductive and/or cogent inductive reasoning.” You have objected to this characterization insofar as it involves agreement between parties on the truth of the premises. But despite my request for you to do so, you haven’t offered an alternative.

      CJ: I have. See below. This characterization of justification represents the standard, traditional philosophical characterization until the lifetime of Ben Wallis.

      BW: …What sort of justification do you think your view has that is so desirable?
      Instead, you glibly affirm that “of course” the only arguments you have given for the truth of Christianity involve premises which are highly controversial. But don’t you see the problem with that?

      CJ: To assume there’s a problem with that is to presuppose Christianity is false, but that is the matter in question.
      Of course the premises are going to be highly controversial, because they involve matters of ultimate concern, beliefs which are at the cores of our beings, beliefs which are at the centers of our webs of beliefs. These beliefs are matters of life and death.

      BW: …How do you know those controversial premises are true? Do you have arguments for them too? Arguments which do not depend in turn on premises which are just as controversial? Feel free to surprise me, but I don’t think you can offer anything better than you have so far. All you can do is throw up arguments whose premises are just as dubious than the conclusion you are trying to draw!

      CJ: “Dubious” is prejudicial. Yes, the arguments involve one another, for anyone. One’s presuppositions determine his conclusions.

      BW: …To be fair, you did suggest one characterization for justification, from the Cambridge Dictionary of Philosophy: “X is justified only if X has been or at least can be justified through adducing reasons.” This is actually quite compatible with my view. I too require reasons for justification, and I was even explicit about the sort of reasons I demand: they must be composed of valid deductive and/or cogent inductive inferences from agreeably true premises. This, of course, puts us right back where we started. You reject the “agreeably” part of my definition. That’s fine as far as it goes, but then what would you put in its place? Apparently nothing. You seem undisturbed by the prospect that the only premises you can marshal in your arguments for Christianity are highly controversial and have in turn no good supporting arguments.

      CJ: Many good supporting arguments. One’s presuppositions determine his evaluation of evidence.
      Note that when you critique my worldview, you do so from your own worldview (e.g. “no good supporting arguments.”) When I critique your worldview e.g. your position on induction, I do so putting myself on *your* position.

      BW: The second track of our discussion involves how our respective views deal with induction. On my view, I simply assume that induction works, without justification—by which I mean that I cannot support it with a (noncircular) valid deductive and/or cogent inductive argument from agreeably true premises. Of course, you can’t do that either, as you have admitted. (Recall that when I remarked about your premises being highly controversial, you responded, “Of course.”)

      CJ: Agreeably? No. “Agreeably”, which has never been involved in philosophical characterizations of justification or warrant (before BW), is anti-Christian from the outset.

      BW: So how do you think your view gives us a better account of induction? Well, you claim that there exists a being (God) whose wishes/promises always come true, and who wishes/promises for induction to hold. It follows immediately from these premises that indeed induction does hold. I asked you how you think this is better than simply assuming that induction holds, without adding all that extra stuff. In response, you claimed that my assumption is “arbitrary,” whereas presumably you think yours is not. But do you really think induction is an arbitrary assumption? It seems to me that your belief in a wishes-come-true deity is a lot more arbitrary than my assumption that induction holds.
      So maybe you had better explain what you mean by “arbitrary,” and why you think it is arbitrary to assume induction holds, but not arbitrary to believe in an unembodied mind whose wishes always come true and who wishes for induction to hold!

      CJ: You (plural) have thrown an induction tenet into your worldview arbitrarily, because at some point you realized that you needed it. It doesn’t comport with the rest of your worldview. You have said that for both of us the conjunction of all of our beliefs entails the Inductive Principle. That’s not true for you because beliefs in your conjunction are contradictory. “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.” I realize that you are still arguing about this on the “Necessity” thread (maddening that we are having two different arguments at once), but as I just posted about the “force”, “If there were nothing to make the future be like the past, why believe the future will be like the past?”

      Another way to answer you would be to say that the Christian worldview is concrete. God speaks. Here’s a Book. The worldview, with all its detail including induction, is there. Induction wasn’t arbitrarily included.

      A third way to answer you would be to say, “Huh? I can’t hear you. Without any warrant for induction and therefore language, you have failed to make your arguments intelligible.”

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