Logic, Math, and Presuppositionalism

Theists who employ what is known as “presuppositional apologetics”, and more specifically, the transcendental argument for God, often make confused claims about logic. John Frame claims that logic is based on the nature of God[1], and Matt Slick says that the laws of logic are absolute and independent of the human mind[2]. There are others who use such argumentation in slightly different ways (such as Eric Hovind and Sye Tenbruggenate), but the general view seems to be that theism, and specifically Christianity, is needed in order to justify one’s use of logic.

But this view of logic is sorely mistaken. The so-called “laws of logic” are merely conventions that exist within a man-made, formal system. To see why, we merely have to look at “logic” for what it really is – an entire field dedicated to the study of inference and relation. In the past century, many methods of doing this have appeared. Graham Priest writes:

Despite this, many of the most interesting developments in logic in the last forty years, especially in philosophy, have occurred in quite different areas: intuitionism, conditional logics, relevant logics, paraconsistent logics, free logics, quantum logics, fuzzy logics, and so on. These are all logics which are intended either to supplement classical logic, or else to replace it where it goes wrong.[3]

Relevant logic, for example, differs from classical logic in that it attempts to solve the paradox of material implication. The paradox of material implication is the observation that “If the moon is made of cheese, then 2+2=4” is true, even though the antecedent is in no way related to the consequent. Material implication just does not capture what we really mean by “if…then” – yet it is classically valid. Relevant logic attempts to solve this by saying that andecedents must be “relevant” to consequents.

This seems to make sense, but it leads to an interesting feature of relevant logic. Relevant logic is not explosive, which means that unlike classical logic, you can sometimes have contradictions which do not entail the trivial truth of every proposition. Thus, “~(A & ~A)”(the so-called “law of non-contradiction”) is not a theorem of relevant logic (while it is a theorem of classical logic).

This is important because it shows that the unchanging, transcendent view of logic that presuppositionalists talk about just isn’t the case. These logical and mathematic systems are just models we invent to examine different ideas. We can and have changed them, or even thrown them out and started over with different “laws”, many times in the past. Relevant logic is just one example. Some other logics even change the definition of truth. Four-valued logics (often used in computing and electronics) don’t have “P v ~P” as a theorem; and fuzzy logics even have an infinite range f truth values. Intuitionist logics aren’t even concerned with truth, but justification. And these all have real-world applications.

Even mathematics does this. In elliptic geometry, for example, the sum of the angles of a triangle is more than 180 degrees; and Euclid’s parallel postulate is false – there are no parallel lines in elliptic geometry. Now, one might object by saying, “well, that’s just a thought experiment, and doesn’t obtain in reality”. The problem with this is that neither does Euclidean  geometry. When’s the last time you saw a triangle? You haven’t. You never have. The only thing that exists in reality is an approximation of a triangle. A “real” triangle would have to have infinitely thin sides in order to have angles that add up to exactly 180 degrees; and would also have to be infinitely flat. We live in a 3-dimensional (at least) universe, and triangles exist in 2 dimensions. A triangle is just a concept, a thought experiment.

All this points to a simple fact: logic and mathematics are made up. We invented them to describe what we see, and they are only approximations.
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[1] http://www.reformed.org/master/index.html?mainframe=/apologetics/martin/frame_contra_martin.html

[2] http://carm.org/transcendental-argument

[3] Priest, Graham. An Introduction to Non-Classical Logic. 2nd ed. New York: Cambridge University Press, 2008. xvii.

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5 responses to “Logic, Math, and Presuppositionalism”

  1. Gman says :

    “Theists who employ what is known as “presuppositional apologetics”, and more specifically, the transcendental argument for God, often make confused claims about logic”

    But isn’t this opening statement a ‘logic’ claim in itself to which your worldview can’t account for, could you be wrong that we are confused and if not, how do you support that statement? Afterall, since the only way to make any absolute or certain logic claim you have to have an absolute starting point of what is considered ‘logical’, otherwise the logic in the statement is arbitrary and profound only to the one who made the statement and thus the statement above is not absolute or certain, therefore it could be (and is almost certainly) wrong. Some may agree with your ‘logic’ because it would concur with their presupposition that all who argue against theist presuppositionalists are right, however, this doesn’t make your statement correct, it still makes the actual logic YOUR logic which was deducted by your own reasoning using observation through unverifiable seneses and uncertain reasonings,

    On the other hand, the presuppositional theist derives his or her logic from a being who is above fallible human reasoning and senses because this entity (we know as God of the Bible) has revealed this to us, not only to us individually but also through his Word and not just through his revalation and word but also through signs of nature and his creation.

    I totally understand why this isn’t accepted by you, and also understand why you wouldn’t accept this to be a valid argument from within your near-sighted worldview, however, just because one may not be able to accept this response, doesn’t make it wrong, as a matter of a fact, one from an atheist worldview couldn’t call it wrong simply because from within that view, nothing can be proven wrong absolutley and would have to concede that the presuppositional theist could be be (and almost certainly) right. To make any other claim would support an absolute certainty from within an atheist worldview without any logical or viable source to label such a possibility, absurdity; in so doing is not only falacious but a wicked disregard of the undeniable fact that one from the atheist worldview can be wrong about everything he or she knows.

    An atheist or anyone not believing in an absolute source for knowledge, debating or arguing against the presuppositional apologetic is simply redundant, as every knowledge or logic claim circles back to the atheists reasoning via observation through fallible senses, none of which are certainties. As Sye has pointed out, it is viciously circular. I simply believe it to be redundant because nothing coming from the atheistic worldview can ever be counted as a valid argument. Not just by the theist, but also by the atheist. Outside of an arbitrary opinion of the person (atheist) there is no other valid or plausible source of knowledge to support the knowledge claim from said person and the problem with this is the confession from the atheist that he or she could be wrong about everything they think they know.

    I’m certainly not here to offend, but you did say that we were free to post… I felt free 🙂

    • Robert says :

      But isn’t this opening statement a ‘logic’ claim in itself

      No, it’s not; it’s an empirical observation.

      to which your worldview can’t account for

      It’s not even about that, not when presuppositionalists don’t seem to understand what logic is. Relevant logics, elliptic geometry, and things like them exist and are used every day. How can anyone say that “laws of logic” are absolute, when we throw them out all the time with no ill effects? Nonclassical logics just completely ignore the law of non-contradiction, disjunctive syllogism, etc., and the presup doesn’t seem able to explain how we can get any work done when we use them (or at least, I’ve never seen an attempt made).

      On the other hand, the presuppositional theist derives his or her logic from a being who is above fallible human reasoning and senses because this entity (we know as God of the Bible) has revealed this to us, not only to us individually but also through his Word and not just through his revalation and word but also through signs of nature and his creation.

      See, this is what I’m talking about. How can you account for the existence of relevant logic, or many-valued logic? To date, no one has even attempted to explain how these things work with an absolutist view of logic. To be quite honest, this seems less like a debate, and more like a math lesson.

      absolute

      This is another point. Why are presups so obsessed with being certain about everything? There’s lots that I’m not 100% confident about, but so what? I’m 99.9999% confident that gravity works. I’m 99.9999% confident that the sun will rise tomorrow. I’m roughly 80% confident that God does not exist. I’m roughly 70% confident that Socrates existed. Is there some epistemic fault in not being certain about everything? If so, why?

      I’m certainly not here to offend, but you did say that we were free to post… I felt free 🙂

      I greatly appreciate the comment. What frustrates me is when I look at the site statistics for today, and see 76 views on my article regarding Sye, and 15 on this one; and 66 referrals from Facebook – where I don’t even have an account! I can only assume that Sye posted a link to my post on his Facebook, where his friends proceed to look at my article, but not comment on it. I think it’s also a reasonable assumption that like him, they also stopped reading partway through. If any of Sye’s fans happens to read this, please, please at least make an attempt to explain nonclassical logics.

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