A Dozen Responses to the Transcendental Argument for God

A Dozen Responses to the Transcendental Argument for God November 30, 2013

Transcendental Argument for GodHave you ever thought about what grounds the laws of logic and mathematics? We know that they work, but why?

The Christian apologist has a quick answer: because of God. They exist and are sustained by God. The Transcendental Argument (TAG) challenges the atheist to resolve this any other way. What besides God could possibly explain the existence of something fundamental like logic? (To see the Christian case for this argument, read the selection from my Cross Examined in an earlier post.)

This argument is of particular interest to me because I was introduced to it in a radio interview—not the best place for careful study and contemplation. (But more on that later.)

1. TAG is just a deist argument

First notice that TAG is a deist argument. If it convinced you, you’d be a deist, not a Christian. The apologist would be obliged to use different arguments to show that the deity was the Christian god, not some other god.

2. We don’t get physics from Christianity

Next, notice that we’ve never gotten physics from Christianity before. Why go to Christianity now to find the fundamental basis for physics? Yes, the Bible tells us how everything got started, but science gives the evidence to make clear that the Bible is wrong.

Nothing useful has ever come from resolving a science question by concluding that God did it. No honest seeker of the truth says, “I don’t know what causes this thing … so therefore I do know! It must’ve been God.”

3. Avoiding logical puzzles invalidates TAG

Many apologists dodge the “Can God make a rock so heavy he can’t lift it?” puzzle by saying that God can’t do anything illogical (here and here)—he can’t make an impossibly heavy rock, a square circle, a married bachelor, and so on. The question is ill-formed.

But by dodging this pitfall, they land in another as God’s actions become constrained by an external logic. If God is bound by logic, logic isn’t arbitrary. God can’t change it. He acts logically because he must, just like the rest of us.

This creates a Euthyphro-like dilemma: either God is bound by an external logic (and God answers to a fixed logic that he can’t change) or he’s not (and logic becomes arbitrary—it is what it is simply because God said so, and he could change it if he wanted to).

The apologist will try to propose a third option (again, as with Euthyphro): logic is simply a consequence of God’s nature. It’s neither external nor arbitrary. But this simply rephrases the problem. Is this nature changeable? Then logic is arbitrary. Is it fixed? Then God is again bound by logic.

Can God be the origin of logic if he’s bound by it?

4. Could God create logic and mathematics? Or is he bound by them?

Let’s think about God creating arithmetic for a moment. “Creation” seems to mean more than simply “bring into existence.” Were God’s hands tied in creating arithmetic, or did he have some creative control? For example, 2 + 2 = 4 in our universe. Could God have made 2 + 2 = 9? If so, prove it. And if not, God was obliged to make arithmetic the way it is and unable to create any other kind. Here again, he answered to an external reality.

5. Consequences of a godless universe

But let’s assume the apologist’s argument and see what happens. God created logic, and logic is the way it is because God made it so. If God’s role here is important, a godless universe must be dramatically different. A godless universe could then have no logic or different logical rules.

In our universe, X can’t be the same thing as not-X (the Law of Identity). Something can’t simultaneously be a rock and not-a-rock. The apologist’s argument tells us that logic is up for grabs. In a godless universe, something might be a rock and not-a-rock. But this is an incredible claim that needs justification. TAG gives none.

Continue with part 2.

Can God make a rock so heavy
that hitting His head with it
would explain the change in personality He underwent
between the Old Testament and the New Testament?
— commenter GubbaBumpkin

Photo credit: Wikimedia

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  • avalpert

    Isn’t the response much simpler – logic and mathematics are self consistent systems that don’t need to be grounded externally in anything. You can have geometries that include the parallel postulate and have geometries that don’t – they are all equally self-consistently true and are each useful in different contexts and inappropriate in others.

    No need to have anything transcendental, nothing surprising to explain here at all. Sure, it may have taken a while for us to accept say alternative geometries, but once we did it was obvious that they were equally valid – this argument may have been interesting in the middle ages but nowadays it just sounds ignorant to me (at least no less so than arguing you need God to explain all these distinct life forms that inhabit the planet sounds after Darwin).

    • Isn’t the response much simpler – logic and mathematics are self
      consistent systems that don’t need to be grounded externally in

      It’s even simpler than that: they’re both human creations, for-us-by-us constructs that are only limited by our ability to conceptualize paradox. Look at the way we talk about infinity as if it’s anything more than a convenient trigonometric concept.

      In the same way, empirical evidential inquiry is a self-validating construct that allows us to conceptualize the staggering complexity of the world and the universe. We’ve created models of reality that currently resist disconfirmation, and in doing so learned a lot about our amazing universe. But it’s storytelling: none of us has anything more than an anecdotal understanding of microbiology or cosmology, so our belief that the universe is tens of billions of years old depends on our willingness to affirm the validity of this human creation.

      • smrnda

        A vote up for mathematical formalism!

        Also, mathematics is not necessarily consistent owing to Godel’s Incompleteness Theorem. At first people thought only highly artificial problems would turn out to be undecidable, but it turned out the Continuum Hypothesis – one of David Hilbert’s “Problems to Solve” was undecidable. (At least under ZF set theory.)

      • It’s even simpler than that: they’re both human creations, for-us-by-us constructs that are only limited by our ability to conceptualize paradox. Look at the way we talk about infinity as if it’s anything more than a convenient trigonometric concept.

        I’ll avoid interrupting this thread. My plain English definitely isn’t up to it. But what is Infinitude?

    • RichardSRussell

      Both math and logic rely on rock-bottom basic assumptions — called “axioms” — which are simply assumed to be true because there’s no way to reduce them to anything simpler, and they seem to be obvious and uncontradictable. Yet one of the very most fundamental ones — that thru any given point you can draw only 1 line parallel to another in the same plane — turns out to have been only an assumption, and either of the other 2 possibilities (0 or many such lines) yield geometries that are just as internally consistent as the one Euclid described.

      If I were a religionist, I’d claim that these axioms must be taken on faith, but of course those guys are always trying to claim faith as the basis for all sorts of things, because they’re desperate to paint it in as good a light as possible. In fact, you don’t need faith at all. You can just forthrightly state that they’re assumptions that yield results consistent with the way the real world appears to work. “Assumption” is no more an evil term with regard to math and logic than “I don’t know” is with regard to mysteries of cosmology and abiogenesis.

      • MNb

        “”Assumption” is no more an evil term”
        I’d say a lot less as we at least know which ones are those assumptions.

      • avalpert

        “If I were a religionist, I’d claim that these axioms must be taken on faith”

        You probably would but it would be a silly claim. I don’t take the axioms on faith, I accept them because the resulting system is useful – I don’t really care if the axiom is ‘Objectively True’ at all – it is just a tool not an end in itself.

      • smrnda

        Some religious people *do* try to go the axiomatic route (along with some bizarre quasi-religious non-theistic philosophies) but overall, when we deal with the real world, we use empirical data. People sometimes try to slip assumptions in as if they were statements of fact by rhetorical tricks.

        There are issues where we have to decide to quantify value judgments – what metrics do you use to decide if a country has a high standard of living? Per capita GDP is often chosen but just because it can be easier to measure so it’s chosen out of laziness. Assumptions aren’t bad, but it’s good to be clear what they are.

      • If I were a religionist, I’d claim that these axioms must be taken on faith,

        I’ve actually heard people of faith mention that they have foundational assumptions that are axiomatic, like the existence of God.

        I’m not sure that’s totally incorrect, because obviously the concept of God itself has qualities of an intersubjective word game more than a coherent construct. But an assumption is axiomatic when it’s self-evident, like a=a, not just because people feel that the assumption shouldn’t be questioned at all.

        • smrnda

          You mean like Ken Ham and the whole ‘pre-suppositional apologetics’ deal? It seems like that whole house of cards is built on saying ‘well, everybody makes assumptions, so any set of assumptions you make is totally equal to any other.’

        • yeah, I hate that. “I won’t bother investigating or minimizing my biases. Heck, everyone has them, right?”

        • But to play devil’s advocate for a moment, a bias like scientism isn’t worth investigating or minimizing?

        • Yes it is. That’s my point. I’m saying that giving one’s own biases a pass because “everyone is biased” is hardly an honest search for the truth.

        • smrnda

          I think its best in that case to define what sort of questions scientism can and can’t answer. Part of that is just making a clear distinction between things being false or being incapable of being known.

    • You may be right, but it’s still difficult to show the TAG proponent why this cool-sounding argument is actually just smoke.

      I think that these 12 arguments attack it from enough angles that there’s a flavor that just about anyone can like that shows TAG to be empty. But I can still vaguely sense the hold that it has on believers.

      My favorite argument will be in the last (third) installment of this series.

    • MNb

      “logic and mathematics are self consistent systems”
      They aren’t; think of Russell’s barber paradox. However that may be turned into an answer to TAG as well. Logic and math can be shown to be imperfect and thus contradict the omni-everything god.
      This needs some elaboration as well.

  • GCBill

    3 and 4 are the most compelling points here.

    With regards to #3, the theist is committed to saying that logic is unchanging (because God is unchanging, and logic is somehow a part of God’s nature). Notice how they’ve just posited logic as a necessary brute fact just like any atheist who takes it to be fundamental and immutable.

    • MNb

      “3 and 4 are the most compelling points here”
      I agree. An atheist shouldn’t be satisfied with 1 and 2. Perhaps it’s possible to elaborate them to show that they rather support pastafarianism iso Christianity. Then we have another tool to show the hypocrisy of apologists. If I have to do it it will take some time.

      • I’ve called these “responses” instead of “rebuttals.” Some, like 1 and 2, are IMO clarifications so that we see TAG for what it is.

  • bob

    When did 5 become a “dozen”? I enjoyed this, but had hoped for more…

    • RichardSRussell

      I believe the answer is to be found in the final 4 words of the essay.

    • $28895381

      God changed the laws of mathematics. See TAG does work.

  • Pedro Regis

    Unfortunately, the hypothesis of possible worlds in any way invalidate the Euthyphro Dilemma


    • MNb

      First show what meaning “possible worlds” has for our reality or we could as well speculate about the Flying Spaghetti Monster.

      • Pedro Regis

        First sorry for bad english, I am Brazilian and I’m using google translator: P

        Second: I’m an atheist and I believe that the transcendental argument is false.

        I agree that this argument maximum sample a deist authority and intellectual dishonesty is trying to prove the Christian god with this argument. The only statement I did was put a link demonstrating the falsity of the Euthyphro dilemma in all its versions. While the hypothesis of possible worlds is not considered false, we can not consider the point three as a valid refutation of transcendental argument. If the Flying Spaghetti Monster created the logic or not is irrelevant to the response of Craig.

    • Paul King

      I’m afraid you’re wrong, The “many-worlds” (actually “possible worlds”) argument provided by the questioner is logically invalid.

      Here’s premise 4:
      (4) But, if moral values are objective, moral perfection represents (or
      at least tends towards) a unique, maximal set of moral values.

      This assumes that moral standards are objective across all possible worlds, and that God’s nature must conform to this standard. i.e. it assumes Horn B which the argument attempts to deny.

  • Paul King

    I’d describe TAG as the most popular argument for God that doesn’t exist.

    There really isn’t an argument there. This version is as close as it gets, but even it lacks a coherent understanding of what logic is – even an erroneous idea. (And if such an idea were included we would almost certainly see it fall apart).

    Correctly understood, logic is a formalisation of semantic rules and the idea of truth. A logically true statement is necessarily true due to the definitions of the terms and the construction of the statement and nothing else.

    Thus a correct understanding of logic successfully explains why it works, while the hypothesis proposed by the TAG proponent actually fails to do so. Cause enough to make this a Transcendental Argument Against God – at least as conceived by the TAG proponent.

    AN argument from “the unreasonable effectiveness of mathematics” is more reasonable and harder to refute. However, even then I think that we might reasonably argue that it is the descriptive power of mathematics that makes it effective rather than some underlying principle.

    • Richard_Wein

      I’m not sure why we should find the effectiveness of mathematics to be surprising. Basic mathematics–like arithmetic and geometry–developed as a means for modelling reality, so it’s no surprise that it’s effective for that purpose. Perhaps more interesting is the fact that new branches of mathematics, developed for no practical purpose, often turn out later to have practical uses. But should we find that surprising? I’m not so sure. Given the amount of scientific advance, is it surprising that uses can be found for many different branches of mathematics? And has anyone ever tried to reckon how much mathematics hasn’t been found a use? To be honest, I don’t know nearly enough mathematics and science to make any such assessment for myself.

      • Paul King

        Good to see you again, Richard. it’s been a long time.

        Let’s be clear, I don’t think that the argument is a very good one – but it is a better one than TAG, and I don’t think that it can be decisively refuted (i.e. shown to be definitely wrong, rather than just probably wrong).

        My understanding is that some aspects of mathematics, like complex numbers and non-Euclidean geometry have turned out to be more useful than expected (and I don’t think that either was developed for practical purposes).

        But, of course, you’re right to say that a lot of the basics of mathematics – arithmetic and geometry being the obvious examples – were developed for practical reasons and it should not be too surprising that extending the powerful basic concepts underlying them has proven fruitful.

      • smrnda

        The example usually given is number theory, which has lots of applications in cryptography but which was for a long time seen as pretty much pure mathematics unlikely to have any application.

    • There really isn’t an argument there.

      None of them are really what you’d call arguments, are they? They really just paint the target around the arrow in the wall.

      It’s easy for humans to look at a phenomenon or artifact in nature and assume that it represents the end result of an intentional process. But using as the basis of an argument the notion that phenomenon X wouldn’t be the way it is unless the Almighty wanted it to be that way is about as presumptuous as you can get.

      • smrnda

        From a psychological angle, this can just be humans having over-active agency detection. There may be some survival value in viewing events as the product of intentional actors – if you think the ice *wants* to break and the water *wants* to drown you, you’d be more careful. Another issue is that an intelligent agent would want to be able to identify the presence of other intelligent and intentional agents, which might leave only vague traces.

        • There may be some survival value in viewing events as the product of intentional actors

          Sure. More of our ancestors survived because they assumed the leaves rustling in the forest were really a lion and hightailed it, rather than the ones who mistook the tiger behind the tree for a striped rock.

          But the more important factor is the phobia that creative Homo Sap has about the concept of design-with-no-designer. Even a century after we’ve been shown the creative power of random variation and natural selection, we’re still squeamish about ascribing design capability to mindless processes.

    • Guest this time

      A logically true statement is necessarily true due to the definitions of the terms and the construction of the statement and nothing else.

      This is the answer. Logic begins from a set of agreed-on definitions and proceeds from there. (Likewise for math; 2+2 = 4 because if you reach back far enough, you see those numbers are defined that way.) Nobody has to magically create it, and, in fact, if you disagree with the original definitions you can royally screw up a conversation based on logic (I’m sure we’ve all seen many examples).

  • Richard_Wein

    “Why go to Christianity now to find the fundamental basis for physics?”

    I think that calling maths or logic “the fundamental basis for physics” is unhelpful, and is conceding too much to the TAG. I would say that maths and logic are tools used by physicists. We can learn about the world around us just by looking at it, relying on our intuitive cognitive processes (as animals do). Over our history our methods of learning about the world have gradually improved, becoming more formal and rigorous, and modern physics is the furthest development of that process to date. But there is no fundamental discontinuity between intuitive learning and physics.

    Maths and logic have also developed gradually, and there’s no fundamental discontinuity between natural language and the language of maths and logic. People must have used numbers in very basic ways long before they developed any formal mathematics. They must have used conditional sentences (if…then…) long before they developed formal logic.

    Facts of pure maths and logic are true just by virtue of the meanings of the words/symbols in which they’re expressed. The meanings of words arise from the roles they play in our discourse (which may include the stipulation of definitions or axioms). For example, the meanings of integer words arise just from our habit of counting objects using a consistent sequence of symbols. Since 3 comes after 2 in our counting sequence, 3 is greater than 2. We don’t need God to make 3 greater than 2!

  • David Evans

    I think some theists would answer to #5 that, since God is a necessary being, it makes no sense to ask what a godless universe would be like. Just as, since 2+2=4 is a necessary truth, it makes no sense to ask what the universe would be like if it were false.

    • But that God is necessary is what we’re trying to show with TAG. You can’t simultaneously take it as a given.

      • JohnH2

        Trying to draw conclusions from a single data point, especially when there is disagreement about the nature of the data point, is silly.

  • idontknow33

    #1 is the only necessary response when in a discussion with a Christian.

  • DJMankiwitz

    I don’t know… could we consider the individual particles of a rock, at a quantum level, to be in superpositional states of rock and not-a-rock? Does quantum physics violate the law of identity? Or, is it rescued in a nice easy, lazy way by just redefining what one means by “rock” to include the behavior of virtual particles.

  • haweha

    The logical “absolutes” were either created by the human brain or created by an unknowable number of unknowable G-Ds or, behold, Dear brethren and sistren, come and see: They were not created at all. They just are, and they can be called the G-Ds that mankind is in search for.

    • Greg G.

      The logical absolutes are, whether there is a god or not. Calling something a god doesn’t make it fit the general definition of a god.

      • haweha

        >>>logical absolutes are, whether there is a god or not.<<<
        How do you know that, Greg?

        • Greg G.

          Are you talking about absolute certainty or reasonably justified certainty? Absolute certainty is impossible. But if logic doesn’t work, then no epistemology works so we wouldn’t know anything.

        • haweha

          Excellent response! Thank you. Kindest regards from GERMANY.

  • haweha

    The logical “absolutes” were either created by the human brain or
    created by an unknowable number of unknowable G-Ds or, behold, Dear
    brethren and sistren, come and see: They were not created at all. If so, then the unknowable number of unknowable G-Ds (in other words the entities to which the creation of the cosmos is ascribed to, well !!!IF!!! the cosmos was created) have got some “company”

  • Michael Neville

    In our universe, X can’t be the same thing as not-X (the Law of Identity).

    No, that’s the law of contradiction. The law of identity is X=X. There’s also the law of the excluded middle, either X or not-X.