Notes on a Transcendental Argument from Logic

Nearly ever since I was first exposed to transcendental argumentation through listening to that famous debate between Greg Bahnsen and Gordon Stein,1 I have retained the intuition that there is an interesting potential argument from the fact that there are necessary propositions (necessary, that is, simpliciter) to the conclusion that there is a necessary mind. While the analysis of what it means to be a necessary mind will fall short of the God of perfect being theology or classical theism, it will still provide a being which so resembles God that it significantly undermines atheism. This being may not have all the superlative attributes, but it will be a metaphysically necessary immaterial spaceless timeless being with an intellect (and whatever that entails), et hoc omnes intelligunt Deum. However, to avoid the charge of using St. Thomas’ famous phrase in order to paper-over the chasm between my conclusion and full-blown theism, I will state the conclusion more modestly in terms of which the good old reverend Bayes would approve. Enjoy;

1) There are laws of logic.
2) Logical laws are identical to necessary propositions (exempli gratia [P v ~P])
3) Therefore, there are necessary propositions.
4) Propositions are not real entities which exist mind-independently, but are mind-dependent (i.e., there is no proposition for which there is not at least one subvenient mind).
5) A necessary truth is a truth which obtains in all logically possible worlds.
6) Necessary truths are either grounded in at least one contingent mind, or at least one incontingent mind.
7) There are logically possible worlds without any contingent minds.
8) Therefore, there must be at least one necessary mind.
9) If there is at least one necessary mind then it is a being with intellect (plausibly knowing all necessary truths), which is immaterial (spaceless, timeless) in nature.
10) The conditional probability of theism is, ceteris paribus, greater than the conditional probability of not-theism on the condition that there is at least one metaphysically necessary immaterial being with intellect. 
11) Therefore, theism is probably true, 
ceteris paribus.

There are plenty of points at which one could still object to this argument, but it seems to me that most objections are philosophically more costly than the conclusion. One might also just accept the conclusion but deny that, in fact, things really are equal (i.e., cetera non sunt pariba) in this case. For instance, the objector could insist that there are no propositions which are ‘necessary’ in the sense required here (that is, necessary simpliciter – not a merely model-dependent necessity). They might also insist, for some odd reason, that there are not possible worlds without contingent minds, or that those worlds are possible in a merely model-dependent way while other possible worlds are possible simpliciter. That would be pretty wild. Another might argue that the existence of a metaphysically necessary immaterial mind doesn’t raise the conditional probability of theism at all (maybe because the probability of theism is ‘0’ – or because it is ‘1’). Somebody could, of course, deny the major premise, that there are laws of logic. Somebody may also insist that laws of logic are not identical to the propositions which express them (though that seems to reify them so much as to put the objector, for other reasons, in the near occasion of belief in theism anyway). Alternatively one may think that each premise on its own seems more plausibly true than false, but that the collection of them together seems to have a upper-bounded probability of lower than or equal to 0.5, and that would be a principled way to object.

Edit*: it occurs to me that there’s no way of which I’m aware to really set an upper-bound on the probability of a conclusion. What the objector could say, then, is either that the conclusion just seems to be no more likely than 0.5 (notwithstanding the plausibility of the individual premises), or that the premises collectively set a lower-bounded probability on the conclusion of less than or equal to 0.5, in which case the argument fails to be compelling.

To be fair, this argument of mine very likely draws significantly from the influence of James N. Anderson and Greg Welty,2 whose argument seems, to me, much better than what often passes for responsible argument among presuppositionalists (among whom, I should take a moment to clarify, I adamantly do not count myself).

1 For those interested, you can find the audio of the debate, and the transcript (because the audio is really not great) at the following two links: https://youtu.be/ZLZdOGCE5KQ?t=34s and http://www.brianauten.com/Apologetics/apol_bahnsen_stein_debate_transcript.pdf

2 James N. Anderson and Greg Welty, “The Lord of Non-Contradiction: An Argument for God from Logic” Philosophia Christi 13:2 (2011). http://www.proginosko.com/docs/The_Lord_of_Non-Contradiction.pdf

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8 thoughts on “Notes on a Transcendental Argument from Logic

  1. Thanks for posting this,good to see you posting after a long time,

    There are two objections I am thinking of
    1.It seems to presuppose some kind of dualism or at least it seems incompatible with most versions of physicalism.(they preclude immaterial minds)

    2. It seems absurd to think that If there was no subvenient mind..there would have been no necessary propositions..afterall thats what “necessary” means ..and wouldn’t this argument imply that God can somehow change laws of logic ..which seems impossible ..

    • Thank you for your comments as well. It looks like this roughly sketched argument has elicited some interesting reactions.

      So, if one really is a physicalist then to accept my argument they’d have to believe in a necessary physical mind. As with most absurdities, that is far from unprecedented in the history of philosophy. There may be reasons to think that a metaphysically necessary physical object is an absurdity, but not one of those reasons figures into the premises of my argument. As far as I can tell, for instance, Spinoza would have been happy to accept my argument, as would Hobbes.

      To your second point: if my argument is sound then the trouble with imagining a world without a necessary mind upon which analytic truths supervene is that such a world is not merely counter-factual, but counter-possible. I’ve addressed this in response to another comment in this thread, so perhaps you’ll allow me to direct you to that. However, I do not think that analytic truths supervening upon God’s mind implies that God could somehow change the laws of logic – I just don’t see how one gets from premise to conclusion in that case. An argument would have to be offered to bridge that gap, I think. Maybe something with a premise like “for any A, if A supervenes upon B, then A does not necessarily supervene upon B.” But any argument including that (or a roughly equivalent) premise seems unsound; why should we accept anything like that principle?

    • I don’t want to disparage anyone… but no. In fact, I have mixed feelings about presuppositionalism in general. I do think van Til was interesting (Greg Bahnsen was as well, and I greatly enjoyed listening to John Frame’s courses on RTS via iTunes). However, the whole tradition is riddled with so much vitriolic anti-Catholic sentiment, along with such disdain for natural theology in general, that I am deeply suspicious of it. I have come to think that presuppositionalism is the only viable way to be a genuine protestant, but I do not think that presuppositionalism is a viable philosophy. I also think that the only way to make good sense of the work of presuppositionalists like Bahnsen and van Til is to interpret it, at some points, as subliminally committed to a coherentist theory not just of knowledge but of truth itself. This is perhaps no big surprise given that van Til was so obviously influenced by early 20th century epistemological idealism (according to which, approximately, reality itself was a form of thought, and our thought is a form of participation in it). However, that makes it no less unacceptable to me; I am adamantly not a coherentist about truth. Now, maybe presuppers can rescue presuppositionalism for people like me by either dissuading me from the belief that they are committing themselves to coherentism about truth, or offering some correspondence relation between our thoughts and God’s thoughts – I’ll leave that door open for them.

  2. “5) A necessary truth is a truth which obtains in all logically possible worlds.
    6) Necessary truths are either grounded in at least one contingent mind, or at least one incontingent mind.”

    You’ve no clear idea about what it is for something to be “grounded” in some other thing.

    Minimally, whatever else it means, for A to be grounded in B is for A to fail to obtain in those cases where B fails to obtain. But (logically) necessary truths never fail to obtain. So what is it you imagine you are asking when you ask what (logically) necessary truths are “grounded” in?

    The problem with “grounding” or any other intuition-pumping metaphor here is that it takes an in-world notion to stand in for a trans-world modal concept. We have intuitions built up around breadbox-size objects physically pushing one another in the actual world that simply lose all meaning and relevance when applied to abstract objects existing across worlds.

    The foundation “makes” the building stand up, because in (nomologically) possible worlds without it, the building falls down. By analogy, my argument about healthcare reform is “grounded” in the data, because if the data were otherwise, my conclusions wouldn’t be “supported”. In arguing for a (logically) necessary mind grounding (logically) necessary truths, you are literally trying to talk about (logically) possible worlds where a being who exists in all possible worlds nonetheless does not exist.

    Modal logic is like a sort of Monty Haul problem of apologetics. There is a simple, objectively correct answer that flies in the face of the intuitions of even very very very intelligent, highly-educated people, who will argue at great lengths about why switching doors is pointless, since the Host opening an empty door does not “make” the prize move from one door to another.

    • Thank you for that thoughtful comment. There are a few observations I’d like to make here. First, when you say “We have intuitions built up around breadbox-size objects physically pushing one another in the actual world that simply lose all meaning and relevance when applied to abstract objects existing across worlds” you’ve rather shown your hand, I think, in that you are implicitly assuming an empirical epistemology in contrast to a rationalist one. On the one hand, I think that wholesale empiricism can be demonstrated to be logically incoherent (see, for instance, my immediately previous post). On the other hand, you are quite right that if we should be empiricists about our modal intuitions, then the argument I’ve sketched here has a problem.

      You make a particularly interesting comment when you write: “in arguing for a (logically) necessary mind grounding (logically) necessary truths, you are literally trying to talk about (logically) possible worlds where a being who exists in all possible worlds nonetheless does not exist.” On the one hand, if you do regard the argument as sound then you’ll (likely) regard the non-existence of a necessary mind not merely as a counter-factual, but as a counter-possible, and counter-possibles can be a little more problematic; they are true, if ever, only in a degenerate or merely formal sense. I think that popular versions of the moral argument for God’s existence (for instance, W.L. Craig’s moral argument) suffer from the same problem. All arguments for atheism suffer from the same problem as well. However, clearly in the context of debates over things like the existence of God or platonic forms (or other theses which are true, if at all, necessarily) interlocutors agree to suspend their commitment to the belief that their view expresses a metaphysical necessity. We agree, for the sake of argument, to regard what we take as counter-possible in fact to be counter-factual, at least where the assumption of counter-possibility would cause our arguments to be viciously circular. In fact, anytime we offer a deductive argument for something which, if true, is necessarily true, we must suspend our commitments to its necessary truth for the sake of (non-circular) argument.

      Let me also say a word about the correspondence theory of truth; I recognize that the view I espouse is unconventional, to some extent, insofar as I want even my analytic truths to be grounded in some way. What, though, is the alternative? If we are not wedded to correspondence theory then we could simply regard analytic statements as true in virtue of pragmatic value or true in virtue of belonging to a maximally coherent worldview (or something like that, if we are coherentists about truth). Those are non-starters for me. If, on the other hand, we are wedded to correspondence theory, then to what must an analytic statement correspond, and in virtue of what is it true? If we appeal merely to a language or a model then the necessity of any analytic statement will always be conditional (conditioned, I mean, on the nature of the language or model), but that won’t allow for absolute necessity or metaphysical necessity, or necessity simpliciter. To deny that, I think, commits us to an unconscionable modal anti-realism… Is it really unconscionable? Well, it is to me because I’m too much of a rationalist (as opposed to an empiricist) to deny that reality objectively has a modal structure. At least some statements about possibility, necessity and impossibility are unconditional truths. In fact, this is my fundamental objection to what is sometimes called ‘absolute creationism’ according to which abstract objects (platonic forms) exist, but they are created beings – beings created, in fact, by God.

      However, even if my view about analytic statements requiring some grounding or something like a truth-maker seems plausible to me, you are right that my argument hangs on it.

      • I’m not sure what any of this has to do with “assuming an empiricist epistemology”. The psychology of intuitions strikes me as a rather banal statement of noncontroversial fact. We have serviceable intuitions about rocks and trees and numbers less than 100 and timescales less than a lifetime. Quantum entanglement and trillion-dollar Federal budgets, not so much. It’s not intuitive that uncoordinated selfish actors can produce more efficient market outcomes than central planning, but they do. It’s not intuitive that you should switch doors in MH, but you should.

        Unless you seriously want to argue that no cognitive tasks are more consistently unintuitive than any other, or that their intuitiveness is completely uncorrelated with their relatedness to everyday tasks. In which case, good luck with that.

        Q.V. https://en.wikipedia.org/wiki/Monty_Hall_problem#Confusion_and_criticism
        ic and logical modalities

        ”On the one hand, if you do regard the argument as sound then youíll (likely) regard the non-existence of a necessary mind not merely as a counter-factual, but as a counter-possible, and counter-possibles can be a little more problematic; they are true, if ever, only in a degenerate or merely formal sense…. interlocutors agree to suspend their commitment to the belief that their view expresses a metaphysical necessity.”

        Oh, great. So now, on top of logical possibility and epistemic possibility, we also have this EVEN LESS well-defined notion of “metaphysical impossibility”! (I wonder if any thoughtful commenters have impressed this distinction on you before, he asked mischievously…)

        Let’s simplify: something is either logically necessary, or it isn’t.

        All logically necessary truths are true in all logically possible worlds. There is no sense in which any of them is “grounded” (a metaphor derived from nomological possibility) in any other; or if you like, every one of them is equally as grounded in every other. So the whole project of these kinds of Transcendental arguments is meaningless, in the strong sense of meaningless. You literally might as well be asking if bachelors are still unmarried in worlds where 2+2 does not equal 4, or if necessarily existing apples are “grounded” in necessarily existing carrots (when everyone knows it’s the other way round!)

        Any language game that allows me to “imagine” (epistemic possibility) worlds with and without necessary minds to conclude that necessary propositions become “ungrounded” without them will, ex hypothesi, allow me to imagine that there are no such worlds.

        This is a game of tennis without a net that tells us diddly squat about what is and is not a logical necessity. Remember, it’s the formal relation of logical necessity that you need to establish to make the argument work.

        ”In fact, anytime we offer a deductive argument for something which, if true, is necessarily true, we must suspend our commitments to its necessary truth for the sake of (non-circular) argument.”

        No, just, no. Deductive arguments for logically necessary truths proceed from things like the operation of rules of inference on axioms, not “suspending our commitments”. Suspend your commitments a moment and answer me: if seven weren’t a prime number, would morality still be as objective as it is now?

        ”If we are not wedded to correspondence theory then we could simply regard analytic statements as true in virtue of pragmatic value or true in virtue of belonging to a maximally coherent worldview (or something like that, if we are coherentists about truth). Those are non-starters for me.”

        To be a bit flip for a moment, neither your interlocutor nor (especially) the universe are beholden to your threshhold of credulity. But the CTT is neither here nor there when it comes to something being “grounded” in some other thing when both things are logically necessary. Something is either logically necessary, or it isn’t. Full stop. Something is either logically contingent, or it isn’t. Full stop. Something is logically contingent upon some other thing if and only if there exists no logically possible world where the former obtains without the latter. Just as a house standing up is nomologically contingent upon having a firm foundation, in the sense that all worlds conforming to our laws of physics lack standy-uppy buildings when they lack solid foundations.

        But since all logically necessary truths obtain in all logically possible worlds, no one is any more “grounded” (note scare-quotes) than any other, or in any other more than any other. Your intuition that propositions or analytic statements or whatever must be “grounded” (can’t emphasize the scare-quotes there enough) is your intuition about nomological modality (where things really do “make” other things happen or fail to happen) illicitly trying to export itself to questions of logical modality. And hey, I get it. The logically possible world where the house stays up even though the earth turns to soap bubbles underneath it is wildly counterintuitive to me, too. But that’s because what’s counterintuitive to me is what is and is not nomologically possible, given the laws of physics that describe my everyday interactions with the world.

        ”However, even if my view about analytic statements requiring some grounding or something like a truth-maker seems plausible to me, you are right that my argument hangs on it.”

        If you wanted to turn this into something publishable, you’d do well to do what I’ve never seen anyone in this field do: make an affirmative case that the asymmetric notion of specifically logical grounding for logically necessary truths is even remotely coherent. It’s definitely an original paper topic, and probably a lot more fulfilling than the set-piece skirmishes you and I are both tired of over subsidiary issues like how having mental traits like beliefs and desires could conceivably be meaningful for a “timeless” being, or what relation this philosophers’ idol bears to the character who once called off the murder of Moses because he was fooled by a bloody foreskin pressed against the latter’s genitals.

      • You’re always such a delight. 🙂

        So, as you undoubtedly know, I think that we have at least some purely rational intuitions which inform our conception of modality. There are at least some things which are possible simpliciter, necessary full-stop, impossible absolutely. I don’t think we can make sense of that if our modal intuitions are based on breadbox-sized objects. It may be quite undeniable that many truths are counter-intuitive (I think the Monty Hall problem only appears counter-intuitive because people fall for the power of suggestion and sleight of hand, but that sober thinking finds the solution extremely intuitive), but the point is that our modal intuitions are the best we have for discovering the modal structure of reality (that is, discovering the nature and extent of metaphysical possibility). Take a narrowly logically possible proposition: “there is a square circle.” Translate that to sentential logic and you derive no contradiction (without auxiliary assumptions). It remains, however, clear that square-circles (and the like) are metaphysically impossible.

        Typically philosophers distinguish between narrowly logical possibility/necessity, broadly logical possibility/necessity, conceptual possibility, nomological/physical possibility and epistemic possibility/impossibility. That’s pretty standard. Broadly logical possibility is also often called ‘absolute possibility’ or ‘metaphysical possibility.’ There’s nothing particularly uncommon about the distinction.

        You suggest “All logically necessary truths are true in all logically possible worlds. [*agreeable nod*] There is no sense in which any of them is “grounded” (a metaphor derived from nomological possibility) in any other” Alright, now, first of all, to think that the metaphor is derived from nomological possibility seems to me to be an admission of empiricism. Second of all, this seems false (within a mathematical system, for instance, I can offer a proof for a proposition in terms of axioms or simpler theorems which themselves can be derived from axioms – and in that sense we can talk about some mathematical proofs being accounts of ‘grounding’ within those systems). Third of all, it is at least question-begging to simply say that analytic truths are true and there’s nothing more to say about them (no possible explanation of why they are true or in what their truthmakers consist, etc.); how would you, for instance, respond to the work of people like Dr. Leftow in his book “God and Necessity” where he makes a serious and apparently viable attempt to ground modality in God. Graham Oppy, one of the world’s sharpest atheists, says about this book that “…it provides a rigorous, rich, and detailed discussion of a problem that many (and not just analytic philosophers) will find puzzling.” Now, maybe that doesn’t mean much to you, but does dismissing it with ostensibly hubristic confidence really not give you pause at all? The question of what, if anything, accounts for the truth of analytic statements is intellectually live to the rest of us. Are you so sure it’s the rest of us who are missing something?

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