Knowability and a Dilemma for the Naturalist

In a previous post I argued that the knowability of truth entails an omniscient mind. But the whole argument is predicated on the knowability principle, KP, which states that truth can be known. But, who would defend such a position? “Only theists” one might suspect. As it turns out, KP follows upon some versions of anti-realism and idealism.1 Of course, in light of the paradox, many anti-realists have modified their form of anti-realism so that it does not fall prey to “paradox”.2 Whether these more subtle anti-realists escape the knowability paradox is still a matter hotly debated (Brogaard 2009).

The (naïve?) anti-realist is not the only one who commits herself to KP. Verificationists, like the logical positivists of yesteryear, also hold to KP, since meaning is predicated on analytic or empirical verifiability.3 If KP is expressed in the slogan “To be true is to be provable”, one can still faintly hear Ayer and his acolytes chanting their implicit consent to KP. Ironically, so long as the positivists admit that there is a maximally big conjunctive truth, they would have to concede that an omniscient mind exists. How embarrassing!

Perhaps less surprising, though also worthy of note, is that Aquinas, a metaphysical realist, would also be a proponent of KP:

There is nothing, however, that the divine intellect does not actually know, and nothing that the human intellect does not know potentially, for the agent intellect is said to be that “by which we make all things knowable,” and the possible intellect, as that “by which we become all things.” For this reason, one can place in the definition of a true thing its actually being seen by the divine intellect, but not its being seen by a human intellect, except potentially, as is clear from our earlier discussion (De Veritate Q. 1,A.2).4

I mention this because the literature on the knowability paradox seems to equate KP with antirealism. But, as Aquinas proves, there is no reason why KP should be restricted to anti-realism.5 It is clear that for Aquinas all things are known to some mind, i.e. God, and knowable to all other minds. Of course my non-theistic interlocutor should hardly be moved by any of this, unless she were to embrace the particularities of Thomistic psychology while eschewing his metaphysics. I suspect dodos would be less rare.

I would also like to consider some objections to KP. Some of my interlocutors have already countered my claims that all truths are knowable by referencing the Münchhausen trilemma or Gödel’s incompleteness theorems. Münchhausen trilemma offers us three options, each of which appear to be untoward for the tenability of epistemology. The trilemma runs as follows:

1. Justifications for some knowledge must be justified, ad infinitum, which abandons foundationalism.
2. Justifications are eventually circular, which means that knowledge is question begging.
3. Justifications are not sought for some truths, which abandons justification arbitrarily.

But before we despair, its readily apparent that the trilemma is answered by various epistemologies. Infinitists take the first horn. Infinitism does not abandon knowability, but argues that knowledge may be justified by an infinite chain. I wouldn’t personally take this horn, but it seems to me that many, especially non-theists, claim to have no problem with infinite regresses. For justification can emerge out of the infinite chain of reasoning much like an effect can arise out of an infinite sea of prior causes. So, if my non-theistic interlocutors reject knowability on the basis of this trilemma, I might ask them to reconsider the force of Thomas’s Five Ways.

The second horn is accepted by coherentists. They reject the charge that these, so called, loops of justification beg the question. Rather, they see knowledge in a holistic way. Beliefs fit within a reinforcing and consistent web. The literature is rife with defenses of this position, so it is at least a plausible alternative to utter skepticism.

Furthermore, it seems to me that the Reformed Epistemology argues that justifications are unnecessary in knowing some truths, i.e. those truths that are properly basic. But this is not to embrace the third horn, since there are specific conditions offered by which a belief can be considered properly basic. Hence, stopping points are not inherently arbitrary, or in violation of some PSR. Even the foundationalist typically will concede that the law of non-contradiction needs no support. But RE allows for stopping points that extend beyond mere logical principles and analytic truths, and so extends the foundation of knowledge out much further.

So the Münchhausen trilemma does not force us into some form of Pyrrhonism, nor does it explicitly assert that some truths are unknowable. It merely forces us to think more clearly about epistemology, which is a good thing. So in my assessment, the Münchhausen trilemma is not a good reason to reject KP.

As for Gödel’s incompleteness theorems, while they do seem to suggest that truth transcends proof, it should be noted that “proof” must be understood within the context of an axiomatic system, and does not mean justification or warrant in some broader epistemological sense. It is for this reason that we cannot simply concede to the highly controversial thesis that the results of the incompleteness theorems are applicable to human minds, or any other minds for that matter. In fact, Lucas and Penrose have argued that Gödel’s theorems are an indication that the mind is not a Turing-Machine, that human intelligence is not restricted to axiomatic proofs, and that truths that no machine could know, can be known to us. If so, AI will never be analogous to human intelligence. In sum, I do not think it is compelling to say that Gödel’s incompleteness theorems count against KP without the additional support of the premise that all minds are functionally equivalent to Turing machines.

So, I have suggested that there are philosophical defenders of the knowability thesis, both realists and anti-realists, theists and atheists. Also, I have defended KP against the two main objections raised by my interlocutors thus far. Still, are there any good reasons to endorse KP? I have no deductive argument or a priori argument to offer. I’m an optimist, and I’d like to think that all truths can be known in principle. Absent a defeater, I think there are good inductive reasons for accepting KP. They can be summarized as follows:

1. No specific instance of a truth that one might point to is unknowable.
2. Therefore, all truths are knowable.

(1) is equivalent to the fact that all specific instances of truth that one might point to are knowable. In other words, KP is continually confirmed, and counterexamples are not forthcoming, and never will be forthcoming. For to confirm the truth of a counterexample would require that we know that something unknowable is true, which is a contradiction. If induction may be used to support a principle, then it certainly offers abundant evidence in support of KP.

One last point, and this is for the naturalists:

Suppose the metaphysical naturalist were to reject the knowability principle in an attempt to escape my argument for an omniscient mind. The rejection of the knowability principle would entail that there are some truths that cannot be known, verified, etc. by our best, or even ideal, natural sciences. If a truth is defined as natural insofar as it comports with and can be subjected to analysis and empirical verification by a natural science, it follows that there would some non-natural truths. This raises an interesting dilemma for the metaphysical naturalist:

1. Either all truths are knowable, or not all truths are knowable. (LEM)
2. If all truths are knowable, then an omniscient mind exists. (see this post for proof)
3. If not all truths are knowable, then some truths cannot be verified by the natural sciences even in principle.
4. If some truths cannot be verified by the natural sciences in principle, then metaphysical naturalism is false.
5. Therefore, either an omniscient mind exists, or metaphysical naturalism is false.

I think both disjuncts are true, but it seems that we are forced to pick one! And its on odd metaphysical naturalist who admits that there is an omniscient mind.

1 B. Brogaard & J. Salerno, 2009. “Fitch’s Paradox of Knowability”, The Stanford Encyclopedia of Philosophy (Winter 2012 Edition), Edward N. Zalta (ed.), URL = <;.

2 S.A. Rasmussen. 2009. “The Paradox of Knowability and the Mapping Objection”. In New Essays on the Knowability Paradox. Ed. J. Salerno. New York: Oxford University Press. 53-54

3 J. Beall “Knowability and Possible Epistemic Oddities”. In New Essays on the Knowability Paradox. Ed. J. Salerno. New York: Oxford University Press. 113-4

4 Thomas Aquinas. 1952. Questiones Disputatae de Veritate. Trans. Robert W. Mulligan, S.J.Chicago: Henry Regnery Company. Ed. Joseph Kenny, O.P. Accessed July 20, 2013. URL = <;

5 Plantinga seems to identify Thomas as a theistic anti-realist, since Thomas thinks that truth would not exist without minds. However, Thomas is careful to note that “truth”, though found primarily in the intellect, is secondarily found in things. It is for this reason that I reject Plantinga’s assessment. See A. Plantinga. 1982. Proceedings and Addresses of the American Philosophical Association, Vol. 56, No. 1. 47-70

Posted on July 20, 2013, in Arguments for God and tagged , , , . Bookmark the permalink. 3 Comments.

  1. Great work! I know this is an old post. But I’m still curious: why do you think (4) is true?

    • Hi Bálint, I think I was taking it as definitional of metaphysical naturalism that all truths can be verified through the natural sciences. I suppose one might defend a position of naturalism such that all the truths that are possibly verifiable are verifiable through the natural sciences.

  1. Pingback: A Video on the Modal Epistemic Argument | vexing questions

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