god and triviality

I find interesting the idea that God, if (s)he existed, would be a trivial being. Trivialism is the view that every proposition is true, i.e. ∀p Tp. Since every proposition is true, it is also true that every proposition is false. In this way, triviality is interchangeable with inconsistency: every proposition and its negation is true. Trivialism is stronger than dialetheism, according to which some contradiction is true, ∃p (p & ¬p). The inconsistency of God, viewed from the direction of God’s omnipotence, is a mark of power, of unboundedness.

Of course, if it is impossible for God to exist, then the existence of God is inconsistent, since (on plausible assumptions) that is just what the envisaged impossibility amounts to.  This conditional is valid if

    1. is impossible and so false in every possible world, yet also true in one of those worlds, and ex falso is available.
    2. in a paraconsistent set-up all worlds where is true and false are possible, i.e. there are no non-trivial impossible worlds.

Given (A) or (B), any atheist who believes that God necessarily fails to exist ought to believe that God’s existence is trivialising. But so what? Given this reasoning, any impossible object is trivialising – this does not quite entitle us to infer, from the premise that God’s existence is trivialising, that God is a trivial being. The question is then: is it possible to establish the connection between God and triviality before establishing that God cannot exist, in order to establish that conclusion? Although I don’t have a proof of this sort at hand, it is useful to think about how one might be constructed.

Let’s begin with the premise that there is some theological motivation for thinking of God in trivial terms. Take the following passage written by Nicholas of Cusa in the fifteenth century:

Cusanus5And it is not, as well as is, all that which is conceived to be; and it is, as well as is not, all that which is conceived not to be. But it is a given thing in such a way that it is all things; and it is all things in such a way that it is no thing; and it is maximally a given thing in such a way that it is it minimally. For example, to say “God, who is Absolute Maximality, is light” [is to say] not other than “God is maximally light in such a way that He is minimally light.”*

This can be read as positing the truth of all contradictions, of many, or perhaps even (if we are subtle enough) of none. No need to decide which – I am only highlighting a tendency, namely the tendency to equate omnipotence with the ability to burst constraints, so that when logical laws are viewed as constraints, they seem apt for bursting. Such a tendency is not expressed unambiguously in any text I am aware of in the history of thought, since the latter finds contradiction distasteful for the most part. But it does seem to exert a subterranean influence.

In any case, part of what is interesting about juxtaposing God and trivialism is the apparent certainty with which we know the latter to be false. After all, if trivialism is true, then it is true that I am presently having the experience as of a white elephant dancing on my desk. By modus tollens, since I am evidently not having an experience of this sort, it follows that trivialism is false. (A similar though perhaps less forceful observation can be made from within classical logic, assuming contradiction rather than triviality.) Now, perhaps this is not robust against every conceivable form of scepticism, but it is arguably about as certain for me as anything could be. This comparative judgement of certainty amounts to saying that the type of inference pattern and phenomenal judgement involved are common to virtually any belief we might care to form, so that no such belief could be more certain than the belief that trivialism is false.

Regardless of how strongly we estimate this certainty, the dialectical situation with regard to the trivialist is slightly different than that with regard to the sceptic. For suppose it is objected that I have used modus tollens not merely to render explicit the incompatibility of trivialism with my present experience, but as part of my justification for believing they are incompatible. I will then have begged the question. I am not sure what the best response to this is, but there are several plausible alternatives on offer. I could point out, for example, that it is impossible to beg the question against the trivialist, since she accepts the truth of all of my premises. This response seems adequate as far as it goes, but it does not provide a means of distinguishing between a seemingly illuminating argument against trivialism – like the one I have just given (hopefully) – and the banal argument that since trivialism is false, trivialism is false, which is also accepted by the trivialist.

Alternatively, I could begin by positing the existence of non-inferential justification for beliefs regarding appearances. This would allow me to say that I just see that trivialism is false, and that my use of modus tollens does not first create my epistemic position, but rather more nearly describes or models it.

It is worthwhile reflecting on what has been said just now, as it is often thought that there is an insuperable difficulty here, one touched on in some of my earlier posts, e.g. this one. To wit, how does one ‘see’ in the relevant sense without judging, and judge without depending upon a rule of inference, i.e. a license to transition between propositions affirmed?

Putting aside the first response to the charge of question-begging just formulated, the idea behind the second is to treat the definition of trivialism as a template that is placed over experience by the mind’s eye. Try to imagine what your experience would look like through this template. The whole of it is inconceivable I guess, but particular points of incongruity ought to be manifest – such as there not being any elephants on your desk. Here the absence of content is important, as that is what the challenge of trivialism boils down to: how to understand the negation of trivialism, given that it lays claim to any such negation as being already part of its content? When an artist looks at a white canvas, she wants to add something to nothing, but also to take something away from everything, namely everything that has already been painted. The canvas is a plenum. But nothing is absolutely plenary, in particular, my experience is not. There are so many things that I don’t see. This lack hollows out a modal structure that I can then describe. What I am suggesting is that consistency-preserving inferences (or at any rate, some of them) are descriptions of the structure of phenomenal experience. In a nutshell, sometimes we have the experiences before us, and we can then define positions to be incompatible with those experiences. This belies the Humean idea that experience is merely particulate and incapable of supporting modal knowledge (an idea that Hume did not consistently adhere to in any case).

Following Francesco Berto, to deny trivialism we need a basic notion of material exclusion or incompatibility, which can then be used to define a negation operator that cannot be re-inscribed within the trivialist’s position. Berto writes (2007: 310, 314):

To face a choice is to perceive an incompatibility. [The envisaged sort of incompatibility] may also be entailed by the simple and basic capacity to recognize the boundary (even a blurred one) between something and something else, between an object and another one… [My note: if this boundary is modalised into a real distinction then seeing contingency and negative triviality become very nearly the same thing.] Our sense of exclusion… comes from our having to do with mutually exclusive colour ascriptions, spatial locations, actions, and, of course, mental states.

To summarise, if trivialism were true, (by definition) its truth would be self-evident to me. Moreover, my phenomenal experience would be of everything and nothing. But my phenomenal experience is not like this, and trivialism is far indeed from being self-evidently true. (Indeed, given that trivialism requires that I be certain that I am the world’s greatest footballer, I dare say that trivialism is self-evidently false…) The trivialist (or indeed the sceptic about consistency, these being not quite identical) is confronted with the positivity of phenomenal experience. In a manner of speaking, experience immediately expresses consistency. I think it is fair to say, moreover, that it does so with something approaching certainty. In any case, whatever the precise pedigree of this argument, its cogency, together with the connection between God and triviality posited above, offers a way of aligning immediate experience with atheism.

* Quoted in Paul Kabay’s intriguing and informative book On the Plenitude of Truth: A Defense of Trivialism, (Lambert: 2010), p. 10, 23. Yes: such a book actually exists.

References

  • Francesco Berto, How to Sell a Contradiction: The Logic and Metaphysics of Inconsistency, (King’s College: 2007).
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One Response to god and triviality

  1. Pingback: univocity and nihilism | atheology: a blog about nothing

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