three types of certainty

Whatever exactly certainty amounts to, we can think about it using the framework of possible worlds. To begin with, as typically understood, ¬p is epistemically (rather than metaphysically) possible for me iff I do not know that p. Is this the sort of possibility that we should employ when thinking about certainty? Well, since most of us nowadays distinguish between knowledge and certainty, the answer is: probably not. To see this, think about cases where I do know that p, but still have some doubts about p. That is something that happens quite often, and it seems our analysis should accommodate this datum.

The term “epistemic possibility” is better reserved for something else, in any case. Here I’ll assume that epistemic possibility is co-extensive with doubt or dubitability, where the latter is construed as a self-confirming state. Since knowledge is arguably not indubitable in this sense, epistemic possibility should be understood so that the epistemic possibility that what I believe is false is compatible with that belief being knowledgeably held.

Thirdly, let’s stipulate that certainty also ought to involve indubitability in this sense, so that putting the two equations together we get:

is dubitable for S ↔ S is uncertain that p ↔ it is epistemically possible for S that ¬p

Finally, before getting further into the question of how to analyse epistemic possibility, structurally speaking it seems that any analysis must agree with the following requirements:

  1. That epistemic possibility involves compatibility with my epistemic state, if not with what I know, then with e.g. what I justifiably believe, or what I know that I know, or some other thing.
  2. That at the reflective or second-order level, when I consider whether is epistemically possible for me I am considering whether the metaphysical possibility of is excluded by, or consistent with, what I take my epistemic position to be. That doesn’t mean that whatever is epistemically possible must thereby be metaphysically possible, as, to give just one example, many necessary falsehoods are epistemically possible for me (and perhaps also for you, dear reader). At the first-order level, we can say that an epistemic possibility is or involves a relation between a proposition that is a candidate for metaphysical possibility, and a set of propositions M that describe my epistemic position.

Now, it is normal to distinguish between subjective and objective certainty, in roughly the following way:

subjective certainty: this is a state akin to supreme confidence as felt “from the inside”, that in principle does not guarantee anything. Subjective certainty is frequently described as a “psychological” state, such that, in particular, I might be subjectively certain that even though is false. To be clear, I take for granted here that, after having absorbed enough epistemology, the likelihood of such an occurrence diminishes to a vanishing point. In this way, subjective uncertainty approximates to a normative state after all: it is the state I am in when lacking the property, whatever exactly it is, that I would have if I were legitimately subjectively certain in the bare psychological sense. To get this legitimacy, I suggest, I would need to have some sort of special access to my being objectively certain.

objective certainty: this state at least guarantees the truth of my belief, but is not in principle transparent to me, i.e. I might falsely believe that I am or am not objectively certain that p. Objective certainty is usually understood as something like perfect objective probability or reliability, etc.

With these two characterisations in place I want to offer a third – absolute certainty – which mixes these two states but is not merely their sum. Basically, absolute certainty is transparently or immediately objective certainty, it is supreme confidence that can reflexively access its own guarantee-conferring property with supreme confidence, etc. What I am calling “transparency” or “immediacy” here is the third element not present in either subjective or objective certainty taken alone. Thus, note that whilst the absence of either subjective or objective certainty suffices for the absence of absolute certainty,  their conjoint presence only approximates to a state of absolute certainty (I won’t try to be more precise about this here.)

The question I would like to begin by exploring in this post is an old one: if everything is uncertain, is this fact also uncertain? Focus on subjective uncertainty. Here we have an interesting situation. On the one hand, from our finite viewpoint, it appears the divide between subjective and objective certainty cannot, in principle, be bridged. This is due, it seems, to the impossibility of the transparency of absolute certainty, the latter being the state that would unite them. Moreover, this is to be expected if we equate uncertainty with epistemic circularity: since anything I could believe would be justified in an epistemically circular manner, nothing is certain – including this fact about epistemic circularity. It seems we are stuck in the straightjacket of absolute uncertainty.

On the other hand, given the equation of uncertainty and epistemic possibility, if I am uncertain that everything is uncertain for me at T1, then it is epistemically possible for me at T1 that not everything is uncertain, in other words, my epistemic position is compatible with my being certain about something at T1 – it does not rule out the (metaphysical) possibility of my presently being certain of something.

Here then is our puzzle: by hypothesis, if everything is absolutely uncertain, then this proposition too is absolutely uncertain. That means that my epistemic position is compatible with something being absolutely certain for me. But surely if my epistemic state is such that everything is uncertain for me, this is not compatible with my also being certain of something (paraconsistency aside). Yet, if these are incompatible, it follows that it is epistemically impossible for me that I am presently certain of something, which is also contradictory – given the premise that epistemic impossibility is always the flip-side of certainty – since it is thus equivalent to saying I am certain that I am certain of nothing.

Nor can we simply accept this contradiction and continue merrily on our way. Absolute certainty, as I understand it, is the ultimate reflexive, self-transparent and immediate state. It is akin to the divine gaze, divine knowledge. As such, it is not the sort of state I could be uncertain about being in – its presence would be emphatically beyond question. The problem is that by trying to leave open the possibility that I am presently certain of something, I am effectively trying to countenance the possibility that this is not so, i.e. that the absence of absolute certainty is not itself a matter of absolute certainty. But that doesn’t seem to make sense. The puzzle, to reiterate, is that something like absolute certainty could only be conspicuously present, and so its absence must be conspicuous also.

Given this seeming reductio, the interesting thing is that it does not quite produce in me a state of absolute certainty. Part of the reason for this might be that the sort of transparency involved in absolute certainty actually requires omniscience, understood as involving an actual (rather than merely potential) infinity of belief states – i.e. a belief set of such immense magnitude so as to be forever outside my reach. In a nutshell, it is hard to feel certain about something that I have not consciously entertained, or could not entertain. (As such, it might be better to think of the divine light of certainty as occluded behind the moon of finitude, in a state of perpetual eclipse – rather than as flowing straightforwardly through to us.) I think this usage of the actual/potential infinite distinction helps us understand what is going on here with the sceptical dialectic. The unshakability of uncertainty (what we might call the normative opacity of belief) seems itself to be quite certain, and yet not: it eludes the gaze of certainty but in doing so confirms itself once again, almost as if approaching certainty at the limit. To put things in slightly different terms once again, the problem is that uncertainty requires perfect indistinguishability (of my epistemic position and some other incompatible state), whereas certainty is the opposite, perfect distinguishability: an uncertainty of uncertainty is therefore the possibility of a state at once perfectly distinguishable and yet perfectly indistinguishable from impostor states.

Classically speaking the reductio can be concluded here. Might this push us in the direction of the paraconsistent? Have we reached a new dialetheia beyond the limits of thought, as Graham Priest might suggest? As I said above, I doubt whether the dialetheist can do much better here. For one thing, the concept of absolute certainty appears to materially exclude uncertainty: that is, it is not the sort of thing that can be modelled as true and false in some paraconsistent logic. Of course, what I am saying here is question-begging according to the sceptic, and this charge can now be helpfully recast as follows. It is a version of the charge that there is, after all, no way to enter “The System”. By analysing the concept of absolute uncertainty and arguing that it cannot apply to itself, I have (the sceptic says) been reasoning from within the system, whilst pretending (in effect) to be offering a neutral means of entering it. I have been proposing our very inability to enter as a means of entry – and the sceptic thinks this is hopeless. Are we then going in circles? Let me at least offer a modest alternative to this pessimistic conclusion. Remember that the sceptic cannot say that certainty is epistemically impossible, since that is to say she is certain that there cannot be any certainty. But if I am right she cannot say it is possible either, and thus cannot assert the uncertainty of uncertainty. That is why I said above that perhaps the sceptic is ultimately reduced to not really saying anything, or to saying something inconsistent. This seems like an interesting result, even if it is not enough to break to interminable debate between sceptic and non-sceptic.

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