In my last blog post, I took up the idea that fallibilism should be taken seriously in the philosophy of mathematics. In doing so, I did not mean to imply that philosophers of mathematics (or mathematicians for that matter) deny that we are fallible creatures. Rather, my intent was to state, following Tymoczko, that fallibilism has highly non-trivial consequences. To that end, I will here concentrate on some of such consequences, though not in the philosophy of mathematics, but more generally.
Let us take an ordinary claim such as (1) “That is a table over there”. How does one go about seeing whether (1) is the case? One might ask others whether there is a table over there, one might go and try to touch the table, and so. Why would one do that? Because bitter experience has taught us that we are occasionally mistaken about our sensory experiences. That is, we might be mistaken. The same goes for memory, deduction and so on. An important part of (at least some kinds of) knowledge is being cognisant of the possibility of mistakes and working to avoid them. We are more certain of (1) if others agree that there is indeed a table there, more certain of our calculations and proofs if we (and others) have checked them, more certain of our experimental results if they have been vetted and replicated.
I have now linked knowledge to the possibility of checking for mistakes, but is this appropriate? Is it not enough that we acknowledge the possibility of mistakes? Do we need this idea of checking for mistakes on top of that? Yes, we do. Why? Because simply admitting “I might be mistaken” without any means of checking whether I actually am mistaken, is either a call for scepticism or just empty posturing – putting on airs of epistemic virtue. So, any fallibilism worth its salt will require the possibility of checking for mistakes.
Let me now turn to some of the consequences of fallibilism. When we come to accept that we are fallible, we can start doing things to ensure that we are not, after all, mistaken. This will be relatively straight-forward in the case of sensory experience, memory, calculation, and deduction. We use different modalities, check archives and records, redo calculations, and – importantly – collaborate and corroborate with each other. But what about intuitions, revelations, and the like? As long as these are about matters we can independently check, we are fine. But what if they are not? Notable cases here are (some) metaphysical theories, theological claims, and – interestingly enough – some claims in physics and mathematics.
Take the claim (2) “a person seeing something red will have the quale ‘red’”. If we define qualia in accordance to the usual way as “non-behavioural, non-neurological, and completely intrinsic properties of conscious experience,” we will face the following problem. What would count as being wrong when asserting (2)? We might ask that person, but that will only give us behavioural evidence. We might use neural imaging, but that will only give us neural evidence. So, while one might concede to the possibility of mistake in claiming (2), one will have no way of checking whether (2) is indeed the case.
For similar reasons the same problem holds for the theological claim “the change of the whole substance of bread into the substance of the Body of Christ[.] [B]rought about in the eucharistic prayer through the efficacy of the word of Christ and by the action of the Holy Spirit. However, the outward characteristics of bread […] remain[s] unaltered[.]” (Vatican 2005.) There is no way of checking whether such a change has occurred.
In quantum physics the claims that in measurements the world splits into two (or more) worlds, or alternatively that there are Bohmian trajectories, or that the wave function is simply a representation of an agent’s degree of beliefs, are all similarly removed from any possibility of checking – here for the simple reason that all interpretations of quantum mechanics have the same empirical content.
A proponent of such claims will be at best a fallibilist in name only! True fallibilism forces us to be quietists about such claims until such time that a check is possible.
Vatican (2005): Compendium of the Catechism of the Catholic Church. Libreria Editrice Vaticana, https://www.vatican.va/archive/compendium_ccc/documents/archive_2005_compendium-ccc_en.html