Reflecting On Reflection

Reflection has ever been the philosopher’s most prized capacity, thought capable of rendering clear our beliefs as a mode of second-order cognitive scrutiny.  I intuitively believe that there is a keyboard here at my fingertips, a monitor before my eyes; I may call these beliefs into question, distancing myself from the immediate cognitive impressions they form on me.  If I reflect on these beliefs aptly, I ought to find that I have good reasons to hold these beliefs.  Indeed, some have claimed that it is just this capacity which cuts between human and animal cognition.  My (sadly hypothetical) dog cannot distance himself from the belief that we will go out for a walk when I show him his leash – he cannot question whether he has good reason to hold this belief, any more than he can question whether having arrived at this belief in just the way that he did constitutes a good method for arriving at beliefs.  However, qua human beings, our beliefs are called into question constantly, from the flights of fancy of minds in vats to the complex assignment of statistical probabilities to the possible truth-values of a possible set of facts which are thought to occur in (possibly) the real world.  Just as the line between human and animal has been drawn along these lines, so too has the line of freedom and moral responsibility.  The ability to scrutinize our beliefs with some higher-order reflective capacity seems, to some, essential to explain the phenomenology or reality of human freedom and agency.  Agency is thought to imply responsibility.  Hence, we are thought able to be judged praise or blameworthy, in virtue of our freedom to chart the paths of our own actions from among a sea of possible alternatives.

However, the value of our capacity for reflection may not hold up to close scrutiny.  In On Reflection (2012), Hilary Kornblith argues that this faculty, as we have hitherto conceived of it, is not the kind of thing which could possibly enlighten our inquiries about knowledge, reason, freedom, and normativity.  Our treatment of reflection seems to be essentially phenomenological; Kornblith notes an important dissimilarity between this, and our rather more empirical orientation towards other phenomena in the natural world.  The reader should note the operative ‘other’ in the previous sentence.  Kornblith considers knowledge and related epistemological phenomena to be natural kinds – see his arguments for a naturalized epistemology in Knowledge and its Place in Nature (2002).  This phenomenological bias manifests particularly in the common tendency of philosophers in the reflectionist orthodoxy (a poor ad hoc moniker to be sure – the category is meant to include Sosa, Korsgaard, Goodman, BonJour, and many others) to use first-person language to describe features of reflection.  Naturalized epistemology can be characterized as the view that explanations of the objects of epistemological inquiry are ultimately natural explanations, rooted in the natural world.  If correct, this view provides a strong reason for scrapping our phenomenological bias, in favor of a more empirical orientation towards epistemological inquiry – including our reflections on ‘reflection’.

Kornblith’s main arguments against the received view of reflection show that, on that view, scrutinizing our beliefs always falls into infinite regress.  When I reflect on my first-order belief B that there is a keyboard at my fingertips, I form a second-order belief B’ that I do indeed have strong reasons in support of the first-order belief.  But I do not know whether I have strong reasons in support of B’ unless I reflect on those reasons, thus forming belief B’’ that I do indeed have strong reasons in support of B’; et cetera ad infinitum.  Therefore, our beliefs are never ultimately justified, and we never know what ultimately counts as having sufficient reasons for accepting a belief.  It follows that we must remain mute on normative claims about belief formation.

To infinity, not beyond.  I suspect that the severity of an infinite regress is a pain much more immediately felt by those with a naturalist suasion.  If explanations about objects of epistemological inquiry are ultimately natural explanations, and the received view of reflection leads in every case to an infinite regress, then one is at pains to devise a naturalistic explanation of infinity.  The human brain must thereby be supposed to be capable of performing supertasks, provided we are not meant to reflect on even our most banal beliefs on into eternity.  A supertask is a task consisting of a countably infinite set of calculations or operations, which occurs sequentially within a finite amount of time.  Kornblith offers no argument as to why infinite regress is to be avoided in epistemological explanations.  Presumably, it is his naturalistic aversion to something like a cognitive supertask that underwrites his argument.  Another likely assumption is that cognitive tasks in humans are not such that they can perform operations on infinities.  This is not necessarily true – the phenomenology of reflection provides good reasons to believe that at least one epistemological explanandum (reflection itself) performs operations on infinities.  Mathematicians reflect on set-theoretic proofs involving greater and smaller infinities, as Cantor did with his diagonalization argument.  On a similar vein, Roger Penrose has argued that Kurt Gödel’s incompleteness theorems – and their subsequent comprehension and acceptance by fellow mathematicians and human reasoners – provide a strong reason to consider that human cognition must contain exponentially more processing power than any possible mechanical system could (though these arguments fall quite far short of wide acceptance themselves).  Again, this assumption falls on prima facie naturalistic inclinations.  Naturalized explanations just cannot, or cannot easily, contain infinities, greater or smaller.

I am differently inclined.  Some kind of infinitesimal calculus sounds to me like a potentially plausible way to model our capacity for reflection.  I form a first-order belief B, which defines the limit to a probability function that models my certainty in that belief (to a max- or minimum infinity).  Reflective scrutiny is hence a process somewhat like calculating a limit with reasons for belief in B, with a max-limit providing an idealized objective certainty in B, and a min-limit its absolute refutation.  We can no more conceive of each of the elements in an infinite set than we can the requirements of absolute certainty in or refutation of B; we can, however, form a transcendent ideal of the concept at hand in order to understand some part of it.  Here, I am somewhat indebted to a colleague from during my undergraduate work in Victoria, who once described Anselm’s ontological proof to me as calculating a limit towards God’s existence.  Of course, the procedure that I propose would involve some sort of conceptual analysis, or analysis of our epistemic intuitions.  Experimental philosophers have recently raised many issues with this practice, which I haven’t the space to consider in this post – see especially Stitch’s The Fragmentation Of Reason (1990), and Alexander and Weinberg’s “Analytic Epistemology and Epistemic Intuitions” (Philosophy Compass 2/1, 2007).

Infinite regress only seems menacing if we share Kornblith’s epistemological naturalism; otherwise, his main arguments against the received view of reflection simply are not knockdown arguments.  Kornblith often takes Ernest Sosa’s epistemological views as his target in On Reflection.  Sosa is a main proponent of the use of a virtue vocabulary to describe and reflect on our standards of excellence in all matters epistemic.  I believe that the cultivation of epistemic virtue might have some import to a view modeling reflection as an infinitesimal probability calculus operating on our beliefs.  Consider the phenomenon, familiar to many and well-studied by psychologists, linguists and other researchers in the field of child development, of the explosion of explanation-seeking questions in preschool aged children.  The attitudes of many parents towards this phenomenon are neatly summed up by comedian Louis C.K. in the following routine.

Children between roughly the ages of 2.5 and 5 never seem to know when to stop asking why.  The increasingly metaphysical nature of Louis’ daughter’s questions demonstrates a certain tendency to exceed what adults typically consider to be sufficient reason for holding some belief.  The phenomenon is particularly well documented in Frazier et al, “Preschoolers’ Search for Explanatory Information Within Adult-Child Conversation” (Child Development 80/6, 2009).  They will often seek to over-explicate their beliefs, because a reasonably reliable calculus for belief acceptance has not yet been developed.  Refinement of this calculus would constitute the cultivation of an epistemic virtue, essentially inscribing on one’s cognition a sort of cut elimination theorem.  As is the case with the cultivation of virtue in general, experience is required, to establish a mean relative to the individual child between excess and deficiency with respect to explanations.  Children must become proficient in the use of explanatory language, with causal connectives and representational concepts, to add to their own epistemic intuitions.  A pre-theoretic epistemic intuition such as ‘justification’ is refined by honing in on a reasonably reliable mental probability calculus to operate on our beliefs.

If it is plausible to model reflection on our beliefs as a probability calculus – and certainly more argument is required than what little I have entertained here – then a strong counterargument to Kornblith’s naturalized epistemology exists.  I agree with Kornblith’s assumption, that natural explans cannot, or cannot easily contain infinities.  All the more reason not to consider epistemological kinds as natural kinds.  In Metamind (1990), Keith Lehrer develops a different account of the human mind: the human mind is a metamind.  It is a representation of mind.  This is to say that the human mind in some sense essentially transgresses the natural, at least as Kornblith conceives of it.  Again, for lack of space, I cannot here entertain the idea that something like a metamind might better ground the argument that reflection is a sort of (meta-)mental probability calculus.  I shall continue to reflect on these thoughts henceforth, for a time.  For now, suffice it to say that Kornblith’s main arguments against the reflectionist orthodoxy are grounded in assumptions informed by his epistemological naturalism; unmoved by this proclivity, I lean towards a view like Lehrer’s.  The burden of argument falls on Kornblith to tell us why infinite regress is a bad thing, even if we do not wish to accept epistemological naturalism.  However, I find myself more inclined towards cautiously abandoning naturalism, to test the limits of infinity as an explanatory concept in the reflective scrutiny of our beliefs.  And I suspect that this endeavour shall keep me asking, “Why?” ad nauseam; in this, the philosopher resembles the preschooler.  Perhaps, a preschooler who has grown up having poorly refined the virtue of knowing how much reflection is sufficient for the reasonable acceptance of our beliefs!