In Response to Peter Keeble/Two Kinds of Intelligibility

Peter Keeble's article 'The Philosophical Method of Exception' (Philosophy Now, Issue 169) prompted my piece 'Two Kinds of Intelligibility / What Induction Cannot Explain.' Peter kindly responded to me by email after reading the expanded version on this site. What follows is the exchange.

Peter Keeble, by email, 17 April 2026:

Hello Aoife

Rick Lewis passed on your letter (sadly too late for publication in PN) to me and I hope you don’t mind if I respond to the interesting points it raises. Actually, I struggled to understand the letter but then found the expanded version on you website which I got to grips with much more easily.

 So, yes, the broad distinction between human-imposed probabilistic understanding and reality-based structural necessity is one I did not refer to, and it is an interesting one. It also plays into an area I’ve been devoting much thought (and writing) to recently, which is the adaptation of Aristotle’s idea of natural kinds by the philosopher Brian Ellis and how this relates to Hume’s scepticism about induction. I think in the terms that you lay out Hume would see induction as human-imposed and based on the probabilistic psychology of constant conjunction, whereas Ellis, Aristotle, me and I think you are realists in the sense that we believe there are physical structures that necessarily lead to certain effects from certain causes. It’s a fascinating debate and I’m not quite convinced that Hume cannot always retort that the structures do in fact not have inevitable results and we just think they do. That seems to me to be a sort of supernatural account of nature (anything could cause anything), but a difficult one to refute. It also collapses the distinction you highlight by saying there are no structural necessities or that at least we are unable to know them, only our unjustified imposition of regularities on an unfathomable world. 

Feel free to put this up on your website and to respond to it if you would like to.

All the best

Peter Keeble

post script: I’ve copied Rick in in case he’s interested.

Aoife in response

Many thanks to Peter Keeble for his thoughtful and generous response, and for taking the time to engage more fully with the expanded version of my piece.

I would like to begin by slightly adjusting the framing. The distinction I was trying to draw is not quite between human-imposed probabilistic understanding and reality-based structural necessity as such. Rather, the axis that interests me is epistemological: not whether structural necessity exists, but what happens when our justification for it fails.

In this respect, Hume's position is often taken to imply something like a collapse into arbitrariness - that anything could in principle cause anything. But strictly speaking, this is not his claim. Hume's point is that we have no justified grounds for believing in necessary connection, not that there are none. The difficulty, then, is not metaphysical but epistemic.

This is where I find the pressure of the problem becomes most interesting. The question is not simply whether we can defend structural necessity against Humean scepticism, but what is revealed when such a defence cannot be secured. The breakdown of justification does not merely threaten the distinction - it makes visible the difference between two kinds of intelligibility that ordinarily go unmarked.

From this perspective, the appeal to realism (whether in Aristotle or Brian Ellis) does not quite resolve the difficulty, since the question of how necessity is accessed remains in place. The issue is not only whether structures necessitate outcomes, but how such necessity becomes intelligible to us at all.

Here I think a contrast with geometry is instructive. A square will not have three sides at some future time T. This is not a probabilistic expectation, nor is it subject to revision by experience. It expresses a form of intelligibility that is not mediated by induction, and which Hume's scepticism does not seem to reach.

My suggestion, then, is that the problem is less about choosing between Hume and realism, and more about understanding the structure of the tension between them. It is in that tension - rather than in its resolution - that something important about our knowledge of the world comes into view.

This remains an open question, and one I hope to continue exploring here.