Abstract
In this paper, I consider the relationship between coming to understand why something must be the case and coming to understand why it actually is the case in some particular instance. Peter Lipton uses the possibility of coming to understand a phenomenon via a necessity proof as an argument that there can be understanding with no explanation. Lipton’s argument has come under criticism, at least partially because one might think that understanding why something must be the case has a different object from understanding the actual phenomenon. In this paper, I argue that that under certain circumstances it is fairly straightforward to come to understand an actual phenomenon on the basis of knowing why it had to be the case. Rather than relying on brute intuitions, my primary strategy will be to show that on least some modern accounts of understanding we can validate Lipton’s general point with respect to a variety of possible necessity relations.
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Notes
For purposes of this paper I am primarily considering cases that are absolutely necessary—i.e., where there is no contingent fact that itself is responsible for the necessity. I will return to cases where the claim of necessity can itself be interpreted as contingent with the discussion of physical necessity in Sect. 5.3.
Interestingly, the author (Randall Munroe) does not present this fact as understanding conducive, though I will argue later that he should have.
At least, I take it to be so in its modern-day presentations. Khalifa (2017, 135) argues that in its historical context it was only partially a guide to understanding by way of refuting Aristotelian notions. However, he acknowledges that this is not how Lipton uses the example, and it is certainly often used in classrooms divorced from discussions of Aristotle.
Or this group of attempts at fire-starting—see section Sect. 5.3 for why the statistical nature of the second law might require tweaking the example slightly.
Examples of people who allow for non-causal explanation and understanding include Grimm (2010), Lange (2016), Steiner (1978), and many others. Even one of the main proponents of causal explanation, James Woodward (2003) acknowledges that there are other forms of explanation and understanding as well (see his Sect. 5.9).
I borrow this example from a talk I heard roughly ten years ago, but regrettably I cannot remember who the speaker was. I apologize.
I follow Salmon (1989) in thinking that Hempel’s account is ultimately about expectability rather than causation, but nothing turns on this point.
It is unfortunate that Lipton didn’t select the name “Cain”.
Suppose that Baker was sinful and that God cannot tolerate sinners winning boxing matches.
There are numerous excellent works on how things can be approximate truth well enough to suffice for understanding, such as Khalifa’s Understanding, Explanation, and Scientific Knowledge (2017).
Technically this is a case of understanding a non-occurrence via an impossibility rather than a phenomenon via a necessity, but (aside from the terminological confusion engendered by frequent double negatives) this difference does not run very deep.
One reader was concerned that this caveat makes the central claim of this paper contextual—whether something suffices for understanding depends on what one cares about. I take this as a feature rather than a bug, as whether someone understands really does seem to vary by context—see Wilkenfeld (2013) for a defense of this claim.
for the classic proof of this see https://www.math.utah.edu/~pa/math/q1.html.
As it happens it is irrational (https://www.math.hmc.edu/funfacts/ffiles/30002.3-5.shtml), but proving that is far trickier than the non-constructive proof presented here.
Intuitionistic philosophers of logic have presented other reasons for being suspicious of non-constructive proofs that have nothing to do with their possible value to understanding. For example, Dummett (as presented in Schroeder-Heister 2012) argues based on a general inferentialist approach to language that we could never learn that classical logic is genuinely valid; this paper is silent on such related issues.
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Wilkenfeld, D.A. Understanding Necessarily and Understanding Actually. J Gen Philos Sci 54, 287–303 (2023). https://doi.org/10.1007/s10838-022-09611-8
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DOI: https://doi.org/10.1007/s10838-022-09611-8