That explanations are ubiquitous in science will be taken for granted. Scientists, or at least a great many of them, hold that science not only seeks to describe and organize natural phenomena, moreover, can and does explain these phenomena.
But what exactly is an explanation; how, if at all, is one explanation better than another; and what, if anything, distinguishes a scientific explanation from the common-or-garden variety? How are we to understand oft-heard pronouncements in scientific discourse that, for example, such-and-such a theory offers the best explanation for such-and-such a domain of phenomena, or that such-and-such is a theory of great explanatory power? Is explanatory goodness an epistemic virtue? In other words, all else being equal, does a hypothesis-theory attributed with a high degree of explanatory power merit greater epistemological warrant than a scrawny rival with punier explanatory muscles? Put another way, do we have more reason to believe that the former is true?
As far as I understand, the first attempt at providing a philosophical explication of scientific explanation was unveiled around the middle of the last century by Carl Hempel and another fellah -- Paul Oppenheim -- who, much like an Alfred Russell Wallace or a chaperone on a hot date, is regarded, if at all, as an annoyance and ignored. The present monograph will uphold this noble tradition of disregarding unwanted ballast.
Accordingly, and simplifying slightly, Hempel's [sic] explication consisted of two elements. A scientific explanation can be subsumed under either:
(i) the deductive-nomological (or D-N) model, also commonly known as the covering law model, or
(ii) the inductive-statistical (or I-S) model
Under the D-N model, scientific explanation takes the form of a deductive argument: the event or phenomenon to be explained (the explanandum) is construed as the conclusion of a deductive argument derived from the initial conditions and one or more true scientific laws (these premises jointly constitute the explanans -- that which does the explaining). In other words, given the initial conditions and the relevant law or laws of nature, the event in question had to happen.
It goes without saying that scientists, by and large, do not present their own explanations in accordance with the Hempelian protocol. What Hempel is attempting, rather, is what philosophers, particularly those of a positivist persuasion, would describe as a rational reconstruction of actual scientific practice.
Clearly, though, not all events and phenomena of interest to science can be subsumed under such a strict relationship of deductive entailment. Enter the second component of Hempel's account of scientific explanation, the I-S model, applicable to cases where the relevant laws are merely statistical rather than strictly deterministic. Whereas under the D-N model the explanandum is entailed by the explanans, with the I-S model the explanandum is supposedly explained in virtue of the high degree (> 0.5) of likelihood conferred upon it by the explanans.
Think, for example, of poor Higgins, say, who kicked the bucket at the prime of life after thirty years of smoking four packs of Camels per day. Now, given that his identical twin and fellow quotidian quadropacker continues to puff away undeterred, Higgins' untimely demise does not comfortably lend itself to the D-N mode of explanation. On the other hand, so Hempel's account goes, the I-S model can be deployed in cases such as this to yield a bona fide scientific explanation insofar as Higgins' smoking predilections rendered the outcome -- though by no means inevitable -- highly probable.
The premises of the full, unpacked I-S argument in this case, therefore, would consist of both Higgins' smoking habits, i.e., the initial conditions, together with the relevant statistical laws pertaining to smoking cigarettes, nicotine, lung cancer, and so on. The conclusion of the argument -- the explanandum, a statement of the event to be explained -- would be something like "Higgins contracted lung cancer" or "Higgins died of lung cancer".
Herr Hempel himself explains the manner in which his I-S model explains:
Thus, probabilistic explanation, just like explanation in the manner of schema (D), is nomological in that it presupposes general laws; but because these laws are of statistical rather than of strictly universal form, the resulting explanatory arguments are inductive rather than deductive in character. An inductive argument of this kind explains a given phenomenon by showing that, in view of certain particular events and certain statistical laws, its occurrence was to be expected with high logical, or inductive, probability.
Now, if there's one thing philosophers with no lives and too much free time on their hands are devilishly good at, it's coming up with catastrophic counterexamples to ruin a respected colleague's life work. In the years following the publication of Hempel's pioneering forays into the realm of scientific explanation, various scenarios were concocted purportedly exposing the shortcomings of the Hempelian project. Both D-N and I-S model alike, we were told, constituted neither necessary nor sufficient conditions for scientific explanation. That is to say, scenarios were devised which fail to satisfy the Hempelian criteria, yet seem intuitively to be perfectly good cases of scientific explanation; and conversely, other scenarios were put forward that do satisfy the Hempelian criteria, yet intuitively don't appear to be the kinds of creatures to which we'd want to ascribe the epithet scientific explanation.
In the particular case of the I-S model -- the one that concerns us here -- the failure of Hempel's criteria to constitute necessary conditions for scientific explanation is demonstrated in the literature over and over, time and time again, ad infinitum, ad nauseum, with precious few exceptions, by the same hoary, timeworn example: of all things, wait for it... syphilis!
Explanation guru Wesley Salmon elaborates:
If someone contracts paresis, the straightforward explanation is that he was infected with syphilis, which had progressed through the primary, secondary, and latent stages without treatment with penicillin. Paresis is one form of tertiary syphilis, and it never occurs except in syphilitics. Yet far less than half of those victims of untreated latent syphilis ever develop paresis. Untreated latent syphilis is the explanation of paresis, but it does not provide any basis on which to say that the explanandum-event was to be expected by virtue of these explanatory facts. Given a victim of latent untreated syphilis, the odds are that he will not develop paresis.
There we have it. Hempel, on the one hand, tells us that to be a self-respecting scientific explanans, short of entailing your explanandum-event, you'd better at least make it likely. Appeal to antecedent, untreated syphilis, on the other hand, seems intuitively to afford a perfectly satisfactory explanation for the dreaded paresis which follows, yet, contra Hempelian explanatory strictures, the syphilis does not render the development of paresis probable.
High probability, we conclude with a coquettish pout, does not in fact constitute a necessary condition for scientific explanation. And that was just an assault on one front. The upshot of all this violence, then, is that despite being enormously influential, cited frequently by scientists themselves as an explanatory paradigm, Hempel's model is nonetheless fubar. QED.
Meanwhile, Bas van Fraassen, who attained vertiginous fame for his own "pragmatic" theory of scientific explanation, continues to flog the venereal dead horse:
Second, not every explanation is a case in which good grounds for belief are given. The famous example for this is paresis: no one contracts this dreadful illness unless he had latent, untreated syphilis. If someone asked the doctor to explain to him why he came down with this disease, the doctor would surely say: 'because you had latent syphilis which was left untreated'. But only a low percentage of such cases are followed by paresis. Hence if one knew of someone that he might have syphilis, it would be reasonable to warn him that, if left untreated, he might contract paresis -- but not reasonable to expect him to get it. Certainly we do not have here the high probability demanded by Hempel.
Quite so. Although another explanation that springs immediately to mind for why he came down with the dreadful paresis is: 'because you're a shameless whoremonger who hangs around in seedy brothels', though, given the circumstances, to say as much might be considered indelicate. Indeed, perhaps Bas van Fraassen has precisely this kind of contextual sensitivity in mind when he speaks of the 'pragmatics' of explanation. But let us not divagate...
So, now, let's have a show of hands: who else is sick of hearing about syphilis and paresis? There must surely be some knight in shining armor out there can come up with an alternative counterexample to refute the putative necessity of Hempel's V-D model of scientific explanation. Er, I mean I-S model.
Fear not, friends, relief is at hand. But first, trivia time: Did you know that back in days of yore an apron used to be a napron, and that a notch was once an otch? You didn't, eh? Well, turns out that thanks to the peculiarities of the English language and her duo of indefinite articles, nouns such as napron and otch are susceptible -- via a phenomenon known as "rebracketing", or more specifically "false splitting" -- to either acquiring or shedding an initial /n/ sound. Thus napron morphs into apron, and otch gets botched as notch.
Read all about it here:
http://www.quickanddirtytips.com/educat ... e-an-apron
http://en.wikipedia.org/wiki/Rebracketing
Grit your teeth if you have to, but for the sake of ridding the world of syphilitic counterexamples, all members will now magnanimously grant linguistics the status of a bona fide science. Furthermore, it will be supposed that the above account of linguistic rebracketing has been approved and endorsed by a leading linguistics hierophant. Someone we can trust; Noam Chomsky, say, or if he's busy, Quang Phúc Đông.
What more could one ask for? A scientific explanation par excellence is at hand, viz., the transmutation of an English word like nadder into adder is explained by the linguistic phenomenon of false splitting.
Well, yeah. Except that there is clearly no universal law governing n-switching. Neither can it be plausibly upheld, judging by the paucity of instances Wikipedia is able to adduce, that unsuspecting false-splitting candidates such as anaconda, oboe, or umbrella are even remotely likely to undergo the transition into nanaconda, noboe, and numbrella, respectively.