Yours is a very thoughtful comment.
You are quite right in wondering why I didn't mention the inability to deduce an s from an r as an explanation of the uncertainty the inference s from r. Chalk it down to internet sloppiness. I meant to emphasize (in the portion of my original comment that you discuss) the occasional role of warrants or ancillary hypotheses that license or support inferences, not the uncertainty of factual inference. (If the uncertainty of inferences had been my main theme, the principle F = MA would probably have been a bad one to use an example of what I had one mind.)
Though you are right in saying that uncertainty about the meaning of statements, sentences, or words is a source of uncertainty about a statement asserting something, I suspect that some folks would say that you are talking about different varieties of uncertainty. For example, one kind of uncertainty occurs when we are uncertain about the meaning of "relative" or when we are uncertain about the thing to which a speaker means to refer when (s)he says "Ike"; and another kind of uncertainty occurs when the meaning ["Sinn", sense] and referent of the statement are relatively plain but we are uncertain about whether the proposition in question (e.g., "Ike is John's relative", "O.J. killed his wife [ex-wife?]") is true. (I know, I know, my O.J. examples just shows how much justice there is in Vern's comment.)
I have been thinking a bit more about the way that legal scholars tend to think about inference and causality. First, my impression is that among the "legal Bayesians" only one scholar -- Richard Friedman -- expressly embraces ["embraced," Rich?] Pearl's interpretation of Bayes' nets as "the" right way of understanding or depicting factual inference. Most other "legal Bayesians" (e.g., David Kaye) have been silent on the question. Do I have that right? (Bernard [& Tony V. {a non-lawyer}], where do you stand? Is your thesis that [all?] evidence is "trace evidence" an implicit endorsement of a Pearl-like model of factual inference?) Second, I think that most traditional evidence scholars (e.g., Morgan, Maguire, Wigmore, Trautman, Weinstein) have embraced an "associationist" rather than a "causal" model of factual inference. Most of them also embraced the notion that there are ancillary hypotheses or generalizations or evidential hypotheses that have a bearing on any factual inference an
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thus need to be conisdered -- explicitl;y considered, if possible. (See, e.g., Morgan, BASIC PROBLEMS OF EVIDENCE.). The idea that ancillary hypotheses, generalizations, or principles are important in inference, or can be, is not limited to legal scholars, of course. See, e.g., Chaim Perelman, Stephen Toulmin. For an AI variant see Thomas F. Gordon, THE PLEADINGS GAME: AN ARTIFICIAL INTELLIGENCE MODEL OF PROCEDURAL JUSTICE (Kluwer, 1995).
There is more to say but, alas, I have real work to do!
Thanks again for your very thoughtful comment, Vern. You have made some very important points and I wish I had the time to say more about them.
Yours, Peter T.
P.S. One of my basic inclinations is to think that causal explanations are truly lovely things to have but that when our understanding of causal mechanisms is poor (as is often or usually the case) but we still need to make decisions and draw inferences, we need a model of inference that is not as monochromatic or as elegant as Pearl's.
If one is wedded to a "causalistic ontology" (and I count myself in that number), I suppose that one might view non-causal models of inference as way-stations (to the ultimate goal of causal models of inference). Having said that, I am not sure that this explanation works in the legal sphere. The project there -- in the legal process, that is -- is not, as such, to develop causal explanations for phenomena.
I am more inclined to think that in the legal sphere a useful model of inference will call attention to, or make more explicit, the principles -- including "causal" principles -- that may be swimming (murkily) around in our heads, or that ought to be swimming around in ouir heads, when we ponder a possible inference (and it is possible that causal diagrams will not succeed in making these ideas seem less murky to us).
Indeed: the aims of science and law sometimes really are different and the differences in their objectives may explain why one model is suitable or necessary in one realm but not in another. What do you folks think about such a notion? (I myself am a bit uncomfortable about the relativistic implications that some people might derive from such a principle.)
Having said all of THAT (in this postscript), I cannot help wondering whether even folks such as scientists generally believe that "causal thinking" is the only or principal way of thinking coherently about matters such as evidence, inference, induction, abduction, and discovery. But this last is a BIG question, and I do not really expect anyone on the list to try to answer it here. (I will instead read your books & papers.)
Vern R. Walker wrote:
> At the risk of snapping a worn thread, I am prompted by Peter*s honest plea and by the subsequent exchange to make a few brief observations.
> First, I agree that, with regard to many propositions, the act of asserting is warranted by (and perhaps only by) also asserting certain causal statements to be true or probably true. For example, my assertion that the sun will indeed *rise* once again tomorrow is warranted by my theory of astronomical physics. Such causal statements may or may not support observably testable frequency statements. It is also true, but only marginally relevant, that asserting warranted propositions is itself a result of cause-and-effect, as is any activity that occurs in space and time.
> But inferential activity (that is, asserting warranted conclusions) does not ALWAYS proceed by positing a causal explanation. A mundane but classic example is the case of warrant by appeal to linguistic meanings. *An unmarried neighbor is a bachelor* is an example. My warrant for asserting it to be true rests in part on the meaning of *unmarried* and *bachelor.*
> On the other hand, there are examples of propositions whose warrant is less straightforward, and which appear to be hybrids or perhaps of some other kind altogether * such as *2 is less than 3,* *human beings die,* and *F = MA.* I prefer to be agnostic on how many types of warrant we COULD usefully distinguish -- this depends, after all, upon devising a successful taxonomy of warrant, which depends in turn upon our objectives in engaging in such taxonomizing. So, without a context to provide objectives and criteria of success, I am not inclined to sign on to Peter*s nomenclature of *propositions about facts,* *ancillary hypotheses,* and *ancillary evidence.* Nor on to any other abstract formalism. It all depends upon what you*re up to.
> My minimal point here is that it is generally useful to treat inferring conclusions and providing causal explanations as conceptually distinct activities, and these activities should not be confused or needlessly conflated.
> Second, Peter*s list of *distinct possibilities explaining why, e.g., s is uncertain given r* (7/29/98) is intriguing for its omissions. I would have thought that the paradigmatic reason why *s is uncertain given r* is that we cannot DEDUCE s from r. This is not a circular or uninteresting account. We have invented in Western logic a reasonably well-defined test of *necessarily implies* or *is deducible from,* and this test now functions as the meaning of *necessary inference.* To be (merely) probable is to be not deducible.
> A psychological analog of deducibility is imaginability. If I can imagine a world in which r is true but s is not, then this also warrants my asserting *s is uncertain given r.*
> The linguistic analog is meaning. If I assert that I can imagine a married bachelor, then it must be that I have misunderstood the meaning of either *unmarried* or *bachelor* (or perhaps the word *imagine*).
> But the success of this paradigm of certainty or necessity, and its extreme usefulness, derives from the conceptual alignment of deducibility and imaginability and meaning. These three together provide the opportunity for understanding uncertainty. Historically, our quantitative work on probability as an operational account of uncertainty is parasitic on our conceptions of necessity, imagination, and meaning.
> Third, and finally, propositions cannot exhaust meaning, nor are they ever more than pieces to be moved in a highly evolved linguistic/mental game. Peter*s levels of diagram, employing different types of propositions or linguistic entities, can never capture the rules by which the game is played. Can never capture the meaning of the linguistic pieces. The game of *inference* is a product-in-development that our species has worked on very successfully for many thousands of years. Its evolutionary usefulness is beyond doubt.
> It is also beyond doubt that *inference* is not the only successful game in town! The *games* of love and of war, for example, generally claim higher places in the pantheon of evolved human activities. But as academics, one of our favorite games * besides the game of inference -- is the game of *modeling.* When we play our modeling game about the game of inference, when we attempt to model inference, we call the formal model a *logic.* But it would be unfortunate if we ever thought that modeling IS inference, or that any model or set of models could EXHAUST or entirely capture the rules or meaning of inference, or that we fully understand the rules and criteria for the game of MODELING itself. The river of thought is in flux, Heraclitus would have reminded us, and our models (and even our ideas about modeling) are mere flotsam in the spring snowmelt. The major modern advance over Heraclitus is Darwin: we now find it very useful to think that our inferences, our models
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> and our ideas about inference and modeling are all evolving in useful ways. But only time will tell. We have to see how useful our logics are at solving discrete problems.
> My three major points are connected. It is generally useful to distinguish inferring conclusions from providing causal explanations. The observable world is contingent and causal because we can imagine it being other than it is, while the linguistic models we use to describe that world are held together internally by our concepts of meaning and necessity. But even those concepts are to be judged by their usefulness, and we should always keep an open mind about modifying them. That is, after all, one of the main things we academics get paid to do! (And I do believe that academies are generally useful institutions in the long run.)
> If these reflections are not as hard and concrete as some would like, perhaps it is fitting to commend the words with which Peter began this thread: these are, more than we care to think, merely *summer night dreams.*
> Vern.
> * * * * *
> Vern R. Walker
> Professor of Law
> Hofstra University School of Law
> Hempstead, New York 11549