The Hart-Fuller Debate Post-Modernized: Motor Vehicles versus Animals in the Park

An ordinance originally enacted in 1921 provides that on Sunday afternoons it is impermissible to take motor vehicles into the park but that it is permissible to take animals (even large and noisy ones) into the park on Sunday afternoons. (This is very probably a German city such as Munich.)


One fine Sunday afternoon I take a robotic cat - a robot that functions, in many ways, like a cat, but also, obviously, in some ways, like some other machines - into the park.
How now brown cow?
Shall we use Bayesian logic? (Unlikely.) Shall we flip a coin? ("Heads, it's a motor vehicle, tails it's an animal. That's a fair way to settle this question.") Delphic oracles? (cf. "I will gaze at the starry heavens - especially Sirius - and seek inspiration there.")  Our unbridled discretion? ("I can and will rule the way I want. There is no applicable rule here. I will make law. Nothing else is left to me - thank God.") Or shall we (or the judge or the jury) use fuzzy logic? ("This thing partakes of an 'animal' to some degree. This thing partakes of a 'motor vehicle' to a substantial degree. ... [missing matter?] ... Therefore ...[?]")
What will or should we (or the judge or jury) do: How will or should we or they think about this problem?
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Supreme Court's Unacknowledged Recognition of Fuzzy or Rough Sets

The important thing about Griswold v. Conecticut 381 U.S. 479 (1965) was not what it said about privacy or sex. The important thing about Griswold v. Connecticut is that in it the Supreme Court of the United States put its constitutional imprimatur on the proposition that sets (classes, categories, concepts), in the constitutional realm, are fuzzy or rough. For example, the Supreme Court said:

The foregoing cases suggest that specific guarantees in the Bill of Rights have penumbras, formed by emanations from those guarantees that help give them life and substance. See Poe v. Ullman, 367 U. S. 497, 516-522 (dissenting opinion). Various guarantees create zones of privacy.

Lotfi Zadeh's seminal article in fuzzy sets was published in 1965. It is extremely unlikely that any of the Justices had read the article or had even heard of the article or the theory. So there is no direct lineage from Zadeh's theorizing to the Supreme Court's theorizing in Griswold v. Connecticut. Nonetheless, ...

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Fuzzy on Fuzziness

Words they may regret:

    "Fuzzy theory is wrong, wrong, and pernicious. What we need is more logical thinking, not less. The danger of fuzzy logic is that it will encourage the sort of imprecise thinking that has brought us so much trouble. Fuzzy logic is the cocaine of science."

-Professor William Kahan UC Berkeley

    "’Fuzzification’ is a kind of scientific permissiveness. It tends to result in socially appealing slogans unaccompanied by the discipline of hard scientific work and patient observation."

-Professor Rudolf Kalman UFlorida

Source:  History and Objections [to fuzzy logic] 
Professor Zadeh particularly enjoys trotting out the statement by Kahan.

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First Circuit Seems to Approve of Holism and Abduction

See Milward v. Acuity Specialty Products Group, Inc., 639 F.3d 11 (1st Cir. 2011):

[7] "Unlike a logical inference made by deduction where one proposition can be logically inferred from other known propositions, and unlike induction where a generalized conclusion can be inferred from a range of known particulars, inference to the best explanation—or `abductive inferences'—are drawn about a particular proposition or event by a process of eliminating all other possible conclusions to arrive at the most likely one, the one that best explains the available data." Bitler v. A.O. Smith Corp., 391 F.3d 1114, 1124 n. 5 (10th Cir.2004).

[snip, snip] 

At times, the court's error in excluding Dr. Smith's testimony derived from a mistake in its understanding of the weight of the evidence methodology employed by Dr. Smith. The court treated the separate evidentiary components of Dr. Smith's analysis atomistically, as though his ultimate opinion was independently supported by each. For example, the court referred to "Dr. Smith's opinion that because benzene metabolites inhibit topo II and because some classes of topo II inhibitors appear to have a causal relationship to APL, therefore benzene has a causal relationship to APL." Milward, 664 F.Supp.2d at 148 (emphasis added). This overstates Dr. Smith's conclusion as to the topo II evidence, and is indicative of an error in the court's understanding of the nature of Dr. Smith's analysis. 

In Dr. Smith's weight of the evidence approach, no body of evidence was itself treated as justifying an inference of causation. Rather, each body of evidence was treated as grounds for the subsidiary conclusion that it would, if combined with other evidence, support a causal inference. The district court erred in reasoning that because no one line of evidence supported a reliable inference of causation, an inference of causation based on the totality of the evidence was unreliable. Cf. Nutra-Sweet Co. v. X-L Eng'g Co., 227 F.3d 776, 789 (7th Cir.2000) (holding that an expert's reliance on individual pieces of evidence, insufficient in themselves to prove a point, "did not render his opinion speculative").[16] The hallmark of the weight of the evidence approach is reasoning to the best explanation for all of the available evidence. Cf. Dalkon Shield, 156 F.3d at 253 (reversing district court's exclusion of expert testimony as "guesswork" or without "basis" when testimony was based on differential diagnosis and there was no showing that any one of the expert's premises was "so faulty that it could not even be tendered to the jury for its consideration"); see also Hardyman v. Norfolk & W. Ry. Co., 243 F.3d 255, 261 (6th Cir.2001).

A hat tip to Phil Segal!
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DNA and Fiber Evidence in the Dobson and Norris Trial

Go here to see a brief visual summary of the the DNA and fiber evidence in the Dobson and Norris trial in the UK.

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