John, (01)
thanks for the illuminating answer. How would you judge the so-called
principle of economical understandability PEU? (02)
PEU is a fusion of the principle of economy, and the principle of
understandability. Both principles evaluate the relative fitness of
two or more theories, in respect to some specific thing that the
theories explain, and only in respect to the thing that the theories
explain. Thus, given two or more theories that explain exactly the
same thing: (03)
The principle of economy maintains that the simplest theory ought be
adapted. To
be simple in this sense means that the theory should use as few
concepts as possible. Every theory contains some concepts —independent
and unexplained axioms that are not explained by the theory itself—
but “not more independent elements are to be supposed than necessary”
(Peirce [8, 6.24]). Also, the space —like the total area of the pages—
that it takes to represent the theory should be as small as possible. (04)
The principle of understandability maintains that the theory that is
the easiest to understand ought to be adapted. (05)
When the two principles are united, using as few concepts as possible
means that the use of a smaller amount of concepts would already make
the theory harder to understand: the number of used concepts should be
reduced only if the reduction increases understandability. Thus, if
the theory gets easier to understand by introducing a new concept,
then the new concept ought to be introduced. According to PEU,
introducing new concepts ought to be severely constrained rather than
embraced; while new concepts are sometimes required, the
‘Heideggerian’ style and the tendency of its post-modernist successors
to introduce new concepts on the fly ought not to be followed. According
to PEU, unnecessary prose should not be incorporated in ontology. The
requirement of the minimal size of the representation means that the
size should be decreased only if the decreasing does not make the
theory harder to understand. If the theory gets easier to understand
by increasing the size, then the size ought to be increased. (06)
-Avril (07)
Lainaus "John F. Sowa" <sowa@xxxxxxxxxxx>: (08)
> Avril and Anders,
>
> Those are good observations. But I'd like to add a few comments.
>
> AS quoting Mach:
>> I was struck by the strange way in which scientists went on about
>> selecting the simplest, thriftiest and the most efficient method
>> of reaching their goal. Ernst Mach [19, p30]
>
> Mach, as Einstein observed, was a good experimental physicist.
> He was also a persuasive writer, as those quotations show.
> But the principle of economy is not sufficient. All it can give
> us is data mining, which is useful for finding patterns in data.
> But it cannot distinguish a scientific law from a coincidence
> that happens to occur in an unrepresentative sample.
>
> The quotation by Einstein (who was highly critical of Mach) is
> based on AE's way of thinking, which made great abductive leaps
> beyond the data:
>
>> Make everything as simple as possible but not simpler.
>> Albert Einstein [46, p121]
>
> Part of Mach's PE is that a theory should never introduce concepts
> or variables that could not be defined in terms of observables.
> That principle became dogma for the Vienna Circle and behaviorism.
>
> For physics, Mach and his followers stifled a huge amount of
> research based on the hypothesis of invisible atoms. They drove
> Boltzmann to suicide. (He suffered from depression, but it is
> significant that he hung himself just as his family was leaving
> to take the train back to Vienna.)
>
> AS
>> Mach derived extreme empiricism by using PE, among other things.
>> This is why Planck’s criticism against Mach’s PE can be seen as
>> criticism only against extreme empiricism, not against PE itself.
>
> PE is a useful guideline for choosing between alternatives that
> have equal predictive power. But Mach used it as a weapon against
> any theory that used abduction to introduce concepts that were not
> observable.
>
> Note what Max Planck said:
>
>> ... if the Machian principle of economy were ever to become central
>> to the theory of knowledge, the thought processes of ... leading
>> intellects would be paralyzed, and the progress of science might
>> thus be fatally impeded. Max Planck [21, p26]
>
> Planck had been persuaded by Mach to reject Boltzmann's hypothesis
> of atoms. But when he was studying black body radiation, he found
> that Boltzmann's mathematics (with the addition of the now famous
> Planck's constant) correctly predicted the observed data. That
> discovery completely changed his attitude toward Mach and Boltzmann.
>
> In 1905, Einstein took the next great leap of abduction to assume
> that the light traveling in free space could appear as streams
> of particles quantized in units that involved Planck's constant.
> De Broglie later took another huge leap to assume that streams of
> material particles, such as electrons, could also appear as waves.
> And Schrödinger took another leap to write his famous differential
> equation that governed matter waves. Mach would not have approved.
>
> Einstein's abductive leaps for both the special and general
> theories of relativity went far beyond the data. One might say
> that they followed PE because their equations were simpler.
> But Lorentz had discovered the equations that Einstein adopted
> for special relativity, and he was much more cautious in his
> interpretation. Einstein applied some math to those equations,
> and out popped his most famous equation: E = mc^2
>
> For anybody who followed Mach, the idea that mass and energy
> could be converted from one to another was a reductio ad absurdum
> that made them reject the whole line of thought. That was so
> controversial that the Nobel committee awarded their prize to
> Einstein for his work on quantum mechanics -- not relativity.
>
>> [T]he conflict between scientific ideas [can be seen] as a struggle
>> for life and as the survival of the fittest. Ernst Mach [19, p30]
>
> That is a horrible metaphor. Mach and his followers used their
> conception of PE as a weapon that killed a great deal of promising
> research. Fortunately for Einstein, he had three brilliant papers
> in 1905, and the Machians couldn't kill all of them. Peirce had
> a very accurate appraisal of Mach long before Einstein:
>
> CSP
>> Find a scientific man who proposes to get along without any
>> metaphysics... and you have found one whose doctrines are
>> thoroughly vitiated by the crude and uncriticized metaphysics
>> with which they are packed. (CP 1.129)
>
> Although Einstein saved physics from the clutches of Mach and
> the Vienna Circle, psychology and linguistics didn't have anyone
> of his stature to save them.
>
> In 1914, Leonard Bloomfield wrote his _Introduction to Language_,
> which contained a good presentation of the ongoing work in semantics.
> But in the 1920s, the behaviorists persuaded him that talking about
> unobservable semantic issues was "unscientific". So in 1933, he
> dropped semantics from his highly influential book _Language_.
> That became the primary textbook for the next generation of
> linguists -- including, among others, Noam Chomsky. Note that
> Chomsky also used PE as a weapon to stifle his opponents.
>
> AT quoting Scott Moore
>> ... promise, swear, vow; also contract, bet, swear that,
>> guarantee that, guarantee x, surrender, invite. In uttering e,
>> S promises H to A if S expresses:
>> 1. the belief that his utterance obligates him to A,
>> 2. the intention to A, and
>> 3. the intention that H believe that S’s utterance obligates
>> S to A and that S intends to A.
>
> That's a good statement, but note that it involves a Peircean triad:
> "S promises H to A", and it uses concepts that are unobservable.
> In legal terms, you can observe a killing, but you can only infer
> murder -- because intention is not observable.
>
> The behaviorists and logical positivists (i.e., the Vienna Circlers)
> tried to avoid talking about beliefs, intentions, obligations...
> In his later years, Carnap did some good work on modal logic, but
> he was very cautious in limiting his logic to the barest minimum he
> was able to formalize. But Quine never accepted any modal logic.
> He tried to reduce everything to first-order logic plus set theory.
>
> Clarence Irving Lewis, who founded modern theories of modal logic,
> was strongly influenced by Peirce, and he was very critical of
> the ideas coming from Mach, behaviorism, and logical positivism.
> Following is a comment that Lewis wrote in 1960:
>
> CIL
>> It is so easy... to get impressive 'results' by replacing the
>> vaguer concepts which convey real meaning by virtue of common
>> usage by pseudo precise concepts which are manipulable by 'exact'
>> methods - the trouble being that nobody any longer knows whether
>> anything actual or of practical import is being discussed.
>
> Alonzo Church was a famous logician who was willing to talk about
> abstract entities and use intensional methods for representing them.
> When he was invited to give a talk at Harvard, he deliberately chose
> a topic that would irritate Quine:
>
> http://www.jfsowa.com/ontology/church.htm
> The ontological status of women and abstract entities
>
> Note Church's concluding paragraph:
>
>> To return to Quine and Goodman, it is possible, even likely, that the
>> failure of their program will demonstrate the untenability of their
>> finitistic nominalism....
>
> Many people working in ontology today have been infected with the same
> virus as Mach, Russell, Carnap, Quine, and Goodman. Those people write
> clearly and persuasively. But their influence on psychology, semantics,
> and ontology made it impossible to formalize or even talk clearly about
> issues that are critical to law, finance, and business.
>
> As I said in my previous note, philosophers like Searle rediscovered
> some of the principles that Peirce enunciated. But they are still
> being attacked by people who caught the virus from Mach and the VC.
>
> John
>
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> (09)
--
Always forward towards the supreme maxim of scientific philosophizing (010)
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