Lancelot Fletcher (lance.fletcher@freelance-academy.org)
Tue, 21 Sep 1999 02:31:42 -0500
Responding to my request that he cite at least one falsifiable proposition
contained in Pratt's paper, Stephen replied:
> I must be able to
> back up my claims. The
> > difficulty is that within the specific context of Pratt's paper, it is
> > difficult to "cite at least one falsifiable proposition". I would
> > tanatively propose this statement as being falsifiable:
> > "Identifying and adjoining are canonically
> denotational tasks that
> > mathematicians are accustomed to performing on their spaces,
> groups, and
> > other algebraic objects. This is the realm of the physical.
> > Copying and deleting are canonically operational tasks
> that logicians
> > and computer scientists are accustomed to performing on their proofs,
> > spreadsheets, and other symbolic objects. This is the realm of the
> > mental." page 4-5<<<
Since it is not self-evident that this is a single statement, or that any
or all of it is falsifiable, I responded:
> Please
> > describe an observation which you, or Pratt, would accept as
> demonstrating
> > that this collection of statements (or any part thereof) is false.
Stephen now responds:
>
> Well, let us see. Is it observationally true that
> a) Identifying and adjoining are canonically denotational tasks that
> mathematicians are accustomed to performing on their spaces, groups, and
> other algebraic objects.
>
> b) Copying and deleting are canonically operational tasks that logicians
> and computer scientists are accustomed to performing on their proofs,
> spreadsheets, and other symbolic objects.
>
> These seem trivially true... Is the problem in the
> definition of the
> words used?
To which I now respond:
No, Stephen. The problem at this point is that you have not satisfied my
request. I requested that you describe an observation which you, or Pratt,
would accept as demonstrating that this collection of statements, or any
part thereof, is false. Instead, you have offered your opinion that two of
the four sentences you originally quoted are "observationally true."
Remember that the issue is whether or not Pratt's paper contains
"falsifiable" propositions. What does it mean to say that a proposition is
falsifiable? It means (or so it appears to me) that there must be some
condition or possible observation whose truth would lead you to conclude
that the proposition in question is false. If I assert that "All men have
brown eyes" is a falsifiable proposition and somebody asks me to describe
an observation which I would accept as demonstrating that this proposition
is false, I would say that a valid observation of a man with blue eyes
would demonstrate the falsity of my proposition.
This may look like a trivial matter, but in fact constructing genuinely
falsifiable statements is more difficult than it may appear, but I think it
is a useful intellectual discipline, especially if you claim -- as you have
done -- that a particular theory has the virtue of falsifiability. The
fact that you believe a statement to be true, even the fact that you can
cite what you take to be confirming observational evidence for its truth,
does not prove that the statement is falsifiable. The only way you can
demonstrate the falsifiability of a statement is to specify a condition or
observation which, if true, you would accept as proving your assertion
false.
Having said that, let's look again at the set of statements which you cited
in response to my demand that you show me a falsifiable statement in
Pratt's paper:
>>"Identifying and adjoining are canonically denotational tasks that
mathematicians are accustomed to performing on their spaces, groups, and
other algebraic objects. This is the realm of the physical.
Copying and deleting are canonically operational tasks that logicians
and computer scientists are accustomed to performing on their proofs,
spreadsheets, and other symbolic objects. This is the realm of the
mental." page 4-5<<<
If you read these statements carefully -- and especially if you read them
in their context -- I think you will have to agree that they cannot
possibly be falsified. Why? Because these are not intended to be factual
statements. The function of these statements is essentially taxonomic:
What Pratt is doing is defining classes or categories of things. It's as
if he were saying, "I am going to call things like this fruits and things
like that nuts."
If you had any doubt that this is a taxonomic exercise, the giveaway is
Pratt's use of the word "canonically." Canonical means "as specified by
some authoritative rule;" the word is derived from the legal vocabulary of
the Catholic Church.
I think one could fairly paraphrase Pratt's statements as follows:
I am about to say what I mean by the "the realm of the physical" and "the
realm of the mental." I will define these two realms by identifying each of
them with one of the two sets of tasks which I am about to distinguish. The
two sets of tasks are (1) denotational tasks and (2) operational tasks. By
definition, the fundamental denotational tasks are what I call identifying
and adjoining, by which I am referring to the tasks that mathematicians
perform on spaces, groups and other algebraic objects. By definintion, the
fundamental operational tasks are copying and deleting, by which I am
referring to the tasks that logicians and computer scientists perform on
proofs, spreadsheets and other symbolic objects.
In paraphrasing Pratt I have emphasized the stipulative or nominal
character of his statements. But I do not think I have violated his
meaning. Taxonomic statements necessarily contain empirically descriptive
content to the extent that they are intended to classify observable things.
If I say that vertebrates are animals with internal skeletons featuring a
segmented bony or cartilaginous spinal column, I presuppose that my reader
has some experience of skeletons, bones and spines. But my definition of
vertebrates is not a factual assertion. It might be a bad definition, but
it cannot possibly be a false statement because it simply announces how I
intend to use a certain group of words.
Likewise, I submit that it would not be possible to specify an any
observational statement which, if true, would demonstrate that any of the
statements quoted from Pratt is false, because those statements simply
announce how Pratt intends to use certain words.
Therefore, I conclude that, so far, Pratt's paper has not been shown to
contain any falsifiable statements.
>
> Lance, I think that we are getting sidetracked here! Pratt
> et al, are
> offering us an alternative way of, at least, thinking about the
> mind-body problem and also time and causality. Just because the writting
> does not conform to the "standards" of people like Spinoza, etc. is not
> a reason to dismiss it! The fact that it is hard if not impossible to
> understand it is an indication of the difference in the paradigms
> involved.
Stephen, in the foregoing paragraph, it looks as if you are attributing to
me the following two assertions: (1) That I have dismissed Pratt's paper
because it does not conform to the standards of people like Spinoza, and
(2) that I object to Pratt's paper because it is hard to understand. If
that is what you meant to say, let me be clear: I have never made either of
those assertions, nor would I since they do not reflect what I think.
My quotation from Spinoza in one of my private messages to you was
tangential to my main point, as I so stated, prefacing my quotation with,
"Here, incidentally, is what Spinoza had to say about this..."
In fact I do not find Pratt's paper especially hard to understand. Or,
rather, as I said in my private message, the difficulty it presents
resembles the difficulty of reading papers by mediocre undergraduates which
are typically so full of ignorant mistakes and incoherence that it is
difficult to figure out what they are trying to say, even though what they
are trying to say is not at all profound. In section I of Pratt's paper he
is discussing material that I am much more familiar with than he is, and it
is clear to me that, with regard to Descartes and mind-body dualism, Pratt
simply doesn't know what he is talking about. The later sections of the
paper are at first a bit daunting because of the references to some
unfamiliar mathematical terms. But when I began to work through these
sections carefully, what I discovered was that Pratt's math doesn't really
do any work. That is to say, Pratt seems to use references to arcane
mathematical structures as images or metaphors, possibly useful analogies,
but whenever he begins to try to connect this material, his references,
like bad poetry, are extremely vague or questionably ambiguous (as, for
example, his distinction between "algebraic objects" and "symbolic objects"
or between mathematicians, on the one hand, and logicians and computer
scientists, on the other. Finally, Pratt's conclusions seem grandiose and
utterly unsubstantiated. Consider the following paragraph entitled
"Essence of Quantum Mechanics:"
"We claim that quantum mechanics has not previously been reduced to lay
terms by physicists, who have been content to leave the subject as a
mysterious jumble of properties of Hilbert space that a working physicist
can become acclimatized to and even confident with after sufficient
exposure. Mind-body duality and interaction explains respectively
complementarity and the inner product in relatively elementary terms making
a clear connection with other structures such as the above model of
computation and the following foundation for mathematics. The central role
of the mental plane in this account of quantum mechanics makes it a
rational mechanics."
Pratt's paper reminds me of a famous passage in Schopenhauer's "Criticism
of the Kantian Philosophy" in which, after expressing great respect for
Kant's achievement, he writes, "...the most injurious result of Kant's
occasionally obsure language is that it acted as exemplar vitiis imitabile;
indeed, it was misconstrued as a pernicious authorization. The public was
compelled to see that what is obscure is not always without significance;
consequently, what was without significance took refuge behind obscure
language."
It seems to me that a similar caution is warranted with respect to the use
of mathematics in writing about the philosophical foundations of physics.
The educated public has been taught that mathematical representation is not
merely convenient, but is essential to the power of modern physics, such
that modern physics cannot be presented without distortion except by using
mathematical concepts that are virtually unknown to all but trained
physicists and mathematicians. I believe, however, that this respect for
the power of obscure mathematics has led to an unfortunate and uncritical
tolerance for what amounts to mathematical obscurantism. Just because one
uses mathematical terminology, it does not follow that one's reasoning is
guaranteed to be rigorous, nor is it the case that the use of mathematics
protects one from being trapped by unconscious presuppositions. For this
reason I think it is a salutary practice to demand, especially in
discussions about the foundations of physics where the boundary between
physics and philosophy is indistinct, that mathematical arguments be
translated into non-mathematical terms or, if that is not possible, that
the fundamental terms be explained as clearly and non-mathematically as
possible.
One of the points that first attracted me to Hitoshi's work some years ago
was his recognition that the problem of time in modern physics is
essentially a philosophical problem, and that, therefore, it is not likely
to be susceptible to a merely technical solution.
Now, to finish with Pratt, let me say this to Stephen:
I have concluded that Pratt's paper is too incompetently written to be
worth discussing directly. I understand that you believe it contains some
brilliant and possibly important and original insights. That may be true.
It's also possible that you have had some important and original insights
of your own while you were reading Pratt's paper which were not actually
Pratt's insights but yours. It doesn't really matter whose insights they
are. If you can express them more clearly and rigorously than Pratt has
done, I will be very happy to listen to you.
Lance Fletcher, President
The Free Lance Academy Foundation
http://www.freelance-academy.org
lance@interactive.net
This archive was generated by hypermail 2.0b3 on Sat Oct 16 1999 - 00:36:41 JST