FOM: Re: fom-digest V1 #245
jmyciel at euclid.Colorado.EDU
Fri Dec 10 21:45:16 EST 1999
I think we ironed it out in private correspondence. So let me only
state the outcome of our letters in hope it may interest others (but of
course if you find my account inadequate please complete it).
You think that the term formalist is useful because it is
used and everybody in philosophy of mathematics knows what it means.
I think that it should be avoided because those who do pure
mathematics (such as well orderings of the real line), are making a formal
constructions just like architects who draw projects of houses that will
never exist. On the other hand, a formalist is a bureaucrat who carefully
avoids trouble by mechanical application of rules, or does it from spite.
This is not what distinguishes us from Platonists. What distinguishes us
is our plain rationalism (in the common sense of this word).
But some philsophers like such biased terminologies and they
support their pet theories and fuels empty disputations.
For example they say: A realist is a person who takes mathematical
objects to be real. False! A realist is a person who can distinguish
imaginary from real.
And they oppose rationalism to empiricism, as if it was rational
to neglect experiment. In our culture rationalism means something else, at
least since the time we assimilated the work of Galileo.
In a philosophical discussion one should not accept the
terminology of our opponents when it is at variance with the common
significance of words. If one does so, one can loose the argument
before even starting it. Totalitarian states and some religious
leaders know this and often they attempt to impose a biassed terminology.
This issue was stressed in a briliant way by Orwell. Sometimes it takes
heroic efforts to keep the language straight. And in your country Vladimir
this must be known better than here in the West.
Some of the terminology I was criticising came from middle ages.
Intellectual freedom was not the sign of those times. In fact it came
from efforts to marry Greek Rationalism with Christian Theology. Surely
those eforts had a positive impact on the latter. But the dissonance
remains vivid and sometimes it is intolerable (especially in good
In all honesty do not understand your letter.
When an engineer does a calculation he produces a physical object
on paper, or a physical state of his brain, a memory.
What do you mean when you write that something is abstract?
(The main meaning of "abstract" which I know is "admits many
interpretations". Interpretation is a certain way of using certain
objects. We classify thoughts. Exists distinguishes those thoughts which
refer to something from those thoughts which do not refer to anything.
Abstract distinguishes those which refer to many things or those for which
reference does not matter (like in pure mathematics), from those which
refer to only one thing. But recall also that the intended meaning of most
words depend very much on the context or situation in which they are used.
E.g., in pure mathematics exists means something else than in biology and
interpretation means something else than in physics. So your "abstract"
may mean other things. My point is that I do not see any important
ontological significance of being abstract other than having many
And again, what do you mean by "the generally accepted separation
between word and object"?
(I know only that words are OBJECTS and pencils are OBJECTS. They
serve different purposes and in practice I can recognize a word from a
And again, the same trouble with your qualifier abstract attached
to calculations. (As before all I know is "admits many interpretations".)
Abstractness does not seem to have any significance for the
issue of justifying or condemning the term formalism in the ontology of
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