John, P-listers,
I wonder why science(s) seems to be left out of the context in the
discussions in this thread. To my mind they are direly needed in order
to make sense , ecp. of the latter part of the title, to start with.
So:
What does a variable refer to?
Within empirical science(s) a variable refers to something specifically
measured , and to something specifically controlled & by any means
attepted to keep constant OR taken as non-significant in relation the
issue under study.
Theories and theoretical models are needed in order to make sensible
decisions on which are the variables that matter. – Thus "a variable"
(in this context )refers to the model chosen for the investigation.
The model may or may not be presented as a diagram. All models present
simplifications of reality. Just as any map presents a simplification
of the terrain. – Otherwise it simply does not do the job. – EG's
present a certain kind of logical maps .
John wrote:
" When we use the words 'possible' and 'actual', we must distinguish
pure mathematics and applied mathematics:
1. Pure mathematics is pure possibility. It can never make any
claims about what is or is not actual.
2. But *applied* mathematics must determine which of the infinitely
many theories are the best approximations to some actuality
Lets take up the logical form of the first assertion. It is about the
relation between pure math and pure possibility, with the logical
connection "IS".
This seemingly inocuous connective smuggles in the assumption that we
are dealing with an existent relation, a relation between two existents
we can simply name. – With existents, a question of the type: is OR NOT
is, makes sense. With other kinds, it does not.
(Remember Hamlet: to be OR NOT to be? – Hamlet got stuck in the
question. Ofelia went mad with Hamlet stuck in it.)
When *applied* math enters, it never does so but within and into a stage
and scene and plot already *there*.
The audience is also already there. – With no audience, the play just
flops.
A division between *pure' and *applied* makes sense only within a
historical, ongoing context.
I do understand that John does have a context, an actual, ongoing
discussion (ontology) he is taking part in. I do not wish to interfere
with that. Thus I only send this to the Peirce-list.
Just because I was left wondering wether the ontology context proves out
to be a Procrustean bed for a Peircean frame of thought?
Best,
Kirsti Määttänen
John F Sowa kirjoitti 22.8.2018 08:31:
Azamat,
When we use the words 'possible' and 'actual', we must distinguish
pure mathematics and applied mathematics:
1. Pure mathematics is pure possibility. It can never make any
claims about what is or is not actual.
2. But *applied* mathematics must determine which of the infinitely
many theories are the best approximations to some actuality
[JFS] Challenge: I claim that it's impossible to find or
describe anything that is somewhere in between possible/actual
or mathematical/physical -- according to the way I defined it.
[AA] It was shown by Aristotle that the method of dichotomy is
not good in making an exhaustive division into two and ONLY two
classes.
But that statement is about applied mathematics, where we have to
choose among all the possibilities. That is the gray area where
there is no certainty. We can never do an exhaustive analysis.
AA
Reality is so rich and diverse that hardly any formal science
or logical scheme could meet its infinite complexity.
Yes. But I would prefer to emphasize the choice:
JFS
Reality is so rich and diverse and the possibilities are infinite.
We can never be certain which formal science or logical scheme is
best.
John
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