Re: Epistemology 201: The Science of Science

stephen_at_nomail.com
Date: 03/13/05 

Date: 13 Mar 2005 18:37:03 GMT

In sci.math Allan C Cybulskie <allan.c.cybulskie@yahoo.ca> wrote:

: <stephen@nomail.com> wrote in message
:> Consider a 2 cup measure. The possible values you could
:> measure with it are in the range [0,2]. Consider a 1 pint
:> measure. The possible values you could measure with it
:> are in the range [0,1]. Of course, 2 cups equals 1 pint in the
:> English system, and it is clear that any amount that fits
:> in the 2 cup measure also fits in the 1 pint measure. There
:> are not twice as many measurements possible with the 2 cup
:> measure. Similarly, using meters instead of feet does
:> not result in fewer possible results. The fact that
:> the number of possible measurements is independent of the
:> units used is quite intuitive.

: The example is also totally wrong. I can get far more accuracy of
: measurement from the 2 cup example than the pint example. Why? Because
: there are more numbers that I can retrieve from the 2 cup measure than the 1
: cup measure, allowing me to subdivide the measure further than I can with
: the pint measure.

You are assuming your conclusion. Do you really believe there are more
possible quantities that fit into a 2 cup measure than a 1 pint measure?
They are exactly the same size. Any quantity you can fit in one
will fit in the other. Any lines you mark on a 2 cup measure you
can also mark on a 1 cup measure, because they are exactly the same
size. Apparently you think there is some quantity of y cups such that
y/2 pints is an impossibility. I think most people intuitively recognize
that the units used in measuring do not affect the number of possible
measurements. Anything I can measure in feet I can measure in meters and vice
versa. Anything I can measure in Celsius I can measure in farenheit. It
does not matter that the ranges of the measurements differ, because each
measurement can be translated into any appropriate units. It is clearly
true in the world of finite precision and only a finite number of possible
measurements that anything measurable with a 2 cup measure is measurable
with a 1 pint measure.

Stephen

Relevant Pages

  • Re: Epistemology 201: The Science of Science
    ... :>:> are not twice as many measurements possible with the 2 cup ... :>: measurement from the 2 cup example than the pint example. ... Any quantity you can fit in one ... cardinality agrees with our naive intuitions. ...
    (sci.math)
  • Re: Epistemology 201: The Science of Science
    ... :>:> are not twice as many measurements possible with the 2 cup ... :>: measurement from the 2 cup example than the pint example. ... Any quantity you can fit in one ... cardinality agrees with our naive intuitions. ...
    (sci.cognitive)
  • Re: Epistemology 201: The Science of Science
    ... :>:> are not twice as many measurements possible with the 2 cup ... :>: measurement from the 2 cup example than the pint example. ... Any quantity you can fit in one ... cardinality agrees with our naive intuitions. ...
    (sci.physics)
  • Re: Epistemology 201: The Science of Science
    ... :> in the 2 cup measure also fits in the 1 pint measure. ... :> are not twice as many measurements possible with the 2 cup ... Any quantity you can fit in one ... true in the world of finite precision and only a finite number of possible ...
    (sci.cognitive)
  • Re: Epistemology 201: The Science of Science
    ... :> in the 2 cup measure also fits in the 1 pint measure. ... :> are not twice as many measurements possible with the 2 cup ... Any quantity you can fit in one ... true in the world of finite precision and only a finite number of possible ...
    (sci.math)
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