Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 adj. Possessing dimension
Etymologies
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Examples

Carl called this egoless, dimensionful area the Zone.

In fact, you clearly don't need M_W because it is dimensionful and it must therefore drop out.

Anyway, a large part of what you sought to argue for was simply that we can't currently explain the values of dimensionful (as opposed to dimensionless) universal constants  which I agree with  but I sought to take things a step further and say that with regard to the fundamental universal constants, we will never be able to explain their values

If the hypothetical change in fundamental constants occurs only in dimensionful fundamental constants (e.g., doubling the speed of light), then by changing one or more units of measurement (e.g., halving the unit of time, e.g., the second) one is able to establish a correspondence to a universe in which no such change took place.

If you are speaking of a dimensionless constant, which clearly you are in this case as it is the exponent in the inverse square law, then you are dealing with the problem that I suggested  of attempting to explain a dimensionful constant, that is a constant which requires one or more units of measurement with which to establish its value.

Not dimensionful constants, that is constants that are measured along a given dimension, which are contrasted against dimensionless constants.

This is what renders a change in the scale of dimensionful fundamental constants meaningless  the observational indistinguishability of the universe before and after such a change.

(otherwise they wouldn't be fundamental)  and that a world in which the fundamental dimensionful universal constants were different from what they are would be observationally indistinguishable from our own.

… a world in which only the fundamental dimensionful universal constants were different from what they are would be observationally indistinguishable from our own.

(e.g. 3.14 or 1 or 0.618 but not 19171107 or 0.00000025021948) and that this rule can only be applied to dimensionless parameters because the numerical magnitude of dimensionful quantities depends on the choice of units and in various units, it can be much greater than one, much smaller than one, comparable to one, or equal to one, according to your choice of units.
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