Principle of Minute Differences: Proof or Counter-Example
- Oinkyboinky
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Principle of Minute Differences: Proof or Counter-Example
(PMD): If x is a paradigm F and y is an entity that differs from x in any respect relevant to being an F only very minutely, then y is an F.
There seem to be plenty of instances where this principle is obeyed.
For example, if a cloud-candidate differs only by a few water droplets from a paradigm cloud, then it seems the cloud-candidate is also a cloud.
Of course, though, many instances of the principle do not show that it is true in general.
What are some potential proofs of the PMD or any counter-examples where it does not hold?
- -1-
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Re: Principle of Minute Differences: Proof or Counter-Exampl
I present a counter-example to your claim.
A could with a few droplets fewer than the previous state of the same cloud.
If you still take some drops away, it's still a cloud.
If you keep taking drops still away, eventually you are down to one or two droplets, which a cloud don't make.
So there is a qualitative transformation resulting from quantitative transformations.
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Marx expressed the same thing in reverse: "Quantitative changes always precede qualitative changes."
- Oinkyboinky
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Re: Principle of Minute Differences: Proof or Counter-Exampl
Ok, but this isn't a counter-example, since you did not specify an object that is a paradigm F, and a different object that differs minutely from the first, and show that this second object is a non-F.-1- wrote:I read this just the other day. I forgot the name of the author and of the argument.
I present a counter-example to your claim.
A could with a few droplets fewer than the previous state of the same cloud.
If you still take some drops away, it's still a cloud.
If you keep taking drops still away, eventually you are down to one or two droplets, which a cloud don't make.
So there is a qualitative transformation resulting from quantitative transformations.
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Marx expressed the same thing in reverse: "Quantitative changes always precede qualitative changes."
Rather, what you gave is a reductio argument against the principle (in the form of a sorites paradox). While this is a valid way to show the PMD is false, I'm looking for a particular counter-example.
In addition, one might respond to your argument as follows:
At some point in the sorites series, the typical cloud changes from typical to atypical, so the principle is not violated when the atypical cloud changes into a non-cloud (since we did not go from a typical cloud to a non-cloud abruptly).
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