John,
You'll get no argument from me! Especially as regards Peirce's view of
continuous vs. discrete. He held that both of them (as 3rd & 2nd, along
with the vague or indefinite, as 1st) pervade positive phenomena; for
example, and as you said, the sharply defined frequency of a chemical's
spectral line located on a continuous spectrum. He said more than once
that matter is discrete and once that it "no doubt" consists of
"Boscovichian points." (Peirce also spelt it "Boscovitchian" and I
mistakenly quoted him with the "t" spelling in a previous email).
[BEGIN QUOTE]
The things of this world, that seem so transitory to philosophers,
are not continuous. They are composed of discrete atoms, no doubt
Boscovichian points. The really continuous things, Space, and Time,
and Law, are eternal.
[END QUOTE]
— Peirce in his 1898 lectures, on p. 115 in Reasoning and the Logic
of Things, Ketner, ed., 1992.
On 12/12/2019 2:15 PM, John F. Sowa wrote:
Ben,
I agree that space and time in quantum mechanics are continuous. But
there is one issue that Peirce understood very well: the discrete
lines in the spectrum of any chemical element that is heated on earth
or in any distant star.
In the so-called "black body" radiation, the filament of an
incandescent light bulb emits a continuous spectrum with a peak at a
frequency that is determined by the temperature. But a photon emitted
when an electron of an atom falls from a higher state to a lower state
has a sharply defined frequency.
Peirce learned that fact when he studied chemistry, and he used it in
his photometric studies of distant stars. Although it may be wrong
to consider a continuous line as a set of discrete points, there are
phenomena in physics whose measurements are discrete.
John
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