John, List,
The chirality issue somehow rings a bell (of possible relevance) to me. I understand, that a molecule can only be chiral, if it contains more than two atoms. Though I think, that four are reqired: Three define a plain and, and the fourth is either on one or the other side of the plain (telling the sides has to do with sequence and/or angles...). Now, do you think that there is chirality also in other contexts than molecules, e.g. in signs?
Best,
Helmut
16. Dezember 2017 um 16:39 Uhr
"John F Sowa" <s...@bestweb.net>
"John F Sowa" <s...@bestweb.net>
On 12/16/2017 12:37 AM, Jeffrey Brian Downard wrote:
> It appears to me that there is a natural progression of sorts. The
> polarity of a dyadic relation can be represented as positive and
> negatives on a line in one dimension. The order in the complexity of the
> correlates in a triadic relation can be represented in two dimensions.
> The representation of the chirality of carbon based enantiomers is best
> expressed in three dimensions.
I agree.
But I believe that he's using geometrical examples to counter the
claim that dyadic relations are sufficient for logic. For example,
the triadic relation between(x,y,z) can be defined in terms of
two dyads:
between(x,y,z) is defined as leftOf(x,y) & leftOf(y,z).
By using examples of chirality, Peirce shows that triads are essential
even for the "hard sciences" of physics, chemistry, and geometry.
There is no way to define chirality in terms of dyads.
Note what Peirce says at the beginning of 3.4:
> I will sketch a proof that the idea of Meaning is irreducible to
> those of Quality and Reaction. It depends on two main premisses.
> The first is that every genuine triadic relation involves meaning,
> as meaning is obviously a triadic relation. The second is that a
> triadic relation is inexpressible by means of dyadic relations alone.
The discussion of chirality supports the second premise.
John
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> It appears to me that there is a natural progression of sorts. The
> polarity of a dyadic relation can be represented as positive and
> negatives on a line in one dimension. The order in the complexity of the
> correlates in a triadic relation can be represented in two dimensions.
> The representation of the chirality of carbon based enantiomers is best
> expressed in three dimensions.
I agree.
But I believe that he's using geometrical examples to counter the
claim that dyadic relations are sufficient for logic. For example,
the triadic relation between(x,y,z) can be defined in terms of
two dyads:
between(x,y,z) is defined as leftOf(x,y) & leftOf(y,z).
By using examples of chirality, Peirce shows that triads are essential
even for the "hard sciences" of physics, chemistry, and geometry.
There is no way to define chirality in terms of dyads.
Note what Peirce says at the beginning of 3.4:
> I will sketch a proof that the idea of Meaning is irreducible to
> those of Quality and Reaction. It depends on two main premisses.
> The first is that every genuine triadic relation involves meaning,
> as meaning is obviously a triadic relation. The second is that a
> triadic relation is inexpressible by means of dyadic relations alone.
The discussion of chirality supports the second premise.
John
-----------------------------
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