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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