Dear John, (01)
As is often the case in dyadic thinking you and the others that have responded
find the third in yourself (the apprehender) and not objectively in the syntax.
In other words in a triadic statement decomposed to dyads something is lost. (02)
You knowing that lost thing, that lost conception, and you find it immediately
when reviewing the dyadic statement but cannot see that it is lost (it's a
mental act not, in fact, present in the syntax/representation). Another human -
from a similar background - might also have the same experience (indeed, we
rely upon it) but a computing machine will certainly not. This is what Peirce
was talking about in my earlier quote when he says to Victoria Welby that
Russell's dyadic logic relies upon the very thing that it omits. (03)
So, for example, in the case of the statement "A gives B to C," - that I claim
Peirce shows is impossible to decompose as you have been suggesting (certainly
"conventional means," I accept). However, to be exact Peirce says (CP 1.474):
"Thus, A gives B to C becomes A makes the covenant D with C and the covenant D
gives B to C." It is necessary to introduce D in the decomposition to a
necessary "triadic tetrad" - which none of the proposals made here so far have
done - and so information was lost in the naive triadic syntax and dyadic forms
you have both proposed. (04)
In short you cannot take language naively as evidence but must be aware of the
nature of apprehension and the semeiotic process (semeiosis) that is active
across what Peirce called "the living mind." It is for this reason that Peirce
and Ladd-Franklin objected to the "Russellization of logic" - which sanitized
all 20th Century logic of such broader consideration. (05)
The resulting formal logic is a pure mathematics that is not suitable to be
mapped to natural language. I am confident that any modern logician must accept
the inverse to be true. For modern practical needs it is more effective, and no
doubt cheaper, for humans to simply adopt formal logic as natural language. (06)
Peirce's view of logic, indeed much of logic before Russell, is logic as
semeiotic theory - it deals with logic both as the natural science of
conceivable consequences and as a pure mathematics (the science of necessary
conclusions). (07)
If you wish to understand natural language and the behaviors of the individuals
using it (i.e., complex biophysical structures) then it is this broader
conception of logic that you must consider. (08)
I imagine some software smarty-pants will think this question can be resolved
quickly by writing clever software and taxonomies. But they will be wasting
their time because no matter how exhaustive you try to be in implementing what
I have described above the problem is combinatorial. Binary relations are not
your friend when dealing with the real bindings across these complex conceptual
manifolds the ghost of which is merely reflected by natural language. (09)
You cannot compete in modern computing machines with the low power dynamics in
biophysical structure that has no need to store results or move input data from
its natural path. (010)
There is an important distinction in what I have said before that has been
missed by most responders. When I speak of "the third" I am referring to
Peirce's "thirdness" and not to the syntax of triadic forms. (011)
As Peirce says in the following a third always deals with the general, and not
an individual, the general was lost in the earlier example. It's difficult
avoid quoting Peirce, so forgive me - I know that his 19th century language can
seem cryptic at times - the following is taken from CP 1.475 - CP 1.480 on the
subject of TRIADS: (012)
== Peirce quote ==
"It may be said that it is a psychical fact. This is in so far true, that a
psychical fact is involved; but there is no intent unless something be
intended; and that which is intended cannot be covered by any facts; it goes
beyond anything that can ever be done or have happened, because it extends over
the whole breadth of a general condition; and a complete list of the possible
cases is absurd. From its very nature, no matter how far specification has
gone, it can be carried further; and the general condition covers all that
incompletable possibility. (013)
There, then, we have an example of a genuine triad and of a triadic conception.
But what is the general description of a genuine triad? I am satisfied that no
triad which does not involve generality, that is, the assertion of which does
not imply something concerning every possible object of some description can be
a genuine triad. The mere addition of one to two makes a triad; and therein is
contained an idea entirely indecomposable into the ideas of one and two. For
addition implies two subjects added, and something else as the result of the
addition. Hence, it is wrong to define two as the sum of one and one; for
according to such a definition, two would involve the idea of three. The idea
characteristic of two is other. The corresponding idea characteristic of three
is third. ... (014)
The genuine triad contains no idea essentially different from those of object,
other, third. But it involves the idea of a third not resoluble into a formless
aggregation. In other words, it involves the idea of something more than all
that can result from the successive addition of one to one. This "all that can"
involves the idea of every possible. (015)
The world of fact contains only what is, and not everything that is possible of
any description. Hence, the world of fact cannot contain a genuine triad. But
though it cannot contain a genuine triad, it may be governed by genuine triads.
So much for the division of triads into the monadic, dyadic, and triadic or
genuine triads. (016)
Dyadic triads are obviously of two kinds, first, those which have two monadic
subjects, as a high perfume and a burning taste are united in many essential
oils, and secondly, those which have [for] all their subjects individuals. (017)
Genuine triads are of three kinds. For while a triad if genuine cannot be in
the world of quality nor in that of fact, yet it may be a mere law, or
regularity, of quality or of fact. But a thoroughly genuine triad is separated
entirely from those worlds and exists in the universe of representations.
Indeed, representation necessarily involves a genuine triad. For it involves a
sign, or representamen, of some kind, outward or inward, mediating between an
object and an interpreting thought. Now this is neither a matter of fact, since
thought is general, nor is it a matter of law, since thought is living."
== End Peirce quote == (018)
Best regards,
Steven (019)
--
Dr. Steven Ericsson-Zenith
Institute for Advanced Science & Engineering
http://iase.info (020)
On Mar 26, 2013, at 3:28 AM, sowa@xxxxxxxxxxx wrote: (021)
> Steven,
>
> > I'm not sure that I Peirce would accept the functional notation as
> > triadic, but - as you say - he would prefer a a diagram/graph...
>
> The basic arithmetic operators -- add, subtract, and multiply -- take two
>inputs and generate one output. That is certainly triadic.
>
> You can reduce the triads to dyads by Currying, but those dyads only
>represent intermediate results. You still get triadic connections in the
>complete diagrams.
>
> Divide taks two inputs (dividend and divisor) and generates two outputs
>(quotient and remainder). But it can be represented by two triads -- one that
>takes the two inputs and generates the quotient, and the other that takes the
>same inputs and generates the remainder.
>
> If you use a purely relational notation (as Peirce did for his algebra of
>1885 or his existential graphs of 1897), all those functions must be
>represented by triadic relations.
>
> As another example, look at Prolog. It represents the basic arithmetic
>operators by triadic relations.
>
> John
> (022)
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