Steven, (01)
You wrote: (02)
> Dear John,
>
> 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.
>
> 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. (03)
On what evidence do you base this assertion? A computing machine has no
conception of anything. A particular software product creates a machine with
the concepts that are built into the software. If the software 'understands'
ternary relations, then it is not necessary that there be a dyadic rewrite of
the statement. If the software accepts dyadic syntax and converts it
internally to the ternary relation, then the unit triadic concept is
maintained, not lost. The software model, of course, is not the world it
represents, but neither is the human conceptual model. The human conceptual
model is doubtless richer, but whether that richness is either valid or
relevant to the communication at hand is 'quite another thing entirely'. The
software may also have some additional richness in the form of axioms and facts
about the verb and the nouns involved. (04)
> 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. (05)
This may well be, but it is not clear to me that semanticists in the last 100
years generally agree with Peirce on the subject of the relationship between
conceptual content and syntax, or on the idea that relationships beyond binary
are necessarily unitary in concept. I fully agree that there are ternary
relations that are conceptually unitary, but there are also ternary (and
quaternary, etc.) relations that have a meaningful factorization, or perhaps
multiple meaningful factorizations. I agree that "John gives the book to Mary"
is conceptually a unit. (06)
> 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." (07)
That may be what Peirce suggests, but Daniel Davidson suggested an alternative,
to wit, that one describes a unitary 'event' -- a 'giving', and then describes
roles that are played in that event. The unitary concept is maintained as the
event object -- what happens -- not some strange factorization (covenant D)
that has no real meaning. The nature of a giving event involves three roles,
and those roles can be represented by three dyadic relationships that assign
role players to those roles. This is a useful general model for the
description of conceptual events, whether or not they can be described as
instances of a single natural language verb. (08)
The problem with this approach is the need to support truly meaningful binary
verbs with a different model, and the value decisions in factoring larger
conceptual situations into interconnected subordinate situations. "The airship
industry declined because the Hindenburg disaster demonstrated the danger of
using hydrogen for buoyancy, and the substitute -- helium -- was too
expensive." Humans must decompose that thought in order to conceptualize it,
but we also impose viewpoint in determining how to organize the interrelations
of the subordinate concepts. (09)
> 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. (010)
It not necessary, nor even semantically appropriate, to introduce the nonsense
'covenant D', as the Davidsonian model that John and I have described shows.
And when you describe the triadic relation as 'naïve', I wonder on what basis
you think the natural language syntax: A gives B to C is any less 'naïve'. (011)
> 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. (012)
> The resulting formal logic is a pure mathematics that is not suitable to be
> mapped to natural language. (013)
That is probably a fair assessment of Russell's approach, yes. But I think
the record will show that logic in the latter half of the 20th century, and its
relationship to semantics, departed significantly from Russell. (014)
> 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. (015)
I disagree completely. The function of language is to communicate. The
language must be chosen with attention to the content being communicated and
the nature of the audience. Formal logics have their place in the spectrum of
languages, along with English, classical Sanskrit, and road signs. (016)
> 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).
>
> 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. (017)
I doubt you will find much disagreement with this in the ontology community.
We know that we are making models, and those models are necessarily inaccurate
in whatever ways they (intentionally) fail to represent the whole of the domain
they describe. That is the nature of models. (018)
> 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. (019)
It is more than "combinatorial". In general, models made from different
perspectives may present conflicting assertions, precisely because they ignore
aspects that are important differentiators in other perspectives. (020)
> 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. (021)
And yet, European languages have only unary (intransitive) and binary
(transitive) verbs. All of the rest of the conceptual environment is made up
by what our Latin educational heritage calls "adverbial phrases" that are said
to "modify" the verb, or to assert "general roles" of noun phrases (agent,
patient, instrument, purpose, location, etc.). The problem of conveying
"complex conceptual manifolds" did not originate with logic languages. (022)
> 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. (023)
I have no idea what this means.
>
> 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.
>
> 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:
>
> == 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.
>
> 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. ...
>
> 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.
>
> 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.
>
> 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.
>
> 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 ==
> (024)
I must here confess my ignorance. I have no idea what the subject of the above
excerpt is -- the "genuine triad" that seems to elude clear definition or
description by Peirce, if the excerpt is any indication. And I cannot imagine
how it might relate to the development of ontologies. So, Steven, you have
convinced me to stop reading this thread. (025)
-Ed (026)
> Best regards,
> Steven
>
> --
> Dr. Steven Ericsson-Zenith
> Institute for Advanced Science & Engineering http://iase.info
>
>
>
>
>
>
>
>
>
> On Mar 26, 2013, at 3:28 AM, sowa@xxxxxxxxxxx wrote:
>
> > 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
> >
>
>
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