Re: SUO: irreducible triadicity vs. essential triadicity
Nicola,
>Let me spend my 5 cents (is it the proper expression?) on
>this old issue.
The traditional phrase is "2 cents worth", but there has been
a lot of inflation.
>At 10:13 AM -0400 14/3/01, John F. Sowa wrote (quoting Whitehead):
>> The difficulties which cluster around the relation of
>> situation arise from the obstinate refusal of philosophers
>> to take seriously the ultimate fact of multiple relations.
>> By a multiple relation I mean a relation which in any
>> concrete instance of its occurrence necessarily involves
>> more than two relata. For example, when John likes Thomas
>> there are only two relata, John and Thomas. But when John
>> gives that book to Thomas there are three relata, John,
>> that book, and Thomas.
>At 4:18 PM -0400 14/3/01, John F. Sowa wrote:
>>The only point that Peirce, Whitehead, and I have been trying
>>to make is that there are concepts in English, such as Give,
>>which cannot be defined without using a frame, a lambda
>>expression, or some such formal device that contains three
>>distinct slots, variables, boxes, or whatever.
>Let me first remark that Whitehead's quotation is an ontological
>observation, while John's statement has a more "representational"
>flavor. Whitehead says that some entities (namely, giving events, or
>- if you prefer - occurrences of the "gives" relation) *necessarily*
>involve something else, namely three other different entities. [Note:
>Whitehead uses a modal notion]
In that particular statement, I said "cannot be defined", which is
just as modal as "necessarily involve". And in the axiom in Ch. 2
of my KR book, I used the operator for necessity.
>In my understanding, this means that, necessarily, if a giving event
>exists, then three other different entities (of suitable kinds) must
>exist.
Yes. But in some cases, the three entities might reduce to two,
such as giving something to oneself or giving oneself to somebody.
>This is basically a form of ternary existential dependence: the
>existence of a giving event depends on the existence of an actor, an
>object, and a recipient.
Yes, I would agree.
>This *ontological* truth (which captures, in my opinion, the essence
>of Whitehead and Peirce's intuition) can be labelled as a truth about
>"essential triadicity". This *can* be syntactically "reduced" to an
>expression where only a binary relation appears, namely the
>dependence relation. [Note: there are various ways of suitably
>characterize this dependence relation - this is another story, see
>Simons' book]. So I believe that the notion of "reducibility" is
>inappropriate to characterize the ontological relevance of
>Whitehead-Peirce-Sowa's distinctions. [Maybe there are other
>non-ontological considerations, as Pat pointed out].
I agree that "irreducibility" is insufficient, by itself, to characterize
the ontological notion. It is a necessary condition, but not a sufficient
condition. But necessary conditions are certainly "appropriate". You
just need some other conditions in addition to them.
>A further clarification is needed on the way John uses the notion of
>"Mediating entity" in his book. John proposes a plan as an example of
>mediating entity, which mediates between a builder and a building.
>But a plan, as such, is different from a giving event: the latter is
>ternary dependent, while the former is only binary dependent (the
>existence of a plan implies the existence of a builder and the
>existence of a [potential] building). What is ternary dependent is a
>planning event, which requires all three participants. It seems to me
>that mediating entities are different from mediation relationships,
>and triadicity only applies to the latter.
A plan is the result of a planning event, and it implies a planner who,
by means of the plan, tells the builder what to do to create the building.
You cannot define the concept "plan" without saying that a planner has
specified a goal to be achieved (such as a correspondence between the
drawing and the building). The dyadic relationship between a drawing
and a building has the nature of a proposition. The added goal, which
says "do this", is what distinguishes a plan from a proposition.
>This is in my opinion a serious and systematic confusion in John's
>book, that unfortunately uses the vague term "corresponds" (e.g.:
>"mediating corresponds to Peirce's Thirdness") just to suggest some
>interesting interpretation keys, which often are not suitably
>formalised.
This point raises a different issue: how should one write a book that
presents a large number of new ideas to people who may never have heard
or thought of them before. The approach I took is one of "progressive
deepening", which introduces new ideas through examples, historical
overviews, and informal discussions. For many people (including most
philosophers), Ch. 2 is the first exposure to Peirce's triads that they
may have seen. A complete formalization at that point would be totally
unmotivated. In Ch. 3, 4, and 5, I come back to the ideas again and
again. It isn't until Ch. 6 that I give a brief (8 page) summary of
Peirce's semiotic, but I agree that much more is needed.
Ideally, what I would like to do is to assume that the reader already
had a thorough grounding in Peirce's semiotic at the beginning. And
as a matter of fact, for my next book, I am collaborating with Menno
Hulswit, a philosopher from the University of Nijmegen, in writing
a book on "Causality and Causation" (see the table of contents below).
Menno has a very strong background in the philosophies of both Peirce
and Whitehead, and he has done the very hard work of digging out the
relevant sources and relating them to what everybody has said about
causality and causation from Aristotle to the present. In that book,
I am writing Ch. 1 (the introductory overview), Menno is writing the
next 6 chapters, and I return with the last three chapters, in which
I show how the foundation that Menno has presented can be applied to
modern physics, reasoning methods in artificial intelligence, and the
semantics of natural languages, as used by both scientists and
ordinary human beings.
>[BTW, it is not clear to me whether all binary and
>ternary dependent entities always involve some kind of mediating
>phenomenon, so I don't know whether the notion of "mediation" is
>appropriate to fully characterize these classes].
Many dyadic relations are just "brute matters of fact", so it is
reasonable to represent them as dyads without considering what "caused"
them to be the way they are. But as Peirce said, all the laws of science
have the form of a "would-be" conditional: if there exists a state of
affairs with such and such properties, then there would be a resulting
state with some other specified properties. He considered all such laws
to have a necessarily triadic form that relates what is to what will be.
Therefore, the dyadic matters of fact result from some physical laws,
which are triadic -- although there are many laws that are still unknown
or are too difficult to calculate in the required detail. (As Pat Hayes
mentioned, nobody uses quantum electrodynamics to compute what actually
happens in real life.)
>Bottom line: existential dependence is a formal ontological relation
>that can help clarifying (and extending) Sowa's trichotomy: there are
>independent entities, unary dependent entities, binary dependent
>entities, ternary dependent entities (of course, the list may
>continue, but these seem to be the most interesting classes).
Yes, I would agree. Following is the outline of the forthcoming book.
John
________________________________________________________________
Causality and Causation
In Philosophy, Physics, and Artificial Intelligence
by Menno Hulswit and John F. Sowa
Part I: Problems and Issues
1. Causality in Science and Ordinary Language (JS)
2. History of the concept of cause (MH)
3. Philosophical Debates (MH)
Part II: A Semeiotic Account of Causation
4. Peirce on final causation (MH)
5. Final causes and natural classes (MH)
6. The riddle of semeiotic causation (MH)
7. A Peircean approach to causation (MH)
Part III: Reasoning About Processes and Causality
8. Causality in Physics (JS)
9. Reasoning about causality (JS)
10. Language about causality (JS)