Franklin, regarding this point:
[ I would also like to point out that "Upon Logical Comprehension and
Extension" (ULCE) only deals with terms, not propositions or arguments. I seem
to recall that in his later years Peirce had specified what information would
be like for propositions and arguments, but after looking around a bit, I can't
find a text to cite and I don't exactly recall how it worked, only that it
didn't work the same way for them as for terms. ]
You may be thinking of this note to CP2:406:
[[ I restricted myself to terms, because at the time this chapter was first
written (1867), I had not remarked that the whole doctrine of breadth and depth
was equally applicable to propositions and to arguments. The breadth of a
proposition is the aggregate of possible states of things in which it is true;
the breadth of an argument is the aggregate of possible cases to which it
applies. The depth of a proposition is the total of fact which it asserts of
the state of things to which it is applied; the depth of an argument is the
importance of the conclusions which it draws. In fact, every proposition and
every argument can be regarded as a term.—1893. ]]
One place where Peirce uses the terms breadth and depth in reference to the
proposition (rather than the term) is “Kaina Stoicheia” (1904), EP2:305:
[[ If a sign, B, only signifies characters that are elements (or the whole) of
the meaning of another sign, A, then B is said to be a predicate (or essential
part) of A. If a sign, A, only denotes real objects that are a part or the
whole of the objects denoted by another sign, B, then A is said to be a subject
(or substantial part) of B. The totality of the predicates of a sign, and also
the totality of the characters it signifies, are indifferently each called its
logical depth. This is the oldest and most convenient term. Synonyms are the
comprehension of the Port-Royalists, the content (Inhalt) of the Germans, the
force of DeMorgan, the connotation of J.S. Mill. (The last is objectionable.)
The totality of the subjects, and also, indifferently, the totality of the real
objects of a sign is called the logical breadth. This is the oldest and most
convenient term. Synonyms are the extension of the Port-Royalists (ill-called
extent by some modern French logicians), the sphere (Umfang) of translators
from the German, the scope of DeMorgan, the denotation of J.S. Mill.
Besides the logical depth and breadth, I have proposed (in 1867) the terms
information and area to denote the total of fact (true or false) that in a
given state of knowledge a sign embodies. ]]
Gary f.
} The future ain't what it used to be. [Yogi Berra] {
<http://gnusystems.ca/wp/> http://gnusystems.ca/wp/ }{ Turning Signs gateway
From: Franklin Ransom [mailto:[email protected]]
Sent: 7-Nov-15 23:34
To: Peirce List <[email protected]>
Subject: Re: [PEIRCE-L] Vol. 2 of Collected Papers, on Induction
Jerry, list,
Well, this turned out longer than I anticipated.
You wrote:
BTW, this is just another example of CSP's usage of his chemical knowledge to
ground his logical explorations.
Yes, I was surprised some such reference to chemistry and its importance in
influencing Peirce's work wasn't in your first post; I suppose you were winding
up for the pitch. There is a very decidedly chemistry-centric direction that
your posts take here on Peirce-L. I think it's important to notice that I'm not
a chemistry whiz, but that I will do my best to keep up. For what it's worth, I
would like to point out that I see no reason to deny your claims about the
important influence of developments in chemistry on Peirce's work in logic. I
just don't always see the relevance in a given discourse.
What is the information content of a symbol (as a diagram, icon, index or any
term) if the change of the sign does not indicate a change in information?
Recent extension of the discussion point out that both "breadth" and "depth"
can be viewed as changes in the distinctiveness of the sign (or information
content.)
This question needs some clarification before it can be answered. When you say
"What is the information content of a symbol (as a diagram, icon, index, or any
term)," it is unclear whether you mean for diagrams, icons, indices, and any
term to be understood as a symbol. Strictly speaking, icons and indices cannot
be symbols, a diagram is a type of icon, and terms, well, that depends on how
one means term; in particular, it matters if one envisions dicisigns as
involving terms (rhemes?), or whether one restricts terms to propositions
proper, and then specifically the predicate term. My guess is that you
understand all of this, but your wording was vague, and I wanted to be clear
that we are specifically talking about symbols. If you want to include
diagrams, icons, indices, and any term, then it is important to note that icons
only serve content for information; indices also serve content for information,
and some types of indices also convey information--i.e., dicent indices. But
they do not possess information in the sense that a symbol does. Information is
the ongoing relating of informed breadth and informed depth relative to one
another, which is possible only in a symbol.
I would also like to point out that "Upon Logical Comprehension and Extension"
(ULCE) only deals with terms, not propositions or arguments. I seem to recall
that in his later years Peirce had specified what information would be like for
propositions and arguments, but after looking around a bit, I can't find a text
to cite and I don't exactly recall how it worked, only that it didn't work the
same way for them as for terms. (At least in the case of propositions, I think
it had to do with the possible cases in which a given proposition was applied
or true, or followed validly, or some such thing.)
So if we talk about the information content of a symbol, we must limit
ourselves to terms. Moreover, it's not clear that the term in some sense
contains anything, but rather the term's information relates to the synthetic
propositions, or facts, in which it participates as either subject or
predicate. So the information of a term-symbol is something that the term has
relative to other terms given in synthetic propositions that collectively
inform what Peirce referred to as the state of information. This idea of the
state of information is important to keep in mind. Consider how in ULEC Peirce
treats of the idea of distinctness (in a footnote following the quote he
references the introduction of the idea of distinctness to the work of Scotus):
If T be a term which is predicable only of S', S'', and S''', then the S''s,
the S'''s, and the S''''s will constitute the informed breadth of T. If at the
same time, S' and S'' are the subjects of which alone another term T' can be
predicated, and if it is not known that all S''''s are either S' or S'', then T
is said to have a greater informed breadth than T'. If the S''''s are known not
to be all among the S''s and S'''s, this excess of breadth may be termed
certain, and, if this is not known, it may be termed doubtful. If there are
known to be S''''s, not known to be S''s or S'''s, T is said to have a greater
actual breadth than T';but if no S''''s are known except such are known to be
S''s, and S'''s (though there may be others), T is said to have a greater
potential breadth than T'. If T and T' are conceptions in different minds, or
in different states of the same mind, and it is known to the mind which
conceives T that every S''' is either S'' or S', then T is said to be more
extensively distinct than T'.
And then
The depth, like the breadth, may be certain or doubtful, actual or potential,
and there is a comprehensive distinctness corresponding to extensive
distinctness.
So extensive distinctness (distinctness in breadth) and comprehensive
distinctness (distinctness in depth) have to do with there being two terms, say
T and T', in a given state of information. The term T, identifying every S'''
as either S'' or S', is more extensively distinct than T', because T' applies
to S' and S'' like T, but does not identify S''' in its breadth as T does; T'
simply doesn't account for any S''', because it is not predicated of any S'''.
But if it did, it would be the term T, which is already understood by the mind.
Even if T' came to be predicated of every S''', it would not add information.
Instead, it would show itself as really being the term T, which is already
known. So by comparison, we can see that one term would be more distinct than
another. Peirce avers that all deductive inference is simply a matter of
increasing distinctness of terms, in which there is an exchange between two
terms, a sort of sharing of information already known.
I submit that I think Peirce could have been clearer about this. He says in
ULCE that deduction is easily understood in terms of the increase of
distinctness in terms, and so does not need explanation, and simply moves on to
induction and hypothesis. Personally, I wish he had explained deduction anyway.
I might guess that somewhere along the way it is possible for two terms to be
understood as turning out to be identical, and this might be what deduction
ultimately aims at as a form of reasoning. But more likely, T and T' don't
typically meet in deduction, and so won't become identified with each other,
but we might compare T participating in a deduction that makes it more
distinct, while T' remains less distinct because it is not involved in the
deduction. Say, for example, that we have the term human being, and the term
featherless biped. We know that both human being (T) and featherless biped (T')
involve all cases of men (S') and all cases of women (S"). But human being also
is predicated of all cases of animals that can learn to reason (S'"). It turns
out that all the animals that can learn to reason (S'") are either men (S') or
women (S"), so human being (T) now is more extensively distinct than
featherless biped (T'), though it does not have greater actual breadth; but it
does have a greater potential breadth, because it may turn out that some
animals that can learn to reason may turn out to be neither man nor woman. For
example, someone who is transgender.
Now, moving on, you wrote:
Thus, CSP used these advances in chemical abstractions to ground his extension
of information from "breadth and depth" to graphs, then alpha, beta and gamma
graphs. see: CP 4.510-511 for specific claims about the rhetorical meaning of
graph extensions and to compare with his work in the 1860's. Is this what CSP
is referring to when he writes, "dispatch reasoning of a very intricate kind"
and "utmost clarity and precision"? Such terms as "depth" and "breadth" are
crude by comparison.
I looked at the paragraphs you referenced, but I'm not sure where the
connection is to be found to which you are pointing. My guess is that you are
suggesting, as you say, that "Such terms as 'depth' and 'breadth' are crude by
comparison." I'm not sure they are quite so crude as you represent them to be.
Peirce is in fact pointing out in the second paragraph that not only the alpha,
but also the beta graphs are incapable of treating of qualities or relations
treated as subjects. Not being able to reason about qualities, nor about
relations treated as subjects, means that the alpha and beta graphs are
deficient insofar as they cannot fully account for logical depth and logical
breadth, because they fall short in the analysis of predicates and subjects.
Supposing they were to become accurately represented in the gamma graphs, the
motivation for continuing to develop the gamma graphs is just because of these
noted deficiencies, which could only be observed as deficiencies because we
have a theory of logical quantity and information that says that such things
need to be given an accurate account in the theory of inference and reasoning.
The way I see it, the conceptions of breadth and depth are not so much crude as
they are basic, forming as they do the basic elements from which classes of
terms are formed and differentiated from one another, and in some cases
eventually identified with one another, in part or in whole. My own thought is
that as Peirce continued to develop his theory of signs and sign classes, the
conceptions of breadth and depth took on nuances that Peirce didn't typically
notice in an explicit way. So for instance we know from ULCE that not only is
there a distinction between depth and breadth, but that there is actual and
potential, certain and doubtful, etc. as distinctions that can modify the
significance of some received breadth or depth. With more refined sign
classification, it may very well be the case that more modifiers can be applied
to differentiate between kinds of breadth and depth.
Now what I have said about information above does not, I think, lessen at all
the significance of graphical logic. I would certainly consider myself among
those who believe that Peirce's graphical logic reaches the height of
representation of logical inference and reasoning. I simply wish to point out
that, rather than replace or supplant the importance of breadth and depth in
the theory of information, graphical logic can be seen to incorporate the
conceptions of breadth and depth in their construction. Well, at least
potentially so in the gamma graphs. I remain optimistic about the project.
Finally, a word on this:
The assertions of CSP are primitive relative to the modern state of information
theory, chemical notation and mathematics and hence I could not accept them as
meaningful in modern terminology of the natural sciences.
I'm not entirely sure there is a correspondence between what Peirce's theory of
information aims to explain and what 'modern' information theory aims to
explain; seems to me that there could be a case of two ships sailing different
seas. But maybe Jon Awbrey will prove me wrong. As for chemical notation, I'm
not even sure how to compare. But as to mathematics, I don't know how you could
imagine this to be the case. Set theory, as far as I know, is still used and
studied. But set theory is simply a theory of elements, and what Peirce offers
is a competing account, and I'm given to understand a viable one. See John
Sowa's book Knowledge Representation, ch.2 on Ontology, for a clear account of
the differences between set theory, mereology, and Peirce's theory of
collections.
Franklin
On Sat, Nov 7, 2015 at 2:42 PM, Jerry LR Chandler <[email protected]
<mailto:[email protected]> > wrote:
Franklin:
I fear that you missed the essential element of my post.
Let's go back to the assertion that motivated it:
In any case, change in distinctness is not change in information.
Your response fails to address the substantial notion of the meaning of the
symbol "distinctness".
So, allow me to ask a question:
What is the information content of a symbol (as a diagram, icon, index or any
term) if the change of the sign does not indicate a change in information?
Recent extension of the discussion point out that both "breadth" and "depth"
can be viewed as changes in the distinctiveness of the sign (or information
content.)
I recall clearly my own puzzlement at reading this paper in the first decade of
this century. The assertions of CSP are primitive relative to the modern state
of information theory, chemical notation and mathematics and hence I could not
accept them as meaningful in modern terminology of the natural sciences.
More recently, I have accepted the fact that I must follow CSP's mental
development from period to period is within the texts I have available to me.
A difficult but necessary chore. In this case, CSP extends these very simple
notions of information to his constructions of logical diagrams in the 1890's
and later, after he developed his remarkable views on relational logics.
Historically, the parallelism between his texts on logic and logic of
relations overlap with the corresponding development of chemical diagrams. The
deep changes in chemical notation that occurred in this period were a
consequence of Pasteur's separation of the optical isomers of the tartaric acid
and the explanation for these isomers in terms of three-dimension spatial
diagrams with different arrangements of the SAME parts into different wholes
(van't Hoff and LaBel, ca 1880.) (These two advancements in chemical inquiry
dramatically changed the symbolization and signage for chemistry and propelled
it toward its modern form. The morphism of chemical notation from one based on
mass to its current form which is dominated by electrical particles in space is
continuing even today in molecular biology, eg, DNA as a double helix)
Thus, CSP used these advances in chemical abstractions to ground his extension
of information from "breadth and depth" to graphs, then alpha, beta and gamma
graphs. see: CP 4.510-511 for specific claims about the rhetorical meaning of
graph extensions and to compare with his work in the 1860's. Is this what CSP
is referring to when he writes, "dispatch reasoning of a very intricate kind"
and "utmost clarity and precision"? Such terms as "depth" and "breadth" are
crude by comparison.
See:The Philosophical Status of Diagrams (Mark Greaves), CSLI, 2002 for a lucid
and compelling argument on the nature of CSP's argument and it's relation to
modern logic.
BTW, this is just another example of CSP's usage of his chemical knowledge to
ground his logical explorations.
Cheers
Jerry
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