Jon AS, Auke, and Jeff BD,
Both subject lines are closely related. For modes of being,
I'll quote Bertrand Russell, whom I rarely cite:
Mathematics may be defined as the subject in which we never know
what we are talking about, nor whether what we are saying is true.
That is a dramatic way of making a point that Peirce repeated many
times in many ways: Every theorem in pure mathematics is hypothetical.
It has the form "If hypothesis (and/or axioms), then conclusion."
That means the subject matter of pure mathematics is pure possibility,
and the theorems are necessary statements about those possibilities.
If a mathematical theorem is applied to something actual in some
branch of science or in common sense, then its conclusion is a
prediction about those actual entities that must be tested by
methodeutic. For quotations by Peirce, search for the phrase
"pure mathematics" in CP. There are 49 instances.
As for semiotic, there is a reason why CP 1.190 is just one line:
Phenomenology is, at present, a single study.
Please look at CP 1.300 to 1.353, which he wrote in 1894. That is
his study of the "conceptions drawn from the logical analysis of
thought." Since he had previously written that long analysis,
there was no reason for him to say more about phenomenology in 1903.
In 1905, he used the term 'phaneroscopy':
Phaneroscopy is the description of the _phaneron_; and by the
_phaneron_ I mean the total of all that is in any way or in
any sense present to the mind, quite regardless of whether it
corresponds to any real thing or not. (CP 1.284)
Whether or not phaneroscopy/phenomenology are identical or closely
related, Peirce's writings from CP 1.284 to 1.353 include his
phenomenological categories -- a major part of semiotic. Then
CP 1.190 says that phenomenology is "at present a single study".
That study would be his 1894 version of semiotic (or some update).
But he left open the option that he might include more later.
But CP 1.191 about normative science is longer because it's his first
statement about the normative sciences. In 1906, he wrote much more:
Normative Science forms the mid-portion of coenoscopy and its
most characteristic part.... Logic, regarded from one instructive,
though partial and narrow, point of view, is the theory of
deliberate thinking. To say that any thinking is deliberate is
to imply that it is controlled with a view to making it conform
to a purpose or ideal. (CP 1.573)
Note that he says logic applied to the normative sciences is
a "partial and narrow" point of view as "the theory of deliberate
thinking." Since phenomenology/phaneroscopy includes anything
"present to the mind" in any way, the theory of deliberate thinking
would be a special case.
JAS
JFS: Semiotic, the general theory of signs, would also be pure
mathematics, either formal or informal.
Not according to Peirce; he classified it as a Normative Science.
Three points: (1) Peirce himself placed formal logic under
mathematics;
(2) he put logic (without the word 'formal') under normative science;
and (3) the deliberate thinking in normative science is a "partial and
narrow" view of logic.
JAS
As Auke noted, phenomenology is the study of appearances,
not actualities. Actuality is a subset of Reality, and it is
metaphysics that deals with the Reality of phenomena.
Since phenomenology studies everything "present to the mind", it deals
with signs that occur in actuality. The question whether those signs
refer to anything actual outside the mind requires the normative use
of logic to determine truth.
AvB
I would argue that: phenomenology is concerned with what appears,
semiotics with signs... Since the sign evolves what is involved
and a sign only can do this by appearing at some point, there seems
some overlap between both sciences.
Yes. The subject matter of phenomenology is the totality of signs
that appear to the mind, and CP 1.300 calls the semiotic categories
"conceptions drawn from the logical analysis of thought". Therefore,
the science of phenomenology is applied semiotic (logic in the broad
sense). Logic as a normative science has a "partial and narrow" sense.
JBD
Here is one place where Peirce provides a relatively clear explanation
of the relation between these tones of thought--considered as formal
elements and as material categories--as they are studied in
phenomenology and these three modal conceptions.
Thanks for those citations (CP 1.530 to 1.532) from 1903. They follow
and develop themes in (CP 1.417 to 1.520) from 1896. The title of
the 1896 section is "the logic of mathematics: An attempt to develop
my categories from within."
Both of these sections develop semiotic as a mathematical theory.
In 1894, Peirce developed the categories from "a logical analysis of
thought". That analysis started with observations of the phaneron.
But the title "logic of mathematics" implies a purely mathematical
development, and the phrase "from within" indicates a starting
point from axioms within the theory.
Those passages and their dates show the steps in the development:
Semiotic was inspired by an analysis of thought (1894). But Peirce
later developed it further as a theory of pure mathematics (1896).
That mathematical development enabled him to generalize the theory
and make it more systematic. Then he could take the pure theory and
apply it to subjects beyond the ones that originally inspired it.
See below for a summary of the points in these discussions.
John
____________________________________________________________________
Summary of what Peirce wrote or implied in his 1903 classification
as supplemented by the references cited above:
1. There are two sciences that do not depend on any other science
for their subject matter: mathematics and phenomenology.
2. Mathematics, formal and informal, contains all possible theories
that can be stated with a finite alphabet in any language,
natural or artificial. But before those theories are applied
to anything actual, the subject matter is hypothetical. Theorems
are necessary conclusions about the assumed possibilities.
3. Phenomenology is the subject that studies anything "present to
the mind" in any way from any source (internal to the body or
external through the senses). Its subject matter is any and
every sign that may appear in the phaneron.
4. Peirce said that every science depends on mathematics. Pure
mathematics contains all possible hypotheses -- formal or informal
-- before they have been applied to anything. Every theory of any
subject whatever is an application of mathematics.
5. When a pure theory is applied to something actual, indexes in
the theory (e.g., variables) are linked to actual entities. Its
theorems are claims that certain statements about those entities
are necessarily true. The reliability of those claims depends
on testing by methodeutic.
6. Every theory of logic or semiotic, before it is applied, is
a version of pure mathematics. The theories of phenomenology
are applied semiotic. Logic as a normative science is, as
Peirce said, "a partial and narrow" view.
