Jeff,
As to your second response, you wrote:
First: what are the phenomena that we were talking about here? The dualism
is a phenomena we observe in everyday experience where we evaluate things
as right or wrong, and it supplies is with observations from which we can
draw abductive inferences in the normative sciences.
Dualism is most certainly something "we observe in everyday experience,"
and if we (colloquially) call everything we observe a 'phenomenon' then, I
suppose this observation of dualism is also phenomenal. But this is not, or
at least not exclusively, the kind of phenomenon that Peirce speaks of as
'secondness' in consideration of the science of phenomenology. Consider,
for example, these passages:
CP 1.23. My view is that there are three modes of being. I hold that we can
directly observe them in elements of whatever is at any time before the
mind in any way. They are the being of positive qualitative possibility,
the being of actual fact, and the being of law that will govern facts in
the future.
Secondness, then, is not characterized as duality as such or exclusively
but, rather, as "the being of actual fact." It does have essential aspects
of duality, no doubt, but this is not how Peirce typically characterizes it
but, rather, as 'brute' and 'factual' (action and reaction, resistance,
etc.) In the passage immediately following the one quoted just above he
writes:
CP 1.24. Let us begin with considering actuality, and try to make out just
what it consists in. If I ask you what the actuality of an event consists
in, you will tell me that it consists in its happening then and there. The
specifications then and there involve all its relations to other existents.
The actuality of the event seems to lie in its relations to the universe of
existents. A court may issue injunctions and judgments against me and I not
care a snap of my finger for them. I may think them idle vapor. But when I
feel the sheriff's hand on my shoulder, I shall begin to have a sense of
actuality. Actuality is something brute. There is no reason in it. I
instance putting your shoulder against a door and trying to force it open
against an unseen, silent, and unknown resistance. We have a two-sided
consciousness of effort and resistance, which seems to me to come tolerably
near to a pure sense of actuality. On the whole, I think we have here a
mode of being of one thing which consists in how a second object is. I call
that Secondness.
So, secondness, as the "The actuality of the event seems to lie in its
relations to the universe of existents." It is "brute", that is, has "no
reason in it." Certainly it is "a two-sided consciousness of effort and
resistance, "a mode of being of one thing which consists in how a second
object is," and so characterized as secondness. But the language Peirce
uses ('existent', 'brute', 'effort and resistance', 'objective being') is
an existential extension of the mathematical idea of duality and, as I
believe I'm conservatively claiming, is not identical to it.
Second: is this phenomena something that we could draw on in developing a
phenomenological theory? It could, on my understanding of the texts,
supply us with an example. Having said that, we are particularly
interested in the question: what are the most fundamental elements--formal
and material--present in any phenomena we might observe? Why do we need
such an account of the elemental categories. One reason is that it will
help us analyze the phenomena we observe in inquiry in the normative
sciences. Another reason is that we need to correct for observational
errors in inquiry in the normative sciences.
I would tend to agree with this except to reiterate that Peirce's
phenomenology concerns itself with the formal categories, not the material
ones.
*Third: we can draw on math in order to understand the dualism. In doing
so, we are developing what one might call a mathematical phenomenology,
just as might develop a mathematical physics, psychology or economics.*
I haven't any trouble with this, I think, as long as one doesn't
attempt to *reduce
*phenomenology to a "mathematical phenomenology" which, I believe, would be
a major mistake. Yes, phenomenology has its mathematical underpinnings, but
they are not, in my opinion, the most interesting aspects of phenomenology
when its principles are applied especially to logic as semiotics (which is
not to say that they are not at all interesting or important).
But, perhaps we're talking past each other.
Best,
Gary
*Gary Richmond*
*Philosophy and Critical Thinking*
*Communication Studies*
*LaGuardia College of the City University of New York*
*C 745*
*718 482-5690*
On Fri, Aug 22, 2014 at 2:02 PM, Gary Richmond <[email protected]>
wrote:
> Jeff,
>
> I doubt that in this post that I'll get to your second response to my
> message calling for a distinction which I think would be useful, namely,
> that between the essentially mathematical ideas of monad, dyad, triad and
> the essentially phenomenological ideas of firstness (1ns), secondness
> (2ns), and thirdness (3ns). But let me at least tackle for now your first
> response.
>
> I'd begin with a thought experiment: try replacing monad, dyad, and
> triadic in valency theory (or, for that matter, in consideration of EGs)
> with 1ns, 2ns, and 3ns. It doesn't work. So there is *some* sort of
> distinction which *could* be made, at least in *that* direction, and
> especially as Peirce will in most of his phenomenological writings attempt
> to describe the characters, give examples, etc. of the three universal
> categories, which characterization dominates his discussions of
> phenomenology.
>
> In the passage you provided a short snippet from, Peirce certainly does
> speak in terms of valency in the division of the phaneron. Here's a
> somewhat larger excerpt with the bit you quoted italicized:
>
> CP 1.292. *If, then, there be any formal division of elements of the
> phaneron, there must be a division according to valency; and we may expect
> medads, monads, dyads, triads, tetrads, etc. *Some of these, however, can
> be antecedently excluded, as impossible; although it is important to
> remember that these divisions are not exactly like the corresponding
> divisions of Existential Graphs, which have relation only to explicit
> indefinites. In the present application, a medad must mean an
> indecomposable idea altogether severed logically from every other; a monad
> will mean an element which, except that it is thought as applying to some
> subject, has no other characters than those which are complete in it
> without any reference to anything else; a dyad will be an elementary idea
> of something that would possess such characters as it does possess
> relatively to something else but regardless of any third object of any
> category; a triad would be an elementary idea of something which should be
> such as it were relatively to two others in different ways, but regardless
> of any fourth; and so on. Some of these, I repeat, are plainly impossible.
> A medad would be a flash of mental "heat-lightning" absolutely
> instantaneous, thunderless, unremembered, and altogether without effect. It
> can further be said in advance, not, indeed, purely a priori but with the
> degree of apriority that is proper to logic, namely, as a necessary
> deduction from the fact that there are signs, that there must be an
> elementary triad. For were every element of the phaneron a monad or a dyad,
> without the relative of teridentity (which is, of course, a triad), it is
> evident that no triad could ever be built up. Now the relation of every
> sign to its object and interpretant is plainly a triad. A triad might be
> built up of pentads or of any higher perissad elements in many ways. But it
> can be proved -- and really with extreme simplicity, though the statement
> of the general proof is confusing -- that no element can have a higher
> valency than three.
>
> Here Peirce is attempting to *ground *phenomenology on a mathematical
> concept, the thrust of this entire passage being to demonstrate
> mathematically that while "*according to valency . . . we may expect
> medads, monads, dyads, triads, tetrads, etc." *that "no element can have
> a higher valency than three," while the "relative of teridentity" (an idea
> especially useful in EGs) is essential since it is "a necessary deduction
> from the fact that there are signs, that there must be an elementary
> triad"--and the reference to "the fact that there are signs" already points
> ahead to semiotics, of course--and that monadic and dyadic elements could
> not bring about a triad without this *relative*. In addition, some of the
> valental expectations you quoted in your snippet prove impossible (his
> example of the medad). At the same time he makes the point that "it is
> important to remember that these divisions are not exactly like the
> corresponding divisions of Existential Graphs, which have relation only to
> explicit indefinites."
>
> So there are in this passage, it seems to me, a mix of mathematical,
> phenomenological, and semiotic ideas, quite appropriate at this level of
> analysis, I think. But, again, I would suggest that (1) the use of -adicity
> here is *principally* mathematical, (2) that "these divisions are not
> exactly like the corresponding divisions of Existential Graphs" (nor, I'd
> add, not exactly like the corresponding divisions of valency theory in the
> simplest theoretical mathematics) and (3) that for the most part Peirce's
> phenomenological discussions are *not *concerned with valency once the
> three universal categories *as such *are discovered (in phaneroscopy,
> Peirce holds), and that their 'characters' transcend the strictly
> mathematical in the myriad descriptions of them Peirce offers in his
> writings: again, in my opinion one should not identify the *characters *of
> the three universal categories with those of the monad, dyad, and triad.
>
> Still, while I employ, and will continue to make the distinction I'm
> arguing for, I hardly expect everyone else to do so. And, yes, there are
> certainly places--as in the passage you quoted--where Peirce *seems* to
> identify the three universal categories with the monadic, dyadic, and
> triadic. But this is, as I see it, a mere *seeming*, since, in speaking
> of the first two requiring the *relative*, teridentity to build triadic
> and higher valental structures, Peirce is already moving toward a kind of
> descriptive characterization of these three--and only 1ns, 2ns, 3ns--which
> is at the heart of his phenomenology.
>
> If I can make sense of it and have something to add to what I've already
> said, I'll try to get to your second response later in the week.
>
> Best,
>
> Gary
>
>
> *Gary Richmond*
> *Philosophy and Critical Thinking*
> *Communication Studies*
> *LaGuardia College of the City University of New York*
> *C 745*
> *718 482-5690 <718%20482-5690>*
>
>
> On Fri, Aug 22, 2014 at 1:39 AM, Jeffrey Brian Downard <
> [email protected]> wrote:
>
>> Hi Gary R.,
>>
>> You've raised questions about some comments I've offered about how we
>> might understand Peirce's phenomenological categories. Here is your first
>> question: "As I see it, monad, dyad and triad pertain to mathematics while
>> firstness, secondness, thirdness are terms of phenomenology. They are, in
>> my opinion, not equivalent (as your 'or' would seem to imply). Peirce says
>> that the categories are 'discovered' in phenomenology and that only
>> retrospectively, so to speak, does one find in pure mathematics the monad,
>> dyad, and triad as expression of these universal categories." My response
>> is that there are a number of places in the texts where Peirce uses the
>> terminology, monad, dyad and triad to refer to the formal elemental
>> categories in phaneroscopy. Here is one: "If, then, there be any formal
>> division of elements of the phaneron, there must be a division according to
>> valency; and we may expect medads, monads, dyads, triads, tetrads, etc."
>> (CP, 1.292). I don't see him reserving this terminology of monad, dyad and
>> triad to mathematics. He uses is in phenomenology and in semiotics quite
>> freely. It is a classification of kinds of relations, and they can be
>> found in different areas of inquiry.
>>
>> Your second question seems to involve two points. Let me separate them.
>> You say: "But 'phenomena' as you use it here ("i.e., the dualism in the
>> normative sciences") is not the 'phenomena' considered in phenomenology.
>> Duality is certainly a mathematical concept in the normative science, but
>> to call it 'phenomenological' is, for me, problematic. The dualism (which
>> is not secondness) which you point to in the normative sciences is drawn
>> from mathematics (again, the distinction between dyad, or dualism, and
>> secondness) and not from phenomenology."
>>
>> First: what are the phenomena that we were talking about here? The
>> dualism is a phenomena we observe in everyday experience where we evaluate
>> things as right or wrong, and it supplies is with observations from which
>> we can draw abductive inferences in the normative sciences.
>>
>> Second: is this phenomena something that we could draw on in developing a
>> phenomenological theory? It could, on my understanding of the texts,
>> supply us with an example. Having said that, we are particularly
>> interested in the question: what are the most fundamental elements--formal
>> and material--present in any phenomena we might observe? Why do we need
>> such an account of the elemental categories. One reason is that it will
>> help us analyze the phenomena we observe in inquiry in the normative
>> sciences. Another reason is that we need to correct for observational
>> errors in inquiry in the normative sciences.
>>
>> Third: we can draw on math in order to understand the dualism. In doing
>> so, we are developing what one might call a mathematical phenomenology,
>> just as might develop a mathematical physics, psychology or economics.
>>
>> With that much said, I don't yet see a confusion over these matters in my
>> initial comments. It doesn't mean, however, that I wasn't confused. I
>> just don't see it yet.
>>
>> --Jeff
>>
>> Jeff Downard
>> Associate Professor
>> Department of Philosophy
>> NAU
>> (o) 523-8354
>> ________________________________________
>> From: Gary Richmond [[email protected]]
>> Sent: Thursday, August 21, 2014 2:07 PM
>> To: Jeffrey Brian Downard
>> Cc: Peirce List
>> Subject: Re: [PEIRCE-L] Phaneroscopy, iconoscopy, and trichotomic
>> category theory
>>
>> Jeff, list,
>>
>> For some reason I can't find the original of this post from which I'm
>> quoting you, I'm assuming. In any case, I am learning a great deal about
>> the form/matter distinction in these exchanges. Of course Peirce's
>> universal categories are formal ones, so in a sense what you've been doing
>> here is, at least for me, preliminary work in consideration of the Subject
>> of this thread, which I hope we'll return to eventually: namely, the
>> possible division of phenomenology into several branches.
>>
>> For now I have just a few concerns and questions. You wrote:
>>
>> JD: . . . the question of how our understanding of the mathematical form
>> of something such as a figure or diagram is supposed to inform our
>> understanding of the formal categories of monad, dyad and triad (or,
>> firstness, secondness, thirdness)--and how we might use those categories in
>> performing a phenomenological analysis of something that has been observed.
>>
>> My concern here may be more about terminology than anything else, but I
>> think the terminological distinctions are important. As I see it, monad,
>> dyad and triad pertain to mathematics while firstness, secondness,
>> thirdness are terms of phenomenology. They are, in my opinion, not
>> equivalent (as your 'or' would seem to imply). Peirce says that the
>> categories are 'discovered' in phenomenology and that only retrospectively,
>> so to speak, does one find in pure mathematics the monad, dyad, and triad
>> as expression of these universal categories. Related to monad/dyad/triad is
>> the reduction thesis, such that the valency theory which follows is, it
>> seems clear enough, a mathematical, not a phenomenological theory. It will
>> prove quite valuable in semiotic, of course (e.g. in EGs). Continuing:
>>
>> JD: Peirce says that he has introduced this explanation in order to
>> account for the emphatic dualism we find in the normative sciences. The
>> dualism is especially marked in logic and ethics (e.g., true and false,
>> valid and invalid, right and wrong, good and bad), but it is also found in
>> aesthetics. As such, he is noticing a phenomena that has been widely
>> observed to be a part of our common experience in thinking about how we
>> ought to act and think, and he is getting ready to venture a hypothesis to
>> explain what is surprising about the phenomena. The explanation of the
>> dualism that follows might seem a bit hard to make out, but I think it is
>> clear that this is what he is trying to do.
>>
>> I would agree that that "dualism is especially marked" in ethics (good vs
>> bad, etc.), but I have some reservations about this apropos of logic. While
>> dualism is, perhaps, "especially marked" in the second division of logic,
>> critical logic (esp. T v F propositions, etc.) there is some room for
>> triads even here e.g. the three inference patterns), while both the 1st and
>> 3rd branches, while not lacking dualistic elements, have considerable room
>> for triads (e.g. the triadic diagrams of semiotic grammar, and the three
>> phases of a complete inquiry in theoretical rhetoric, or methodeutic).
>> Continuting:
>>
>> JD: That might have seemed a bit opaque, so let me try to restate the
>> point. I think Peirce is drawing on an understanding of mathematical form
>> for the sake of performing an analysis of a particular phenomenon that
>> calls out for explanation. We need to see what it is in the phenomena
>> (i.e., the dualism in the normative sciences) that really calls out for
>> explanation. Otherwise, we will not have a clear sense of whether one or
>> another hypothesis is adequate or inadequate to explain what needs to be
>> explained.
>>
>> But 'phenomena' as you use it here ("i.e., the dualism in the normative
>> sciences") is not the 'phenomena' considered in phenomenology. Duality is
>> certainly a mathematical concept in the normative science, but to call it
>> 'phenomenological' is, for me, problematic. The dualism (which is not
>> secondness) which you point to in the normative sciences is drawn from
>> mathematics (again, the distinction between dyad, or dualism, and
>> secondness) and not from phenomenology.
>>
>> JD: Why does Peirce say that the importance of everything resides in its
>> mathematical form? On my reading of this passage and what follows in the
>> next several pages of the essay, I think he is developing the claim I
>> asserted above. That is, every kind of formal relation that might be found
>> between the parts of a figure, image, diagram and the space in which such
>> things are constructed must have the form of what we are calling, in our
>> phenomenological theory, a monad, dyad or triad.
>>
>> Again, I think that it is a mistake to conflate the mathematical
>> categories here (monad, dyad, triad) with the phenomenological categories
>> (firstness, secondness, thirdness). What I think that the normative
>> sciences draw especially from phenomenology are exactly the kinds of
>> trichotomic (== 3-category) relations which, I propose, are studied in a
>> third branch of phenomenology, trichotomic category theory. Where else
>> would the myriad trichotomic structures of logic as semiotic come from in
>> principle?
>>
>> Best,
>>
>> Gary
>>
>> Gary Richmond
>> Philosophy and Critical Thinking
>> Communication Studies
>> LaGuardia College of the City University of New York
>> C 745
>> 718 482-5690
>>
>>
>> On Wed, Aug 20, 2014 at 3:05 PM, Jeffrey Brian Downard <
>> [email protected]<mailto:[email protected]>> wrote:
>> Hi Jerry, List,
>>
>> First off, if things are sounding mystical to your ears, I hope it is a
>> by product of the richness of the ideas Peirce is examining--and not a
>> by-product of the comments I'm offering.
>>
>> To a large degree, the answers to the questions you are trying to raise
>> are going to be found in the larger story that is articulated in the theory
>> of semiotics. At this point, I am trying to offer some comments on some of
>> Peirce's explanations and definitions as a kind of run up to the
>> phenomenological categories--and especially the distinction between the
>> formal and material aspects of those categories. The general suggestion
>> I'm making is that Peirce is not providing two entirely separate lists of
>> the categories, one formal and that other material. Rather, there is a
>> close connection between the two even if they do not, in experience, match
>> perfectly because our experience of the material categories of quality,
>> brute fact and mediation is always so richly complex. My general
>> suggestion may seem controversial because some interpreters seem to be
>> offering a different reading of the relevant texts.
>>
>> Confining myself to the subject of the phenomenological categories and
>> the role of mathematics in informing our understanding of the essential
>> formal elements of the monad, dyad and triad, I do take Peirce to be
>> offering an account of the elements needed for setting up the frameworks
>> necessary for referring to grounds, objects and interpretants. One might
>> call them three interrelated "frames of reference."
>>
>> What do the signs that we use in mathematics refer to? Much depends upon
>> whether we are using the signs to seeks answer to questions in pure or
>> applied mathematics. Let's consider the case of pure mathematics. What do
>> the signs used in topology refer to? In the account he offers in the New
>> Elements, the key operations for setting up a system of mathematical
>> diagrams are those of generation and intersection. These are the
>> operations used to generate a line by moving a particle from a point, or
>> for determining the location of a point on a line by intersecting it with
>> another line.
>>
>> As we try to understand the conditions that make it possible for the
>> different representations to refer, we'll need to be clear in identifying
>> the representations we're talking about. It is one thing to ask: what
>> does that particle in the diagram that is being moved refer to? It is
>> another thing to ask, what does the symbol "particle" refer to? I hope it
>> is clear that the conditions under which the symbol "particle" refers is
>> dependent, in many respects, on the conditions under which the iconic
>> particle that is draw on the page is able to refer. As a hypo-icon, the
>> particle we move as we draw the line is remarkably rich as a sign. At any
>> time in the act of drawing the line on the paper, there are qualisigns,
>> sinsigns and legisigns working together so that the particle can function
>> as a rich sign complex in a larger process of interpretation. What is
>> more, the particle embodies the idea of a generator. That is, it embodies
>> a more general rule that determines how we might generate innumerable other
>> possible lines from the point. This is a more general rule that enables us
>> to interpret the larger mathematical space in which the line is being
>> constructed. It enables us to understand how one line my be transformed
>> continuously to give us a line that is homeomorphic with the first, or how
>> various kinds of discontinuities might be introduced to give us another
>> different line altogether.
>>
>> I hope you can see that I'm trying to bracket some of the questions
>> you've raised about the role of real things (i.e., chemical compounds,
>> protein or DNA molecules, and the like) in serving as the grounds or
>> objects to which one or another kind of representation might refer. I'm
>> bracketing those questions for a reason. I'd like to keep the
>> phenomenological analysis of the conditions under which the signs used in
>> pure mathematics refer free from big metaphysical assumptions about what is
>> really the case as a positive matter of fact. There is a long line of
>> philosophers who have tried to import such metaphysical assumptions into
>> their accounts of the reference and meaning of the signs used in math and
>> formal logic (e.g., Mill, Quine, etc.), but Peirce is resisting this
>> move--at least until we're ready to address questions in metaphysics. Once
>> we are ready and we're using the methods appropriate for answering
>> questions in metaphysics, we'll need to think about the real nature of an
>> ideal system of mathematical definitions, hypotheses, theorems, etc., and
>> what it is for that system to be real as a rich and consistent network of
>> possible formal relations.
>>
>> --Jeff
>>
>>
>> Jeff Downard
>> Associate Professor
>> Department of Philosophy
>> NAU
>> (o) 523-8354
>> ________________________________________
>> From: Jerry LR Chandler [[email protected]<mailto:
>> [email protected]>]
>> Sent: Tuesday, August 19, 2014 9:28 PM
>> To: Jeffrey Brian Downard
>> Cc: Peirce List
>> Subject: Re: [PEIRCE-L] Phaneroscopy, iconoscopy, and trichotomic
>> category theory
>>
>> Jeffrey:
>>
>> Your posts become increasingly mystical.
>>
>> This is not a judgement, merely an observation from a philosophy of
>> mathematics perspective.
>>
>> At issue is how to you assign meaning to mathematical symbols.
>> In particular, in light of K.S. and his comments on the meaning of number
>> in the context of his description of gold?
>>
>> More to the point, does the meaning of mathematical symbols reside in
>> mathematics itself or do the meanings refer to the reference systems for
>> the symbol system, that is the application to a particular material
>> reality, such as the atomic numbers? Or the sequence numbers for a genetic
>> sequence? Or protein sequence?
>> In yet other terms, does the concept of order infer a universal meaning
>> or a meaning dependent on the nouns of the copulative proposition?
>>
>> Perhaps you can address these vexing issue?
>>
>> Cheers
>>
>> Jerry
>>
>>
>>
>>
>> On Aug 19, 2014, at 8:28 PM, Jeffrey Brian Downard <
>> [email protected]<mailto:[email protected]>> wrote:
>>
>> > Gary F., Gary R., List,
>> >
>> > In an effort to think a bit more about the form/matter distinction as
>> it applies to the phenomenological categories, let me add few comments
>> about an explanation that Peirce provides concerning the mathematical form
>> of a state of things. I'd like to add some remarks about this explanation
>> because I think it offers us a nice way of responding to a concern Gary F.
>> raised. Here is the concern:
>> >
>> > Gary F. says: "Jeff, I'm interested in your question, 'is there any
>> kind of formal relation between the parts of a figure, image, diagram
>> (i.e., any hypoicon) that does not have the form of a monad, dyad or
>> triad?' . . . I confess that I have no idea how we would go about
>> investigating that question."
>> >
>> > My initial response was: "The answer to the question involves the
>> whole of Peirce's semiotic--and not just his account of the iconic function
>> of signs. So Peirce is bringing quite a lot to bear on the question. For
>> starters, however, I think we should consider the examples he thinks are
>> most important in formulating an answer. What Peirce sees is that, in
>> mathematics, the examples we need are as 'plenty as blackberries' in the
>> late summer. (CP 5.483) What do you know, it is late August. Let's go
>> picking."
>> >
>> > As a first stop on our way to the briar patch, let's consider the
>> following definition from "The Basis of Pragmaticism in the Normative
>> Sciences."
>> >
>> > "A mathematical form of a state of things is such a representation of
>> that state of things as represents only the samenesses and diversities
>> involved in that state of things, without definitely qualifying the
>> subjects of the samenesses and diversities. It represents not necessarily
>> all of these; but if it does represent all, it is the complete mathematical
>> form. Every mathematical form of a state of things is the complete
>> mathematical form of some state of things. The complete mathematical form
>> of any state of things, real or fictitious, represents every ingredient of
>> that state of things except the qualities of feeling connected with it. It
>> represents whatever importance or significance those qualities may have;
>> but the qualities themselves it does not represent." (EP, vol. 2, 378)
>> >
>> > Peirce suggests that this explanation is "almost self-evident." At
>> this point in his discussion, however, he merely ventures the explanation
>> as a "private opinion." I cite this passage because it bears directly on
>> the question of how our understanding of the mathematical form of something
>> such as a figure or diagram is supposed to inform our understanding of the
>> formal categories of monad, dyad and triad (or, firstness, secondness,
>> thirdness)--and how we might use those categories in performing a
>> phenomenological analysis of something that has been observed.
>> >
>> > Peirce says that he has introduced this explanation in order to account
>> for the emphatic dualism we find in the normative sciences. The dualism is
>> especially marked in logic and ethics (e.g., true and false, valid and
>> invalid, right and wrong, good and bad), but it is also found in
>> aesthetics. As such, he is noticing a phenomena that has been widely
>> observed to be a part of our common experience in thinking about how we
>> ought to act and think, and he is getting ready to venture a hypothesis to
>> explain what is surprising about the phenomena. The explanation of the
>> dualism that follows might seem a bit hard to make out, but I think it is
>> clear that this is what he is trying to do.
>> >
>> > That might have seemed a bit opaque, so let me try to restate the
>> point. I think Peirce is drawing on an understanding of mathematical form
>> for the sake of performing an analysis of a particular phenomenon that
>> calls out for explanation. We need to see what it is in the phenomena
>> (i.e., the dualism in the normative sciences) that really calls out for
>> explanation. Otherwise, we will not have a clear sense of whether one or
>> another hypothesis is adequate or inadequate to explain what needs to be
>> explained.
>> >
>> > He says the following about his account of the mathematical form of a
>> state of a things: "Should the reader become convinced that the importance
>> of everything resides entirely in its mathematical form, he too, will come
>> to regard this dualism as worthy of close attention?"
>> >
>> > Why does Peirce say that the importance of everything resides in its
>> mathematical form? On my reading of this passage and what follows in the
>> next several pages of the essay, I think he is developing the claim I
>> asserted above. That is, every kind of formal relation that might be found
>> between the parts of a figure, image, diagram and the space in which such
>> things are constructed must have the form of what we are calling, in our
>> phenomenological theory, a monad, dyad or triad.
>> >
>> > It might sound ridiculous to suggest that the dualism present in our
>> experience of what is valid or invalid as a reasoning or what is right or
>> wrong as an action can be clarified by using a mathematical diagram, such
>> as a drawing on a piece of paper of two dots that we might count by saying
>> "one' and "two," but he says that we shouldn't disregard such a
>> suggestion. He has argued elsewhere that every observation we might make
>> must involve some kind of figure or diagram--and the form of such a figure
>> or diagram can be understood in terms of having the structure of a skeleton
>> set (CP, 7.420-32), or a network figure (CP, 6.211), or some other kind of
>> really basic mathematical structure. I refer to those particular
>> mathematical structures because the first can be applied to things in our
>> experience that are more discrete in character, and the second can placed
>> over things more continuous in character.
>> >
>> > Do you buy his claim here? Does the "importance of everything reside
>> in its mathematical form?" The argument he offers in the rest of section B
>> is worth a look.
>> >
>> > --Jeff
>> >
>> >
>> > Jeff Downard
>> > Associate Professor
>> > Department of Philosophy
>> > NAU
>> > (o) 523-8354
>> > ________________________________________
>> > From: Jeffrey Brian Downard
>> > Sent: Saturday, August 16, 2014 4:09 PM
>> > To: Gary Richmond; Peirce-L; Gary Fuhrman; André De Tienne
>> > Subject: RE: [PEIRCE-L] Phaneroscopy, iconoscopy, and trichotomic
>> category theory
>> >
>> > Gary R., Gary F., André, List,
>> >
>> > Peirce makes two suggestions for doing phenomenology, and both are
>> reflected in the place he gives this kind of science in his architectonic.
>> >
>> > 1) We should ask: what formal categories must be in experience in
>> order to make valid synthetic inferences from the things we've observed?
>> Or, putting the question in a more particular form: what formal elements
>> must be in the observations we made of some surprising phenomenon in order
>> to draw a valid adductive inference to an explanatory hypothesis? The same
>> kind of question could be asked about inductive inferences from a set of
>> data.
>> >
>> > 2) In order to answer this question, we should look to math and see
>> what kinds of mathematical conceptions and principles might be borrowed
>> from this science so as to give us insight into those formal features of
>> the phenomena we observe.
>> >
>> > These suggestions are reflected in Peirce's placement of phenomenology
>> between math and the normative theory of logic.
>> >
>> > In order to see why these suggestions might be helpful for
>> understanding Peirce's theory of phenomenology (i.e., phaneroscopy), I'd
>> suggest that we take up a sample problem. Here is a question that mattered
>> much to Peirce. What kinds of observations can we draw on in formulating
>> hypotheses in the theory of logic about the rules of valid inference?
>> Peirce's answer to this question is that we are able to make a distinction
>> between valid and invalid inferences in our ordinary reasoning, and that we
>> can classify different kinds of inferences as deductive, inductive and
>> adductive. The process of drawing on our logica utens in making arguments
>> and reflecting on the validity of those arguments supplies us with the
>> observations that are needed to get a theory of critical logic off the
>> ground.
>> >
>> > As we all know, any kind of scientific observation we make might
>> contain one or another kind of observational error. As such, we have to
>> ask the following questions. Once we have a set of observations in hand,
>> how should we analyze them? What is more, how can we correct for the
>> observational errors we might have made? We could frame the same kinds of
>> questions about the study of speculative grammar as I've stated for a
>> critical logic. For my part, I'm working on the assumption that Peirce's
>> analysis of the elements of experience is designed to help us give better
>> answers to these kinds of questions than we are able to get from other
>> philosophical methods--including those of Kant, Hamilton, Mill, Boole, etc.
>> >
>> > The study of icons, I take it, is part of a general strategy of
>> thinking more carefully about question (1) listed above. Gary R., are you
>> thinking about "iconoscopy" or "imagoscopy" differently? I think that the
>> careful study of icons can be especially helpful in setting up a theory of
>> logic because of the essential role that icons have in the process of
>> making of valid inferences.
>> >
>> > With this much said, let me ask a question that I think is really basic
>> for understanding Peirce's phenomenology: is there any kind of formal
>> relation between the parts of a figure, image, diagram (i.e., any hypoicon)
>> that does not have the form of a monad, dyad or triad? That is, take the
>> space in which a diagram or other figure might be drawn, and take the
>> relations between the parts of any diagram (both actual and possible), and
>> ask yourself: how are the actual parts of the token diagram connected to
>> each other and to all of the possible transformations that might be made
>> under the rules that are used to construct and interpret the diagram? Is
>> there any formal relation between the parts of the diagram and the space in
>> which it is constructed that does not have the character of a monadic,
>> dyadic or triadic relation?
>> >
>> > We see that Peirce makes much of the role of icons in necessary
>> reasoning, including the necessary reasoning by which mathematicians deduce
>> theorems from the hypotheses that lie at the foundations of any given area
>> of mathematics. The suggestion I'm making is based on the idea that icons
>> have a similarly essential role in the framing of a hypothesis and the
>> drawing of an inductive inference. Do you know of a place where Peirce
>> argues this kind of point? One sort of place that comes to my mind is the
>> discussions he provides of the process of formulating hypotheses in
>> mathematics.
>> >
>> > --Jeff
>> >
>> > Jeff Downard
>> > Associate Professor
>> > Department of Philosophy
>> > NAU
>> > (o) 523-8354
>> > ________________________________________
>> > From: Gary Richmond [[email protected]<mailto:
>> [email protected]>]
>> > Sent: Saturday, August 16, 2014 11:15 AM
>> > To: Peirce-L; Gary Fuhrman; André De Tienne
>> > Subject: [PEIRCE-L] Phaneroscopy, iconoscopy, and trichotomic category
>> theory
>> >
>> > Gary, list,
>> >
>> > I suppose I expected--or at least, hoped--that Gary F. would respond to
>> my post on some of the issues we'd been discussing recently regarding
>> phenomenology, a topic of some considerable interest to both of us and,
>> hopefully, to others on the list as well. So, in an off-list email to him I
>> expressed this hope, and Gary wrote back in a message he said I could
>> reproduce here. (I've interleaved my own comments within the substantive
>> parts of that message)
>> >
>> > I've already agreed that iconoscopy is probably the only way to make
>> phaneroscopy scientific, if its formulations themselves are scientific.
>> >
>> > I would concur, especially if your qualification is met. But, for now,
>> iconoscopy is the subject of but a single, as far as I can tell,
>> unpublished article by Andre de Tienne (who, as I earlier suggested,
>> thought the term 'iconoscopy' didn't exactly catch his meaning, that
>> something like 'imagoscopy' might come closer). There were also several
>> discussions of de Tienne's ideas in 2009 (as interest was shown in then by
>> Martin Lefebvre, myself, and others) and again in 2011 when both Gary F.
>> and I discussed them in the slow read of Joe's paper, "Is Peirce a
>> Phenomenologist?" See:
>> https://www.mail-archive.com/[email protected]/msg00043.html
>> >
>> > Still, the idea of this second phenomenological science seems sound to
>> me, and even necessary. Continuing:
>> >
>> > But I don't have a proper response to this:
>> > So what exactly are "the elements of the phaneron" once one's stated
>> the obvious, that is, the three universal categories?
>> > I don't think that's obvious at all, or maybe I don't get what you mean
>> by "obvious" here. It's not even obvious to many list members what it means
>> that the three "categories" are "universal". So I'm stumped for an answer
>> to that question.
>> >
>> > Hm. I guess I'm stumped by your being stumped. It may be that some,
>> perhaps many, list members don't 'get' Peirce's categories at all, let
>> alone see them as 'universal'. But some people do observe "the elements of
>> the phaneron" and do see them as universal. I would even suggest, by way of
>> personal example, that I saw them before I was even exposed to Peirce's
>> writings, and before I could give them names (certainly not firstness,
>> secondness, and thirdness, but, perhaps, something vaguely approaching
>> something, other, medium). This is merely to say that, if Peirce is correct
>> and that the elements of the phaneron are truly universal, then there's no
>> reason why anyone attuned to that kind of observation shouldn't and
>> couldn't have touched upon them before having Peirce's precise and helpful
>> names for them.
>> >
>> > Phenomenology is admittedly a difficult science to grasp and even more
>> difficult to 'do', so I can imagine that many folk, including many
>> philosophers, haven't developed, or fully developed, the kinds of
>> sensibilities and abilities which Peirce thought were essential in doing
>> this science--that is, they haven't developed them any more than, for
>> example, I've developed some of the mental skills necessary for taking up
>> certain maths. But, as to our interests and talents, vive la difference!
>> >
>> > Also it's still not clear to me how "category theory" or "trichotomic"
>> is related to phaneroscopy and iconoscopy, or why it's part of Peircean
>> "phenomenology" (rather than logic or semiotic, or even methodeutic). It
>> seems to take the results of phaneroscopy (as articulated by iconoscopy, I
>> suppose) and apply them to the analysis and classification of more complex
>> phenomena such as semiotic processes. If so, then it should be subordinate
>> to phenomenology in the classification of sciences, not part of it.
>> >
>> > Here I must completely disagree. While it is true that trichotomic can
>> and will be applied in principle to semiotic, it is my opinion--well, more
>> precisely, my experience--that trichotomies are discovered in
>> phenomenological observation. And I personally have no doubt that Peirce
>> observed them in this way. It may be that one needs a kind of logica utens
>> to sort out some of these structures after the fact of the observation of
>> them, but, for example, it is possible in observing many phenomena, to
>> 'see' that firstness, secondness, and thirdness form a necessary trichotomy
>> within them,so to speak; and that 'something', 'other', 'medium' requires a
>> vectorial progression from 1ns, through 2ns, to 3ns, and in precisely that
>> (categorial, in this case, dialectical) order.These are, of course, two of
>> the most basic expressions of (a) trichotomic and (b) vectorial
>> progression. At the moment I can see no other place for the observation of
>> such trichotomic structure and the establishing of this as a principle for
>> the use by sciences which follow phenomenology except at the end (the
>> putative third division) of it.
>> >
>> > In logic, of course, Peirce considers diagrams more essential than
>> language; but I don't see how diagrams can be used in phenomenology to
>> avoid language, so I don't have a useful suggestion for doing that either,
>> although I wouldn't want to say that it can't be done. I was hoping
>> somebody else would have a better response.
>> >
>> > But certainly very many, perhaps most, diagrams of considerable value
>> to and use in science necessarily require language, or use language as an
>> adjunct. This, for example, is the case for some of the trichotomic
>> diagrams Peirce offers in certain letters to Lady Welby. The diagrams I use
>> in trikonic are meant, first, to show the categorial associations of the
>> terms of a genuine trichotomic relationship (those icons/images identified
>> in what might be called an iconoscopic observation, then given names) and,
>> second, to show the possible vectors (or paths) that are possible--and,
>> some times, evident-- in some of them. A logica utens allows one to
>> extrapolate rather far in this vectorial direction, in my opinion. But such
>> a use of logica utens is the case in theoretical esthetics and ethics as
>> well. Ordinary logic (logica utens) need not and probably cannot be avoided
>> in the pre-logical (i.e., pre-semiotic, pre-logica docens) sciences.
>> >
>> > If any of the above is useful as a prompt for a further explanation of
>> "category theory", feel free to quote it and reply with a correction!
>> Meanwhile, yes, I am busy with a number of things these days ...
>> >
>> > Yes, your remarks have been at least personally useful, especially in
>> seeing that until the first two branches of phenomenology, phaneroscopy
>> and, especially, iconoscopy, are much further developed, trichotomic
>> category theory will lack a solid basis. Still, important science has been
>> accomplished in all the post-phenomenological sciences without this
>> grounding and I expect this to happen in trichotomic as well.
>> >
>> > Peirce clearly saw the categories as a kind of heuristic leading him to
>> a vast array of discoveries along the way. It is not surprising, then, that
>> late in life he settled on an essentially trichotomic classification of the
>> sciences. It seems to me that if one allows for a second phenomenological
>> science, iconoscopy, that it makes sense to at least look for yet a third
>> one--perhaps especially in this science which discovers three universes of
>> experience.
>> >
>> > And further, it seems to me that the first of the semiotic sciences,
>> theoretical or semiotic grammar, gets one of its most important principles,
>> namely, trichotomic structure (cf. object/sign/interpretent;
>> qualisign/sinsign/legisign; icon/index/symbol; rheme, dicent, argument; the
>> trichotomic structure of the 10-adic classification of signs; etc.) not out
>> of thin air, but from some science preceding it according to Comte's
>> principle of the ordering of the sciences, that those lower on the list
>> drawn principles from those above them.
>> >
>> > Suffice it to say for now that in my opinion trichotomic category
>> theory ought be placed in phenomenology, not further down in the
>> classification of the sciences (Gary, you suggested methodology, which
>> makes no sense to me at all), And, rather than being "subordinate to
>> phenomenology," it seems to me that, within phenomenology, and at the
>> conclusion of it, that it provides exactly the bridge leading to the
>> normative sciences, but especially to semiotic grammar.
>> >
>> > Best,
>> >
>> > Gary
>> >
>> > Gary Richmond
>> > Philosophy and Critical Thinking
>> > Communication Studies
>> > LaGuardia College of the City University of New York
>> > C 745
>> > 718 482-5690<tel:718%20482-5690><tel:718%20482-5690>
>> > -----------------------------
>> > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON
>> PEIRCE-L to this message. PEIRCE-L posts should go to
>> [email protected]<mailto:[email protected]> . To
>> UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected]
>> <mailto:[email protected]> with the line "UNSubscribe PEIRCE-L" in the
>> BODY of the message. More at
>> http://www.cspeirce.com/peirce-l/peirce-l.htm .
>> >
>> >
>> >
>> >
>>
>>
>>
>> -----------------------------
>> PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON
>> PEIRCE-L to this message. PEIRCE-L posts should go to
>> [email protected]<mailto:[email protected]> . To
>> UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected]
>> <mailto:[email protected]> with the line "UNSubscribe PEIRCE-L" in the
>> BODY of the message. More at
>> http://www.cspeirce.com/peirce-l/peirce-l.htm .
>>
>>
>>
>>
>>
>>
>>
>> -----------------------------
>> PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON
>> PEIRCE-L to this message. PEIRCE-L posts should go to
>> [email protected] . To UNSUBSCRIBE, send a message not to PEIRCE-L
>> but to [email protected] with the line "UNSubscribe PEIRCE-L" in the
>> BODY of the message. More at
>> http://www.cspeirce.com/peirce-l/peirce-l.htm .
>>
>>
>>
>>
>>
>>
>
-----------------------------
PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L
to this message. PEIRCE-L posts should go to [email protected] . To
UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] with the
line "UNSubscribe PEIRCE-L" in the BODY of the message. More at
http://www.cspeirce.com/peirce-l/peirce-l.htm .
