Gary F., List:
I have been following this thread with considerable interest throughout,
and am finally ready to offer a substantive contribution to it. I agree
that the subject matter "dovetails" nicely with what I have been saying in
the thread about "Logical Analysis of Signs."
CSP: *Corollaries*. It follows that no line of identity can cross a cut.
GF: The first “corollary” is important because Peirce will explicitly
change his mind about it in the spring of 1906.
Perhaps you will address this in your next installment, but I was not aware
that Peirce ever changed his mind about this. My understanding is that
when a Line of Identity *appears *to cross a Cut, it is really a
*Ligature*--two
*different *Lines of Identity that *abut *at the Cut itself, such that
there are *two *indefinite individuals there, which are interpreted as *not
*being identical.
GF: Notice also that the *extremity* of a *line of identity* “denotes” an
*individual* (in the strict logical sense of that word). But this is a
somewhat peculiar use of “denote,” compared to its application to
propositions, where the subject *denotes* the object of the propositional
sign, and that subject is a *symbol*, typically a proper noun (a symbol
crucially involving an index).
Denotation is the function of an Index (cf. EP 2:307; 1904), so on the
standard interpretation of EGs, each extremity of a Line of Identity is an
Index of an *indefinite *individual ("something"). The Line of Identity *as
a whole*, with no Spot at either end, is a Graph of the Proposition,
"something is identical to something."
GF: The upshot of this, if I understand it, is that a *spot of
teridentity* may
be regarded either as a rhema, which is a general concept, or as a denoted
*individual*, which (by definition) is *not* general, but is identical to
the three extremities of the graph of teridentity.
I suggest that a *Spot* of Teridentity by itself is a Seme for the
continuous predicate, "_____ is identical to _____ and to _____";
while a *Graph
*of Teridentity--a Spot of Teridentity with three loose-ended Lines of
Identity attached--represents the Proposition, "something is identical to
something and to something."
GF: The question then is whether this ambiguity of the term represents a
vagueness built into the system of EGs or an indefiniteness which is a
constituent of the phaneron itself — perhaps even a *real* vagueness.
I suggest that this "ambiguity" simply reflects the fact that *any *analysis
of a Proposition--which is what every EG represents--into subject(s) and
predicate(s) is somewhat arbitrary, and this carries over to the
interpretation of EGs. There are two different "ultimate" approaches--we
can throw everything possible into the *predicate*, treating each Spot
as a *discrete
*predicate and each Line as an *indefinite *subject; or we can throw
everything possible into the *subject*, treating each monadic Spot as
a *hypostatized
*subject, and each dyadic or higher Spot ("stands") and each Line as a
*continuous
*predicate.
GF: You can’t have a predicate without a subject of which it is
predicated; that subject must be an actuality or existent in the commens,
and is identical to the object of the proposition; that object is *denoted* by
the *subject* of the proposition while the predicate is *signified* by that
proposition.
I agree, which is why I continue to be puzzled by John Sowa's persistent
attempts to do away with logical subjects altogether. Granted, modern
predicate logic prefers to call them *variables* or *identifiers*, but
there is nothing inaccurate about recognizing them as *indefinite subjects*
instead. Of course, it is not necessary that each subject denote something
that *actually exists* in the metaphysical sense; it just needs to "exist"
within the Commens, the Universe of Discourse as represented by the Sheet
of Assertion--i.e., it must be something *already known* to both Graphist
and Interpreter.
GF: More generally, we can recognize a First as an element of the phaneron
only by prescinding it from the appearance of an existing thing, a Second
which has that First as a *quality*.
Yes--and then we can think and talk *about *a First as an element of the
Phaneron only by (hypostatically) *abstracting *it, such that it can then
be the Object of a Seme that serves as a *subject* of Propositions.
GF: The semiotic corollary is that you can’t have a Sign without both an
Object and an Interpretant as its correlates; you can’t have an Object (in
the semiotic sense!) without a Sign which it determines and an Interpretant
determined by the Object *through* the Sign; and you can’t have an
Interpretant that doesn’t involve the Secondness between Sign and Object.
Indeed, every *actual *Sign (Token) has both a *Dynamic* Object that
determines it and a *Dynamic *Interpretant that it determines. My
understanding is that *none *of these three correlates can be
identical to *either
*of the others, so a Graph of Teridentity with its three "spokes" is
an *inaccurate
*diagram of their relation. For one thing, identity is a *symmetrical*
relation, as Peirce explicitly affirmed in a passage that I recently quoted
in the other thread.
CSP: It is, however, important to state that the relations of identity and
of coexistence are but degenerate Secundan, and that these two are the only
*simple* dyadic relations which are symmetrical, that is, which imply each
its own converse. (R 284:88[83]; 1905)
But he clearly held that the irreducible triadic relation in which a
Sign *mediates
*between its Object and its Interpretant is *asymmetric*.
CSP: As a *medium*, the Sign is essentially in a triadic relation, to its
Object which determines it, and to its Interpretant which it determines. In
its relation to the Object, the Sign is *passive*; that is to say, its
correspondence to the Object is brought about by an effect upon the Sign,
the Object remaining unaffected. On the other hand, in its relation to the
Interpretant the Sign is *active*, determining the Interpretant without
being itself thereby affected. (EP 2:544n22; 1906)
As such, it can only be properly scribed in EGs as a multi-Peg Spot--either
"mediates" with three Pegs, or "stands" with four Pegs including one for
"mediating" as a subject (see attached). This demonstrates conclusively
that it is *false*, or at least misleading, to characterize the Sign *itself
*as a triad; rather, it is the *relation* of mediating (or representing)
that is a triad, since it always requires three correlates--e.g., the Sign,
the Object, and the Interpretant.
GF: Now, what are the phaneroscopic and/or metaphysical implications of
considering every line of identity as “bristling with microscopic points of
teridentity”?
It brings to my mind these comments that Peirce made several decades
earlier.
CSP: A logical atom, then, like a point in space, would involve for its
precise determination an endless process. We can only say, in a general
way, that a term, however determinate, may be made more determinate still,
but not that it can be made absolutely determinate. (CP 3.93; 1870)
CSP: The absolute individual can not only not be realized in sense or
thought, but cannot exist, properly speaking ... All, therefore, that we
perceive or think, or that exists, is general. So far there is truth in the
doctrine of scholastic realism ... That which exists is the object of a
true conception. This conception may be made more determinate than any
assignable conception; and therefore it is never so determinate that it is
capable of no further determination. (CP 3.93n; 1870)
Likewise, no matter how many Spots we attach to a Line of Identity by
adding Points of Teridentity--i.e., no matter how many *discrete *predicates
we attribute to whatever it denotes--it will always remain *indeterminate *in
infinitely many other respects. In other words, even an *individual *is
still *general *to some degree; hence, as you hinted below, we must
prescind 2ns from 3ns *before *we can prescind 1ns from 2ns.
Regards,
Jon Alan Schmidt - Olathe, Kansas, USA
Professional Engineer, Amateur Philosopher, Lutheran Layman
www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt
On Sun, Mar 31, 2019 at 11:49 AM <[email protected]> wrote:
> Gary R, list,
>
> The very concept of *teridentity* is intriguing, and plays a central role
> in the interface between phaneroscopy and Existential Graphs (and thus
> logic) that I am trying to explore — which also makes it central to the
> “major shift in Peirce’s thinking” which I see occurring in the spring of
> 1906. So I guess it’s time I devoted an entire post to the subject of
> teridentity. To get the drift of it, I think we need to regard
> phaneroscopy, ontology, and the conventions of Existential Graphs as three
> parallel universes of discourse such that an assertion in one necessarily
> has implications in the other two, and they frequently draw terms from one
> another to make those assertions.
>
> We begin with the *Syllabus* which accompanied the 1903 Lowell lectures:
>
> [[ *Convention No. V*. Every heavily marked point, whether isolated, the
> extremity of a heavy line, or at a furcation of a heavy line, shall denote
> a single individual, without in itself indicating what individual it is.
>
> A heavily marked line without any sort of interruption (though its
> extremity may coincide with a point otherwise marked) shall, under the name
> of *a line of identity*, be a graph, subject to all the conventions
> relating to graphs, and asserting precisely the identity of the individuals
> denoted by its extremities.
>
> *Corollaries*. It follows that no line of identity can cross a cut.
>
> Also, a point upon which three lines of identity abut is a graph
> expressing the relation of *teridentity*. ] CP 4.405-6 ]
>
> These definitions must be kept in mind as we proceed. The first
> “corollary” is important because Peirce will explicitly change his mind
> about it in the spring of 1906. Notice also that the *extremity* of a *line
> of identity* “denotes” an *individual* (in the strict logical sense of
> that word). But this is a somewhat peculiar use of “denote,” compared to
> its application to propositions, where the subject *denotes* the object
> of the propositional sign, and that subject is a *symbol*, typically a
> proper noun (a symbol crucially involving an index). In the EG system, the
> only means of *denoting* in that sense, i.e. ‘naming’ an individual, is a
> Selective, a letter placed at the extremity of a line of identity. As we
> know from the “Bedrock” manuscript, Peirce will by 1908 come to recognize
> this as a fundamental weakness of the whole EG system.
>
> Further on in the same document, we learn that a *point of teridentity*
> may also be a *spot* of teridentity:
>
> [[ 10. A *spot* is a graph any replica of which occupies a simple bounded
> portion of a surface, which portion has qualities distinguishing it from
> the replica of any other spot; and upon the boundary of the surface
> occupied by the spot are certain points, called the *hooks* of the spot,
> to each of which, if permitted, one extremity of one line of identity can
> be attached. Two lines of identity cannot be attached to the same hook; nor
> can both ends of the same line.
>
> 11. Any indefinitely small dot may be a spot replica called a *spot of
> teridentity*, and three lines of identity may be attached to such a spot. ]
> CP 4.416 ]
>
> In EGs, of course, a *spot* usually represents a logical *rhema* (or
> semiotic *rheme*) which has a valency, and is thus analogous to an
> element of the phaneron. The “boundary of the surface occupied by the
> spot” is purely imaginary and is not drawn on the graph-instance. It is
> visible in the graph only where a *point* on that boundary (a *hook* or
> *peg*) has a line of identity attached to it, and that point coincides
> with the extremity of the line, which also *denotes an individual*. The
> upshot of this, if I understand it, is that a *spot of teridentity* may
> be regarded either as a rhema, which is a general concept, or as a denoted
> *individual*, which (by definition) is *not* general, but is identical to
> the three extremities of the graph of teridentity. The question then is
> whether this ambiguity of the term represents a vagueness built into the
> system of EGs or an indefiniteness which is a constituent of the phaneron
> itself — perhaps even a *real* vagueness. I don’t know whether this
> investigation will arrive at an answer to (or an improved statement of)
> this question or not.
>
> The next stop on this guided tour is Peirce’s draft letter to Lady Welby
> dated March 9, 1906. I’ve placed this document on my website,
> http://www.gnusystems.ca/PeirceWelbyMarch1906.htm, and I would ask
> interested readers to view it with their browsers (rather than me trying to
> paste the many graphics into this email post) to see Peirce’s diagrams in
> their context, as many of my quotes from the letter will refer to one or
> more of those diagrams. You can of course keep your browser window open to
> facilitate moving back and forth between this post and the full version of
> the document. I might wish there were a better transcription of this
> document online, but I am not aware of its publication in any format other
> than the appendix of *Semiotics and Significs*, the source of my
> transcription. (A small part of it is given near the end of EP2, but that
> is not the part I will be focusing on.) Let me start with this remark that
> Peirce makes about the system of Existential Graphs:
>
> [[ If you take in all that I have said and what I am just about to say,
> you will begin to get an insight into the marvellous perfection and minute
> truth and profundity of this system.
>
> Logicians who analyze a proposition into “terms” and a “copula” are guilty
> of overlooking the truth I have just enunciated, that it is out of the
> nature of things for an object to be signified (and remember that the most
> solitary meditation is dialogue), otherwise than in relation to some
> actuality or existent in the commend. ] SS 197; I assume that “commend”
> is synonymous with *commens* and *commind* (a term he used earlier in the
> letter), which in EGs is represented by the Sheet of Assertion. ]
>
> If I may rephrase that: You can’t have a predicate without a subject of
> which it is predicated; that subject must be an actuality or existent in
> the commens, and is identical to the object of the proposition; that object
> is *denoted* by the *subject* of the proposition while the predicate is
> *signified* by that proposition. But that signified predicate can also be
> regarded as an “object,” because it can be an *object of attention* in
> phaneroscopy, namely a First, like the color of the sealing-wax in Peirce’s
> example that I posted earlier. The phaneroscopic point, I think, is that a
> color does not *appear* in the absence of *something* existent which
> actually has that color. More generally, we can recognize a First as an
> element of the phaneron only by prescinding it from the appearance of an
> existing thing, a Second which has that First as a *quality*. But also,
> *recognition*, or indeed any kind of cognition (or *thought* or *sign*),
> must also involve Thirdness. The semiotic corollary is that you can’t have
> a Sign without both an Object and an Interpretant as its correlates; you
> can’t have an Object (in the semiotic sense!) without a Sign which it
> determines and an Interpretant determined by the Object *through* the
> Sign; and you can’t have an Interpretant that doesn’t involve the
> Secondness between Sign and Object. In short, *significance* is a triadic
> relation — and this ‘feeds back’ into phaneroscopy because, as Peirce said
> in the quote I posted yesterday, it is “a necessary deduction from the fact
> that there are signs, that there must be an elementary triad.”
>
> I’m beginning to sense that this post is growing like Jack’s beanstalk, so
> I’ll end it with Peirce’s remarks about *teridentity* in the letter
> draft, and hope that readers can see how it is related to the above.
>
> [[ Introducing the graph of teridentity [diagram] … Quateridentity is
> obviously composed of two teridentities [diagram] but teridentity cannot be
> formed out of binidentity _________ where two lines merely make one longer
> line.
>
> Here let me point out what we mean in logic by *equivalence* and by
> *composition*.
>
> If one rheme, or verb, would be true in every conceivable case in which
> the other would be true, and conversely, then and only then those two verbs
> are *logically equivalent*. For logic has in view only the possible truth
> and falsity of signs.
>
> To say that a rheme is *logically composed* of two rhemes is to say that
> the first rheme is logically equivalent to the composite of the other two.
>
> It follows in the first place that every line of identity ought to be
> considered as bristling with microscopic points of teridentity; so that
> ___________ when magnified shall be seen to be [image: image.png]] SS 199
> ]
>
> Now, what are the phaneroscopic and/or metaphysical implications of
> considering every line of identity as “bristling with microscopic points
> of teridentity”? If you’ve followed me this far, I’ll leave you with that
> question while I work on the next instalment.
>
> Gary f.
>
> *From:* Gary Richmond <[email protected]>
>
> *Sent:* 30-Mar-19 16:31
>
> Gary F, List,
>
> I am intrigued by your commenting "the graph of teridentity (i.e.
> three-way identity), which occurs when a line of identity *branches*,
> cannot represent the basic triadic *sign* relation, because the Sign,
> Object and Interpretant are not *identical* to one another.
>
> Then adding:
>
> GF: Or are they, in some sense? Perhaps we should leave this question
> open, for now.
>
> I think we *should* keep it open for now. While I immediately tended to
> agree with your first statement, your question also immediately had we
> thinking about such things as the notion (developed by Peirce in places)
> that the Interpretant itself is a Sign; and some other half-baked notions
> came to mind. I'm not feeling up to addressing this question today, however.
>
> But I'd like to hear other's thoughts and your furthers thoughts about it,
> Gary F.
>
> Best,
>
> Gary R
>
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