List:
While browsing through various unpublished manuscripts, I came across a few
interesting passages that pertain to recent List discussions.
First, it turns out that Peirce was aware of continuous predicates at least
a few years earlier than 1908, which is when he called specific attention
to them as what is left over when we analyze a proposition by throwing
everything possible into the subject. He initially called them "truly
continuous relations," and gave coexistence (blank sheet) and identity
(line) as examples.
CSP: We have already virtually encountered a logical transitive
anti-alio-relation which is also truly continuous. For when we write,
It snows
It blows
we virtually say that these two facts are in the relation of coexistence
with one another, and taking coexistence in such a sense that everything
that exists is coexistent with itself. By saying that this relation is *truly
continuous*, I mean that if A is coexistent with B, I mean that
A is coexistent with something coexistent with something coexistent with
something coexistent with B,
and that in short intermediaries each coexistent with the next are capable of
being inserted up to *any multitude whatsoever* ...
Identity being the only continuous dyadic logical relation for which a notation
has to be provided, may appropriately be represented by a heavy continuous
line drawn between its relate and its correlate ... (R 515:16-19; 1902?)
CSP: I call a relation *truly continuous*, if, and only if, a collection
of intermediaries of any multitude whatsoever can be interposed in series
between any relate and correlate, all previous ones being in the same
relation to all subsequent ones; just as between any two separate instantaneous
events in time any multitude whatsoever of distinct events are capable of
being interposed. Or between any two marked points on a line any multitude
whatsoever of points are capable of being marked. (R 516:33-34; 1902?)
He also recognized the utility of two other familiar continuous predicates.
CSP: The expression of many difficult assertions is facilitated by using
the verb “possesses as a character.” For it is an axiom *that any set of
individuals whatever have some character which nothing else has*. Equally
useful is the verb “---is in the relation---to---.” For any set of ordered
pairs are in a common and peculiar relation, the first member of each pair
to the second. (R 493:18; c. 1899)
Notice that expressing the continuity of *symmetrical *relations requires
intermediate indefinite subjects ("... coexistent with something coexistent
with something ..." and "... identical to something identical to something
..."), while expressing the continuity of *asymmetric *relations does not
("... possessing the character of possessing the character of ..." and "...
standing in the relation of standing in the relation of ..."). Of course,
any of the others can alternatively be expressed using the last
formulation--"_____ stands in the relation of
coexistence/identity/possessing to _____."
.Second, Peirce acknowledged the need to *improve *EGs in order to
encompass not only determinate individuals, but also *entia rationis* such
as hypostatically abstracted qualities and collections of existing objects.
CSP: In order to represent the reasoning of mathematics in all its
fullness, two improvements must be made. In the first place the operation
of hypostatic abstraction must be rendered practicable ...
The operation of hypostatic abstraction consists in substituting for any
predication that of possessing a quality, or that of standing in a relation
... The hypostatically abstract quality or relation is necessarily *general*,
that is, is not subject to the *principle of excluded middle*. The universe
of characters is thereby quite outside the universe of existents.
The second needed improvement is that there should be some way of
expressing *collective *wholes ...
Corresponding to every abstraction, to every predicate is a possible
collection but whether or not there actually is a collection of say 1001
phoenixes is another question. Such an object may or may not have
existential being, like a phoenix.
In short, a collection is indefinite like any ordinary predicate ...
A collection is an object whose mode of existence is that of an indefinite
object, that is not in all respects subject to the *principle of
contradiction* whose existence consists in the existence of certain
objects, its members, which are such that the existence of none of them
consists in the existence of the collection.
A hypostatical abstract is an object whose being consists in the
possibility of a predicate and which stands in a peculiar relation, that of
being possessed by, to whatever there may be of what that predicate is true.
I have not yet discovered a suitable mode of representing such objects in
existential graphs. (R 145:23-28; 1905)
Here he confirmed that "any predication" can be further analyzed into a
subject (the name for the quality or relation itself) and a continuous
predicate ("possessing a quality" or "standing in a relation"). By
associating the latter with hypostatic abstraction, he further confirmed
that any Subject Spot for a relation is properly classified as an
Abstractive. Even more noteworthy are his statements comparing collections
with predicates, which imply that a Sign for a collection should likewise
be classified as an Abstractive--ironically, not a Collective, perhaps
another reason why he deemed this an unsatisfactory designation for the
class of Signs whose Dynamic Objects are Necessitants. I have hinted at
this before by observing that "belongs to the class of" is equivalent to
"possesses the common characters of every," and Peirce himself put it as
follows.
CSP: To belong as unit to a collection and to *possess *as a quality are
substantially the same relation. To abbreviate we will write
A---possesses---B
meaning A possesses the quality B or A belongs to the class collection
designated by B. (R 513:30; 1898)
CSP: The definition then of a collection is that it is a real individual
object whose being consists in the being of whatever may actually exist
that possesses a certain character. (R 458:16-17; 1903)
This points the way toward resolving my previous uncertainty about how to
distinguish Signs that denote purposes, intentions, tendencies, or habits
in EGs--they can simply have the color and/or font effect that I previously
assigned to Collectives. However, I feel the need to come up with a more
appropriate name for these (Subjunctives?), and I am also still trying to
figure out how to express the corresponding continuous predicate.
Finally, Peirce seems to have anticipated my proposal to use different
colors for (Subject) Spots and Lines (of Connection) according to the
nature of the Dynamic Objects and continuous predicates that they denote
and signify.
CSP: The difficulty of representing a hypostatic abstraction in
existential graphs (which I trust may be conquered eventually) is that what
suggests itself is to distinguish individuals regarded as determinate in
every respect, so that the principle of excluded middle applies to them, by
(for example) using a different colored ink say red from that say blue used
in scribing predicates such as ‘is wise’. But then the dot which denotes
‘something,’ should be red while the continuous line which has a dot at
every part of it should be blue. Perhaps the remedy would be to make this
line *purple*.
Solomon---is wise
But when the operation of hypostatic abstraction is performed, the
proposition takes the form ‘Solomon *possesses wisdom*’ or ‘Solomon is
possessor of wisdom.’ I must interpose a special dyadic relative between
two parts of the line, as well as changing the color of ‘is wise’. (R
96:11-12; 1905)
Rather than making the line purple or inserting a (Predicate) Spot for the
relation of possessing, I have suggested treating the Line (of Connection)
as a Ligature--in this case, consisting of a red Line attached to "Solomon"
for "is identical to" and a blue Line attached to "wisdom" for "possesses
the character of," with the Point where they abut corresponding to the
indefinite subject "something." The literal translation is then "something
identical to Solomon possesses the character of wisdom." Of course, I have
been advocating a different color scheme--red (and bold) for Abstractives,
green (and italic) for Concretives, and blue (and underline) for
Collectives--in accordance with what Peirce later suggested for the
respective Universes of Capacities, Actualities, and Tendencies (R
300:74[39]; 1908).
Regards,
Jon S.
On Wed, Apr 3, 2019 at 9:51 PM Jon Alan Schmidt <[email protected]>
wrote:
> List:
>
> While preparing what I posted in the "Phaneroscopy and logic" thread
> earlier this evening, another related "Prolegomena" footnote caught my eye.
>
> CSP: ... a Graph-instance can perfectly well extend from one Province to
> another, and even from one *Realm *(or space having one Mode of Tincture)
> to another. Thus, the Spot, "-- is in the relation -- to --," may, if the
> relation is that of an existent object to its purpose, have the first Peg
> on Metal, the second on Color, and the third on Fur. (CP 4.558n)
>
>
> I see two things here as noteworthy.
>
> 1. We can scribe a Spot for the continuous predicate "-- is in the
> relation -- to --," where the name of the relation itself is treated as an
> additional *subject*. This is consistent with my proposal below to
> scribe a Predicate Spot ("stands") as the only kind with multiple Pegs when
> we scribe *anything *that must be known to the Interpreter from
> Collateral Experience/Observation as a Subject Spot with one Peg.
> 2. The three Pegs of such a Spot can be scribed on three *different *Realms
> with the three *different *Modes of Tincture, such that the subjects
> attached to them denote Objects with three *different *Modes of
> Being. This is similar to my proposal below to scribe each Subject Spot
> and the Line of Connection that attaches it to a Peg of the Predicate Spot
> using color and font to reflect the nature of its Dynamic Object and the
> corresponding continuous predicate.
>
> The three subjects in Peirce's example are an existent object (Metal =
> Actuality), its relation to its purpose (Color = Possibility), and that
> purpose itself (Fur = Intention or Tendency). Do these match up with their
> counterparts in his division of Signs according to the nature of the
> Dynamic Object? The designation of an *existent *object is obviously a
> Concretive (green/italic in my scheme), and Peirce evidently considered the
> name of a *relation *to be an Abstractive (red/bold). The latter is
> something that I have been wondering about for a while; I went with
> black/plain below because I was unable to settle on any one of the other
> three. But does a Sign for a *purpose *qualify as a Collective
> (blue/underline)? Cases like this might be one reason why Peirce described
> "Collective" as "not quite so bad a name as it sounds to be until one
> studies the matter" (EP 2:480; 1908). Purposes do not seem to fit neatly
> into *any *of the three classes as he defined them only days later.
>
> CSP: In respect to the Nature of their Dynamical Objects, Signs I found
> to be either
>
> 1. Signs of Possibles. That is, Abstractives such as Color, Mass,
> Whiteness, etc.
>
> 2. Signs of Occurrences. That is, Concretives such as Man, Charlemagne.
>
> 3. Signs of Collections. That is, Collectives such as Mankind, the Human
> Race, etc. ...
>
> I was of the opinion that if the Dynamical Object be a mere Possible the
> Immediate Object could only be of the same nature, while if the Immediate
> Object were a Tendency or Habit then the Dynamical Object must be of the
> same nature. Consequently an Abstractive must be a Mark, while a Type must
> be a Collective, which shows how I conceived Abstractives and Collectives.
> (EP 2:489; 1908)
>
>
> "Tendency or Habit" is employed here as a synonym for "Necessitant," and
> Peirce elsewhere directly connected purposes with habits (e.g., EP 2:341;
> 1907). Hence it seems clear that a purpose is a Necessitant, such that a
> Seme *denoting *a purpose is indeed a Collective--or perhaps a
> Complexive, an alternative that Peirce tried out in R 795 (but apparently
> nowhere else). However, it would presumably *not *be married to another
> Seme in a Proposition by the continuous predicate "belongs to the class
> of." Moreover, in English we typically express a purpose, tendency, or
> habit as a *verb*, sometimes accompanied by a common noun--e.g., "the
> purpose of your heart is pumping blood." How should we translate this into
> Peirce's example ("-- is in the relation -- to --") and then scribe the
> corresponding EG? Any specific suggestions would be greatly appreciated.
>
> Thanks,
>
> Jon Alan Schmidt - Olathe, Kansas, USA
> Professional Engineer, Amateur Philosopher, Lutheran Layman
> www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt
>
> On Wed, Mar 27, 2019 at 9:26 PM Jon Alan Schmidt <[email protected]>
> wrote:
>
>> List:
>>
>> It occurs to me that a complex Seme can be analyzed into simple Semes
>> joined by a continuous predicate. For example, just as the copula "is"
>> corresponds to the latter in a categorical Proposition, the preposition
>> "of" plays that role in the Seme "the mortality of man," such that a more
>> explicit translation is "the character of mortality possessed by anything
>> belonging to the class of man." This amounts to a hypostatic abstraction
>> of the Proposition, "Anything belonging to the class of man possesses the
>> character of mortality."
>>
>> Moreover, while further exploring the images of R 284 (1905) in the
>> Digital Peirce Archive (
>> https://rs.cms.hu-berlin.de/peircearchive/pages/home.php), I came across
>> these additional interesting remarks.
>>
>> 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. All other symmetrical relations are
>> compounded and involve asymmetric elements ... In existential graphs,--that
>> is, in the usual, "Beta," form of the system,--there are equally these two
>> modes of connection, the lines signifying identity and the absence of lines
>> coexistence. But, of course, no relations other than these can be
>> expressed except by giving relative significations to spots; and if a spot
>> signifies an asymmetric relation, it is necessary to distinguish connection
>> with one part of it as meaning something different from connection with
>> another side. Of course, if a great variety of colors or other qualities
>> of lines were recognized, although their two ends were alike, a
>> corresponding variety of asymmetric relations could be built up, since, for
>> example, a friend of a cousin is not necessarily a cousin of a friend. (R
>> 284:88,94-96[83,89-91])
>>
>>
>> The standard interpretation of EGs treats a Line of Identity as an
>> indefinite subject to which discrete predicates may be attributed by
>> attaching Spots. Here Peirce instead described a Line of Identity as
>> *itself *a "mode of connection," presumably *between *subjects,
>> consistent with his later concept of a continuous predicate; specifically,
>> "is identical to." He then acknowledged that a Spot for "an asymmetric
>> relation" requires each of its connections (i.e., Pegs) to be distinguished
>> by its location, but also noted that "colors or other qualities of lines"
>> could serve a similar purpose. These comments suggest an alternative way
>> of scribing and interpreting EGs, as follows; see attached for updated
>> examples.
>>
>> - Represent each discrete dyadic or higher predicate with a Predicate
>> Spot ("stands") whose number of Pegs matches the number of subjects,
>> including the relation itself.
>> - Represent each monadic predicate, including the relation itself,
>> with a Subject Spot that is attached to a single Line of Connection.
>> - Use color and font to reflect the nature of the Dynamic Object of
>> each Subject Spot--red and bold for an Abstractive, green and italic for a
>> Concretive, blue and underlined for a Collective, or black and plain for a
>> Relation.
>> - Use the same color for the attached Line of Connection, which
>> represents the corresponding continuous predicate--"possesses the
>> character
>> of" for an Abstractive, "is identical to" for a Concretive, "belongs to
>> the
>> class of" for a Collective, or "(stands) in the relation of" for a
>> Relation.
>> - Arrange the Subject Spots around a Predicate Spot by attaching the
>> subject nominative on the left side, the relation itself above, the direct
>> object on the right side, and any others below (cf. R 670:8[7]; 1911 June
>> 9); i.e., read the Graph *clockwise* in accordance with the principle
>> that syntax ought to be consistent with "the flow of causation" (cf. R
>> 664:11-13; 1910 Nov 27).
>> - Translate each Peg of the Predicate Spot--except the one for the
>> relation itself--and each Point where a Line of Connection changes color,
>> branches, or crosses a Cut as an indefinite subject ("something").
>>
>> I should add that I am by no means claiming that we *must *implement
>> this new approach, or even that anyone *ought *to do so; only that it is
>> *valid*, reflecting a different analysis of a Proposition--the one that
>> throws everything possible into the subject. As such, it appears to
>> confirm that a Seme can be a monad (one-Peg Subject Spot) and a continuous
>> predicate is at least a dyad (Line of Connection); but does it reveal
>> anything about the valency of a leading principle? In EGs, the latter
>> corresponds to a *transformation rule*, which brings to mind part of
>> what Gary F. quoted in the "Phaneroscopy and logic" thread earlier today.
>>
>> CSP: Suppose then a Triad to be in the Phaneron. It connects three
>> objects, *A*, *B*, *C*, however indefinite *A*, *B*, and *C* may be.
>> There must, then, be one of the three, at least, say *C*, which
>> establishes a relation between the other two, *A* and *B*. (EP 2:364;
>> 1905)
>>
>>
>> Can we say that *A* is the initial Graph, *B* is the subsequent Graph,
>> and *C* is the convention that permits the change from *A* to *B*? If
>> so, does this confirm that a leading principle is at least a triad? When I
>> wrote the post below, that felt like its most speculative and least secure
>> assertion, so I am open to being *shown *(not merely *told*) that I am
>> on the wrong track here. In fact, that goes for just about anything that I
>> propose on-List, including all of the above and below; "since in scientific
>> inquiry, as in other enterprises, the maxim holds, *Nothing hazard,
>> nothing gain*" (EP 2:410; 1907).
>>
>> Thanks,
>>
>> Jon S.
>>
>
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