Jeff, List: JD: Every part of the country, down to the smallest detail, is represented on map 1. Every part of the country and map 1, down to the smallest detail, is represented on map 2.
The country is the Object of *every *map in the infinite series, so this is still not a counterexample to the principle that *every *Sign is determined by an Object *other than itself*. Moreover, not only is map 1 represented on map 2, but map 2 is represented on map 1; in fact, since each map "is infinitely minute in its representation," *every *map is represented on *every other* map. JD: What follows from this claim about *that point (any such point) *which is found in all of the maps? Since each map is *continuous*, that point is not really a *part *of *any *map; it is a *discontinuity *that only exists by virtue of being *marked*. Perhaps that is one reason why it cannot represent anything but itself. In any event, self-referential cases are notorious for setting up logical paradoxes, so I am reluctant to draw any lessons from this one beyond what Peirce himself ascribed to it. Recalling the thread topic, I suspect that we are running up against one of the limitations of employing *discrete *Signs to analyze *continuous* semeiosis. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Wed, May 15, 2019 at 5:31 PM Jeffrey Brian Downard < [email protected]> wrote: > Jon S, all, > > For now, I'd like to table questions about the divine--at least for the > time being. In doing so, I'd like to focus on the example of the map and > its semiotic character. We seem to focus on different things when we > interpret the upshot of the example. > > JD: In addition to representing each part of the country, the map seems > to represents itself. As such, a part of the map is the object of the map, > considered as a sign. > > JS: The first sentence is true, but the second is false. The Object of > the map is the country, which includes the map itself; i.e., the Sign is a > part of the Object, not the other way around. Hence the map is still > determined by an Object *other than itself*--namely, the country. > > In order to avoid confusion as we sort part/whole relations, let's number > the maps for the sake of clarity. Let us call map 1, the entire map on the > ground that represents all of the country. Within map 1, there is > a smaller map 2 which is an interpretation of everything in the country > including every part of map 1. The same holds for map 3, and so on, > endlessly. > > Every part of the country, down to the smallest detail, is represented on > map 1. Every part of the country and map 1, down to the smallest detail, is > represented on map 2. Again, for the sake of clarity, I believe Peirce is > suggesting that map 1 is, itself, a part of the country. It is, after all, > lying on the land. That is the reason every part of map 1 must be > represented in map 2, and so on. The same holds for every map n > 1. All of > those maps, too, are part of the country. Each is, after all, a part of map > 1. > > Let us draw some generalizations: > > > 1. Any map n contains, as a part of itself, a representation of > map n+1. Similarly, map n also contains a representation--direct or > indirect--of every map > n as a part of itself. (note: one might > think that it would be simpler to say that map n contains map n+1. We must > not forget, however, that each map is, itself, a representation of the > larger country and all of those maps of which it is a part). > 2. For any map n+1, it is a part of a larger map n for which it is an > interpretation of that larger map. Similarly, map n+1 is an > interpretation--direct or indirect--of every map < n of which it is a > part. > > > Here is the point in Peirce's description of this example that stands out > to me: > > Each map which directly or indirectly represents the country is itself > mapped in the next; *i.e., *in the next [it] is represented to be a map > of the country. In other words each map is *interpreted *as such in the > next. We may therefore say that each is a representation of the country > *to *the next map; and that point that is in all the maps is in itself > the representation of nothing but itself and to nothing but itself. [CP > 5.71] > > What follows from this claim about *that point (any such point) *which is > found in all of the maps? That point will be contained within the > boundary of map n as the value of n goes to ∞. He says that point, found > in common in all of the maps, is "in itself the representation of nothing > but itself and to nothing but itself?" What is that to say? How are the > object, sign and interpretant related, one to the others, in the case of *that > point*? > > Yours, > > Jeff > > Jeffrey Downard > Associate Professor > Department of Philosophy > Northern Arizona University > (o) 928 523-8354 > >>
----------------------------- 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 .
