Rich, first thanks for taking the time to think and the triangle and sharing your observations.

I'll just respond to one of your points. There's plenty more to be said, but only a few hours in the day. Let's plan to circle back around on the other points once we examine the first in detail !

See below ...

On 8/21/2010 12:29 AM, Rich Cooper wrote: [
Of course that's heading for some pretty abstract thinking, but the intent is to represent the metaphysical transformation that Peirce describes in "On a New List of Categories" in the outer counter-clock wise edge of the triangle.

http://www.peirce.org/writings/p32.html

I use the term object to represent an individual in the manifold. I think its pretty important to reject the idea of abstract objects. I'll use your statements above to show why.

RC > "The first cold weather is a sign of the coming Fall and Winter in the Northern Hemisphere."

You claim that there is no (material) object that determines temperature and without a visible representation of Winter there can be no (material) object, only an abstract object which you acknowledge is a sign.

Air is a gas made of molecules. Its temperature is a property of its speed and density. Although we don't see the molecules, they and the gas do exist. Their slower speed and lower density causes the observer to sense cold. There are many individual molecules physically present in the gas. The physical presence of the molecules (object) makes it possible for the observer to sense cold (sign). That's what I intend to communicate when I say materialize.

I think you'll agree that it would be hard to argue that because the air molecules are unseen that they transmute from object to abstract object. They're still there, especially if you live in China ! So I think the case is proven that in your example, the object (molecule) materializes the sign (cold). And as you also point out even where there's no visible object, the sign (cold) actually evokes Winter and its connotations like Christmas, Santa Clause - ho ho ho, etc.

Maybe to some the term sign is synonymous with abstract object. I prefer sign and I think the value of semiotics is to provide a better metaphysics to avoid abstract objects.

All that being said. You're right that the choice of term for the legs of the triangle is important. They describe functions that commute and are isomorphic. Materialize may not be the best term. What do you think of determine?

BTW - Most likely Peirce has a term for this type of sign. Possibly Dicisign. I haven't had enough time to properly study his division of signs. I hope John Sowa or John Awbrey could provide advice on how this sign would be classified.

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