GF: Jon, you’re asking: If the logical depth/signification of a Sign corresponds to its Interpretant … then where does the Sign's information fit into the picture? But you’ve already answered that yourself: “The information (breadth x depth) of a Sign then corresponds to the unity of the Object with its characters; i.e., the Sign's Interpretant.”
GF: I’ve omitted “3ns/Entelechy” from the end of that sentence of yours because I think your use of those terms in that context is confusing--and may even be causing part of the problem you have with “reconciling” what you see as two completely different Peircean analyses.
GF: One is the breadth/depth (extension/intension, extension/comprehension) dichotomy, which is a very old analysis of the meanings of terms, but which Peirce extended to apply to propositions and arguments as well.
CSP: In a paper which I printed in 1867 [CP 4.391-426], I gave the principal senses in which the terms "logical extension" and "logical comprehension" have been widely employed by logicians. They are more numerous than ordinary students of the chief treatises on logic are aware. For such books are not usually read with sufficient thought for the gathering of exact ideas. I shall now simply select one meaning of each of those two logical "quantities," shall employ that one, and shall neglect the others. With that understanding, and without attempting any precise statement which would here be worse than superfluous, I will say that ... (R 200:E85-E86; 1908)
GF: Another is the subject/predicate dichotomy which applies to propositions.
GF: I’m going to speculate that the discrepancy you see results from your attempt to map dichotomies (breadth/depth, subject/predicate) onto the triad sign/object/interpretant.
Jon, you’re asking: If the logical depth/signification of a Sign corresponds to its Interpretan … then where does the Sign's information fit into the picture?
But you’ve already answered that yourself: “The information (breadth x depth) of a Sign then corresponds to the unity of the Object with its characters; i.e., the Sign's Interpretant.” (I’ve omitted “3ns/Entelechy” from the end of that sentence of yours because I think your use of those terms in that context is confusing — and may even be causing part of the problem you have with “reconciling” what you see as two completely different Peircean analyses.
Let me generalize from this a bit. We’re dealing with three analyses of informational semiosis here. One is the breadth/depth (extension/intension, extension/comprehension) dichotomy, which is a very old analysis of the meanings of terms, but which Peirce extended to apply to propositions and arguments as well. Another is the subject/predicate dichotomy which applies to propositions. The third is the standard trichotomy of the ‘elements’ or correlates in a triadic relation, namely sign/object/interpretant. Now, all three of these are analyses of the same semiotic phenomenon, when applied to the structure of propositions, as they all are. But these analyses are made for different purposes and they do not necessarily map onto each other cogently. Nor should they, when we consider that the products of these analyses of semiosic processes are not observable entities but entia rationis. As Peirce said in his description of the “perfect sign,” “The only signs which are tolerably fixed are non-existent abstractions.” And if a sign such as a proposition is not fixed, the components into which it is analyzed are even less fixed. Especially when you try to take their names and map them onto another analysis.
I’m going to speculate that the discrepancy you see results from your attempt to map dichotomies (breadth/depth, subject/predicate) onto the triad sign/object/interpretant. As you say, the mapping of denotation, breadth and subject onto the object seems obvious. But then what do you map the depth, predicate and signification onto? The sign? The interpretant? Some blending of the two? Any of these choices can be made to work in some contexts, and in fact IS made to work in various texts embodying Peirce’s late semiotic. But none of these mappings give you an exact fit. For instance, the subject of a proposition is usually regarded as part of it, but the (dynamic) object of a proposition is external to it; so the “correspondence” between subject and object is not exact. That’s because analyses of continuous processes always have a degree of arbitrariness to them. Peirce’s late semiotic emphasizes this in the case of the subject/predicate analysis, but it applies to some degree to every analysis of semiosis — including the taxonomy of sign types.
I hope this makes some sense, though it may not cause the discrepancy you see to disappear.
Gary f.
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