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REPOST: "The Triadic Form" (2007, about Hegel)
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Jeff Rubard
Nov 23, 2021, 6:59:33 PM11/23/21
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A brief blog post on G.W.F. Hegel from the year 2007. (Since then I have written on Hegel at greater length under a pseudonym.)
The Triadic Form
June 16th, 2007
Yesterday I came up with a formula covering the divisions of the Wissenschaft der Logik. It’s a little pat (the way distinctions people used to work pretty hard were), but it’s more than an analogy or “homology”. Both Hegel’s “Major Logic” and the Encyclopedia Logic have three main parts: sections on Sein (”Being”), Wesen (”Essence”), and Begriff (”Concept”). Just looking at the headings, you can’t quite see what Hegel is going to talk about, and delving into the text isn’t initially much more help. Under the heading “Being” we have being, non-being, generation and corruption, number, and measure; “Essence” deals with reflection, cause and effect, appearance and reality, and the absolute; “Concept” covers subjectivity, objectivity, and the Idea. On the face of it, this looks like an unorganized welter of logical and metaphysical concepts answering to no logical division of labor we could recognize today: and even the biggest contemporary Hegel fans don’t have much to say about such efforts.
But if you really think about the topics covered under each heading, a fairly “natural” or at least recognizable order appears. Here’s the “notion”: the tripartite division of the Logic is equivalent to the modern logical distinctions between extensional, intensional, and intentional discourse. When all terms for something are interchangeable without affecting the truth of sentences containing them, a context is extensional. The early analytic philosophers viewed extensionality as a highly desirable property, and found it in set theory (the Zermelo-Fraenkel formulation of which contains an “Axiom of Extensionality”, stating that two sets containing the same members are equivalent): on such a program, concepts that can’t be stated in the idiom of set theory are second-class at best. Well, is extensionality not what we find in Hegel’s discussion of what we can say about something that simply is: all the determinations that we can make of an object without relating it to others in a way that requires reflection, that is to say the setting-up of “levels” where some features of an object are important and others not — an “essentialist” metaphysics.
Now, a while ago I had something to say about Wesen or “Essence” in the Phenomenology; which is interesting enough, but the concept has a much amplified role in Hegel’s logic. What he has to say about traditional metaphysical concepts involving essence might look like regression from Kant, who systematically defines them in terms of synthesized experience. But we are, after all, living in a newly metaphysical era: and causation and the like are all commonly understood today to be modal notions. Another name for modal logic is intensional logic: so called because modal discourses exhibit intensionality, being “aspect-dependent” and “referentially opaque” in not permitting uniform substitution of terms (even if Aristotle was the greatest philosopher of antiquity, “it is necessarily so that the greatest philosopher of antiquity was the greatest philosopher of antiquity” and “it is necessarily so that Aristotle was the greatest philosopher of antiquity” mean different things — one is a tautology, and one is a matter of some kind of metaphysical discernment). So there is a purely discursive or logical progression at work in Hegel’s presentation here, not merely the ringing of metaphysical changes.
Finally, intentionality. Logical assessments of “intentional idiom” place it one beyond intensionality, in being not only modally aspect-dependent but also knowledge-dependent: we could have two names which are intensionally equivalent, having the same values in all possible worlds, and yet not achieve “intentional identity” of the names because we could be unaware of their modal equivalence. Now, Hegel’s Begriff is declared to be the logical “union of being and essence”; this is perhaps a more useful item for greater sublators than me, but in it is certainly the denial that a “Notion” is directly equivalent to either a statement of a pure “state of affairs” or any set of modally expressible “rich” relations between objects. So if both sorts of reduction are denied, I think that Hegel can be most charitably expounded as having the Notion be the central element of what is today called “linguistic intentionality”, the complex set of attitudes and relations a conscious, reasoning subject can have to the world — without making it appear that the human ability to have complex conscious “object relations” itself denies the importance of “objective” structures.
The Triadic Form
June 16th, 2007
Yesterday I came up with a formula covering the divisions of the Wissenschaft der Logik. It’s a little pat (the way distinctions people used to work pretty hard were), but it’s more than an analogy or “homology”. Both Hegel’s “Major Logic” and the Encyclopedia Logic have three main parts: sections on Sein (”Being”), Wesen (”Essence”), and Begriff (”Concept”). Just looking at the headings, you can’t quite see what Hegel is going to talk about, and delving into the text isn’t initially much more help. Under the heading “Being” we have being, non-being, generation and corruption, number, and measure; “Essence” deals with reflection, cause and effect, appearance and reality, and the absolute; “Concept” covers subjectivity, objectivity, and the Idea. On the face of it, this looks like an unorganized welter of logical and metaphysical concepts answering to no logical division of labor we could recognize today: and even the biggest contemporary Hegel fans don’t have much to say about such efforts.
But if you really think about the topics covered under each heading, a fairly “natural” or at least recognizable order appears. Here’s the “notion”: the tripartite division of the Logic is equivalent to the modern logical distinctions between extensional, intensional, and intentional discourse. When all terms for something are interchangeable without affecting the truth of sentences containing them, a context is extensional. The early analytic philosophers viewed extensionality as a highly desirable property, and found it in set theory (the Zermelo-Fraenkel formulation of which contains an “Axiom of Extensionality”, stating that two sets containing the same members are equivalent): on such a program, concepts that can’t be stated in the idiom of set theory are second-class at best. Well, is extensionality not what we find in Hegel’s discussion of what we can say about something that simply is: all the determinations that we can make of an object without relating it to others in a way that requires reflection, that is to say the setting-up of “levels” where some features of an object are important and others not — an “essentialist” metaphysics.
Now, a while ago I had something to say about Wesen or “Essence” in the Phenomenology; which is interesting enough, but the concept has a much amplified role in Hegel’s logic. What he has to say about traditional metaphysical concepts involving essence might look like regression from Kant, who systematically defines them in terms of synthesized experience. But we are, after all, living in a newly metaphysical era: and causation and the like are all commonly understood today to be modal notions. Another name for modal logic is intensional logic: so called because modal discourses exhibit intensionality, being “aspect-dependent” and “referentially opaque” in not permitting uniform substitution of terms (even if Aristotle was the greatest philosopher of antiquity, “it is necessarily so that the greatest philosopher of antiquity was the greatest philosopher of antiquity” and “it is necessarily so that Aristotle was the greatest philosopher of antiquity” mean different things — one is a tautology, and one is a matter of some kind of metaphysical discernment). So there is a purely discursive or logical progression at work in Hegel’s presentation here, not merely the ringing of metaphysical changes.
Finally, intentionality. Logical assessments of “intentional idiom” place it one beyond intensionality, in being not only modally aspect-dependent but also knowledge-dependent: we could have two names which are intensionally equivalent, having the same values in all possible worlds, and yet not achieve “intentional identity” of the names because we could be unaware of their modal equivalence. Now, Hegel’s Begriff is declared to be the logical “union of being and essence”; this is perhaps a more useful item for greater sublators than me, but in it is certainly the denial that a “Notion” is directly equivalent to either a statement of a pure “state of affairs” or any set of modally expressible “rich” relations between objects. So if both sorts of reduction are denied, I think that Hegel can be most charitably expounded as having the Notion be the central element of what is today called “linguistic intentionality”, the complex set of attitudes and relations a conscious, reasoning subject can have to the world — without making it appear that the human ability to have complex conscious “object relations” itself denies the importance of “objective” structures.
Jeffrey Rubard
Feb 15, 2022, 11:22:58 AM2/15/22
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Pat Monardo
Mar 3, 2022, 7:19:18 PM3/3/22
to
I would focus on the actual definition of a triadic form.
The triadic form was actually a Kant-Fichte creation.
Kant created the triadic form in his Logic.
It is about ancient concept of a "Division" or a "Disjunction".
The idea is that to form a Division requires a precise Logic.
Kant covers this all in his Logic. Since A Prior Divisions are only Dichotomies
and all other Divisions are Tricotomies and above and there can only be
"spelled out" but a Dichotomy has a specific stucture.
There are two terms. These two terms must oppose one another
and together form the logical sphere of the enclosing concept.
Kant maxim here is that all Divisions presuppose a concept being divided.
This becomes in Fichte Thesis-Antithesis-Synthesis. dont discount this it is vital
to everthing. So to understand this form: consider Being
The opposite of Being is Existence so the division is Being-Existence.
This is the Dichotomy and the containing concept, the concept being divided
is Being-For-Self. So Being-For-Self is the Concept that encloses the division
Being-Existence.
Is this group interesting? I am looking at people interested
in Transcedental Arguments.
Jeffrey Rubard
Mar 15, 2022, 3:36:50 PM3/15/22
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