Stephen Toulmin wrote:
Frege, Bertrand Russell, and their colleagues confined logic to the study of formally valid arguments, as discussed in Aristotle's Analytics, and, by the same decision, expelled from logic all consideration of substantively sound arguments, as discussed, for example, in the Topics. ["The Construal of Reality," p. 109]
And Toulmin, like Aristotle, would like to leave room for both, formal logic and "substantive" or "dialectical" reasoning when it comes to knowledge. However, Aristotle is clear about how formal logic should work in this context.
It is a 'demonstration', when the premisses from which the reasoning starts are true and primary, or are such that our knowledge of them has originally come through premisses which are primary and true …. Things are 'true' and 'primary' which are believed on the strength not of anything else but of themselves: for in regard to the first principles of science it is improper to ask any further for the why and wherefore of them; each of the first principles should command belief in and by itself. [Topics, Book 1, §1 translated by W. A. Pickard]
If we begin with a first principle, something true in and of itself, then the rigorous consistency of formal logic insures what follows is true. But if we reject the very idea of first principles, that there can be anything in and of itself known to be true, formal logic can only claim consistency. The first rule of lying is to keep it consistent, and formal logic, without first principles, is an unquestioning accomplice in such efforts.
Professor Ian Dove gave a talk at UNLV entitled
"Doing Philosophy through Painting? On Danto and Taylor on Tansey on Art" in which he discussed Mark Tansey's picture "Derrida Queries de Man". I was reminded of a quote from Peirce:
A man's portrait with a man's name written under it is strictly a proposition, although its syntax is not that of speech, and although the portrait itself not only represents, but is, a Hypoicon. But the proper name so nearly approximates to the nature of an Index, that this might suffice to give an idea of an informational Index. [CP 2.320]
Perhaps, being more complex, Tansey's painting could provide a better example than the portrait for exploring the nature of propositions and indices.
On the one side, there is a predicate, a Hypoicon, in this case the picture itself. It is a metaphor, based on Sydney Paget's illustration, "The Death of Sherlock Holmes". The illustration shows Holmes and Moriarty fighting at the Reichenbach Falls, and in the story, "The Final Problem," both of them plunge to their deaths. There are no doubt similarities and contrasts I'm unaware of, but there's at least the cliffs which are more prominent, they seem built out of text, and and the two figures appear to be dancing more than struggling in Tansey's painting.
One point that doesn't come out so clearly in Peirce's example of the portrait, is that there are already indices of a sort within the painting. The two figures, if seen closely, look like Derrida and DeMan. The text-filled cliffs perhaps indicate the texts of the two men, or of Deconstruction in general, and perhaps their steepness portrays their rigor or uncompromising nature. But all this is an analytic kind of thought, Peirce's a priori method, contained within the context of the painting.
On the other side, the subject, the title of the work, "Derrida Queries de Man," creates a substantial index. This subject-index works in two ways.
1. It puts the focus on the two figures in the painting, and it identifies the one, Derrida, as ostensibly questioning de Man. This I would refer to as the denotative aspect, a definition of the indices from within, or in terms of, the predicate-icon.
2. But this subject-index of the title also brings forth information drawn from sources other than the predicate-icon itself. In this case it is the controversy surrounding de Man's collaboration with the Nazis in Belgium from 1940 to 1942, and Derrida's article, "Like the Sound of the Sea Deep within a Shell: Paul de Man's War" (Critical Inquiry 14 [Spring 1988]: 590-652) trying to minimize those actions. He was "questioning" de Man in a way that was more like dancing with him. Deconstructive methods, what would be the poison to any and all forms of totalitarianism, are being used to justify a collaboration with one the worst of them. This "collateral" information I would refer to as the reference of the subject-index.
Subject-index and the predicate-icon thereby produce this proposition that these two men are dancing under the guise of one questioning the other in a very precarious place, that their own texts put them in danger of falling, of both of them being discredited.
Diagrams are fictions:
"The artist introduces a fiction; but it is not an arbitrary one; it exhibits affinities to which the mind accords a certain approval in pronouncing them beautiful, which if it is not exactly the same as saying that the synthesis is true, is something of the same general kind. The geometer draws a diagram, which if not exactly a fiction, is at least a creation, …" [CP 1.383]
So how is it that these fictions can be true or false? To answer that question I think we have to look Peirce's notion of a metaphor which he defined as "representing a parallelism in something else" [CP 2.277].
The diagram is built on an analogy with its object. The diagram runs from that analogy and its applications to the consequences that can be inferred from it; and as a metaphor, if it runs "parallel" to the object and its interactions, the diagram would be true. The parallelism must be maintained in three respects: (1) a realistic analogy, (2) consistent inferences, and (3) corresponding consequences. Something similar, I would venture, is going on with art as well.
Anyway, the catch in all this is the object. Is it the object in all the obscurity of it’s secondness? Or, is it an object constructed, more or less articulated, in thirdness? This is a problem with metaphors in general. If we say “this person’s a wolf” what’s the object we have in mind? The animal in the wild? Or, have we seen one staring blankly at us in a zoo? Or, perhaps, it's a conglomeration of encyclopedia entries, school courses, or fairy tales? We have these denotations and connotations for “wolf,” but most of us have no referent, no direct acquaintance with the animal itself. Thus, the thirdness of those denotations and connotations become the referent, the object, on which our understanding and use of “wolf” is based, and the whole thing becomes an exercise in analytic viruosity. The virtue of science, but not all that calls itself “science”, is that it demands a direct contact with the secondess of the object, both in applying the diagram and in testing its consequences.
