Jon, Gary R, Jeff, list, Picking up where I left off in Monday’s post, I’ll reproduce here [[in brackets]] the penultimate paragraph of Peirce’s April 1906 address to the NAS, CP 4.583, and insert between parts of it some comments of my own and some other Peirce quotes which I take to be variations on the same theme. I hope these variations will clarify the themes by restating them in somewhat different forms.
[[ The System of Existential Graphs recognizes but one mode of combination of ideas, that by which two indefinite propositions define, or rather partially define, each other on the recto and by which two general propositions mutually limit each other upon the verso; or, in a unitary formula, by which two indeterminate propositions mutually determine each other in a measure. ] CP 4.583 ] [[ To illustrate this, take two monadic Spots on the recto, each representing a different concept, but connected by a line of identity. For instance, the two Spots may be labelled “red” and “rose”, so the graph “red——rose” can be read as “something is red and that very thing is a rose” (ignoring the white pixel in the middle of that heavy line-of-identity instance, which would appear to be a gap in the line’s continuity if we didn’t ignore it. Thus we have two indefinite propositions (“Something is red” and “Something is a rose”) which partially define each other by both being predicated of the same individual thing. Alternatively, we could take each concept as denoting the individual represented by its end of the line of identity, so that the graph informs us that “red” and “rose” are both names of the same individual. The graph means the same thing either way. On the other hand, or rather on the other (verso) side of the sheet — or inside a cut — the same graph denies that any one thing is both red and a rose, so that the two general concepts of “red thing” and “rose” mutually limit each other: “No rose is red” and “Nothing red is a rose.” This is, of course, a very simple example. In the “Prolegomena,” Peirce puts it this way: [[ A mystery, or paradox, has always overhung the question of the Composition of Concepts. Namely, if two concepts, A and B, are to be compounded, their composition would seem to be necessarily a third ingredient, Concept C, and the same difficulty will arise as to the Composition of A and C. But the Method of Existential Graphs solves this riddle instantly by showing that, as far as propositions go, and it must evidently be the same with Terms and Arguments, there is but one general way in which their Composition can possibly take place; namely, each component must be indeterminate in some respect or another; and in their composition each determines the other. On the recto this is obvious: “Some man is rich” is composed of “Something is a man” and “something is rich,” and the two somethings merely explain each other's vagueness in a measure. Two simultaneous independent assertions are still connected in the same manner; for each is in itself vague as to the Universe or the “Province” in which its truth lies, and the two somewhat define each other in this respect. ] CP 4.572 ] Getting back to CP 4.583, [[ I say in a measure, for it is impossible that any sign whether mental or external should be perfectly determinate. If it were possible such sign must remain absolutely unconnected with any other. It would quite obviously be such a sign of its entire universe, as Leibniz and others have described the omniscience of God to be, an intuitive representation amounting to an indecomposable feeling of the whole in all its details, from which those details would not be separable. For no reasoning, and consequently no abstraction, could connect itself with such a sign. ] CP 4.583 ] In other words, a perfectly determinate sign would be a real medad, i.e. something with no relation to anything else. Or to put it more or less as I did in Turning Signs, it would be a sign with no context, and therefore meaningless, because there is no meaning without context. One implication of this is that when Peirce said (in 1903) that the Universe was a vast Argument, he was also saying that the Universe is not perfectly determinate, thus rejecting metaphysical determinism by saying that the process of determination is ongoing. He said much the same about the “perfect sign” (EP2:545). But this is true of all signs — terms, propositions, arguments, Semes, Phemes, Delomes. All semiosis that is “sufficiently complete” consists of mutual determination of signs by one another. The Prolegomena specifically applies this principle to conditional propositions (which are basic to logic itself): [[ The composition of a Conditional Proposition is to be explained in the same way. The Antecedent is a Sign which is Indefinite as to its Interpretant; the Consequent is a Sign which is Indefinite as to its Object. They supply each the other's lack. Of course, the explanation of the structure of the Conditional gives the explanation of negation; for the negative is simply that from whose Truth it would be true to say that anything you please would follow de inesse. ] CP 4.572 ] [[ This consideration, which is obviously correct, is a strong argument to show that what the system of existential graphs represents to be true of propositions and which must be true of them, since every proposition can be analytically expressed in existential graphs, equally holds good of concepts that are not propositional; and this argument is supported by the evident truth that no sign of a thing or kind of thing — the ideas of signs to which concepts belong — can arise except in a proposition; and no logical operation upon a proposition can result in anything but a proposition; so that non-propositional signs can only exist as constituents of propositions. But it is not true, as ordinarily represented, that a proposition can be built up of non-propositional signs. The truth is that concepts are nothing but indefinite problematic judgments. The concept of man necessarily involves the thought of the possible being of a man; and thus it is precisely the judgment, “There may be a man.” ] CP 4.583 ] In other words, we don’t make propositions by putting terms together, we only get terms by analysis of propositions. Similarly in the psychology of language acquisition, a child’s first words are really one-word sentences, and as the child learns to handle more words, the sentences grow more complex. The parallel in phaneroscopy is that the phaneron is a whole, and the separate objects of our attention (which become the objects of our signs) are produced by making distinctions between parts or constituents of the phaneron, so that each part becomes a thing. In the Prolegomena, Peirce extended this holism (or Synechism, as he called it) to the Argument: This “Process of Transformation, which is evidently the kernel of the matter, is no more built out of Propositions than a motion is built out of positions” (CP 4.572). That brings us to the line of identity, where Peirce follows up on his remark to Lady Welby “that every line of identity ought to be considered as bristling with microscopic points of teridentity” (SS 199). [[ Since no perfectly determinate proposition is possible, there is one more reform that needs to be made in the system of existential graphs. Namely, the line of identity must be totally abolished, or rather must be understood quite differently. We must hereafter understand it to be potentially the graph of teridentity by which means there always will virtually be at least one loose end in every graph. In fact, it will not be truly a graph of teridentity but a graph of indefinitely multiple identity. ] CP 4.583 ] I hope the context will make this clearer than it was in the Welby letter. It was at this point that Peirce told his audience: [[ We here reach a point at which novel considerations about the constitution of knowledge and therefore of the constitution of nature burst in upon the mind with cataclysmal multitude and resistlessness. It is that synthesis of tychism and of pragmatism for which I long ago proposed the name, Synechism, to which one thus returns; but this time with stronger reasons than ever before. ] CP 4.584 ] And that is why I consider all these ideas important — especially for anyone who considers himself a Peircean. I should mention that thinking through these ideas has helped me to see what Jon Alan Schmidt has been driving at in recent weeks. I may not agree with everything he has said, but I’m beginning to see where he’s coming from. Gary f.
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