Jeff, list: Yes, I think that Peirce's rejection of Hegel's 'Absolute One' provides us with a richer, and more accurate outline of reality as complex - and I agree that Thirdness is relative.
That relative nature refers to the operative nature of Thirdness, while the operative nature of both Firstness and Secondness is their capacity for non-relational interaction. Firstness is just 'absolute' as itself, while Secondness is a brute action that relies on no mediation. I am sure you are familiar with Spencer Brown's Laws of Form; his concept that 'a universe comes into being when a space is severed or taken apart' 1972,v. And, Spencer Brown's four classes of statements: true, false, meaningless and imaginary. I wonder how these relate to the Categories, both genuine and degenerate and also, to theories of truth and logic. As Spencer-Brown writes, 'If the weakness of present-day science is that it centres around existence, the weakness of present-day logic is that it centres around truth" [101]. That is "A theorem is no more proved by logic and computation than a sonnet is written by grammar and rhetoric" 102. And, "we cannot escape the fact that the world we know is constructed in order [and thus in such as way as to be able] to see itself....But in order to do so, evidently it must first cut itself up into at least one state which sees, and at least one other state which is seen. In this severed and mutilated condition, whatever it sees is only partially itself" 105. I don't mean to turn the thread to Spencer Brown, but his work [which does reference Peirce] seems to align with some of Peirce's focus on the metaphysics of the world. The paragraph above, to me, recalls 1.412, that 'explosion' of matter at the beginning of the universe; and also, the lines on the blackboard. Edwina ----- Original Message ----- From: Jeffrey Brian Downard To: Edwina Taborsky ; [email protected] Sent: Monday, November 07, 2016 1:04 PM Subject: RE: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was Metaphysics and Nothing (was Peirce's Cosmology)) Edwina, Jon S, Gary R, List Let's take up Peirce's rejoinder to Hegel about the character of the absolute. He says: "Hegel is possessed with the idea that the Absolute is One. Three absolutes he would regard as a ludicrous contradiction in adjecto." (CP, 5.91) Compare that remark about the three absolutes to what he says about two absolutes in "A Guess at the Riddle": According to the mathematicians, when we measure along a line, were our yardstick replaced by a yard marked off on an infinitely long rigid bar, then in all the shiftings of it which we make for the purpose of applying it to successive portions of the line to be measured, two points on that bar would remain fixed and unmoved. To that pair of points, the mathematicians accord the title of the absolute; they are the points that are at an infinite distance one way and the other as measured by that yard. These points are either really distinct, coincident, or imaginary (in which case there is but a finite distance completely round the line), according to the relation of the mode of measurement to the nature of the line upon which the measurement is made. These two points are the absolute first and the absolute last or second, while every measurable point on the line is of the nature of a third. We have seen that the conception of the absolute first eludes every attempt to grasp it; and so in another sense does that of the absolute second; but there is no absolute third, for the third is of its own nature relative, and this is what we are always thinking, even when we aim at the first or second. The starting-point of the universe, God the Creator, is the Absolute First; the terminus of the universe, God completely revealed, is the Absolute Second; every state of the universe at a measurable point of time is the third. If you think the measurable is all there is, and deny it any definite tendency whence or whither, then you are considering the pair of points that makes the absolute to be imaginary and are an Epicurean. If you hold that there is a definite drift to the course of nature as a whole, but yet believe its absolute end is nothing but the Nirvana from which it set out, you make the two points of the absolute to be coincident, and are a pessimist. But if your creed is that the whole universe is approaching in the infinitely distant future a state having a general character different from that toward which we look back in the infinitely distant past, you make the absolute to consist in two distinct real points and are an evolutionist. This is one of the matters concerning which a man can only learn from his own reflections, but I believe that if my suggestions are followed out, the reader will grant that one, two, three, are more than mere count-words like "eeny, meeny, miny, mo," but carry vast, though vague ideas. (CP, 1.362). The mathematical conception of the Absolute, as that is worked out first in projective geometry, and then in group theory, is a rich idea. In order to get a handle on this idea, it is worth taking a close look at examples of proofs of particular theorems within this mathematical system--such as Desargues's proof of the 6 point theorem that Peirce considers in RLT. Peirce makes it clear that the mathematical conceptions are informing the development of the metaphysical conceptions of what is first and last: The Absolute in metaphysics fulfills the same function as the absolute in geometry. According as we suppose the infinitely distant beginning of the universe are distinct, identical, or nonexistent, we have three kinds of philosophy. What should determine our choice of these? Observed facts. These are all in favour of the first. (MS 928:7 or W8: 22) In the Century Dictionary, Peirce provides a definition of the Absolute in Projective Geometry: In math., a locus whose projective relation to any two elements may be considered as constituting the metrical relation of these elements to one another. All measurement is made by successive super positions of a unit upon parts of the quantity to be measured. Now, in all shifting of the standard of measurement, if this be supposed to be rigidly connected with an unlimited continuum superposed upon that in which lies the measured quantity, there will be a certain locus which will always continue unmoved, and to which, therefore, the scale of measurement can never be applied. This is the absolute. In order to establish a system of measurement along a line, we first put a scale of numbers on the line in such a manner that to every point of the line corresponds one number, and to every number one point. If then we take any second scale of numbers related in this manner to the points of the line, to any number, x, of the first scale, will correspond just one number, y, of the second. If this correspondence extends to imaginary points, x and y will be connected by an equation linear in x and linear in y, which may be written thus: xy + ax + by + c = 0. The scale will thus be shifted from x = 0 to y = 0 or x = -c/a. In this shifting, two points of the scale remain unmoved, namely, those which satisfy the equation x2 + (a + b) x + c =0. This pair of points, which may be really distinct, coincident, or imaginary, constitute the absolute. For a plane, the absolute is a curve of the second order and second class. For three-dimensional space it is a quadric surface. For the ordinary system of measurement in space, producing the Euclidean geometry, the absolute consists of two coincident planes joined along an imaginary circle, which circle is itself usually termed the absolute. Let's try to apply these mathematical conceptions of the absolute to the philosophical questions that we are raising about the metaphysical absolute. The first steps in such an inquiry, I would think, would be to see how the conceptions might apply to the phenomenological questions, and then to the questions that arise in the normative semiotic. Once that is done, we will be in a better position to take up the questions in metaphysics. So, how might these mathematical conceptions of the absolute be used to shed some like on the phenomenon that we seek to explain with respect to the origins of the homogeneities of connectedness that we see within each of the universes of experience, between any two of them, and between all three taken together? --Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354 ________________________________________ From: Edwina Taborsky [[email protected]] Sent: Monday, November 7, 2016 7:23 AM To: [email protected] Subject: Re: [PEIRCE-L] Re: Super-Order and the Logic of Continuity (was Metaphysics and Nothing (was Peirce's Cosmology)) Jeff, list: Peirce considers this situation, as I read it, in his continued examination of the categories, see 5.90-92. He imagines a dissnter with an attack on his views: "We fully admit that you have proved, until we begin to doubt it, that Secondness is not involved in Firstness nor Thirdness in Secondness and Firstness. But you have entirely failed to prove that Firstness, Secondness and Thirdness are independent ideas for the obvious reason that it is as plain as the nose on your face that the idea of a triple involved the idea of pairs, and the idea of a pair the idea of units. Consequently, Thirdness is the one and sole category. This is substantially the idea of Hegel and unquestionably it contains a truth. Not only does Thirdness suppose and involve the ideas of Secondness and Firstness, but never will it be possible to find any Secondness or Firstness in the phenomenon that is not accompanied by Thirdness". This is the argument of ' The Dissenter' - who follows Hegel in positing the primacy of the continuous order of Thirdness. Then, Peirce himself writes: 5.91 "If the Hegelians confined thmselves to that position they would find a hearty friend in my doctrine. But they do not. Hegel is possessed with the idea that the Absolute is One. Three absolutes he would regard as a ludicrous contradiction in adjecto. ...... Peirce continues on [I only have time to write part of this long paragraph]..."Thirdness it is true involves Secondness and Firstness, in a sense. That is to say, if you have the idea of Thirdness you must have had the ideas of Secondness and Firstness to build upone. But waht is required for the idea of a genuine Thirdness is an independent solid Secondness and not a Secondness that is a mere corollary of an unfounded and inconceivable Thirdness; and a similar remark may be made in reference to Firstness." 5.92 "Let the Universe be an evolution of Pure Reason if you will. Yet if, while you are walking in the street reflecting upon how everything is the pure distillate of Reason, a man carrying a heavy pole suddenly pokes you in the small of the back, you maythink there is something in the Universe that Pure Reason fails to account for; .........you will be perhaps disposed to think that Quality and Reaction have their independent standing in the Universe". My reading of the above is that two independent random points, the stick and a man's back can have no ordered relation - other than an accidental, unordered one. In addition, the power of chance and spontaneity in generating relations and thus evolving the habits - and these include novel habits- of Thirdness is, I think, a powerful force within the Peircean semiosis. Edwina On Sun, Nov 6, 2016 at 8:15 PM, Jeffrey Brian Downard <[email protected]<mailto:[email protected]>> wrote: Jon S, List, For the sake of clarity, let me point out that the interpretative hypothesis I have been exploring is quite limited. The claim is that, on its face, it appears that some dyadic relations are not, in themselves, ordered. This is brought out in those that are classified as accidental and unordered (both materially and formally). I was extending the claim to degenerate triadic relations based on the general tenor of his remarks about such degenerate relations in "The Logic of Mathematics, an attempt..." The points you are making about different sorts of collections and other kinds of groupings (including those that are based on some shared negative character) all seem to involve genuine triadic relations that apply to the collection as a whole. As far as I can tell, all such genuine triads essentially involve ordered relations. So, to make the point clearer, a set consisting of members that are two distinct dots on a page is ordered if there is some general characteristic that applies to the set as a whole. Having said that, it does not follow that every sort of degenerate dyadic relation or degenerate triadic relation that holds between two dots is an ordered relation. The general property that makes the set the kind of thing that it is necessarily involves a genuine triadic relation. That is what is involved in all such generalities. You seem to be claiming that every relation, regardless of how degenerate it may be, must involve some sort of order--otherwise the relation would not be intelligible. If this is your claim, you may be right, but I'm trying to explore a different line of interpretation. --Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354<tel:928%20523-8354> ________________________________ ----------------------------- PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ------------------------------------------------------------------------------ ----------------------------- PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] . 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