Jeff, List: I need to offer a correction (in bold) to one of your Pierce quotes.
CSP: The Absolute in metaphysics fulfills the same function as the absolute in geometry. According as we suppose the infinitely distant beginning *and end *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 favor of the first. (R 928:7, W 8:22; 1890) As for your concluding question, I hope that you will share with us your own answer to it. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Mon, Nov 7, 2016 at 12:04 PM, Jeffrey Brian Downard < [email protected]> wrote: > 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 >
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