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[NOTES AND ADDENDA TO LINEAR ASSOCIATIVE ALGEBRA]

Peirce, Charles S. Indiana University Press PDF

312

W R I T I N G S OF C H A R L E S S. P E I R C E , 1879-1884

[Note on the Algebra g^ ]

P 188: American Journal of Mathematics

4 (1881): 132

In relative form, i = A:A,j = A:B, k = B:A, I = B: B. This algebra exhibits the general system of relationship of individual relatives, as is shown in my paper in the ninth volume of the Memoirs of the

American Academy of Arts and Sciences. In a space of four dimensions, a vector may be determined by means of its rectangular projections on two planes such that every line in the one is perpendicular to every line in the other. Call these planes the A-plane and the

B-plane, and let v be any vector. Then, iv is the projection of v upon the A-plane, and Iv is its projection upon the 5-plane. Let each direction in the A -plane be considered as to correspond to a direction in the B- plane in such a way that the angle between two directions in the A-plane is equal to the angle between the corresponding directions in the B-plane. Then, jv is that vector in the A-plane which corresponds to the projection of v upon the B-plane, and kv is that vector in the B- plane which corresponds to the projection of v upon the A-plane.

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4. Philosophy and the Conduct of Life (1898)

Edited by the Peirce Edition Project Indiana University Press ePub

 

MS 437. [Published in CP 1.616–48, in part, and in RLT 105–22. Delivered on 10 February, this was the first of eight Cambridge Conferences Lectures Peirce gave in February and March 1898.] Peirce objects here to “the Hellenic tendency to mingle philosophy with practice” and argues that true scientific investigation must not be conducted with the question of utility in mind. The purpose of philosophy is not to win adherents and to improve their lives. Peirce makes a telling distinction between matters of vital importance and the selfless advancement of knowledge, and argues that, for the former, reason is a poor substitute for sentiment and instinct while, for the latter, reason is key. The upshot is that belief has no place in science but is what must guide action in practical affairs.

The early Greek philosopher, such as we read about in Diogenes Laertius, is certainly one of the most amusing curiosities of the whole human menagerie. It seems to have been demanded of him that his conduct should be in marked contrast with the dictates of ordinary common sense. Had he behaved as other men are supposed to do, his fellow-citizens would have thought his philosophy had not taught him much. I know that historians possessed of “higher criticism” deny all the ridiculous anecdotes about the Hellenic sages.1 These scholars seem to think that logic is a question of literary taste, and their refined perceptions refuse to accept those narratives. But in truth even were taste carried to a point of delicacy exceeding that of the German professor,—which he would think was pushing it quite into that realm of imaginary quantities which lies on the other side of infinity,—it still would not weigh as logic, which is a matter of strict mathematical demonstration wherein opinion is of no weight at all. Now scientific logic cannot approve that historical method which leads to the absolute and confident denial of all the positive testimony that is extant, the moment that testimony deviates from the preconceived ideas of the historian.2 The story about Thales falling into the ditch while pointing out the different stars to the old woman is told by Plato about two centuries later.3 But Dr. Edouard Zeller says he knows better, and pronounces the occurrence quite impossible.4 Were you to point out that the anecdote only attributes to Thales a character common to almost all mathematicians, this would afford him a new opportunity of applying his favorite argument of objection, that the story is “too probable.” So the assertion of half a dozen classical writers that Democritus was always laughing and Heraclitus always weeping “proclaims itself,” says Zeller, “an idle fabrication,”5 notwithstanding the support it receives from the fragments. Even Zeller admits that Diogenes of Sinope was a trifle eccentric.6 Being a contemporary of Aristotle and one of the best known men of Greece, his history cannot well be denied even by Zeller, who has to content himself with averring that the stories are “grossly exaggerated.”7 There was no other philosopher whose conduct according to all testimony was quite so extravagant as that of Pyrrho.8 The accounts of him seem to come direct from a writing of his devoted pupil, Timon of Phlius,9 and some of our authorities, of whom there are a dozen, profess to use this book. Yet Zeller and the critics do not believe them; and Brandis10 objects that the citizens of Elis would not have chosen a half insane man high priest,—as if symptoms of that kind would not have particularly recommended him for a divine office. That fashion of writing history is I hope now at last passing away. However, disbelieve the stories if you will; you cannot refuse to admit that they show what kind of a man the narrators expected a philosopher to be,—if they were imaginary legends, all the more so. Now those narrators are a cloud of the sanest and soberest minds of Antiquity,—Plato, Aristotle, Cicero, Seneca, Pliny, Plutarch, Lucian, Elian, and so forth. The Greeks expected philosophy to affect life,—not by any slow process of percolation of forms, as we may expect that researches into differential equations, stellar photometry, the taxonomy of echinoderms, and the like, will ultimately affect the conduct of life,—but forthwith in the person and soul of the philosopher himself rendering him different from ordinary men in his views of right conduct. So little did they separate philosophy from esthetic and moral culture that the docti furor arduus Lucreti11 could clothe an elaborate cosmogony in noble verse, for the express purpose of influencing men’s lives; and Plato tells us in many places how inextricably he considers the study of Dialectic to be bound up with virtuous living.12 Aristotle, on the other hand, set this matter right. Aristotle was not much of a Greek. That he was of full Greek blood is not likely. That he was not altogether a Greek-minded man is manifest. Though he belonged to the school of Plato, yet when he went there he was already a student, perhaps a personal pupil, of Democritus, himself another Thracian; and during his first years in Athens he cannot have had much intercourse with Plato, who was away at Syracuse a large part of the time. Above all, Aristotle was an Asclepiades,13 that is to say, he belonged to a line every man of whom since the heroic age had, as a child, received a finished training in the dissecting-room. Aristotle was a thorough-paced scientific man such as we see nowadays, except for this, that he ranged over all knowledge. As a man of scientific instinct, he classed metaphysics, in which I doubt not he included logic, as a matter of course, among the sciences,—sciences in our sense, I mean, what he called theoretical sciences,—along with mathematics and natural science,—natural science embracing what we call the physical sciences and the psychical sciences, generally. This theoretical science was for him one thing, animated by one spirit and having knowledge of theory as its ultimate end and aim. Aesthetic studies were of a radically different kind; while morals, and all that relates to the conduct of life, formed a third department of intellectual activity, radically foreign in its nature and idea from both the other two. Now, Gentlemen, it behooves me, at the outset of this course, to confess to you that in this respect I stand before you an Aristotelian and a scientific man, condemning with the whole strength of conviction the Hellenic tendency to mingle Philosophy and Practice.

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3. [Lecture on Logic and Philosophy]

Peirce, Charles S. Indiana University Press PDF

Lecture on Logic and Philosophy, 1879

7

/^Lecture on Logic and Philosophy7

MS 342: May 1879

We have hitherto applied the rule of clearness to ordinary conceptions and have found our advantage in it. In a paper in the Popular Science Monthly I have analyzed in a similar way the notion of reality, with the result of reaching a certain ontological theory the full development of which might occupy us for the remainder of this evening. I prefer, however, upon the present occasion, in order to make my remarks as useful as possible to young students of philosophy, to consider a very singular class of conceptions which represent, not facts about the objects to which those conceptions are applied, but the facts and principles of logic itself.

You are all more or less familiar I suppose with the common doctrine of logical extension and comprehension. Take any ordinary

[ . . . ] comprehension of the latter, N, embraces the whole of that of the former, M, and more besides. For since the extension of M embraces the whole of that of N (that is, since of whatever thing we can predicate N we can also predicate M) it follows that

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Terry Tempest Williams: Derrick Jensen, Listening to the Land: Conversations about Nature, Culture, and Eros, 1995

Michael Austin Utah State University Press ePub

Terry Tempest Williams has written that “it’s strange to feel change coming. It’s easy to ignore. An underlying restlessness seems to accompany it like birds flocking before a storm. We go about our business with the usual alacrity, while in the pit of our stomach there is a sense of something tenuous.”

Where, Terry Tempest Williams asked, can we find refuge in change? She has answered that question as well, “I am slowly, painfully discovering that my refuge is not found in my mother, my grandmother, or even the birds of Bear River. My refuge exists in my capacity to love. If I can learn to love death then I can begin to find refuge in change.’’

Terry Tempest Williams is naturalist-in-residence at the Utah Museum of Natural History in Salt Lake City. Her first book, Pieces of White Shell: A Journey to Navajoland, received the 1984 Southwest Book Award. She is also the author of Coyote’s Canyon, Refuge: An Unnatural History of Family and Place, two children’s books, and most recently, An Unspoken Hunger: Stories from the Field. She is the recipient of the 1993 Lannan Literary Fellowship in creative nonfiction.

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2. Ants

Robert B. Ray Indiana University Press ePub

In the celebrated, mock-heroic rendering of an ant war, from “Brute Neighbors,” appears the source of Walden’s difficulty, its alternation between inspiration and tedium. For like all virtuosic set pieces, in which rhetorical brilliance remains thematically under-motivated, this passage serves primarily as a record of the desire to write. As such, it implies underemployment, a modern condition detectable in places like the Village Voice, where grandly educated, poorly paid intellectuals huff and puff over the latest pop records. With Thoreau, this twin condition of being out of work and eager to write finds its confirmation in his journal’s twenty-six volumes, a labor impossible for a working man.

Thoreau’s desire to write, however, confronted him with immediate problems. For a major prose writer, he has the least gift for narrative imaginable; even the anecdote eludes him. Thus, going to Walden appealed to him because there nothing could happen. Even Thoreau’s situation, a mere mile and a quarter from his family’s house, deprived his book of Robinson Crusoe’s great propelling question: will the hero get home? Thoreau, in effect, was already home, so Walden had to take up other things. Dismissive of both official news and local gossip, Thoreau effectively isolated himself from information, the sine qua non of storytelling. As a result, Walden had to redefine information, insisting on Nature’s communiqués.

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