But logic begins to be a positive science; since there are some things in regard to which the logician is not free to suppose that they are or are not; but acknowledges a compulsion upon him to assert the one and deny the other.

Mathematics is not a positive science; for the mathematician holds himself free to say that A is B or that A is not B, the only obligation upon him being, that as long as he says A is B, he is to hold to it, consistently.

Instinct is capable of developement and growth -- though by a movement which is slow in the proportion in which it is vital; and this developement takes place upon lines which are altogether parallel to those of reasoning.

Once you become inflated with that idea, vital importance seems to be a very low kind of importance, indeed.

Mathematics is the most abstract of all the sciences. For it makes no external observations, nor asserts anything as a real fact.

To say that relations go all the way down is a corollary of what Sellars called “psychological nominalism,” that is, of the doctrine that there is nothing to be known about anything save what is stated in sentences describing it. PasAA p.89 #Pragmatism #Rorty #Panrelationalism

We believe the proposition we are ready to act upon. Full belief is willingness to act upon that proposition in vital crises, opinion is willingness to act upon it in relatively insignificant affairs.

…belief, that is, the adoption of a proposition as a ktéma es aei [a possession for ever] …has no place in science at all.

Thoughts? #philosophy

Do not block the way of inquiry.

The system of natural numbers is a good model of the universe because in that system it is obvious, and obviously harmless, that there are no terms of relations which are not simply clusters of further relations. PasAA p.88 #Pragmatism #Rorty #Panrelationalism

...since history does not occur in the void, includes the earth and the physical relatives of man.” -John Dewey, “Appendix 2: 1. Experience and Philosophic Method” (1925 LW 1:370)

Happy Earth Day from the Center for Dewey Studies! “When we say that experience is one point of approach to an account of the world in which we live, we mean then by experience something at least as wide and deep and full as all history on this earth, a history which...

But the disputants are one and all men who cannot discuss any mathematical problem without betraying their want of mathematical power and their gross ignorance of mathematics at every step.

Incessant disputations have, indeed, been kept up by a horde of undisciplined minds about quadratures, cyclotomy, the theory of parallels, rotation, attraction, etc.

Thoughts? #philosophy

Any ideas? #philosophy

And yet that which seems the most arbitrary in the ideas created by the two men are one and the same form. This phenomenon is not an isolated one; it characterizes the mathematics of our times, as is, indeed, well known.

Riemann had apparently never heard of his contemporary Listing. The latter was a naturalistic geometer, occupied with the shapes of leaves and birds' nests, while the former was working upon analytical functions.

Dr. Dianda’s Lyceum address was excellent, effectively making the Jamesian point that a complex and multi-relational self is rarely “fractured” beyond repair.

While whatever is true of a species will form a datum for the discovery of the wider truth which holds of the whole genus.

So far as the sciences can be arranged in such a scale, these relationships must hold good. For if anything is true of a whole genus of objects, this truth may be adopted as a principle in studying every species of that genus.

This double assertion, first, that logic ought to draw upon mathematics for control of disputed principles, and second that ontological philosophy ought in like manner to draw upon logic, is a case under a general assertion which was made by Auguste Comte, namely, /2

I feel confident [my] book would make a serious impression much deeper and surer than Bergson's, which I find quite too vague.

It is far better to let philosophy follow perfectly untrammeled a scientific method, predetermined in advance of knowing to what it will lead. If that course be honestly and scrupulously carried out, the results reached, even if they be not altogether true, /1

It simply does not pay to be an essentialist about numbers. Pan-relationalism holds that it also does not pay to be essentialist about tables, stars, electrons, human beings, academic disciplines, social institutions, or anything else. PasAA p.88 #Pragmatism #Rorty #Panrelationalism

In addition to that, in philosophy we have prejudices so potent that it is impossible to keep one's sang-froid if we allow ourselves to dwell upon them at all.

“… every work of science great enough to be well remembered for a few generations affords some exemplification of the defective state of the art of reasoning of the time when it was written; and each chief step in science has been a lesson in logic.” — @charlespeirce.bsky.social

Hence, although his proceeding is not infallible,—which is shown by the comparative frequency with which mistakes are committed and allowed,—yet it is so easy to repeat the inductions upon new instances, which can be created at pleasure, /1

Nor is the reason for this immunity of mathematics far to seek. It arises from the fact that the objects which the mathematician observes and to which his conclusions relate are objects of his mind's own creation.

Such occurrences suggest that discoveries become virtually inevitable when prerequisite kinds of knowledge and tools accumulate in man’s cultural store and when the attention of an appreciable number of investigators becomes. /1

The pages of the history of science record thousands of instances of similar discoveries having been made by scientists working independently of one another. Sometimes the discoveries are simultaneous or almost so; sometimes a scientist will make anew a discovery which, unknown to him, /1

Do not block the way of inquiry.

“This brilliant scientist, this great philosopher, this astounding polymath was never able, throughout his long life, to find an academic post that would allow him to pursue his major interest, the study of logic, and thus also fulfill his destiny as America’s greatest philosopher.” —J.P. Brent

“The first and most important of these [motives] is to be found in the character of the man himself, a tormented and in many ways tragic figure. He suffered throughout his life from various ailments, including a painful facial neuralgia, and had wide swings of mood which frequently left him /1

“Peirce was by turns arrogant, humble, affectionate, and cruel.” —J. P. Brent

Mistakes in mathematics occur not infrequently, and not being detected give rise to false doctrine, which may continue a long time.

It is a remarkable historical fact that there is a branch of science in which there has never been a prolonged dispute concerning the proper objects of that science. It is the mathematics.

Having thus shown how much less vitally important reason is than instinct, I next desire to point out how exceedingly desirable, not to say indispensable, it is for the successful march of discovery in philosophy and in sight by the investigator.

The instincts of those animals whose instincts are remarkable present the character of being chiefly, if not altogether, directed to the preservation of the stock and of benefiting the individual very little, if at all, except so far as he may happen as a possible procreator /1

Yet Zeller and the critics do not believe them; and Brandis 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, /1

The accounts of him seem to come direct from a writing of his devoted pupil, Timon of Phlius, and some of our authorities, of whom there are a dozen, profess to use this book.

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." /1

In probable reasoning where the evidence is very insufficient, or almost entirely wanting, we often hear men appeal to the “burden of proof” and other supposed logical principles; and in metaphysics logical theory is the only guide.

Now there are two conceivable ways in which right sentiment might treat such terrible crises; on the one hand, it might be that while human instincts are not so detailed and featured as those of the dumb animals, /1

Not only does this account for the many cases of contemporaneous but independent discoveries of similar matters, such as the calculus, but it covers the more mundane claim that independent repetitions of the same experiment with similar results tend to confirm a hypothesis over time.

Such occurrences suggest that discoveries become virtually inevitable when prerequisite kinds of knowledge and tools accumulate in man’s cultural store and when the attention of an appreciable number of investigators becomes.

Sometimes the discoveries are simultaneous or almost so; sometimes a scientist will make anew a discovery which, unknown to him, somebody else had made years before.

The pages of the history of science record thousands of instances of similar discoveries having been made by scientists working independently of one another.