Each readily falls into excess

Bacon’s 55th aphorism in the Novum Organum, translated by Joseph Devey, some two centuries before Darwin on lumpers and splitters:

The greatest and, perhaps, radical distinction between different men’s dispositions for philosophy and the sciences is this, that some are more vigorous and active in observing the differences of things, others in observing their resemblances; for a steady and acute disposition can fix its thoughts, and dwell upon and adhere to a point, through all the refinements of differences, but those that are sublime and discursive recognize and compare even the most delicate and general resemblances; each of them readily falls into excess, by catching either at nice distinctions or shadows of resemblance.

Cf. Stravinsky.

A non sequitur of numbing grossness

Strawson on Kant in The Bounds of Sense:

In the Second Analogy Kant expresses in a number of ways the thought that the order of perceptions of htose objective states of affairs the succession of one upon the other of which constitutes an objective change is—as, in the sense examined and with the qualifications mentioned, we see it is—a necessary order. The order of perceptions is characterized not only as a necessary, but as a determined order, an order to which our apprehension is bound down, or which we are compelled to observe. These may all perhaps be admitted as legitimate ways of expressing the denial of order-indifference. But from this point the argument proceeds by a non sequitur of numbing grossness.

Admirers so few and so languid

Samuel Taylor Coleridge, age 18, to his brother George, with a very green poem setting Euclidean reasoning to verse:

Dear Brother,

I have often been surprising that Mathematics, the quintessence of Truth, should have found admirers so few and so languid. Frequent consideration and minute scrutiny have at length unravelled the case; viz. that though Reason is feasted, Imagination is starved; whilst Reason is luxuriating in its proper Paradise, Imagination is wearily travelling on a dreary desert. To assist Reason by the stimulus of Imagination is the design of the following production. In the execution of it much may be objectionable. The verse (particularly in the introduction of the ode) may be accused of unwarrantable liberties, but they are liberties equally homogeneal with the exactness of Mathematical disquisition, and the boldness of Pindaric daring. I have three strong champions to defend me against the attacks of Criticism; the Novelty, the Difficulty, and the Utility of the work. I may justly plume myself, that I first have drawn the nymph Mathesis from the visionary caves of abstracted Idea, and caused her to unite with Harmony. The first-born of this Union I now present to you; with interested motived indeed—as I expect to receive in return the more valuable offspring of your Muse.

This is now—this was erst,
Proposition the first—and Problem the first.


On a given finite line
which must no way incline;
To describe an equi—
—lateral Tri—
—A, N, G, E, L, E.
Now let A. B.
Be the given line
Which must no way incline;
The great Mathematician
Makes the Requisition,
That we describe an Equi—
—lateral Tri—
—angle on it:
Aid us Reason—aid us Wit!


From the centre A. at the distance A. B.
Describe the circle B. C. D.
At the distance B. A. from B. the centre
The round A. C. E. to describe boldly venture.
(Third postulate see.)
And from the point C.
In which the circles make a pother
Cutting and slashing one another,
Bid the straight lines a journeying go.
C. A. C. B. those lines will show
To the points, which by A. B. are reckon’d,
And postulate the second
For authority ye know.
A. B. C.
Triumphant shall be
An Equilateral Triangle,
Not Peter Pindar carp, nor Zoilus can wrangle.


Because the point A. is the centre
Of the circular B. C. D.
And because the point B. is the centre
Of the circular A. C. E.
A. C. to A. B. and  B. C. to B. A.
Harmoniously equal must forever stay;
Then C. A. and B. C.
Both extend the kind hand
To the basis A. B,
Unambitiously join’d in Equality’s Band.
But to the same powers, when two powers are equal
My mind forebodes the sequel;
My mind does some celestial impulse teach,
And equalizes each to each.
Thus C. A. with B. C. strikes the same sure alliance.
That C. A. and B. C. had with A. B. before
And in mutual affiance
None attempting to soar
Above another,
The unanimous three
C. A. and B. C. and A. B.
All are equal, each to his brother,
Preserving the balance of power so true:
Ah! the like would the proud Autocratix do!
At taxes impending not Britain would tremble,
Nor Prussia struggle her fear to dissemble;
Nor the Mah’met-sprung wight
The great Mussulman
Would stain his Divan
With Urine the soft-flowing daughter of Fright.


But rein your stallion in, too daring Nine!
Should Empires bloat the scientific line?
Or with dishevell’d hair all madly do ye run
For transport that your task is done?
For done it is—the cause is tried!
And Proposition, gentle maid,
Who soothly ask’d stern Demonstration’s aid,
Has prov’d her right, and A. B. C.
Of angles three
Is shown to be of equal side;
And now our weary stead to rest in fine,
‘Tis raised upon A. B. the straight, the given line.

Right for the wrong reasons

from George Eliot, Middlemarchwith a funny rhythmic echo of the bromide “all good things come to an end, but diamonds are forever” in the second sentence:

Miss Brooke argued from words and dispositions not less unhesitatingly than other young ladies of her age. Signs are small measurable things, but interpretations are illimitable, and in girls of sweet, ardent nature, every sign is apt to conjure up wonder, hope, belief, vast as a sky, and colored by a diffused thimbleful of matter in the shape of knowledge. They are not always too grossly deceived; for Sinbad himself may have fallen by good-luck on a true description, and wrong reasoning sometimes lands poor mortals in right conclusions: starting a long way off the true point, and proceeding by loops and zigzags, we now and then arrive just where we ought to be. Because Miss Brooke was hasty in her trust, it is not therefore clear that Mr. Casaubon was unworthy of it.

We hear a lot about being right for the wrong reasons, but not so much about being wrong for the right reasons—arguably just as common, if not more so, and perhaps less of a sin. As for being wrong for the wrong reasons, that is still not so bad as being “not even wrong.”

If we care to be scholastic, we might map this fourfold way onto the apparatus of informal logic. If we fudge Eliot’s focus on “conclusions” and take rightness instead to be a matter of having given true premises, then to be right for right reasons is to be sound; to be wrong for right reasons is to be valid but unsound; to be right for wrong reasons is to be invalid and epistemically lucky; and to be wrong for wrong reasons is simply to be a user of Twitter.

If we care, instead, to be cancelled, we might look to the work of heterodox philosopher Donald Rumsfeld, who took his cue from analytical chemistry. In this typology there are known knowns, known unknowns, unknown knowns, and unknown unknowns. (Rumsfeld himself is an instance of the third.) He thus extends the great philosophical tradition of drawing squares, from Plato and Aristotle to Levi-Strauss.

The method has become so popular it has since been taken up by statisticians.

Cannot one say what is true?

Stanley Cavell, The Claim of Reason, pp. 205–206:

“[…] Are you suggesting that one cannot sometimes say what is true?” What I am suggesting is that “Because it is true” is not a reason or basis for saying something; and I am suggesting that there must, in grammar, be reasons for what you say, or be a point in your saying of something, if what you say is to be comprehensible. We can understand what the words mean apart from understanding why you say them; but apart from understanding the point of you saying them we cannot understand what you mean.

The clouds and mists of their own raising

From the translators’ preface of the first English edition (1685) of Arnauld’s La Logique ou l’art du penser (1662):

The Common Treatises of Logic are almost without number, and while every Author strives to add something of his own, sometimes little to the purpose, sometimes altogether from the matter, the Art is become, not only Obscure and Tedious, but in a great measure Impertinent and Useless.

Thus the Schoolmen may be said to have clogg’d and fetter’d Reason, which ought to be free as Air, and plain as Demonstration itself, with vain misapplications of this Art to Notion and Nicety, while they make use of it only to main­tain litigious Cavils and wrangling Disputes. So that indeed the common Logics are but as so many Counterscarps to shelter the obstinate and vain-glorious, that disdain Submission and Convincement, and therefore retire within their Fortifications of difficult Terms, wrap themselves up in Quirk and Suttlety, and so escape from Reason in the Clouds and Mists of their own Raising.

Supplies are limited

the introductory note to “Further Reading” in Nigel Warburton, Thinking from A to Z:

There are a number of books which purport to give a thorough grounding in critical thinking. Unfortunately many of them demonstrate their authors’ limited abilities to think critically.

The world is awash in bullshit

from the introduction to the course Calling Bullshit: Data Reasoning in a Digital World, taught by Carl T. Bergstrom and Jevin West at the University of Washington:

The world is awash in bullshit. Politicians are unconstrained by facts. Science is conducted by press release. Higher education rewards bullshit over analytic thought. Startup culture elevates bullshit to high art. Advertisers wink conspiratorially and invite us to join them in seeing through all the bullshit — and take advantage of our lowered guard to bombard us with bullshit of the second order. The majority of administrative activity, whether in private business or the public sphere, seems to be little more than a sophisticated exercise in the combinatorial reassembly of bullshit.

We’re sick of it. It’s time to do something, and as educators, one constructive thing we know how to do is to teach people. So, the aim of this course is to help students navigate the bullshit-rich modern environment by identifying bullshit, seeing through it, and combating it with effective analysis and argument.

What do we mean, exactly, by bullshit and calling bullshit? As a first approximation:

Bullshit involves language, statistical figures, data graphics, and other forms of presentation intended to persuade by impressing and overwhelming a reader or listener, with a blatant disregard for truth and logical coherence.

Calling bullshit is a performative utterance, a speech act in which one publicly repudiates something objectionable. The scope of targets is broader than bullshit alone. You can call bullshit on bullshit, but you can also call bullshit on lies, treachery, trickery, or injustice.

In this course we will teach you how to spot the former and effectively perform the latter.

The mind is assailed, as it were

Edward Thorndike, “Reading as Reasoning: A Study of Mistakes in Paragraph Reading,” The Journal of Educational Psychology, 1917:

Understanding a paragraph is like solving a problem in mathematics. It consists in selecting the right elements of the situation and putting them together in the right relations, and also with the right amount of weight or influence or force for each. The mind is assailed as it were by every word in the paragraph. It must select, repress, soften, emphasize, correlate and organize, all under the influence of the right mental set or purpose or demand.


It thus appears that reading an explanatory or argumentative paragraph in his text-books on geography or history or civics, and (though to a less degree) reading a narrative or description, involves the same sort of organization and analytic action of ideas as occur in thinking of supposedly higher sorts.


It appears likely, therefore, that many children fail in certain features of these subjects not because they have understood and remembered the facts and principles but have been unable to organize and use them; or because they have understood them but have been unable to remember them; but because they never understood them.

It appears likely also that a pupil may read fluently and feel that the series of words are arousing appropriate thoughts without really understanding the paragraph. Many of the children who made notable mistakes would probably have said that they understood the paragraph and, upon reading the questions on it, would have said that they understood them. In such cases the reader finds satisfying solutions of those problems which he does raise and so feels mentally adequate; but he raises only a few of the problems which should be raised and makes only a few of the judgments which he should make.