Quotes

You insist that there is something a machine cannot do. If you will tell me precisely what it is that a machine cannot do, then I can always make a machine which will do just that!

To anyone who has reached this note legitimately — that is, by following the proof of Theorem 4.18 — we offer our congratulations and suggest that some strong refreshment is in order. Try combining some hard-frozen strawberries, raspberries, or peaches in a blender with enough dark rum so that the result is a stiff mush (add powdered sugar if the fruit was not sweetened). Pour into a stemmed cocktail glass and relax! For an alternative, see the Notes to Barwise [1975, §II.6].

When used in a class or seminar, section 6 should be supplemented with coffee (_not_ decaffeinated) and a light refreshment. We suggest Heatherton Rock Cakes. (Recipe: Combine 2 cups of self-rising flour with 1 t. allspice and a pinch of salt. Use a pastry blender or two cold knives to cut in 6 T butter. Add 1/3 cup each of sugar and raisins (or other urelements). Combine this with 1 egg and enough milk to make a stiff batter (3 or 4 T milk). Divide this into 12 heaps, sprinkle with sugar, and bake at 400 °F. for 10—15 minutes. They taste better than they sound.)

Every thinker puts some portion of an apparently stable world in peril and no one can predict what will emerge in its place.

It is important to understand very clearly that strengthening a particular technique—putting muscles in it—contributes nothing to its validity. [...] If a bad idea is to be converted into a good one, the source of its weakness must be discovered and repaired. A person falling into a manhole is rarely helped by making it possible for him to fall faster or more efficiently.

Peirce's contribution to our subject is the most considerable of any up to his time, with the doubtful exception of Boole's. His papers, however, are brief to the point of obscurity: results are given summarily with little or no explanation and only infrequent demonstrations. As a consequence, the most valuable of them make tremendously tough reading, and they have never received one-tenth the attention which their importance deserves.* If Peirce had been given to the pleasantly discursive style of De Morgan, or the detailed and clearly accurate manner of Schröder, his work on symbolic logic would fill several volumes. (*: Any who find our report on Peirce's work unduly difficult or obscure are earnestly requested to consult the original papers.)

Let us take a pair of contrary names, as man and not-man. It is plain that between them they represent everything, imaginable or real, in the universe. But the contraries of common language embrace, not the whole universe, but some one general idea. Thus, of men, Briton and alien are contraries: every man must be one of the two, no man can be both. [...] The same may be said of integer and fraction among numbers, peer and commoner among subjects of a realm [...], and so on. In order to express this, let us say that the whole idea under consideration is _the universe_ (meaning merely the whole of which are considering parts) and let names which have nothing in common, but which between them contain the whole of the idea under consideration, be called contraries in or with respect to that universe.

Truth emerges more readily from error than confusion.

De Jongh’s original proof was semantic and so complicated he never showed it to anyone; Sambin’s original proof was syntactic and so complicated I never read it completely.

[A] science-fiction story is a story about human beings, with a human problem, and a human solution, that would not have happened at all without its science content.

Any algorithmic task can be sabotaged to create real-life versions of a hostile environment. This can be done by turning it into a game, which can be studied by know techniques. Thus, in Clausewitz’ immortal phrasing, game theory is “algorithmics pursued by other means”.

By the law of excluded middle, either ‘A is B’ or ‘A is not B’ must be true. Hence either “the present king of France is bald” or “the present king of France is not bald” must be true. Yet if we enumerated the things that are bald, and then the things which are not bald, we should not find the present king of France in either list. Hegelians, who love a synthesis, will probably conclude that he wears a wig.

Mathematicians are necessarily rational, but not necessarily bipeds. Cyclists are necessarily bipeds, but not necessarily rational. But then, what about mathematician cyclist Paul K. Zwier: he is both necessarily rational and not necessarily rational... and his motion is as contradictory as his mind?

This is the old Platonic riddle of nonbeing. Nonbeing must in some sense be, otherwise what is it that there is not? This tangled doctrine might be nicknamed Plato's beard; historically it has proved tough, frequently dulling the edge of Occam's razor.

...in order to be able to set a limit to thought, we should have to find both sides of the limit thinkable (i.e., we should be able to think what cannot be thought).

The fundamental-seeming philosophical question, How much of our science is merely contributed by language and how much is a genuine reflection of reality? is perhaps a spurious question which itself arises wholly from a certain particular type of language. Certainly we are in a predicament if we try to answer the question; for to answer the question we must talk about the language, and to talk about the world we must already impose upon the world some conceptual scheme peculiar to our special language.
Yet we must not leap to the fatalistic conclusion that we are stuck with the conceptual scheme that we grew up in. We can change bit by bit, plank by plank, though meanwhile there is nothing to carry us along but the evolving conceptual scheme itself. The philosopher's task was well compared by Neurath to that of a mariner who must rebuild his ship on the open sea.
We can improve our conceptual scheme, our philosophy, bit by bit while continuing to depend on it for support; but we cannot detach ourselves from it and compare it objectively with an unconceptualized reality. Our standard for appraising basic changes of a conceptual scheme must be, not a realistic standard of correspondence to reality, but a pragmatic standard. Concepts are language, and the purpose of concepts and of language is in communication and in prediction. Such is the ultimate duty of language, science, and philosophy, and it is in relation to that duty that a conceptual scheme has finally to be appraised.
Elegance, conceptual economy, also enters as an objective. But this virtue, engaging though it is, is secondary—sometimes in one way and sometimes in another. Elegance can make the difference between a psychologically manageable conceptual scheme and one that is too unwieldy for our poor minds to cope with effectively. But elegance also enters as an end in itself—and quite properly so as long as it remains secondary in another respect; namely, as long as it is appealed to only in choices where the pragmatic standard prescribes no contrary decision. Where elegance doesn't matter, we may and shall, as poets, pursue elegance for elegance's sake.

Till created the first version of beamer for his PhD defense presentation in February 2003. A month later, he put the package on ctan at the request of some colleagues. After that, things somehow got out of hand.