Over time, Tarski laid claim to a great deal of territory in the world of logic, mathematics, and philosophy, especially in the areas of set theory, model theory, semantics of formal languages, decision procedures, universal algebra, geometry, and algebras of logic and topology. Between the late 1940s and 1980 he created a mecca in Berkeley to which the logicians of the world made pilgrimage, but he had to push and keep pushing for position, priority, and recognition. For better or worse, it became a habit that he continued long past the point of necessity — or at least so it seemed to others. Even one of his greatest admirers, the philosopher John Corcoran, said: “He was such a glory hound, it was embarrassing. He once confided to me that he considered himself ‘the greatest living sane logician’,” thus not so subtly avoiding the problem of comparison with Kurt Gödel.
“Eliza–” I said, “so many of the books I’ve read to you said that love was the most important thing of all. Maybe I should tell you that I love you now.”
“Go ahead,” she said.
“I love you, Eliza,” I said.
She thought about it. “No,” she said at last, “I don’t like it.”
“Why not?” I said.
“It’s as though you were pointing a gun at my head,” she said. “It’s just a way of getting somebody to say something they probably don’t mean. What else can I say, or anybody say, but, ‘I love you, too’?”
“You don’t love me?” I said.
During my trip to Ilium and to points beyond—a two-week expedition bridging Christmas—I let a poor poet named Sherman Krebbs have my New York City apartment free. My second wife had left me on the grounds that I was too pessimistic for an optimist to live with.
Krebbs was a bearded man, a platinum blond Jesus with spaniel eyes. He was no close friend of mine. I had met him at a cocktail party where he presented himself as National Chairman of Poets and Painters for Immediate Nuclear War. He begged for shelter, not necessarily bomb proof, and it happened that I had some.
When I returned to my apartment … I found [it] wrecked by a nihilistic debauch. Krebbs was gone; but, before leaving, he had run up three-hundred-dollars’ worth of long-distance calls, set my couch on fire in five places, killed my cat and my avocado tree, and torn the door off my medicine cabinet.
He wrote this poem, in what proved to be excrement, on the yellow linoleum floor of my kitchen:
I have a kitchen.
But it is not a complete kitchen.
I will not be truly gay
Until I have a
Dispose-all.
There was another message, written in lipstick in a feminine hand on the wallpaper over my bed. It said: “No, no, no, said Chicken-licken.”
There was a sign hung around my dead cat’s neck. It said, “Meow.”
… for law, in its true notions, is not so much the limitation as the direction of a free and intelligent agent to his proper interest, and prescribes no farther than is for the general good of those under that law: could they be happier without, the law, as an useless thing, would of itself vanish; and that ill deserves the name of confinement which hedges us in only from bogs and precipices. So that, however it may be mistaken, the end of law is not to abolish or restrain, but to preserve and enlarge freedom: for in all the states of created beings capable of laws, where there is no law, there is no freedom: for liberty is, to be free from restraint and violence from others… to dispose, and order as [one] lists, his person, actions, possessions, and his whole property, within the allowance of those laws under which he is, and therein not to be subject to the arbitrary will of another, but freely follow his own.
…both posets and monoids are themselves special kinds of categories, which in a certain sense represent the two “dimensions” (objects and arrows) that a general category has. Many phenomena occurring in categories can best be understood as generalizations from posets or monoids.
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Any preorder P can be regarded as a category by taking the objects to be the elements of P and taking a unique arrow a → b if and only if a ≤ b. … A poset is evidently a preorder satisfying the additional condition of antisymmetry… It’s often useful to think of a category as a kind of generalized poset, one with with “more structure” than just p ≤ q. One can thus also think of a functor as a generalized monotone map.
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…a monoid is a category with just one object. The arrows of the category are the elements of the monoid. In particular, the identity arrow is the unit element u. Composition of arrows is the binary operation m⋅n of the monoid. …a monoid homomorphism from M to N is the same thing as a functor from M regarded as a category to N regarded as a category. In this sense, categories are also generalized monoids, and functors are generalized homomorphisms.
Whoever leads a solitary life and yet now and then wants to attach himself somewhere, whoever, according to changes in the time of day, the weather, the state of his business and the like, suddenly wishes to see any arm at all to which he might cling — he will not be able to manage for long without a window looking on to the street. And if he is in the mood of not desiring anything and only goes to his window sill a tired man, with eyes turning from his public to heaven and back again, not wanting to look out and having thrown his head up a little, even then the horses below will draw him down into the train of wagons and tumult, and so at last into the human harmony.
Like … ant colonies, or the cells of a developing embryo, neighborhoods are patterns in time. No one wills them into existence single-handedly; they emerge by a kind of tacit consensus: the artists go here, the investment bankers here, Mexican-Americans here, gays and lesbians here. The great preponderance of city dwellers live by those laws, without any legal authority mandating that compliance. It is the sidewalk — the public space where interactions between neighbors are the most expressive and the most frequent — that helps us create those laws. In the popular democracy of neighborhood formation, we vote with our feet.
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The key here is that sidewalks are important not because they provide an environmentally sound alternative to freeways (though that is also the case) nor because walking is better exercise than driving (though that too is the case) nor because there’s something quaintly old-fashioned about pedestrian-centered towns (that is more a matter of fashion than empirical evidence). In fact, there’s nothing about the physical existence of sidewalks that matters [here]. What matters is that they are the primary conduit for the flow of information between city residents. Neighbors learn from each other because they pass each other — and each other’s stores and dwellings — on the sidewalk. Sidewalks allow relatively high-bandwidth communication between total strangers, and they mix large number of individuals in random configurations. Without the sidewalks, cities would be like ants without a sense of smell, or a colony with too few worker ants. Sidewalks provide both the right kind and the right number of local interactions. They are the gap junctions of city life.
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