Frank

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Frank is Currently Reading

Frank is currently reading

Girl with Curious Hair

by David Foster Wallace

bookshelves: literature, usa, currently-reading

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Sep 19, 2026 09:11AM

“..First, we need to get clear on the subject matter of mathematics. What is mathematics about? Is it really concerned with abstract objects..? We obviously need to listen to what mathematics itself has to say.. As Frege emphasized, however, the questions are also in part concerned with language. How should the language of mathematics be analyzed? Should apparent talk about numbers and sets be taken at face value? This concern with language means that we shall also need assistance from linguistics and perhaps also psychology. Second, we need to understand how mathematicians.. settle on their first principles (or axioms), and how do they use these to prove mathematical results (or theorems)? .. The challenge is to make our answers to these two sets of questions mesh. How is it that our ways of forming mathematical beliefs are responsive to what mathematics is about? How are the practices and mechanisms by which we arrive at our mathematical beliefs conducive to finding out about whatever reality mathematics describes? In short, why is it not just a happy accident that our mathematical beliefs tend to be true? There must be something about what we do that keeps us on the right track., Since the challenge is to integrate the metaphysics of mathematics (namely, what mathematics is about) with its epistemology (namely, how we form our mathematical beliefs), we shall call this the integration challenge.”
― Øystein Linnebo

tags: philosophy

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“Suspicion of the senses remained the core of scientific pride until in our time it has turned into a source of uneasiness. The trouble is that "we find nature behaving so differently from what we observe in the visible and palpable bodies of our surroundings that no model shaped after our large-scale experiences can ever be 'true' "; at this point the indissoluble connection between our thinking and our sense perception takes its revenge, for a model that would leave sense experience altogether out of account and, therefore, be completely adequate to nature in the experiment is not only ''practically inaccessible but not even thinkable.”
― Hannah Arendt

tags: scientific-realism

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“In the 1950s, at the very beginning of the integration process, Raymond Aron wrote that “the European idea is empty, it has neither the transcendence of messianic ideologies nor the immanence of concrete patriotism.” Aron was half right. The idea of Europe did not evoke emotional commitment. It did not stir people’s hearts as nations sometimes had done. It was not something for which many would have been willing to give their lives. But the European idea was not empty—or rather, it only seemed empty when compared to the traditional idea of the nation. The European idea was full, not of national enthusiasm and patriotic passion, but of a widespread commitment to escape the destructive antagonisms of the past..”
― James J. Sheehan

tags: europe, history, politics

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“Stan got the message. He allowed the chicken assignations. What did that make him? A chicken pimp. Better that than dead.”
― Margaret Atwood, The Heart Goes Last

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“In the beginning, everything was void, and J. H. W. H. Conway began to create numbers. Conway said, "Let there be two rules which bring forth all numbers large and small. This shall be the first rule: Every number corresponds to two sets of previously created numbers, such that no member of the left set is greater than or equal to any member of the right set. And the second rule shall be this: One number is less than or equal to another number if and only if no member of the first number's left set is greater than or equal to the second number, and no member of the second number's right set is less than or equal to the first number." And Conway examined these two rules he had made, and behold! They were very good.
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And Conway said, "Let the numbers be added to each other in this wise: The left set of the sum of two numbers shall be the sums of all left parts of each number with the other; and in like manner the right set shall be from the right parts, each according to its kind." Conway proved that every number plus zero is unchanged, and he saw that addition was good. And the evening and the morning were the third day. And Conway said, "Let the negative of a number have as its sets the negatives of the number's opposite sets; and let subtraction be addition of the negative." And it was so. Conway proved that subtraction was the inverse of addition, and this was very good. And the evening and the morning were the fourth day.

And Conway said to the numbers, "Be fruitful and multiply. Let part of one number be multiplied by another and added to the product of the first number by part of the other, and let the product of the parts be subtracted. This shall be done in all possible ways, yielding a number in the left set of the product when the parts are of the same kind, but in the right set when they are of opposite kinds." Conway proved that every number times one is unchanged. And the evening and the morning were the fifth day.

And behold! When the numbers had been created for infinitely many days, the universe itself appeared. And the evening and the morning were N day.

And Conway looked over all the rules he had made for numbers, and saw that they were very, very good.”
― Donald Moses Knuth

tags: mathematics

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