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Realm Quotes - page 5 - Quotesdtb.com
Realm Quotes - page 5
P. Bernays has pointed out on several occasions that, since the consistency of a system cannot be proved using means of proof weaker than those of the system itself, it is necessary to go beyond the framework of what is, in Hilbert's sense, finitary mathematics if one wants to prove the consistency of classical mathematics, or even that of classical number theory. Consequently, since finitary mathematics is defined as the mathematics in which evidence rests on what is intuitive, certain abstract notions are required for the proof of the consistency of number theory.... In the absence of a precise notion of what it means to be evident, either in the intuitive or in the abstract realm, we have no strict proof of Bernays' assertion; practically speaking, however, there can be no doubt that it is correct...
Paul Bernays
...classic philosophy maintained that change, and consequently time, are marks of inferior reality, holding that true and ultimate reality is immutable and eternal. Human reasons, all too human, have given birth to the idea that over and beyond the lower realm of things that shift like the sands on the seashore there is the kingdom of the unchanging, of the complete, the perfect. The grounds for the belief are couched in the technical language of philosophy, but the grounds for the cause is the heart's desire for surcease from change, struggle, and uncertainty. The eternal and immutable is the consummation of mortal man's quest for certainty.
John Dewey
I always say-a prejudice on my part, I'm sure-you can tell a lot about a person's character from his choice of sofa. Sofas constitute a realm inviolate unto themselves. This, however, is something that only those who have grown up sitting on good sofas will appreciate. It's like growing up reading good books or listening to good music. One good sofa breeds another good sofa; one bad sofa breeds another bad sofa. That's how it goes. There are people who drive luxury cars, but have only second- or third-rate sofas in their homes. I put little trust in such people. An expensive automobile may well be worth its price, but it's only an expensive automobile. If you have the money, you can buy it, anyone can buy it. Procuring a good sofa, on the other hand, requires style and experience and philosophy. It takes money, yes, but you also need a vision of the superior sofa. That sofa among sofas.
Haruki Murakami