The above comparison of the domain R of rational numbers with a straight line has led to the recognition of the existence of gaps, of a certain incompleteness or discontinuity of the former, while we ascribe to the straight line completeness, absence of gaps, or continuity. In what then does this continuity consist? Everything must depend on the answer to this question, and only through it shall we obtain a scientific basis for the investigation of all continuous domains.
Richard DedekindRelated topics
above absence answer basis certain comparison completeness consist continuity discontinuity domain everything existence former incompleteness investigation led line numbers question rational recognition straight whileRelated quotes
"But," it will be asked of the Anarchists at this point in the argument, "what shall be done with those individuals who undoubtedly will persist in violating the social law by invading their neighbors?" The Anarchists answer that the abolition of the State will leave in existence a defensive association, resting no longer on a compulsory but on a voluntary basis, which will restrain invaders by any means that may prove necessary.
Benjamin Tucker
Speed in itself is not exciting. As you sit in a Boeing, are you thrilled that it's ripping up the sky with a 500mph orgy of big numbers? No, and it's the same deal in a straight line in a straight road in a car. Two hundred mph. So what. What matters is acceleration and handling, an ability to take corners as though they're not there, and this is why the Ferrari F50 has been so well received by those who know. It's light, and simple, like a choux pastry in a world full of suet pudding.
Jeremy Clarkson
The recognition of authority to impose previous restraint upon publication in order to protect the community against the circulation of charges of misconduct, and especially of official misconduct, necessarily would carry with it the admission of the authority of the censor against which the constitutional barrier was erected. The preliminary freedom, by virtue of the very reason for its existence, does not depend, as this Court has said, on proof of truth.
Charles Evans Hughes
What I affirm is the intuition that where God's presence is no longer a tenable supposition and where His absence is no longer a felt, indeed overwhelming weight, certain dimensions of thought and creativity are no longer attainable. And I would vary Yeats's axiom so as to say: no man can read fully, can answer answeringly to the aesthetic, whose "nerve and blood" are at peace in sceptical rationality, are now at home in immanence and verification. We must read as if.
George Steiner
The spirit of a production-centered, commodity-greedy society is such that only the non-conformist can defend himself sufficiently against it. Those who are seriously concerned with love as the only rational answer to the problem of human existence must, then, arrive at the conclusion that important and radical changes in our social structure are necessary, if love is to become a social and not a highly individualistic, marginal phenomenon.
Erich Fromm
