The real significance of the Russell paradox, from the standpoint of the modal-logic picture, is this: it shows that no concrete structure can be a standard model for the naive conception of the totality of all sets; for any concrete structure has a possible extension that contains more 'sets.'
Hilary PutnamRelated topics
conception concrete extension model naive paradox picture possible real significance standard standpoint structure totality russellRelated quotes
All sentiment is right; because sentiment has a reference to nothing beyond itself, and is always real, wherever a man is conscious of it. But all determinations of the understanding are not right; because they have a reference to something beyond themselves, to wit, real matter of fact; and are not always conformable to that standard.
David Hume
The Hindu religion appears ... as a cathedral temple, half in ruins, noble in the mass, often fantastic in detail but always fantastic with a significance - crumbling or badly outworn in places, but a cathedral temple in which service is still done to the Unseen and its real presence can be felt by those who enter with the right spirit.
Sri Aurobindo
I will say without reservations that from my point of view there can be no abstractions. Any shape or area that has not the pulsating concreteness of real flesh and bones, its vulnerability to pleasure or pain is nothing at all. Any picture that does not provide the environment in which the breath of life can be drawn does not interest me.
Mark Rothko
Far from being the smartest possible biological species, we are probably better thought of as the stupidest possible biological species capable of starting a technological civilization - a niche we filled because we got there first, not because we are in any sense optimally adapted to it.
Nick Bostrom
We got a real clear picture of what they all value. Every Republican's voted for it. Look at what they value and look at their budget and what they're proposing. Romney wants to let the - he said in the first hundred days he's going to let the big banks once again write their own rules, 'unchain Wall Street.'
Joe Biden
