Warning: Undefined array key "visitor_referer_type" in /var/www/vhosts/wordinf.com/core/app/libraries/Core.php on line 98
Prove Quotes - page 16 - Quotesdtb.com
Prove Quotes - page 16
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
Giving then to matter all the properties which philosophy knows it has, or all that atheism ascribes to it, and can prove, and even supposing matter to be eternal, it will not account for the system of the universe or of the solar system, because it will not account for motion, and it is motion that preserves it. When, therefore, we discover a circumstance of such immense importance, that without it the universe could not exist, and for which neither matter, nor any, nor all, the properties of matter can account, we are by necessity forced into the rational and comfortable belief of the existence of a cause superior to matter, and that cause man calls, God.
Thomas Paine
I HAVE never met with a man, either in England or America, who hath not confessed his opinion, that a separation between the countries, would take place one time or other: And there is no instance, in which we have shewn less judgment, than in endeavouring to describe, what we call, the ripeness or fitness of the Continent for independance. As all men allow the measure, and vary only in their opinion of the time, let us, in order to remove mistakes, take a general survey of things, and endeavour, if possible, to find out the very time. But we need not go far, the inquiry ceases at once, for, the time hath found us. The general concurrence, the glorious union of all things prove the fact. It is not in numbers, but in unity, that our great strength lies; yet our present numbers are sufficient to repel the force of all the world.
Thomas Paine