In summary, then, the set theoretic 'needs' of physics are surprisingly similar to the set theoretic needs of pure logic. Both disciplines need some set theory to function at all. Both disciplines can 'live' - but live badly - on the meager diet of only predicative sets. Both can live extremely happily on the rich diet of impredicative sets. Insofar, then, as the indispensability of quantification over sets is any argument for their existence - and we will discuss why it is in the next section - we may say that it is a strong argument for the existence of at least predicative sets, and a pretty strong, but not as strong, argument for the existence of impredicative sets.
Hilary PutnamRelated topics
argument diet existence function indispensability least live logic need needs next physics predicative pretty pure quantification rich say section set similar summary theoryRelated quotes
The meaning that I have given to the word administration and which has been generally adopted, broadens considerably the field of administrative science. It embraces not only the public service but enterprises of every size and description, of every form and every purpose. All undertakings require planning, organization, command, co-ordination and control, and in order to function properly, all must observe the same general principles. We are no longer confronted with several administrative sciences but with one alone, which can be applied equally well to public and to private affairs and whose principal elements are today summarized in what we term the Administrative Theory.
Henri Fayol
There is no pure visualization in the sense of a priori philosophies; every visualization is determined by previous sense perceptions, and any separation into perceptual space and space of visualization is not permissible, since the specifically visual elements of the imagination are derived from perceptual space. What led to the mistaken conception of pure visualization was rather an improper interpretation of the normative function... an essential element of all visual representations. Indeed, all arguments which have been introduced for the distinction of perceptual space and space of visualization are base on this normative component of the imagination.
Hans Reichenbach
Consider your state of mind-your consciousness-before going to sleep. This is extremely important. Make a commitment to spend at least fifteen minutes spiritualizing your consciousness before going to bed. Read something spiritual, listen to spiritual discourse or music, or engage in discussion on a spiritual topic. Push aside the chaos and confusion that were a part of your day, and focus on spiritual reality. In this way, you will prepare yourself for the next six to eight hours of sleep. If you allow yourself to focus spiritually, you will provide less of an opportunity for negative elements to enter your dreams. You can then benefit most from your sleeping state.
Bhakti Tirtha Swami
Do everything simply and meekly. Do nothing with an ulterior motive. Don't say, I'll do this in order to have that result, but do it naturally, without taking cognizance of it. That is, pray simply and don't think about what God will bestow on your soul. Don't make any calculations. You know, of course, what God bestows when you enter into communion with Him, but it is as if you don't know. Don't discuss the matter even with yourself. So when you repeat the prayer, "Lord Jesus Christ, have mercy on me”, say it simply and ingenuously and think of nothing other than the prayer. These are very delicate matters and the intervention of the grace of God is required.
Porphyrios of Kafsokalyvia
Throughout the nineteenth century, apart from the division in theoretical sciences and arts, classifiers attempted to divide the sciences into two groups. Already they had before them the examples of Francis Bacon (speculative and descriptive) and Hobbes (quantitative and qualitative). For Coleridge, the sciences were either pure (Grammar, Logic, Rhetoric, Mathematics, Metaphysics) or mixed. Arthur Schopenhauer's similar groups were called pure and empirical, Wilhelm Wundt in 1887 called them formal and empirical, Globot mathematical and theoretical, and the St. Louis Congress of Arts and Sciences (1904) normative and physical.
Brian Campbell Vickery
