Rudolf Carnap (1891–1970) German philosopher
Rudolf Carnap (1937) cited in: Irving J. Lee (1967) The Language of Wisdom and Folly: Background Readings in Semantics. International Society for General Semantics, p. 44
Metaphysics, again, is the Dynamics of Thought; treats of the primary Powers of Thought; occupies itself with the mere Soul of the Science of Thinking. Metaphysical ideas stand related to one another, like thoughts without words. Men often wondered at the stubborn Incompletibility of these two Sciences; each followed its own business by itself; there was a want everywhere, nothing would suit rightly with either. From the very first, attempts were made to unite them, as everything about them indicated relationship; but every attempt failed; the one or the other Science still suffered in these attempts, and lost its essential character. We had to abide by metaphysical Logic, and logical Metaphysic, but neither of them was as it should be.
Pupils at Sais (1799)
Rudolf Carnap (1891–1970) German philosopher
Rudolf Carnap (1937) cited in: Irving J. Lee (1967) The Language of Wisdom and Folly: Background Readings in Semantics. International Society for General Semantics, p. 44
“Pure mathematics is in its way the poetry of logical ideas.”
Albert Einstein (1879–1955) German-born physicist and founder of the theory of relativity
1930s, Obituary for Emmy Noether (1935)
Context: Pure mathematics is, in its way, the poetry of logical ideas. One seeks the most general ideas of operation which will bring together in simple, logical and unified form the largest possible circle of formal relationships. In this effort toward logical beauty spiritual formulas are discovered necessary for the deeper penetration into the laws of nature.
Albert Einstein (1879–1955) German-born physicist and founder of the theory of relativity
1930s, Obituary for Emmy Noether (1935)
George Alec Effinger (1947–2002) Novelist, short story writer
Source: What Entropy Means to Me (1972), Chapter 9 “A Moral Dilemma” (p. 140).
Hans Freudenthal (1905–1990) Dutch mathematician
Source: Realistic models in probability (1968), p. 1
Edward Abbey (1927–1989) American author and essayist
George Boole (1815–1864) English mathematician, philosopher and logician
Source: 1840s, The Mathematical Analysis of Logic, 1847, p. i: Lead paragraph of the Preface; cited in: R. H. Hutton, " Professor Boole http://books.google.com/books?id=pfMEAAAAQAAJ&pg=PA157," (1866), p. 157 <br class="br">Context: In presenting this Work to public notice, I deem it not irrelevant to observe, that speculations similar to those which it records have, at different periods, occupied my thoughts. In the spring of the present year my attention was directed to the question then moved between Sir W. Hamilton and Professor De Morgan; and I was induced by the interest which it inspired, to resume the almost-forgotten thread of former inquiries. It appeared to me that, although Logic might be viewed with reference to the idea of quantity, it had also another and a deeper system of relations. If it was lawful to regard it from without, as connecting itself through the medium of Number with the intuitions of Space and Time, it was lawful also to regard it from within, as based upon facts of another order which have their abode in the constitution of the Mind. The results of this view, and of the inquiries which it suggested, are embodied in the following Treatise.
Charles Sanders Peirce (1839–1914) American philosopher, logician, mathematician, and scientist
The Law of Mind (1892)
Charles Sanders Peirce (1839–1914) American philosopher, logician, mathematician, and scientist
Vol. IV, par. 5
Collected Papers (1931-1958)
Context: The ordinary logic has a great deal to say about genera and species, or in our nineteeth century dialect, about classes. Now a class is a set of objects comprising all that stand to one another in a special relation of similarity. But where ordinary logic talks of classes the logic of relatives talks of systems. A system is a set of objects comprising all that stands to one another in a group of connected relations. Induction according to ordinary logic rises from the contemplation of a sample of a class to that of a whole class; but according to the logic of relatives it rises from the comtemplation of a fragment of a system to the envisagement of the complete system.
Robert A. Heinlein book The Cat Who Walks Through Walls
Gwen Novak (Hazel Stone); chapter 18, p. 230
The Cat Who Walks Through Walls (1985)
Context: The hardest part about gaining any new idea is sweeping out the false idea occupying that niche. As long as that niche is occupied, evidence and proof and logical demonstration get nowhere. But once the niche is emptied of the wrong idea that has been filling it — once you can honestly say, "I don't know", then it becomes possible to get at the truth.