"With the synthesis of every new concept in the aggregation of coordinate characteristics the extensive or complex distinctness is increased; with the further analysis of concepts in the series of subordinate characteristics the intensive or deep distinctness is increased. The latter kind of distinctness, as it necessarily serves the thoroughness and conclusiveness of cognition, is therefore mainly the business of philosophy and is carried farthest especially in metaphysical investigations." (Immanuel Kant, “Logic”, 1800)
“Metaphysical inquiry attempts to trace things to the very first stage in which they can, even to the most penetrating intelligences, be the subjects of a thought, a doubt, or a proposition; that profoundest abstraction, where they stand on the first step of distinction from nonentity, and where that one question might be put concerning them, the answer to which would leave no further question possible. And having thus abstracted and penetrated to the state of pure entity, the speculation would come back, tracing it into all its modes and relations; till at last metaphysical truth, approaching nearer and nearer to the sphere of our immediate knowledge, terminates on the confines of distinct sciences and obvious realities. Now, it would seem evident that this inquiry into primary truth must surpass, in point of dignity, all other speculations. If any man could carry his discoveries as far, and make his proofs as strong, in the metaphysical world, as Newton did in the physical, he would be an incomparably greater man than even Newton.” (John Foster, “Essays”, cca. 1805)
“Physics is unable to stand on its own feet, but needs a metaphysics on which to support itself, whatever fine airs it may assume towards the latter.” (Arthur Schopenhauer, “The World as Will and Representation”, 1819)
“The science of the mathematics performs more than it promises, but the science of metaphysics promises more than it performs. The study of the mathematics, like the Nile, begins in minuteness but ends in magnificence; but the study of metaphysics begins with a torrent of tropes, and a copious current of words, yet loses itself at last in obscurity and conjecture, like the Niger in his barren deserts of sand.” (Charles C Colton, “Lacon”, 1820)
"Logic and metaphysics make use of more tools than all the rest of the sciences put together, and do the least work." (Charles C Colton, "Remarks on the Talents of Lord Byron and the Tendencies of Don Juan" 1823)
"All parts of knowledge have their origin in metaphysics, and finally, perhaps, revolve into it. Mathematics has not a foot to stand upon which is not purely metaphysical." (Thomas De Quincey, "Kant in His Miscellaneous Essays", Blackwood's Edinburgh Magazine Vol. 28, 1830)
"Metaphysics is the attempt of the mind to rise above the mind." (Thomas Carlyle, "Critical and Miscellaneous: Collected and Republished", 1839)
“Therefore science always goes abreast with the just elevation of the man, keeping step with religion and metaphysics; or, the state of science is an index of our self-knowledge.” (Ralph W Emerson, “The Poet”, 1844)
Quotes and Resources Related to Mathematics, (Mathematical) Sciences and Mathematicians
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