Mr. Dodgson had a mathematical, a logical and a philosophical mind; and when these qualities are united to a love of the grotesque, the resultant fancies are sure to have a quite peculiar charm, a charm so much the greater because its source is subtle and eludes all attempts to grasp it. Sometimes he seems to revel in ideas which are not merely illogical but anti-logical.
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Henry Holiday, The Snark's Significance, Academy, 29 January 1898.Lewis Carroll
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My suggestion is that at each state the proper order of operation of the mind requires an overall grasp of what is generally known, not only in formal logical, mathematical terms, but also intuitively, in images, feelings, poetic usage of language, etc. (Perhaps we could say that this is what is involved in harmony between the 'left brain' and the 'right brain'). This kind of overall way of thinking is not only a fertile source of new theoretical ideas: it is needed for the human mind to function in a generally harmonious way, which could in turn help to make possible an orderly and stable society.
David Bohm
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
Logical analysis applied to mental phenomenon shows that there is but one law of mind, namely that ideas tend to spread continuously and to affect certain others which stand to them in a peculiar relation of affectibility. In this spreading they lose intensity, and especially the power of affecting others, but gain generality and become welded with other ideas.
Charles Sanders Peirce
Common Logic is the Grammar of the higher Speech, that is, of Thought; it examines merely the relations of ideas to one another, the Mechanics of Thought, the pure Physiology of ideas. Now logical ideas stand related to one another, like words without thoughts. Logic occupies itself with the mere dead Body of the Science of Thinking. — 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.
Novalis
Carroll, Lewis
Carroll, Peter J.
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