A Quote by Henri Poincare
A sane mind should not be guilty of a logical fallacy, yet there are very fine minds incapable of following mathematical demonstrations.
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If you let your mind talk you out of things that aren't logical, you're going to have a very boring life. Because grace isn't logical. Love isn't logical. Miracles aren't logical.
Mathematical demonstrations being built upon the impregnable Foundations of Geometry and Arithmetick are the only truths that can sink into the Mind of Man, void of all Uncertainty; and all other Discourses participate more or less of Truth according as their Subjects are more or less capable of Mathematical Demonstration.
--Why are we fighting them? --They're mad. We're sane. --How do we know? --That we're sane? --Yes. --Am I sane? --To all appearances. --And you, do you consider yourself sane? --I do. --Well, there you have it. --But don't they also consider themselves sane? --I think they know. Deep down. That they're not sane. --How must that make them feel? --Terrible, I should think. They must fight ever more fiercely, in order to deny what they know to be true. That they are not sane.
I think it is fine to have sports divided into men's and women's, just as it is fine to say a fifteen-year-old is incapable of consenting to sex. But we should recognize these are social distinctions based on biology, and not categories foisted upon us by nature.
Logical positivists have never taken psychology into account in their epistemology, but they affirm that logical beings and mathematical beings are nothing but linguistic structures.
I myself, a professional mathematician, on re-reading my own work find it strains my mental powers to recall to mind from the figures the meanings of the demonstrations, meanings which I myself originally put into the figures and the text from my mind. But when I attempt to remedy the obscurity of the material by putting in extra words, I see myself falling into the opposite fault of becoming chatty in something mathematical.
What distinguishes a mathematical model from, say, a poem, a song, a portrait or any other kind of "model," is that the mathematical model is an image or picture of reality painted with logical symbols instead of with words, sounds or watercolors.
Mathematics is a logical method. . . . Mathematical propositions express no thoughts. In life it is never a mathematical proposition which we need, but we use mathematical propositions only in order to infer from propositions which do not belong to mathematics to others which equally do not belong to mathematics.
We know that mathematicians care no more for logic than logicians for mathematics. The two eyes of science are mathematics and logic; the mathematical set puts out the logical eye, the logical set puts out the mathematical eye; each believing that it sees better with one eye than with two. Note that De Morgan, himself, only had sight with only one eye.
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.
There is no permanent place in this universe for evil... Evil may hide behind this fallacy and that, but it will be hunted from fallacy to fallacy until there is no more fallacy for it to hide behind.
I remember feeling a little guilty every time I opened a Chipotle. I felt guilty because I wasn't following my true passion. But that eventually went away. And I realized that this is my calling.
I was never very good at math and science, to be honest, so it's fun to play a character that is so scientific and mathematical, and whose brain functions at such a high pace. The biggest difference is that Maura is very linear in her thinking and very logical. I'm not quite like that. I'm much more laid back and not quite so type A. That's the big difference.
The line is very delicate and fine between being what one might call sane or insane, well or unwell.
In fact, Gentlemen, no geometry without arithmetic, no mechanics without geometry... you cannot count upon success, if your mind is not sufficiently exercised on the forms and demonstrations of geometry, on the theories and calculations of arithmetic ... In a word, the theory of proportions is for industrial teaching, what algebra is for the most elevated mathematical teaching.
So long as the processes of healing were not understood and man thought that the power to heal resided in substances and things outside of him, he logically sought for extrinsic means of healing, and a healing art was a logical development. The system of medicine, as we know it today, was a logical development out of the fallacy that healing power resides in extrinsic sources.
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