The first intellectual operation in which I arrived at any proficiency, was dissecting a bad argument, and finding in what part the fallacy lay; and though whatever capacity of this sort I attained was due to the fact that it was an intellectual exercise in which I was most perseveringly drilled by my father, yet it is also true that the school logic, and the mental habits acquired in studying it, were among the principal instruments of this drilling. I am persuaded that nothing, in modern education, tends so much, when properly used, to form exact thinkers, who attach a precise meaning to words and propositions, and are not imposed on by vague, loose, or ambiguous terms. The boasted influence of mathematical studies is nothing to it; for in mathematical processes, none of the real difficulties of correct ratiocination occur.
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Ch. 1: Childhood and Early Education (pp. 13-14)John Stuart Mill
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The definition of random in terms of a physical operation is notoriously without effect on the mathematical operations of statistical theory because so far as these mathematical operations are concerned random is purely and simply an undefined term. The formal and abstract mathematical theory has an independent and sometimes lonely existence of its own. But when an undefined mathematical term such as random is given a definite operational meaning in physical terms, it takes on empirical and practical significance. Every mathematical theorem involving this mathematically undefined concept can then be given the following predictive form: If you do so and so, then such and such will happen.
Walter A. Shewhart
The process of philosophizing, to my mind, consists mainly in passing from those obvious, vague, ambiguous things, that we feel quite sure of, to something precise, clear, definite, which by reflection and analysis we find is involved in the vague thing that we start from, and is, so to speak, the real truth of which that vague thing is a sort of shadow.
Bertrand Russell
For want of the apparatus of propositional functions, many logicians have been driven to the conclusion that there are unreal objects. It is argued, e.g., by Meinong, that we can speak about "the golden mountain," "the round square," and so on; we can make true propositions of which these are the subjects; hence they must have some kind of logical being, since otherwise the propositions in which they occur would be meaningless. In such theories, it seems to me, there is a failure of that feeling for reality which ought to be preserved even in the most abstract studies. Logic, I should maintain, must no more admit a unicorn than zoology can; for logic is concerned with the real world just as truly as zoology, though with its more abstract and general features.
Bertrand Russell
The more physical the activity, the less the difficulties will be. The more the activity becomes intellectual and turns into motives which exercise a determining influence on the commander's will, the more the difficulties will increase.
Carl von Clausewitz
The principle itself of dogmatic religion, dogmatic morality, dogmatic philosophy, is what requires to be rooted out; not any particular manifestation of that principle. ¶ The very corner-stone of an education intended to form great minds, must be the recognition of the principle, that the object is to call forth the greatest possible quantity of intellectual power, and to inspire the intensest love of truth: and this without a particle of regard to the results to which the exercise of that power may lead, even though it should conduct the pupil to opinions diametrically opposite to those of his teachers. We say this, not because we think opinions unimportant, but because of the immense importance which we attach to them; for in proportion to the degree of intellectual power and love of truth which we succeed in creating, is the certainty that (whatever may happen in any one particular instance) in the aggregate of instances true opinions will be the result; and intellectual power and practical love of truth are alike impossible where the reasoner is shown his conclusions, and informed beforehand that he is expected to arrive at them.
John Stuart Mill
Mill, John Stuart
Millar, Fergus
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