“All acts of mathematical reasoning may… be considered but as applications of a corresponding axiom of quantity”

— William Stanley Jevons

The Substitution of Similars, The True Principles of Reasoning (1869)
Context: Aristotle's dictim... may then be formulated somewhat as follows:—Whatever is known of a term may be stated of its equal or equivalent. Or, in other words, Whatever is true of a thing is true of its like.... the value of the formula must be judged by its results;... it not only brings into harmony all the branches of logical doctrine, but... unites them in close analogy to the corresponding parts of mathematical method. All acts of mathematical reasoning may... be considered but as applications of a corresponding axiom of quantity...

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William Stanley Jevons69

English economist and logician 1835–1882

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“All acts of reasoning seem to me to be different cases of one uniform process which may perhaps be best described as the substitution of similars… The chief difficulty consists in showing that all the forms of the old logic, as well as the fundamental rules of mathematical reasoning, may be explained upon the same principle; and it is to this difficult task I have devoted the most attention.”

William Stanley Jevons (1835–1882) English economist and logician

Preface
The Substitution of Similars, The True Principles of Reasoning (1869)

“All scientific conclusions are based on axioms, all reasoning depends ultimately upon faith.”

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Context: Reality is not exhausted by knowledge. Inaccessible to research are the ultimate facts. All scientific conclusions are based on axioms, all reasoning depends ultimately upon faith. Faith is virgin thinking, preceding all transcendent knowledge. To believe is to abide at the extremities of spirit.