“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...

Adopted from Wikiquote. Last update Aug. 14, 2024. History

Help us to complete the source, original and additional information

Do you have more details about the quote "All acts of mathematical reasoning may… be considered but as applications of a corresponding axiom of quantity" by William Stanley Jevons?

William Stanley Jevons 69

English economist and logician 1835–1882

Related quotes

“A good deal of my research work in physics has consisted in not setting out to solve some particular problems, but simply examining mathematical quantities of a kind that physicists use and trying to get them together in an interesting way regardless of any application that the work may have. It is simply a search for pretty mathematics. It may turn out later that the work does have an application. Then one has had good luck.”

Paul Dirac (1902–1984) theoretical physicist

P.A.M. Dirac, "Pretty Mathematics," International Journal of Theoretical Physics, Vol. 21, Issue 8–9, August 1982, p. 603 http://link.springer.com/article/10.1007/BF02650229#page-1

“The fundamental doctrines of motion have [herein]… been more immediately referred to axioms simply mathematical than has hitherto been usual; and the application of these doctrines to practical purposes has [herein]… been facilitated.”

Thomas Young (scientist) (1773–1829) English polymath

Preface (March 30, 1807)
A Course of Lectures on Natural Philosophy and the Mechanical Arts (1807)

“If we wish to express our ideas in terms of the concepts synthetic and analytic, we would have to point out that these concepts are applicable only to sentences that can be either true of false, and not to definitions. The mathematical axioms are therefore neither synthetic nor analytic, but definitions. …Hence the question of whether axioms are a priori becomes pointless since they are arbitrary.”

Hans Reichenbach (1891–1953) American philosopher

The Philosophy of Space and Time (1928, tr. 1957)

“Knowledge of God is obedience to God. Observe that we do not say that knowledge of God may also be obedience, or that of necessity it has obedience attached to it, or that it is followed by obedience. No; knowledge of God as knowledge of faith is in itself and of essential necessity obedience. It is an act of human decision corresponding to the act of divine decision; corresponding to the act of the divine being as the living Lord; corresponding to the act of grace in which faith is grounded and continually grounded again in God. In this act God posits Himself as our object and ourselves as those who know Him. But the fact that He does so means that our knowing God can consist only in our following this act, in ourselves becoming a correspondence of this act, in ourselves and our whole existence and therefore our considering and conceiving becoming the human act corresponding to the divine act. This is obedience, the obedience of faith.”

Karl Barth book Church Dogmatics

2:1
Church Dogmatics (1932–1968)

“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.”

Abraham Joshua Heschel (1907–1972) Polish-American Conservative Judaism Rabbi

"The Holy Dimension", p. 338
Moral Grandeur and Spiritual Audacity: Essays (1997)
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.