“Equality gives rise to challenging questions which are not altogether easy to answer… a = a and a = b are obviously statements of differing cognitive value; a = a holds a priori and, according to Kant, is to be labeled analytic, while statements of the form a = b often contain very valuable extensions of our knowledge and cannot always be established a priori. The discovery that the rising sun is not new every morning, but always the same, was one of the most fertile astronomical discoveries. Even to-day the identification of a small planet or a comet is not always a matter of course. Now if we were to regard equality as a relation between that which the names 'a' and 'b' designate, it would seem that a = b could not differ from a = a (i. e. provided a = b is true). A relation would thereby be expressed of a thing to itself, and indeed one in which each thing stands to itself but to no other thing.”

— Gottlob Frege , Sense and reference

As cited in: M. Fitting, Richard L. Mendelsoh (1999), First-Order Modal Logic, p. 142. They called this Frege's Puzzle.
Über Sinn und Bedeutung, 1892

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Gottlob Frege 22

mathematician, logician, philosopher 1848–1925

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“Equality gives rise to challenging questions which are not altogether easy to answer… a = a and a = b are obviously statements of differing cognitive value; a = a holds a priori and, according to Kant, is to be labeled analytic, while statements of the form a = b often contain very valuable extensions of our knowledge and cannot always be established a priori.”

Gottlob Frege Sense and reference

The discovery that the rising sun is not new every morning, but always the same, was one of the most fertile astronomical discoveries. Even to-day the identification of a small planet or a comet is not always a matter of course. Now if we were to regard equality as a relation between that which the names 'a' and 'b' designate, it would seem that a = b could not differ from a = a (i.e. provided a = b is true). A relation would thereby be expressed of a thing to itself, and indeed one in which each thing stands to itself but to no other thing.
As cited in: M. Fitting, Richard L. Mendelsoh (1999), First-Order Modal Logic, p. 142. They called this Frege's Puzzle.
Über Sinn und Bedeutung, 1892

“It is plain, of course, that any proof of this depends upon the validity of the doctrine of a priori cognition; only by our proved possession of such cognition can there be any evidence that we are self-active realities. It is in this reference noteworthy, therefore, that Lange, as defender of agnosticism, sees he cannot afford to admit the theory upon which alone cognition strictly a priori can be established.”

George Holmes Howison (1834–1916) American philosopher

Source: The Limits of Evolution, and Other Essays, Illustrating the Metaphysical Theory of Personal Ideaalism (1905), Later German Philosophy, p.175

“Let me first explain, then, what I mean by moral and moral science. A moral or ethical proposition, is a statement about a rank order of preference among alternatives, which is intended to apply to more than one person. A preference which applies to one person only is a taste. Statements of this kind are often called "value judgments." If someone says, "I prefer A to B," this is a personal value judgment, or a taste. If he says, "A is better than B," there is an implication that he expects other people to prefer A to B also, as well as himself. A moral proposition then is a "common value".”

Kenneth E. Boulding (1910–1993) British-American economist

Source: 1960s, Economics As A Moral Science, 1969, p. 1

“Unlike vision, touch, or smell, which are prewired and based on Kantian a priori knowledge, the spatial map presents us with a new type of representation, one based on a combination of a priori knowledge and learning.”

Eric R. Kandel (1929) American neuropsychiatrist

In Search of Memory (2006)
Context: Unlike vision, touch, or smell, which are prewired and based on Kantian a priori knowledge, the spatial map presents us with a new type of representation, one based on a combination of a priori knowledge and learning. The general capability for forming spatial maps is built into the mind, but the particular map is not. Unlike neurons in a sensory system, place cells are not switched on by sensory stimulation. Their collective activity represents the location where the animal thinks it is.

“In the algebra of fantasy, A times B doesn't have to equal B times A. But, once established, the equation must hold throughout the story.”

Lloyd Alexander (1924–2007) American children's writer

"The Flat-Heeled Muse", Horn Book Magazine (1 April 1965)

“As complexity rises, precise statements lose meaning and meaningful statements lose precision.”

Lotfi A. Zadeh (1921–2017) Electrical engineer and computer scientist

George Holmes Howison (1834–1916) American philosopher

Source: The Limits of Evolution, and Other Essays, Illustrating the Metaphysical Theory of Personal Ideaalism (1905), The Limits of Evolution, p.17-8

“Slowly, under our feet, beneath our consciousness, is forming that new philosophy, and it is in times of new philosophies that Art, itself in essence always a discovery, must flourish.”

John Galsworthy (1867–1933) English novelist and playwright

Vague Thoughts On Art (1911)
Context: I cannot help thinking that historians, looking back from the far future, will record this age as the Third Renaissance. We who are lost in it, working or looking on, can neither tell what we are doing, nor where standing; but we cannot help observing, that, just as in the Greek Renaissance, worn-out Pagan orthodoxy was penetrated by new philosophy; just as in the Italian Renaissance, Pagan philosophy, reasserting itself, fertilised again an already too inbred Christian creed; so now Orthodoxy fertilised by Science is producing a fresh and fuller conception of life — a love of Perfection, not for hope of reward, not for fear of punishment, but for Perfection's sake. Slowly, under our feet, beneath our consciousness, is forming that new philosophy, and it is in times of new philosophies that Art, itself in essence always a discovery, must flourish. Those whose sacred suns and moons are ever in the past, tell us that our Art is going to the dogs; and it is, indeed, true that we are in confusion! The waters are broken, and every nerve and sinew of the artist is strained to discover his own safety. It is an age of stir and change, a season of new wine and old bottles. Yet, assuredly, in spite of breakages and waste, a wine worth the drinking is all the time being made.

“The first statement of the two principles reads as follows. First: each person is to have an equal right to the most extensive basic liberty compatible with a similar liberty for others. Second: social and economic inequalities are to be arranged so that they are both(a)reasonably expected to be to everyone's advantage, and (b) attached to positions and offices open to all.”

John Rawls book A Theory of Justice

Source: A Theory of Justice (1971; 1975; 1999), Chapter II, Section 11, pg. 60

“Man was formed with an understanding for the obtainment of knowledge; and happy is he who is employed in the pursuit of it. Ignorance is in its nature unprofitable; but every kind of knowledge may be turned to use. Diligence is generally rewarded with the discovery of that which it seeks after; sometimes of that which is more valuable.”

George Horne (1730–1792) English churchman, writer and university administrator

Prose Quotations from Socrates to Macaulay, 1880

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