„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, Über Sinn und Bedeutung

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

Letzte Aktualisierung 22. Mai 2020. Geschichte
Gottlob Frege Foto
Gottlob Frege5
deutscher Mathematiker, Logiker und Philosoph 1848 - 1925

Ähnliche Zitate

Gottlob Frege Foto

„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, Über Sinn und Bedeutung

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

Ronald H. Coase Foto
Sylvia Plath Foto

„The sun gives you ulcers, the wind gives you T. B.
Once you were beautiful.“

—  Sylvia Plath American poet, novelist and short story writer 1932 - 1963

Quelle: Ariel: The Restored Edition

R. G. Collingwood Foto
Leonard Peikoff Foto

„A: "Your objection to the self-evident has no validity. There is no such thing as disagreement. People agree about everything."
B: "That’s absurd; people disagree constantly, and about all kinds of things."
A: "How can they? There’s nothing to disagree about; no subject matter. After all, nothing exists."
B: "Nonsense. All kinds of things exist, you know that as well as I do."
A: "That’s one. You must accept the existence axiom, even to utter the term “disagreement.” But to continue, I still maintain that disagreement is unreal. How can people disagree when they are unconscious beings who are unable to hold any ideas at all?"
B: "Of course people hold ideas. They are conscious beings. You know that."
A: "There’s another axiom, but even so, why is disagreement about axioms a problem? Why should it suggest that one or more of the parties is mistaken? Perhaps all of the people who disagree about the very same point are equally, objectively right."
B: "That’s impossible. If two ideas contradict each other, they can’t both be right. Contradictions can’t exist in reality. After all, A is A."
Existence, consciousness, identity are presupposed by every statement and by every concept, including that of "disagreement." … In the act of voicing his objection, therefore, the objector has conceded the case. In any act of challenging or denying the three axioms, a man reaffirms them, no matter what the particular content of this challenge. The axioms are invulnerable.
The opponents of these axioms pose as defenders of truth, but it is only a pose. Their attack on the self-evident amounts to the charge. "Your belief in an idea doesn't necessarily make it true; you must prove it, because facts are what they are independent of your beliefs." Every element of this charge relies on the very axioms that these people are questioning and supposedly setting aside.“

—  Leonard Peikoff Canadian-American philosopher 1933

Objectivism: The Philosophy of Ayn Rand (1991) ; Dialogue used to show that existence, conciousness, identity, and non-contradiction are axioms, using A as a defender of the axioms, and B as an opponent of the axioms,
1990s

William Kingdon Clifford Foto

„In regard, then, to the sacred tradition of humanity, we learn that it consists, not in propositions or statements which are to be accepted and believed on the authority of the tradition, but in questions rightly asked, in conceptions which enable us to ask further questions, and in methods of answering questions. The value of all these things depends on their being tested day by day.“

—  William Kingdon Clifford English mathematician and philosopher 1845 - 1879

The Ethics of Belief (1877), The Weight Of Authority
Kontext: In regard, then, to the sacred tradition of humanity, we learn that it consists, not in propositions or statements which are to be accepted and believed on the authority of the tradition, but in questions rightly asked, in conceptions which enable us to ask further questions, and in methods of answering questions. The value of all these things depends on their being tested day by day. The very sacredness of the precious deposit imposes upon us the duty and the responsibility of testing it, of purifying and enlarging it to the utmost of our power. He who makes use of its results to stifle his own doubts, or to hamper the inquiry of others, is guilty of a sacrilege which centuries shall never be able to blot out. When the labours and questionings of honest and brave men shall have built up the fabric of known truth to a glory which we in this generation can neither hope for nor imagine, in that pure and holy temple he shall have no part nor lot, but his name and his works shall be cast out into the darkness of oblivion for ever.

Hermann Weyl Foto

„Matter… could be measured as a quantity and… its characteristic expression as a substance was the Law of Conservation of Matter… This, which has hitherto represented our knowledge of space and matter, and which was in many quarters claimed by philosophers as a priori knowledge, absolutely general and necessary, stands to-day a tottering structure.“

—  Hermann Weyl German mathematician 1885 - 1955

Introduction<!-- p. 1-2 -->
Space—Time—Matter (1952)
Kontext: The Greeks made Space the subject-matter of a science of supreme simplicity and certainty. and certainty Out of it grew, in the mind of classical antiquity, the idea of pure science. Geometry became one of the most powerful expressions of that sovereignty of the intellect that inspired the thought of those times. At a later epoch, when the intellectual despotism of the Church... had crumbled, and a wave of scepticism threatened to sweep away all that had seemed most fixed, those who believed in Truth clung to Geometry as to a rock, and it was the highest ideal of every scientist to carry on his science "more geometrico". Matter... could be measured as a quantity and... its characteristic expression as a substance was the Law of Conservation of Matter... This, which has hitherto represented our knowledge of space and matter, and which was in many quarters claimed by philosophers as a priori knowledge, absolutely general and necessary, stands to-day a tottering structure.

Matthew Stover Foto
John Ruskin Foto
Étienne Bonnot de Condillac Foto
John Desmond Bernal Foto

„One of the questions on which clarity of thinking is now most necessary is that of the relation between the methods of science and of Marxist philosophy. Although much has already been written on the subject, yet there is still an enormous amount of confusion and contradictory statement.“

—  John Desmond Bernal British scientist 1901 - 1971

J.D. Bernal (1937) "Dialectical Materialism and Modern Science" in: Science and Society, Volume II, No. 1, Winter 1937; Online ( here http://www.marxists.org/archive/bernal/works/1930s/dsams.htm) on Marxists Internet Archive (2002).

Ludwig Wittgenstein Foto
George Holmes Howison Foto
E. W. Hobson Foto

„The second period, which commenced in the middle of the seventeenth century, and lasted for about a century, was characterized by the application of the powerful analytical methods provided by the new Analysis to the determination of analytical expressions for the number &pi; in the form of convergent series, products, and continued fractions. The older geometrical forms of investigation gave way to analytical processes in which the functional relationship as applied to the trigonometrical functions became prominent. The new methods of systematic representation gave rise to a race of calculators of &pi;, who, in their consciousness of the vastly enhance means of calculation placed in their hands by the new Analysis, proceeded to apply the formulae to obtain numerical approximations to &pi; to ever larger numbers of places of decimals, although their efforts were quite useless for the purpose of throwing light upon the true nature of that number. At the end of this period no knowledge had been obtained as regards the number &pi; of the kind likely to throw light upon the possibility or impossibility of the old historical problem of the ideal construction; it was not even definitely known whether the number is rational or irrational. However, one great discovery, destined to furnish the clue to the solution of the problem, was made at this time; that of the relation between the two numbers &pi; and e, as a particular case of those exponential expressions for the trigonometrical functions which form one of the most fundamentally important of the analytical weapons forged during this period.“

—  E. W. Hobson British mathematician 1856 - 1933

Quelle: Squaring the Circle (1913), pp. 11-12

George Boole Foto
Oscar Wilde Foto
Max Wertheimer Foto

„Often, in great discovery the most important thing is that a certain question is found.“

—  Max Wertheimer Co-founder of Gestalt psychology 1880 - 1943

Quelle: Productive thinking, 1945, p. 123

Kazimir Malevich Foto

„Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam egestas wisi a erat. Morbi imperdiet, mauris ac auctor dictum.“