Knowledge Quotes

"If I were to awaken after having slept for a thousand years, my first question would be: has the Riemann hypothesis been proved?"

"The problem of knowledge is not one for the world of sense but one for the mind."

"Science is organized knowledge that has been verified by experience."

"No one shall ever expel us from the paradise of abstract mathematics that Cantor created."

"Logic is the foundation upon which all human knowledge rests."

"The pursuit of perfect knowledge is itself a form of infinite progress."

"Mathematics is the bridge between the visible and invisible worlds."

"The distinction between concept and object is fundamental to all thought."

"The sense of a word determines what objects it refers to."

"Understanding requires grasping both sense and reference."

"Logic reveals the structure of all coherent thought."

"Clarity in expression requires clarity in thought."

"Abstract objects are as real as concrete physical ones."

"The compositionality of language reflects the structure of thought."

"Logical form is universal across all languages."

"Proper analysis reveals what appears confused in natural language."

"An object's properties determine which concepts it falls under."

"The meaning of a word is public and objective, never merely private."

"A sentence expresses a thought and asserts a truth-value."

"We understand a concept when we can use it correctly in all contexts."

"The logical structure of language reflects objective reality."

"Sameness of reference requires sameness of meaning."

"Language is the vehicle for the objectivity of thought."

"Reality consists of facts, not things alone."

"A concept must have determinate boundaries for clear thinking."

"Logical analysis reveals what ordinary language conceals."

"The capacity for mathematics is one of the most distinctive features of the human intellect."

"Knowledge becomes genuine and alive in our hands only when it passes through the process of our active thinking."

"In mathematics you don't understand things. You just get used to them."

"An algorithm must be seen to be believed."