Philosophy Quotes

"Mathematics is the pursuit of meaning through abstract form."

"The proof is the bridge between intuition and certainty."

"A mathematical truth is eternal only because it is eternally verifiable."

"Mathematics without meaning is mere symbol manipulation."

"In mathematics, necessity and freedom are one and the same."

"The infinite! No other question has ever moved so profoundly the spirit of man."

"We cannot think of any object, nor can we think any single thought, that would not depend upon the axioms of logic."

"Philosophy is the attempt to answer the deepest questions through reason alone."

"The infinite regression of causes must eventually resolve in something eternal."

"Every mathematical axiom is a question about the nature of existence itself."

"A thought is a sense-impression of the future."

"Without a sign we cannot have a thought."

"We must distinguish between the sign and what it signifies."

"Thoughts are not private mental entities but objective contents."

"Language mirrors the structure of logical reality."

"Concepts are fundamentally different from mental images."

"We cannot think without language, yet language can mislead us."

"The object of thought is independent of the thinker."

"The same sense can have different modes of presentation."

"The law of non-contradiction is the foundation of all reasoning."

"Concepts exist in a realm independent of human minds."

"Objects fall under concepts; concepts do not fall under objects."

"The meaning of a sentence is not the sum of word meanings."

"Thoughts exist independently of any particular person thinking them."

"The laws of logic are neither psychological nor physical laws."

"Language must be regimented to avoid philosophical confusion."

"Thoughts are the contents of judgments, not mental images."

"Objects are what fall under concepts; concepts are what objects exemplify."

"Analysis progresses from the familiar to the fundamental."

"Thoughts are independent of the thinker yet dependent on language."