Knowledge Quotes

"Mathematics is not discovered but invented within conceptual schemes."

"Realism about mathematics requires platonism we cannot justify."

"Numbers are nothing but useful fictions for science."

"Semantics is holistic; no word has meaning in isolation."

"Coherence in belief justifies, not correspondence to facts."

"Epistemic justification is always relative to a conceptual system."

"Knowledge requires both belief and reliability, not correspondence."

"Language is the instrument through which we clarify our thoughts and communicate the structures of reality."

"The distinction between object language and metalanguage is crucial for avoiding paradox and confusion."

"The work of the logician is to make explicit what the ordinary speaker leaves implicit."

"We cannot speak truly about what we have not first carefully defined."

"The universal principles of logic transcend culture and history; they are the common heritage of humanity."

"We are all, in a sense, linguists; we all use language daily without understanding its structure."

"The greatest enemy of understanding is the belief that we already understand."

"The distinction between use and mention is subtle but essential for any coherent philosophy of language."

"The logical form of a statement is often hidden beneath its grammatical form."

"The boundaries of our language are the boundaries of our world, but analysis can extend these boundaries."

"Mathematics is a mixture of reasoning and intuition."

"To understand a program you must become both the machine and the programmer."

"We cannot, at present, keep completely accurate track of the state of the machine at all times."

"The contradictions we encounter in our attempts to formulate the rules of thought are of great interest."

"A person supplied with paper and pencil and rubber, and subject to strict discipline, is in effect a universal computing machine."

"The degree to which a machine can simulate human thought is limited primarily by the breadth of the machine's programming."

"The universal computing machine is capable of computing any sequence that can be computed."

"Mathematics reveals structures that seem to precede and transcend physical reality."

"Consciousness might bridge the apparent divide between science and the humanities."

"The hard problem teaches us that not all important questions yield to the standard scientific method."

"The human mind is incapable of formulating certain concepts which are essential to a correct understanding of the world."

"The incompleteness theorems show us the limits of formal systems, but not the limits of human understanding."

"To abandon logic is to abandon the only tool we have for understanding anything."