Tarski, Alfred

"Variables in a logical formula behave much like pronouns in natural language: their reference depends on context."

"Infinity cannot be manipulated carelessly; it demands a respect born of understanding its properties."

"The foundations of mathematics rest on axioms that we accept without proof, by an act of intellectual faith."

"To master a subject is to master the precise language in which that subject can be expressed."

"Nominalism and realism in mathematics are not merely different opinions; they are different ways of seeing the world."

"The growth of knowledge is often the growth of clarity about our own limitations."

"A theory that explains everything explains nothing, for it makes no predictions about what must be false."

"The logical form of a sentence may be hidden beneath its grammatical form."

"We call true those statements that correspond to the structure of reality, but describing that structure requires care."

"Quantification over infinite domains introduces complexities that finite minds must strain to comprehend."

"The beauty of a mathematical proof lies in its necessity, not in the elegance of its expression."

"What appears obvious to the untrained mind often proves subtle upon careful examination."

"Logical truth is discovered, not invented, though the methods of discovery are creations of human ingenuity."

"The relationship between language and reality is not one of simple mirroring but of complex interpretation."

"To communicate is to take the risk that others will misunderstand what we mean."

"Science advances by learning not just new truths but new ways of asking questions."

"The paradox of the liar sentence shows that truth and falsity are not exhaustive categories for all linguistic expressions."

"We are tempted to ask what exists, but first we must understand what we mean by 'exists'."

"The logical connectives 'and', 'or', and 'not' are not mere convenience; they mirror fundamental structures of reality."

"To understand another person is partly to understand the language they use and the meanings they project onto it."

"Mathematics is not about things; it is about the relationships between things."

"The quest for a complete description of reality must reckon with Gödel's incompleteness theorems."

"We inherit language as a gift, but we inherit it also as a limitation from which we must learn to think beyond."

"Truth is not a property that sentences possess independently; it is a relation between sentences and the world."

"The attempt to ground all mathematics in formal logic revealed both the power and limits of that approach."

"In formal languages, ambiguity is the enemy; in natural languages, it is often the friend of efficiency and flexibility."

"The study of logic teaches humility: the deeper we look, the more we realize how much we did not understand."

"Sets behave in ways that violate our intuitions formed by dealing with finite collections."

"To be clear is to exclude certain possibilities; every clarification is also a kind of rejection."

"The law of non-contradiction is not a law of nature but a law of thought we find ourselves unable to violate."