on truth

“the question of truth- what it is and how we can recognize it- is among the oldest and most controversial in philosophy. Truth is also an important concept in mathematics. Historically, in both fields, truth has generally been assumed to be an absolute quality, elusive of definition or proof, perhaps, but invariable- although the ancient Greek SOPHISTS’ philosophy of RELATIVISM, holding that subjective judgments are “the measure of all things,” including truth, has long influenced the debate. The Euclidian idea that all mathematical axioms are statements of self- evident truths was challenged in the 19th century by the development of geometrics that did not assume EUCLID’s postulate concerning parallel lines. It was further undermined by 20th century mathematics, for example, set theory, according to which what is true in one sphere may not be true in another, and Kurt Godel’s incompleteness theorem, which states that not all true statements can be proven.
Most philosophical definitions of truth have been based on the notion of “correct description,” although there is a wide disagreement over what constitutes “correct.” Three major theories of truth have been proposed. The most intuitive approach is the correspondence theory, which was defined by Thomas Aquinas as “the correlation of thought and object,” that is, our idea of something is true is it corresponds to the actuality of that thing. An objection to this theory, that our subjective perceptions may not accurately capture reality, is addressed by the coherence theory, according to which something can be said to be true if it is consistent with the other elements in a coherent conceptual system."