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From Nordan Symposia
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Sometimes two theories have exactly the same explanatory [[power]] because they make the same predictions. A pair of such theories is called indistinguishable, and the [[choice]] between them reduces to convenience or philosophical preference.
Sometimes two theories have exactly the same explanatory [[power]] because they make the same predictions. A pair of such theories is called indistinguishable, and the [[choice]] between them reduces to convenience or philosophical preference.
The form of theories is studied [[formal]]ly in [[mathematical]] [[logic]], especially in [[model]] theory. When theories are studied in mathematics, they are usually expressed in some formal language and their statements are closed under application of certain procedures called rules of [[inference]]. A special case of this, an [[axiomatic]] theory, consists of axioms (or axiom schemata) and rules of inference. A theorem is a statement that can be derived from those axioms by application of these rules of inference. Theories used in applications are abstractions of observed phenomena and the resulting theorems provide solutions to real-world problems. Obvious examples include [[arithmetic]] (abstracting concepts of [[number]]), [[geometry]] (concepts of [[space]]), and [[probability]] (concepts of [[random]]ness and likelihood).
The form of theories is studied [[formal]]ly in [[mathematical]] [[logic]], especially in [[model]] theory. When theories are studied in mathematics, they are usually expressed in some formal language and their statements are closed under application of certain procedures called rules of [[inference]]. A special case of this, an [[axiomatic]] theory, consists of axioms (or axiom schemata) and rules of inference. A theorem is a statement that can be derived from those axioms by application of these rules of inference. Theories used in applications are abstractions of observed phenomena and the resulting theorems provide solutions to real-world problems. Obvious examples include [[arithmetic]] (abstracting concepts of [[number]]), [[geometry]] (concepts of [[space]]), and [[probability]] (concepts of [[random]]ness and likelihood).[http://en.wikipedia.org/wiki/Theory]
==Notes==
==Notes==
# Frisk; derivation from θεός was suggested by Koller Glotta 36, 273ff.
# Frisk; derivation from θεός was suggested by Koller Glotta 36, 273ff.
