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In a deductive theory, any sentence which is a logical consequence of one or more of the axioms is also a sentence of that theory. [11] This is called the received view of theories. In the semantic view of theories, which has largely replaced the received view, [18] [19] theories are viewed as scientific models. A model is an abstract and ...
A satisfiable theory is a theory that has a model. This means there is a structure M that satisfies every sentence in the theory. Any satisfiable theory is syntactically consistent, because the structure satisfying the theory will satisfy exactly one of φ and the negation of φ, for each sentence φ.
Sentences are then built up out of atomic sentences by applying connectives and quantifiers. A set of sentences is called a theory; thus, individual sentences may be called theorems. To properly evaluate the truth (or falsehood) of a sentence, one must make reference to an interpretation of the theory.
The theory of an equivalence relation with exactly 2 infinite equivalence classes is an easy example of a theory which is ω-categorical but not categorical for any larger cardinal. The equivalence relation ~ should not be confused with the identity symbol '=': if x=y then x~y, but the converse is not necessarily true. Theories of equivalence ...
Dummett believes a speaker must know three components of a sentence to understand its meaning: a theory of sense, indicating the part of the meaning that the speaker grasps; a theory of reference, which indicates what claims about the world are made by the sentence, and a theory of force, which indicates what kind of speech act the expression ...
For example, consider the sentence "There exists x such that x is a philosopher." This sentence is seen as being true in an interpretation such that the domain of discourse consists of all human beings, and that the predicate "is a philosopher" is understood as "was the author of the Republic." It is true, as witnessed by Plato in that text.
Ramsey sentences are formal logical reconstructions of theoretical propositions attempting to draw a line between science and metaphysics. A Ramsey sentence aims at rendering propositions containing non-observable theoretical terms (terms employed by a theoretical language) clear by substituting them with observational terms (terms employed by an observation language, also called empirical ...
A scientific theory is an explanation of an aspect of the natural world and universe that can be (or a fortiori, that has been) repeatedly tested and corroborated in accordance with the scientific method, using accepted protocols of observation, measurement, and evaluation of results.