Lexicon of Arguments

 Philosophical and Scientific Issues in Dispute
 
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IX 232f
Enlargement/system/theory/Quine: Enlargement is not equal to expansion: through an added axiom, a system can be inconsistent. However every consistent theory has a model in natural numbers. So also the enlargement can be consistent.
Expansion: each true/false system can be expanded to a true/false finitely axiomatized system when we add predicates. The extension of a system needs not to enrich the universe. The additional axiom might as well clarify an open existence question by the decision in favor of sparseness. That was done by the foundation axiom and the continuum hypothesis.
>Additional hypotheses, >Hypotheses, >Continuum hypothesis, >Theories, >Consistency.

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