• DOI:10.1007/BF00485426
• Corpus ID: 46962297

A counterpart of Occam's razor in pure and applied mathematics ontological uses

@article{Menger2004ACO,
  title={A counterpart of Occam's razor in pure and applied mathematics ontological uses},
  author={Karl S. Menger},
  journal={Synthese},
  year={2004},
  volume={12},
  pages={415-428}
}

• K. Menger
• Published 2004
• Synthese

One of the most efficient methodological tools, Occam's celebrated razor, is the maxim that it is vain to do with more what can be done with fewer. This principle is primarily ontological: Entities must not be multiplied beyond necessity. But the razor may also be construed as a semantic maxim opposing the use of synonyms. Occam's principle is often called the Law of Parsimony. A thorough examination of science and mathematics reveals that they include only few superfluous entities but that, on the contrary, many ideas have merged and lost their identity in misconceptions. Perhaps the most important example are variables a term applied to totally discrepant ideas 1) to which mathematicians and scientists, overparsimoniously, have denied individual names, thereby making variables in certain ways unmanageable. Thus what is needed is a eounterpart to the Law of Parsimony so to speak, a Law against Miserliness stipulating that entities must not be reduced to the point o f inadequacy and, more generally, that it is vain to try to do with fewer what requires more. This law, too, has what might be loosely called ontological as well as semantic applications. It condemns gaps in ontology just as Occam's law rePudiates redundancies; and it may be construed as a maxim denouncing equivocations just as Occam's law oppbses synonyms. The present paper is devoted to the former uses. ~