Abstract
We define a formal language for sortals with a lambda operator. By means of this language, a formal representation of the logical structure of complex sortal concepts and complex sortal predicates is possible. A formal semantics for the language is also defined together with a formal system. The system is proved to be complete and sound with respect to the semantics. Both the system and the semantics do not have commitments regarding which lambda abstracts will stand for sortal concepts. The possibility of comprehension schemata for this sort of postulational commitments is discussed at the end of the chapter.
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Notes
- 1.
Clearly, this does not mean that the concepts these predicates stand for have the same simplicity.
- 2.
When n = 0, then \(D^{n}=\{\varnothing \}.\) So, \(\wp (D^{{ }^{{ }_{0}}})=\{\varnothing ,\{\varnothing \}\}.\) We shall represent the set \(\{\varnothing \}\) with the number 1 and \(\varnothing \) with the number 0.
- 3.
Note that δ is a meaningful subexpression of itself.
- 4.
By strong induction on the complexity of φ, it can be shown that the principle is λBS-valid. Then, by the completeness theorem, the principle is a theorem of λBS.
- 5.
They are clearly incompatible, since nothing is black and brown all over.
- 6.
This might not be a problem for a realist stance since the metaphysical senses of individuation and identity are the ones that will be involved.
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Freund, M.A. (2019). Complex Sortal Predicates. In: The Logic of Sortals. Synthese Library, vol 408. Springer, Cham. https://doi.org/10.1007/978-3-030-18278-6_7
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DOI: https://doi.org/10.1007/978-3-030-18278-6_7
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