Abstract
Two intensional logics for sortal concepts are characterized in this chapter. One is a modal-temporal bidimensional logic, with a constant domain interpretation of the second-order quantificatiers. The other is also a bidimensional logic but with a varying domain interpretation of second-order quantification. Both logics shared the same formal language and differ in their formal semantics. Soundness and completeness theorems are proved for their formal systems with respect to their corresponding semantics. Natural necessity is the modal notion represented in the logics in question. Its content and connection to conceptualism is presented.
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- 1.
Other interpretations of modality relevant for conceptualism may be explored, such as conceptual necessity and logical necessity. The formal semantics that we shall characterize in this chapter can be easily extended to formally represent many of those other senses by just adding the accessibility relation among possible worlds. Although in the case of logical necessity, there will be important limitations in its formalization given the results shown in Cocchiarella and Freund (2008).
- 2.
The concept of a law of nature should be understood in the ample sense of the word, that is, as covering not only laws of physics, but also other sorts of laws regarding natural phenomena in general, such as the laws of biology, astronomy, geology, and chemistry.
- 3.
- 4.
This approach explain laws of nature as logical consequences of particular higher order facts that relate properties and relations. For details on these facts, see Armstrong (1980), Dretske (1977), and Tooley (1978). For a critique of these theories, see, for example, Hochberg (1981). We should add that alternative philosophical theories on the ontological foundations of the laws of nature have been developed. Some of these views assume that laws of nature do not require any other foundation beyond themselves, and so they would oppose their grounding on natural properties and relations. For a survey of the alternative theories, see Carroll (2016).
- 5.
How natural properties and relations ground natural laws is controversial. An approach favored by several philosophers has been in terms of higher order facts relating properties and relations. For details of this sort of theories, see Armstrong (1980), Dretske (1977) and Tooley (1978). For a critique of this higher order approach, see Hochberg (1981).
- 6.
- 7.
For a defense of this point, see Putnam (1971).
- 8.
There are important differences between the notions of ontological dependence, metaphysical grounding, and supervenience. These different notions are supposed to capture most of the possible ontological underpinnings of abstract objects by natural objects. See Tahko and Lowe (2015), Bliss and Trodgon (2014), and McLaughlin and Bennet (2018).
- 9.
- 10.
It will be remembered that we have assumed the epistemic or cognitive interpretation of the identity and individuation criteria.
- 11.
Thus, conceptualism is compatible with naturalism and weak versions of conventionalism regarding natural kinds. For the former view, there are genuinely natural ways to classify things, and we do have cognitive access, in principle, to such natural classifications. Most versions of naturalism assume that natural kinds have essences that constitute their metaphysical principles of identity. Weak versions of conventionalism do not necessarily deny that are natural kinds in nature (although there are variants that do) but rejects the view that we can cognitively capture such natural classifications. (See Wolgar (1988) and Hacking (1999)). Conceptualism is also coherent with a stance alternative to naturalism and conventionalism, according to which there are countless natural ways to classify things into kinds. (See Dupre 1993).
- 12.
Independently of whether or not their criteria of identification can be associated with a metaphysical principle.
- 13.
A logic of sortals, with natural necessity as its background notion of necessity, should consider all natural possibilities, that is, should not reject any natural possibility. Since both sorts of views are naturally possible, that is, do not contradict the laws of nature, then the logic should allow for both of them.
- 14.
The existence of sortal concepts for artifacts is coherent with the interpretation of necessity as natural necessity. On the other hand, there are no ultimate sortals for such concepts since, as already pointed out in Chap. 2 (Sect. 2.8), there are many ways to modify, add or generalize their identity criterion so that ever new and more general sortal concepts can in principle be formed.
- 15.
Possible examples of this class of concepts are to be found in those associated with natural kinds. If summa genera for natural kinds were postulated, as well as sortal concepts whose criteria are grounded on such genera, these concepts would be the ultimate sortal concepts for the above class of concepts.
References
Armstrong, D. M. (1980). Universals and scientific realism (Vol. 1 and 2). Cambridge: Cambridge University Press.
Bliss, R., & Trodgon, K. (2014). Metaphysical grounding. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy (Winter 2016 Edition). https://plato.stanford.edu/archives//win2016/entries/grounding/
Carroll, J. (2016). Laws of nature. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy (Spring 2016 Edition). https://plato.stanford.edu/archives//fall2016/entries/laws-of-nature/.
Churchland, P. (1986). Neurophilosophy: Toward a unified science of the mind/brain. Cambridge: MIT Press.
Cocchiarella, N. (2007). Formal ontology and conceptual realism. In L. Nowak (Ed.), Synthese library (Vol. 339). New York: Springer.
Cocchiarella, N., & Freund, M. (2008). Modal logic: An introduction to its syntax and semantics. New York: Oxford University Press.
Dretske, F. (1977). Laws of nature. Philosophy of Science, 44, 248–268.
Dupré, J. (1993). The disorder of things: Metaphysical foundations of the disunity of science. Cambridge: Harvard University Press.
Hacking, I. (1999). The social construction of what? Cambridge: Harvard University Press.
Hochberg, H. (1981). Natural necessity and laws of nature. Philosophy of Science, 48, 386–399.
McLaughlin, B., & Bennet, K. (2018). Supervenience. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy (Winter 2018 Edition). https://plato.stanford.edu/archives//win2018/entries/supervenience/
Putnam, H. (1971). Philosophy of logic. New York: Harper & Row Publishers.
Rescher, N. (1975). A theory of possibility: A constructivistic and conceptualistic account of possible individuals and possible worlds. Pittsburgh: University of Pittsburgh Press.
Smart, J. J. C. (2007). The mind/brain identity theory. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy. https://plato.stanford.edu/archives//spr2017/entries/mind-identity/
Tahko, T., & Lowe, E. (2015). Ontological dependence. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy (Winter 2016 Edition). https://plato.stanford.edu/archives//win2016/entries/dependence-ontological/
Tooley, M. (1978). The nature of laws. Canadian Journal of Philosophy, VII(4), 667–698.
Wolgar, S. (1988). Science, the very idea. London: Tavistock.
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Freund, M.A. (2019). Natural Necessity and the Logic of Sortals. In: The Logic of Sortals. Synthese Library, vol 408. Springer, Cham. https://doi.org/10.1007/978-3-030-18278-6_4
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