Abstract
Comparative formal ontology is the study of how different informal ontologies can be formalized and compared with one another in their overall adequacy as explanatory frameworks. One important criterion of adequacy of course is consistency, a condition that can be satisfied only by formalization. Formalization also makes explicit the commitments of an ontology.
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Notes
- 1.
- 2.
Wittgenstein (1961, P. 1). It is an issue of debate as to whether the Tractatus allowed for negative facts. But there definittely are negative facts in Russell’s version of logical atomism.
- 3.
This observation was first made by Ramsey in his adoption of logical atomism. Cf. Ramsey 1960.
- 4.
Cf. Carnap 1946, pp. 37 and 1947, Section 40. Unlike Carnap, Barcan assumed the formula as an axiom, and gave no explanation or reason why it should be assumed.
- 5.
Carnap 1946, T10-3.c, p. 56.
- 6.
If object constants do occur in a formula, they can be replaced uniformly by distinct new object variables not already occurring in the formula.
- 7.
See Hintikka, 1956 for a development of the exclusive interpretation.
- 8.
- 9.
For some philosophers, e.g., Arthur Prior, being encompasses only past and present objects, apparently because, unlike the past and the present, the future is as yet undetermined in their ontology. See Prior (1967, Chap. viii).
- 10.
See Lambert (1991) for a collection of papers on free logic and its philosophical applications.
- 11.
See Cocchiarella, ‘Quantification, Time and Necessity,’ in Lambert (1991) for axiomatizations of both actualism and possibilism, as well as axioms for tense logic and the modal logics analyzable in terms of tense logic.
- 12.
- 13.
See Hintikka, 1973, Chaps. V and IX.
- 14.
Cf. Putnam (1967), for a fuller discussion of this type of situation.
- 15.
For a formalization of the topology of space-time based on the light-signal relation see Carnap (1958,§§48–50).
- 16.
See Cocchiarella 1984, Section 15, for the details of a semantics for these operators. The signal relation, incidentally, provides yet another example of a concrete interpretation of an accessibility relation between possible worlds, reconstrued now as the momentary states of the universe at different space-time points.
- 17.
This formula would be true at a given moment t of a local time X if in either the prior cone or posterior cone of that moment there is a space-time point \(t^{\prime }\) of a world-line Y such that \(\varphi \) is always true in Y, even though \(\varphi \) is never true in X. See Putnam (op. cit.) for an example of how this is possible in relativity theory.
- 18.
In Everett’s original version of the axioms of the many-worlds interpretation no account was given of how the branching into different parallel worlds takes place. Later proposals by Graham and DeWitt introduce the complicated notion of a measuring device that results in observations (by humans or automata) upon which the splitting into parallel worlds is based. See De Witt and Graham (1973).
- 19.
For a fuller account of the many-worlds interpretation see De Witt and Graham (1973).
- 20.
See Tegmark (2003).
- 21.
See, e.g., Kaku (2005).
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Cocchiarella, N.B. (2010). Actualism Versus Possibilism in Formal Ontology. In: Poli, R., Seibt, J. (eds) Theory and Applications of Ontology: Philosophical Perspectives. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-8845-1_5
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