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Possible World Semantics and the Complex Mechanism of Reference Fixing


Possible world semantics considers not only what an expression actually refers to but also what it might have referred to in counterfactual circumstances. This has proven exceptionally useful both inside and outside philosophy. The way this is achieved is by using intensions. An intension of an expression is a function that assigns to each possible world the reference of the expression in that world. However, the specific intension of terms has been subject to frequent disputes. How is one to determine the intension of a term? Carnap has shown how the intension of a term depends on the type of that term. Two-dimensional semantics has shown how intensions also depend on the actual state of affairs. I will show how, in addition, intensions are no less dependent on metaphysical criteria of identity. Furthermore, I will reveal how these three factors interact to fix the exact intension of a term. In other words, I propose an outline of the overall mechanism by which intensions are being fixed.

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  1. Taking proper names to be rigid designators is common to most contemporary semantic theories, including many (if not most) descriptivist theories—in particular those that endorse widescopism (notably Dummett 1973 111–135) and those that analyze names as actualized descriptions (e.g., Nelson 2002).

  2. Putnam (1973).

  3. The thought experiment is borrowed from Steward (1990), although Steward uses it to question the rigidity of ‘H2O.’ Supervenience-based worries about the very possibility of such stuff (since a physical duplicate is presumably a duplicate in all respects) are addressed by stipulating some microscopic difference between the pink solid H2O molecules and the watery H2O molecules, which makes them ultimately physically distinct, thus allowing for the manifest difference.

  4. I use ‘value’ and ‘variable’ here similar to the way these terms are used in algebra or propositional logic and unlike in the way they are used in predicate logic, which involves quantification. So, no issues of domain, binding, scope, etc. apply here.

  5. See footnote 3 above.

  6. (Frege 1892); Russell (1905).

  7. Notably advanced by Kripke (1980) and Putnam (1975).

  8. Either by ostension—i.e., ‘Let this stuff [pointing to a sample of the watery-H2O stuff,] be called “water”,’ or by a reference-fixing description, i.e., ‘Let the stuff, which is actually watery, be called “water”.’

  9. As in the case of proper names (noted earlier, in footnote 1), some versions of ‘descriptivism’ endorse the rigidity of natural kind terms too; this is done by rigidifying the relevant descriptions (notably by means of actualizing them, or by applying a wide-scope reading). However, under the present definition of ‘de jure rigid’ and ‘descriptive,’ such views will be considered de jure rigid.

  10. Admittedly, the rigidity of natural kind terms like ‘water’ or ‘gold’ has been the subject of much debate (see Soames 2002 and LaPorte 2013, for elaborate discussions).

  11. Referentialists disagree on whether such terms are obstinately or persistently rigid (i.e., on whether they designate their actual referent in every possible world or only in those worlds in which that referent exists). The argument advanced in this paper by no mean depends on the answer to this question.

  12. Kripke (1980 128-9).

  13. Kripke (1980 21, footnote 21). De jure rigid terms are contrasted with de facto rigid terms. The latter are descriptive terms that simply happen to be rigid, e.g., ‘the successor of 3’ designates the number 4 in every possible world. De jure rigid terms, by contrast, are stipulated to be rigid; e.g., the term ‘the actual originator of evolutionary theory’ designates Darwin in the actual world and is then stipulated to designate that same person in each counterfactual world W (regardless of who originated the theory in W).

  14. Davies and Humberstone (1980). Note that thus defined, ‘the actual originator of the calculus’ is explicitly a de jure rigid term (see footnote 13 above.)

  15. This type of dependence is highlighted in the two-dimensional semantics literature. Philosophers who are associated with this approach are notably Chalmers (e.g., Chalmers 2006), Jackson (e.g., Jackson 2004), Kaplan (1989), and Stalnaker (e.g., Stalnaker 2004).

  16. Note that unlike Gibbard’s (1975) ‘Goliath,’ which names only the statue (whereas ‘Lumpl’ names only the lump of clay) ‘David’ here names, neutrally, that thing, whatever it is, that is made of clay and has a shape of David.

  17. This second scenario is based on the famous puzzle of the ship of Theseus (Plutarch, Life of Theseus, XXIII 1859).

  18. For example, Noonan (1993). This view is sometimes referred to as ‘mereological constancy’ (Wasserman 2013).

  19. For an interesting defense of such a view, see Burke (1994). He says, ‘of the sortals satisfied by an object, the one that tells the object’s sort is the one whose satisfaction entails possession of the widest range of properties’ (p. 252). Based on this criterion, Burke selects, for example, ‘tree’ over ‘hunk of cells’ and ‘statue’ over a ‘piece of copper’ as determining the object’s sort (p. 253).

  20. Some may suspect that this latter view conflicts with the supervenience of the non-material on the material and hence question this view’s legitimacy. Yet, there appears to be no such conflict. For it seems perfectly consistent to assume that the world is populated by, e.g., animals, that can survive gradual replacement of cells, and yet, also that these animals supervene, at each given moment t, upon the cells from which they are composed at t.

  21. For example, that there are two objects—a statue and a lump of clay—in the same place at the same time (e.g., Wiggins 2001); or, that what David is, is relative to the way it is described/intended/thought of (e.g., Quine 1960: 199; Geach 1967); or, that David is a temporal part of a four-dimensionally extended object, shared by two different collections of such temporal parts—a statue collection and a lump collection (e.g., Sider 2001).

  22. According to standard possible world semantics, the semantic value of an expression is a function from counterfactual worlds to extensions (viz., the expression’s intension); according to two-dimensional semantics, the semantic value of an expression is a function from worlds considered as actual to intensions (viz., the expression’s two-dimensional intension). (Schroeter 2012, section 1.1.1.)

  23. I have recently indicated the implications of this dependence of intension on criteria of identity in Pelman (2014) and Pelman (2015).

  24. To remind, a de jure rigid term is fixed either by ostension or by a reference fixing description. See footnote 8.

  25. Note that if M-properties are the shape of objects, then the relevant criterion of identity is not likely to be based on simply sharing the same M-property, but rather on keeping that property. For otherwise, different statues with a shape of David, for example, will all be identical to David, which is untenable.

  26. The criteria of personal identity in such a case will likely be, respectively, bodily—i.e., x and y are the same person iff x and y share the same body (e.g., Thomson 1997; for a closely related, animalist version, see Snowdon 2014)—or, by contrast, psychological—i.e., x and y are the same person iff they share the same mind (e.g., Unger 2000 and Shoemaker 1999).

  27. Needless to say, Table 5 can be extended to include more values for each variable, namely, more possible semantic rules, more possible actual referents of the term, and more possible criteria of identity (see footnote 21 above). However, the principles of determining the intention in each of these extended cases should be fairly clear by now.

  28. To remind, ‘value’ and ‘variable’ are used here similar to the way they are used in algebra or in propositional logic and not in the way they are used in predicate logic, i.e., no quantification etc. is involved (see footnote 4).

  29. I wish to thank Alon Chasid and an anonymous referee for helpful comments on earlier drafts.


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Pelman, A. Possible World Semantics and the Complex Mechanism of Reference Fixing. Acta Anal 32, 385–396 (2017).

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