Abstract
I will enrich the framework of Chapter
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Notes
- 1.
The details of the resulting understanding of physical and intentional objects depend on how one interprets the notion of world line. Above, I have given preference to the transcendental interpretation of world lines and discerned a number of alternative construals: epistemic, anti-realist, and metaphysical interpretation.
- 2.
For using world line semantics to analyze cases in which an agent has contradictory beliefs about a physical object, see Sect. 6.3.
- 3.
For an example of this latter type of approach, see, e.g., Jespersen [56].
- 4.
For an overview of this theory, see, e.g., Crane [20].
- 5.
The notion of a possible world thus represented is not meant to be the same as that of a first-order model: the totality of possible worlds does not allow arbitrary reinterpretations of predicates (cf. footnote 24 in Sect. 1.4). As Hintikka [45, p. 378] puts it, ‘[in each possible world] those and only those things are to be called red that are red’. Predicates are merely linguistic surrogates for sets of instantiations of characteristics. In possible world semantics, a predicate standing for a set of instantiations of a characteristic in one world stands for the set of its instantiations in all worlds. As long as we need not quantify over properties and relations, we can content ourselves with speaking of characteristics via their linguistic surrogates. (Should we wish to quantify over characteristics, even properties and relations should be construed as world lines of a suitable type.)
- 6.
In any event, proceeding in this way leaves all options open. If it turns out that there is a well-defined totality of all individuals that we can talk about independently of the world in which we find ourselves (unrestricted quantification), this assumption is readily accommodated by stipulating that the set of available individuals is the same for all worlds.
- 7.
What is important for the purposes of the present book is that the distinction between typical cases of physical objects (stones, planets, tables, elephants, and persons) and typical cases of intentional objects (objects of perceptual experience, fictional objects) is articulated in a way that can be utilized in semantic theorizing and that is compatible with the idea that an existing intentional object is a physical object. It is not important to fix precise metaphysical interpretations of the semantic notions of physically individuated world line and intentionally individuated world line. For example, I leave open the question of whether numbers or events can be considered as physically individuated world lines. For the metaphysical question of how physical objects are to be distinguished from other types of objects, see van Inwagen [122] and Markosian [83].
- 8.
Recall that it was indicated in Sect. 1.3 that by the ‘existence’ of a world line in a world, I mean that it is realized in that world. The fact that a world line does not in this sense exist in a world precisely does not preclude that it is available in it—i.e., that it is a possible value of a suitable quantifier in that world. It is indeed typical of intentional objects that they may be available without existing—without being realized.
- 9.
A simple example of a true belief about a non-existent object is the belief that Pegasus does not exist. Another example is \(\alpha \)’s belief that Pegasus is a winged horse, supposing that \(\alpha \) does not seriously believe that Pegasus exists. If \(\alpha \) believed that Pegasus exists, Pegasus would be realized throughout \(R(w_0)\). This would rule out the possibility that \(w_0 \in R(w_0)\) and indeed the truth of the belief, given that Pegasus does not exist in \(w_0\).
- 10.
In Sect. 4.8, it will be seen that the idea of \(\alpha \)’s intentional state representing a specific physical object \(\mathbf {J}\) in \(w_0\) cannot be taken to mean that \(\mathbf {J}\) itself is intentionally available to \(\alpha \) in \(w_0\). Rather, there must be an intentional object \(\mathbf {I}\in \mathcal {I}^\alpha _{w_0}\) and a large enough subset U of \(R(w_0)\) such that \(\mathbf {J}(w)=\mathbf {I}(w)\) for all \(w \in U\). It is necessary but not sufficient that \(w_0 \in U\).
- 11.
I am not suggesting that it would be somehow contradictory to consider worlds with no local objects or worlds with a local object that is not the realization of any physically individuated world line. However, from the interpretative viewpoint, it is a reasonable (and modest) assumption that in every world, we can talk about at least one physical object—a physical object realized in that world.
- 12.
In Sect. 5.6, we will see that the notion of logical form is quite intricate in the logic L, but as a matter of fact, this notion is unproblematic as long as we stay with formulas not using any non-logical predicates—that is, formulas whose only atomic subformulas are identities.
- 13.
If Alice thinks of her intentional object \(\mathbf {I}\) as being non-existent, \(R(w_0) \not \subseteq marg (\mathbf {I})\). Her belief about \(\mathbf {I}\)’s non-existence is correct if \(w_0 \in R(w_0)\), even though \(w_0 \notin marg (\mathbf {I})\). For a systematic discussion of why the inclusions \( marg (\mathbf {I}) \subseteq R(w_0) \subseteq marg (\mathbf {I})\) may fail, see Sects. 4.7 and 6.2.
- 14.
For necessitism, see Sect. 3.7.
- 15.
We must be able to pinpoint the logical form of such statements if we take it to make sense in the first place to say anything of the sort. For this issue, it is irrelevant how unlikely it might be that a given statement of such a form is in fact true.
- 16.
Clark distinguishes three senses of ‘visual field’: (1) the sum of physical things seen; (2) the sum of visual representings: an array of visual impressions organized so that spatial relations obtaining among the impressions resemble the spatial relations among things; and (3) the sum of things as represented visually: what the world would be if it were just as it visually appears to be.
- 17.
Postulating unrestricted quantification is not the same as subscribing to necessitism. If among all the things that exist (in the unrestricted sense) there was a thing that is possibly nothing, then necessitism would fail. Cf. Williamson [127, pp. 15–6].
- 18.
Namely, if w and \(w'\) are worlds and the value of x belongs to \( range (w)\), then by the mentioned extra assumption, its value satisfies \(x=x\) in \(w'\). If quantification is unrestricted, then \( range (w)= range (w')\), from which it follows that the value of x satisfies \(\exists y\,x=y\) in \(w'\). Note that if we further assume that a value of x cannot satisfy a predicate P(x) in a world without satisfying the identity \(x=x\) therein, we may infer what Williamson [127, p. 149] calls the being constraint, expressed by the formula \(\square \, \forall x \square (P(x) \rightarrow \exists y \,\, x=y)\).
- 19.
He states that his book is about metaphysical modality, not about intentionality [127, p. 217].
- 20.
However, this is merely a fact concerning the specific language L. For some purposes, it is desirable to consider an intensional identity predicate (applied to world lines instead of local objects); see Sect. 5.6. The corresponding extended language would be committed to an identity pool.
- 21.
Some of the models I describe are acceptable to the necessitist only from the viewpoint of a non-standard interpretation of quantifiers. The necessitist could view the sets \(\mathcal {P}_w\) I define as subsets of the fixed quantification pool consisting of physical objects that are concrete in w. Williamson [127, p. 19] finds it preferable to avoid using the word ‘exists’ but notes that if a necessitist nevertheless wishes to use this word, it can be construed as an existential quantifier restricted to concrete things.
- 22.
For CP, see, e.g., Priest [95, Sect. 4]. Both Crane [21, pp. 27, 58–9] and Williamson [127, p. 19] identify CP as the source of the problematic consequences of Meinongianism.
- 23.
Priest postulates impossible worlds and countenances impossible objects, so he is prepared to accept even instances of CP corresponding to contradictory conditions P(x); see [95, pp. 15, 58].
- 24.
Priest reports that Nicholas Griffin and Daniel Nolan have likewise considered the idea that those objects that have the characterizing properties as postulated by CP have them in suitable non-actual worlds. He refers to the unpublished papers ‘Problems in Item Theory’ (Griffin) and ‘An Uneasy Marriage’ (Nolan), both read at the 1998 meeting of the Australasian Association for Logic.
- 25.
In Priest’s view, an object cannot lack an actual identity: all objects are defined in all worlds.
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Tulenheimo, T. (2017). Two Modes of Individuation. In: Objects and Modalities. Logic, Epistemology, and the Unity of Science, vol 41. Springer, Cham. https://doi.org/10.1007/978-3-319-53119-9_3
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