Abstract
One significant feature of the possible-worlds theories considered in Chaps. 5 and 6 is that they each treat intensional entities by means of some sort of extensional reductionism. That is, intensions on these approaches are construed as either (extensional) functions, or perhaps sets of possible worlds.
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- 1.
See Goodman’s (1983) for more on this.
- 2.
Furthermore, Bealer argues that only the predicate approach is able to represent a range of intuitively valid arguments, such as:
Whatever x believes is necessary
Whatever is necessary is true
∴ Whatever x believes is true.
He also claims that the predicate approach is amenable to standard first-order quantifier logic, which, he thinks, is the ‘currently accepted theory’. Ceteris paribus, he thinks it is desirable that one work within this well established framework. See Bealer (1982), pp. 23–25, and pp. 31–33, for details.
- 3.
Bealer takes these logical operations on intensional entities to correspond to the relevant syntactical operations on intensional abstracts. He uses this correspondence to provide a recursive definition of a denotation relation for all complex intensional abstracts in L ω . This is briefly discussed below.
- 4.
Bealer claims that propositions do not have constituents in the sense that they are comprised of either set-theoretical or mereological parts. By ‘constituent’ Bealer means only an item which appears on the node of a decomposition tree (apart from its initial node at the bottom of the tree). See his paper ‘A Solution to Frege’s Puzzle’ (1993), pp. 30–31. Bealer seems to think that propositions are, in some sense, metaphysically simple. .
- 5.
Arguably, by analysing these notions through definition one gains a clearer and more comprehensive understanding of them. Incidentally, it will be shown in Chap. 13 how all the modal notions may be defined by means of an inscriptional syntax. Clearly, this is an account which is radically at odds with Bealer’s approach.
- 6.
In his (1982) Bealer thought that Mates’s puzzle might be handled by means of a pragmatic (i.e. meta-linguistic) approach similar to that employed by Church (see Chap. 3 above). However, he developed a different approach in his (1993) and (1998). While he never appears to have renounced the earlier approach to this problem, the later approach appears to be his preferred approach. I discuss the later approach here.
- 7.
In his (1982) Bealer suggested that apparent substitution failures involving proper names could be solved in a Fregean way by taking names as disguised descriptions. Where the names are not taken to have descriptive content, then a pragmatic (i.e. meta-linguistic) approach similar Church’s could be employed (see Chap. 3 above). In his (1982) he thought his theory could accommodate both views. As mentioned above, he appears to have preferred a different approach in his later work. I address his later work here.
- 8.
In his (1993) and (1998) Bealer was also concerned to show that these propositions are necessarily true in accordance with Kripkean essentialism; that they are expressible without the use of definite descriptions; that they can exist though the relevant socially constructed modes of presentation don’t exist; and that they are not meta-linguistic in any usual sense (Bealer 1993, pp. 37–38) (Bealer 1998, pp. 18–19). In the present context, it is not vital that these claims be tested.
- 9.
Bealer mentions in passing that other candidates for non-Platonic modes of presentation are ‘…clusters of recognitional routines causally involving [the relevant object] in an essential way; percepts which are essentially individuated by their objects; expressions in the “language of thought”; etc.’ (Bealer 1998, p. 20). Bealer provides no further explanation regarding these purported modes of presentation, so it is rather difficult to assess their viability.
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Parsons, D. (2016). Bealer’s Theory of Properties, Relations and Propositions. In: Theories of Intensionality . Springer, Singapore. https://doi.org/10.1007/978-981-10-2484-9_7
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