'A priori, for any intentional property P and state x, P is an experiential-intentional property of x iff there is an experiential character E, such that (i) x has E, (ii) x is P, and (iii) x is P in virtue of x having E.'
(Kriegel, Uriah (2011): The Sources of Intentionality, 44)
This is Kriegel's definition of the first-order tracking account of experiential-intentional states:
'There is a tracking relation T, such that (a) metaphysically-necessarily, for any mental representation x and property F, F figures in the representational content of x if x bears T to F, and (b) nomologically-necessarily, for any mental representation x and property F, F figures in the representational content of x only if x bears T to F.'
(Kriegel, Uriah (2011): The Sources of Intentionality, 71)
'Still, for such a substantive pure tracking account to work, there would have to exist properties that can only be tracked experientially. The tracking of those properties would have to somehow bestow experiential character on the state doing the tracking – and do so even though the tracking of other properties does not. It is hard to wrap one’s mind around the notion that the tracking of some properties, but not others, could spark conscious experience in this way.'
(Kriegel, Uriah (2011): The Sources of Intentionality, 81)
'The thesis of this chapter is that although tracking accounts of experiential intentionality are implausible, a higher-order tracking theory is quite plausible. Since the only materials such a theory uses are tracking relations, it retains the naturalistic credentials of tracking accounts. At the same time, it may well get the extension of experiential intentionality right, whereas tracking accounts fail to do so at least in cases of higher-order misrepresentation. This makes the higher-order tracking theory of experiential intentionality very attractive.'
(Kriegel, Uriah (2011): The Sources of Intentionality, 109)
Intentional states can be about non-existent objects. This is Kriegel’s master argument for adverbialism and against relational theories of intentionality:
'1. For some state x and some putative property F, (i) F figures in the experiential-intentional content of x and (ii) F does not exist.
2. For no state x, putative property F, and relation R, (i) x bears R to F and (ii) F does not exist; therefore
3. For no state x, putative property F, and relation R, F’s figuring in the experiential content of x = x’s bearing R to F.'
(Kriegel, Uriah (2011): The Sources of Intentionality, 159)
 
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