change to occur along the moments? The basic trouble here is that, it seems, changes are things that occur in time, and so cannot occur to time itself, unless another dimension of time is posited in which the changes in the first dimension (i.e. the timeline itself) happen. This is to posit what is called ‘hypertime’. As Curtis and Robson put this point:
[I]f there are to be changes with regards to which B-series moment is the present moment, then there must be a second-order time series of ‘hypertimes’ relative to which these changes occur. (Curtis & Robson, 2016: 70)
To be more specific, as above-stated, the present moves along the moments of the B-series so that there is a constant change that appears in time, and for this reason it is seems we must say that such change takes time to happen. And so, then it it seems we must assume further that there is supposed to be a second-order time series of ‘hypertimes’ regarding which moments are present.
This seems strange enough. But Broad (1938: 277-279), when he discusses this point, goes even further. He argues that if this second-order dimension of hypertime is to be thought of as a genuine time across which changes happen, then it must be that for changes to occur across it, there must in fact be a third-order time series of hypertimes, and if there is a third-order time series, then there must be a fourth-order time series, and so on. Obviously, as this generalises, this hierarchy of time series turns out to be infinite. And this, it seems, is very strange indeed, and highly counterintuitive.
However, despite the fact that Broad himself thought this objection was fatal to the moving spotlight view, it is not so clear that it is. The approach is clearly not ontologically parsimonious, but many metaphysicians claim that it is not clear why such hierarchy of time series is considered as problematic. According to Curtis and Robson (2016: 71), it is not clear why defenders of the moving spotlight view can’t simply accept this consequence of their view, despite it being counterintuitive. As stated above, some argue that there could be an infinite hierarchy of hypertimes for each moment, and there could also be hyper-hypertimes and hyper-hyper- hypertimes, so on and so forth to an endless extent. Despite that this hierarchy does not seem to be ontologically parsimonious, some argue that it is unclear why this should be a major issue for the moving spotlight theorist to deal with. More precisely, there is an argument to justify the infinite hierarchy in this moving spotlight scenario, by appealing to the Platonist view on objects and their properties.
According to the Platonist view, there are two essential features as to how the physical objects possess properties, one is that ‘objects possess properties in virtue of standing in relation to Platonic universals, viz. immutable and transcendent entities.’ (Curtis & Robson, 2016: 71) For instance, all my leather jackets are black, so it is a Platonic fact that my jackets possess the property of being black in virtue of standing in the relation to the Platonic universal of being black. The other feature is that, just like objects, Platonic universals have properties as well. If this is the case, then there are second-order universals, which entails the existence of third-order universals, which leads to fourth-order universals, to an endless extent. As discussed by Curtis and Robson (2016: 71), the Platonists accept that there are infinite hierarchies of properties possessed objects and of universals, and do not seem to be
words, the Platonists believe that an infinite hierarchy of universals is the ‘metaphysical structure of reality’ (Curtis and Robson, 2016: 71)
By applying this strategy to the moving spotlight scenario, it looks like the moving spotlight has now discovered a solution to overcome the hypertime objection by claiming that an infinite hierarchy of hypertimes is actually the metaphysical
structure of reality. Furthermore, the moving spotlight proponents, such as George
Schlesinger (1980), takes this reply to the hypertimes objection even further, and questions its legitimacy as an objection by claiming that, according to Schlesinger (1980: 32), first-order times suffice to explain change in terms of their second-order temporal locations and second-order times suffice to explain change in terms of their first-order temporal locations, and that it is not necessary to include the third-order time series in the mix to justify the moving spotlight ontology. If this is so, then defenders of the moving spotlight view can avoid a committment to an infinite heirarchy of hypertimes, and accept just two levels of time, ordinary time and hypertime. This, it seems, is not too much to swallow, and so makes the claim that this is just how the metaphysical structure of reality is seem more plausible.
Furthermore, some moving spotlight proponents claim that there is another argument that has newly become an option for developing Schelsingers view, that is, primitive tense operators. As discussed in the previous chapters, primitive tense operators are first invented by Prior (1967) in order to restrict tense operators in a proposition. According to Prior (1967: 8 - 10), there are three different tense operators, past-tense, present-tense, and future tense; and among these operators, ‘primitive’ represents that these three operators are the primary ones, and restricts that these operators cannot be explained any further. By applying primitive tense operators to the moving spotlight view ontology, it may be able to restrain the
commitment to only first-order moments by claiming that flow of time is simply a
primitive change in the tenses possessed by first order moments (i.e. they can say
this is what a so-called ‘hypertime’ is). At any rate, it seems clear that this objection to the moving spotlight view can be met by the defender of the view and causes no significant problems.