david_schenks_new_referential_version_of_the_date_theory_of_time_by_jeffrey

[1] In this paper, I do not consider any “chronon-like” (temporally extended, but somehow irreducible) temporally located relations with a fundamental durations, as they are apparently problematic, for the following reasons.

If the relation, 10 seconds apart, were temporally extended, and considered in terms of two or more non-simultaneous times, the relation, 10 seconds apart must in fact be composed of continuum many, temporally unextended, but temporal (temporally located) sub-relations. 10 seconds apart, then, would be a temporally extended complex relation composed of continuum many temporal, durationless sub-relations. If the fundamental constituents of the temporally located complex relation, 10 seconds apart, were not continuum many, temporally unextended, sub-relations, but were discrete constituents, then the fundamental constituents of the relation, 10 seconds apart, would instead be a finite number of temporally extended sub-relations. If coherent, these relations could be said to have a “fundamental duration”. If such temporally extended sub-relations were the fundamental constituents of the relation, 10 seconds apart, then the fundamentalness of these sub-relations means they are irreducible, lest they not be fundamental. These sub-relations of fundamental duration must also be simple (temporally partless), for if they had parts they would not be “fundamental durations”. But such temporally extended, irreducible sub-relations are apparently contradictory, for the following reasons. These temporally located sub-relations of “fundamental duration”, being relations of a non-zero temporal size, would occupy a duration in a time series. If the fundamental duration of a sub-relation (of the complex relation, 10 seconds apart) is of non-zero temporal size, it necessarily has two halves. Even though the “fundamental duration” may be imagined to have a temporally partless, irreducible duration, it however cannot, since its having a size necessarily requires it has halves, and having halves means this fundamental duration has at least two aspects, or parts, not occupying the same temporal place. If a temporal sub-relation of “fundamental duration” has two halves, necessarily, one half is temporally before the other in the time series. If one is temporally before the other, necessarily, one half is past (P), and the other future (~P, or F). For this reason, these sub-relations of “fundamental duration” would be describable in a contradictory way, since any sub-relation has contradictory properties, ~P ^ P. This argument could be given for any alleged irreducibly simple temporally extended, “fundamental duration”. Since such “fundamental durations” are apparently contradictory, the basic constituents of temporally extended, temporally located, complex relations, such as, 10 seconds apart, would be temporally unextended sub-relations, which means that if 10 seconds apart is a relation between times that is itself temporally located, then there are continuum many temporally located, but temporally unextended (durationless), sub-relations constituting a spatially located, complex relation 10 seconds apart.

[2] Complex relations (or properties) are relations that have conjunctions of other relations as (simpler) parts. Armstrong writes:

Consider conjunctions of universals. If there are complex universals at all, then conjunctions of universals should qualify… Given that F and G are distinct universals, then F&G can be a universal, provided always that a particular exists at some time which is both F and G… But, it may be objected, if there are complex properties, then they must be complexes of simple properties, or at least complexes of simple properties and relations. If it is also maintained… that all universals are instantiated, then any complex property can then be replaced in each of these instantiations by a conjunction of states of affairs involving simple properties and relations. The alleged conjunctive property, or any other complex property, will supervene on these states of affairs. And then what need to recognize anything but the complex of states of affairs involving nothing but simple universals? (Armstrong, 1997, 31-32)

Some, such as David Mellor (Mellor, 1991, 1992) deny that there are any complex properties. This would not matter to my reasoning in this paper, since I am also going to argue that there are not any. I am considering that there are complex relations here for the sake of argument, and as a way of showing that temporally located, temporally extended, complex properties are problematic.

[3] This infinite regress that attempts to complete a task by an infinite sequence of steps, where the “completion” “at infinity” in fact never occurs, since an infinite set of items has no last item. Chisholm considers this sort of regress vicious; Moreland lucidly writes about Chisholm’s position:

There are at least three forms of infinite regress arguments… [One form] involves claiming that a thesis generates a “vicious” infinite regress. How should “vicious” be characterized here?... Roderick Chisholm says that “One is confronted with a vicious infinite regress when one attempts a task of the following sort: Every step needed to begin the task requires a preliminary step”. [Chisholm, 1996, p. 53.] For example, if the only way to tie together any two things whatever is to connect them with a rope, then one would have to use two ropes to tie the two the two things to the initial connecting ropes, and use additional ropes to tie them to these subsequent ropes, and so on. According to Chisholm, this is a vicious infinite regress because the task cannot be accomplished.(Moreland, 2001, 24)

Wolterstorff, 1970, Chapter 4, disagrees, and maintains that the task can be completed.

[4] Considering relations as neither in space or time is the standard position on platonia. Jubien, a platonist, writes:

There are a number of different philosophical accounts of properties. Two very different kinds of account are of special interest to us here. According to one of these, properties are “abstract” entities—they exist apart form and independently of their instances. Plato is famous for his detailed version of this position, and this more modern versions are often called Platonism… A Platonist philosopher who holds that the concept of mass is simply the property of having mass therefore thinks that this concept is an abstract entity. It exists independently of any physical objects that happen to instantiate it, and also independently of any physical objects that happen to instantiate it, and also independently of anyone’s mind or mental activity. Although the instances of the concept of mass are of course physical the concept itself is not. It does not even occupy spacetime. (Jubien, 1997, 14-15) (Emphasis added)

Grossman, also a platonist, writes about the atemporality of platonistic entities:

I shall speak of abstract things (entities, existents) in general. An abstract thing is a thing which is neither temporal nor spatial. A concrete thing, on the other hand, is a thing which is temporal and/or spatial… [P]roperties, as we assumed in the last section, are abstract things; they are not spatio-temporal. It follows that they do not belong to the universe. They are not part of the universe. (Grossman, 1992, 7-8)

Another lucid comment is found in Maddy’ work:

Some platonistically-inclined observers [Maddy cites Resnik, 1985] have argued that [Hartry] Field’s spacetime points and regions are as abstract as numbers, and thus as susceptible to epistemological challenge. If numbers are understood traditionally, as causally inert, non-spatiotemporal, etc, I think this charge cannot be correct. Physicalistically speaking, “the main ground for suspicions about mathematical entities"... is that they bear no physical relation to us at all, causal or otherwise. (Maddy, 1990, p. 296.) (Emphasis added.)

[5] I borrow the phrase “realm crossing” from one of D. M. Armstrong’s passages where he discusses the platonistic exemplification (but where he calls it an instantiation relation) between non-spatiotemporal entities (platonic universals, one of which might be 10 seconds apart) and temporal entities (t₁ and t₂):

Once you have uninstantiated spatially unlocated] universals you need somewhere to put them, a “Platonic heaven,” as philosophers often say. They are not to be found in the ordinary world of space and time. And since it seems that any instantiated universal might have been uninstantiated… then if uninstantiated universals are in a Platonic heaven, it will be natural to place all universals in that heaven. The result is that we get two realms: the realm of universals and the realm of particulars, the latter being ordinary things in space and time… Instantiation then becomes a very big deal: a relation between universals and particulars that crosses realms. (Armstrong, 1989, 76.) (Emphasis added.)

Armstrong apparently means that the instantiation relation is a special, or non-ordinary, relation, between spatiotemporal and non-spatiotemporal entities. But Armstrong is probably incorrect in naming that platonistic instantiation a “relation”—whether special or not—since such predicating ties apparently cannot be relational for reasons discussed in endnote vi below. In a recent paper (Grupp, 2003) it is argued that such “realm crossing” ties (or special relations) are impossible.

[6] The concept of unmediated attachments comes from responses to F.H. Bradley’s work on the paradox of the relations regress. Loux very lucidly explains:

According to the [platonist], for a particular, a, to be F, it is required that both the particular, a, and the universal, F-ness, exist. But more is required; it is required, in addition, that a exemplify F-ness. As we have formulated the [platonist’s] theory, however, a’s exemplifying F-ness is a relational fact. It is a matter of a and F-ness entering into the relation of exemplification. But the realist insists that relations are themselves universals and that a pair of objects can bear a relation to each other only if they exemplify it by entering into it. The consequence, then, is that if we are to have the result that a is F, we need a new, higher-level form of exemplification (call it exermplification₂) whose function it is to insure that a and F-ness enter into the exemplification relation. Unfortunately, exemplification₂ is itself a further relation, so that we need a still higher-level form of exemplification (exemplification₃) whose role it is to insure that a, F-ness, and exemplification are related by exemplifiaction₂; and obviously there will be no end to the ascending levels of exemplification that are required here. So it appears… that the only way we will ever secure the desired result that a is F is by denying that exemplification is a notion to which the realist’s theory applies.

The argument just set out is a version of the famous argument developed by F.H. Bradley. Bradley’s argument sought to show that there can be no such things as relations… [Platonists] claim that while relations can bind objects together only by the mediating link of exemplification, exemplification links objects into relational facts without the mediation of any further links. It is, we are told, an unmediated linker; and this fact is taken to be a primitive categorial feature of the concept of exemplification. So, whereas we have so far spoken of exemplification as a relation tying particulars to universals and universals to each other, we more accurately reflect the realist thinking about the notion if we follow realists and speak of exemplification as a ‘tie’ or ‘nexus’ where the use of these terms has the force of binging out the nonrelational nature of the linkage this notion provides. (Loux, 1998, 38-40) (Underlining added.)

I have altered Loux’s passage to read as if he only discusses platonic realism, rather than metaphysical realism in general.