He says that before the fourdimensionalist view of spacetime, there was an "utter absence of any timetravel stories whatsoever" and that this is "at least partly explained by the utter universality of presentism prior to the nineteeth century" [pp. 35-36]. It is easy to see that that timetravel is compatible with fourdimensionalism in a number of ways, but there are, perhaps less obvious, ways of seeing that it is compatible with presentism. Consider a multiverse view according to which our world is a system of universes u, each such that the only things that exist at u are the things that presently exist at u. One then time travels by moving from one universe to another within the multiverse. (We briefly discussed this view in a class on time travel.) When I travel back 100 years, I travel to another universe that is (mutatis mutandis) exactly the way ours was 100 years ago except that I exist there and then.
In order for a relational statement of the form Rxy to hold, both relata, i.e. x and y, must exist. In other words, relations are what Bigelow calls "existence entailing". Since there are true relational statements involving a present and non-present thing (e.g. that Othello loves Desdemona), it follows that non-present things exist, i.e. that presentism is false.
He considers an ordinary truth (let us assume) such as "Othello loves Desdemona". Loving, like admiring or believing in, is an intentional notion: it is something that is essentially tied up to the mental. We can think about unicorns, believe in Santa, etc. and they don't exist, so if loving is like thinking about and believing in, then the truth of 'Othello loves Desdemona' does not entail the existence of either Othello or Desdemona.
He says that the principle that relations are existing entailing is supported (or follows from?) a truthmaking principle, e.g. that every truth has a truthmaker (something that necessitates its truth), or that truth supervenes on being. (He also claims that the fact that relations are existence entailing is an a priori truth.) He is not clear what this says against his preliminary argument against existence entailment involving Othello. I guess he will have to say that such a statement does not express a genuine relation; rather, e.g., it expresses something about Shakespeare's play. He will have to say something similar for every other case, e.g. on involving belief in Santa.
Let the principle be that every truth has a truthmaker. (There are complications with Bigelow's supervenience formulation, i.e. that there cannot be a difference in truth without a difference in what exists, since obviously there can be: we can have two worlds where only I exist, but I'm sitting in one and standing in the other. Hence a difference in what's true without a difference in what exists, at least intuitively. One may say in defense of the supervenience principle, e.g., that the trope "me-sitting-in-exactly-this-way-at-this-time" exists at only one of the worlds, but that is a controversial thesis that seems independent truthmaking.) The principle seems to me intinimately tied up with whether presentism is true. Consider a truth like 'Socrates was wise'. If I'm a presentist I don't think Socrates exists, and I don't see why I should have the intuition that it is made true by something presently existing. Rather, what I would think is that it was made true by something even if it is now not. What I would endorse is a tensed truthmaking principle: every truth has, had or will have a truthmaker (depending on whether the truth is past-, present- or future-tensed).
A relation Rxy is e.s. just in case the existence of one of the relatum implies the existence of the other. Causation is given as an example of such a relation partly becuase it is not intentional.
The Stoic solution was to hold that causation is a relation, not between events, but between corresponding propositions, and that propositions about the past and future exist now even if what they are about do not. E.g. the proposition that Socrates was wise presently exists even though Socrates does not. And we can say that the ingestion of poison caused Socrates to die because there is an appropriate relation holding between the proposition that Socrates ingested poison hemlock and the proposition that Socrates died.
Not intuitively since a Lucretian ontology does not admit of propositions, just atoms, vacuity, propositions and accidents of these. But Bigelow will explain a way of reconciling the two.
The solution is to say that past-tensed sentences such as 'The Trojans were conquered' are true in virtue of some location having the property of it being the place where the Trojans were conquered. Since the location exists at present, we have present truthmakers for past-tensed sentences.
Bigelow modifies this solution by holding that it is the world as a whole that has the property of being such that Trojans were conquered there. He does this so that propositions may be identified with world properties. (One could also identify a proposition with a set of worlds, which is more common, and identiy properties with sets, so that one once again identifies propositions with properties.)