1. Lucretianism
Bigelow

2. The argument from relations and the argument from causation
There are many arguments that are put against presentism, one of the most famous is the “argument from relations”. This argument can be faced and refuted through the ideas of the Stoics and of Epicureans (they were presentists, someway). The argument from relations imply that in order for a relationship between two things, both of them have to exist; so all relations are existence entailing. Moreover there are relations that can involve both present and past things. (So past and present can both exist).
According to Bigelow the first premise in this reasoning, the one about the relationships that have to be existence-entailing, is implausible. When we talk about a relationship that is made up of two parts, we talk about a situation in which there are different roles, that Bigelows describe as relator and relatee (or lover and beloved, when he uses the example about Othello and Desdemona).
When we wonder if all the relations are existence-entailing we have to ask ourselves: Is every relationship existence-entailing on the relator? And is every relationship existence-entailing on the relatee?

3. We have seen that this premise is not correct, but we should ask why people think and believe that all relations have to entail existence. (?) The reason of this thought may lie behind a principle, that imply that every thuth requires a truthmaker; so if something is true there must exist some thing or things in the world in virtue of which this is true.
But let’s suppose that the existence-entailing principle is not true and that, one or both the terms of the relation are nonxistent. Even if some relations are not existence-entailing there may be other relations which are existence- entailing. One of these is causation. In order for the causal relation to hold between cause and effect, both of them have to exist. So if the causal relation holds between two things and the cause exists, then the effect must exist as well; and, on the contrary, if the effect exists, then the cause must exist as well.
When talking about causal relation we should remember that it is existence symmetric, so if an event exist and it is a cause of other event, then the other event exists; and if an event is caused by another event, then the other event exists. Some present events are caused by events that are not in the present, and some present events are the causes of effects that are not present. This is the argument from causation and it is a problem for presentism.

4. Stoic doctrine
Ancient philosophers of the Hellenistic period held onto presentism even if they were perfectly aware of the argument from causation; they managed to retain both the principle of existence entailment and presentism. How they did is explained by Sextus Empiricus in an exposition of the Stoic doctrine, in which he says: «they say that the sign must be a present sign of a present thing». The term “sign” has to be intended as a causal relation; “sign” shall be understood as something natural, so the effect is a sign of the cause and the cause is a sign of the effect. As long as there’s a natural law that links two things, one would be a sign of the other, even if this law does not concern causal mechanism.

5. Stoics says that it would be a mistake to think that causal relation could be hold between a present thing and a thing that is not present, so causal relation is presence symmetric, as they assume the fully general principle of existence entailment (all relations are existence entailing on both sides).
The stoic defense (that may be an advantage for presentism) against the argument from causation argues that causal relation holds between two propositions, and a proposition exists provided that is true. For example: a proposition that used to be true in the past, such as “this man will die”, turns into false when another proposition, as “this man is dying”, becomes true.

6. Lucretius
Stoic ontology doesn’t include anything that is not present but at the cost of posting the existence of true propositions. This perspective was criticised by the epicurean philosopher Lucretius, who said that what exists are atoms and their properties, that can’t be separated from something without destroying it. Anyway there could be accidents, that are things whose arrival or departure leaves the essence of a thing untouched.
 If the ontology of Lucretius wants to maintain presentism, it has to deny the existence of things that are not present, and we could ask: how can it preserve presentism in front of the arguments from relations and the arguments from causation? Lucretius answers that whatever has taken place is an accident of a particular tract of earth or of the space it occupied. According to Lucretius earth can not cease to exist, but it can be moved to another place or it can be scattered. Perhaps being scattered would not exclude it from still bearing the accident which he attributes to it: perhaps it would still be true of this scattered earth that is the same earth in which Helen was ravished (that’s an example used by Lucretius). We can rely on the continuing existence of the region of space in which that earth once occupied.

7. Lucretius says that whatever has taken place should be taken as an accident of matter or of space. It is existence-dependent, as it wouldn’t exist without past events; if there was no matter, space or place in which things can happen, then events would not happen. So events can not be matter of space, but they can be accidents of matter and space.
Lucretius talks about facts and events instead of true prepositions, but the problem - faced both by the stoics and Lucretius - is the same. He states that past events can’t be considered as existent in the same way of matter and space, so they can’t be taken as substances. This enables Lucretius to save presentism without falling in front of the problem of the arguments from relations.  
There are three things that are present: matter, properties and accidents. They can be expressed in language by using the past or the future tense, but this doesn’t mean that this theory supports the existence of past and future things , because the only thing that exists is the possession of this properties in the present.

8. Bigelow’s Theory
Bigelow proposes a modified version of Lucretianism. He says that one of the things that exist is the whole world, that can have properties and accidents, such as its parts. It is a present property of the world.
A stoic’s true proposition can be identified as a property of a world as a whole. In this perspective every difference between Stoics and Lucretius disappears. What appears from the two theories is an answer to the challenge submitted by the arguments from relations and the arguments from causation. Causal relation can not be hold between two things happened in two different moments. In every moment the causal relation involves properties, each of which is present. These (present) properties can involve references to the past and to the future, but the admission of properties does’t imply an abandonment of presentism.
In this view past doesn’t exist anymore, but there’s a sense in which past is never lost: the world will continue to have, in the present, properties refered to the past or the future. According to Bigelow the world is a changing ground made up of unchanging truths