John West wrote:

I hate to be pedantic about this first part, but for the presentist there are no claims about the qualities of the past and future, the past and future simply don't exist….
I'm not sure why you think some of the other stuff. Eternalism in particular just says that time is a big, continuous quantity from the beginning of time, to its end. 

We study time in a metaphysical way and also in a way linked to our perspective. From our perspective, (which is where our intuitions tend to arise from), there is a difference between past, present, and future: namely, that we have experienced, are experiencing, and have yet to experience them each respectively. So when I said that “everyone agrees that the present has exactly the same qualities; where they differ is the qualities of the past and future” I of course didn’t mean that the Presentist holds that the past and future have different qualities metaphysically (since they’re not existent) but that they have different qualities relative to our perspective. It seems pretty uncontroversial that the quality of our experience of the past and future is different from that of the present.

You’re suggesting that there’s something difficult with defining what counts as the present metaphysically. Either we pick an arbitrary measurement of time to count as the present, or we say time is discrete (neither of which is desirable). Either way, the issue is coming up with a good metaphysical account which accords with our experiential account. The Eternalist  agrees with the Presentist that we have the experience of the present, even if he denies that metaphysically the present differs in reality from the other tenses. But if that’s the case, why is Presentism in any worse position than Eternalism with regards to how it defines the present? If there’s no non-arbitrary or counter intuitive way to understand our experience of the present, why should that tell only against Presentism? You seem to

John West wrote:

You've confused truthmaking with reference in this paragraph. For instance, the truthbearing statement "There are no unicorns" is made true by the totality of horse-like animals, none of which have horns. Craig argues against Quine's use of reference in first-order predicate logic for making ontological commitments, not against truthmaking.

Er, I don’t know anything about Craig on Quine, but I am indeed talking about truth makers not referents. Originally writing on counter-factual knowledge, he touches on this subject writing:
 
 

William Lane Craig wrote:

“[Certain] abstract entities do not stand in causal relations. This invalidates at a single swoop the crude construal of the grounding objection expressed in Robert Adam’s demand ‘Who or what does cause them [counterfactuals of creaturely freedom] to be true?’ The question is inept because the relation between a proposition and its truth-maker is not a causal relation…. [Past tense statements] about persons who no longer or do not yet exist and so cannot have such persons among their truth-makers… reveal just how naïve an understanding grounding objector have to the notion of truth-makers. For if these statements have truth-makers, their truth-makers are not physical objects out there in the world but are abstract entities like state of affairs or fact.”

(Sorry it’s a little chopped up. I wanted to avoid a mass of text. The full text is in Divine Knowledge: Four Views)
 

John West wrote:

It's not an epistemological objection. It follows from the definition of presentism that the presentist is committed to a present moment that exists, and that the past and future do not. That's an ontological point.

You’re definitely right that that part of the objection is ontological. But your question was about different measurements of ‘now’, saying “ How do we choose one over the other?” which strikes me as a question about how

lawrence89 wrote:

Thanks for your answer. Probably I'm a bit confused. I was thinking that if God is Timelessness, then we had to be eternalists. But you say we could also be presentist. So I'm asking: given that God is Timelessness, doesn't it mean that He "sees" our past and future events together? And in that case, doesn't it mean that presentism is false?

Depends on your theory of truth. Presentists who want to affirm the eternality of God might say that while it is true that only the present exists, God has such intimate knowledge of both the past and future that he "sees" them as equally well and with equal immediacy as he does the present. What he has done and will do was ordained before the creation of the world,so that his relation to the present is the same as it is to any other time.
 

OK, hold up, I just read an old post of Feser's and now I'm confused again. He wrote in a post on human genesis that this is his preferred theory: 

Ed Feser wrote:

The Flynn-Kemp proposal is this.  Suppose evolutionary processes gave rise to a population of several thousand creatures of this non-rational but genetically and physiologically “human” sort.  Suppose further that God infused rational souls into two of these creatures, thereby giving them our distinctive intellectual and volitional powers and making them truly human.  Call this pair “Adam” and “Eve.”  Adam and Eve have descendents, and God infuses into each of them rational souls of their own, so that they too are human in the strict metaphysical sense.  Suppose that some of these descendents interbreed with creatures of the non-rational but genetically and physiologically “human” sort.  The offspring that result would also have rational souls since they have Adam and Eve as ancestors (even if they also have non-rational creatures as ancestors).  This interbreeding carries on for some time, but eventually the population of non-rational but genetically and physiologically “human” creatures dies out, leaving only those creatures who are human in the strict metaphysical sense.  On this scenario, the modern human population has the genes it does because it is descended from this group of several thousand individuals, initially only two of whom had rational or human souls.  But only those later individuals who had this pair among their ancestors (even if they also had as ancestors members of the original group which did not have human souls) have descendents living today.  In that sense, every modern human is both descended from an original population of several thousand and from an original pair.  There is no contradiction, because the claim that modern humans are descended from an original pair does not entail that they received all their genes from that pa

…