I'm not entirely sure what you mean by 'Spinoza-style', but I get the gist of it and find this analogy interesting. Could you explain what you mean by Spinoza-style? My knowledge of ancient philosophers is a little rusty.

No, the distinction between MWI and Copenhagen would have actual physical consequences. For instance, if you die in the Copenhagen interpretation, you die in real life. If you die in MWI, there is still a copy of you elsewhere that didn't die. MWI allows for quantum immortality.

The distinction between presentism and eternalism, as far as I can tell, does not imply any difference in the way the world works.

I have always heard the affine line defined as an R-torsor, and never seen an alternative characterization. I don't know the alternative axiomatization you are referring to. I would be interested to hear it and see if it does not secretly rely on a very similar and simpler axiomatization of (R,+) itself.

I do know how to characterize the affine line as a topological space without reference to the real numbers.

Torsors seem interesting from the point of view of Occam's razor because they have less structure but take more words to define.

It's worse than your typical verbal dispute IMO, because in this case the two verbal conventions could live happily side by side, without over-complicating our communications. All we need to do is be careful with tensed verbs. I haven't argued for this. But try it out for yourself, and see if it works. Here is a blog post I read that I think supports my view, even though the author winds up in a different post thinking there is a genuine puzzle.

Edit: Luke_A_Somers seems to have beaten me to it. Further edit: A-theory, on some ways of fleshing it out at least, may be richer than presentism.

I think that the distinction may be clarified by the mathematical notion of an affine line. I sense that you do not know much modern mathematics, but let me try to clarify the difference between affine and linear space.

The A-theorists are thinking in terms of a linear space, that is an oriented vector space. To them time is splayed out on a real number line, which has an origin (the present) and an orientation (a preferred future direction).

The B-theorists are thinking in terms of an affine line. An affine line is somewhat like the A-theoriests real line, but it doesn't have an origin. Instead, given two points a & b on the affine line, one can take their difference a-b and obtain a point on the real line. The only defined operation is the taking of differences, and the notion of affine line relies on a previously defined notion of real line.

The meanings are much clearer now.

However, I still think that it is an argument about semantics and calef's argument still holds.

I'm trying to understand those A-theorists who aren't bothered by the implications of the B-theory for free will.

You're trying to figure out what the payoff is in believing A-Theory, if it's not being used to solve some conceptual tizzy over free will, or are you trying to figure out how they manage not to have a tizzy over the implications of B-Theory for free will?

Except it is testable, I think. If the A-theory of time is true, we would expect our best theory of space-time to contain an objectively definable notion of "present". However, our best theory of space-time contains no such notion, and in fact actively militates against it.

It is true that the original formulation of GR is covariant, i.e. has no time evolution built in, only a "block" spacetime manifold whose curvature is precisely its matter content. Similarly, classical EM, though originally formulated as an initial value problem, also looks better in a "timeless" form, where second derivative of the 4-vector potential is charge-current density.

It is, of course, possible to posit an undetectable preferred foliation of space-time or some such, but this just shows that you have to complicate your physical theory in order to sustain A-theory.*

I disagree. You have to recast GR into an initial value problem and then pick a foliation to model interesting physical phenomena, like stellar collapse and black hole collision. Completely independent of any underlying ontology. There is no intent to "sustain A-theory", that's just silly. You want to know how to detect the dying cry of a star torn apart by a supermassive black hole in the center of a galaxy, not whether to pick A or B from some book.

Plain relativity, interpreted naturally, is simply incompatible with it. So the experimental success of the general theory of relativity is strong evidence against the A-theory.

Are you saying that this A-theory predicts that there is a preferred foliation? By that logic, wouldn't B-theory predict that no foliation is possible at all? Or that all foliations are equal, whether they are timelike, null or spacelike? If so, the B-theory has been clearly falsified (if you can ever falsify anything in philosophy of physics).

the fact that our experience of the passage of time can be adequately explained within B-theory in terms of the Second Law of Thermodynamics

This seems like a major category error to me, mixing qualia ("experience of the passage of time") with statistical mechanics. They are about a dozen of abstraction and energy levels removed from each other. I can't take arguments like this seriously.

A-theory is a theory that requires us to complicate our best physical understanding of the world for no perceivable explanatory benefit. That is a bad theory in scientific, not just philosophical, terms.

What requires us to "complicate our best physical understanding of the world", such as recast the beautiful Einstein equation into an ugly ADM form, is the drive to explain and predict what we see or will see. The ontological narrative is a byproduct.

• I see this move as a slightly more respectable version of protecting biblical creationism from empirical refutation by saying that God created the universe 6000 years ago but made it look exactly as if it was billions of years old.

This was almost verbatim the Hoyle's criticism of the Big Bang model, wasn't it?

After reading your comment, I agree that this is probably just a semantic question with no real meaning. This is interesting, because I completely failed to realize this myself and instead constructed an elaborate rationalization for why the distinction exists.

While reading the wikipedia page, I found myself interpreting meaning into these two viewpoints that were probably never intended to be there. I am mentioning this both because I find it interesting that I reinterpreted both theories to be consistent with my own believes without realizing it, and because I would like to see what others have to say about those reinterpretations. I should point out that I am currently really tired and only skimmed the article, so that probably wouldn't have happened under ordinary circumstances, but I still think that this is interesting because it shows the inferential gap at work:

I am a computationalist, and as such the distinction between the two theories was pretty meaningless to me at first. However, I reinterpreted the two theories in ways that were almost certainly never intended, so that they did make sense to me as a reasonable distinction:

• the A theory corresponds to living in a universe where the laws of physics progress like in a simple physical simulation, with a global variable to measure time and rules for how to incrementally get from one state to the next. I assume for the purpose of this theory that quantum-mechanical and relativistic effects that view time non-linearly can be abstracted in some way so that a single, universal time value suffices regardless. I interpreted it like this because I thought the crux of the theory was having a central anchor point for past and future.

• the B theory corresponds to living in a highly abstracted simulation where many things are only computed when they become relevant for whatever the focus of the simulation is on. For instance, say the focus is on accurately modelling sapient life, then the exact atomic composition of a random rock is largely irrelevant and is not computed at first. However, when the rock is analyzed by a scientist, this information does become relevant. The simulation now checks what level of detail is required (i.e. how precise the measuring is) and backpropagates causal chains on how the rock came to be, in order to update the information about the rock's structure. In this way, unnecessary computations are avoided. I interpreted it like this because I thought the crux of the theory was the causal structure between events.

In essence, the A theory would correspond to a mindless, brute-force computation, while the B theory implies a deliberate, efficient computation that follows some explicit goal. This is nowhere near what the A and B theory actually seem to say now that I have read the article in more detail. In fact, the philosophical/moral implications are almost reversed under some viewpoints. I find it very interesting that this is the first thing that came to mind when I read it.

What are the different perceptions that would explain the different intuitions about whether the future exists?

You don't have a qualia for "becoming" therefore it's no important concept for you. Other people perceive a qualia for that concept.

I'm not 100% sure on that but I know that it's a common stumbling block when talking about the experience of being. Some people do have a qualia for that others don't.

In the case of time, we have the same biological and cultural heritage, and we have the same experience with time itself

I don't think that's the case. Typical mind fallacy makes you believe that other people have the same experience with time itself.

If I would guess than I would think that people who are strongly associated with their bodies are more likely to prefer A-theory while nerds without a relationship to their bodies prefer B-theory.

For that matter I personally don't feel a strong preference for either of the two.