 Okay. So let's start. Welcome, welcome everybody to the third meeting of the Seminar of Metaphysics of Science. It's my pleasure to introduce Peter Kiesan from the Université Capolito de Luban. The title of the presentation is Conventionality and Reality. Peter, as you know, you have one hour roughly and then we can take five minutes break and then have a discussion. So whatever you want, Peter. Yep. Thanks, Christian. I would say it's a pleasure to be here, but I'm at home. So it's a pleasure seeing you virtually and giving this talk. If there would be any urgent questions, feel free to just jump in because I can't see the chat. So just switch on your mic and feel free to interrupt me. So my talk for today is based on a paper I wrote for a special issue of the Foundations of Physics with Kardo Rovelian and Benjami, which was called Conventionality and Reality. So there have been two debates in the philosophy of special relativity. First one is the debate on the conventionality of simultaneity and the second one is the debate on the reality of spacetime or you could say the dimensionality of the world. Now the first debate was sparked by Albert Einstein in 1905 when he claimed that the notion of distant simultaneity really is a conventional notion as opposed to a factual one. And the latter debate was initiated by Minkowski in 1908 when he claimed that the world, according to special relativity, is fundamentally four dimensional. Now an important contribution to this latter debate in favor of Minkowski's claim was an argument that was developed by Ritek and Putnam which is now known as the Ritek-Putnam argument for the four dimensionality of the world. But it has to be said that 100 years later both debates remain unresolved. There haven't been any clear cut answers to any of those two debates. But what is perhaps most interesting is that the link between those two debates has rarely been explored. Now what I want to do in this talk is to look at how these two debates are related to one another and in particularly how the conventionality thesis impacts the Ritek-Putnam argument for the four dimensionality of the world. Now I could only find three relatively obscure little papers that actually explored this relationship. One was a paper by Weingart, one by Sklar and one by Deeks. And it seems that they all reached the same conclusion, maybe that the conventionality thesis would undermine the Ritek-Putnam argument. So what I want to do today is to question this conclusion and show you that the situation is actually much more subtle than that. Now I didn't want to assume too much prior knowledge and special relativity and so I decided to actually spend quite some time introducing those two debates, spending some time introducing the necessary concepts, which I will do in the first three parts and only in the last part will I actually look at the relationship between those two debates. But so let me start by introducing you to the first debate, which is the debate on the conventionality of simultaneity. So the idea that simultaneity is a conventional notion already originated in some of the writings of Henri Poincaré and as I just said in the 1905 paper on the electrodynamics of moving bodies by Albert Einstein. Now this conventionality thesis was then further developed by Hans Reichenbach in the 1920s and by Grunbaum in the 1950s. So in order to introduce this debate, just imagine two distant events, one event at location A, another event at location B. Now to say that those two events are simultaneous with one another is actually just to say that they occur at the same time. So in other words if you were to place a green clock at location A to measure the time of occurrence of event A and a blue clock at location B to measure the time of occurrence of event B, you would notice that both clocks are indicating the same time. That is if TA equals TB, you can maintain that both events are simultaneous with one another. But of course in order to do so, you first need to ensure that your two clocks have been previously synchronized. If your blue clock is still indicating summer time and not winter time, obviously you won't reach the right conclusions. And so this leads to the question how should one actually synchronize distant clocks in special relativity. Now Einstein proposed a clock synchronization procedure in his 1905 paper, which is now known as standard synchrony. And the way to synchronize these distant clocks is actually very simple. It only involves a beam of light that travels from A to B and back to A. Now in his paper, Einstein also wrote that we will establish by definition that the time required by light to travel from A to B equals the time it requires to travel back from B to A. That is the speed of light here is taken to be a constant. Now if I were to draw this synchronization procedure on a Minkowski diagram, it would look something like this. So on a Minkowski space time diagram, time is running upwards vertically, space is represented horizontally. So what you see here is the world line of the first clock at A, the green clock. Clearly it's only verticals. It's not moving in space. It's only moving in time. You see time evolving from 0 to 4. And a certain distance away, you have the second clock, the B clock, where I haven't indicated any times as of yet because we're in the process of synchronizing this clock with the green clock. And now Einstein says what you need to do is to send a light beam from A to B. Let's say it leaves the green clock at time tA and it arrives at B at time tB. And then you immediately send that light beam back from B to A. And so it comes back to the green clock at time tA prime. Then since the speed of light is a constant, since it takes an equal amount of time to go from A to B as from B to A, obviously tA prime minus tB will equal tB minus tA. And now we can rewrite that expression in terms of tB because that's the value we're looking and you get the following expression. And so if now you would actually fill in the numbers as indicated here, tA equals 0, tA prime equals 4. So you get 4 divided by 2. So tB occurs at 2 o'clock. And with that, I've actually successfully synchronized my two distant clocks. And of course, once I've done that, what I can do is connect the events, the distant events that happen at the same time, the events that are simultaneously with one another as follows. And what you see is that this imposes a filiation of Minkowski spacetime into three-dimensional hyperplanes of simultaneity. And those represent moments of time. Now with the synchronization procedure, it's actually very simple to show the relativity of simultaneity, not the conventionality, but the relativity. So if I were to apply the same synchronization procedure, but to moving clocks, here are two clocks that are moving to the right. I again send a light beam from C to D and back to C. You can see that the time Td is again equal to 2. I've synchronized my clock and now I again connect the events that are simultaneously with one another. You will see that the hyperplanes of simultaneity are no longer horizontal, but actually have been slanted as a consequence of the fact that those clocks are moving with respect to the green and the blue clock. And that is known as the relativity of simultaneity. So here again, you see two observers, observer A and observer B, observer A standing still, observer B is moving to the right relative to observer A. And due to their relative motion, they will draw their hyperplanes of simultaneity differently, horizontally for A slanted for B. And so they will disagree on what events are simultaneous with the here and now at point O. So for observer A, it's the event P and Q that are simultaneous with O, but for observer B, it's R and S that are simultaneous with O. Good. But that brings me finally to the conventionality thesis. After all, I'm not sure you notice, but Einstein had to make one important assumption in his clock synchronization procedure. And that was the assumption that the speed of light is isotropic, that is the speed of light is the same in all spatial directions. And here in particular, it's the same in the AB direction and the BA direction. And here's a trouble because in order to verify this assumption, empirically, you would have to measure both one way speeds of light and then compare them to one another to check that they're indeed equal. But now imagine you want to measure the one way speed of light in the AB direction. The way to do so is just to take two clocks, a green clock and a blue clock, one at location A, the other at location B, and then you send the beam of light from A to B. You measure the point of departure with the green clock. You measure when the beam of light arrives at B with the blue clock. And then you take the difference of those two times to know how long it took light to travel between A and B. You divide it by the distance between A and B and you get an expression for the speed of light in the AB direction. But so in order to measure this one way speed of light, you need to have those two clocks, the green and the blue clock, and those have to be synchronized. And that's of course, the whole problem because this is what we started with, how should one synchronize those two clocks. So as Einstein observed in 1916, it appears as if we are moving here in a logical circle. After all, if you want to measure the one way speed of light, you first need to have two synchronized clocks. But in order to synchronize those two clocks, you need to know what the one way speed of light is. And so it looks as if the only way out of this logical circle, or what Reichenbach called the philosophy simultaneous circle argument, the only way out of this is by breaking the circle, as Einstein did in his 1905 paper, by simply assuming that the one way speed of light is isotropic, and then using that assumption to define a notion of distance simultaneity. Now, Einstein was very well aware of this fact. He explicitly wrote, we will establish by definition that the speed of light is isotropic. And he also called the title of that paragraph of school, definition of distance simultaneity. So he was very well aware that this definition of simultaneity, dependent on this assumption, and was therefore to be taken as a conventional notion, and not a factual one. Now, there's another way to arrive at this conventionality thesis, and that is via the causal theory of time, which is actually Reichenbach's way of arriving at the same thesis. Now, according to the causal theory of time, all temporal relations are reducible to causal relations. So take any two events A and B. A is said to be earlier than B. Even only if A is a potential cause of B, that is, if A and B are somehow causally connected to where A is the cause, and B is the effect. I think that makes a lot of sense. Once you apply that to the synchronization procedure of Einstein, it actually leads to an interesting conclusion. So you notice here three important events, EA, EB, and EA prime. The light beam is sent from A at EA. It arrives at B at EB, and is then sent back and re-arrives at A at EA prime. Now, if you want to look at the temporal order between EA and EB, you notice that those two events are linked via a light beam that is traveling between those two. So in a sense, EA is a potential cause of EB. Therefore, you can maintain that EA happened earlier than EB. Similarly for EB and EA prime, since those are connected via light beam as well, EB is a potential cause of EA prime. As the Reichenbach concludes, EB must happen before EA prime. But now comes the interesting thing. Now consider any other event E on the word line of A that is in this open interval between EA and EA prime. And now let's try to look at what are the temporal order is between E and EB. So in order to do so, you need to establish what the causal order is. You need to establish whether E is a cause or an effect of EB. But in order to be a cause or an effect, they have to be causally linked via some kind of causal chain, which I've represented here with this dotted line. And as you can see, in order for a causal signal to travel here between E and EB, that signal would have to travel at superluminal speeds, which is forbidden according to special relativity. And so this shows you that those two events here are not causally connectable. And since their causal order is left indeterminate, their temporal order as a consequence is also left indeterminate. So Reichenbach, on the basis of his causal theory of time, maintains that E is neither earlier than nor simultaneous with nor even later than EB. That E is neither in the past, present, or future review of EB because their temporal order is fully indeterminate. And this is not only the case for the event E that I've shown here. It's actually the case for any event in this open interval between EA and EA Prime. That is, if you were to draw a light cone on EB, you can see that any event in the absolute elsewhere of EB, so any event that is space-like separated from EB is going to be causally disconnected from EB and so the temporal order for those events will remain indeterminate, which implies that if you want to speak about the simultaneity of these distant events, you need to put in a definition of simultaneity by hand, which is exactly what Einstein did. So once again, here you see what Einstein did. Einstein just maintained that it's the event that is exactly midway between EA and EA Prime that is simultaneous with EB, just leading to this kind of formation of Minkowski spacetime and leading to the following expression for standard synchrony. But as Reichenbach now clearly showed, you could have taken any other event in this interval as being the event simultaneous with EB. So you could have actually introduced a very different way of synchronization, a non-standard synchronization method, where you replace this parameter a half by any other value between zero and one. Call that epsilon, call that the Reichenbach synchronization parameter. So just to give you one illustration, suppose you didn't use epsilon is a half as in standard synchrony, but epsilon is one fourth, then TB would not equal two, but TB would equal one. And if you would connect that with the one o'clock at A, you see that you would actually foliate Minkowski spacetime differently. And so your hyperplanes would now be slanted. And of course, that leads to two important differences. For example, on the left, you can see that it takes light, two units of time to travel from A to B, and another two units of time to travel back to A. So the speed of light is indeed the same in both directions. But on the right, it takes light only one unit of time to travel from A to B, but three units of time to travel back to A. So somehow the speed of light here is, light is somehow traveling faster to the right than it travels to the left, which is a perfectly okay consequence of the conventionality of simultaneity. Now with that, I can move on to the second debate, maybe the debate on the reality of spacetime. The problem here is that there's a whole variety of metaphysical positions about the nature of time on the market today. And so to keep the discussion focused, I'm going to only look at the debate between eternalism and presentism. Now even presentism really is an umbrella term of various metaphysical positions. For example, different flavors of presentism can be distinguished, depending on which spatial temporal shape the present is taking on. So on some accounts, the present may be reduced to a single point, to a single spacetime event, as in point presentism. But on other accounts, the present is taken to be bowtie or cone-shaped as in bowtie, presentism or cone-presentism. Now some of those flavors will be discussed further on, but for the moment I'm going to stick to what I think is the most standard flavor of presentism, which I've called hyperplane presentism, and where the present is taking to be this three-dimensional hyperplane of simultaneous events that I've already shown a few times before. Now let me unpack that position just a little more. So on this presentist account of time, the present is singled out as a uniquely special moment that we call the now. And so only those events that constitute the present moment are taken to be real. So past events obviously were real in the past, but they're no longer real at the present moment. And future events will be real in the future, but they're not yet real as of now at the present moment. So this implies that the reality is somehow reduced to what is happening presently, that this reality is reduced to all those events that are simultaneous with the here and now. Or in other words, reality is this three-dimensional hyper surface of simultaneity that is the world is fundamentally three-dimensional according to the hyperplane presentist. So to summarize, the presentist takes there to be an objective present, only present events are real. And typically the presentist will also assume time to pass. So present events disappear into the past as future events coming to existence, leading to a succession of nows or some kind of moving now. Now this dynamical aspect of time is called the passage of time or temporal becoming. And now contrast this presentist account with the eternalist outlook on time. So according to the eternalist, you should treat the temporal dimension on much the same footing as the three spatial dimensions. And so just as the Eiffel Tower in Paris is considered to be real, even though we can't see the Eiffel Tower because we're spatially removed from the Eiffel Tower by living here in Belgium, in much the same way since the eternalist, should we treat past and future events as real, even though we can't see them because they are temporarily removed from us by living now on a 2021. That is, not only present events are real, past and future events are equally real according to the eternalist. And so the world as a consequence doesn't only stretch out in the three spatial dimensions, but also in the temporal dimension, and is therefore fundamentally four dimensional and not three dimensional. Now this account finds a natural representation in the so-called block universe where all events are somehow frozen in this four dimensional block. There's no objective present in the block universe. As I said, past, present and future events are all equally real. They're ontologically on a par. And finally, there's no obvious passage of time or temporal becoming in the block universe. But so notice that these fundamental differences between presentism and eternalism can actually be cashed out in terms of what events are taking to be real. According to the presentist, present events are real. For the eternalist, all events are real. But this, of course, leads to an interesting question. What does it actually mean to say that a particular space-time event is real? And actually quite surprisingly, these questions remained largely untouched in the philosophical literature. I can only think of two exceptions worth mentioning. One is a paper by Craig Callender called Shedding Light on Time. The other one is a more recent paper by Peterson and Silverstein. I'll start with Callender. So Callender asks us to consider a manifold of space-time events where each event carries a light bulb that is either on or off, depending on whether that event is real or not real. So on that basis, the presentist will claim that only present lights are on, whereas the eternalist will maintain that all lights are on. And a possibility, as you can see, is really an intermediary position between presentism and eternalism, according to which only past and present events are present lights are on, but the future lights are off. Possibilism here could, for example, be a growing block universe. Now, instead of associating a light bulb with each event, Peterson and Silverstein introduced a reality field that denotes the authentic status of each space-time event by assigning it a so-called reality value or an r value for short, that is either 1 or 0, depending on whether that event is taken to be real or not real. Now, what is important about this is that the reality field is a scalar field. So that means that the reality value that it assigns to a particular space-time event is unique and observer-independent. So all observers, irrespective of their frame of reference, will agree on the reality value that is assigned to a particular space-time point. Next, Peterson and Silverstein introduce a reality relation, r, that holds between any two events that share the same r value. So to give you a simple example, on the left you see the manifold of space-time events. Take any two events, for example, a and b. Since both are assigned to the r value 1, that is since both are taken to be real, the reality relation will hold between those two, and you can say that a and b are equally real or that a is real for b. Now, due to the uniqueness of the r value for each and any event, the reality relation is also reflexive, that is a is real for a, since a has only one unique r value. The reality relation is also symmetric. If a is real for b, then b must also be real for a, because a and b share the same r value. And finally, the reality relation is transitive. So if a is real for b and b is real for c, it follows that a must be real for c. Once again, a and b share the same r value, b and c share the same r value, so obviously a and c will also share the same r value. Now, this of course turns the reality relation to an equivalence relation that is then able to partition the spacetime manifold of events into two disjoint equivalence classes, one class of real events and another class of unreal events. Now, with this concept of reality values and reality relations, we can actually rewrite the present is credo according to which all and only present events are real. So to do so, consider again, a manifold of spacetime events. And let me also introduce the relation of distance simultaneity that holds between any two simultaneous events. Now, imagine that b here represents our here and now we are located at b at this very moment. So obviously b is real for us. Now, if a turned out to be simultaneous with b, then a was present for us at b. Hence, following the present is credo, a must be real for b. So you get this very simple expression that somehow links the co-occurrence of two events with their coexistence. And with that, I can introduce the ETEC-Putnam argument. So you may have noticed when I presented presentism and internalism that presentism is much closer to our intuitions about time and eternalism. After all, we intuitively feel as if time is flowing at a speed of one second per second on average. It's flowing in one particular direction from the past to the future. We typically only take the present to be real. Not many people believe that dinosaurs are still real or that super intelligent robots are already real. So all of this seems to be much closer to what the present is disclaiming than what the eternalist is saying. But with the advent of special relativity, these presentist intuitions were being challenged more and more. And so when you actually look at some services that are being done today, such as a survey on fill papers, you can see that the majority of philosophers today have become eternalists and no longer presentists. Now, perhaps the most important argument from special relativity for eternalism, for the four-dimensionality of the world, is this infamous ETEC-Putnam argument that was developed, as I said, independently by the Dutch physicist Willem Rietek in 1966 and by the American philosopher Hilary Putnam in 1967. Now, their argument is really a reductio ad absurdum. So their aim is to establish eternalism, but they do so by assuming the opposite thesis. So they assume presentism and then subsequently show the untenability of this position, thereby refuting presentism and actually indirectly confirming eternalism. So here's how the argument runs. What you see is a Minkowski diagram once again with two observers, a green and a blue observer. The green observer is standing still. The blue observer is moving towards the green observer. Now, since these two observers are in relative motion with one another, they will also draw their hyperplanes of simultaneity differently. Horizontal for observer one, slightly slanted for observer two. Now, consider the two events A and B on the wordline of observer one. And finally, there is a third event, event C on the wordline of observer two, that is space-like separated both from A and B. That's the setup. Now, notice that event C is simultaneous with A according to the first observer's frame of reference. That is, C is present for observer one at A, and hence, following the presentist credo, C must be real for A. Similarly, you can see that B is simultaneous with C, that is, B is present for observer two at C, hence, B must be real for C. And now, using the transitivity of the reality relation that I introduced above, if B is real for C and C is real for A, it follows that B must be real for A. But notice that B is actually in the absolute future. It's in the future-like cone of A, that is, B is definitely not present with A. It's in the future of A. B is not simultaneous with A. Hence, following the presentist credo, B is not real for A. And so, we arrive at this contradictory conclusion that B is somehow both real and unreal for A. And so, according to Rita Camputnam, the only way out of this contradiction is by rejecting the fourth premise, according to which a future event is not real. And now, if you were to play this argument once again, you could, of course, move the second observer to the left and the right, and you could have it move at different speeds in different directions. And by doing so, you can actually make any event real. So any event in the future of A, or in the past of A, or even in the elsewhere of A, will turn out to be real based on this argument, which refutes presentism and actually confirms eternalism. All events are real. So Putnam in his paper writes, I conclude that the problem of the reality, I can't read it because my thing is in front of it, in any case, he concludes that the problem is solved, it's solved by physics and not by philosophy. And so, we've learned that we live in a four-dimensional and not a three-dimensional world. What's more, he believes that there are actually no longer any philosophical problems in time, which is a pretty bold claim to make in 1967. But as I said, this Pied Putnam's confidence in his own argument, the Eritek Putnam argument has repeatedly come under fire in the philosophy of special relativity. And so various objections have been raised against the argument, exposing different flaws and fallacies in the argument by Eritek and Putnam. In my own doctoral dissertation, I distinguished no less than 11 objections to the Eritek Putnam argument. Yet surprisingly, the argument is still taken as one of the most important arguments in favor of eternalism. But so before moving to the very last part of my talk, which is the conventionality objection to the Eritek Putnam argument that depends on the conventionality thesis, I wanted to very briefly show you the transitivity objection, which is probably the most common objection to the Eritek Putnam argument. So whereas Eritek and Putnam reject the premise for the transitivity objection actually takes issue with the third premise. That is, they take issue with the transitivity of the reality relation. After all, the idea is, in special relativity, the present is no longer absolute. The present has become a relative observer-dependent notion. What is present for me doesn't have to be present for you. And so if now the reality of events is tied up with there being present or not, clearly the reality is going to be relativized as well. And so you can see this actually quite clearly here. It's not because B is simultaneous with C and C is simultaneous with A that therefore B is simultaneous with A. This is clear from the diagram. And so using the present as credo that whenever two things are simultaneous, they're also real for one another, you see that from the non transitivity of simultaneity, you just derive the non transitivity of reality, contrary to what Eritek and Putnam were claiming. Or to put it even more explicit, the point is that in special relativity, the relation of distant simultaneity is no longer a binary relation between two events. It's actually a ternary relation between two events seen from the point of view of a particular observer or from the point of view of a particular reference frame. And so the mistake here in the Eritek and Putnam argument is that they took the reality relation to be a binary relation and not a ternary relation. Now I think the transitivity objection makes a lot of sense and it's actually pretty convincing. But notice that giving up on the transitivity of reality of course comes at a relatively high cost. Because if reality is a relative notion, if what is real for me can be very different from what is real for you, it of course leads to a plurality of observer dependent realities. So in other words, if I were to meet another observer in my here and now, and we are in relative motion to one another, then not only will we disagree on what events, distant events are simultaneous, but we will also disagree on what is real. So you get a form of ontological pluralism, which too many philosophers is just one step too far. Gallender calls this nonsense, or at the very least a desperate move to try to refute the Eritek-Putnam argument. But let me move on to the conventionality objection, which is perhaps even simpler. So instead of rechecking the fourth or the third premise, the conventionality objection takes issue with the first two premises. Because remember, according to the conventionality thesis, the relation of distance simultaneously is a conventional one and not a factual one. That is for any two space-like separated events, their temporal order is left indeterminate, because there is no causal connection possible between these two. And so as you can see here, event C is space-like separated from A, hence there's no causal connection possible between those two events. And so their temporal order is left indeterminate. So you can't maintain that C is simultaneous with A as we did in the first premise. Similarly, B is space-like separated from C, so their temporal order is left indeterminate. And so once again, you can't simply maintain that B is simultaneous with C as in premise two. So both premises are false, and that renders the whole argument unsound. Now as I said, this type of objection has been raised by people like Weingart, Sklar, and Deeks. And just by way of example, here's one quote by Sklar. He says, if we associate to real with simultaneous, then accepting the conventionality of simultaneity, you also get a conventionality theory of reality four. So it's only a matter of arbitrary stipulation that one distant event rather than another is taken as real for an observer. So that brings me to the very last part. What I want to do in this last part is to actually question this conclusion. I want to argue that in order to determine the strength of this conventionality objection, the one first is to decide whether the conventionality thesis is an ontic thesis or an epistemic one. And so on an ontic reading of the conventionality thesis, the relation of distant simultaneity is taken to be conventional as opposed to factual, because it doesn't exist in the objective world. There just isn't a relation of distant simultaneity out there to be measured. Whereas on an epistemic reading, the relation of distant simultaneity is conventional as opposed to factual, not because it doesn't exist, but because it is unverifiable. So even if this relation were to exist, even if there was effect of the matter as to whether two distant events are simultaneous or not, we fail to have epistemic access to that due to this velocity, simultaneous circle argument that I raised before. And so we're somehow forced to treat this notion in a conventional manner because we fail to have epistemic access to that notion. Now, how does the conventionality objection to the retake put the argument fair on both of these readings? Now, let me start with the ontic reading. So once again, here's Grunbaum actually subscribing to an ontic reading of the conventionality thesis. It's because no relations of distant simultaneity exist to be measured, that measurement cannot disclose them. Now, I think on this reading, it's pretty obvious that if there's no such thing as distant simultaneity, then clearly the first two premises in the retake put them argument are without any substance. And so the conventionality objection certainly applies that is the retake put them argument doesn't go through. So perhaps not surprisingly, when you read the papers by Weingart's Clara and Deeks, you can see that at least implicitly, they seem to be assuming, or they seem to be adopting an ontic reading of the conventionality thesis that seems to be what they have in their minds. That once again, even granting that an ontic reading of the conventionality thesis successfully undermines the retake put them argument, you can still ask where does it leave us with respect to the present is an eternalism debate. And here the consequences again can be pretty big. If you take distant simultaneity not to exist, if it's not part of the ontological furniture of the world, then if the present is constituted of all the events that are simultaneous with your here and now, but there's no such thing as distant simultaneity, the present is actually reduced to a single point that here and now to a single spacetime point. And if according to the present this only present events are real, then reality itself will be reduced to a single point, which as Stein said, is a peculiarly extreme but realistic form of solipsism. And again, you may wonder if you want to go all this way, just to reject any of that put them argument. But as I said, there's also an epistemic reading possible of the conventionality thesis. And here it's worth distinguishing two further positions. So you have the agnostic, who remains noncommittal about the possible existence of distant simultaneity. So it may exist, it may not exist, we actually don't know. And then you have what I will call the epsilon epistemicist. And she on the other hand is convinced that distant simultaneity really exists, but that we failed to have epistemic access to it. So you could compare this position with any hidden variable interpretation of quantum mechanics. For example, in Bohmian mechanics, the hidden variables are the particle positions. So the idea is that every particle always has a definite position and thereby traces out a classical or semi classical trajectory, but we fail to have epistemic access to those particle positions. And so we're forced to treat them as hidden variables. So in the same way, the idea here is that there may be such a thing as distant simultaneity, there may be a fact of the matter as to which two events are simultaneous with one another. But since we failed to have epistemic access to it, we're forced to treat this notion in a conventional way. But the fact remains that the epsilon synchronization parameter actually has a determined value on this account. So just to recall, if epsilon equals a half, we have standard synchrony and all the hyperplanes are orthogonal to the word line of the observer. If epsilon were to have any different value, you would get a different formulation of Minkowski spacetime. So how would you treat the Putnam argument now fair on this epsilon epistemicist interpretation of the conventionality thesis? Notice that we can put them actually implicitly assumed epsilon to be equal to a half. That is, they applied standard synchrony and that's why the hyperplanes of simultaneity here are orthogonal to the world lines. But now imagine that it so happens that we live in a world where epsilon is not equal to a half, but is actually one for it. In that case, Minkowski spacetime would no longer be foliated in hyperplanes of simultaneity, but actually one sheet of hypercoase, which is quite odd. But despite this fact, the relativity of simultaneity still holds and you can see that the Putnam argument actually goes through unaffected. Now, most philosophers and physicists don't really like this notion of hypercoase of simultaneity because it turns the notion of distant simultaneity into something that is non-symmetric and non-transitive. I think you can actually see this quite clearly on the diagram here. You can see that C is simultaneous with A because C is on the hypercone of A, but A is not simultaneous with C because A is not on the hypercone of C. So that's quite odd. So one way to restore symmetry and transitivity is by making epsilon direction dependent, which is actually often bummed in the literature. The idea is that if epsilon has the value 1 fourth to the right, it should have a value of 3 fourths to the left. And by making epsilon in that way direction dependent, you will no longer have a foliation to hypercoase, but a foliation to hyperplanes. The hyperplanes will still not be orthogonal with the work line as in standard synchrony. They will be slanted, but at least you get a hyperplane. And so you get a notion of simultaneity that is symmetric and transitive. And once again, I think even on this account, with a direction dependent epsilon, you can pretty clearly see that the direct put in an argument still goes through unaffected. But of course, and finally, if I can make epsilon direction dependent, why couldn't I make it observer dependent? I could argue that epsilon actually depends on the state of motion of the observer. For example, here you can see that for observer 1, I've taken epsilon to be equal to a half standard synchrony. That's why its hyperplane of simultaneity is orthogonal to the work line. But for observer 2, who is in a different state of motion, I've taken a different value of epsilon such that her hyperplane of simultaneity coincides with his plane of simultaneity. And so by making epsilon observer dependent, I can actually reintroduce a notion of absolute simultaneity in special relativity. So any neo-Lorentian interpretation of special relativity, for example, would be very happy to do something like this. And even in Bohmian mechanics, for example, where they get into a lot of trouble because of the local correlations between distant events, it has been argued that we may have to reintroduce a preferred foliation of Pinkowski spacetime much along the lines presented here. But of course, once you reintroduce an absolute notion of simultaneity, the Litek-Kudnam argument will fail to go through. So to summarize, whereas Weingart, Deeks, and Esklar were claiming that the conventionality thesis of distant simultaneity undermines the Litek-Kudnam argument, I hope to have shown you that the situation is actually more subtle than that and depends first and foremost on whether this thesis is taken to be an ontic or an epistemic one. And so I grant that along ontic reading, it successfully undermines the Litek-Kudnam argument. But on an epistemic reading of this thesis, you can still go many ways. And on many of those ways, the Litek-Kudnam argument goes through without any problem. So to conclude, I've argued that the way in which the conventionality thesis impacts the Litek-Kudnam argument depends on whether the conventionality thesis is an ontic or an epistemic one. Perhaps more importantly, I hope to have shown you that the soundness of the Litek-Kudnam argument hinges on our interpretation of reality, and in particular on the alleged transitivity of this reality relation and its intimate link with simultaneity. Now, I think it's pretty clear that the reality relation doesn't belong to the formalism of special relativity. There's no textbook of special relativity that talks of the reality of events. And as such, the special relativity alone leaves the debate between presentism and eternalism under determined. That is, physics at most constrains our metaphysics, but it can't settle it. So any metaphysical inquiry into the nature of time will actually quickly outrun the scope of physics. I think your metaphysics will always remain within the straight jacket of physics, but physics alone will never be able to settle any of those metaphysical debates. And I think this actually beautifully resonates with a quote by David Lewis, and I'll end with that one. He said that a reasonable goal for a philosopher, well again, I can't read it. So I'll let you read it. In any case, you need to be looking for equilibrium. A suppressant is maybe one equilibrium. Eternism may be another equilibrium that can withstand further examination, but it's going to be very difficult to settle for one or the other by purity and empirical or physical means. Thank you very much.