And for me, I think this is sort of one of the reasons one one might care about my life curves to begin with So here's this here's the question. So so I'm going to fix I'm going to fix five complex numbers So very general So the question is for how many T Is the hyperliptic curve so the hyperliptic curve of genus 2? So I'll call it CT it's going to be to cut defined by the equation y squared Okay, so it's going to be branched over the six these six points. So x minus eight one Say five D elliptic by which I mean There exists a cover of some elliptic curve of degree D So so he's an elliptic curve, okay? So the first enemy check is why would you expect this answer to be finite? So why finite? Well, okay, so as we know there's a there's a three-dimensional family of genus 2 curves and So how many among these genus 2 curves? How many of them have this property? Well, so such a map So this will have two branch points by Riemann Hurwitz and So if I think about the family of covers So if I think about just the family of sort of all covers of a genus 2 curve mapping to a genus 1 curve degree D So it's a standard fact Well, I can turn this around and say if I specify the base curve and the the two branch points Then I get finitely many covers after well, I get a unique cover after specifying the monodromy So in particular I get finitely many covers If I just specify the base with its two branch points and so we have a two-dimensional family of covers Okay, so Okay, then you have to give some argument to to convince yourself that you know if you have one genus 2 curve You don't have infinitely many maps coming out of it But the point is now I have a two-dimensional family and if I start with a one-parameter family I should expect to see finitely many intersection points So I should have finitely many fibers that live in this family. Okay, so how might you hope to answer this question? Well, so I've defined for you a family. I guess over P1 Inside M2 bar. So over here I have sort of I Have a map like this Which I guess I will call phi and it sends t to this curve Ct And on the other hand I have this locus of de-liptic curves But I'm working M2 bar. So I need to take a closure so this is a closure of De-liptic locus and what you want to do is you want to intersect these classes, right? So you want to take these classes and the chowering of M2 bar and you want to multiply them. So Want to intersect in Chowering or if you want the co-mology ring of M2 bar and by M2 bar. I will always mean the stack All right, so the problem with this as I've stated it is that I've done some something drastic Which I've said which is I've said take some locus and take its closure, right? And this is a And the problem with this as well. I mean there are a number of problems One is that a priori we have no idea which boundary curves are in this closure, right? and Another problem is even if we did you can start with some sort of nice locus and M2 without a bar and take its closure and get Sort of something sort of arbitrarily bad, right? You could introduce sort of horrible singularities. You could you could pick up sort of sort of really bad deformation spaces So I mean so so so the problem is that Is that taking closure is sort of difficult in particular the question arises that sort of what are the limits of Smooth D-lip the curse right so our prayer is not so obvious So let me instead sort of phrase a What turns out to be a more reasonable question? So better question is what if I just remember the whole data of the family of the Cover so instead I can ask what are the limits of branch covers? So this is essentially answered In the paper of Harrison Mumford, which we've already heard about so this is the paper in which they Prove that MG is general type for g-large This is Harrison Mumford 82 so what do they what do they do so they show that there's a proper Okay, so I'm gonna throw some adjectives up so Cohen Macaulay Lee Mumford stack Which I will call Curly ADM So G over H come a D. Okay, so this is just some object Containing a Dense open sub-stack Which I'll call ADM Cirque and So I'll tell you what the dense open sub-stack parameterizes. So these parameterizes these parameterize Or this parameterizes Primitrizing So degree D Simply branched covers a genus G curve to a genus H curve. Okay, so I guess I'll write the genus up here We're excellent XMI are smooth are smooth And let's say connected So I have this open sub-stack of sort of nice objects of sort of honest covers of curves And what Harrison Mumford do is they they compactify it, right? So this is some kind of open stack and then they give some some bigger moduli space That allows these things to degenerate So, okay, so what are these parameterize so? This compactified stack parameterize parameterizes something called admissible covers Okay, so let me tell you what these are. Yeah, simply branched. Oh, yeah, so right So, okay, so at the beginning I said I said pick the points very general so Yeah, pick them general enough so that you only get simply branched covers. Okay, so what are admissible covers so definition? All right, this takes a bit of setup Okay, so I'm going to use the same notation here. So X X Y this will have genus G and H and these will mean the arithmetic genus So this is a going to be a finite Degree D So this degree D means degree D over every component of Y morphism of nodal curves Okay, and I'm going to call the branch points Well, okay, so I'm going to I'm just going to think about for now I'm just going to think about the branch points there in the smooth locus of Y So I'm going to call them Y1 through YB Y smooth, okay, so with smooth branch points Okay, so that's the setup so F is admissible if Okay, they're going to be four conditions Okay, so one is that when I take the cover with the sorry the base with all of its branch points I want I want a stable curve so to I want F to map smooth points to smooth points and nodal points to nodal points Okay, so I'll just write this in the following compact way. So X is smooth if it only if It's images smooth Okay, I want F to be simply branched over to the Y I So so far these are fairly mild conditions Okay, and the crucial one is called the balancing condition so balancing or at least that's what I'm going to call it So for each node of Y. Let's see. So the ramification indices over the two branches Okay, so let me let me explain what this means Okay, so what do I mean here? So So okay, so F is some kind of cover and so if I zoom in on some node of Y So this is supposed to be a picture of a node So I have so okay, so this this condition says that nodes have to map to nodes so I can look at these two nodes and I can say that so each node has two branches through it and well one branch down here has to map to some branch down here and the other one maps to the other one and At this node there's gonna be some ramification index on both sides And I'm just requiring that those two branches have the same ramification index Okay, so another way to say this is well Okay, let me erase this cartoon So if I look at the deformation space if I look at the complete local ring down here I'll get something that looks like this Or maybe I think I called it Z and then the map will go in the other direction Okay, so W and Z are the two branches here and X and Y are the two branches here So the map has to look like something like W goes to X to some power and Z has to go to Y to the same power So the condition is that these two numbers are equal No, I didn't say that. Yeah, so let me give some examples. Okay, so are there any questions about the definition? Okay, so I think I started at 53. Is that right? Okay. I think I started a little later than that, right? Okay. Thank you All right, so let me give some examples so we'll start sort of Reasonable and then I'll try to convince you that these get kind of wild Okay, so one one easy way to make admissible covers is you can start with sort of nice covers of smooth curves and then start gluing together nodes Okay, so the simplest was a simplest example of this I can start with a double cover of P1 so it's like this and then Okay, let's see if I can use And then I can start gluing together some points. So I'm going to just pick two points down here away from the branch points I'll glue these two points together then I'll glue these two points together and then I'll glue these two points together And then I get a picture that looks something like this So I've set this up in such a way that I've made two nodes upstairs that map to the one node down here and The value of E here is just one because I've glued together points where this map is at all and then I still have my two branch points And this is a stable curve, right? This is this has arithmetic genus one and it has two marks points Cool. Okay, let's do something a little wackier So one way to so okay, so I'm going to start Okay, so this is so the base is going to be so this this has a Irreducible base, so let me make one with a reducible base so let me start with a An isogeny of elliptic curves, so this will be just any map from E to E prime and Then on the base, I'm going to glue on P1 with two marks points Okay, so I need to put mark points on here so that the base is stable and Okay, so now I need to add a bunch of components over this P1, right? Okay, so let's I guess this map is degree four. So here's one way you can do it, right? So you can I'm going to attach two P1s that just map isomorphically and Then while I need to have two branch points, so I need I need a two-to-one cover, right? So I can this picture is going to look kind of I'm going to sort of cheat and draw this backwards. So I have two P1s mapping isomorphically I have some kind of okay, so that's going to be my E and then I'm going to attach another P1 But that maps sort of by a two-to-one map down to this P1 So I have I have three copies of P1 and All but one of them map isomorphically to the P1 down here But I have one that has degree two where I get these two branch points okay, and Let me point out this curve this this this the source curve is not stable, right? Because I as a just as a curve it's just an E with three P1s attached to it And all three of them have not enough nodes and Again, I have four nodes up here and my my my E is going to be one This is example one Two and let me do one more example. I'm not going to explain it in detail But I just want to sort of draw a weird-looking picture Okay, so this is going to be a genus one curve These are going to be These are all going to have genus zero Okay, so I'm going I'm first going to map to a P1 the genus zero curves are going to map by Sort of X goes to X to the a All right, so it's going to be totally ramified at two points and unremifed everywhere else So I'm writing in the ramification indices at these points and Then the genus one curve maps to the genus zero curve by some map That's totally ramified at two points and simply ramified at two other points Okay, so this isn't quite enough right because of a bunch of nodes here and no nodes down here But I can do the following I can say well look at the two points Look at the two sort of highly ramified branch points and glue them together and This will be a curve arithmetic genus one and this is now an admissible cover where at this node I have five modes mapping to it and I've made this ramification index as large as possible and you can imagine I mean you can make this polygon have any size So these things even though this just has arithmetic genus two and this just has arithmetic genus one Which are the numbers we're dealing with in this in this talk? The admissible covers can get quite complicated great any questions So the upshot of all this so I have a forgetful map, so I have a map Where I can just start with admissible cover Okay, so let me specialize the case of genus two and genus one and I have a forgetful map that only remembers the source Right, so I can just remember The source and what I want to say is well, okay, so take some cover and just remember x But this is not quite good enough because as we already noted Often you get non-stable curves, so you can't just take x but you have to take x and sort of stabilize it right, so you have to contract non non non-stable components right, so for instance in these cases, I think you get a Sort of Irreducible no, but no to curve genus two and say same over here Because you here you start with an elliptic curve, but you sort of glue two points together after you kill all the rational tails And here it's the same and so why do we like this map? Well the image, so let's call this map pi d so the image of Pi d is exactly So exactly compactifies Okay, maybe exactly is not useful so compactifies The d elliptic locus Right because I'm taking the stack of all Covers from a genus two curve to a genus one curve suitably compactified and then I'm only remembering the genus two curve Okay, and so why is this better than the formulation? I I I stated the beginning, so there are two reasons so upshot So one reason is that well, we actually have a modular interpretation of this now, so have a modular Interpretation yes of the image It's a divisor. Yeah, so I mean this is the computation that we did at the beginning Yeah, yeah, it's a divisor So we actually have a modular interpretation maybe I also should have said let me say generically finite because that's So we have a modular interpretation so I can tell you in principle Or I mean not just I can tell you what the image of this map is in terms of what the points are and Not only that we're doing intersection theory So in order to compute intersection multiplicities, we need to know something about deformations and in fact Harrison Mumford give Explicit explicit descriptions for its deformation spaces or of Information spaces and I said before I threw in the word co-mikali and because we're doing intersection three That's the property we really want. All right, so in the Three four minutes I have I can now state the theorem So for those of you who like formulas, this is for you. Okay, so theorem so the class of I d in the chowering Is okay, so these sigma d's is this is the sum of divisors function And these deltas are the are the boundary classes. We've seen before so this is the class of the closure of the the locus of irreducible genus two curves and this is the locus of Curse where you have a Union of two genus one curves that meet at one node and My class of this map while I told you was generically finite, so I mean the class of the proper push forward Okay, so and I'm using this okay. I'm gonna write this is this is gonna be sort of a cop out, but I'm gonna write Maybe okay, maybe I just won't say this but I'll say it more. It's So using this right So if you want to answer the original question now you can do something sort of much more reasonable than before So now you can just make a fiber square So this was fee this was pie and you can See and this will be some finite. This will be some finite stack scheme scheme And now you can really just multiply these two classes right And you can get a formula once you integrate for this intersection Okay, and I won't write it down But let me maybe say in the last 60 seconds how you would prove such a formula So and this is really made possible by sort of Mumford's Description of the chowering of of M2 bar So, I mean so what do we know about it? Well, we know that it has dimension two in degrees one and two so a one and a two With a frank two So what do you need to do? Well, you need to take this locus and you need to intersect it Well, okay, so how do you pin down a class in here you intersect it with? You intersect it with two classes over here that are linearly independent and you invert some matrix And so how do you do this well? You can make a list of admissible covers of this type and it it's rather complicated We know they're deformation spaces and once you make this list this sort of tells you it sort of pops out Which classes in here are sort of the correct things to try to intersect with? and then using this rather delicate analysis of Deformation spaces you can compute these intersections you can compute their Multiplicities and then you can recover this formula Okay, I think a lot of time so thank you


This theory is going to deal with systems of equations and their applications. As a general rule, we need to write equations that represent the same thing in each part of the equation. So it's like apples and apples. We're not going to add apples and oranges. If we know a total number of items, then the equation needs to have the number of items in each term. If we know a total value, then the equation needs to have a value in each term. Two families go to the movie together. One family purchases four children's tickets and two adult tickets. The other family purchases three children's tickets and two adult tickets for $24. How much of each type of ticket? Well, first we have to figure out what our unknowns are. And they're asking us for type of ticket. So that would be what our unknowns are going to represent. So let's let C equal children. That way it'll make sense when we get done. And let's let A equal adult. So if we want to write our system, we need to then go back and read the problem. One family purchases four children's tickets and two adult tickets. And then we have a total of $28. Another family gets three children's tickets and two adult tickets. And then that gives them a total of $24. So we're going to take each family, since that's the two different things that we're dealing with, we're going to take each family and let them represent one equation by themselves. So for C, I'm going to do the first one in all red, plus 2A, which is our adult, and that was equal to $28. And then the other family was three children plus two adults, and that was only $24. So now we have a system here that we could easily solve by elimination, because our A's have the same coefficient, we just need to multiply by a negative. So if I come through and multiply the bottom equation by a negative one, just because they're smaller numbers, then I'm going to have a new system of 4C plus 2A equal to 28. And my new equation is going to be negative 3C when I distribute, and negative 2A equal to, and don't forget to go all the way through, negative 24. Now I'm ready to add my two equations. And when I add my two equations, I get 4C minus 3C, so that's just 1C. My A's cancel out, and we're left with 28 minus 24, which is 4. So now we know C, and we just have to find A. Again, remember, you just plug it back into one of your original equations. I'm going to plug it back into the bottom equation only because it was a little bit smaller. The numbers were a little bit smaller. That's the only reason why. So 3 times my C, which is 4, and then plus 2A is equal to that 24. Well, 3 times 4 is 12 plus 2A equal to 24. And then I'm going to subtract my 12 from both sides, and 2A is going to be equal to 12. And if you divide by 2, then we find out that A is equal to 6. So if I write a nice little sentence, I would say that children, a child ticket is $4, and adult ticket is $6. So let's look at another example. Lori makes her own trail mix with her natural foods grocery stores. She makes a Spanish cashews costing $9 per pound, and almonds costing $7.50 per pound. If a three-pound bag costs Lori $24, how many pounds of Spanish cashews and how many pounds of almonds are included in the mixture? We want to fill in the table here. The white part is not the green one. This table will help us set up our equations. So we need to know the amount. We have our items here, so the cashews and the almonds. I already set that one up for us. So we want to know how many pounds of cashews. Well, that's what the question is asking. How many pounds of cashews and how many pounds of almonds? So those are our unknowns. So we're going to say that there's C pounds of cashews to keep it straight, and there are A pounds of almonds. But we do know that the total pounds, here's another pound, is 3. So really we have an equation here. We'll write it across, but up and down is C plus A is equal to 3. Now we need to talk about values. Well, the value of the cashews up here says that it's $9 per pound. So we have $9. And the almonds cost $7.50 per pound. So that would be 7.5. We don't need to have a value of the total yet, because that is in the next column. So now we have a total value that we need to think about. The total value here is the amount times the value is equal to the total value. So we have 9C, since we used to put the number first, and we have 7.50A. And then we have the total that we're spending, or the total value of that bag is $24. So again, we have two equations. This is our second equation. Up and down, we can write it also left and right. So C plus A is equal to 3. And 9C plus 7.50A is equal to 24, which I have right here. So now we have options. We could multiply the top equation. Probably the 9 would be the easier one to do by negative 9. And we could use elimination. Or we could solve A or C for A or C, and use substitution. The last problem we did by elimination. So let's try this one by substitution. So A looks like it would be nice to distribute into, because 9 would distribute nicely. So I'm going to solve for A. And this equation, I'm going to subtract C from both sides. So that gives me nothing on the left-hand side but A. And then 3 minus C on the right-hand side. So rewriting this bottom equation then for substitution, I have 7.5. I dropped the 0. It's the same thing as 7.50. Plus 9, but now instead of A, I'm going to write 3 minus C. And then that's equal to R24. Alright, doing our work then. 7.5 C plus, and then we're going to distribute here. And we're going to get 27. And distribute here and get minus 9 C equal to R24. So 7.5 minus 9 and negative 1.5 C. And then plus to 27 is equal to the 24. So track the 27 from both sides. Negative 1.5 C is going to be equal to negative 3. And if we divide by negative 1.5, that should be 2. So we now know that cashews cost $2. But we still don't know what our almonds cost. But remember we have this nice equation up here where A is equal to 3 minus C. And we can plug and chug again. So we have A equal to 3 minus, but now we know C to be 2. So that tells us that A is equal to 1. So putting it in a sentence then, cashews are 2 pounds and almonds 1 pound. To make the 3 pound mixture.


Hi, I'm JJ Joaquin and welcome to the third episode of Philosophy and What Matters, a forum where we discuss things that matter from a philosophical point of view. Now today's topic is a problem of persistence, the problem of explaining how things persist. Now here's one way of wrapping our heads around the problem. I've been driving the same car for the last seven years. Even that the car has seen many changes over the years, from its wheels to the fuel to its gears and so on, is it still true to say that it is the same car? Well, come to think of it, is it still true to say that I am the same person I was seven years ago? Now to guide us to this conundrum, we are joined by our good friend Chris Similler, an ARC fellow associate professor of philosophy, joint director of the Center of Time at the University of Sydney. So hello, Christy. Hello everyone. Okay, so let's start the ball rolling here. So I'll ask you, what do philosophers mean by persistence? Well, they mean that there is some good sense, the same object at multiple different times. So it's really just a technical notion for picking up the idea that there are at least some things in our world that exist at one time and that in some good sense those things exist at some other time as well. And in fact, most of the ordinary things around us seem to be like that.  Okay, so you're saying that some things do persist. So it doesn't mean that all things persist. So what's the difference here? What things do persist and what things do not persist? Yeah, it's a good question. And I guess that's sort of what's up for grabs in a way. So it certainly could be that there are entirely momentary things that only ever exist for a single moment of time. And in some ways you might think that's a kind of empirical question whether there are such things or not. But it seems like most of the ordinary things that we come into contact with, both the kind of micro and macro things. So ordinary things like cars and dogs and people and houses, but also subatomic particles and quarks and things like that. These all seem to be the kinds of things that exist at multiple times. They seem to be the kinds of things that we can trace through time and we can ask sensible questions about what was this particular thing doing back at some earlier time. And in fact, when you think about science, a lot of what scientists are doing sort of requires that there's some notion of the same thing over time because after what they're doing is kind of asking all various things where they were and what they were doing at previous times. And then the real the question then becomes how to make sense of this idea that things do exist at different times. So sometimes philosophers use identity over time or identity to time to refer to persistence. Is that right? And what does that mean? Yeah, so they do which is either a good thing or not. Sort of depending on how you think about it. So it's it's a natural thing to think right. So where the way I the way that we both kind of put this talk about persistence, it was in sort of fairly ordinary kind of language. So you said, look, this is the same car I had seven years ago, even though it's had various things done to it. My car is also the same car I had seven years ago. This is a very sad story for completely different reasons not to do with the system. OK. And. And so when we use the kind of phrases in English, like the same thing, the same car or I'm the same person, it's very natural to me that as being a claim about identity, that the thing that existed back there in the past is the very same thing as the thing that exists now. And in fact, you know, that would be if you heard that in ordinary talk, your kind of first stab at saying what's meant by that would be something to do with identity. So, you know, find a thing here, find the thing in the past and then notice that it's the same thing. And I think that's a pretty natural way to start thinking about these kinds of questions. And then it's a kind of open question. Then I guess what the right way to think about the use of identities. So the way that we were both just talking then, it seemed like the relevant question was, look, there's some object which is kind of located in the past and there's some object that's kind of located around here. In this case, kind of car-like thing.  I think later you're going to ask some questions about different accounts of persistence and we're going to see that different people take different views about whether that's the right way to think about where identity gets into the picture or whether there are better and different ways to think about that. OK, so why does this question matter? Why is it important for us to think about persistence? Yeah, so it certainly seems to matter whether or not there's some perfectly good sense in which things exist. So you can imagine somebody being kind of erytherist about persistence and saying you can imagine a kind of argument in which somebody tries to show that in fact there aren't any persisting things. So off the top of your head, we could probably create such an argument now we could say something like, well, what it is for your car to have persisted is for the car now to be the very same car as the car in the past because what matters is identity. But look, the car that you have now is not identical to the car you had in the past because like you've had breaks changed and so on and so forth. So it's not the same car. And then you could you could run this argument for any object that's changed and you could say, OK, well, nothing really persists. And that would be a kind of startling conclusion in philosophy. But you might think, look, that would actually be a pretty startling conclusion full stop because if it was really the case that in the very ordinary English sense of it being the same car now as it was earlier, if we couldn't even make sense of that, then like just tons of our very ordinary practices seem like they would not be in good standing. So, you know, if you if in ordinary English, we would be tempted to say that, you know, you now are responsible for some things that you did three years ago, you know, perhaps three years ago you ran into a lamppost with that car and caused a lot of damage to the electricity grid. And now the government is trying to find you in order to hold you responsible. They, you know, they want to take some money from you to fix up the electricity grid and a very natural way to think about that question about whether you're responsible, at least in part is we would want to ask the question, well, was that in fact you that ran into the electricity pole? So obviously just it doesn't follow from the fact that it was you that you are responsible, but it does seem to follow from the fact that it wasn't you that you're not responsible. But if you don't really persist at all, because we can't make any sense of this idea that you are the same thing now as you were in the past, then the kind of question about moral responsibility seems to be one that has no good standing at all, because there's just no sense in which you're the same person now as then, and that cause that sort of worry just generalizes across the board to all of the things that we might sort of care about. And quite generally, it seems like most of the ways we engage in the world are kind of engaging in the world in such a way that we think of both ourselves and other things as kind of temporarily extended. And that seems to be just kind of crucial in all respects. So when you think about not just about kind of moral responsibility, but think about kind of planning for what you're going to do at some future time. It's like, two of the kind of crucial things about that. One, it seems like crucial that you think of yourself as existing at some future time. And so you can reasonably ask the question, well, what, what should I do at that time? And that might be a moral shooter, it might be a prudential should. So you need to kind of think of yourself as continuing on. But it seems like you also need in some sense to think of yourself as having existed in the past, and of other things of having existed in the past. So if I want to reason about the kinds of things I should do in the future, I have to do that by thinking about the ways things were in the past. Otherwise, there's kind of no basis on which to make any decisions. So if I know nothing about what has happened up until now, then I have no basis to kind of choose one action over another. And so almost all of the things that we do every day are kind of grounded in some sense in this idea that the world around us is kind of a persisting thing and that we are persisting and that we have a kind of coherent life story that with these kind of temporal extended objects, and that all the things around us are kind of like that too. And it would be kind of deeply disturbing to our way of thinking of ourselves. If that turned out not to be true. So it seems like we want some kind of account of what persistence is. Yeah, so persistence really permeates in a lot of our decision making our notion of property as well, moral responsibility. But how do philosophers think about this there are two wildly held philosophical views, right? So about the nature of persistence, you have the endurance disposition, or the three dimensional view, and the bergerent disposition or the four dimensional view. Now let's focus first on the first view, the insurance position. Now you you labeled this or a lot of philosophers label this as the three dimensional view. So what's what's going on in this view? Yeah, so in some ways, this is probably the natural way to think about persistence. And in fact, there are ultimately, there are more views than this, because as philosophy goes on, people create new, new all different kinds. But as you say, these are the kind of two natural starting points. And this is probably the most obvious. So when we were initially talking about persistence, and your car, the sort of one very natural way to think about what's going on there is to say, Well, look, here's your car, like that's we can go outside and point to it and be like, Okay, there's your car right there. And now we can, we can sort of mentally time travel back in time, we can imagine there was your car back there at some previous time. And we can ask whether the car back then is the same power as the car now. And so we're asking about a kind of identity relation between something that exists in the past and something that exists now. And the things in question kind of thought of as being what philosophers sometimes call holy present, or they're the kind of that all of them is there. So the idea is that when we walk outside, you know, you're trying to sell your car, you take a buyer up, you say, Here's my car. And the idea is that you're kind of showing the buyer the whole of your car, like here it is, you can take it away. You're not just showing them some bit of your car, as you would be, for instance, if you took them outside and you just had the bumper bar on the pavement, you're like, Here's my car. And they'd be like, Whoa, wait, wait, that's not right. And so it's a, it's a fairly natural view that sort of all of your car existed at some previous time, and then all of it existed the next time, and then all of it existed the next time. And then the interesting question is, if it's the same car, then there'll be a kind of identity relation between each of those car objects, because it's the very same car effectively just at different times. And the reason people call it sometimes three dimensionalism is the idea that your car is really three dimensional. It has these, it's extended in, in space by having, you know, length, breadth and depth. But it's not extended in some sense in the temporal dimension, rather, it exists, all of it exists at each moment in time. Okay, so the idea here is that physical objects or macro physical objects are three dimensional objects. So they're located in space. And as they move through time, the whole, the whole thing moves through time. Is that idea there? Yeah, so that's roughly the idea. And I think sometimes people definitely put the idea as the whole thing moving through time, which I think is a natural, again, a kind of natural value to put it, although it could be, it could potentially be misleading. So I think sometimes people then read that as the view that sort of like, imagine all of space timers is kind of carpets. And then we imagine we take your car and they think of this idea that the three dimensional car is moving through space time, they imagine that what we should do is sort of imagine putting the car into the couple of space time and then sort of moving it along. And so we're imagining is that when we look down on the couple of space time, first we don't see the car at one time, and then the car sort of appears at that time. And then the car leaves that time and it arrives at the next time. And it's sort of so we're imagining the space timers in a little bit like the way we imagine a road outside our house, you see the house and there's no car on it and then a car arrives and it kind of zooms past and then the car is gone. But on many views about time, that's not quite the right way of thinking about that view, which is why some people will now talk about this view as a kind of multi-locationism view, rather than talking about it as endurantism. So on that way of thinking about things, if we imagine looking ourselves kind of looking down at the great carpet of all of space time, what we in fact see is that kind of all of the car is located at on Tuesday, say, and then all of the car is located on Wednesday and all of the car is located on Thursday. And so when we look down what we see is that the car is at all of those different locations. But what makes it the case that endurantism is true is that, as you say, the object is merely three dimensional. So it's literally multi-located in the way that some people think that universals are multi-located.  And so one way of thinking about that is this is kind of universal redness, and it's located both in the couch and in the garbage bin. It's sort of holy in the in the garbage bin and holy in the couch. And that's why the garbage bin is red. And so is the couch. And this way of thinking about persistence is a little bit like that. It's like, it turns out that objects are a little bit like universals in the sense that they can be holy in multiple different places. So the car is kind of, it's wholly located at one time, and then it's wholly located at the next time, and it's wholly located at the time after, but it's not in any real sense moving through time, at least on many kind of pictures of a kind of eternalist model. Yeah, so I'm trying to get a picture of insurance system here. So here's an object located a particular space time. And then that thing vanishes in that location and moves wholly in another location. So what guarantees that these two things are identical according to this picture? Yeah, I think that's not the right way of thinking about it. So I don't, unless you have to have some quite odd view of time. So I think there's no sense in which the object vanishes from the previous location, right? So that really would be a view on which things move through time the way that cars move along the street. Rather it's the view that, so it's not like redness moved through my couch and into my garbage bin.  And then it like moves back to the couch. So on that view, there's no sense in which the car moves locations, rather, you know, there's just a static set of locations. And the car is wholly located at one, as well as wholly located at the next, as well as wholly located at the one after. And it's not, it's not moving locations, it's just, it's literally multiply located. Okay, but what guarantees the identity of that thing? Ah, right, yes. Yeah, so that is a good question. So yeah, so the question is sort of what makes it the case that the thing that's multi-located is the same thing. Is the same thing? Yeah, that's right. And that seems like a difficult question to answer in a way, because we typically think of kind of identity as primitive. So if you ask, like, so if I were to ask, like if somebody walked up to you on the street and said, so why are you self-identical? Like you would be super puzzled, right? And you'd be puzzled that they asked the question, but you'd also be deeply puzzled about how to answer that question. Because you're like, look, identity is not the kind of thing, you can't kind of ask a question, like, why is everything identical to itself? Like that's just sort of a primitive matter of fact. And so if you think of identity that way, then the question, why is the car here on the car here the same car? On the one hand, it looks like a perfectly reasonable question to ask, because we can imagine they weren't the same car. On the other hand, it's like a difficult question to answer, because you seem to be asking a kind of question that in some sense looks like it doesn't have an answer. So I guess some endurantists are going to say, look, there are kind of, even if identity itself is a kind of primitive matter, so it's just a, it's, there's no, there's no good answer to the question, why is this thing multi-located, rather than it being distinct things? They might still tell some story about how it is that we come to form reasonable beliefs about this. So, no, I meet you today and then you call me up on Zoom tomorrow and you look very similar and you appear to have similar memories and so on and so forth and the endurantist can say, well, look, sure, there's no answer to the question, why are you now, and that person then, the very same person who's multi-located, but they might be able to tell some perfectly reasonable question about how I come to the belief about that. Namely, I look at the fact that there's a lot of similarity between you and I might look at the fact that there's a kind of continuous spacetime connection between the you now and the person I talk to tomorrow and so on and they might say that this all gives me some kind of defeasible evidence for the fact that it's one and the same object that's just located at different times. Okay, so another review that philosophers have, most philosophers have is the pre-durantist view or the four-dimensional view. So how should we understand this view? Yeah, so the view sort of, I guess one way to think about the view is to think, is to kind of motivate it a little bit. So I said a bit earlier that you can imagine someone being kind of an error theorist about persistence by thinking something like, well, look, you showed me your car yesterday and then you showed me what you said was the same car today, but look, since then, various things have happened to the, you know, it isn't the same car, right? In some good sense it looks like it's got, you know, it's got more miles on the odometer and it's got new dirt on it and various things. And so that person says, look, how can it possibly be that the thing now and the thing then are one and the same thing? Because identity is a relation that everything bears to itself such that, you know, if it's more identical than they have all and only the same properties. But we've just said that your car now has different properties to the car yesterday. And so obviously they're not the same car, right? And so the perjurantist is kind of motivated by that worry, the worry that it couldn't be that most of the ordinary things around us are persisting by being identical through time because, in fact, those things are changing all the time and so they're changing their properties. And so the perjurantist says, okay, well, look, it's much more sensible to think that the car yesterday and the car today are actually distinct things. But obviously they bear an important kind of relationship to one another and they bear some kind of important relationship to this thing, which is your car. What could that be? Well, an actual thing to think is it's sort of that your car turns out to be this thing that's extended through space time. So it's instead of thinking that it's wholly located yesterday and wholly located today, instead we think of the car itself as kind of pulled through the fourth dimension. And then whenever we see your car, we're really just seeing a little bit of the car. And so that can then accommodate the idea that the various different parts of the car can, of course, have different properties consistent with this, you'll be one whole thing that is made up of those properties and is identical to itself. So no one's going to be worried by the fact that your left hand has different properties to your right hand. Only something like, oh my god, wait, how can it be that you're this whole thing that's kind of extended through space because, look, your left hand is different from your right hand. You'd be like, yeah, look, dude, that's okay because what happens here is, look, I'm made up of my left hand and my right hand and my head and well these various other parts. And I'm sort of the aggregate of all of those things and of course my different parts have different properties. That's actually quite important because if they didn't have different properties, things would not go well for me. And so the purgerantist just says, look, it just works exactly the same in time as it works in space. In space, we just naturally think that you are extended through the three spatial dimensions by having all these different parts that come together in various different ways. Why would we think it's any different in time? Well, in time, you just have all of these parts that come together at different times and create this large cross-temporal thing, which is you. So you are the person I'm, the thing I'm talking to now is not all of you, it's just some little bit of you, namely the Monday bit. Okay, so let's try to figure this out. It's hard to fathom. So aside from the spatial parts that you have, according to this view, you have also temporal parts. What's the motivation there? Why say that there's a temporal part aside from the spatial parts? Yeah, so I guess the motivation is, I mean, there are many, but the prime one just is this idea that the things, the things that exist at different times, the three-dimensional objects, let's call them. So it's pretty clear that there's a three-dimensional object, which is you now, and there's a three-dimensional object, which we want to think of as being you like three seconds ago, and the endurantist wants to say that it's the very same three-dimensional object that exists at each of those times. And what the purgerantist is going to say is no, there are these two, there are two three-dimensional objects, but they are distinct. That's why there's two of them. And the motivation for thinking that is just the fact that, well, maybe not just, but is definitely includes that the three-dimensional object that we are seeing right now is different in various ways to the three-dimensional object we saw three seconds ago or three seconds before that. And so it's very hard to make sense of the fact, it's hard to make sense of how a three-dimensional object here and a three-dimensional object here can be the very same three-dimensional object if like this guy is different from this guy. And so the purgerantist just says, well, obviously they're not the same guy, right? They're two different guys and what they are parts of some larger whole. Okay, so I'm trying, I'm still trying to get to get a grasp of these two positions. So the insurantist would say that you are the same thing over time because you are collocated at those different times. Okay, so you are identical to each of, you know, let's call it the time slices of you. Yeah. Then the purgerantist would say, nope, that's not the case because the whole you is just the sum of your temporal parts and your spatial temporal parts. Is that the thing you're in? Yeah. Okay. Right. Yeah. So what are we? Are we perjuring entities or enduring entities? Are we treated well? I don't think there's any, I don't think there's any broad agreement on that. I mean, I think that the two camps, the endurantist camp and the purgerantist camp, are just still debating with one another about this and it's a little bit difficult to see what sort of evidence you could bring to bear on this because things are kind of sort of going to look the same regardless of which view is right. So, you know, everyone agrees that every time we meet you are going to meet a kind of three-dimensional thing and everyone agrees it's going to have some sort of properties and even the three-dimensionalist or the endurantist agrees that the properties you have now sort of manifest differently than the properties you had like 10 years ago. So that's not like the, it's not like the endurantist is committed to saying like you've always been exactly the same as you are now, like you weren't born as a baby or like you just suddenly appeared as you are now and you're unchanging because clearly that would be a view that's massively falsified. So they're all kind of committed to the same apparent phenomenon it's just that they're going to account for them in somewhat different ways which I guess is why it's going to be a difficult debate to resolve and so there's nothing that you can really point to in the world I think that will vindicate one view over another it's going to come down to things about sort of simplicity and explanatory power and all these sorts of features that we use to determine which kind of metaphysical view is the more appealing view and I guess the thing is that endurantist and perjurantists sort of start things with quite different intuitions about what they want from the theory and what is what constitutes simplicity and the role how much they care about whether it seems like a view that sort of fits with the more everyday notion of persistence and because they come into the debate with somewhat different views about what they want they therefore end up with different views and it's then almost impossible to sort of resolve I mean I don't think anyone's going to declare a winner in this debate anytime soon all right right so so speaking of explanatory power so these two positions try to account about certain puzzles in the philosophy literature in persistence and constitution one intriguing philosophical puzzle is J.J. Thomson's this statue in the lump case so what is this puzzle all about yeah so so she sort of started us off with the statue in the lump and then there have been various permutations of this puzzle where people have messed with it in various different ways but the simplest case she started off with is a case where you start off you've got some lump of clay which is just as a lump and it sits around for a while in your basement while you you know do your administration and then you take your lump out at some point and you form it into a statue which we can there see and then we can imagine that somewhat later so maybe if you don't fire the statue in a kiln but it just sort of stays as clay you can imagine that something befalls the statue so that it gets returned to being a block of clay and so there are these kind of interesting questions about what is the relationship between the clay like this block of clay which we call clay and the statue which you can call statue on the other hand because what the thing we're looking at right now looks like it's both a kind of it's not exactly a block of clay but it's clay and it's also a statue and it looks like we just so you know if we just saw that picture and we were asked how many things are there I think a very natural response would be to say well there's one thing there it's the it's the statue but what the the case sort of draws attention to is the fact that look at this moment it looks like there's this one thing which is a statue that's kind of made out of some clay but when we think about the whole story about how this came into being we see that well that very thing which was kind of the clay looks like it existed before the statue ever did so it sat and we know I can say to people look the clay sat in my basement for three months while I refereed papers and only then did I find the time to form it into the statue which is which we now known as you know now know a statue and so what Thompson points to is that we we seem to have some kind of incompatible or at least intention intuitions about this case so on the one hand we have the intuition there's just one guy there which maybe we we want to think of a statue but on the other equally we sort of had the intuition that the clay Jesus someone at the door Annie stop it we have the intuition that the clay existed before the statue ever did and so given given what we given our other views about identity which is that you know two things can only X and Y can only be identical if they share all the same properties and exist at the same places and so forth that's his puzzling because it now it seems like we're going to be pushed to say that there's really two things there's the clay and then there's the statue but if there were if there are two things then it looks like what we're actually doing here is looking at two objects we're looking at both a clay object as it were in a statue object but then then we are kind of led to other puzzles like well well hang on how can there be two things located at the very same place and time because it looks like the clay and the statue are at exactly the same location and we're also led to other puzzles as well so suppose you you're saying yes of course there's both you know a thing of clay and a statue there then there's this kind of other puzzling things which is well even if we set aside the problem about how they can be two things at the same place and time we now have this other problem which is well they look like quite different things like the statue is a kind of a quite different thing to a lump of clay how is it that they end up with these very different properties given that at this snapshot in time they occupy all and only the same places so we see so this is a kind of case where at all turns we led to kind of puzzles about what we should say yeah so how would the an endurance this we solve this puzzle or for that matter how would the prejudice account for it as well yeah so I guess so I'm trying to think whether there's a the resolution of this puzzle is kind of determined by what view you take it there's certainly a kind of orthodox way that Endurantis will think about this and an orthodox way that Perjurantis will think about this I'm not sure that they're force always forced to think about that that way but many perhaps all Endurantis are going to think okay look so at some point this object came into existence which was the clay and it you know persisted for some period of time by enduring and then at some later you know time it got formed into the statue and at that point an additional object came into being which was the statue and so for some period of time thereafter they really were too enduring things present at the same which was the statue on the one hand and the clay on the other and so they're just going to I don't know if it's a bullet but they're they're just going to say look kind of the ordinary way of describing this actually is the right way to describe it there really are just two holy present things located at the time which are the statue and the clay and they're they're going to have to try and tell some story about exactly how that's meant to work but that's going to be the kind of natural thing for them to say whereas proterantists are going to say well typically going to say something like something that looks a little bit similar but is a little bit distinct so they're going to say well look the clay and the statue are distinct four-dimensional things so the clay is a four-dimensional thing which comes into existence at one time and has a four-dimensional life and ceases existence at whatever the kind of later time is and the statue is also a four-dimensional thing but the statue is kind of a sub portion of the the clay so so think of it Lewis has this nice analogy about roads so they do this with many roads in Australia this is kind of a long stretch of road and then there's some sub portion of the the long stretch of road has a name it'll be like the A39 or something and then there'll be some sub portion of the road that goes through some little town and in the little town it'll also be known as High Street or whatever which can be endlessly confused and so the the proterantists is going to think about the statue on a clay a little bit like our street they're going to think that the the clay is kind of like the Long Street the A39 and the statue is kind of like the High Street which is some little part of the road and it might be that the High Street has somewhat different properties than the the whole road right so it might have you know it has lots of cute little shops on it whereas the A39 doesn't always have cute shops and so yeah they're going to say look all that's going on here really is that one object which is the statue is a kind of proper part but a proper temple part of the one object which is the clay okay so I remember that article so David Lewis uses the Yume Highway I think in Australia it's a whole street yeah okay so you have the adjuvantist position that tells you yep let's accept the conclusion that there are two wholly distinct objects there in the same space-time location for Lewis and the other orthodox adjuvantists they'll say well the lump and the the statue are just part of the whole thing one big space-time worm and they're just temporal parts of that thing is that what you're yeah I guess yeah so the crucial crucial thing I guess for the adjuvantist is so we're looking at just one at the moment that the image you have now is like looking at one temple part of this the whole thing and the the adjuvantist has to sort of say or is almost certainly going to say actually what we're looking at is two distinct objects we're looking at both a clay or the clay and the statue whereas the adjuvantist is going to say no there's just one thing here that we're looking at which is a temporal part and we can call it you know we call it Felicity and is just one she's just one thing and we're looking at her here of course and she is both a part of clay the kind of long extended thing and she's also part of statue the slightly shorter extended thing and so what adjuvantist is going to say is nice about their view is that they don't have to say that we are right now looking at two numerically distinct objects that are just located in the same place we're just looking at one thing Felicity and it just happens to be that Felicity is part of two larger objects but there's kind of nothing puzzling about that in principle so we know of course that there can be objects that are part of two other larger objects that's there's nothing there's nothing weird about that and so they don't have to answer the question which is a kind of puzzling question which is how could there be two things two completely distinct things located at the same place in time okay so yep there's another philosophical puzzle about persistence this is the famous fishing case by Derek Parfit I think the original one came from Denny Robinson Denny's Robinson I think okay so what is this fishing case all about yeah so people set up fishing cases in lots of different ways but let's sort of make it so like Fission can vent that takes what looks like one object and then spits out two objects that each share the same kind of relation with the previous one so imagine so Star Trek is a is a good case because it gives us lots of cool technology to work with so you know imagine we've got Will Weicker and we're going to change this from a little bit from what actually happened in Star Trek but imagine you know he gets into the teletransporter and we all know how it normally works that you know vaporizes him at one end and creates creates him out of matter at the other end but let's suppose that the teletransporter misfires in some way so it does in fact destroy or whatever it does to your body at the end that you get in you know he beams up but the teletransporter instead of just creating Weicker at the other end like reforming him and in fact it creates two versions of him and the two versions are exactly the same in the sense that they just made you know they're materially the same they're made up of the same kind of stuff they've got all the same memory so from his perspective he gets into the teletransporter and then what comes out are just kind of two two Rikers that are when they initially step out they're exactly the same and they bear exactly the same relationships to the Riker that got in and so that's that's kind of what fission is it's any kind of process that generates something like that and you can do it in all sorts of ways and it's obviously going to make make for philosophical puzzles because under the normal course of events you know Riker gets into the machine and then he gets out of it at the other end and we say okay well what happened here is that this was a great way for Riker to travel because he travelled you know 20 light years just through this teletransportation and we have one Riker who persists he gets into the machine and then he gets out at the other end but as soon as we get two versions of him appearing at the other end it looks like we've got all these kind of puzzles which is well hang on the first thing you might ask is like imagine you're married to Riker you're on a spaceship you see them both appear and the first thing you might think is well which one is my husband right like which one am I married to and that seems like a difficult question to answer because they look like they're exactly the same so you're on the one hand you seem like you have intuitions according to which they're both Riker right it seems like if teletransportation is the kind of thing that transports you from one place to another it seems like what's happened here is just that we ended up with two Rikers right it seems like he kind of survived twice over but so it seems it seems like if if before getting into the teletransporter he did something heinous and we wanted to punish him it seems like we should be punishing kind of both of the people who get out because after all they both seem like they are equally good deserving to be Riker so that's kind of one potent intuition on the other hand it just doesn't seem like identity works like that so you know identity is a kind of one-to-one relation it's the relation that we all bear to ourselves and to no one else and so it doesn't make any initially at least it seems like it can't be that both of the people who get out are Riker because if they're both Riker then they're identical to one another so you know if S1 and S2 each both S then S1 and S2 are both equaled you know identical but you know there they are standing next to each other for all the world they look like they're two distinct persons right so now it looks like we are kind of in a in a puzzle here because we on the one hand we seem to want to say that Riker survived as each of them and so that they're both each of them is Riker on the other hand it seems like we definitely don't want to say that because they're not the same person as one another like there's two distinct persons there it looks like and so it seems like we're sort of damned if we do and damned if we don't in that case that's the puzzle okay so how would an injurantist account for this in a projurantist as well yeah so there's different things you could say as an injurantist so I guess in many at least in some ways vision cases for persons are kind of particularly puzzling because they seem to undermine certain views about personal identity so I think it's a very natural view to have about persons that what makes you the same person over time is something to do with the fact that you you're kind of causally connected across time and you have the same sorts of psychological states or there's kind of continuity of psychological states so I'm tempted to think that like if we abducted you now and we wiped your memory and we changed all your values and we completely reprogrammed you with you know you fake memories that the thing that exists after that would no longer be you because not everyone not everyone believes that but at least it's a it's a sort of I think a natural starting point and so the vision case is meant to be particularly puzzling for these kind of views because it's pretty clear that the two rikers bear the very same kind of psychological relationships to the previous riker and so a natural thing to say if you're an injurantist there are there it's look like there are kind of only three options available to you right and none of them none of them sound that great so one option is to say well look which is something that Parfit sort of says so you might say well because identity is a one-one relation it's true that riker would have survived he would have been this enduring thing that had got out of the tele-transporter if it had functioned normally but unfortunately because it misfunctioned and it created these two kind of apparent rikers it turns out that this was actually the death of riker because as soon as you get something like that you no longer have psychological you know psychological continuity has to be in order to support identity has to be kind of one-to-one and so as soon as that fails identity fails so one one one view the endurantist could have is simply that s is not identical to s1 or to s2 so this was this was riker death and so you can see why you would end up with that position a second option would be to try and say that to identify s with either s1 or s2 but not not both so you'd have to tell some story about how riker survived but he's only one of the post teletransportation entities but that's kind of a difficult story to tell because it's there's sort of nothing to just like they're exactly the same so that that's kind of an odd thing to say so people at Parford for instance think that what this shows is that the identity relations not really the interesting and important relation what really matters is this kind of psychological continuity and so although the the riker that gets in is not identical with either of the rikers that gets out that's not really what we care about what we really care about is just this kind of psychological things and so that's all fine for riker like he shouldn't be too worried about this even though strictly speaking he doesn't persist and a third option would be which not very many people have defended would be to actually just say yes look riker does in fact like there are there is this there is a kind of riker before is identical to both of the kind of rikers that get out so this is a to say this you have to embrace some kind of weird consequences right so on the one hand it kind of seems intuitive to think that each of the rikers that gets out of the teletransporter is kind of identical to the riker that got in but of course given the transitive and identity you then have to think that both of the rikers that get out are identical to one another so of course you can say this if you're an endurantist because you're working with this kind of multi-location view so what you can say is well look on a if things had gone well with teletransportation riker would have been multi-located at all these different times he would have been here and here and here and here and here and here and here and if you're an endurantist you just seem like maybe that's weird but if you're an endurantist like that's the view you've signed up for and you think that's you know you think that's a good thing so what happens in in fission is look it's a little weird but instead of being multi-located at different times you're also multi-located at different spaces so what happens is he gets in to the machine and he gets out and he's located multiply at the same time so each of the there's really there's still only one riker but he's both here and here and then here and here and then here and here and it's not so that's not a view that very many people have defended but it seems to me that once you have multi-location there's no reason why you can't have that view so it doesn't seem to me that once you've signed on to think that things can be multi-located at different times why couldn't they be multi-located as it were at the same time so that's that's another view that you could go with if you're an endurantist to try and figure out that case and that has the not okay so I'll so yeah I'll just summarize the three options for the insurantist so the insurantist would account for fission in three particular ways so one way is to say that neither survive neither of those two will be your were continuing so to speak another option is just pick one so it's either this guy or that guy or finally it's both of them of course there are counter those are counter-intuitive intuitions sorry so how about the pejuantist so how would they account for this or yeah so so this is a a nice place to come back to kind of Lewis's road analogy again so imagine instead of having one big long road the a39 which has a sub portion you know the high street which goes through your little town imagine instead you've got you know the high you know who followed the highway along and then at some point the highway kind of splits into two in fact that this almost looks like a highway splitting into two here and so you know people as kind of perjuring things then what happens is that prior to the kind of fusion episode what we have is one big long segment of the like a life which is just you know one kind of piece of spacetime worm and then once he gets into the the teletransporter machine the kind of the worm splits into two sort of two heads and so the the two worms that then shoot off from there are of course distinct from one another but so we end up with two persons also you've kind of labeled the two ends of the the pigeon thing S1 and S2 and then we've got S earlier and so one worm includes all of S1 plus S and the other worm conclude includes all of S2 plus S so what you have is kind of two four-dimensional things but they share a beginning in life so it's sort of it's like S1 and S2 that the two Rikers we can call them Ryker one and Ryker two Ryker one and Ryker two shared the very same life up until the teletransportation they were made up of the same piece of a four-dimensional worm and then the worms kind of split and so we get to preserve quite a few intuitions here because we get to say that what happens after the teletransporter is that we have two people well that's absolutely true we have Ryker one and Ryker two and they are indeed distinct people but we also get to say that prior to that there was just one thing there was this one thing which was S because it was just made up of all of the same people but so in some sense Ryker one and Ryker two have always existed but they've always existed only in the sense that they shared some part prior to fission which existed and so as you can see there are some nice features of that view because you you can both vindicate the claim that that's sort of the products of the fission are distinct things but also vindicate what seems quite plausible that there's some perfectly good sense in which the guy that got into the machine survived this procedure and kind of survived as two different people and you get to say that on this view No well I'm trying to wrap my mind around this one so prior fission or prior the teletransportation thing there is already two people there or there are two people there present in this or what's going on in the picture yeah so some people find this deeply puzzling because as some people will kind of frame this as an objection which is look there's something totally weird going on here because prior to the fission there were these two people but you could kind of only see one guy with Ryker and what's more if he hadn't got into the machine there would only have been one guy this one Ryker but then there's this kind of weird thing it's almost like retrospective causation it's because later he gets into the machine that it kind of makes it the case that there were these two guys even though they look like there was one guy and this is really weird and I think if you describe the case like that it does sound really weird it sounds like in the world in which he hadn't got into the machine there was just one guy but then because he got into the machine it somehow made it the case that in the past there were in fact two guys even though it only looked like there was one guy and you're like wait this is weird but I think that that's a that's kind of unfortunate way if you're a progerenter that would be a very unfortunate way to describe it so I think it may be a better way to think of it is to give all of the temple segments kind of names so imagine that this is taking a temple segment which is you know everything that we would naturally think of as Ryker up to the time of the teletransportation and we could think of this as being called s in your diagram and so in answer to if you want to ask answer the question how many things are there up to teletransportation in some perfectly good sense the right thing to say is well there's just s right it's not like there's obviously your s has lots of parts but there's just this one thing s and it's not it's not the case that there are like two people kind of mysteriously there or rolled into one or two people that kind of come into existence once teletransportation happens there's just this one big four-dimensional thing which is s but when teletransportation happens what happens is that s kind of gains new relational properties so it turns out that s becomes a part of two further things which is the kind of sum of s1 and s and the sum of s2 and s so it's not like suddenly it becomes the case that there were two Rykers there all along which would be deeply puzzling instead it's simply the case that there are these two four-dimensional worms one is made up of s1 and s one is made up of s2 and s and s1 is Ryker s1 and s is Ryker 1 and s2 and s is Ryker 2 and so in ordinary English we might say something well both Ryker 1 and Ryker 2 existed prior to teletransportation which of course is true because they both had a part that existed prior to that but there was just the one part there it's not a Ryker 1 inside a Ryker 2 kind of screaming to get out like and really like two people there it's just the one thing there which is s and so there's kind of nothing serious about there being one thing such that later on new stuff comes into existence and that one thing turns out to be parts of multiple things right so imagine you're you kind of you build a wall and you call the wall jasmine and then later you build two more things which are you know two other walls and then it turns out that jasmine is both part of the kitchen and part of the laundry and so you know she ends up having these two different part of relations and no one it's like wait there's something kind of deeply puzzling here because before you bought you built these extra two walls there was just jasmine but now somehow jasmine's part of a kitchen and she's also part of a part of a laundry someone's just like yes but there was there was jasmine and then she got these new relational properties when you built some more kitchen and some more laundry but there's not like described that way there's kind of nothing it's not like prior to doing more building there was really a tiny kitchen and a tiny laundry both kind of inside jasmine just fighting to get out and then later they got out it's just no there was just a wall that was jasmine and that wall subsequently became part of both a kitchen and a laundry so that's how the pejorantist is going to describe that kind of face okay so your big idea which I read 10 years ago that's why I were here so your big idea is that these two things are metaphysically equivalent what do you mean by this metaphysical equivalence of the 3D and the 4D view so in general I take metaphysical equivalence to be something like the claim that uh so you know imagine that there so imagine you're looking at a possible world because you sort of have cryptian telescopes to look at your possible world so you know you and I are looking at a possible world and you describe the possible world using one kind of set of language and I describe it using a different set of language to kind of talk about what's going on there but if we're talking about the very same world and we're just describing it differently then I'll say that the two things that we're describing are metaphysically equivalent so really it's just a fancy way of saying look there's just one kind of phenomenon here and one person is using one kind of language to describe it and another person is using a different kind of language to describe the very same thing and so they might mistakenly think that they're disagreeing with one another because one's saying one set of sentences and the other saying a different set of sentences but if they're actually just describing the very same bit of reality then it turns out they're not really disagreeing at all they just they merely kind of appear to be disagreeing and so the thought I had way back when was that you might think that the Endurantist and the Pergurantist are just like in that same boat but there's really just this kind of one phenomenon of persistence and that the Endurantist is using one set of language to describe that and the Pergurantist is using a different set of language to describe the very same thing and you can kind of translate between them and I think maybe the easiest way to see that or to think about that whether or not you think it's true is something like look both of the views kind of agree that we can find you the three-dimensional object at all of these different times so we find you know you here and the three-dimensional thing here and the three-dimensional thing here and the three-dimensional thing here and the three-dimensional thing here so everyone agrees that we can kind of describe reality like that and then the three-dimensional says look each of those three-dimensional things is really the very same thing, multi-located, but the purgerantist says no, they're numerically distinct things, and you are the kind of, um, some of those things. And you can sort of see how you would start to translate between these kinds of views if you thought, um, actually there's, uh, there's no sense in which one of those views is right. Um, they're just different ways of describing the kind of the same underlying reality. Yeah. So that, that was the thought. And I think, um, I can see taking different views on that these days. Um, now that we've got more of a kind of, um, multi-locationist, uh, framework set out, I can imagine someone saying, look, you can really easily distinguish the difference between the same thing being multi-located versus there being these distinct temple parts. Um, but yeah, you can, but, but in theory, you can kind of provide a kind of little translation manual between these two ways of talking about the world. Um, and so that might lead some, but it's someone to think, yeah, look, you're just really using two different kind of metaphysical perspectives or languages or something to describe the very same way things are. So I, uh, when I first read your award, you know, 10 years ago, I think I was thinking about it in terms of a meta-metaphysical thesis. It's about how we do metaphysics. So what you're saying here is, here's a 3D view. They have a language. Here's the 4D view. They have a certain language. And there's a way to translate between those two languages. But I think that that's, that leads to a kind of meta-metaphysical thesis we're in. Well, there's nothing really substantial in the debate because it's just a matter of how you describe things. Is that the thing going on here in your thesis? Yeah, yeah, that's right. Yeah. So I mean, that doesn't mean there are no interesting substantive questions, but yes, there would be nothing substantive in the debate because, um, I guess the fundamental take home would be that they're not really disagree. They immediately appear to be disagreeing because there's no, um, it's just using the very, it's just using different language to describe the same way things are. So yeah, it's for a kind of meta-metaphysical position that there's not really a disagreement to be had here. No, I wonder if you could extend this metaphysical equivalence to other debates of metaphysics, like between the compatibilist and the incompatibilist, or between the universalist and the nihilist. Could you use this kind of framework to settle, quote and unquote, their disputes? Yeah, so there's certainly other areas where people have made similar kinds of claims. So, uh, I guess what you have to show is that there is a kind of way of translating between these different languages. Um, and also that, so it's not, it's not quite, it's not quite enough that you can just come up with some translation between them because that's going to be maybe relatively easy. Um, but you have to show that it's a kind of, um, it's, there's something plausible about translating their claims in this way. So I'm not sure whether you're going to be able to do that for things like compatibilism and incompatibilism, but certainly arguably you can do it for other, for other areas. So I think a notable one is something like marriological nihilism versus some kind of compositionalism. I think in a natural, so people have certainly made this case that this, this is not really a genuine dispute at all. It's a kind of meta-metaphysically, you can kind of deflate it.  And then Samantha says, um, yes, all there are are atoms arranged table-wise, and there are tables, and you're going to provide some kind of way of, um, kind of translating between them so that, um, you, assuming you can do that and some various other things hold, you might think that it's not really a substantive dispute at all. So, yeah, various people have tried, have attempted to make that case, that dispute too is not substantive. Okay. So, uh, I'm not sure if you remember, but my first, uh, well, my first attempt to do international philosophy is at the University of Sydney. So, I emailed you if I could give a talk in your university. You said yes. So, you gave me a break in international philosophy, but I have a question about what is, what is it like for a woman? So, I'm an Asian, of course, going to Australia and presenting a paper in your university, but what is it like for a woman doing professional academic philosophy today, like you? Yeah. I mean, I think different people have very different stories to tell and perspectives on the matter. So, I think there's probably no one unified, like, I'm sure there's no one way that it is to, as it were, depending on who you had sitting here on this blue couch, you get lots of different questions to that question, I feel sure. It's certainly true that the numbers of women in philosophy are, particularly as you get, you know, further up the professional ladder, as it were, that they are underrepresented and particularly in certain kinds of areas. So, that suggests that there's something interesting going on there about why it is that this is kind of under representation and why it's kind of area driven in certain kinds of ways. So, I have to say, like, sort of from a personal point of view, I have found, generally found philosophy pretty welcoming of women, although I know that's not everyone's, you know, that's certainly not the story that everyone tells. But yeah, I think in general I've been pretty lucky. I think maybe what this points to is that your experience of philosophy as a woman may be kind of quite highly contingent on where you happen to be and who you happen to be with. So, it may be that different people have very different stories because there's no one overarching way that it is to be a woman in philosophy and there's no one story about what it's like rather. There are lots of different kind of located stories and that your experiences vary a lot depending on what you're doing and who you're with and where you are. So, yeah, I think in general I've found philosophy pretty amenable to women, sort of where I am. But it's certainly still true that there is this kind of under-representation of women in various different areas and so it'd be really interesting to do some more work trying to figure out what exactly is the, why is that, what is the kind of underlying cause and is that something that you want to try to take action to change in various different ways? Yeah, because you have a recent paper on how women in philosophy are treated in Australia with Sam Barron. What is that paper all about just for our... Yeah, so Sam, Tom, Doherty and I did some experimental work, not on professional women in philosophy but on targeted kind of undergraduate students. So, we were interested in some hypotheses about why it is that you get differential representation even at undergraduate level. So, what you tend to find is that you have at least 50-50 men and women at first year, in fact, often it's slightly more women than men and then the numbers just sort of gradually drift towards more men and fewer women so that by the time you've got to honour, you already have significantly more men than women in philosophy and then at graduate level that differential increases again and then at staff level, you know, it's a little bit more even for early career researchers but the gap broadens again as you sort of go up. So, you get this kind of ever-broadening gap so it just sort of starts off even and then they go... There have been various hypotheses about at least at undergraduate level why you see this kind of drop-off of women and so we were interested in testing these hypotheses. So, there's all the kind of hypothesis you would naturally come up with which is that, well, is it something about the modelling? Is it that they see more male philosophers teaching them? Is it something about the kind of content that's been delivered? Is it that the content is somehow more interesting to men or is more targeted to men in some way? Is it something to do with how women feel in discussion? So, there's been all of these hypotheses out there about why you might be getting this drop-off and so we run an experiment. Basically, students come in, we have massive thirsty classes so they come in and we give them these bunch of surveys about how they're thinking about philosophy and how they're feeling and what they're planning to do and so they've never had any philosophy up to then so we kind of get them before they've had any experience of teaching so they're kind of they're not, you know, biased. Yeah, so they have no views yet about what philosophy is actually going to be like. They haven't had any philosophy so they do them very first day and then we retest them again at the end of the course so we ask them lots and lots of different questions about how they're feeling about things and then we see whether that's had a differential effect on men and women so basically, you know, kind of get a baseline for men and women here at the beginning and then you see like, has your teaching or has the experience of taking philosophy like changed the differential? So, has it, for instance, made men more happy to go on and philosophy and women less happy to go on and so we found some interesting things. We found, so interestingly, there was kind of no effect on taking philosophy so, you know, they took the course and at the end, there was, yes, so we tested people right at the beginning of semester before they'd done any philosophy and then we retested them again at the end of the semester after they'd done the whole course and interestingly what we found is that there were no gender differences between men and women so it wasn't, for instance, the case that women came in to philosophy being really positive and then the course sort of differentially made them less positive towards philosophy throughout the course. Instead, we just found that whatever effects the course had, whether they were positive or negative, were exactly the same for men and women, which was really interesting but what we also found were that people had very different kind of intentions and beliefs coming into the course so the course didn't really change the way people were feeling like men and women were feeling about philosophy throughout the course rather women came in to the course being with fewer lower rates of intention to kind of go in philosophy from the beginning so there was kind of, there was already a differential right before the very first lecture. There was a difference in the kind of reporting from men and women about how good the philosophy they thought they would be, whether they were intending to go on, how they thought they would find lectures and then they took the course and the course had no gendered effects on, so the gap didn't widen and it didn't shorten either so the take home message that we got from that was that at least in that course it wasn't so much that the teaching of philosophy was somehow making women feel less at ease or less interested or any of the kinds of things that you might have thought, rather it was that they were coming into philosophy somehow for some reason that's a little unclear why with very different views about whether they wanted to go on in philosophy and different views about how good they would be at doing philosophy and that seemed to be the thing that was mostly generating the differences that we found between the two genders and so that was really interesting. It doesn't mean that there are not things that we could be doing within teaching philosophy to encourage women but it does suggest that there's a kind of prior problem going on here and that for reasons that are a little bit unclear women are already as they can sort of come into the very first year like this is sort of first year university already have the view that they are less likely to want to continue on a philosophy and that they are less confident that they will be you know kind of good at doing philosophy which might just reflect sort of underlying gender differences in confidence or something so our view was that at least one place to kind of target the issue is to try and figure out what's going on there. Yeah that's interesting because it seems like there's a already a preconception so prior getting into university prior think prior to philosophy or is there's already this preconceived notion that women perhaps won't be successful in this endeavor is that what's going on because we're trying to replicate that as well here we're trying to yeah pattern our experiments with your work so yeah so that's what it seems like which is kind of puzzling because there is no philosophy at school so you can see how that could easily be the case for say with something like maths right kids are coming into university they've already done maths they've already had a bunch of experiences they already kind of can have formed a view about whether they're good or bad at it whether they're gonna like it but we don't teach philosophy as a school subject here and philosophy is not particularly visible in the media so it's not like philosophy is not kind of like science where you see you see it all over the place so it was it was very interesting to see that they had these kind of as you say preconceptions because what was puzzling is where they could have come from it seemed like they'd sort of come out of nowhere like how could you have a preconception about something you have never done before which is why we thought you know maybe this is some more general thing about women's confidence in any particular area that they haven't they haven't met before but we really don't know it would be nice to do some more follow-up work at some point i've just been i've been busy doing other kind of experimental stuff so we have never really returned to that but yeah i think that raised some interesting issues about how you might go about tackling some of these issues okay so speaking of future work so what do you think is the future of women in philosophy yeah that's a good question um well i mean i'd like to think that they will you know sort of i guess go on to do whatever it is that they're kind of interested in doing in philosophy so that you know women who are who are interested in metaphysics or you know philosophy of science or whatever will be drawn to those areas and will kind of happily pursue them which maybe is not maybe is not currently the case it's hard to know but certainly i guess women are somewhat underrepresented in some of those areas so i guess my hope is that um we'll just see women pursuing whatever kind of philosophical questions um they find most compelling and interesting and that gender will be kind of no part of what guides where women go okay so that ends our interview so thanks Chrissy for sharing your thoughts with us and so join me yep join me again for another episode of philosophy and what matters where we talk about things that matter from a philosophical point of view thanks