Shall we start? Yes, please start immediately, yeah. Okay, okay. First of all, thank you very much Valeria for organizing this online meeting, also for inviting me. It's obviously a pleasure for me to be here. And I'm also very happy to see so many friends on the screen, so that's, it's really nice. And the second thing I want to say is that this is probably my first steps in this new research that I am on right now. This, I started with the study of symmetries in metaphysics and in philosophy of physics in October, the thesis. So pretty much what I'm going to say here is my first intuition about the philosophical role or the metaphysical role that symmetries can play in metaphysical explanation, but also in philosophy of physics, and what kind of things we can learn about the world, about our reality when we look at the symmetries. So what I really want is that we can have a good discussion because I want to test my ideas with you.  My idea is that you try to convince me that whether I'm on the right track or I should step back and take a different path. So this is the title of the presentation. And one general probably humble aim of the presentation is to merely assess the role that symmetries may play in metaphysical explanation and in physics thesis theorizing. As you know, as you probably know, in the last years, many metaphysicians have found the idea of symmetries as very interesting and a very naturalistic tool to investigate what the words lie, whether the properties of the spacetime, what is the natural properties that we can find out there. So symmetries seem to have this force to involve in many metaphysical discussion and to try to say something new in our traditional metaphysical discussion. So I would try to assess that. This is the general probably humble aim of the presentation and a more particular probably bolder aim is try to focus on a particular attitude, a particular approach to symmetry that how we call symmetry fundamentalism or symmetry realism. I will swing back and forth between these two notions because I'm not still very convinced about what is the specificity of each of them. But the points that I would try to argue or give some hints, but I think that this attitude is another right, the right one to construe the role that symmetries could play in metaphysics but also in physics in general. And the other part of the argumentation would be that I would suggest that probably something like symmetry deflationism is a more appropriate approach, mainly for ontological and theoretical reasons. I'm not saying that that I mean this is the properly philosophical part. We as philosophers or metaphysicians should do with this idea of symmetries. I would recommend that we should pursue something like symmetry deflationism and cast some doubts on symmetry fundamentalism or symmetry realism. This is more or less the aims of the presentation and this is the map. Very, very brief. I would try to go through the first two parts very quickly. So because I want to focus on the third part, what is my proposal, or my doubts or my main arguments. But before to get at the presentation properly I would like to say something broader about what is my approach in general. Because you can focus on the concept of symmetries and try to elaborate the philosophical interpretation of symmetries. What I would like to do is something that go beyond the notion of symmetries and to see how that notion plays a role in a broader philosophical system. And I think that these words by sellers are very, very stimulating in this sense because what we want to understand as philosophers is try to see how things hang together. So I would like to see how symmetries hang together with other notions that we usually study in philosophy of physics, but also in metaphysics. For example, the notion of law, the notion of theory, the notion of models, and so on and so forth. So to my mind the notion of symmetry can only make sense if we try to see how it works in a broader philosophical system in relation to the notion of law, in relation to the notion of theory, in relation to the notion of idealizations, and so on and so forth. So this is the spirit that is guiding this presentation if you want. So the first part, this is probably the boring part because I mean there's a lot of formal details and formal discussions, intellectual discussions that I don't really want to get into here, but just to get a common understanding of what a symmetry is probably if you are not familiarized with the notion in physics, do something like this. We can start giving a formal definition of a symmetry. First, I would say that as symmetries, even, I mean first, first, first, first high point. The notion of symmetry is quite complex and people understand different things about symmetries. You have dynamical symmetries, space and symmetries, internal symmetries, external symmetries, gauge symmetries, blah, blah, and all of them are different, but also people understand differently the notion, for example, of dynamical symmetry. Some people relate dynamical symmetries with gauge symmetries, but other people say that dynamical symmetries aren't just symmetries that are predicated of law. So I would just use the notion of symmetry in general. Probably some of this point is not quite exact if you take a particular notion of symmetry, but just to try to generate that common understanding of what we are talking about. So first, I would say that one of the features, even a formal feature of symmetries, is that they are defined by their symmetry transformation. You formally define a transformation over a space, for example, and this transformation, that's something, transfer things in a particular way. And how these transformations transform things in a particular way is the symmetry that you are going to get. Second, again, from this very formal definition, symmetry transformations mainly apply upon formal structures. And pragmatically, I would say that these formal structures are those given by dynamical equation. So we define a symmetry transformation and we apply the symmetry transformation to dynamical equation, that is formal structure. And we have to see how the elements within the structure transform under the symmetry transformation. So I would say that it's fair to say that symmetries are, at least in principle, formal properties of the dynamical equations. We have some structure, dynamical equation. If we apply the transformation and we see what happens and what happens is the property dynamical equation has. And this property could be further spelled out in terms of being invariant. When we transform the structure, we see if the structure remains invariant after applying transformation. More formal definition is this one, but basically it says what I already said before, that we have some structure in this dynamical equation. We have some elements within this structure. It could be states, it could be observables, we could be differential operator or external parameters, whatever. And we define that information that something transforms the states in a particular way, transforms the observables in a particular way, transforms the differential operators in a particular way, and so on and so forth.  We just compare if the original structure remains invariant under the form after applying the symmetry transformation. So far so good. I mean, I think that is not quite problematic because we are just manipulating symbols in some way. But we can go a step further and say something like under a more semantic or even more than 30 definition of symmetries. When we do something like this, when we do something like manipulating symbols in a particular way, we are doing something like also transforming, for example, solutions of the dynamical equation into solutions to the dynamical equation. So we are preserving somehow the space of solutions of an equation. Going even a step further, we can see that symmetries preserve the truth of the law, that which is represented by the dynamical equation. So if we accept that, for example, some law is represented fairly by that dynamical equation, that dynamical equation remains invariant under some symmetry transformation. We see that all that what happened is that the truth of the law has been also preserved. So the truth of the law is also valid in other possible words, for example. And this is just more or less the same, but in a more specific way. Basically, what this definition tried to say is that asymmetry preserves the models of the theory, in a sense that we are transforming models into models. We are preserving the space of models of the theory. In this edge, we can then define a notion of truth, we can define a notion of possibility and necessity and so on and so forth. But basically, this is what we generally understand by this very general, general notion of symmetry. Then, as I said before, we have more specific notions, more specific symmetries that act in a particular way. And they're more published there, but in general, I would say that symmetries work more or less in this sense. Okay, so we have this first formal or partially interpreted notion of symmetries. But now the philosophy comes in, in this following sense. This notion of symmetry has been found to be for some reason that we are trying to discover interesting for many philosophers, because we can extract from them some philosophical claims. So when we see that we are manipulating these symbols and we find that some theory is invariant under, I know, time reversal is invariant under the space rotation. It's invariant under permutation. Well, from there, from this manipulation of symbols and also this partially interpreted notion of what we are doing when manipulating the symbols, we can say something more, something more interesting about what the world is like. And this is what I would call a philosophical claim. We can say, well, if an invariant and a symmetry holds in this theory, this means something about the world, about the notion of law, about our ontology, about the structure of the spacetime, for example. But what we have to first be aware of here is that there is some inferential mechanism that goes from symmetry to this philosophical claim. So one of the first things that we should do is try to be clear about what is the inferential mechanism that is operating to take us from one point and leaving us in the other. But to give you some examples about what I'm saying. For example, this is Hugh Price's book about the era of time. So we are investigating something about whether our world comes equipped with a direction of time, for example. I would say that it's a probably a philosophical question. And one of the things that Price says here is it's not that he's defending this field, but he's capturing what other people say about this, is that to a very large extent, then the loss of physics seems to be blind to the direction of time. They satisfy the time reversal symmetry, as we may say. So the idea is that because the loss are time reversal asymmetric of time reversal invariant, we can say something about the direction of time. We can say something about the structure of time in our world. So this is a case in which symmetries seem to be playing this role of giving us some information, some relevant information about the world. This much more complete explanation of how this inferential mechanism is working. This is Gene North in a very nice paper about the notion of time reversal again. But what he says, what she says here is that in applying any transformation to a theory, any symmetry transformation, we hope to learn about the symmetry of the theory and of the world that the theory describes. If a theory remains the same after transformation, that it's invariant under transformation, then we say that it's symmetric under that operation. We conclude that a word described by the theory lacks the structure that would be needed to support a symmetry under the operation. And I think this is the one, this is an example of what is going on here. For example, from the space translation invariance of the loss, this is the formal part. We formally showed that the loss of the theory are space translation invariant. We can infer that space is homogeneous. There is no preferred location in space. Again, this could look like a metaphysical thing. We are saying something about the physical space from a result that we obtain in the formal part of our theory, from discovering that the laws were space translation invariant. But this is one way in which we can see this inferential mechanism working in philosophy of physics, but also in metaphysics. But we can go even beyond this by postulating that symmetries are not just one thing that somehow take us from a formal property to some property of the world, but somehow symmetries are aspect of the world, fundamental aspect of the world. And this is what I have called, but also Schrenen has called symmetry fundamentalism in the sense that symmetries again are fundamental aspects of physical reality, where the physical entities, for example, particles or fields come after or depend on ontologically depend on the notion of symmetry. So now we are not just manipulating symbols when we discover that some theory is invariant under some transformation. We are discovering a fundamental aspect of the world, a fundamental structure in the world that again is playing some role in a broader philosophical framework, for example, state space first view or state space sustainableism. But the point is clear that now symmetries play some ontological role that is much heavier than just manipulating symbols in our physical theories. And more or less the same can be read in a French book, the structure of the world. I'm not going to read it completely, but what he says is that laws and symmetries should be considered as features and fundamental picture of the structure of the world in a world where we don't have any entities, but all we have is some structure, laws and symmetries, again, a case of symmetry fundamentalism. So we have two different sort of thesis more or less on the same boat, one of them postulating that symmetries are somehow real in the sense that they can represent or guide us to ontological features. We are not really commitment, we are not really committed to the idea that symmetries are fundamental, are fundamental structure in the world, but somehow they should be real in order to help us to discover fundamental entities, fundamental structures or all these kind of things. I would say that people that, for example, take the notion of time reversal in variance very seriously and then they say something about the direction of time, well, they are somehow taking symmetry realism into consideration as they think that something in the world guide us to discover that there is no direction of time because a symmetry, a time reversal symmetry holds in our physical theory. Or we can say, as I said before, this second position that assumes some, assumes symmetry realism, but go further in the sense that symmetries now are fundamental, are really part of the building blocks of reality. So these are the two, I would say that two parts of the same movement that try to see symmetries are playing a serious metaphysical role and should play a serious metaphysical role in our philosophical systems, either by possible symmetries as somehow real or symmetries are as fundamental. So let me briefly see what is the argument behind this, what is this inferential mechanism working to take something at a formal level and then to say something about what the word. So in general, when we have a symmetry, we should specify what is the formal structure upon which we are applying the symmetry, for example, the laws. So we postulate that there are some laws that govern our work. And then when we apply the symmetry to this structure, we identify in general some property could be magnitude and observable and state that can change freely without changing the overall structure of the law. For example, we can change freely velocities, we can change freely the direction of time, but the structure of the law is the same. So we identify this this variant feature, this variant property when we are working with symmetries in this still formal level. So we have in the argumentation, these first supremacists are mainly formal, in the sense that they are just saying that a symmetry holds in this formal structure. But then if we want to extract from the philosophical conclusion, we need philosophical premises, we need something more than just mathematics. So we need to interpret philosophically what means that a feature can vary freely. What means that I can change the sign of t of the parameter of the time parameter in our physical theory, and then the structure remain the same. I have to give some philosophical interpretation about this. And then I have to postulate some epistemic constraint saying that, well, it's not epistemic advisable to take this variant feature seriously in our ontology. And then I can conclude that because all these premises, I can say, well, the property is not real. So the symmetry we start with took us to a philosophical result by saying that, well, we shouldn't take this feature seriously. Obviously, the tricky part is the part in which we have to give an interpretation of what means that we have some property in our equation that can change freely. What does it mean? There is a lot of ongoing discussion about how this should be interpreted. For example, Shamik Dasgupta says that, well, what means that a symmetry holds, that we find this variant feature, well, we are saying that f, this property, is unobservable. Because it's unobservable, we should just take it out from our ontology. For example, we can say that f is part of a superfluous structure, like Dirac or Ismail and Van Frazen have argued. We can say that probably ontologically heavier, that this variant feature that we discovered by the symmetry is non-objective. So that's why we should remove it from our ontological commitment. For example, NOSIC, but already have said something along this line. Or we can even say that f of these properties are not fundamental. These are just different ways to show you how it's not a straightforward path from symmetries to a philosophical claim. We should do a lot of philosophical work in middle to fill the premises with philosophical premises with some interpretation to say, well, the symmetry that I discovered in my physical theory by manipulating symbols, then it has some interesting claim about the word. Something like this, I think that is going on in this presentation. What is one of the options that I see in this general argument? One is that there is this assumption somehow that we must take symmetries metaphysically seriously because they can guide us to uncover fundamental structure, natural properties, some properties of the spacetime, and so on. That's why we place the symmetries in the argumentation as playing the role of triggering the interpretation and then triggering the philosophical conclusion. Now I would say two things that I'm not completely sure about. Please bear in mind these two claims and we can discuss it afterward. But I see that the argumentation in some sense needs to play the symmetries somehow in the real world. They can guide us because they are somehow real. Even though they are not fundamental, even though they might be no fundamental, they might be no entities of real structure, at least should be instantiated by real stuff in the world. Otherwise, I don't see the connection from the symmetries to the philosophical claim about the word. But this is something I'm not completely sure, but probably this is one of my first intuition. Okay, by symmetry realism, it's assumed by symmetry fundamentalism. Symmetry realism is committed to the idea that symmetries are somehow real and because they are somehow real, they can help us to discover new structures or new entities or new properties. But it's not committed to the idea that symmetries themselves are fundamental. Symmetry fundamentalism accept obviously that symmetries are real, but they add that symmetries are part of the fundamental structure of the world. So this is just to give you the big picture of what is the very general notion of symmetries. I'm mainly thinking of these space and symmetries like reversal, space translation, space rotation, blah, blah, blah. Then we have some people that think that we should, we can do good metaphysics from this. We can discover, we can give an answer to a serious metaphysical question about what is the world like, what is the structure of space, what is the structure of time, whether a time is directed or not. So they have tried to convince us that this is a useful tool through something like the argument that I said before. Now when I start to think in this kind of argumentation, at the beginning I think that it was quite right. I mean it should be, it looks like an interesting idea, also a very convincing idea. But then when I start to think these things through, I start to have some cavities. And what I want to share with you is some of these cavities. And this is probably the first step, steps toward something like symmetry, the flashing ism. Symmetry, the flashing ism, try to see symmetries as not playing a metaphysical serious role in our understanding of the physical world. So one of the first points I want to write is the attention that I found in the literature about symmetries and it's this tension about whether symmetries are stipulated or are discovered. I have called them in this way, but basically the idea is that when we are formulating our physical theories, we stipulate previously that the theory must be symmetric under some transformation or it happens that we build our theory and then we find that the theory comes out symmetric under some transformation. So I was running through the literature and both sides seem to be fairly represented in the in physics in general, even though some of these approaches are more contemporary to us, but in general these two sides are somehow there. For example, in this book, Deur and Toiffel are trying to build a theory of quantum mechanics. So they are doing real physics in a sense that they are trying to be clear about the principles and the dynamics of the theory, the definition of a state and so on and so forth. At some point they talk about the symmetries of the theory and what they say, the assumption that they take into account is the following. They claim that a symmetry can be a priority in the sense that the physical law is built in such a way that it respects that particular symmetry by construction and this is a clear case of the space and symmetries in the sense that we first build the rules of the theory, the symmetries, we say how the spacetime should be, how the structure of time should be. We do this by imposing some symmetries a priority, how they say and then after doing that we build the dynamics according to the laws, to the rules of the field. So in this sense it's looked pretty much like the symmetries are stipulated a priority. It's not the thing that I have some law and then why I'm digging to the law, I discovered that the law is it's the way around. First I say that the theory is symmetric, the law is symmetric and then and then I have the right dynamics for that symmetry. A similar case, I mean it's not quite, it's in the same boat but it's on the same boat but it's not similar but more or less represent the same idea is that for example the discussion about time reversal in classical electromagnetism, from Arseneus and Hillary Griff's, they are discussing about whether, about how to build the right time reversal transformation in classical electromagnetism and what they bring up in this book is what they call the standard, the textbook account and the textbook account to give the right symmetry transformation is to start of assuming that the theory is invariant under time reversal. So we need to figure out how it's the, what are the features of the symmetry transformation. So in order to do this we first stipulate that the theory must be symmetric under time reversal. When we postulate, stipulate that the theory should be symmetric under time reversal then we can figure out what are the right properties that the symmetry transformation should have in order to keep the theory invariant. So I'm seeing in this sort of explanation more or less the same as before. We start with the postulation of the symmetry should be met and then we figure out in this case the time reversal transformation. But now to give you a different approach, I mean this is quite long, I mean the nice quote I found is quite long but I just extracted this refer part but this is John Irman in a things 2002 and 2004 paper about symmetries and he already notes that there are at least two different approaches to symmetries. What I showed before is the a priori approach but what he says is that the received wisdom about the status of symmetry principle has it that one must confront a choice between the posteriori approach versus the a priori approach. The previous cases seem to fit into a more a priori approach. So what is the posteriori approach? The posterior approach is what I call the by discovery approach and one of the best examples when it is in Newton but this is thanks to Alexander that gave me the quote before but I think that this is really perfect. This is by Lagrange and Lagrange thought that the symmetry principles along with the conservation principle must be viewed as general results of the loss of the dynamics rather than fundamental principles of the science. So this is the opposite movement. We don't start with the symmetries of the theory. We don't start by stipulating the symmetries of the theory. We start with a empirically adequate dynamics and then when we are investigating formally or even empirically the dynamics we discover that there are some symmetries. So first this is the this tension. This tension is I think in the literature that I separate in this two sides the by stipulation and the by discovery. The by stipulation seems to suggest that as symmetry in this case I took the dynamical symmetry in the sense that a symmetry that is applied upon a law must be regarded as a priori in the sense that we can come to know it by no empirical means just by postulating a priori that it should be the case and that thought but also is that the case is necessary for a theory dynamics. Particular theory let's say Hamiltonian mechanics, Lagrange mechanics must be a priori and necessarily time reversal invariant, space rotation invariant and so on and so otherwise we are talking about a different theory. So it's our necessary feature of the theory to be invariant under some transformation because it's the way in which we build the dynamics. The discovery approach is completely opposite in the sense that we discover the symmetry at posteriori in the sense that we discover the symmetry once we have the dynamics but also it's contingent. We can have a theory that could be non-time reversal invariant, non-space rotation invariant for example. There's no necessity in a theory to be in such a way, could be different. Obviously the word a priori, a posteriori, contingent and necessary is much more complicated so I'm trying to give you the brief answer but more or less this is the spirit of what I want to say. So when we look into the each of these approaches we see that the by stipulation approach seems to be playing a more heuristic role guiding the reconstruction in a sense that it's helping us to build the dynamics and in contrast by discovery approach at least seem to be partially based on word feature in the sense that we have some empirical adequate laws and then we discover that these laws have some features. So one would say well there's something in the laws that was built independently of the symmetries that reflect the symmetry somehow. One of the results of this tension is that the first approach the by stipulation approach is much more common in current physics that was before. Before in the 19th century physics like I know Lagrange but also before that Newton thought that symmetries are by discovery now it seems to be that physics and that symmetries are stipulated and this is something that Bradley and Castellani in this very famous book about symmetries explicitly say that after a relativity physicists seem to move onto a by stipulation view of symmetries even though they didn't they don't call it in that way but it captured pretty well what is the idea. So what is the my my my capits about it if it's true that current physics implies some sort of by stipulation view how should we interpret symmetry fundamentalism or even symmetry realism. Now if you if you look at the previous argument one of the one of the main premises that say that a symmetry holds are now just a stipulation a stipulation but heuristic reason or whatever but there are stipulations that is made before we can even get a right dynamics. So if we think that symmetries are fundamental structure of the world for example I this is a bit confusing for me this is that if they are stipulated but then they represent somehow or they are somehow fundamental structure we should say that these fundamental structure are a priority also stipulated it's the case that we are somehow doing a kind of a priority in metaphysics and also in which way or may we come to uncover fundamental structure structures through a priority stipulations where this stipulation come from. When I when I asked this question to uh to Sheldon Costin in one say about boya mechanics precisely he told me something that was very interesting but also that shows that there's something more going on if you take this seriously because they start with idea that we live in a sort of a platonic space time in the sense that space time should be metaphysically because we are platonist. Personally it's a morphic, personally homogeneous and so on. So with this idea in mind we impose the idea that some symmetries should be present in our theories but again what is playing the metaphysical role now is that we are assuming previously that space time for example or time or the properties of our world should be in some particular way and then the symmetry just try to recover this idea but again this looks pretty much like a priori metaphysics somehow. So my first problem is that I don't see how symmetry realism or symmetry fundamentalism can deal with the idea that symmetries are stipulated prior to the dynamics. This is the first point. From this it follows a second point that also is puzzling for me. In many many cases I would say that the majority of cases but you can correct me afterwards if you think that I'm wrong and symmetries are properties of fundamental and general equations. There is equations in which we have abstract away many for example non-conservative forces many interactions so we have this very general equation for example the free fold equation and we say that for example time reversal invariance space rotation or space rotation are properties of these dynamical equations of these general equations but again this general equation these fundamental equations are usually given by highly idealized models, models in which for example we have got rid of friction, we have got rid of air, we have got rid of elastic bodies, something like this. So we stipulate that these very general equations that gives us very highly idealized models are symmetric but now that's so far so good. Again we have this structure, this structure gives us some models for example the free fold particles in one case and we discovered that well in those cases a symmetry holds. It's true that you should take the coming in even classical Newtonian classical mechanics and equation and particle moving in a straight line in an empty space is time reversal invariant period. It's true, it's completely true but then I ask myself is there any reason to take such equations or such idealized models ontological seriously what we should rid off from this highly idealized model and I think that we can go two ways basically. We can say that these general equations just are describing highly idealized models that shouldn't be given any ontological privilege. I mean this is just part of our way to represent the world but they are not really representing nothing in the reality. When I say that if I get rid of any, if I get rid of inhomogeneous fields, if I get rid of air, I'm getting rid of friction whatsoever when I have some symmetries in my physical theory but the question is why should I take that this particular model is really unfairly representing the world in which we live in? Why should I say that the world we live in is symmetric because this particular model is symmetric? This one way we can go. The other way is to say that well actually these general equations and these highly idealized models are really representing the fundamental reality. What we are seeing is not the fundamental reality, we are seeing an emerging or apparent reality but if we want to investigate the world into the fundamental level we should pay attention to this highly idealized model because they are giving us the structure of the world as it is at bottom. So in some sense they are playing an ontological, an ontological role and that's why symmetry should be given, should be taken metaphysically seriously because they are giving us information about the world at this fundamental level by assuming that this fundamental level is fairly represented by this highly idealized equation. This discussion, I mean I saw this discussion in a bit older, a bit old papers about the direction of time in classical mechanics about Hutchinson and Calendar. Hutchinson is saying that obviously classical mechanics is non-terms and important because we have friction, we have imperfect springs, we have non-rigid bodies and so on and so forth. Calendar says that he's just missing the point because what we are asking, a philosophical question about the rough time for example, we shouldn't take for example conservative forces seriously, we shouldn't take friction seriously, we shouldn't take imperfect spring seriously, what we should take seriously is this highly idealized model. So again I think that even though I mean we can go both ways but still for me we need some further argumentation to say that why a highly idealized model is ontologically or it's metaphysically more important that a model that is more fairly representing the world in which we live in. I mean I don't have the answer, I am prone to be with Hutchinson in the discussion and to say hang on, probably we are just overloading metaphysically highly idealized models, we are overloading the meaning of the general equation and they shouldn't be taken seriously but I think I'm open to rethink these issues again because I know with sure but in general I would say that this is a problem we have to deal with when we are discussing about symmetries because symmetries in the overwhelming majority of cases are properties of dynamical equations that are quite general that give us very highly idealized models. So this is a problem that I think that we should pay some attention to. So this is the second step, general equations and highly idealized models and my intuition is that people that take symmetries seriously in the metaphysics are somehow refining this general equation on these highly idealized models. They are trying to say as calendars for example that well this equation, these idealized models are doing something more that just representing a very general idea of very abstraction. They are capturing some structure in the world and now the third and final step I think that I'm over after this is that I started by pointing out that one of the features of symmetries is that they are properties of the laws. In general we apply symmetries to laws mainly even though if we take they as stipulated or not this is independent in both cases they are properties of some dynamics. So my question is that there is some sense in which if we take symmetries as real or even more as fundamental do we require in our ontological system a robust view of laws? It's not still pretty clear to me but it seems that somehow symmetry realism or symmetry fundamentally implies a realistic view of laws. When I think in for example humanism of laws or this positionalism I'm pretty sure that we can make straightforwardly the step from the symmetries to the reality because now the symmetries are instantiated in things like laws that are much more deflated that are of either regularities or either axioms in our web system or are something that we can extract from dispositions but now it's not clear how these two views can accommodate a symmetry as real or fundamental. So this is why I think that symmetry realism and fundamentalism somehow is committed to the idea of realism about laws. Obviously if someone is not happy with symmetry realism or symmetry fundamentalism one way to go is well let's go and reject realism about laws. So if I'm not happy with the idea that symmetries are real that symmetries are fundamental I can go with humanism about laws or I can go with dispositionalism and then we are just by modestolence rejecting symmetry realism and symmetry fundamentalism. So I'm not saying that this is bad per se but I am saying that this seems to be a hidden assumption in those defending symmetry realism or symmetry fundamentalism. So this is an additional commitment that I think should take in order to make sense to the idea that symmetries can be somehow real or can be somehow fundamental. So this very briefly the role to symmetry deflationism. First the by stipulation approach I think that well I mean this is just the way in which fixes you symmetries. So I think something that we should accept when we are trying to philosophically elucidate the notion of symmetry well we can accept that they are playing this rule prescribing role erystically guiding theory construction. This is something that we can we can accept and I think that we should accept but as I said before there seems to be some commitment with taking highly idealized model seriously and we can obviously reject this. If we take something like a persistent approach or we can a more human approach we can easily say that it's obvious that these particular particular laws are not recovering any regularity but just playing a representational role trying to capture in the simplest and most informative way those regularities for example. So there is one way in which we can reject one of these assumptions and the second one is more or less the same rejecting realism above laws. So in this in in this sense by rejecting this this last two assumptions that I see that symmetry realism or symmetry fundamentalism is committed to we can reach something like symmetry deflationism and basically what symmetry deflationism deflationism says is that symmetries play a heuristic role in the representation and systematization for physical theories but they neither guide us to the basic ontology nor are part of the basic ontology. The basic ontology should be working out independently of the symmetries because this is not a part in our representation that is playing ontological role. In the sense symmetries should be just properties of the representational apparatus of the way in which we encoded information about the world but it's not nothing in the reality itself. So any problem that we have about symmetries about whether a theory is symmetric under some transformation is just a problem about representation. It's a problem about which is the best way in which we can encode information about the world but it's not a problem about which sort of entities exist in our world or which sort of entities doesn't exist in our world or it also has nothing to do with the structure of the world. This is something that should be working out independently by ontological reasoning by ontological investigation but it's not the symmetries that are going to give us some light or are going to give us some hints about this structure because once again they seem to be just playing a role in the way in which we construct theories in which we construct the dynamics in the most efficient and the most informative and the simplest way but obviously we can think differently we can think that it's not a role of theories to do this but when we can go with a more disposalist view but in that case as well I think symmetries shouldn't be playing at least a fundamental role because they should be so emerging from powers or dispositions and not from something in the in the in the fundamental reality itself. So I think that this is all yeah thank you for listening. Okay so let's continue now we have I hope everybody has returned so we have four persons who want to say something I don't know in which order who was the second and so on but I know that Nuriya was the first so let's start with her then I just proceed in the way in the order I see the the alphabetical order I hope you don't mind so Nuriya please begin. Okay thanks and thanks Christian for the talk and thanks of course Valeria for organizing. And Nuriya I don't hear you do you have your microphone activated? Yes I don't could you begin again? Yes everyone else hears me? Yes yes I don't hear Nuriya If I was here well still Christian do you hear me? Yeah yeah I'm hearing her perfectly. Okay that's weird and I was saying that thank you Christian for the talk and everyone and also Valeria for organizing. Yeah okay now I hear you. And yeah I wanted to ask you two brief questions and I really liked this idea of symmetry deflationism but you just mentioned it very briefly in the end and so I wanted to have a bit more context on this idea like who proposed this idea or like yeah is does it is it in the literature or like what are the others who proposed it and and to solve which problems and is it something that you have taken to solve other kinds of problems or yeah a bit of context on the idea and and also especially because I find it to be useful maybe to think about the way of this them mystifying the concept of spontaneous symmetry breaking maybe which sometimes has been used in order to propose some strong emergentist positions related to specific phenomena of symmetry breaking so yeah I want to hear. Okay many thanks for the questions as to the first one I mean for sure someone else has already proposed this idea I mean obviously I don't know what I can say is that I'm trying I'm pushing forward this idea based on for example some discussion on some paper that I read by David Wallace for example it was in 2019 paper a couple of papers about symmetries even though he doesn't really speak of symmetry deflationism or or the connection between the symmetries and laws and all the stuff he seems to suggest that when we are working on symmetries mainly in in in physical theories where we are just taking a subsystem from a larger system we are doing a lot of idolizations and it's not clear how what ontological role can play in symmetries in that context but also I mean I think that where Alexander knows this better than me but Gordon Bellet also have has casted some doubts on idea that symmetries can play this ontological role so I mean I am probably just trying to systematize this this intuition so these ideas but this labeled off symmetry deflationism and the the context is that probably the context is better understood in metaphysical science when we have these arguments in favor of no direction of time no or certain ontological properties or certain kinds of stuff based on symmetries and for example I always started with my PhD thesis about the era of time and one of the main arguments for eliminating the era of time is time present invariant but I like time so I want to preserve time so my first strategy was try to dismantle the idea of time reversal symmetry and I found these these intuitions there and I thought that probably is the same case with the rest of the symmetries probably we can just take it and say well probably we are taking these symmetries metaphysically too seriously and we should just expose the intuition and premises that are working in there but yeah I will say that but also yeah sorry I just it's easy to have like 40 minutes left for everything so I will just ask you to answer briefly and to those persons who ask questions to also ask them briefly if it's possible please okay it's very hard to me to be to be to make sure but I would try to do my best so this is the the first answer the second answer the honest answer and the short answer is I don't know I didn't I didn't have to I didn't I didn't think about that about the spontaneous symmetry breaking and how this fits together so in for the sake of being brief and honest I would say I don't know probably you're right nice thank you I suggest it we can go to another question so Vasilis Ekelemio please ask your question yes thanks very much for this talk it was a very rich talk and it raised the millions of questions now I try to be brief I have I have a reworked make if we take theories of physics we're talking about symmetries these are these symmetries refer to transformations and these transformations form groups so when we talk about symmetries we talk about symmetry groups now the axioms defining a group structure mathematically are the algebraic or geometric expression of the logical of the logical properties of the notion of identity they correspond one to one to the three characteristics the three properties of identity so having a symmetry means that something a system is changing while at the same time preserves some essential aspects of each identity and these correspond to to conserved magnitudes for example so to have a symmetry seems to be a fundamental first step in articulating a theory about the system if you know what kind of system you're going to to examine then you formulate the theory that incorporates the symmetry if you don't know that then you try to discover it and you look for it but it is the benchmark of any theoretical examination it is the way to circumscribe the object of your investigation so it's a condition for forming a theory so this idea if you I mean I don't know how you assess this idea and how it fits in your scheme and in your classification that you presented okay thanks thanks for the question it's really really interesting and I would try to see something something interesting let me try yeah I mean many of the things that you said are what I have called the the idea of trying to build the dynamics the idea of the states the idea of what are the observables of the theory and try to identify some for example operator with some observables and we use all these to to build a theory to to guide us to build a theory so I don't have any specific problem with that I mean it's it's quite fine and I completely agree that symmetries play this heuristic role my my my problem if you want is that when we have this then we we should talk about something out there in in the world because so far we we have just a formal apparatus that is partially interpreted by the by some concept for example to associate some transformation to some operators to some observables and symmetries plays some role there but then we have when we are doing more ontological work or more metaphysical work we want to say something something else and this is the step that I don't quite see let me put it in some for example in the case of non-latvistic quantum mechanics you have the the Galilean group so for example with the Galilean group you can figure out which operator represents which kind of things you the conserved quantities you have you have all the operators and with with the the Galilean symmetry transformation you can figure out which operator correspond to momentum with angular momentum which operator correspond to energy and so on and so forth that is perfectly fine but when you go to the people working on ontology quantum mechanics they don't just take this this set of observables as properties in the world some people think that well I mean they're playing a dynamical role in our theories but it's not really representing real stuff out there many people are probably I think that David is somewhat somewhere there think that for example the only real property that quantum system quantum system have is positions okay and this is the ontological part of the theory the position is the main and fundamental property and the rest of the property that my theory talk about are just playing a dynamical role but it's just part of the representation of theory but it's not part of the ontological theory I'm not saying that this is the right view what I'm saying is that there is two steps the step we have the symmetry at the formal level how to how to interpret it within the theory to build the dynamics to be a nice theory that physically works and symmetry's play a role there I'm not denying that but then we have the ontological discussion I would say well this is not the fundamental properties this is not the their right structure this is the the or this part of the theory doesn't uh doesn't represent anything well in in the in that case I don't see the the the step from one side or to the other and this is what I I'm trying to say that but let's think these things through but I'm not denying that the single display a very very powerful uh uh representation of role a realistic role in the way which we build and understand the theory but now when it comes to uh ontology or metaphysics now I I become puzzle okay thank you and for the question uh so unfortunately uh the person who wanted to ask this next question had to leave uh so let's be brief and uh Petr were there please ask us the last question before we come to the last part of the story was this meeting yes thanks a lot for a great talk um I was wondering about this idea of an a priori stipulation you mentioned this word several times and it surprises me a little bit like usually we use the words a posterior a posteriori and a a priori to point to knowledge a stipulation cannot be knowledge because we stipulate it it seems empty I mean it it's what of course if you have results about the stipulation logical results that would be a priori logic but I don't see how a stipulation as such could be knowledge and so a priori knowledge um except in a completely trivial sense so it's just a very concrete question yeah I'm very happy to say that because I completely agree with you I mean actually the paper that I wrote about this I mean one of the greatest papers with this idea says something like what you are saying so in this case I try to be much simpler and try to to show the main main points but you're completely right what what what what I say what I say there is that I took the term a priori and a posteriori for from John Irman but also from other people working on foundation of physics like the book I showed but it's true that a priori and a posteriori are epistemic terms referring to whether we know things independently of experience or not and it seems that in the case of symmetries it that's in the case I mean they are not a priori or a posteriori I mean they are a different sort of stuff but what is true that is we think that um a priori what's prior a priori isn't that it comes independently of the dynamics independently of the dynamics in some that is compared to the dynamics and a posteriori comes after the dynamics but I completely agree with you that this is a it's not a happy happy terms to use in these cases because it's not the right sort of thing that they are a priori or a posteriori so in this case I was I was uh sloppy but but I agree with you and you are right okay thanks so thank you all for questions and answers now we should move on so Cristiana I just wanted to ask you if you could put in the chat the reference to Schronen paper you have a reference Schronen 2020 you could just put this in the chat a little bit okay so now thank you for this part now we have around half an hour as the last one I'm supposed to make a presentation we're supposed to have some discussion I don't know the meeting is officially the like the time that Alexander has specified for the meeting was till 1730 so I don't always it will disconnect then or not so I just say it won't disconnect but I should say people are entirely free to go in yeah well in principle you are free to go but obviously we have half an hour so let's do like this I will just announce the next meeting and then I will do my presentation and finish it before 30 minutes and then we see how the discussion goes in principle if you have forces you can stay beyond 30 minutes if you don't then you'll just leave okay so so the next meeting will be the 28th of April we will have two talks on the topic of counterfactuals and thought experiments they will be mature but a lot from city this on the counterfactual side and I rather scarf from side book engineer on the thought experiment side I will send the announcements sometime beforehand to all the lists which I'm using except the list but they have the full program and they can contact me for the links so those who asked me to have links for the three meetings I will send the links myself if you have asked the link just to these reasons and you will need to re ask or to all refer to my announcements on other lists so you may be in one month more than one month but in case you are interested and hope you like the meeting of today but it's not finished I'm just making the announcement now so that those who want to leave half an hour be able to leave it without missing anything important and then there will be the third meeting in one month after the second so the 26th of May so there are two meetings left and now we are finishing with the first one okay so I finished with the announcements now I will make my presentation and I asked Alexander I asked Alexander Gate to chair this because I will be a presenter I ask him to chair the question side so I will not be looking at the chat because I will now demonstrate my screen full screen okay so I will just do it in half a minute yeah okay so let's begin with the presentation I'm Valeria Chasova I'm affiliated to three institutions in the world so further is the CFS at the Siluva and the third is so the University of Salzburg department of philosophy of cultural and social sciences and in between there is the University of Salzburg archives and the institution where I was in between finishing my PhD in antisepticism and going to Salzburg as a postdoc and I'm still affiliated to all the three research centers but as to the universities I'm just in the Salzburg University at the moment but the affiliations from centers you can keep it even if you are not physically at some university it's decided by the centers so the topic is a gradation of empirical statuses for conservation principles and there are no words symmetry here but it's just an appearance so actually empirical statuses are those of symmetries and symmetries are there and our mission is on symmetries so of course my topic my talk is on symmetries as well and let's go here so yeah in my in my topics there are three terms so the empirical statuses conservation principles and gradation so I start with empirical statuses and the gradation will be at the end and conservation principles in the middle so empirical statuses were first introduced by Cosser Peter Cosser in 2000 he has several articles of 2001 which is journal for the philosophical science and in this one he says he較us the distribution between direct and indirect empirical statuses of theoretical symmetries so a direct empirical status is well theoretical symmetries are linked with symmetries in the world which also calls physical symmetries symmetries in the world and theoretical symmetries are symmetries in the theory And the indirect empirical status is when theoretical symmetries are linked with conservation laws. And where is this conservation laws we will see a bit later. So both statuses are about theoretical symmetries which are linked with something else. And for costa, either status is... Contributed to answer the question how theoretical symmetries relate to phenomena and the world. So in this way, so if theoretical symmetries have either status, they acquire empirical significance because they are linked with phenomena and they acquire ontological significance because they are linked with the world, because phenomena is the world. So, connecting this to Christian's talk. So he was saying, he was raising doubts about whether theoretical symmetries are connected with the world, whether they are real, before the answer is asking the question whether they are fundamental issues. He was asking whether they are real and the way for theoretical symmetries to be real is for them to be connected with the world. So costa's answer would be that of course, theoretical symmetries are connected with the world and here are two ways in which they are connected. But Christian was speaking about precise theoretical symmetries which are symmetries of laws or equations as I understand him. So whether those theoretical symmetries who have empirical status is asymmetries of laws is one of the questions which was asked by the literature which followed from costa's article. So actually, this literature, I start with the top. So this literature was asking different questions about direct empirical status and as far as theoretical symmetries are concerned, they were asking for example whether both internal and external theoretical symmetries have a direct empirical status. So whether both external means special temporal and internal means non-special temporal. So both kinds of theoretical symmetries have direct empirical status. Costa was answering affirmatively and since then nobody has said anything which would counter what he was saying. So we think both kinds of symmetries have direct empirical status and so are related with the world and phenomena. The main controversy of the literature on direct empirical status for the last 20 years was whether both global and local symmetries have the status or only global symmetries have it. So the traditional position is only global symmetries have direct empirical status but Gries and Wallace were the first to defend that local symmetries also do it. And the relevant distinction here is between roughly uniform and non-uniform or less roughly specified by parameters versus by functions. The translation is a global symmetry for instance, the fuel of the system is local and the gauge symmetry is local and potential shifts are global. So my view is that local symmetries also have direct empirical status as this was the main idea of my PhD thesis is defended under the supervision of Alexander Gehr. But then there is a third question about symmetrical symmetries having direct empirical status whether these are symmetries of laws or models. And as I was saying, Christian was concentrating on symmetries of laws, but as to myself, I am claiming that direct typical status is a property of symmetries of models. And there's a difference in Christian's talk. It was said that if you have a symmetry of laws, then you can express it as a symmetry of models is the sense of solutions of this laws. But the models I'm speaking here are not the same. So the symmetries do not coincide. So in my case, if you have symmetries of models with direct empirical status, it's not necessarily the case that they correspond to some symmetries of laws in the sense of equations, which also have direct empirical status. So there is a dissociation because which works in other direction, actually, and the fact that I say that theoretical symmetries have in direct typical status a symptom of models, it will help me in the following part of my talk where I claim that the relationship between theoretical and physical symmetries involved in direct empirical status is really direct in the sense of not being mediated by anything. So this is conditional on my approach, not everybody could agree, but in my framework it works and helps me to construct the rest of my argument, which I will be presenting in a few slides. So this is the theoretical side of the literature on direct empirical status as to the physical side in the sense of what concerns symmetries in the world. So because it was not clear enough about which symmetries in the world should be matched with theoretical symmetries to get the direct empirical status. So this was made clear subsequently, so only the next article by Braden and Brown gave what became a physical symmetry which yields direct empirical status, this is an example of Galileo's ship. The ship is boosted with respect to the shore, but the dynamics inside observably is unchanged. So this is a symmetry in the world, observable symmetry, and it corresponds to a theoretical boost on subsystems. So this is how the letter theoretical symmetries gets direct empirical status because there is a Galileo ship symmetry in the world. He really introduced the notion of empirical symmetry and said that Galileo's ship is one case and the farthest case, cage is another, and then there were two more added. And so the kind of physical symmetry which gives rise to direct empirical status became a very precise notion, still not completely precise, so in my thesis I tried to define it a bit better. And so it was still not achieved, but partly achieved. But it's not any physical symmetry which will do to get the direct empirical status, it's something very precise. But the option is that so far the literature has concentrated on just direct empirical status and on the kind of symmetries involved in it, but it was not addressing actually neither direct empirical status, which costs also introduced no conservation principles. So what is this. So to remind the inductive vehicle status was the correspondence between statistical symmetries and some conservation laws, but in questions words, and a conservation principle is my term to to designate the correspondence between symmetries of affections and conservation laws and it's not the just correspondence, it's actually an entailment. So statistical symmetries entail conservation laws, they can be used to derive them. And I ask, I call this conservation principle because, because variational principles are something. I'm going to designate cases where you take symmetries of actions and you derive something from it. So if you direct conservation laws and I call this conservation principle. And of course, the interactive bigger status is very similar to conservation principle and you have a temptation to compare the two and analyze them together. So this is what I will be doing. So I just be short of time. I just keep some details here, but the option is that symmetries and conservation laws are there have been addressed in different contexts, including recently, but these are not a question context where symmetries and conservation laws are analyzed in light of this notion of indirect and vehicle status and in light of its relationship with direct and vehicle status. So this, what is missing in the literature is what I'm trying to do. So here's what I say, let's see what conservation principles tell us about indirect and vehicle status and also direct and vehicle status. So on the left you have the usual presuppositions in the literature and then on the right you have what I will be transforming them into. So usually it's believed that the distinction between the state direct and indirect and vehicle status is a binary distinction. So you just have two terms. And I am claiming that this is a gradation that you have many kinds of empirical statuses which are organized in a certain way from a weaker to stronger for instance. And then the second claim is that the second position is that conservation principles only yield indirect and vehicle status. And why it could be plausible because as you saw conservation principles about conservation laws and indirect and vehicle status is also about conservation laws. So it would be quite natural to think that conservation principles only yield indirect and vehicle status, but I will be claiming that it also yields direct and vehicle status. So this will be the two claims which we will find in what follows, find demonstrated in what follows. So first to begin, we are approaching to the first claim. As I said, one of the usual presuppositions is that conservation principles yield at least indirect and vehicle status. So how do we get even this usual presupposition? This is not very trivial. So on the left we have conservation principle again and on the right we have indirect and vehicle status. In each case, we begin with theoretical symmetries for conservation principle, there are special symmetries. So Christian was saying about laws, about models, but these are not the only things which can be invariant in your theory at which consequently can give rise to symmetries. Also actions which are specific quantities, they can also be invariant. So it is this specific symmetries which you should take in the case of conservation principles. But this is a minor difference. A more important difference is that both conservation principles and indirect and vehicle status are about conservation laws, but I'm claiming that these are not the same laws. Because on the conservation principle side, so on the left, conservation laws should be theoretical because you are speaking about a derivation of some result from something theoretical. So I argue that if you derive something from something theoretical, then what you derive is also theoretical. So conservation laws involving conservation principles should be theoretical. But if you look at the right side, then conservation laws as I'm claiming should be empirical and not theoretical. Why? Because as you recall, because it is an empirical status, so it should be about something empirical and if you compare this with direct empirical status here at the bottom right, you see that it is a matching between theoretical symmetries and what Koso was calling physical symmetries, but which was got, it was made more precise, as I said, and it resulted in empirical symmetries, the one which you can observe, for instance, has got a layer of sheep. So if direct empirical status involves a matching between something theoretical and something empirical, then another empirical status, which is an indirect one, should, as I said, also involve something empirical besides something theoretical. And so conservation laws involved in the indirect empirical status should be empirical. So we have some mismatch between conservation principles where conservation laws are theoretical and indirect empirical status where conservation laws are empirical. However, it does not preclude us from getting the indirect empirical status from conservation principle. How does it happen? Here below is the combination of both things. So first I restrict theoretical symmetries to symmetries of actions. Then I keep theoretical conservation laws which are deduced from theoretical symmetries by a conservation principle, and then I add empirical conservation laws to get the indirectly empirical status. So the point is that with conservation principle you are half the road. So if you can construct some relationship between theoretical conservation laws and the empirical conservation laws, then from a conservation principle you can get an indirect empirical status. And I claim that this relationship between theoretical conservation laws and the empirical conservation laws can be easily constructed. This is just a relation of either representation or instantiation depending on in which direction you go. So this is how briefly you get indirect empirical status from conservation principle. But the thing is that so far you have just got something usual. So even you should understand that even this is not discussed in the literature because the literature concentrates on the direct empirical status. But it just presupposes that there is some relationship between conservation principles and indirect empirical status. So even this presupposition had to be spelled out. And this is what I have just done. But in spelling this out we just get some usual claim demonstrated. But now let's get to my own claim which are unusual. So the first claim I was promising to demonstrate was that the distinction between direct and indirect empirical status is not a binary distinction, it's a gradation. So there are many empirical statuses which are organized in some way which are ordered. So to get there let's compare indirect empirical status and direct empirical status. So indirect empirical status as you have just thought involves the following on the left. So you have theoretical simulators of actions. Then you get from there to theoretical conservation laws and then you get from the letter to empirical conservation laws. And that's how you get an indirect empirical status which obtains between your highest level and your lowest level. So between theoretical simulators of actions and empirical conservation laws. So if you compare this with direct empirical status on the right side, so you also find theoretical simulators which are not made precise here but these are simulators of specific models as I was claiming before. And on the bottom you have empirical simulators which are also something specific. But well if you compare the left and the right, you have some similarities like theoretical simulators upstairs and empirical something at the bottom. But you have a crucial difference. I take it to be crucial. The difference is that on the left you also have this middle level of certain conservation laws. So you have something in the middle between the things which undertakes this relationship of giving rise to an empirical status. So I take this middle term to be characteristic of indirectness. So I claim that indirectness obtains precisely when there are these mediating statistical elements like theoretical conservation laws in our example. And once you notice this, you can also notice that there can be some variation about this middle term. So here we have just one term for example, but we could have several terms or we could have them placed on different levels and not on one level. So once you make the indirectness a function of there being this mediating statistical elements, you understand that indirectness can also obtain to different degrees. And consequently the indirect empirical status is not just a single notion. It's a group of notions which differ by the quantity of theoretical elements which mediate the connection between the main elements. Which also differ by the levels at which these mediating elements are located. So once you get there, you already have the indirect empirical status transformed into a gradation. And consequently the whole distinction is between direct and indirect empirical status is transformed into a gradation because now instead of just two terms you have many terms because of the indirect empirical status side. So this demonstrates the first of my claims which I announced in the beginning. And now in the remaining time let's get to the second claim. So now I just to do this I just showed two examples. The first is long to construct and the second is very short. So now I'm just, there will be several slides at each source to advance by one stage. So I take several stages in this way and I get my example. So first example, first stage, nuance in conservation principles. So I begin with, on the left, with the usual conservation principle. So there you have theoretical symmetry of actions at the top, empirical conservation laws at the bottom. And in the middle you have just one element theoretical conservation laws, the mediating element which gives indirectness, which will give indirectness. The nuance inconsist in that I just, instead of having just one element I have two elements located at different levels. So now I have differential on the right differential conservation laws and integral conservation laws. And I just, I, it's not myself who took this from nowhere. Actually the real conservation principles like those which we get from nurses theorems, they are like what you see on the right. The left scheme is just a simplification of what we usually have and the right scheme is more correct one. So in real life you have two levels of conservation, it's called conservation laws. That's what I'm saying here. Now, the second stage, I extend the matching empirical elements beyond symmetry. So if you on the left you have direct empirical status and what you notice is that at the bottom level so that the empirical level, the empirical thing is a symmetry. And what you notice is the right is just the same nuanced statement of conservation principles as before, which gives rise to an indirect empirical status as before. And what you notice here is that at the bottom you have something empirical as well, but these are not symmetry, strictly speaking, at least not a typical symmetry in the sense of those involved in direct empirical status. But these are just, these are conservation laws instead. So the difference, so the thing just to repeat in the direct empirical status at the empirical level you have symmetries at the bottom and in the indirect empirical status of the kind we are considering. At the bottom you have no symmetry but conservation laws. So the absolute is that when you have an indirect empirical status, Kosovo was saying that this was something about symmetries, but actually this can be something about not only symmetries but also conservation laws, at least on the empirical level. But if at the empirical level you, you make this extension so you are considering not only symmetries but also conservation laws, then why not also make it at the theoretical level. So this is precisely what I do at the next slide. So, on the left you have the same pictures before, and on the right you have the same scheme, and on the right you have also the same scheme except that I now put accent on something else. So as I was saying, if the, if an empirical status can obtain between not only symmetries and symmetries but also between symmetries and conservation laws, so why not also make it obtain between conservation laws and conservation laws. That's precisely what I'm doing at the right scheme. So, consequence, this differential statistical conservation laws which you will consider as a mediated element with respect to the indirect empirical status of symmetries or fractions. Now they get their own indirect empirical status because we have lifted the requirement that empirical statuses obtain just between symmetries. We said they can also obtain between conservation laws. So now actually you have two indirect empirical statuses. So one is for symmetries of actions on the left and another is for conservation laws on the differential statistical conservation laws on the right. So actually it's the same newest conservation principle you will now have two indirect empirical statuses. And this is what is summarized here. So the same empirical conservation laws are linked with differential statistical conservation laws and they are linked with theoretical symmetries or fractions. So in the case you have an instance of indirect empirical status and of course the upper element of the statistical symmetries of action has more indirect status because there are more theoretical elements in between. The differential statistical conservation laws have less indirect status but still indirect one because there are still integral statistical conservation laws in the middle. So there remains to demonstrate that there are also indirect empirical status in this case and this is very easy. So once we compare our previous scheme with the scheme of direct empirical status, so the previous is on the left and direct empirical status is on the right. You notice that we have an analog of the right scheme on the left, namely, so we seek for a relationship where there are no mediating elements and we find it on the left between integral statistical conservation laws and empirical conservation laws. So this relationship by claim is an instance of direct empirical status and that's how we get the gradation of empirical statuses involving direct and indirect ones in the same example of conservation principles. So this demonstrates my second claim, which was saying that we also have direct empirical status in this case and this demonstrates a further claim by which, as mentioned, conservation principles give rise to the gradation of empirical statuses which include direct and indirect empirical ones. And here's the penultimate slide. So once we have finished with this, we can actually do the same elsewhere. So here's my second example, which is just one slide. So on the left you have conservation principles with all the statuses that I have established so far. And on the right you have in the black, the usual directed vehicle status, but now if we reason analogically, then we should expect there to be higher theoretical elements, which give rise to the theoretical symmetry, so which are direct and indirect empirical status, but this higher elements will have indirect empirical status and we also will have a gradation in this case. So my approach generates this prediction conclusions, sorry for being a bit late. So direct and indirect empirical statuses are worth being analyzed together and not separately and actually only directed because status is analyzed in the literature, but I say we should analyze both and together. And conservation principles provide a fruitful context of study because you will find out interesting things about both statuses there and you will get some prediction. So indirectness of an empirical status is a function of mediating theoretical elements. These elements may vary in quantity and level. Therefore, the indirect empirical status is a gradation and therefore the whole direct and direct and because the distinction is also a gradation. If you add to this that match elements are not necessarily involved in an empirical status are not necessarily symmetries, then you get that conservation principles exemplify this gradation of empirical statuses. And moreover, that the usual example of direct and because status should give rise to another such gradation. So the usual example is just the tip of an iceberg. Thank you for your attention. So is there some questions you can raise your hand if you if you don't have access to this feature on your on your computer, let me know. So is there questions for both of our speakers. Okay, so Patricia Palacios first. Thank you. So thank you for the talk. Very interesting. I have first a clarificatory question. So I am glad that you distinguish between different kinds of symmetries because I also think that no, not all symmetries are symmetries of laws. So, but can you explain a little bit more what you mean by symmetries of models. So do you mean that the model the whole model remains invariant under transformation or certain properties of the model quantity. This for example remain invariant under transformation. Yes, thank you for the question and for listening. Yes. So the models can be different. Some models are complicated. So you have many features there. And what I mean by symmetry is that part of this features is preserved. Sometimes it's said that some whole thing should be preserved for this to count as a symmetry. For instance, if we have symmetry of law in the sense of equation. So we think that the form of equation should be preserved for it to be a symmetry. So in the case of for us to get a symmetry of this equation. In the case of models, I admit that just part of the model should be preserved. Why do this because this is this matches well with the kind of situation we have in the case of direct in vehicle status because for instance in the example of a parallel ship, the ship is boosted and the dynamics inside the ship stays observably the same. So the full situation includes both what is happening within the ship and what is happening with the relationship between the ship and the shore. I claim that this relationship should be represented in theory. So in the model you will have some part of your model which is responsible for representing this relationship. The physical ship will change this part of the model. So you will not have a perfect symmetry of your model in the sense it will not be complete symmetry. But I insist that this change is necessary because it will help you to account for the fact that you have a different physical situation before boosting the ship afterwards. So this is a kind of symmetry of model which I claim is involved in the direct in vehicle status case. So this symmetry is a partial symmetry but it preserves that part of the model which is responsible for describing what is within the ship. Yeah, thank you. That's exactly what I thought. Thanks. Thank you. Okay, David Romano, your question. Yes, I have a question for Valeria and then also for Christian, if there is time. The one for Valeria is very naive because I'm not really expert on this field and I wanted to ask an example of the indirect empirical status of a symmetry. So I understand that there is some respect to the direct symmetry. There are some levels and entities that mediate the symmetry. I was curious about one concrete example. Thank you David for listening and for the question. So I was speaking about conservation principles in general. So each such conservation principle gives rise to an interactive vehicle status and concrete examples are just these principles where you feel in concrete symmetry of actions and you get concrete conservation laws. So all the conservation laws, you know, like conservation of charge or from it or whatever, the center of mass motion, they all can, well, usually they can all be derived from some cemeteries of actions. So if you have a relevant theory like electromagneticism, you should have some action where the electromagnetic field figures and you make it vary under the formations of electromagnetic potential and you get conservation of charge if you apply in a test theorem. This is one example and you get all the conservation laws of special relativity by varying suitable actions. He also gets them in general relativity. Thank you already. Thanks a lot. Yeah, I understand. Yeah. My second question was for Christian. I don't see Christian, but okay, I try to make the question. So I start from the observation that you made on the symmetry, the symmetry by stipulation of the guiding law in bombs theory. So that's interesting because in that book, the Galilean symmetry is done by a stipulation. That means they derive the equation that depends on the parameter alpha. And by stipulating that there is a Galilean symmetry, they found that alpha is H over M. And this is the correct parameter for the guiding law. In this case, it's interesting because first of all, it was criticized in a paper by Arby Brown. And Arby Brown in the paper say explicitly that you cannot derive a dynamical law from a by stipulation symmetry. So I don't know if Christian faced this paper, I can send it to him. And also it's even more interesting because in another paper, Anthony Valentini show that bombs theory is not Galilean invariant. So there is no agreement on the fact that the guiding law is Galilean, sorry, is Galilean invariant. The way in which Valentini derive, I think is not by stipulation, but a posteriori. It seems that they really do not agree that bombs theory is Galilean invariant. So for Dur, by stipulation it is and for Valentini a posteriori doesn't. So I think this makes even more interesting this case. And so this is the observation and the question or the consideration was if you think, okay, the by stipulation law in some way must be confirmed then by some feature of the theory. For example, empirical feature of the theory. Okay, thanks David for the observation of the couple. First, let me say something about the observation because what you said is very, very interesting because it's a remember. Currently what Valentini and finally says is that you will end up with a sort of Aristotelian space or something like that because precisely the dynamics doesn't meet the required for the Galilean symmetry. So you will end up with a different underlying space like more like Aristotelian space and not Galilean space. But I think that what would say is obviously interesting because I mean, for me, they are departing from different starting points. I mean, if you look at one way to say that the identity criterion to for a theory is the kind of symmetry that it makes. You can say, well, the quantum mechanic must be must be a Galilean invariant. So if you come up with a theory that is not Galilean invariant, so this is not quantum mechanics. And I think that many people like I know if you read Valentine's book, I think that they have this intuition behind that. Well, this is the right symmetry group of the theory. If you come up with something different, it's no longer quantum mechanics, for example. But again, they are assuming they are stipulated that well, the space time is more or less like Galilean space time. So the symmetry should be the ellen symmetries. There's this connection and then the dynamic just emerged from there. But if you change the starting point, well, you will end up with a different theory. And I think that wave function, wave function realism is no Galilean invariant either. I think that Laurie showed this. But also, I mean, again, we are discussing more or less the same thing. And as to the question, please, can you repeat the question because I forgot. No, no, it's just, you know, that if I do, if I implement a by stipulation symmetry, do you think then I must have a control on the symmetry that I have imposed on some, you know, feature that does not depend from the stipulation that I've done. Okay, yeah. Okay, this is my answer. Yeah, it has two sides. The first side is, well, of course, what you want is dynamics that is empirically adequate. So if the symmetry in the symmetry, the symmetry group, for example, promotes or helps you to build a particular dynamic that comes to be empirically adequate of work very well. Well, I mean, there are some constraints on the symmetry. There are some features that symmetry should meet because you want the theory to be empirically adequate after all. So this is my conservative answer. So there are some constraints. But my second part of the answer is that, well, I mean, there are many cases in which you want a theory to be symmetric. And when you apply a transformation that you think that seems to be true, you will end up with a theory that is not symmetric as you thought before. So what you usually do is to change the symmetry transformation. And there is complete liberty to change the symmetry transformation at will. And sorry for repeat myself, but if you think of how time reversal symmetry is defined in quantum mechanics, you see that, okay, I mean, you start with some idea about what time reversal is in classical mechanics. When you apply the same transformation in quantum mechanics, well, the theory is no longer time reversal invariant. So you have to figure out what is the transformation that keep the theory time reversal invariant. So in that case, there are some people that think that, well, you can always come up with a way to change the transformation in such a way that the theory is kept invariant under the transformation. So in that sense, well, I mean, there is there seems to be no strong constraint under by I mean, not a very strong constraint about what symmetries are should be met or shouldn't be met. You can always play with a we can come up with a mathematical transformation that keep the theory invariant and call it. Well, this is the right transformation that represent space translation. This is the right information that represent time reversal. Okay, thank you. I think Christian Christian you had a question for Valeria. Yes, I have a couple of questions for Valeria. Well, my, my, I mean, my first question is more or less related to Patricia. So but probably you can explain explaining a little bit further, because it's a difference between symmetries of laws and symmetries of models.  But it's not clear to me if they are completely independent of the symmetries of laws. In some sense, when you have some model of the theory and you want to transform them, the model is already a symmetry of the laws behind that guarantee that you can get. You can get to the different model that is the symmetry transform model. So, as I see the issues that there is a difference, but the difference is just the symmetry of laws come first in the sense that it gives you what is the dynamics of your model plus some. This is what we said, the symmetry of models. Then when you put some initial conditions of boundary conditions, you get your model. But if the model is symmetric or not will depend on the on the laws on the first hand, but also on the boundary condition on the initial conditions. So for me, as I see it, the symmetry of models come comes after the symmetry of law or depends on the symmetry of laws. But I'm not pretty sure about this, but I would like to hear you your thoughts about about this. And just briefly, my second question probably is quite silly, but I don't really get what is an empirical symmetry. What they mean by empirical symmetry? For me, in the case of Galileo ship, I don't see what is the empirical part if you put it in this plain sense. Because if you want to get a symmetry from the ship, you have to at least idealize the rest of the environment that is interacting with the ship. Because if I don't idealize the rest of the environment, I can always say that obviously I can realize perfectly well that I'm seeing the shore moving. So obviously there's no symmetry. So there's something else that is not empirical to get to this empirical symmetry. In this case, some idealization that take off the interactions with the ships. Thank you for the questions. I hope I will not forget the different details because there are many things to answer. Okay, so let's begin with the first. You were saying that whether something is a symmetry of models is determined by laws. This is not the case in the context of direct empirical status because in my approach, different models are symmetric if they represent different states of the ship involved in an empirical symmetry. So what determines where the models are symmetric is the representation relationship between them and the vehicle symmetry. So this relationship is like bottom level relationship. It does not involve laws. It does not necessarily involve laws. So why do I think that this relationship is dissociated from symmetry and the symmetry of models which is induced by this relationship. So why do I think that this symmetry of models is dissociated from any symmetry of laws. This is because the symmetries which represent different states of the empirical symmetry. So the theoretical models which represent different states involved in an empirical symmetry and which are related by symmetry of models. So these states can be generated by different laws.  And in the final state of your empirical symmetry, you have solenoid turned on. So in this final state, it is natural to represent it with a model which belongs to some theory which has electromagnetism in it. And it is also natural to represent the initial state of this empirical symmetry which does not have the solenoid turned on with a model which belongs to a theory which does not have an electromagnetism in it. So in this case, one of which you get from a theory without an electromagnetism and another you get from a theory with electromagnetism. These models will be related by symmetry of models because they will represent symmetry in the whole world. But these models will be generated using different theories and these theories have different laws, different equations. So there will be no corresponding symmetry of laws because when you get from one model to another, you get from one kind of laws without an electromagnetism to another kind of laws. With electromagnetism, with electromagnetist potential figure and in your equations. So this is a dissociation of the two and you can have the converse. Symmetry breaking is a converse where you have symmetry of force, which is not a symmetry of models of specific models. So under your second question, now I forgot a bit, but what was it about? What was it about the notion of empirical in the empirical symmetries? Yes, the idealizations. Okay, thank you. Yeah, so it seems like you're supposing that we should abstract away what happens with the environment to get the empirical symmetry in the case of scholarship. Well, actually some rare persons do this, he does this for instance, but usually those who write on directly because they do not abstract away what is happening with the environment. And I think they are making it right. Why? Because if you abstract away which happens, what happens with the environment, then you have a no reason to affirm that any transformation happened with your ship. But if you want to have a real symmetry in the world, you need to have some real transformation which preserves some observable or at least worldly features. So if you just concentrate on the ship, then you have no difference between the ship before and after the boost because the environment is abstracted away. So you can claim that this is not a symmetry, this is just the same state repeated twice, instantiated twice. So I think that the relationship with the environment in the relationship case is essential to saying that you have an empirical symmetry rather than the same state instantiated twice. So you do it need to abstract it away and you therefore get what I was mentioning when I said to Patricia's question. So you also have at the theoretical level that your symmetry is only partial because also at the empirical level it is partial. What happens with the environment is changed, but what happens within the ship is preserved. This is an empirical symmetry, it's empirical because it's in the world that it is symmetry because what is inside the ship is not changed and it is a partial symmetry because we do need to give the relationship with the environment as this relationship changes. Okay, thanks for that. I think that we don't have time right before. Okay, sorry, sorry, thank you very much for the answers. I don't know if Patricia wanted to ask something, but first I wanted to ask you. I would say that his question was already answered. Okay, good, just Patricia. I just wanted to add something to what Valeria said, but I don't know if there is enough time. Last question. Yeah, it's a remark actually, it's not a question. It's very small, so I agree with Valeria, I don't think that all symmetries are symmetries of law, so you can also think about symmetries of quantities. So quantities might be invariant under some transformation, for example, magnetization at a very low temperature, at very high temperature, it can be invariant under up-down symmetry. And I don't see how you can relate that necessarily or why should you relate that necessarily to a law. So I completely agree with Valeria in that sense, I don't think all symmetries are symmetries of laws. Oh, sorry, your microphone. Can I reply or we are out of time? Yeah. I can close the discussion. If Christian you said that all good symmetries are symmetries of laws, it's obviously wrong, but on the other hand, you follow John Ehrman, you follow all these guys, and they say that all this very important symmetry that we are discussing are symmetries of dynamics, so something like that. But we won't stop the discussion about that now, and it's already almost 1800 hours. So I would propose to postpone this discussion to a future. I will thank all the speakers and all the people that asked good questions to these speakers. And hopefully next time we won't have the presentation of the stuff people and old people and it will be on the side. Okay, thank you.