Models, representation & mediation

0:00 So, I have a handover. I've written it down. So, it should be 20 minutes. This is not the paper that's online. That's where all the arguments are. So the abstract I hope summarizes the motivations for what I'm trying to do is make these objections specifically about idealization to the semantics of the war, to the partial structures program in a way that the people in that program are sympathetic to the region, in a way that does not make stronger assumptions, say, about how science works or what models are. So I'm trying to generate these concerns about idealization in a way that they'll be concerned about, rather than saying, oh, that takes a question for another view of science or another view of representation. So according to the semantic view of theories, scientific theories are models or collections of models of the sort studied in model theory, and each such model an ordered n-tuple, where in the first position we have a non-empty set called the model's domain, and the remaining positions are either subsets of this domain, or sets of ordered pairs, ordered triples, et cetera, and we use those to pick out the properties and the relations defined on the domain. And despite individuating theories by these models, language of course can still play a role in science, for it's usually by writing down some equations that we communicate which So a nearly trivial example that I will focus on in this paper

2:30 is the treatment of a pendulum as a simple harmonic oscillator. I'm happy to see that the other papers in this session are actually a few more interesting examples, but it's a bit surprising that even with this simple case, we can generate these sorts of problems. So this yields equations 1 through 3 on the handout, onto the example, which specify in conjunction with the initial state of the pendulum at t equals 0 the trajectory that the pendulum will trace out over time. And so here, of course, theta is the angle of displacement oscillates, and theta prime is the angle of rate of change. And if we think of projecting the trajectories, again, that's not a very complicated diagram, if we think of projecting the trajectories onto a plane with the x-axis theta and the y-axis theta prime, Equation 3 tells us that the trajectories in this base space are all ellipses, so that's a selection of all the possible trajectories, consistent with those equations. One way to think of the associated models of this theory is in terms of a complex relation between the points, beta, theta prime, t, specified in the equation. And so I'll call this the SHO relation. So any two points on an allowable trajectory will be SHO related. and the model includes all such trajectories. Thus, this kind of simple model will have all points in its domain, and one relation, the SHO relation, two-place relation, which says for any two points in the domain, whether or not they're on the same trajectory. So I guess I do this to fit it more directly into the conception of the semantic view. A domain and some relations. Here, just one relation. specified, somewhat complex, but by the equation. Now, this simple harmonic oscillator represents many kinds of physical systems, in addition to my pendulum, and this makes it initially puzzling what we should say the constituents of the model really are. It cannot be states of my pendulum, or the states of all the possible pendulums, as then the model could not represent other kinds of simple harmonic oscillators, for example, the spring. So the obvious solution, although it's resisted by some, or maybe everyone,

5:00 is to take the model to be wholly mathematical, or as I will say, abstract. So in this view, the triples, theta, theta prime, t, are just triples of real numbers. And so the model can represent any system of this type, be it a pendulum or a spring. And so a slogan on the end of the abstract models, the generality of our scientific models requires that they be abstract still if they are abstract we can find another challenge in virtue of what do these models represent anything physically if the models are just set to erect objects solve one problem and create a new one and the answer of course offered by the semantic view is in terms of simple mapping like isomorphism defined on the properties of the physical systems that map these properties to the appropriate constituents of the scientific model. So this is isomorphisms on the handout. In our case, the model represents the pendulum because there is an isomorphism that takes angles of displacement to theta, which is a first position in our circle, rates of change to theta prime and times to t, so that amongst all the possible trajectories available in the model, find a mathematical copy of the actual physical trajectory in the range of this isomorphism. Other physical systems, like a sprain, are represented by this model just in case other isomorphisms take the right physical magnitude to some trajectory in the model, right? So you, if you're going from system to system, of course you're going to change the physical properties. For strange, it would be distant from the equity, not the annual. So, strictly speaking, for this account to work, we must distinguish between representation and accurate representation. And so here's one attempt to be so accurate representation on the handout. What's one way to do this? We could invoke the beliefs of the scientists working with these models and say that if these scientists believe there could be such an isomorphism, then the model represents. But that it's only when these isomorphisms actually exist that the model represents truly or accurate. So there's a potential gap between these beliefs and that the isomorphism is there and it's actually being there. And that's at least one way to capture what we're talking about between representations

7:30 that are accurate or true or inaccurate. And so we're now in a position to challenge the standard semantic view using idealization, and to see how the partial structure program proposes to be better. And in this paper, I'll call a mathematical model an idealized model when it satisfies two conditions, which are formulated in a way that's supposed to make it especially problematic for the semantic view. So in the handout, there are two conditions. One, there's no isomorphism relating the system to the situation. There's no isomorphism relating the model to the situation that it purportedly represents. And two, the relevant agents are aware of it. So on the standard semantic view as I have articulated it, no idealized model represents a physical situation. The problem is that many, if not all, of the models scientists actually work with in just this sense. So if we stick with the traditional semantic view, we're unable to rank idealized models in terms of better or worse representational abilities. They're all equally non-representational. So to return to our example, it appears that our model picked out by the equations 1 through 3 cannot represent the actual pendulum, because we've made a number of idealizing assumptions in the course of deriving these equations. Our four-harmonic oscillators. It's dampened at least by air resistance and friction, and furthermore, in order to derive these equations, we've made use of the small oscillation assumption, which tells us that sine theta equals theta, or can be substituted for theta, or something like that, for small theta. Both types of idealizing assumptions imply that no trajectory in the model will be isomorphized to the actual trajectory, and the crux of the problem is of the resources beyond isomorphism to explain how these abstract models represent. So that's the problem. And of course, any acceptable account of scientific representation must explain why this idealized model, or many, many others, though inaccurate, is still a good representation, and it must do this in a way that does not overgenerate good representation. It's here that the partial-structured program of Acosta, French, and others tries to offer something new on here today. the book, which summarizes a bunch of papers, and I certainly recommend it in the sense

10:00 that it contains a lot of things, you know, beyond just this particular problem. I'm particularly interested in the way that they handle historical cases that we reach over time. But I focus on these very small issues. A partial structure is a different type of set theoretic object, that reduces to these more traditional structures in special cases. So there's sort of a generalization of the semantic use. And the claim is that this generalization allows us to handle idealization. So this is the partial structures on the handout. Unlike a traditional or total structure, in a partial structure, each property and relation is identified with an ordered triple, R1, R2, R3. and so for example for a two-place relation R an ordered pair is in R1 when that ordered pair does stand in the relation R the ordered pair is in R2 when it does not stand in that relation and finally being in R3 indicates that it's left open or indeterminate whether or not the ordered pair stands in the relation R so if we're trying to build a model that represents the world if we don't want to take a stand and say on certain pairs let me put them in R2 And that's something that you can't do with the traditional model. So any given pair from the domain of the partial model must be in exactly one of these three, R1, R2, R3, and similarly for properties and other kinds of relations. And in the limiting case where each R3 is empty, a partial structure becomes a total structure by replacing these ordered triples, R1, R2, R3, by R1. Similarly, a partial isomorphism is a generalization of the traditional class of mappings that we call isomorphisms, and this is a somewhat, I guess, non-symbolic summary of what that is from the book, the second page, Partial Isomorphism. for partial models A and A prime we say that the first is partially isomorphic to the second when a partial substructure of A is isomorphic to a partial substructure of A prime and so this notion of a partial structure or substructure is so conceived that a total structure

12:30 constitutes a particular case a partial structure or substructure but then this last sentence is helpful with regard to a partial isomorphism, certain of the relation, certain of the RIs on subfamily, stand in a one-to-one correspondence to certain of the RI prime. So we have this matching, but it's easier to achieve this sort of matching because it's not required that the structures near each other in total or that there can be a sort of partial connection between the two or partial from the other. So when it comes to idealized models, then, we can still say that the idealized model of a pendulum represents the pendulum, because the claim is that there will be a partial isomorphism between the situation and the model. So how is that supposed to work in our simple example? What's one way to go with our constructive program? The basic strategy for a case like ours is to include not only the SHO chains that are exactly related, but also allowing change where there is some limited variation so virtually a simple example is you can have a very simple picture To include these trajectories, right, where there's some limited variation from the exact equation, we might just replace the 1 on the right-hand side of 3 by 1 plus or minus delta, where delta was some contextually determined term reflecting the looseness of the idealization, right? So that's 3 half of a handbook. So what we have, this is just 1 of the trajectories allowed by the exact equation, and I'm saying, well, if you shift that this 3 half is 1 that has this plus or minus delta, you have these sort of two, and of course they overlap, but this is just one picture of what that two is. So for example, SHO linked to the origin, 0, 0, 0, would not only be the triple 0, 0, T, right, where the pendulum does not move at all, exactly it's not moving,

15:00 but all those trajectories where the values of theta and theta prime fell within the boundary set by delta. In that case, as long as you put a state within some region in there, then you'd still be interested in it in this case. So as it stands, the model is not yet partial, but this could also be introduced by stipulating that in some area around these boundaries, it's indeterminate whether or not the states form the message of change. You could have some guess reflected by these dotted lines. If you get up there, then suddenly you're in R3. You're in that region where the model does not think of standard. And a partial isomorphism will exist between the actual situation and this model, just in case the image of the actual trajectory is caught by our more generous selection from all the possible trajectories. So the relationship between 3 and 3F reflects what we take to be some good idealizing assumptions and the resulting more modest pretensions of our partial model. We do not think it reflects all that's going on in this situation. So when it comes to the trajectories, we allow a limited variation. The model remains a good one, though, and we can capture this kind of goodness by requiring the existence of a partial isomorphism. So that's what I take to be the proposal, at least for some of these synthetists. So there's two kinds of problematic models that also pass this test. So I guess it's an over-generation word. First, very briefly, I introduce what I'll call the full model F, under a worry on the end of. F has, as its domain, same things as before, the ordered triples of real numbers that go proxy for the possible states of the pendulum. But F is a full model because all pairs of points definitely do stand in this one relation, POS, or RF. So you just make delta really, really big. It was everything. Now for any trajectory of an actual pendulum, of course, we can find a partial isomorphism from the trajectory to F. And this partial isomorphism will relate the right physical magnitude to a trajectory in the model, but it seems like the full model does not represent the pendulum in any interesting way. This shows that once we allow partial isomorphism, it's no longer sufficient for a model to represent permit a mapping whose domain is restricted to the appropriate physical magnitude, additional

17:30 constraints aren't needed in specifying what the range of the mapping is. Intuitively, how big can we make delta, you know, consistent with actually having a good representation of what's going on? We can always capture the motion intended by making delta big enough, but, you know, what exactly, uh, what cost do we pay in terms of a good representation So that's, I think that's somewhat of a side issue, but more disturbing is this second sort of case that I want to talk about, and this is the last thing I have to say. More disturbing, though, is that the partial structure's approach decides whether or not a model represents well just by looking at the model, without considering how that model was constructed. And here, here I'm really just taking a lot of objections from the main issue, and I'm find it translated into the vocabulary that people in the partial structure of the community will be sympathetic to. So when constructing and evaluating idealizations, we're interested in more than what this analysis of idealization says we are. And to see this, consider the model picked out by our more generous equation 3F. The problem is that it is possible to pick out these same two using the same model. a different and much less satisfactory series of idealizations. So consider the exact equation 3 delta as an alternative to 3. So this is on the end of, of course, it's just plus delta, there's no minus delta there. So that's a sort of crazy, crazy equation. A trajectory that satisfied 3 delta would be an ellipse whose major and minor axes were delta units too large. But this exact equation with different idealizing assumptions could lead to the very same partial model constructed using 3F. So this is the dramatic unveiling. So that's our new exact equation, and I just combined that very bad exact equation with some idealizing assumptions that are also very bad. You're only allowed to idealize inward for every reason. and of course the trajectories that you pick out will just match towards two. You get the same model as a result of two bad sets, a bad exact equation and a bad idea. They cancel each other out.

20:00 So we've got three delta and then we allow only approximations inward up to a threshold of two delta and set as indeterminate any trajectories in the immediate neighborhood of the resulting two. So while in such a case, with partial isomorphisms, there is something defective about this sort of idealization, both in its original equations, which deliver the widened trajectories, and in its approximating techniques. So I intend this case as a counterexample to the claim that idealization can be suitably analyzed using the tools that the partial structures program has employed to date. What is needed is some way of disqualifying 3 delta and its strange inward idealizations. Given that it generates the same model as our free app, it's hard to see how to do this. If we focus just on the model, we only have the resources to discriminate proposals based on the trajectories that we end up with. In cases of idealization, this pushes the proposal into a rather unsatisfactory version of an instrumentalist approach to models. We're not allowed to investigate how the class of trajectories would be done. But as our example shows, and there's many others, of course, this can be crucial when evaluating idealization. So 3-app was arrived at by a series of supposedly well-motivated assumptions. The forces due to friction and air resistance are ignored, and the small oscillation assumption is used to replace sine theta by theta. But 3-delta might have resulted from some bizarre new hidden variable proposal, or it might be completely unmotivated. want to rule it out, or at least rate it very low as part of an idealization. So in conclusion, it seems clear that something more is needed, but I fail to see what more the costum pranks could appeal to, without making their models concrete, or abandoning certain guiding principles of the partial structures program, or at least in light of the session yesterday's supplementing it. So this shows that, at least now, as of now, the partial structures program has not given an adequate account of these abstract and idealized models. Of course, it does not show that the only or best way to resolve these issues is to invoke, along with Cartwright, causes or capacities, for such a move appears to get idealized

22:30 models that represent, only by sacrificing the generality of our scientific models. I think your problem has a rather simple solution, namely what you are missing is that the space of paths in the phase space and then the first approximation with the plus minus delta corresponds to this standard topology while the outward or the inward approximation does not. And so if you add the feature of that the set of paths of the phase space is not simply a set, but is a topology, then you can blame the second kind of proposal. So the idea is that this inward idealization... The inward idealization corresponds to a one-sided topology that is not the natural topology of the phase space. That's all what you need for a structural approach. I think what you're saying is probably sufficient for this particular case, but I worry that it's not really a topological issue. It's topological or it's a metrical or whatever. The point is to replace sets of structures by spaces of structures. And this is standard in science itself and often forgotten in philosophy of science, or in this kind of philosophy of science. And if you add this feature, a lot of these approximation programs disappear. I'm sympathetic to the idea that the structures that we're considering now with the parts of structures program are incorporated, and that something richer needs to be considered. I don't know the details in particular suggesting you're making, but...

25:00 I mean, it has been done 20 years ago by the so-called structuralism, who introduced topology, topological structures on sets of models, this is nothing new. No, but I'm saying I don't see how it's going to respond to the general issue of I think you might have something to say about the particular problem. I'm rather sure that topology is a ubiquitous feature that applies to a lot of cases, not only for this simplified example. I'm glad to hear that. It's quite a separate case, but I think you have two separate primitive concepts. One, that models like a full model don't represent any interesting concept, but they counter this representation. It seems so. I mean, it seems that they get counted, right? I guess there I'm worried about what's in any interesting concept to do in the same topic. I mean, I'm perfectly willing to go out, it's not an interesting model. but you've heard your argument you have to say it's not a model and so it's a problem that you can count as a well I focus not on models that are so I have to say either it's not a representation or it's not a good representation and I feel good saying it's not a good representation but that's compatible with the partial argument because well what's trivial and always available Because if you sort of add, you can set a rod up the one we want out of representation, it doesn't give us any of them. Well, that's what I'm asking you to do, part of this question. Okay. And I think things can be done there by talking about what the range of the mapping is looking like. That's something that's discussed a little bit in the presentation. and so I'm not so pessimistic about that one but I am relatively pessimistic about this other but correct, there's two over generation problems and additional principles cut down those problems and you know we need to see but no we need to see them and we need to really work through them and that's something that I would like to say maybe Thomas is suggesting

27:30 maybe there are other yeah I think there are and because part of the motivation is to look at the details of how the practice goes right and a lot of time we spend as you mentioned looking at the way which those models are constructed actually part of the practice rules out those models for various reasons, topological reasons, or reasons that you see, well, these are idealizations, they're not well-motivated, so there are several heuristic principles that go into selecting those models. And so, when you're in the business of doing representation, of course, it's more than just the mappings. You have to select which of them are the appropriate ones. And And that's where the business of the risk comes in, so that you can actually rule out those models. So if you ask, oh, we need an account of representation that's just structural, that you can actually rule out just by the features of the model, what are the mappings, then I think that's an unstuck. We need more. well I think there's two I mean there's two issues I think it's part of my I think both the strength and the weakness of this particular book the strength is that it takes on historical cases it talks about how models were augmented at a time but to me that's quite a separate issue from the criteria that we should have for models at a time for whether or not they're good representations now it's fine to say Look at the particular cases, you'll see that there are these veristic principles that push scientists in this direction versus that. But I would like to at least investigate whether or not there's something more generalist. It seems like there's some sort of category of thing out there, good representation, that all of these practices are ending up with. And what do these principles have in common? Why do we prefer these sorts of principles over the others? I think there's a more modest version of the partnership of these children, maybe, that is there with such

30:00 formulations of principles. No, you just go face-to-face with different principles, different principles. But I think something more is a natural thing to ask, So, it might be an unfair request, but I think some aspects of the work we've done that that is what they owe us. And it's just that representation has to be always contextual, right? So, there's one... Yeah, but that's not the issue. The issue is, in a context, what are the principles that make this a good representation in the way? Oh, thanks. Thank you. Let me start with a few observations concerning representation and models in the philosophy of science. Firstly, representation is discussed in the context of modeling, which poses the question why is this so? And it seems to me that one reason we see that very diverse kind of things are called models in scientific practice. And this poses the question of how will these diverse things then add to our knowledge. And the standard answer given by the philosophers of science has been that this is because the models represent. Models have to be less sensitive in order to keep us models. Well, it sounds nice. But there the agreement stops. Even philosophers and science both try to keep the conceptions of representation and the main alternative of both are structuralism or semantic conceptions and we can have this one. And now this poses the problem that motivates the rest of my talk today.

32:30 Given the different accounts or analysis of representation, why is it that we do want to tie the epistemic value of model representation even though we do not agree what representation involves? other ways. Again, there are approaches with extensive values of models in science. Now, before moving on to those other ways of approaching models in science, I however take a look at the pragmatic approaches to scientific representation, because I do agree that representation is a pragmatic phenomenon. Now, what the pragmatic approaches agree is that representation is a triadic relationship involving the users of representations and their interpretation. This means to shift the way from the semantic structure of the conception of models with this integrated diadic. Now, also Ronald Geary, Geary's views of models and representation have changed substantially since the semantic concepts profoundly in explaining science. He still claims that representation is based on a similarity of some kind. Geary notes that even though no objective measure of similarity can be given, the existence of the specified similarities that makes use of the model to represent the real system. No general analysis of similarities needed and neither can be given because of the geometric nature of scientific representation. And he proposes that representation can be thought of as having at least four places with roughly the following form S uses M to represent W meaning for the purpose of P which can be expressed more informally. Scientists use models of a particular type to represent something in the world for specific purpose.

35:00 But yes, a theory is careful to note or to point out that scientists also use models for various other purposes besides that of representation. In line with Miri, Mauricio Suarez criticizes the proper dyadic conceptions of representation because they attempt, I quote, to reduce the essentially intentional judgment of representation and users to facts about the source and carving objects or systems and their properties. So close to Geary, however, Suárez doesn't want to naturalize representation, which means that he resists saying anything and substantive about the so-called basis of its representation and power of the representative vehicle stress, i.e. viero de rest, for instance, on isomortism, similarity or denotation. Consequently, Suárez presents us a declarationary, influential account of scientific representation in which no deeper features of a representative relationship is sought after. Instead, one settles with the surface features of surrogate reasoning provided by models. The formulation Suárez gives to the inferential conceptional representation is the following. A represents B only if the representational force of A points towards B, and A allows competent and informed agents to draw specific inferences regarding B. The representational force, according to Suarez, is relational and contextual and maintained in part by the intended representational uses of the source by the agents. Part two in the formulation requires, I quote, A to have the internal structure that allows informed agents to correctly draw inferences about B. Thus, even though Suárez does not want to specify what kind of a relation there is between representation and its object,

37:30 it somehow has to be grounded in the structure of the representative method. Now, I do agree with this pragmatic approach to representation, and I even think that in some sense they are complementary. So that is a question of how, but I still think that representation has something to do both with similarities and its inherent by nature. Anyway, if we adopt pragmatic approach to models, the focus of representation appears unnecessarily limiting. From a scientific practice point of view, representation is truly only one of the uses the models are put to. So how, then, to approach the epistemic value of models? I find it fruitful to approach models as independent scientific objects, things or artifacts. Now, I read Morrison and Morgan's view of models as mediators as an attempt to approach epistemic functions of models from various angles. They consider models as alternate agents which through their construction gain indicators, at least partly, from theory and data. Moreover, Morrison and Morgan stress the importance of workability and manipulability of models for the scientific research. As I see, their approach actually has the potential to release the epistemic value of models from their supposed representative content due to their stress on models as independent entities. Concentrating on models as independent entities is a more radical move than it might seem at first class. It has been customary thus far to understand models as abstractions, idealizations, idealizations or theoretical replicas of something external to themselves. This is built into the semantic model. It is the underlying abstract structure that matters. In contrast to this approach, the specific focus on models as independent entities makes us realize that scientific models are typically man-made things that are made with a variety of ingredients, which is nicely discussed by Marcel Balmans,

40:00 who argues that there are many other ingredients in models than theoretical notions and empirical data. And in the field of social studies of science, Martina Merz has studied models as multiplex and unfolding scientific objects. Now, building on this line of work on models, I, an upper-volt liner, have proposed that we to treat models as epistemic artifacts. Now, to call models artifacts might seem an unfortunate choice of work to start with. I mean, aren't we in science trying to distinguish the artificial from the reality? Well, however, in the recent research in cognitive science, there is a lot of literature that suggests that our knowledge is importantly bound to our abilities to construct tools and manipulate our external material environment. Thus, we can approach models as epistemic artifacts, which are intentionally constructive things that are materialized in some medium and used in our epistemic endeavors in a multitude of ways. This implies that models have intentional material and epistemic dimensions, and the epistemic dimension being partly a product of the first tool. The most important epistemic properties of models are exactly used the way in which intentionality and materiality intersect in their diverse uses. It has even become customary to speak of theoretical or formal models as tools or theoretical technologies, while much of that talk is metaphorical. In writing, it is precisely the material dimension of models and representations in general that makes them collective objects or knowledge and enables them to mediate it between different people and various practices. Without materiality, mediation is empty. But I want to stress that models shouldn't be taken simply as material objects, that is not what I mean, but rather as things that are variously materialized.

42:30 There exists a strong tendency to distinguish material things from theoretical, abstract and or ideal things. Nevertheless, as parts of collective human environment, even material things are already endowed with interpretations, meanings and knowledge concerning them. On the other hand, theoretical ideas that are presented with diagrams, pictures or formal and natural analogies are also materialized as various descriptions on paper and on screen. So, all objects of human culture have both ideal or virtual, if you like, and material dimensions, even totally fictional ones, which are nevertheless materialized in texts and pictures concerning them. Thus, I don't see how it is possible to make any strict demarcation between what is material and what is not. Instead, one should, especially in the context of models and scientific representations, take into account the media through which they are materialized, that is, one should be media-specific in relation to representation. Now, the media-specific approach to models focuses on their constraints and enablements. As materialized things, models have their own constructions, and thus, their own ways of functioning. They are not open to all possible interpretations and uses which simplifies or modifies the cognitive tasks that scientists face in their work. In scientific work, Mark typically tries to turn into enabling limitations of the models or constraints built into them. One devises the model in such a way that one can learn from using or manipulating it. Learning is thus made possible through the material dimension of models which provide scientists a worthy object. The material dimension which is actually required of models is they are, to be independent in the sense that they can be transferred to other tasks and to other contexts, are also critical for their productivity. Models often produce something unexpected and they typically breed in addition to new applications, new problems and new

45:00 lines of inquiry. So from this point of view, it seems that the question representation is too often approached from the point of view of end use of ready-made models. Thus, I think it is characteristic of modeling that models are built by representing and that this task is dependent on what data, knowledge and computational methods are available. The ready-made models then are often valued rather for what they produce than for being truthful representations of the supposed natural target systems. Usually, we don't know enough of those systems, which is exactly the point of modeling, of constructing models. So, seeing models as epistemic artifacts helps us understand that a model can give us knowledge in many other ways than simply by virtue of some kind of re-established abstract representational function. Most of the information scientific models give us the result of inferences of various kinds. The representative links to reality provided by models are less straightforward and more fragile and complexly mediated than philosophical traditions Now this should lead us to take a new look at representations by approaching representations provided by models as two of the numbers, comprised of alternatives. Material sign vehicle and a triadic relation or representation, that true interpretation or use connects the sign vehicle to its object. The sign vehicle should be thought of as a material constructed historical artifact, which leads us to consider the complex, culturally, constructive, and artificial traits through which our knowledge of the world is actually mediated and constructive. The relational part of the representation reminds us that no signing vehicle is representative in and of itself, but that representation is both the process and the result of diverse intentional human actions

47:30 actions taking place in highly specialized activities. Representation as a twofold phenomenon is implicit in the mathematical account of representation of Geary and Suarez, in my opinion. Suarez takes representation to be a differential activity that relates representation for source as deposit to the target and is also somehow grounded on the structure of the source. Geary relies on similarity, so it is based on the properties of the side vehicle. Similarity is nevertheless established in the specific uses of the model which related to something in the world. The structural account for its part tries to merge the two aspects of representation into one by claiming that representation is grounded on the structural properties model and its target system. It is as if the things taken as representations did their representing job, that is created relational representation by themselves, by virtue what they are and their target systems are. Well, this actually often appears to be the case, when the application or interpretation of the model in question has to become routine. Now, the distinction between the material sign-behavior and the relational representation is largely conceptual. As part of the intentional human activity, models come with interpretations and are thus already embedded in epistemic relations of diverse kinds. Yet the sign-behavior can be detached from the relations in which it is embedded. And this is actually a characteristic feature of modeling. In modeling, sign vehicles are often transferred to different contexts and uses. The heuristic value of models has been ascribed to this procedure to describe it to entities of one domain with the help of already existing theoretical tools from another domain. Well, as conclusion, the twofold account I've been proposing is what must be minimally involved in representation. And I agree it is not much.

50:00 But I think it's quite difficult to say anything more general about representation. Since, as I see it, the difficulty with representation arises in science as elsewhere when we realise the materiality and the media specificity of our representations. Thus, we need to examine constraints and enablings that are specifically diverse representative meanings and the histories and uses of the actual scientific artifacts. Now, where or not this kind of work is bound to lead to new analyses of representation or new conceptualizes or alternatively to new conceptualizations that ultimately displays much of the discussion and representation reminds of all the questions. Thank you. Can I just ask your view intentionality so you say models are an intentionally instructive artefact naively one would think there's two ways you could go you could say that intentionality is not a constitutive part of a model, it plays a role, I might say it plays a role in picking out one relationship over another I think Maurizio has tried to suggest in some of his work that intentionality is in a sense of a model. And the worry that one might have there is that then it ties, that ties a model because you can intentionally have to link it to the purpose, ties it to a specific purpose, to a specific system. And then the worry there is issues of individuality and identity of models arise. If, as you say, models have this heuristic value that can be applied to new domains, is that the same model being applied to the new domain, or how can it be if its purpose is, in a sense, a constitutive part of it? I wasn't quite clear where you stood on that, because if you're with Maurizio, to put it crudely, it seems that conflicts with your last comment about the heuristic values of

52:30 models. I can't quite see how those mesh. If you think that intentionality is not a constitutive part of a model, then I think a lot of what you say, many people would be able to assimilate to accommodate. I would like to argue that I would add both models as models in use, which means that once you are using models, then you can treat them as intentional. But of course, I mean, if somebody, a lay person would be presenting or say some kind of a model, it's totally less intentionality in that context, I mean, the person who now this representation is presented would lack the knowledge of how to sort of relate this representation to something else. So I wouldn't say that it's the part of this material science vehicle or materialized science of this intentionality but it's sort of a part of the use of it and I think that well it's difficult to say what is actually a model in that sense because on the other side I sort of sympathize with the idea that models are intentional because exactly they are all the time used so we don't where you have models in abstract, oh well, except in philosophical theorizing, but that happens for some purposes also. Thank you. I actually, I liked a lot the idea that models are artifacts, and that has to be right. My worries about the materiality part, obviously there are many cases in which models have that materiality, no question, but in other cases it becomes less clear. So suppose you ether and we cannot just say that the models are the inscriptions of the equations right because we don't say well I wipe out the equations there goes the model right so on the other hand we cannot say that the models are just exemplifying the world because there isn't the ether nonetheless the physicists were actually trying to model something and so my question how can you that. Particularly if you think about the materiality of the model that gives it subjectivity, as you mentioned.

55:00 Well, there is a few ways to do it. And I don't know a much better way now is to say that models are naturalized and they're very naturalized. and some models and we have these three-dimensional models and obviously they are very material but then what about equations and so what yeah they're sort of their way of naturalization is totally different and sort of uh well they depended on certain conventions and so on how to handle them so that is you know my preliminary answer but actually this is something I really want to think about more if I want to argue for this materialization. But I think still, I mean, it has to be somehow this epistemicity of models to be bound to materialization. Well, one quick suggestion. Instead of using the materiality of the model as a means of its objectivity, look at the practice. Because you already have the practice built in when you say, well, models are artifacts. doing things, and the practice would have conventions about the use of those models that probably will help out in terms of giving the sort of objectivity that you want. That's actually implied in this, I suppose, this activity. But then I think again that this kind of scientific activity is very much about using these artifacts. So, and models are, you know, artifacts, pariks, and las, which scientists are using. So, I don't know, they are sort of complementary, I mean, this artifactual and then practice approach. Would it be fair to say that one of the things you're doing is, as Ian Hacking said 20 years ago, focusing not on representation or the object, but focusing on the practice of representing. Exactly, yes. So if you start, if you say, here's what you've got to say, the process is representing, or then you say, by a modeling, then it takes away the idea that somehow this abstract thing has this all by itself. Natural powers. Yeah, it has natural powers all by itself to represent. Whereas the power, so to speak, is coming from the agents who are doing their representing. and then you get all the stuff you want.

57:30 That's all part of that process. So that is an okay way to say what you're doing. Yes, well, that was nice. Thank you. Everyone just asked my question. Okay. That's nice. The problem with that viewpoint, though, is with the value that science has put on the model. models are in the minds, in the eyes of scientists, in terms of value. And a model becomes more valuable, the less triadic it is, and the more dyadic it becomes, the less purposeful it is. So a model that is for a specific purpose has some value, but the greater number of purposes that one model can be applied, the more valuable it is to a scientist, and the most valuable model they can think of is one that applies for all purposes. Yeah, I can agree with that, but, you know, in that case, I would say that this model is, well, then the use is routine, and it's very generalized, I mean, when we have generalized models, the use of which is routine, of course, they have the ones which are most popular, and so on and so forth, so I don't see why this seems to contradict Maya goes to us. Well, is epistemic value then in proportion to the lack of purpose that goes into the model? It's in proportion to the multiplicity of purposes. Or, that's a different way of looking at it. If it's good for all purposes, then purpose no longer plays. No, no, that's not good for all purposes. Good for all purposes. We've got lots of purposes. Doesn't your theory blur the difference to scientific instruments? In my own work I make a difference between constructive instruments and representative instruments. And I cannot make any more the difference between a representative instrument and a model in the end. I think that the same thing, you talk about models, can be used both as tools and objects, so that you know, and also models can be used as tools, as instruments, and then the scientists, for instance, I'll be studying language technology, I'm not worried about them as representations, they are just interested in what they produce,

1:00:00 But in the same time, those theories and models can be sort of a representative or a more epistemic object. Then I can rephrase my question and ask, when do you use a material object as a model and when do you use it as an instrument? Well, I mean, if I use it as an instrument, it's sort of a tool to achieve some other end. But if I use the model as a representation, so now this, I see your point, but still I think that if I use it as a sort of representation, so then I want to get some knowledge via it from something else. There is, if I use it as a tool, say, well, it's some, this is, I think this is more easy, these things are made in, say, engineering sciences, where some of the models are tools for doing some other things, and then some scientists who use them as tools don't consider them as representation, that's not important for them. But for some others, these very same things can be represented in every person. They might use them for incurring something about them, because I will use the claimability as a community. So I think the same things can have different functions in both objects and tools, in both instruments and representations, depending on who is using them and for what purposes. Thank you. Thank you. of quantitative modeling and modeling systems. It's advantages to qualitative modeling at work. After defining Yapanov's stability in Section 2, I analyzed how a loop analysis, what method of qualitative modeling, can be used to assess the stability of ecological communities. Based on this analysis, in Section 3,

1:02:30 I defend qualitative modeling against four-second servers criticism that it's conceptually and methodologically Thank you.