Risen from the dead? Carnaps's Logischer Aufbau

0:00 The speaker from Salzburg is going to talk about the living dance, or from a more Christian perspective, rise from the dead. Manigate is going to be connected with the carnivores. Thank you. Well, that's the last talk of the conference. It's a pity. Really? So, Philip, of course, it's my pleasure to inform you about a new project of mine. Besides the things that I'm doing in logic, I have this new project that I like to think of as being an epistemological one. And it is about the revival of certain parts of Kama's logischer Aufbau der Welt, the logical structure of the world. It's a systematic project, it's not a historical project. So, you now might probably think, that's a little crazy, we all know that the outbound is such a drastic, notorious failure, so how can someone stand there and say, well, let's try to revive it. If there is an aim behind this talk today, then the aim is, I would like to convince you that there is some point in doing that, and that it is not as hopeless as it may seem. That's the idea of this hope. But let's step right from the heart of the matter. According to the traditional interpretation, the Aufbau had a certain aim. When I say the traditional interpretation, I mean the interpretation that you find if you read the Klein on the Aufbau, means if you read what Quine criticized when he referred to the Aufbau. But it's also the interpretation that Carnap gives retrospectively when he talks about that time. And according to that interpretation, the Aufbau's aim is to prove a certain thesis, and it is roughly that thesis. It says that, give me some scientific sentence of a scientific language, then that sentence can be translated on the basis of definitions, such that the image of that translation is equivalent to the original sentence, and furthermore the image solely consists of logical signs on the one hand, and on the other hand terms referring to the given, where the given

2:30 means given by experience, and we can even constrain that to given by sense experience. So that is what is usually meant when we say, be given. So, it's not so clear what was meant at that time by an equivalent sentence. Sometimes they say it's a logically equivalent sentence, but that cannot be our sense of logical equivalence. Taken strictly is that the translations are not logically equivalent to the original sentences. But roughly it means something like, if you replace aid by the translation of aid, which is given by definitions, then you can do that for all scientific purposes without doing any harm. In fact, it's even a virtue. You might clarify certain issues, you might think more precise, it's like an explication. something gets more precise. In particular, the original sentences and the translation of the sentence should have the same truth values. In fact, there is an extensional account built into the logical structure of the word. So, extensions of sentences, truth values should be preserved by that translation. Now, as we all know, the alpha of course fails. that program doesn't work. So there is overwhelming evidence that it does not work. I've made Goodman and Quine, but it goes on. You can think of, I don't know, Sellers or Chisholm or Kuhn and so forth. So the number of deficits is legal. There is also a different interpretation, an interpretation that differs from the traditional one, and it was introduced by Michael Friedman and Alan Richardson and a few other people, but those are the most prominent ones. According to that interpretation, that is not the real aim of the Aufbau. It's a kind of additional artifact, so to speak, of a certain constitutional that is described to me also. But the real aim has more to do with Neo-Kentian trade, the Neo-Kentian tradition. I won't say much about this, because I want to start with that traditional interpretation. There will be a point in my, I think, last section where

5:00 I will say something about this different interpretation. Now, I'm actually not interested in that thesis, because that thesis is false, and I totally subscribe to the statement that it is false. But I'm interested in a weaker thesis, which goes like this. It says that, give me, again, a scientific sentence, then that scientific sentence can be translated to an empirically equivalent sentence, such that the image under that translation is a sentence that thoroughly consists of logical mathematical science on the one hand and terms that refer to experiences. Now there are three differences. First of all, I do not claim that the images under these translations are equivalent in the sense that I've sketched before to the original sentences. They are just empirically equivalent. The translation of A, so to speak, determines the empirical content of A, but I do not claim that they I do not even claim that they have necessarily the same proof value, just that whatever has to do with the empirical content, okay, is preserved, and that is everything. But we know that meaning goes beyond empirical content, at least so I would claim. Furthermore, the translation sentences may concern mathematical science, and I do not regard these mathematical signs as logical signs. So, obviously some program of logicism was still present when Conor broke the outfall, of course, but I do not subscribe to that. And furthermore, I replaced the term given by experiences. And you will see in a minute what I mean, so I also do not adopt the kind of phenomenalistic tradition of what the given is, something like that. Or, well, you will see how I change the basis. So, it's no longer re-given in the original sense of the rule. So, my question is, is it possible to defend that weaker thesis by methods that are either already contained in the Aufbau, or closely resembled the methods in the Aufbau? That's the question. put differently. Are there aspects of the oath Aufbau that can be saved? And is there a weakened and restricted new Aufbau? Weakened in the sense like

7:30 that this thesis is a weaker thesis? By constrained or restricted I mean, I'm not interested in this broad picture that Karl is. You know, he wants to constitute everything. Everything? So, yeah. See what I mean? In particular, he wants to constitute, for example, a cultural object. That that is included. Things ranging from, I don't know, societies to, yeah, you name it. So I'm happy with what Karnoff called the auto-psychological domain in the Aufbau. Everything that's going on within the mind of the person whose experiences we refer to. And then I'm interested in the first steps into the physical domain. And I'm absolutely happy with that. It's much more restricted than the original outbound. That's the plan of the fall. I will start by saying something about the basis, the basis of the original outbound and of my new constitution system. Then I will turn to the definitions that are stated in the alpha in the so-called auto-psychological domain, and I will show how we have to amend them, how we have to replace them. Then I will deal with the first steps into the physical domain. I will say something very briefly, just a sketch about disposition turns, and I end up structuralism. That's the plan. Let's start at the basis. Karnas did not really specify the language that he uses in his constitutional systems in the outcast. A few years later, he would surely have started by saying, what is my vocabulary, what are my syntactic information rules and so forth, but he didn't do that in the alpha. But you can read it off what he said. It's easy to determine. The language of the old alpha system was on the one hand the language of simple type theory. So you might use the membership predicate, but you can eliminate it by qualification over

10:00 properties or classes. And you have a second predicate, that's a binary descriptive predicate. It's not belonging to the logical part. In fact, it belongs to the empirical part. And that is what is usually called the basic relation in counter-system. And it's not defined. It's a primitive predicate, of course. But Carnot tells us, extra systematically, on a meta-linguistic level, what the intended interpretation is of that predicate. And I will briefly sketch this. So what I'm now saying is now not within the Constitution I'm talking about the computation system. What Carnot tells us is that if x stands in the relation e to y, this is to be read as x is recollected as being part similar to y. So this relation is a recollection of part similarity relation, if you want. What does that mean? First of all, what are the variables running over? They range over Carnot's basic elements. And these basic elements, it tells us, are what he calls elementary experiences of a fixed subject. Let's fix a certain subject. Of course, a human being, but it might in fact also be some fancy artificial intelligence agent if you want. That doesn't really matter. Let's fix the subject S. let's consider it as a stream of experience say there is something like a stream of experience, or a sense experience then we might slice up that stream of experience into certain units such that every such unit is experienced by the subject as being present as being momentary That's James Batch's presence, if you want And now these total momentary slices through S's stream of experiences are precisely what are the elementary experiences of S So those are the basic elements, and those are the things that the variables range over So E is a binary relation of such elementary

12:30 experiences, Goodman called them elites, you know, yeah, yeah, the American likes to have, you know, short-term, sorry, sometimes I don't use that, it makes really text shorter, you know, it's an elite. And, now, what does this relation amount to? Assume that the subject is able to do the following. He might compare a memory image, so he stores, so to speak, the ellipse, previous ellipse. The memory image of a previous ellipse, he compares that with his current ellipse. That is what he does. That is the resemblance or recollection component. And in that comparison, he tries to find out whether the previous ellipse, or rather its memory image is part-similar to the current allebe. And part-similar means roughly the following. There are two quality points, p and q, in some sensory quality space, visual space, auditory space, and so forth, which are metrically close, they're close to each other, and the one allebe realizes the one point, and the other allebe realizes the other point. That's the idea. So for example, I now, Kamas would say, I have that's my visual field and I have visual experiences and there is this green point in the lower left part of my visual field. That's important, yeah. Okay, and now I wait a little. Now there's a new elite. And now I've moved a little, you see, so it's not precisely, the green point is not precisely where it was. Perhaps now the sun shines a little different, so it's not precisely the same kind of green. But think of the following space, it's a five-dimensional space, two dimensions for the place in my visual field, and three dimensions characterizing the color, so hue, brightness, saturation, then the green, the previous green at that point, would correspond to a point in the five-dimensional space, the later green, at a slightly different point, still corresponds to a point in the five-dimensional space. They are metrically close, so we have a metric space, actually, and metrically close means the distance of the two points would be less or equal than some fixed epsilon, fixed small

15:00 epsilon. So they are metrically close. The one ellipse realises the one green point in my visual field, the second ellipse realises the second point, they are metrically close, so the two ellipse apart are similar, and if I have this recollection, then they stand in that E relation. That's the basic relation of karma. To realize this relation, that's like a type token. Something like that. The x's and y's are tokens. Yeah. The points in the state space are types. Yes, you can think of that as that way. And these quality points, I really think of them as abstract mathematical entities as I've described them now, in this five-dimensional space that I use to represent visual qualities. Now, there are already here some problems, but these problems, of course, only show up later in the system. First of all, this relation is rather weak. So, normally, this all depends on what kind of experience the subject has, but normally, you may assume that too many alleles are similar to too many other alleles. And if this recollection takes place, then there are too many e-pairs. So, in a sense, this slogan, everything is somehow similar to everything else, you know. You only have to be creative concerning the respect of similarities. And, you know, it suffices a little point there, we're going to call it suffices. The other things do not matter, you see. They are roughly the same, then the two alleles are quite similar, independently of what else is going on. First of all, this relation is not colored. So we have got, it's like a graph, but the edges are not colored. We forget about the respect of similarity. Two ellipse might be similar, part similar, concerning a particular call point. Two other ellipse might be similar because, you know, because of some auditory information. But once you start out with E, you forget about all these different types of similarities. And then, actually, it may be seen that this gives you a probability. And there is no gradation of similarity. That is, we do not have a numerical similarity measure. We do not have a comparative similarity measure. Nothing like this. It's purely qualitative. These deficits affect the later definitions in the original system.

17:30 So I change the basis. That's my new basis. That's the language of my new system. I have a binary membership predicate, and that's just a standard step-theoretic membership predicate. And I presuppose some standard step-theory plus ur-elements. The ur-elements, or atoms, will be my new basic elements. And I again have a descriptive predicate, an empirical one. It's no longer binary, it's 7-ery, or 7-edic, if you want. And it's very important that it has seven places. Actually, there's something true, what I said. No, it might have, as you can see, much more places. But it shouldn't have, the numbers of places shouldn't be smaller. And I will return to that point. But in my final version, you know that is work in progress, what I'm just presenting. version, I will, in a sense, leave that open. I would just say that O is a class of sequences. It might contain pairs or triples, seven tuples, but perhaps ten tuples, and in some physicalistic interpretation, it might even contain infinite sequences. So then I'm open. This corresponds to something that Lewis and Quine have suggested in different papers. So what they say is binary is not good enough. Even ternary similarity is not good enough. We need some notions of collective similarity, where we might say of arbitrarily many things that they are similar, and we leave open the number of places that the similarity relation has. This has led to a lot of criticism, but once you're given set theory, it's not a real problem. But this is no similarity relation. You mean that they can't be reduced to pairwise? Yeah, yes. That's critical. Yes, yes. But that's not a similarity relation, but it has a different interpretation, this new predicate O. First of all, I read it as overlap. So we are back to Calguero. So I will read this as x1 to x7 overlap. left. What do these variables refer to? They range, again, over my basic elements, which differ from Carnot's basic elements. My basic elements may be characterized as what could

20:00 be called phenomenal tropes. So usually tropes are explained in the following way, again the bottle, but that's not now about my visual field, I mean the bottle. So the green of that bottle, that would be a trope, and the green of that bottle is different from the green of that green board, black board, yeah, yeah, chalkboard, yeah, chalkboard, that's good. So take another green, that's a different trope there. Tropes, they are bound in time, so that's the trope now, that one. But that would still be true if there were an identical green bottle over there, it would still be a different green, wouldn't it? Yeah. You're talking about localized green. Yeah, localized green. And that's the second one. If it was one sitting over there, it would be a different one. You're right. Take these. Yeah, I should have. Yeah, that would be a better example. Actually, I was looking for a second bottle of that type, but it didn't find it. Sorry. We should have prepared to talk about that. You should have taken those two blue ones. You're right. You're absolutely right. So they're not only bound in time, they're also bound in space. at that place. It's the green of that very bottle, even not a different bottle here. That's the usual way how you try to explain what you mean by a trope. Now, the tropes that I mean, they are phenomenal tropes. So, it's not a trope belonging to that bottle, it's a trope belonging to an erlebe, in the kind of sense. Okay? So, we could call, we could say that my basic elements are property bits, like this green bit, but not of bottles, of total momentary slices of S's stream of experience. So, for example, take again my visual field. I have this green spot here. Now, there is a property bit which applies to my current Aleve, and which is there because within the visual field there is this green spot. And those are the tropes that I'm really referring to. I can tell you more. I can tell you something about the formal structure. Again, this is all on the matter level of the system. It's not part of the system. Formally, my basic elements correspond to pairs of sets. So that's not a formal model that I give in order to give you a clear understanding of what I'm referring to. That's all that I'm doing. Okay, and see? Formally, there is a correspondence between my basic elements in such pairs.

22:30 On the first place of such a pair, there is a convex set, more particularly a bounded, extended, closed convex set of quality points in the sensory quality space. So think of the visual space, that's now the image of the visual space. And it could be the five-dimensional one again. So this is a five-dimensional convex set, not just in the plane. And that could be such a set CQ. Bounded, I mean it in the standard sense, so it doesn't extend to infinity into some direction. Extended, I won't say the precise definition, but the idea is it shouldn't be point-like. And it shouldn't, yeah, it shouldn't be point-like. That's okay in the context where you additionally say that. Yeah, and it shouldn't be, if it's five-dimensional, well, probably, I'll tell it. It shouldn't be line-like either. Yeah, it shouldn't be line-like either, in the case of a five-dimensional. Right. Yeah. Yeah, absolutely. And it should be convex, and actually, that's the most important point. I'll return to that point in a minute. The second component of this formal representation of my basic algorithm is again a convex set, but now a bounded extended closed convex set of temporal instance on the real-time axis. So apart from the visual space and the auditory space and whatever sense modalities you think of, we've got time in the sense of the physicist, so that's just the real-time axis. And such a CT will be a compact interval on the real-time axis. And they are, so to speak, associated. So that pair is the full representation of my evidence. Now, if there is this green point, then in a sense the green point instantiates that convex subset of the visual space if the green point at that place in my visual field is within that convex set and in that case i would say such a probe is there you know and within that uh interval of time not later and not before i'm not saying that all of the convex sets together paired with all of the intervals here

25:00 here, are former correspondence of my ellipse, you know, so I might have my basic elements. I might still have a finite number of basic elements, so then we have finitely many of those pairs. So why don't you take the Q and the T, as it were, as one, so why do you have to separate them out? Well... Add another dimension? You mean a six-dimensional space? By doing that together? So this isn't subjective time, is it? This is external, physical time? Is it inside the head or outside the head? Yeah, in my full representation I would say it's outside the head. So if it's outside the head, that's an important issue. Later, I want to follow Kana in using dimensionality of spaces in order to separate the sense modalities. And in order to separate time from the sense modalities. So I wouldn't like to put them together because then I cannot no longer separate them anymore. the point. Okay, and how does my basic relation now? What's the extension of a basic relation? So these are the former representatives of my basic elements. First of all, I should say there is an elite which instantiates CQ within CT. That's what I've just explained verbally. And now I say that O, my predicate, is true of such pairs, seven of them, if and only if either of two cases holds. Either they overlap concerning the qualitative component, or they overlap concerning the temporal component. So for example, if you've got a second, if you've got an auditory convex set, auditory convex set, so this is now a different space than that one, you know, But it occurs at an interval of time that overlaps the interval of time of that basic element, then the two overlap. Furthermore, if you've got, say, another visual convex set, but at a totally different time, still the two overlap, but not qualitatively. And I'll put that into my basic relation, though, except for the fact that it's a seven-ary relation, not a binary one, as I just suggested.

27:30 But the binary one is somehow contained in the seven-ary one. You could write x1 and then x2, x2, x2, x2, and you fill out the places. Okay, as I said, an overlap relation of higher elasticity would be adequate as well, but not one of lower elasticity. And this has to do with a certain theorem in convex geometry that I will later make use of in order to get my definitions of dimensionality going. So I will come back to that point later. Why am I focusing on convex sets? I won't defend it here now. But someone has tried to defend it, to defend that, and I'm building on that. and that was Peter Gavinfall. He has written a whole book, more or less, on that topic, Conceptual Spaces. But he has also written papers on it. The 1990 paper is in Philosophy of Science. So what he did was, he looked at quality spaces and was looking for something that would correspond within such quality spaces to the notion of natural class or natural property. What might that be? you started from some kind of evidence so for example natural properties we should be able to make use of them in the context of confirmation and in particular if you think of problems of projectability so for example what about to predicate non-black somehow that's not natural or so you would say or think a groove paradox, then you have some kind of disjunctive property or a disjunctive predicator on the syntactical level. That should also not count as natural. That somehow confirms to the closure conditions of convex sets. So, not necessarily is the complement of a convex set convex. Not necessarily is the union of two convex sets convex. Of course, that's just very, very mild evidence because you could have other classes of sets But if you look at the quality spaces that might be attached to colors, indeed non-black is not convex there. If you think of the group paradox or the group predicate, and you take any typical visual

30:00 quality space that psychologists would give you, then the group predicate really the extension of it would be a region that is not convex. Where does the idea of linearity come in in these things? Are you assuming that everything's equipped with a mesh shape or something? Yeah, that's a good idea. I would have said, anyway, something. Convexity, in the most general sense, means that you've got some set and a between-ness relation on that set. That is the way I would put it. Okay? And then you would say a set of our individuals, of points if you want, is convex. points in that set, everything that is between the two points is contained in the set. So that's the standard definition. Now, if that space is a linear space, then normally the between-its relation is defined in terms of the linear structure of that space. So you would say, what is in between is something that is on a straight line, and furthermore something such that the distance from that two plus the distance from that two is precisely identical to the distance from that two. Something like that. You can put it differently. So, and I will, in fact, presuppose that my quality spaces are, in the end, linear spaces. So I will really think of between us in terms of linearity between us. And comparison of distances. Yeah. I mean, you can put it differently. So you can compare distances and have a notion between us and reconstruct lines. That's right. That's right. you can actually augment that list arguments from a whole range of other things a whole range of things where we want to introduce natural classes, real that's true, but that's the most specific list it's a specific list for convex sets as plausible candidates so you're right of how we can use natural properties, natural kinds, the natural slice of the world. That's perfectly right, yes. Or nonetheless, at least, that's why we want to introduce a notion of that kind. That's absolutely right, yes. And I should also say that if I speak to you now, in the sense of Gavin, of natural property or natural cross, natural region in a visual space, one has to be careful. I mean, there are several traditions of what a natural cross is. So one comes from quine, natural kinds. That's not necessarily what you think of if you think of Christie and Pafner and so on.

32:30 I'm still not so sure how all these threads go together. It's more in the tradition, but what Gandalf does is more in the tradition of crime. And it's more in the tradition of naturalness is something that comes from the subject. It's not there in the world. Okay, there are arguments for prototypes, so if you have a bounded convex set, you have a center of gravity that you can attach to the bounded set that might count as a prototype of that set, so that's something a cognitive scientist like. I would add that convex sets are plausible candidates as being representatives of what might be called a respect of similarity. If these two points are similar in a certain respect r, and that point is between them, qualitatively, in the same respect, then also that point should be similar in the same respect to that one and to that one. So closure of the between is somehow corresponds to closure under similarity in the same respect. And that makes, I think, good sense. So we can view such convex sets as respects of similarity. In a sense, I start from respect of similarity and not from a similarity relation. Okay, then furthermore, I've chosen my basic elements to satisfy further methodological demands, different ones than, for example, Goodman had in the structure of appearance. So my basic elements are extended, in particular they are not point-like, they are not atoms. Then they are actual, so everything has to be actual among my basic elements. There are no possible tropes or something that I'm looking at. I think of them as being concrete. Now, the standard way of putting things about tropes is to say they are abstract, abstract particulars, something like that. But if you read, for example, Campbell or other people who try to explain this, then it's just because they say they come before the mind through an act of abstraction or something like that. Okay, that's one version of abstract. But I think it's also good to say that something is concrete if it is somehow bound in time and place. And in that sense, I would say it's concrete. But these labels are not so important for me. As long as you understand what I'm referring to, I'm totally happy. Well, I'm not sure. You mean, for example, the green of that bottle? No longer. I mean, my tropes are not the green of the bottle,

35:00 but it's the, so to speak, the green of my L. You know, I have these phenomenal tropes. I started out by this standardized way of putting things about tropes. That is what I was starting with. But no longer, no longer. Because then I would have to presuppose already the bottle or something, and that is not what I'm doing. And I have no presuppositions concerning cardinality. That means I could have a finite number of basic elements or an infinite number of basic elements. In the original Aufbaukahn of that, we have finitely many elements. And from a phenomenalistic tradition, in a phenomenalistic tradition, that's of course the way to go. But, in fact, I want to leave open whether there is a physicalistic interpretation of my set of basic elements. And then I might well have infinitely many tropes. Like there are infinitely many states in a certain phase space in physics, something like that. I do not assume that the subject as perceives the basic elements. That is not what I'm saying. So, I have no sense data theory in the traditional sense of the word. Everything I say is compatible with direct realism. You really perceive, of course, the bottle. But I'm just saying that my sentences that involve O may be used to describe my experiences. That might even be an external description from a neuroscientist. He describes something that goes on mentally, even in my brain if you want. And I'm sure something goes on when I perceive the bottle. But I do not say that I'm really perceiving my throat. I perceive the bottle, and while I'm doing that, something goes on, and I can describe that by making use of my predicate dose. That is what I'm saying. But I think that would be a false theory of perception, and I do not subscribe to that. As I said, these descriptions in terms of goals are not necessarily first-person descriptions. They might be third-person descriptions. Someone else might describe them. And the subject is not assumed to be consciously aware of this basic element. Not even that is supposed. Now, if you want to describe a scientist making an experiment, for example, you might want to have this presupposition that he is consciously aware of what he's doing because that's all that

37:30 counts if you want to speak of confirmation or disconfirmation of theory he has to be aware of the results of the experiment but that's a certain context, not necessarily the case Did you have collective ones? What do you mean by collective ones? Like the experience of inhabitants and the experience of members of Bristol University No, I want to exclude that, it's just one person And that's because, in the end, I have my experiences, you have your experiences. I mean, we can talk about that. We should. But, in the end, it's subjective. And that is preserved. So, I won't say much about this. I do not presuppose some kind of epistemological foundationalism. So, O sentences may be uncertain, O sentences may be false. You know, I'm not presupposing anything of that. So, you can now see that it's not traditional programs at all. And I have no problem, Stella has had this problem, how can you go from the qualitative elements to something that is in the space of reason, something that's somehow propositional. In a sense, my basis is propositional from the start, because I start with things like saying, that trope is in the O relation to that trope. That's the sentence. It expresses the propositions properly, and so forth. But it's just, we do not only have the basic elements, I also have the basic relations. I'm not committed to any way in which it always calls to hold between certain basic elements so that's just a description of the experiences in our subject it might well be that these experiences are caused by something that's going on through my senses plus something that's going on internally theoretical beliefs that I have might have an impact on my experiences if that is the case, so be it whatever level that is the one that I start with. Already at that level some knowledge that I have, the attention that I give to something, you know, all that might have an impact. So as I said, there might be a phenomenalistic interpretation of my basis and a physicalistic one. The physicalistic one. Klein is well-known as someone who criticizes the outfall, but in fact, at several places, he suggested a kind of physicalistic counterpart to the outfall. He did that in epistemology natural line, not so long ago, ten years ago,

40:00 in his impressive observation sentences in Journal of Philosophy, and in between from stimulus to science. So there he really sketches the physicalistic analogue of the outbought program. And it might be curved in that, but you might also view it as a kind of enlightened phenomenalism, except for the fact that I'm only, remember, only trying to preserve empirical content. I do not say like old phenomenalistic tradition would say that you can really, everything is preserved, you know. I wouldn't say that. But that refers to your question again. the basis is always subjective. So I'm not starting with a physicalistic basis in the sense that I take world lines or particles in the world something like that. My basic relations are not gene identity or coincidence or something like that. There are constitution systems that even come up described in the alpha which have a basis like this. But I'm interested in an epistemological project. And that's why I start from the subject. And furthermore, there are other possible choices of taking different, you could take different basis. And in fact, I changed the basis system in the last few months. And I'm still trying to find out what would be the best option. But probably there is not the best option, there are several possible options. And it might be that within the one basic system, you can define the basis that you could have used, and even vice versa, that's possible. For example, as you will see, I will define the basic relation of, actually I do not really show you, I'm able to define the basic relation of Carnot in the alpha. I'm able to define the class of LX in my system, so I can reconstruct the Carnot system in my system. And the choice of the basis may well be guided by theoretical considerations. Okay, so the old Aufbau system doesn't work as part of the language and the intended interpretation of the terms in the language. What about the system? The old Aufbau system consisted of the following parts. We had logical axioms, which is the part theory. we have what Karnoff called empirical theorems so you can think of E is given by a long list of pairs

42:30 of pairs of ellipse that is again the basic relation of Karnoff and now you have a sentence that just describes properties of that set of lists that's an empirical theorem it depends on what the subject what kind of ellipse the subject has and what the relation is like. But systematically, it functions like an axiom. You have to state it, and then you can derive something, things from it. But it's made true by the extension of the basic predicating kind of systems. And then, that's the essential part of the system, you have definitions. Lots of, lots of definitions. Constitutional definitions. So he defines the set of elements. It's a little funny, but the set of basic elements is defined in terms of the given basic relation. Then he defines a set of qualities, set of sense classes, the visual sense class, the auditory sense class, a preliminary time order, and so forth. That's all within the auto-psychological domain. We are not yet going, stepping into the physical. Now, Goodman, in the structure of appearance and in later papers, showed that the methods that cannot be used in order to constitute the qualities and the sense clauses are affected by substantial problems. That are the well-known difficulties of companionship, imperfect community, accidental overlap. Those are Goodman's terms, original terms. And now I will not say too much about that. I've just written a paper on that topic. We're not talking about human companionship or human community. No, no, no. Okay, sorry. I should at least... Terminology. I should at least say so much that that is excluded, yeah, you're right. So, for example, imperfect community. So, say you've got three elites, back to the Conor system, three elites. These two elites are similar because they share nearly the same red spot in the left lower field of the visual, in the left lower visual field. These two are similar because there is a certain sound contained in both. These two are similar by some tactile, you know, sensation. Okay, what Karnab then does, he's looking for maximal cliques in that graph. That is, subsets, such that every two members of such a subset is related by E,

45:00 and the set is maximal having that property. So, for example, that triangle, leaving out the other connections, would be a maximal clique. And then he tries to define qualities in terms of these maximal cliques. But there is a problem there because they are not similar in the same respect. I mean, the three of them. They are similar for three different reasons. So we now get some kind of mixed quality that we do not want to have. That's the problem of imperfect communities. And there are different problems, companionship, if one quality is contained in the other, that's a problem. So the larger quality soaks up the smaller one, and so forth. I've just written a paper on that, in which Goodman only states examples. And that's not very satisfying. So in my paper, I state necessary and sufficient conditions under which Carnoff's method of abstraction that he uses, so-called method of quasi-analysis, works. And again, if these conditions fail, then the method does not work. And then you can show that Russell's application of that method in our knowledge of the external rule works, because my conditions are satisfied. Carnap's application in the output does not work, because these conditions are not satisfied. So if someone is interested in the paper, I'm happy to send it to him or her. Furthermore, as I said before, Carnap distinguishes, then the difference, so he constructs the sense classes. Which of those is the visual one? Which of those is the auditory one? How can we separate them? And the idea is, let's separate them by dimensionality. Here you have to presuppose something. You have to presuppose that this visual space is five-dimensional, as I said before. The auditory space is not five-dimensional, because then the method wouldn't work. It's two-dimensional. So what if some cognitive psychologist tells us, no, the auditory space is five-dimensional. If that is the case, then we have to change the constitutional definitions. So on the meta-level, you've got a kind of background theory, and you presuppose that background theory. And you only can set up the constitutional definitions relative to that given meta-theory. If the meta-theory changes, then you have to change the constitutional system. That's the way it goes. And I'm happy to admit that. That's the way it goes. So, but still kind of has a problem. The problem is how to define dimensionality.

47:30 Now, he's able to reconstruct some kind of topological structure by his definitions. That's good. But he also assumes that the number of elements of basic elements is finite. So, he constructs finite topological spaces. But if you use the standard topological notions of dimensionality, every finite topological space has dimensions zero. So, in fact, all of these topological spaces that he constructs collapse as far as dimensionality is concerned. How can we replace, how can we find a notion of dimensionality that works in our context? So that's a problem. Carnival overlooked that problem. He was well aware of those problems. But he overlooked the dimensionality problem. But Goodman pointed that out. Here's my new system. As I told you, I've got now first-order logic for set theory with new elements. So, I have a lot of mathematics, and that's good. This is not a nominalistic program, not at all. You might have thought in that way, because some nominalists like to think of tropes as something that they could make use of. That's not the point, not the point. It's not all a nominalistic project. Indeed, fully-fledged mathematics is essential to it. That is precisely what I need, otherwise everything breaks down that I need. Okay, then I also got empirical theories, for example. Think of the intended interpretation of O, that's overlap. Now, overlap is not really depending on the way you order the argument. If x and y and z overlap, then you can permute x and y and z, it doesn't matter. And if you've got five elements that overlap, or sorry, it's a seminary relation, so you've got, say, six elements, you say they overlap, and you say T1 overlaps with T1, overlaps with T2, T3, T4, T5, T6, so you take T1 two times, you could just take it one time, it doesn't matter at all for overlap, and you could say instead T1 overlaps with T2, T2, and then fill up again, T3, T4, T5, T6, T7. this is what is stated here. That's the kind of empirical theorem. Now we've given a list of seven tuples. A list of tuples of length five. That is the list that we are studying. That's the kind of empirical theorem. So I will usually now say O applied to a set, and that's it, because all of

50:00 these things are not relevant. I might also, at one place, I also use the notation O applied to a set where the set has more than seven elements. That is not explained now, up to now. But by that I mean of cardinality 7, every subset of the set of cardinality 7 are in the O relation Ok, then I can constitute the set of my basic elements, just take the members of the field of low, collect them together, that's all you do So that's now my set of basic elements, not those Then I define the notion of k heliades That's not my notion of course It's a well known notion in convex geometry, but it's also used in more abstract settings, like hypergraph theory. And it goes like this. So you take a set of basic elements, set of probes. You restrict O to that set, to a sub-relation. You take some sub-relation of that relation, so you forget about some overlappings. Okay, now put the two together, X and O, and you've got a pair. And you say that pair is k-hali, where k is a natural number, I could take arbitrary numbers, but I'm only interested from 1 to 6. So you say that pair is k-hali, which is the following goal. And the definience is the following. Consider an arbitrary subset of x, that's the set of basic elements. Then the following two conditions should be equivalent. That's for the moment, just think of this set, y, say it has six elements. because it's easier to think of that. And k, say, 2, so that's 2 heli-ness. Then what is the monsters to follow? If the six elements overlap, then of course every two members of that set overlap. If all of the six overlap, then every two overlap. But the interesting point is that equivalence, in postulating equivalence, is the other direction. It says that if every two members of that set overlap, then all six of them overlap. And now make it more general, you go to k heli and s, that's the point of that definition. And I will motivate the definition in a moment. And furthermore, I will motivate that definition. I say that such a pair is k-dimensional if it's k plus 1 heli, but not k heli.

52:30 so that's the lowest PELI number that may be assigned to XO. So anything bigger than 7 is automatically PELI? Yes, yes, that's it. But the point is I'm not interested in dimensions that are larger than... actually 5, as you will see, because 5 means 6 PELI. Okay. But, as I said, I will definitely start with a class of sequences or even a class of sets will be my basic relation, so I forget about places, and then nobody will wonder why 7 or something. Okay, here's my constitution of temporal overlap. Some of these overlapping relations are there because of temporal overlap. Some of the overlapping relations are there because of qualitative overlap. I'd like to separate them. And I try to do this in the following way. Oh, temporal, that's a temporal overlap relation, should be the relation y, such that y is So among all sub-relations of O, having the property that if you take now as X all basic elements, instead of all basic elements, and you take that O, then that is one-dimensional. So, in a sense, if you think now of these intervals, the idea would be that that gives you a one-dimensional structure. I will justify the new thing. and I can take here the total set of basic elements because every trope is within time independently of whether it's a visual trope or an auditory trope so everything has to have some kind of temporal overlap relations I use here a definite description for that definition so there's a presupposition the empirical presupposition is that There is a unique why such that the basis of the definite description holds. How can I justify that empirical presupposition? In the following way, there is a classic theorem of Halley, that is why, that is usually called K-Halliness, or Halley property. By the way, in Austrian mathematician, I have to say. The theorem says that if you consider r to the n, and you consider an arbitrary class of compact, convex subsets of r to the n, then that class is n plus 1 heli.

55:00 So, if you consider subsets of R that are compact and convex, and you collect them together into a clause, that clause is 1 plus 1 heli, that's 2 heli. And this is true because you can easily see that in the following way. Think of the real numbers. So, 2 heli means we have to look for the following properties. Say we've got one interval, another interval, has non-empty overlap with the second one. And now, say we are looking for a third interval, having non-empty overlap with that one and with that one. The only way to draw the picture is to draw it in a way that it overlaps the two in a way such that all three of them overlap in at least one point. You cannot do that differently. If two overlaps, then you have to put the third somewhere, you have to shift it at some place that all three of them overlap So if every two of them overlap, all three of them overlap And in fact, it holds for arbitrarily many of them If you only think of finite classes of such convex sets, you can forget about compactness, you do not need that And that was how I got the idea to use K-Halimans in order to define dimensionality Now, the theorem only says that these sets are m plus 1 heli. If the set is non-degenerate, doesn't collapse into something that's trivial, then it's also not m heli anymore. The problem is, think of the Euclidean plane, and the Euclidean plane also contains the real axis at various places. So if only convex subsets of that real axis would occur, that would be bad luck, something like that. But if that is not the case, if the class of convex sets that you're looking at is varied enough, then it's also not n-hali. So you can use the heli-ness condition in order to specify dimensionality. And the dimension of the real-time axis is one-dimensional, and so I can use the dimensionality of the real-time axis in order to separate temporal overlapping from the other overlapping. And then I can define time instance. These are subsets of beds, so sets of basic elements,

57:30 such that every two of them overlaps. The idea is, again, well, think of that... Oh, no, I'm blue now. Think of that interval. You overlap it with another one, so it's getting smaller. Then you overlap the two of them with another interval, something like this, it gets again smaller, and it somehow converges to points. If you take maximal overlappings, then you get the constitutional counterpart of points. If you've got finitely many ellipse, then it will not really be a point in that sense, but it's as point-like as can be, given the basis. So if you have time instances, you can also interpret these time instances as I mean, those are the clauses of that mutually overlap each other that are at a point of time. So you collect everything together that is at a point of time. That's an The definition of the basic element is at a time, then you can define betweenness of time instance, and so you have a kind of geometrical structure now, you've got betweenness, yes? I should probably come back to this discussion that is connected to Albert's remark earlier about separation. These are the subjective mental thought of time instance. This isn't the physicist's time instance. That's true, that's true. The time slice of the cosmological time, it's not that. These are the subjective mental thought. And the formal structure, you know, is not, normally, I mean, save it by finally being an element. So, not the real-time structure, the formal structure. But still, it's one-dimensional. So, you would say that subjective time is two-dimensional in some sense, or three-dimensional? I wouldn't say that. But, again, I have to say, I've just presupposed it in my meta-theory. If there are good reasons to believe that, given some reasonable notion of dimensionality, subjective time is not one-dimensional, then I have to change my... Oh, it is discrete. But it's still one-dimensional in my sense of the word. It's discrete. I mean, at least if you've got finite in the other one. The point I wanted to make was only just the distinction between subjective time and objective time. Yes. It makes it look as if you're... the definition is giving you a feature of the objective world, whereas there's a separate issue. Yes. There's still subjective time. Yes. Yes.

1:00:00 Okay, and once we've got that, we've got some kind of a fine geometry structure, and we can make use of that, and blah blah blah. I've omitted several things. Temporal order. Maybe I can say something about that in the discussion. And analogously, now you just have to relate that, it can constitute a five-dimensional visual field, a two-dimensional auditory field, and so forth. Some steps into the physical domain. And Klein would say that's not a big problem. Goodman's problems, they are problems, but that's not a big problem. And indeed, in Goodman's structure of appearance, the whole book is about this auto-psychological domain, except for, I think, the last two pages. And then he said, well, we might also try to step into the physical domain, you know. Ah, now the book ends. So that's not really a bad one. Kant thought what is least intended to give definitions, still, definitions now of the assignment of colors to points of space-time, which projects now the subjective colors into space and time. That is what he does. So if I've got this blue point here, I want to somehow have a line of sight and I want to put it somewhere. That was the idea. And once Once you've got that, we've defined the set of perceived entities and so forth. As Klein has pointed out famously in the two documents, statements of the form quality q is a point instance x, y, z, t. That's the color assignment. Where, according to Carnot's canons, to be apportioned truth values in such a way as to maximize and minimize certain overall features. So what Carnot says is he wants to have inertness. to project colors in a way such that there are as few color changes as possible. The speed things go in this four-dimensional world should not be high. Neighborhood relations should be preserved as good as can be and so forth. These are the things that Klein refers to. And then Klein says, I think this is a good schematization of what science really does. But it provides no indication of how a statement of the form, Quality q is a point instance x, y, z, t Could ever be translated into Carnot's initial language So translation fails That is what Quine said That is part of his attack on the second dogma

1:02:30 Now the general point behind that is I would say And that is the way it is often put If you go from the auto-psychological domain To the physical domain You have to make use of what is Often called theoretical terms And these theoretical terms cannot be defined in terms of, well, we would say observation terms, in that case, the phenomenon is the basic language, so to speak. Now, in fact, this color assignment is not the typical instance of a theoretical term. But relative to that basic system, it is like a theoretical term. It's given by a certain theory that Karloff intuitively describes. So, this leads us not to the problems of holism, either in the conformational form or in the semantic form. Now, in my system, I want to approach the problem by a version of branchification, and some further elaborations of that by Carnot and by Lewis. That's what I do in his paper, How to Define Theoretical Terms. We consider college data. That's just an example. It should work more generally, of course. The first thing I did was I axiomatized Carnot's theory. He doesn't state the theory precisely. Up to that point, he states precisely the definitions that he wanted. He was extremely specific. But at that point of time, he just sketches the idea. But I tried to axiomatize that. You can do that. You can define what I call a color assignment tuple. That's a sixth tuple consisting of certain functions, line of sight, those are straight lines, to certain visual sensations, and so forth. You can, this inertness condition, you can define in terms of partial orders on these color assignment tuples. So, one tuple would be more inert than another, even only it, and so forth. And you get, then you get a theory. Within the theory, at first it's a kind of axiomatic theory where we think of CA as something that denotes a specific color assignment function. So it's an axiomatic theory for the color assignment function. How can we get rid of CA? Because in the end, you know I want to have translations where we only have our basic predicates, the membership predicate and my own predicate, not CA. Well, let's ramcify the sentence, first option. So whenever you've got a sentence

1:05:00 involving CA, you translate it to the ramcification. There is an X such that X satisfies the on color assignments, and additionally has the property B. So that would be the idea. Then we get rid of CA. Now, there's another thing that I should say. Normally, if we ramcify a sentence, then we still quantify all the things that we've referred to before. I mean, so, then we say there is a, say, a mass function or something like that. There is a, you know, you name it. Some people would sometimes say, not quite correctly, a theoretical here the variables run over my cumulative hierarchy my set hierarchy based on my set of basic elements so I say there is a function that maps something that I already constituted sets of classes of pairs of basic elements to say points in R to the 4 which are mathematical entities and that function is again in my cumulative hierarchy I'm not, ontologically I'm not stepping outside of my system it's not that I'm now referring to things in the world or something like that Now, that is also the step where we would say, normally if we have a sentence, then we, part of the meaning of that sentence, what the terms in the sentence refer to, that is somehow built into the meaning of the sentence. If I take that step, I'm not quantifying over just things in my cumulative hierarchy. Something goes wrong now. And as I said in the beginning, I'm not claiming that I'm preserving meaning or something like that. I'm preserving empirical content. The idea would be that that information is still enough to characterize the empirical content of the original sentence. And then reference to my sets, my cumulative hierarchy based on my experience, that's precisely what I'm looking for. There are alternatives. I could take Lewis's way, say color assignment is the function x such that a of x. Now, in some cases there might be a unique x such as a of x and that's fine. In other cases, that is not the case Then the definite description doesn't work. The uniqueness condition is not the case. How can Lewis avoid that? Lewis says, well, in all the cases that we need, that is avoided by saying that what we actually quantify over here is not arbitrary sets or functions but natural sets for natural functions not arbitrary properties but natural properties so that is built into

1:07:30 the system that he uses so if I go that way then I might add perhaps that I have some underlying notion of natural set theoretic object in my cumulative hierarchy now I do not know whether I want to go that way but at least that's an option finally We could say CA is VX such that it satisfies A, and then by convention we single out X in a certain way. Say it's the least in a certain way, and we've well-ordered, say, the things that we're interested in. Normally we can't do that, but we can do it if we take some finite approximations of the things that we're interested in. And that is something that I make use of. But that's like choosing that definition of ordered pair over that definition. It's just by convention. It's another possibility. And he still researches something of Quine's ideas, so he says, if he can aspire to a sort of logischer Aufbau der Welt at all, it must be one in which the texts slated for translation into observational and logical and environmental terms are mostly broad theories taking as holes. Now, in a sense, in the Renzi by Sentences, theories, or possible theories, are filled and in the sense that it belongs to what he said. Now, is there any time left? How much time? Yeah? Okay. Michael Friedman has raised another problem. He said that, well, think of color assignment. Say we can do that. No, he didn't think of that version, but say Carnot's definition will have worked of color assignment. it. Okay. Then we step up in our constitutional system. We have then, say, constituted other persons. Other persons are also to be constituted. Other persons tell us something about color assignment. New information comes in. So, in a sense, we would have to revise our previous extension of this color assignment function. But we needed color assignment in order to constitute the persons. How can the persons help us in order to constitute the color There's some kind of vicious circularity going on. That is how he describes the point. I don't think that is true. I would look at it the following way. You start with a kind of preliminary color assignment. Then you climb up the ladder. And then you get a more elaborate version of

1:10:00 color assignment. That's a different one. Index it. I mean, distinguish it. But it's a better version. And then you climb up again. So it might be a system, different versions of a common concept show up. What I've just done is to get extra-systematic. That's my way of telling you about this problem. Within the system, you would have just different terms. Whenever you have a sentence that you want to translate, you have to take care, which version of color assignment do you need? Some kind of intuitive one, where you do not make use of physics or the information of other people, or a more elaborate one. but I think that's still acceptable. I won't say much about disposition terms I actually just got it with me in case you want to talk about it in the questions time. Okay, then I'll do it. Is that okay? Then I will skip. Yeah, no, no, there's no problem, so wrong. How do you say the structuralist and the dispositions? Well, I mean, this isn't good before, but you're going to have to say... Absolutely. I think both questions are important, so... Please choose. I thought I'd go to the structuralist account, but I could well go to the disposition account and leave the structuralist account. Would you do that quickly? Both quickly. Yeah. Okay, both quickly. Yeah, speed up. I've learned how to speed up the question. And take it from a discussion time. So, we start the discussion now. Okay. Questions, please. Let me first thank you to speak. So, thank you for these two interesting questions. I will try to answer them very briefly. Concerning disposition terms. I do not regard them in the way I did regard the theoretical terms. They are not theoretical terms. The idea that I have here is, that's more or less about testability and meaning, something like that. It kind of separates the problem. The idea is, define notions of similarity. I have not introduced similarity up to now, but I can do that. For example, I can define a similarity metric on visual qualities. That's the way how I define it. I will not go into detail. that measures how similar are two visual qualities, and you can do that for all kinds of qualities that you have.

1:12:30 You can show it as a metric. Then you find possible worlds of experience combinatorially in terms of O. So you've already constituted different kinds of qualities. Take different ways of putting them together. You know how they overlap. That is already constituted. But you still have the possibility, I might have experienced not this green bottle, but just this blue bottle. It's not a possible world in a strict sense, it's a possible world of experience, of course. Do that. Then extend the similarity measures that we have for qualities to comparative similarity of these possible worlds of experience. That's possible. You can raise the similarity. Once you've got comparative similarity of worlds, you can somehow rewrite the Lewis semantics for counterfactuals. So you can somehow introduce a new subjective conditional, like when Lewis says, in the most similar worlds to that world, in which A is satisfied, and in each of these worlds B is satisfied. So you have these possible worlds of experience with comparative similarity, then you can get the sphere semantics that Lewis has, you can introduce the subjective conditional, and then you can try to express this positional predicate in terms of that conditional. not in his way, of course, because it was not within a constitutional system. But some people said, it's more a problem of materialification, and that is the way I would go. In the same tradition, Kwai, again, in natural kinds, he suggests that once we we've got a notion of similarity, we can define things like what's soluble in water. That's the smallest class of things that is natural, and that contains all the things of which we already know that when we put them into the water, they be so. So you get natural kinds from similarity. Then he says, but we do not have similarity. What is similarity? It would be lovely, but we don't get it. Let's eliminate the traits of similarity that we have in natural land. I have similarity. I've already constituted it. It's built into my system. So I think moves like that work. But that is much more Factualism. Is that sufficient for the moment?

1:15:00 Yeah, yeah. I mean, I think... It's the counterfactuals that you really need. I mean, strictly speaking, people don't think that you can define the position of the counterfactuals in various details. But even if that's true, it doesn't matter, because the counterfactuals are going to be important to you in getting the equivalence. your map of jobs is going to be telling you about what would happen under certain circumstances, whether that's equivalent to a disposition or not, perhaps it isn't terribly important, but you want to get the counterfactuals in order to get the dictations and the equivalent stuff. So, yeah, that's fine for me, yeah. For the moment, at least. But, yeah, yeah, yeah. Let's talk about that later in more detail. Structurally, in one section, Carnot says, you can skip the section if you want. But according to some interpretation, like Friedman's and Richardson's, that's an essential section. So originally it was meant to be a very essential section, and then having some pressure, you don't know, by Schlick or whoever, it was something to be skipped. he defines E, this space, by definite description so he says E is that relation that's a binary relation satisfies say, take some high sentence to the constitutional level the visual space is five dimensional the relation that is binary such that given all the definitions the visual space is five dimensional that is not good enough knew if he permutes the domain, then he gets non-intended interpretation, how can I avoid that? Plus, the relation should be founded. And this term is, he said, a logical term. We could just as well say natural. So what he does, I think that one should really say that's something quite remarkable. He has Lewis's theory of how to define theoretical terms. That's precisely in this theory. It's just that Karloff makes explicit reference to natural properties, whereas Lewis says, my variables are over there. Of course, there is a standard criticism, defined in Demopoulos and Friedman, and Jeff has written a very nice paper on a problem that's closely related to that in the British Journal of Philosophy

1:17:30 found this term is of course not a logical term. We wouldn't say that. So, it's impossible to translate into a purely structural language if you think of purely structural as a purely logical language. And Lewis has the same problem. His, taken strictly, his variables, or if you want his existential quantifiers, are no longer logical quantifiers. They are logical if they quantify over arbitrary sets. But I wouldn't say that they are logical if they quantify over something that's more restrictive. In my new opera system, I just have to say, I'm not tied to this proposition of, say, structuralism. Also, it's not structural realism, but it's a modern-day version in the physical world of structuralism. I'm not tied to that, not at all. And I'm just, you recall, I just want to be certain very complex, that's all. So I cannot even start with structural realism. And that is also the problem that they have raised and that you made more precise do not really occur here. with empirical adequacy and such things. I do not want to go beyond empirical adequacy. Well, my comment on that, the issue is really realistic. To begin with, it looks as if what you're saying, say the magnetic field, and you'll view that some kind of mathematical construct out of Ehlers. That would make them feel it. But we don't, we don't. I'm not, if I, if I said it, if I had said at the beginning, I want to preserve meaning and truth-like, then now you just have, I put your finger on the right point, but I didn't. My constructs are, I try to reconstruct what the imperial concept is. But it's not even neutral about anti-realism, it's not even neutral between realism and anti-realism. I think it actually is an anti-realist. No, it would be anti-realistic if I would say that the translations are not to be used by the scientists, but that's not the case. You're not making an identification that the magnetic field is a magnetic structure. Yeah, I'm not saying that. You're just saying that when you construct a translation, the quantifier that replaces the magnetic field, there is an X which satisfies Maxwell's equations, then the witness for that existential quantifier will be something constructed out of your cumulative hierarchy over your basic. It's an empirical counterpart to the magnetic field, but it is not the magnetic field. I'm sure that anti-realists might be happy about my system but reinterpret it again.

1:20:00 You see? But I'm not doing that. I'm a scientific realist. I just want to give a precise way of putting what is the empirical concept. The empirical concept is really explained in terms of my experience. That's usually not done. Philosophers of science have decided to start with an intersubjective basis, but I do not want to do that because it's an epistemological project. Well, that was a separate thing as well that I was thinking of asking about. You've got to kind of slip this. I mean, the kind of slick Neurath's objection was to go physicalistic, and Van Fraassen passed this with these empirical sub-structures are not normalistic. They're the redux of the structure of the world to the physical observable domain. I think it would be a good idea to conclude the official part of the discussion. Yes, just a little bit more because there are several people who have to catch the train. So I propose to thank you. Thank you very much. Thank you.