Theory & Object (Session 4)

Hello and welcome to the fourth session of Theory and Object. I'm going to pass the mic to the instructor, resident Gristani now. Thank you very much, Theo. So today, as I promised, we are going to look at the work of a signal error by way of, of, you know, which is basically the formalization of the concept of scientific theoretical structure and dynamics by way of the work of Joseph Sneed. First, I want to continue that kind of light introduction that I tried to give at the end

of the last session, finishing that light introduction, then I will just very briefly look at the main concept of Stegmuller's work, which is, which, in which he tries to formalize by way of Sneed and Ramsey, Cohen's theory of scientific revolution, namely theory dislodgement, And then I will make a digression into the work of Joseph Ramsey. I will introduce a little bit of formalism. We will look at one particular example, which is classical collision particle mechanics,

which I briefly mentioned at the end of the last session. And then we go back and conclude what Seymour actually tries to achieve by way of such formalizations, how he tries to broaden the scope of Kohnian structure and dynamic of scientific theories and thereby shedding some of its unfortunate sociological relativistic, a strong relativistic by that I mean, a strong relativistic residues. So before moving forward,

I also need to tell you that next session, unfortunately, we don't have our class, but we will continue the week afterward. So before moving forward, let's hear if you have comments, if you have questions or anything to say. Anyone? Joven, Jeff, Peter, Sepideh, who has been fundamentally silenced.

I'm the Grand Inquisitor, I will get words out of your mouth at some point. Well, just kind of a general question. Absolutely. So as I've told you, my familiarity with set theory and theoretical language is really limited. I see. So as I'm working through the material, I'm also working through the material with understanding set theory and some logical theory.

So I guess the basic question is really just about context for it feels like kind of being dropped into the middle of this discussion among Sneed, Kuhn, Stegmuller, Freyarabend. And I wonder if you can provide just some basic context for this discussion and include, if you will, just some general thoughts about the specifics of set theory or formal theory that are mainly applied in this discussion.

You're being indexed by such theories, yes. Exactly. So sorry for the generality of my question. No, no, no, no, that's a very good question. Short version, and I will give a rather longer version during the class. The short version is that, you see, set theory for example, we can say it is the ultimate mathematical formalization for structures. It's the generalization of logical mathematical structures. Many people think that set theory has been restrictive in its handling of indexing mathematical or logical structures, and hence they propose that, for example, we should adopt things

like category theory or higher categories or topos theory. But I would say that such proposals are actually fundamentally naive in the sense that even category theory, for example, which tries to generalize mathematical structures, is itself predicated on the generalization of sets. Sets are fundamental. Sets, memberships, union of sets, unitary sets, power sets, all of these, the taxonomies of set theory are, I would say, are the most adequate tools in the arsenal of mathematics,

once understood sufficiently. most importantly, once understood sufficiently, are capable of formalizing any known structure. Obviously people like Stegmuller, Sneed, try to give a coherent formalization of scientific theories and dynamics in the sense that it is not the case that for example they try to say that such formalization is what you might call to be an intrinsic part of justifying

the course of scientific evolution. But rather, what they try to achieve is that by formalizing the idea of structure and dynamic of scientific theories, they actually try to shed light on what actually scientists do implicitly when they do stuff, working within the context of a certain specific theory. So, they try to capture these structures, these structure and dynamics of theories, precisely because logic allows you to make explicit what is already implicit in doing

theory and science in the scientific practice. So once we actually make such endeavor explicit by way of logical mathematical formalization, And we are capable of actually analyzing how the evolution of science fits together, but more importantly even than that, we are capable of looking at the implicit components that scientists themselves never give proper attention to. So in that sense what you might call to be the use of set theory or logic in order to

formalize the structure and dynamics of scientific theories is what might Hegel would have called a syntactic semantic consciousness of doing science. Just because some genius scientist is capable of arriving at new discoveries, this doesn't mean that he's essentially conscious of what he is or she is actually doing. So from this perspective, the formalization of a structure is really syntactic and semantic self-consciousness of the scientists. And hence it opens the way of doing science, the practice of science in laboratories open

to philosophical discussion. If you look at the sidebar, Arthur makes a very good question. You see, in the realm of mathematics, mathematics like philosophy is a way of world building.

The world that it builds are of mathematical structures. When we are talking about world building, we should understand that within the ways of world building, worlds are always being made by the existing worlds. So we can only talk about world versions. This does not mean, however, that all worlds that we make, for example, world of types, world of categories, so and so forth, world of topoi in mathematics, can be indiscriminately

reduced to one and single fundamental world. For example, that of said theory. The whole idea of an indiscriminate reduction of the plurality of worlds within any domain of discourse to one rooted final fundament is an illusion. However this does not mean that there are no such thing as foundations. We should rule out the idea of a final and total foundation. But in fact, there are worlds that allow us to generalize even further, make even more worlds.

And set theory in this sense should be precisely thought in the second sense of the foundation, whose elements allow us to generalize mathematical structure and diversify them even further, make new mathematical boards. And it is only in this sense that set theory can be said to be fundamental, but not in the first sense, which was a stronger sense, in the sense of a firm, total fundament. Yeah, thank you for that. Absolutely.

Yeah, reading Goodman too, I mean, it makes sense in the sense of world making. I really, really suggest everyone, I have suggested this to Jeff, you read Nelson Goodman, Ways of World Building. You know, it has nothing to do with mathematics. It's what you want all to be a cross-disciplinary understanding of what worlds are and what they are made of and how they can be built. The kind of operations that he proposes, you can imagine them in any local mode of thinking, mathematics, politics, logic, art, literature, so on and so forth.

Sorry, it's actually ways of world making, sorry. Yes. Everyone, hi. So, when you say that attempts to formalize theories using category theory, for example, is naive, I wonder… No, Mary, one second to interrupt for the sake of clarification. I didn't say that the use of category theory for formalization is naive. I said that the idea that category theory is in fact something more fundamental than said theory generalization is naive.

So please, my apologies for interrupting you, but I thought that it was necessary to make this clarification. I'm sorry, did you say that category theory is more fundamental or more general? Sorry, I missed what you just said. It's not more fundamental. It can carry the labor of generalization of mathematical structure as put forward by set theory even further. But that does not mean that it is that it is more fundamental than set theory. Set theory is what you might call to be the core of generalization of program inside the mathematical domain. A very good article that I can suggest,

I will find the exact title, it's by Steve Aoudi, was a student of Sanders-McLean, the inventor of category theory, one of the inventors of category theory. And he actually talks about this at length, why category theory should not be understood as the fundament of the mathematical universe. That's good, but still you could use something like category theory. Absolutely, absolutely, absolutely. The whole point is that not only category theory, and category theory is just a simple tool. I mean, it's basically, when you look at, example something like morphisms the idea of morphisms that category theory presents you with

are still a static are still actually far uh beholden to the set theoretic idea but you can even go to higher categories or topos theory and then you see that there is a whole zoo of mathematical structure in front of you yes absolutely you all of this stuff needs to be use and not just set theory, but simply the whole idea of using set theory, first of all for two reasons, one for the historical reason that for example, Sneed and Stegmuller, yes, they were working during the time that category theory had somehow lightly was established, But it was more of a technical mathematical domain, and hence they wanted to...either

they weren't aware of it, or simply it was the case that they wanted to still work inside the canonical instrument or tools, mathematical tools for formalizing such things. And two is that the use of set theory in the sense that it is simply generalization of the structure should be adapted, but that does not exclude the possibility that other mathematical tools and fields can be implemented as diversification of such structures.

The more structure we have, and a structure is simply as Carnap says, is a form. The whole idea is that Kantians think that forms without content are arbitrary. My answer to such orthodox Kantians is that, could you please tell me what a content without form is? The whole point of a structure or form is that it should be diversified. The diversification and generalization of form or qua structure is tantamount to the enrichment of the reality that we index by such structures or forms.

However, this completely leaves the most important question unanswered and unfortunately I don't think that we can go into this direction because that would be a completely a fundamentally different course. The idea that on what premises can we coordinate mathematical logical structures with our experiential observations. The idea that for example someone thinks that category theory is a richer mathematical tool

to index reality is predicated on this confusion that there is already a, what you might call to be worked out correspondence or isomorphic between generalization of mathematical structures and the content of experience or the structure of reality, if it has any. SEAL SILVAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVALAVAL

because it's I noticed that your connection is a little bit choppy today oh is it yes maybe it's can you hear me okay now I'll just I'll read it out first having a hard time understanding and have for a while now how we can have mathematics without fundamentals or mathematics without a grounding and don't in some way revolutions in science require some claim to, or at least putting forth an idea of grounding?

Yes. Yes, no, that's exactly what I was trying to say. That's, you know, the idea of grounding or the foundation should be taken at least in two senses. one the strong firm foundation or basically a totalized foundation or foundation more as a platform foundation more as a platform in the sense that certain kinds of constraints within the domain of mathematics as imposed by set theory allow us to generate more mathematical structures generalized sets even further the same thing about science

foundation as an anchor or foundation as a platform is this kind of the problem i'm again i i'm in the same boat as jeff my knowledge of set theory is really limited but is this kind of the problem that russell points out in his paradox of set theory that yes you see what the thing is that that i would say is not really what you might called to be essentially a corrosive assault on the idea of foundation in the first sense, namely an anchor, a totalized foundation.

However, you can in fact accept and accommodate the second sense of foundation as a platform within Cantorian or Rossellian idea of metal logic or meta-mathematics in which you basically create nested structures, generalizations. And a generalization can only be approached by way of a different hierarchy, nested hierarchy, nested metal logic. It's like a good metaphor for it is like you have some operating system as your platform

in your computer. Of course operating system can be diagonalized in a Cantorian sense or in the Godelian lemma sense. Then you can think of different hierarchies of apps that you install on such a platform. Some of these apps are simply what you might call to be feeding off of the platform and simply allow us for better, more accurate and precise interface with the platform, with the OS. But then some of the apps you can in fact invent that they can go back and do something

that the operating system itself cannot do. Like for example an app running on your OS that can change the speed of the fan, heat up the hot, you know cool off the hardware. system itself cannot do that. So you can think of this as this kind of a kind of a metaphor that these nested hierarchies of meta-mathematics or meta-app or meta-logic work in a very complex dynamics. Some of them simply calibrate the potentials of the platform and some of them

actually can go even further and change the physical substrate or basically the stuff that are responsible for us to envision new os systems new operating systems new platforms Precisely because of the limitations that they point out within that domain of activity inside built on top of a platform. I mean look at the difference between different kinds of operating systems.

I don't want, however, this is just a metaphor, I don't want you to overextend the analogy here. But you can somehow intuitively think about it like between Linux, Windows, DOS, so on and so forth. So I don't know if you're going to get into this when we talk about Stegmuller, but I thought it was a good time to ask. I was a little bit confused about reading the Stegmuller, he was making this distinction between using metamathematics and formal axiomatizations as opposed to informal set theory.

Yes. explain that distinction? Sure. I will elaborate on this but to be quick about it, you see informal set theory is what you might call to be the natural, the predication of natural language translated into axioms of set theory, okay? Hence we are essentially what you might call to be doing a naïve set theory or a set theory, not in a canonical sense of naïve set theory, but rather in the sense that a set theory that is simply tries to take apart, translate, the

the kind of predications, the kind of judgments that we can do in natural language. But of course, natural language is clunky, is vague, it's not the language of science. So the move from informal axiomatics, informal Hilbertian axiomatics, which simply indexes natural language, and it's what you might call, it's a theoretic translation of natural language. To formal Hilbertian axiomatics is the idea that you, in this transition, you fundamentally abandon predication afforded by natural language. You no longer use natural language as the language of science. It's pure axiomatics, no reference to natural

language and its predication whatsoever. So is this related to the idea of like an abbreviated definition or sort of the terms or the objects in a Hilbertian framework are kind of only implicit, whereas in informal set theory you would have some kind of pre-existing semantic sense from natural language? Well, you see, it's the other way around. The informal one is implicit. The formal one is fully explicit because every relation is being indexed by axioms of set theory. You can think about this, that this does not mean, so there are, you know, usually the critiques of,

for example, when we look at Carnap's work in future sessions and logical syntax of language, like work that he wrote after writing the logical structure of the world, Afbau, is that you notice that many people, you know, critics of car novels have thought about this that, you know, we always need natural language. In order to interpret the syntax of a fully formal axiomatized system couch in terms of formal Hilbertian axiomatics

that when we are talking when we are basically trying to formalize a scientific theory by way of Hilbertian formal Hilbertian axiomatics you always need what you might call to be a messiah, a semantic messiah at the end, to interpret the syntax for you. To somehow translate it to the ordinary language. Because scientists are not just syntax manipulators. They require a certain kind of conception, and that conception is not auxiliary to how they do science.

People who say that, for example, a computer can do this better than a scientist, no, they don't understand the idea that conception, namely the semantic dimension, is absolutely necessary for not only understanding what you are actually doing Why is this? So the point of objection that is usually levied against this kind of Carnapian vision is that we always need semantics at the end of the day. So you need to have some semblance of a natural language to translate this for you so as you

can do something more to this theory than what you were only capable of doing when you were merely in the realm of formal syntax. But in answer to such an objection two things can be said. One, formal syntax does not mean that it is absent of semantic. In fact we can imagine with, syntax as really the ultimate foundation of semantics. Semantic is not just ex machina, it doesn't come out of nowhere, it obviously generated by syntactic structures, but under what conditions, that is a question. So this is one. And that's why Carnot calls its logical

syntax of language semantic in disguise semantic in disguise in in its work to this idea is that again this is complement of the first answer the properties of the object objection levied against formalization are usually those those people who think that natural language is the ultimate, what you might call, to be guardian of semantic dimension or semantic translatability or semantic interpretation.

But this is again predicated on the idea that we have already ruled out the possibility that we can indeed invent formal syntactic language which can have semantic dimensions. So if I understand it right, the Carnapian view is basically to use model theory in the mathematical sense and then try connect somehow a referential semantics that will connect to empirical objects at the end of the day? Yes, this is his project in Afbaha,

which we will go over in details. Well, later on, Carnap actually became fundamentally unconvinced by such an ambition in the sense that a language or a medium or a calculus of symbol design by language here i mean simply a calculus of symbol design where you can obtain rules among your symbols and hence you can come combine in a in a combinatorial sense, your symbols. He thought that if we do such a thing,

if we try to restrict the design of symbols, and hence the design of language qua calculus, to the kind of relations that should be obtained within empirical observations, we are restricting the scope of formalization and thus the structure. And hence we cannot really think of additional structures by which we might be capable of enriching empirical reality, the concept of empirical reality. Hence, you see that there's a transition in Carnap work from this idea of designing calculus, namely language,

language, tuned to the constraints of empirical observation to the design of a calculus that is unconstrained and ultimately free from such constraints. In a sense, and also another thing that probably allow you to think about this more in tune with what we are talking about, what Carnap's language or linguistic framework is ultimately a theoretical framework. So far as we cannot do science without theory, the expansion of the linguistic framework,

or theoretical framework is tantamount to the expansion of the intelligible reality, empirical reality. Melissa? Yes. So would you say that every theory, every, yes, or anything that tries to be saying, should strive to be also formalized. You see, formalization, the thing is that with formalization we should look at it, I will try to introduce in the next sessions what we actually mean by formalization.

But before that, I completely recognize that formalization in, for example, today's way of, for example, neuroscientists or businesses doing formalization, what they mean by formalization is extremely, extremely narrow and restricted. They basically mean a set of established formulas. But then there is another form of formalization, the one that Carnap's put forward, formalization. form is itself destruction reality does not give us this structure because if reality we say that reality gives us structure then we fall in the trap of that ideological fixation so Lars calls the myth of the given the whole idea is

that observational data need to be cut up within a calculus of symbols and the rules obtained between them. And it is only then that we can talk about the structure of reality, how things hang together in the broadest possible thing. And that's really what I mean by formalization. what you might call to be the organon of a structure, with the understanding that a structure is not something that reality itself kindly gives us or provides us. Those people who think that a structure is something

that we have some immediate access to are basically exactly the kind of people that they think that our knowledge at some specific level bottoms out in an ultimate foundation like sensation, like empirical data, like inductivism, so on and so forth. In fact, Carnap's formula for expanding the formal dimension or the dimension of destruction, the more I have read it, is the ultimate weaponry against this whole charade of inductivism

in science, that science can simply go by mere induction and observation and nothing against or that theories can be simply automated. Any more questions? If not, allow me to get some stuff for myself so i can start in earnest okay take a five minute break actually wasn't my not heard that

Thank you. Thank you.

Thank you. Theo suggested we had a five minute break. What was that question?

So, come on. Theo suggested we maybe have a five minute break. Oh, okay, okay, okay, you go five minutes break. I kind of have some questions maybe I'll just sure go on Christian go because it has to do with particular aspects of of the stigma of formalism it got brought up I had the thought because it has to do with this whole nested hierarchy thing because it seemed that the way that the special laws

and the particular constraints that correspond to these particular laws have some sort of lattice-like hierarchy. When you are talking about law, what do you mean by law? Are you talking about natural laws? No, I'm talking about law in the strict sense that Sheckmuller is talking about. Okay. Like laws as particular constraints that apply to a certain redux and how the redux apply to what they are a reduct of

and like the theoretical and non-theoretical functions that send them to certain, more certain elements. And that, I mean, my understanding is like law and the constraints. What it does is it restricts what type of elements are able to be... Yeah, what kind of relationships can be obtained from them, yes. Right, yeah, and the intent of application and whatnot. And that seems like that the way that the law-based constraints function is through, because you have, like, for example, the ones that only have, like, the singletons, you know, that would be, like, upwardly included in all the ones that are more general, so to speak.

than the ones merely with the singletons. And so I sort of felt like that there was sort of a sort of hierarchy of specialized components of theory and the expanded core of a theory. And I just sort of that was kind of like the trajectory of my thoughts, It's not particularly clear, like, how I'm putting it, but I think you see, like, what I'm trying to gesture at. So let me try to reformulate, and please let me know if I'm, you know, making the wrong move.

You are basically saying that there are always, when we are talking about, are you, okay, well let me, my question, constant question would be, are you talking about the relation between an expanded core and a core, or are you talking about the relation between core of theory one and core of theory two with their associated expanded cores like for example Newtonian second law as the core and other laws of Newtonian mechanics as its expanded core versus for example

relativity I mean it could apply to both but I think the first one just the core and the expanded core insofar as the expanded core has a sort of wider range of intended application. Yes, and the singleton phase or the singletons are what you might call to be essentially pertain to what you might call to be your core, your theoretical core, like the second law and of course that's exactly exactly and of course a single turn doesn't mean that is

essentially a singleton because even i will actually this is one i will try to formalize the the us need formalization um the the second law of newton f equals ma or f equals to sigma I mean a equals to sigma f over m so even the singleton itself what you might call to be a set that is not a singleton it actually is obtained by way of certain kind of constraints that which are obtained between theoretical and

non-theoretical elements of a theorem for example momentum position position is always non-theoretical momentum energy mass function so on so forth so So singleton is what you might call to be encapsulation of such relations. It's not that it is simply taken as a fundamental. No, no, no, there is no such fundamental. You are basically working within a theory and we are talking about the components within this theory. Some of the components can be encapsulated into a core. versions of relations between such components can in fact be derived from

the core once we encapsulate it's like you might might think of it like this as this metaphor that you have a bunch of stuff together then you encapsulate this becomes a law and this core law can itself be unpacked into different kind of laws which show us that different kinds of relations under different kinds of constraints can be obtained between our theoretical elements Yeah, that makes a lot of sense.

In the sense that, also Christian, you shouldn't think about core and expanded core as a nested hierarchy. it's more of a triage structure rather than a nested hierarchy the relation between the core and expanded core yeah i was i was thinking more of like a sort of kind of like lattice like structure yeah i mean uh well that's the whole idea of theory nets Okay, okay, yeah, I have not read much of this technical book. I read the Structures and Dynamics of Theories, the essay, and that is about the extent my exposure is.

You might say that the core of the structure of Newtonian mechanics is really the second law in so far as it indexes essential relationships that preserve and are preserved under any kind of deformation into different kinds of Newtonian laws within Newtonian mechanics. And when you think about this, then other laws, other than the second law, what you might call to be not just elaborations, but theoretical dynamics, the dynamics of the theory

that you derive from your aesthetic structure, namely the range of application. Dynamics of a theory is always its range of applications. And in so far as other laws in Newtonian mechanics actually shed light on how it can be applied to the heavenly bodies, we are basically saying that dynamics, its range of application is ultimately predicated on its structure but in two sets one and micro analytical in the sense of atomic statements about the elements which comprise the core of your theory and also the macro analytical in

the sense that the relations between such a statements or atomic facts? What I found what I'm finding somewhat difficult to grasp is what is exactly gains from What's including fear from expanded struck an expanded core because Because specifically, my impression of what is added in the expanded core are the various specializations or limitations of theory,

which inclines me to think that what would be, so to speak, the bottom of the tree would be the most limited. And that seems to be smaller than the core. And so the only thing that I could imagine being gained in the expanded core is the fact that you're also including all of the more limited or specialized versions of the theory. but you're not gaining a greater range of phenomena which you are able to explain.

Well, this is the whole thing, is that you see the formalization put forward by Sneed and adopted by Stegmuller Stegmuller is essentially its aim is to show that theory dislodgement, or basically how can we explain theory dislodgement in Kohnian sense? Of course, Cohen doesn't basically, he gives them more of a pseudo-sociological way of understanding the structure of scientific revolutions.

But once we transform them into logical propositions, then we are capable of, as I mentioned last session looking at the idea that theory dislodgement does not happen no matter how we expand the core. Basically no matter how many laws you derive from the second law of Newton, you are still in the course of the normal science in Kuhnian sense so the expanded core does not extend the range of application no it does range of

application but the whole idea is a range of applications is not tantamount to basically replacing one theory with another theory you are still working working in the realm of the dynamic of that structure, dynamic afforded by that structure, by the second law, it is only when you see that there are limitations in the range of your applications in the sense that you put it forward, that they cannot simply describe or explain certain kinds of observations then you might actually look and if they are cumulative

in the kuhnian sense of cumulative anomalies then you might actually look at your core theory theory core the second law and if there is a way that you can expand it even more than you will do it but But usually with the cumulative anomalies, observational anomalies, then you understand that it is the time to replace that structure, that core, second law, with a new law so as to expand the range of applications and hence apply it to the kind of observational anomalies

Hitherto you could not explain. This isn't exactly, thank you, thank you, but this isn't exactly answering my question. It's most likely because I just did not read carefully enough. But my impression is that what is added by an expanded core is the limitations or specializations of the theory. I think what the technical meaning of limitation that he's referring to is a little bit different than... Specialization is a good word. Basically, expanded core specializes that theory.

Right, and so, like, what I'm trying to find so hard to grasp is how an expanded core can have an extended range of application than the core. And the reason why I say this is because my impression is that what is added by the expanded core are all of the limitations or specializations of the theory, which restricts the appropriate domain of application and does not expand it.

You see, the thing is that restriction of the domain of application coincides with the specialization of that theory. It means that you can calibrate your structure of your theory, like the second law of Newton, to certain kinds of phenomena when you are observing the motion of heavenly bodies. Okay? And so my understanding is that's the only thing that the expanded core adds. And so there's no expansion of the intended range of application. No, no, no, not range of application. No, range of application, the idea is that it's not broadening the range of application.

Expanded core is the range of application. but a range of application not in a common sense that we think that, for example, the more we expand the core, we can basically subsume some observational phenomenon under the second law of Newton, the core of the theory. No, it simply means that there are only certain kinds of phenomena that can be studied by that core, by the second law of Newton. It's what you might call to be crystallization, crystallization of application, rather than diversification of application.

Okay, yes, yes, that's exactly the impression that I had. So, this Newton's second law, if it's a core, and then we add Newton's law of gravity or Hooke's law, then we start to kind of build the expanded core. And I wonder what's, there should be something common for Newton's law and Newton's law of gravity and other laws like Hooke's law that would allow those elements of X, expanded core, to be considered like linked to the core, which is Newton's law.

It's the order of derivability. It's the order of derivability. Derivability. Derivability, yes. The order of derivability that can be justified by logical structuration, which of course Stegmuller tries to couch and it's needs also in the same way to try to couch it in terms of the theoretic order of derivability. There are relations between the component, so there are some components like position, velocity, mass function or mass points that constitute the second law of Newton. And of course that's encapsulated in a very specific ways in the second law.

Now if you are capable of deriving, basically unpacking this core into diversify the relations between again such components but express in different ways then what you might call to be this is the relation between the expanded core and the core. So at best, the extended core will have the same range of application as the core. And what we don't know it, this is you see the whole thing of the transition from a core to an expanded core from the second law of Newton to those auxiliary laws is not a priori

given. Only and only we can do that by way of somehow what you might call to be looking at the logical structures in which the premise is the core and the conclusions are in a deductive chain of influence are the expanded core. Okay, so what you're saying... It's an inferential process, it's an inferential process in the sense that you might say that expanded core is what you might call to be the explicitation of what the second law of

Newtonian mechanics, namely the core, encapsulates. like all encapsulation you should think of them in metaphorical sense as when you are encapsulating this stuff you are obviously idealized and simplifies many many relations between components during this process of idealization and simplification through which you derive your core many details are getting lost It is only when you explicitize the core or unpack the encapsulated core that you can see what range of applications it might have.

Okay, so there's the whole formalism of like Y sigma B, which is like B is like a reduct of Y. Yeah. And so then what is impossible to extend is the B. The reduct. But then what the expanded core can indeed achieve is an expansion of the Y. That is, the types of conclusions you are able to draw by the types of redux permissible within the core itself absolutely absolutely it's the

whole idea of the permissible types that you can derive from the type of your core so you can now see so you can now see that essentially a stegmuller Stegmuller's formalization or ethnification of a structure and dynamics of theory is what you might call to be a scientific theory of types. What types are computable given the type that we have just invented? And that type that we have invented is what you might call to be the core law of our theory if we have this type what kind of other universes of types can we derive from it

it's a computational problem i mean was your computational problem so so is it then so it's a question of the physicists being confronted with a qualitatively new sort of physical system and then kind of having to conceptualize that system and show how after conceptualization show that you can find a mathematical law for it that's derivable from the core? Yes, for a regular scientist it's absolutely true, that basically if I have this mathematical,

physical system in does and so way then given the kind of mathematics or logic or computation that I have implemented to encapsulate this kind of conceptual infrastructure or platform what I can build on top of this given the armamentarium or possible ways that I can derive further logical computational or mathematical structures from such a mathematized physical system. However, this completely leaves the question, as I mentioned to Theo, the idea of why is that I have actually used

this mathematics as the observational language of my physical system out of the room. It This is still not answered. And we cannot answer it until we go through Karna, and some of the other stuff. But yes, that is absolutely the case. So mathematical physics, you use, you have a choice, And this choice is never arbitrary in fact. It might be implicit but it is never arbitrary for a scientist.

You have a choice of a mathematical structure to index certain observational statements And under such co-constituted mutually constrained components of physics and component of mathematics, you arrive at a certain core or encapsulated vision of your physical system. Then, given the kind of mathematics, logic and computation that you have used to basically put forward such a core, you can derive mathematically, logically or computationally,

other kinds of structures and hence possible range of applications for that law, for that core. I just wanted to clarify that when I was asking you about the core expanded and not expanded, first I understood when you said about something, when you talk about deriving expanded core elements from the core, I saw that you are talking about deriving Hooke's law or other laws from the second war of Newton but you're talking about different derivability are talking about logical yes well the whole point is that in I'm not saying that this order

of drivability can be couched in terms of other types of drivation all I am saying is that in the structuralist namely a stegmularist need paradigm of of scientific revolutions and so as Carnap actually yeah when we look it look at it in the future sessions this order of derivability is logical mathematical why because Carnap let me read this for you again um I think that that sheds light on some of this stuff that we have been talking about There is nothing wrong to repeat stuff.

There was this, sorry, I... Okay, this is from Carnap. How should science come to objectively valid statements? if all its objects are constituted by individual subject, by an individual subject. The solution to this problem lies in that of course the material of the individual streams of experience is completely diverging. But certain structural features agree of all streams of experience.

Science has to restrict itself to such structural properties since it aims to be objective. And it can restrict to structural properties, as we have seen earlier, for all the objects of knowledge are not content but form, and they can be represented as a structural entities. The whole point is that the use of logical or mathematical drivability is what you might call to be a way of circumventing the diverging experiences of individual observers. A structure is what is invariant, not individual observers' experiences, which are always diverging.

What was that from? That's from Afbau. Afbau. I really like that. Carnap is the god and sooner or later you are going to face the god and you will see how scary it is. Okay, let us start. And please don't, as I have said many, many, many times, you shouldn't be afraid to pose questions just out of the thoughtfulness and consideration that you are delaying the class.

Whatever material that I have not taught, I will make free sessions at the end. This is always the case. So shoot any questions at any time you want. In any case, one second. Let me bring the last part that I read, those notes that I read at the end of the last session, precisely because we are going to work with them. And also I don't want to simply continue with, if you have forgotten what we were talking about.

So I gave a little bit of introduction to Karna, like a flash forward and then try to then try to somehow lightly introduce the idea of structuralism in philosophy of science. So let me, allow me to share my screen with you. My apologies, I really sometimes have trouble with this stuff.

For some reason when I'm trying to share the screen it does... Okay, okay. So I said that in a structuralist philosophy of science, empirical theory consists of its models, which are sequences of the following form, D1 to Dn, R1 to Rn. Di are so-called basic sets and the Rj are relation constructed on these sets. So this is another kind of implicit answer to Jeff's original question, why set theory? Precisely because set theory allows us to capture the kind of relations obtained

between such and such components and the members of these sets. The elements of the DI comprise of the ontology of the theory, i.e. they contain the objects of which the theory is about. The rj are usually functions, they usually are functions mapping empirical objects into real numbers or some other mathematical entities. So for example when we are talking, actually like a recording tape, and I'm not going to make an example of a human observer, a recording tape. Under such and such parameters of being introduced to the spectrum red,

such and such traces are being embedded on or written on this tape, on this computer or this tape recorder. From now on, we can actually talk about the color red in terms of real numbers. There is a whole session on this idea that Carnap introduces in Aufbau, but for now, you are thinking about this mapping from empirical objects into real numbers you can think about the

place and the time of the registration of the light spectrum on a specific tape i am absolutely at this point not talking about a human observer because that creates more confusion when we are talking about a human observer we are might think about you know illusion psychological color distortion so on so forth all i want to talk about is that you can replace the human observer with a computer with a tape recorder that's sensitive to light

once being introduced to the color red this rose is red we have rose prime number a real number this real number is a combination of the place and the timing of the registration and the color spectrum you can even forget about the real number and just think about simply symbols, symbols in a, in, in, not, not in a natural linguistic way of understanding symbols, but simply what you might call to be symbol design

within a calculus, a combinatorial, syntactical regime, where you can do in fact obtain rules between your symbols. The association of the color red with a rose. Can I ask a question about the above? Sure, sure. So, could you go back? You mean sharing the screen? Oh, sorry. Yes, yes. Sorry. My question is, so, from core, if we were to, like, let sort of that slide interact with Stegmuller,

it would be from core to expanded core at best with the DI that would remain unchanged from core to expanded core at worst it would be limited no no no no No, no, Christian. You see, you can think of the core as, you see, a core is what you might call to be a stable set of basic sets and relations constructors on them. So it's It's not just the I, it's also R-J.

It's what you might call to be invariant stable relations. Okay, okay. Okay, maybe I should just go on and forget what I just said. Okay. But thank you so much for making these things because I completely understand these are just alien materials for us, I mean, definitely was an alien material for when I was reading this stuff. And any kind of objection can shed more light, you know, on the complexity of the matter. Anyway, an example, the potential model MP

of classical collision mechanics requires five requirements. NP, potential models, is a quintuple, is a five-fold tuple, an order set. Don't get scared by these notations just search a tuple or an order set on Wikipedia and it should light what these things are. You know that are nothing serious np equals to p t r v m so what are these things place time real number

velocity and momentum actually here we are m if it was a bolzmanian mechanics a statistical mechanics we could say it's momentum but here is m signifies a mass function a mass point um question so what di be dj di yes di would they both be uh the the redux which are like so to speak like the atomic facts but also what the relations are able to send them to yes so so absolutely okay you see the mp is an order set an order an

well-ordered set or a cube means that you not only have the elements of the set but also the atomic relations that are being obtained from them. Yes, this is different from an ordered, well-ordered set where a tuple, here we have a quintuple, a five-fold tuple, which means that we are not simply talking about elements of a set but also their atomic relations, rj rj we don't have just di we have also rj is this clear i mean i i really uh want you precisely

because these things are getting more nasty as we are moving forward i just want you to just like if you really don't understand these things just let me know you know what the question is. So the model is basically just the objects of the physical system and then the functions... It's a picture, it's a logical or a structural picture of the physical system. And then the functions, they're just giving basically the values for the variance. And so does that mean it's taking into account measurement? Well, you see, the thing about measurement is that we obviously without measurement we can neither derive

the elements nor the functions measurements are absolutely required for derivation of both di and rj sets and now what is the implication of this science is dependent on measuring instruments what even more fundamentally what is the measurement you know i i know you guys have been trained in continental philosophy where measurement is like pesticide it's basically you you think that measurement when we are talking about

measurement we are talking about some sorts of really tyrannic thing no measurement is simply what you might call to be articulation of atomic forms of intelligibility that's what measurement is degree by degree There's nothing, basically without measurement, of course Plato is the first philosopher who puts this forward, without measurement there is no intelligibility, no metron in In a Greek word, the Greek word for measure, no metron, no intelligibility, no theory,

no science. You are just in the business of mysticism. But what is really important is that your theory should allow you to always revise your measurements that are the degree by degree articulation of intelligibilities so I'm just trying to relate this to like what a scientist would do so I guess the scientists would experiment on the physical system on a physical system yes and a physical system for a scientist is always a black box you see scientists does not look at

something as a given world is always a black box of course I know that a black box is also being valorized like you know we say that oh well this is just a black box means that it's absolutely unknowable but no when you actually look the idea of black box in science and engineering you know this a very different approach to this black box theme scientists always give some disturbance into the black box some what you might call to be inputs of course this input can be introduced by way of the controlled way it's always a controlled way it's not just whimsical so you give it this black box some inputs

and then you see that under these range of inputs what output this black box yields then you give it another set of inputs then you see what kind of other other inputted yields and then you see a pattern. The only way to uncover a black box is to play with it scientifically. Okay, so on the basis of this black box, of this defined system, the scientist then inputs some things, makes measurements, gets a set of values, and then a successful application

for expansion of the core, I guess. We are not still in the business of expansion. We are what you might call to be in the business of observational statements. These observational statements are yet to be incorporated within the theory that we have somehow postulated about this black box, how it behaves under such conditions. So I imagine that the scientist then sort of analyzes the plot of the values and tries to show that these values correspond to the law to a law yes a law which is theoretically laden

okay so then how how does that exactly fit into stegmuller's uh formalization well you might say that as Christian said, DI and RJ, namely sets of basic atomic facts or elements, and the relations constructed on them are what you might call to be your core. If you are capable of building such relations between such atomic facts then you have arrived at the core a law like the second newtonian law which i will i will i will try to do with a requires a little bit of formalism

and then once you do this then you okay so you have this core theoretical core now let's see what this theoretical core can accomplish i will give this system this black box fundamentally different kinds of input within the context that's this is really important these are all context sensitive within the context that we have obtained my theoretical core and not other whimsical contexts well you might actually take this to some imaginary world and it won't be fundamentally

different i'm not talking about counterfactuals at this point which are absolutely important But right now, we are not talking about counterfactuals. Under such constraints that can be coordinated with the constraints to which we consider the theoretical core, if we give this black box such and such input, it should give such and such output. We can diversify our input, and hence diversify our output. And then we can think of possible other patterns that might be actually derived from such theoretical

core. These are what you might want to be an expanded core of your black box. We would need another DIRI tuple. Yes. Okay. And one question is, I have two questions here then, is how would you expand domain of inputs? And secondly... Well, you see, that's a really good question. And I think that I'm still trying to struggle. I'm struggling with it. It's something that I need to think about coherently

and read more and more stuff. You see, obviously, the expansion of your input is always under your theoretical core. Basically, the kind of input that you will feed into your black box are going to be informed. But what you have already constituted as your theory core. In the sense that, okay, a metaphor. So expanding it implies a change. If I think that the world has such and such function, like it has gods and angels as humans so on so forth and they're all in such and such relations to one another then obviously when I am trying to feed my

black box this universe this cosmos some input these inputs are always going to influenced by the kind impression I have of how this world works things like angels gods and humans hang together so you see this is actually quite a quandary now because that is a bias that's the bias The bias of giving the kind of input that this black box needs is always going to be what? My theoretical core.

Yes. Yes, so my inclination here would think that without changing the core, the movement to expanded core could at best limit your inputs. Yes. Insofar as, yes. Yes. But then you see, how can we arrive? i mean theo i'm sure that theo the chief skeptic is now apparently applying theo would object i i'm sure that he's going to say something like this he would object that then how the can you

move from one theory core, T1 core, to T2 core, to another theory core. Because if your inputs are always under the kind of theoretical biases that you have already formed, then how can you actually make new kind of range of applications that might point out to the limitations of your theoretical core. Well, my dear friends, that's when we should take the idea of technoscience seriously as

the prosthesis of science. invention of theoretical instruments means of observations so as we can in fact arrive at new observational anomalies that might not be in fact part of our ordinary sense of observation and the kind of input that we give to our black box is absolutely necessary and indispensable for the progress and the evolution of science. Think about the invention of a medieval telescope and I hope that you know what medieval telescope

look like just look at Omar al-Khayyam in his observatory and think about Hubble telescope the kind of observational that the yields are fundamentally different from the kinds that have simply been by way of naked eyes or some sort of ordinary optical instrument. Think about a James Webb telescope that is going to be constructed by NASA and Hubble telescope.

James Webb telescope does not is not an optical instrument it's entirely a radiographic telescope you can detect observational data on radiographic spectrum these are not available to any optical instrument So, Theo, go on and finally put your corrosive and skeptical question. Well, I think this ties into last week when we brought up this question of why would

theories need to dislodge each other? Theories do not need to a priori, do not need to dislodge one another. There is no a prior requirement for dislodgement or replacement of one theory by another. It is, that's the Cohenian thesis that Sekumuler and Sneed try to formalize and make it precise. This is when the kind of observational statements and the relations obtained from them, namely di and rj, we arrive at new sets of atomic observational facts

or statements and relations constructed from them. Once such fundamentally new, sets of the I and RJ are being constructed, then this is time, and if they accumulate and they pose a threat, by that threat means, I mean, that the old theoretical core is no longer capable of explaining the phenomenon that it observes. That's when we move from one theory to another. The theory two, which now supports the new DI and RJ set is what you might call to be

dislodging theory for theory one. It just seems like that definition of a theory is grading the efficacy of a theory in its ability to explain. So efficacy, not just efficacy to explain, but you see, efficacy to explain is always predicated on the efficacy to describe the kind of data that you are dealing with. Like imagine you are looking into a kind of pre-Boltzmanian gas theory in which we are

talking about pressure and the volume of a gas inside a bottle okay we can explain a lot by volume and pressure of a gas but then do the maximum route open the bottle and see how it escapes Do it in different contexts, in a vacuum, so on and so forth. Can you really explain the DI and RJ relations of the old pressure and volume theory of gas

in order to justify the kind of observations that you have seen? No. You can't. that's when a new theory a new theoretical core should be invented should be discovered so the core is always an equation is encapsulated by an equation you see the core is what you might call to be a model. Model in the sense that it depicts, like a picture, what is being depicted. It describes what ought to be depicted, what ought to be described,

a phenomenon, a physical phenomenon. So in this sense, what you might call to be the core is a model in a very rudimentary sense not in a sophisticated sense of the model that we i i mentioned a few sessions ago basically model is like in a common sense x pictures y x pictures y Y is depicted by X and so on and so forth. It's simply what you might call to be a descriptive, elementary, explanatory paradigm.

But of course, insofar as elementary, it's what you might call to be an atomic picture, a static picture, you need to have range of applications. You need range of application or the expanded core in a Sigmularian sense, what you might call to be a model in a true sense that we call it today. A model that does not basically sensitive to the dynamic representational resolution criteria of the assignment and scope of the phenomenon at hand is not really what we call it a model. It's simply a picture, what you might call to be a pseudo-atomic picture of the kind of observation that we have tried to describe and explain.

Nothing more, nothing less. So maybe I'm missing something on the level of the formalism. So why couldn't we see this in terms of like Carnap's model theoretic approach so that a successful application is then just interpreting the variables of an equation semantically with these sets of objects and values? Does that make sense? Yeah, no, no, it completely makes sense. And that's really the whole point of Carnap. Although Carnap would tell you that we probably shouldn't use the word variable. We are talking about functions at this point. logical mathematical functions and yes absolutely this is exactly what Carnap tries to achieve

and as we move forward with Carnap we notice that it actually fundamentally what you might called to be shedding a Hegelia light both in the sense of the evolution of science, dialectical evolution of science, and the condition of the possibility of science. If you don't have logical structures you don't have a phenomenon. Sensible data without formal structure is a myth. That's just what you might call to be an empirical pessimism. Empiricism, naive empiricism, there are good empiricisms, I don't want to fight them.

Naive empiricism, in the sense that you think that simply sense datum, the kind of interactions at the level of sensation or observation you had with the reality can actually yield the structure about the world. Carnap fundamentally trashes this idea and this is almost ironic precisely because Carnap is a logical empiricist. But the whole idea is that this idea of logical is very very important a structure can only be yielded by logic and mathematics and not by the

sense that's all even before salars became the enemy you know the grand enemy of the myth of the given the idea that bold is something like a block of wax that imprints its own structures on us on a blank slate of mind carna was the enemy of the myth of the given logical empiricism once fundamentally understood and analyzed you see that it absolutely against that kind of naive cynical empiricism that is put forward by hume

and his followers so what then is exactly the difference between the stegmullerian and and carnappian formalization okay the the i think the difference between a signaler and carnapp is not about the commitment formalization they are both committed the formalization as what you might call to be the dimension of the structure and by structure i simply mean intelligible that which is intelligible okay now the difference between carna and the stegmuller is that carnapp thinks that we can have in fact an isomorphic

but this is the premature Carnap the Carnap of Afbaw the logical structure of worlds he thinks that we we can have somehow an isomorphic between empirical statements or observational statements or observational atomic facts and logical structure, as if there is a one-to-one bijective relation between them. Stegmuller rejects such an idea, so as later Carnap. In fact, Carnap of the logical syntax of language is the ultimate terminator of his earlier works.

So I just want to push back to sellers if I can right now. Sure. If experience and sensation is itself not a given atom and should be thought of more along the lines of linguistic structure or theory simulation of an object, of an object which i think is already problematic why is okay no no you can't just pose this question without first explaining why it is problematic i'll i'll get to it no no okay okay

i think it's a it's it's this really at odds notion of what uh yeah i guess maybe it's a pitting correspondence theories and coherence theories against each other. So, yeah, if experience is not itself a given datum, why would there be a disconnect between our... Well, no, you see, I have to interrupt you on this point, Theo. Experience is different from sensation. You see? Now you are making a human mistake here. Sense, sensation or sensedatum are different from experience.

Experience are always structured by categories of understanding, in the Kantian sense, in the sense that they are amalgam of logical structure plus sensation. but you are trying to sell me sensation as experience to quote well I could see taking the side of the only forms of sense that are maybe necessary for our experience are themselves space and time but I think that's the aspect of Kant's philosophy that profoundly limits philosophy and science. But you see, Theo, I don't think

that it fundamentally, in fact, I would say that science is the only, is the only avenue and not philosophy. And yes, sure, philosophy, I mean, philosophers, I mean, look at Parmenides, Look at Plato, look at Hegel. They are the people who point out to the kind of restrictions that our ordinary perceptions of space and time impose the limitations, which are the fruits of our ordinary perceptions of space and time, impose our idea of reality.

So I wouldn't call it just scientific, but I would say that it is only science that can actually lead us from this, what you might call, to be a spatiotemporal dilemma. In the sense that you see, Theo, So, science has in fact a notion of an observer, a unifying point, a structuring point, that's basically a structured sense data.

Now, the thing is that however science never mistakes or never confuses the notion of human observer as the ordinary human observer that has a certain kind of biases about space and time with the notion of an ideal observer. You see, the idea of space and time as proposed in modern physics are not what you might call to be propositions made by a human observer, but an ideal observer. What is this ideal observer?

I already mentioned it. It's a recording tape. A computer. A computer. It sees the traces, the traces are being registered under tape, and these traces are being structured by way of a logical program. Could I kind of say something here? It's kind of related to what you're saying. Can you hear me? Absolutely, yes. Okay. Yeah, I mean, this is kind of how I'm interpreting what you're saying, that I'm thinking of this as you know the object of investigation is the thing that's putting the inputs into the black box and the black box itself it's almost like this fishian hegelian realization of the self

through the logical process but but logic like i think stegmuller had said it's it's um you know carnivore's misjudgment wasn't that it was something he didn't misjudge the power of logic but our ability to understand it so it seems like it's beyond human ability but it's actually ourselves alienated from itself and trying to understand itself yes or something like that yes you might say that in a good alien Carnapian sense there's no logic without the metal logic the logic is the limitation of the understanding of our basically the inferential logical you know things that we obtain from our formulas.

But then you can go to another level to show that all, that within that specific limitation of the logical relations that you have as a human being, such relations can never be proved to be right or wrong. The proof of such a statement, a la Gödel's lemma, is impossible. Hence you have to construct a nested hierarchy of ever more adequate and expansive logical organones, logical armamentoriums or toolboxes. And that's basically the ultimate vision of Carnap, what Steve Aoudi calls the unbound

ocean, Carnap's vision of the unbound ocean. That's kind of how I'm interpreting this, is like the ultimate goal is kind of, yes, this realization of this unbound ocean and, you know, like the ultimate scientific object is, you know, what is it that we are? What is it that's trying to understand this? like I don't know like a planet or something yes but but the thing is that it's not just us you see from it you see from at least from the Salars incarnate and point of view we are nothing yes sure there is Salars actually respect the idea of the manifest image and he does believe that

there are aspects of the manifest image and by the way if you don't know why what manifest image so Salars, Wilfred Salars, American philosophers, introduces the idea of what you might call to be the labor of conception and explanation about who we are in this world under two different paradigms. One is called the manifest image and one is called the scientific image so what is really the manifest image you might think of the manifest image as the kind of ordinary way of thinking about the universe oh there are nice roses there are nice

sweets there is a house out there and i can see you know my partner you know approaching this is a manifest image the scientific image does not see such things the scientific image sees that this tree is not a tree anymore it's a bundle it's a bundle of absolute logical computational processes absolute statistical processes everything that is going on in my garden right now is what you might call to be a version of the absolute processes,

constitutive explanation of what these things are rather than what they appear to me as human observer so however Salars make this fundamental caveat that there are components or elements of the manifest image or ordinary image of the world that can never be put into the garbage. But aren't there, I mean, like, the way you're describing it, I mean, it feels like those phenomena themselves aren't external to me.

Like, it seems like I could also, the way I'm interpreting it, the use of the word phenomena could also be something I'm producing. Yes, yes, and that's the whole point. You see, those, those, what you might call to be, when you get all the fats, separate all the fat from the manifest image, there is a still, there will be a still a manifest image, what you might call to be the lean image of the manifest portrait of ourselves in the world. What is this lean image? It's the idea that there is no such a thing as a phenomenon. without our rational and conceptual resources.

But you still want to retain that term as the input for the black box or something like that. You still want to have this idea of having the phenomena to test the black box. Yes. Okay, let me go to the black box example. So inside the manifest image, you will give all these inputs to your black box to see how it behaves and then so you can extrapolate a pattern that can describe this black box that can give it a name but of course within the manifest image uh you are basically in the business of what you might call to be an inflated biased image of ourselves and how we perceive the world and how we bring

it into conception. So everything can be biased but Selaar's point is that if we get all this fast from the manifest image and make it lean in the sense that the manifest image is now what you might call to be in the labor of inhuman sense. Certain kinds of invariances required, absolutely required for thinking and intentional action, reasoning, theoretical reasoning and practical reasoning, then we can imagine different kinds of rational practices, theoretical and

practical reasonings, that are not bound to our entrenched evolutionary given perceptual biases which restrict us to identify an observable phenomena. That's the whole point. I know, and I agree with you here, and it seems to get very, it gets into some really tricky ethical territory too, because it's like, but what is it about the human or something that's so important that we want to protect, or it almost seems as if there's some, you know, duty to protect the human being or something, but I know what I do with you. human being we are not talking about human being we are simply talking about humanism as a specific qualitative functional integration we can think of an ai

that is armed with all sorts of algorithmic goodness that basically it has capable of all source of highly advanced algorithmic machines of loving grace right yeah machines of the loving grace yes but now think about this what makes us distinguish from simple algorithms is the kind of mode of integration that if these algorithms can actually be integrated qualitatively and not quantitatively under a certain mode of integration that they can shed light to what they actually do peacewise in a peacewise manner in a peacewise manner reflect on what is that

that they actually do this is ultimately what i call human human is nothing human is not a biological he's not human, he's not the child's god to use Cormac McCarthy's term. We are nothing, we are absolutely nothing. All we are is a certain mode of integration of certain kinds of algorithms that allow us not only to observe, describe and explain phenomenon, but also that's really more importantly it's a qualitative integration a qualitative dimension that cannot just be reduced to quantitative algorithms

it allows us to think about what we actually do when we are doing things I mean why do you think that we humans are the only species on this planet who can come with the idea of AI precisely because we can reflect on what we are doing when we are knowing about the world. Yeah and this idea of emptiness you know I was reading like a you know some Confucian philosophy like you know the house the emptiness of the house is the utility of the house or the emptiness of the hub of the wheel is what produces the utility as opposed to the value. yes it's the hole you know it's the hole there the emptiness yes and and and you really i i you know i i hear it this from over and over from this post-humanist anti-humanist step well human is

nothing unique you know you go guys go off and uh you know there are animals there are alien things But first of all, there is no such a thing as an intelligent being or intelligent behavior in the universe that is not beholden to the labor of intelligibility. Science does that. Philosophy does that. If we cannot explain why is that we call something an intelligent behavior, then we are in the business of negative theology. via the negative. We can as well just go talk about angels dancing on the pin of a needle.

But that's the whole point. That if we are capable of, and I agree with Sellars that the scientific image of human combined with this lean manifest image is what ultimately human is. That human needs to be understood in terms of certain kinds of practices that allow it to expand the intelligibility of world of which it is a part, but also, more importantly, explaining what it actually does when it tries to anchor, identify itself as part of an intelligible world.

And once we understand human under this pretext, then we see that the idea of an artificial general intelligence of an automated human being comes naturally. In fact, we are the only people, as I mentioned, that we can posit the idea, whether it is illusionary or not. We can come up with the idea of an AI, an intelligence that not only has all the were retails that we have, but something more.

So this self-reflection, it's a kind of self-reference ultimately. So is it a kind of Hegelian thing where the self-reference has to be contradictory or like a liar's paradox or something? Or is there a flattening out? Yes, yes, absolutely. Self-reference is always, I mean, I'm still trying to really gauge Hegelian idea of the self-reference, but I think if we read Hegel generously, that is essentially, you see that the idea of self-reference in Hegel coincides with that of Goodell, in the sense that our self-reference and our reflection on our self-reference

coincides with a different hierarchy of referential resources a different kind of intelligence but that kind of intelligence cannot arise out of the blue as if it was a Dios ex machina. Because that will be just theology, not the business of science and philosophy. So is there this grandiose, so when we think ourselves through that, we're also thinking nature in itself, which has become for itself, and we're kind of fused with the absolute, or do we need that? To be honest with you, Adam, this is something that I'm still struggling as a philosopher

in the sense that I am not committed to adopt all the maximalist Hegelian metaphysics. I don't think that they are necessary. But I need to actually look deeper into these notions, Hegelian notions. But what I want to tell you is that I think that when metaphysics of human is over-inflated, then again we are in the business of theology, not philosophy or science. Sorry, so it's a question of the observer, the scientific observer that gives the inhuman the kind of the crux of scientific knowledge.

I mean, that is the ego core that you're really driving in. Am I misunderstanding you? Not just observer. observer is what you might call to be an ideal observer is what you might call to be the agent in a weak sense not in a Kantian sense an agent that derives atomic observational statements however these observation statements ought to be integrated within a formal dimension the dimension of the structure or theory if you may.

So I wouldn't call a tape recorder a human. I would say that the position of human observer actually can be more elegantly with less confusion can be captured by a tape recorder precisely because when we are talking about a human we have so much presupposition about perception, about conceptualization, about self, so on and so forth. We shouldn't talk about a human observer, we should talk about an ideal observer. at the level of observation, at the level of how we structure such observational statements,

then I think that human is necessary. And human is simply a name, or I would call theory. Hence the name of this whole course, theory and object. So the ideal observer is, correct me if I'm wrong, the ideal observer is that which it never, I mean in a sense, is that which never bottoms out? It never bottoms out, but also you see, I'm sure that you have read some neuroscience, all of you have read some neuroscience, you see that for example when neuroscientists talk about what we call in physics, like observational statements, they call it perception. that these are not perceptions.

Observational statements are not perceptions. Kant had it fully that perceptions are ultimately judgments, which means that they are beholden to the norms of conceptualization, material and formal inferences. What we call observational statements are simply what you might call to be traces of light on a light sensitive tape recorder. That's what I would call an ideal observer. Where we do not talk about perception or conception, we are just simply talking about the recording,

time sensitive or time series, recording of atomic observational statements, traces of light and a light sensitive tape. Nothing else, nothing more. But so if we think that perceptions are reducible to judgments, does this not- They are not reducible to judgments. They are judgments. They are judgments. They are judgments. Does this not get us into just another mind-body problem in that we've reduced kind of the qualia to a computational system? You see, okay, you might not like this.

I do not believe in qualia. There is no such a thing as qualia. I would say that qualia are what you might call to be epiphenomenalistic. products of certain kinds of processes like pain, like pleasure, so on and so forth. They are essentially what you might call qualia or composite perceptual noetic elements. They are not raw as if we have some immediate access to pain and pleasure. they always are what you might call to be diluted beliefs or diluted perceptual judgments.

But they're so present, so even if they need noetic contribution, they're still present to us. Of course, of course, all perceptual judgments are present to us and we move by them precisely because you see for example pain and pleasure judgments which which of course are judgments rather than feelings are uncritical forms of judgment in the sense that for example the difference between a pain and I believe that pain is something like a symptom of some other things is like the difference between Kant's famous example or Rosenberg, J. Rosenberg's famous example,

the difference between an uncritical judgment and a critical judgment. When I put a pen in a glass of water, the uncritical judgment, namely the talk of the qualia would more be something akin to the statement that the pen looks bent. The pen is not bent, the pen is bent in water. The qualitative judgment or the critical judgment about pain is more akin to the The statement that pen inserted in a body of water in a glass appears, appears, you see, a seeming, an appearance.

It appears to be bent, but I know that it is not bent precisely because it's a product of refraction. i just i just feel like the the the biological substrate for how consciousness emerges doesn't seem to me to be computational because it seems it seems to be its own form of self references as like autopoasis of self-organization well you see adam you see computation uh when i talking about computation I not mean it in a kind of a classical sense of computation in the sense of Alonzo Church and Turing and by the way Turing

was extremely cautious about not to restrict the general notion of computation to his own and church pattern you see what is really computation when a system go evolves along an abstract or multiple trajectories in a space and time like you know we know that a dynamic system like for example you put a ball inside a ball and just let it go you know with a force let go and then you see that from perspective of a complexity theory this system can

evolve along many trajectories it can go in all different ways. The whole point is that what you might call to be computation which is responsible for the evolution of a system trajectories is essentially the product of its real-time and concurrent interaction with the environment. If we think that our perception, even our noesis in a Hosellian sense, is that real-time product of our interaction with the phenomenal world, then that's what I call the computation I do not mean computation in a what you

might call to be digital sense I simply refer to computation as a real-time and concurrent mode of interaction between a system and its environment okay then I then i think i don't disagree so yeah i'm kind of i'm thinking about like like someone like jean petitot who kind of like tries to understand the sort of syntax of perception that we have i would say john pedito so as other philosophers like you know michelle with bull run a thumb all of these people who might call to be you know proponents of post-Poincaré and

proponents of first dynamic systems but also what you might call to be naturalized phenomenology. I would say that there are essentially in the business of computation in that sense that I mentioned. Can I just briefly interrupt and ask, was that a PowerPoint that you had constructed that you were showing us? Yes. So basically we are, my goodness, it's 2.38. I will, this week, I have already made some notes, I told you when I was making notes

this morning, which are about formalization of SNEED, SNEED's understanding of what theories are and how they can be actually logically formalized. And the only example that I have made in these notes is classical collision particle theory. I have left relativistic collision theory out of the equation because just too much formalization. But yes, okay, I will turn it into a PDF and put it on our Google Classroom.

Thanks. Yeah, this session was a little bit question-ridden, but as I said, that shouldn't really impede you from posing more questions, because ultimately, we just want to learn. But nevertheless, let's try, let's reconvene. Not next week. Next week, we don't have a class. The week after. And then we are full force. No question at all until the end of the session. And we will go to pure formalization. And I'm telling you, if those of you who have not studied those chapters

and that book that I mentioned by Stegmuller, you should precisely because I know once I start this session those of you haven't read you will you feel that you are basically in no man's land it's it's a little bit difficult yes bring out yeah we will work and maybe Theo I didn't fully answer Theo, maybe Theo can answer, I mean, can pose this question and so is Svitlana and also Chagis. I completely am aware that I did not fully answer your questions. So

make, pose these questions on the Google Classroom and I will be on them. Okay, great, great. Bring out the formula straight edge. But I'm going to, it's 2.40 in the morning here, so I'm going to go and doze off at this point, I think. Someone cornered me at the dinner and talked to me forever, so I didn't get a very long nap. Yes, just please, just stop talking philosophy. Just go live your life. So for next week, the material that we're going over is...

Not next week. Not next week. Sorry, next session, not next week, but the week after. Yes. The material we're going over is the... We're still going to go over the Stegmuller? Stegmuller, and I will put the PDF, some notes I have written, and a little bit of formalization. You see, what I'm trying to do, just so you can get the overall idea of what we are going to do. You see, so we know that a Stegmuller tries to formalize the structure and dynamics of scientific theories by way of a sneak formalism. So first I want to give, finish my light introduction to Stegmuller, then the next stage is that we'll look at the exact definitions of Josephus Neid's formalization.

We will make this explanation or this elaboration concrete by way of a couple of concrete examples in classical collision particle mechanics. It will show that how such and such relations, given such and such elements, DI and RJ in a Sigmularian sense, once obtained and once worked out, can in fact lead logically and not observationally to the second law of newton hence corroborating the idea that the formal

dimension is primary so once i do that via snit then i will go and talk about a stegmuller's takes on Joseph Esnit and Frank Ramsey, formalization of a structure and dynamics of theories. And then I move forward to the kind of conclusions that a signaler derives from such a formalization, some of which my corroborating Cohen's vision of the progress of science or evolution of science and some of which might actually challenge it.

All right. Are there any last questions about two weeks from now, the next session? I think in the classroom right now there's the essay by Stegmuller, the Structure and Dynamics of Theories. Not that one, not that one. Right. I want you to read the structuralist view. That's far more accessible, yes. And that chapter is one and two, or did you just try and want us to skim through the entire thing? It's came through things and particularly, I mean introduction in the first chapter, but particularly give adequate attention to that chapter which is called Theory Nets.

Okay. sounds good I'll that that book is posted in the classroom right now everyone but I'll just post the chapters that we need to concentrate on too already okay my friends ciao for today thank you have fun absolutely have fun and please do feel free to email me whenever you want personally I would be glad to answer you. Take care, my friends.