Complexity & Computation (Session 13)

We are live. OK. Hello, everyone. Hi Adam. Hi Aaron. OK. So as usual, let's start with some discussion, questions, stuff from previous sessions. Next session will be our last one. I mean, obviously, I haven't managed to cover all the grounds, but nevertheless, we managed to go through some stuff. But the whole, I mean, I think the whole mission of the course was really the idea of introduction. And it's just obviously it's impossible to capture

or analyze any of these topics in details in such short time. It's more of a, you know, hopefully this class just gives you some, you know, providing a set of pointers so you can start to do your own research. But other than that, I don't think that we can really even, not only we can't cover this stuff, these topics in a meticulous way, but also, as I said, because especially the contemporary science, like in the past few decades,

has gone through so much development that it's almost now impossible to really find a kind of overarching narrative of the whole field. Yes, you can see where it's basically headed, but I don't think that you can chronicle it in a kind of a cohesive narrative. So the last point, as I said a number of times, the whole idea of giving a philosophical examination

of computer science, I think, is something that hasn't been done. Precisely because philosophers, even analytic ones, are not really familiar with what's going on in theoretical computer science. Only a minor of them. I mean, the whole idea of talk of algorithms, computations, when you really look at the stuff that social commentators or content of philosophers or even analytic philosophers talk about, they just really have no clue about what these concepts are, really. So there is obviously, you know, I think it's precisely because of the fundamental dimension of computer science, there's so many other things.

And it's extremely sophisticated methods and research fields. There should be definitely a kind of bridging this gap between philosophy and computer science. And I don't think that, you know, obviously content of philosophers are not really interested in these kinds of stuff. And if they are interested, just they are interested in some sort of sloppy social commentary and computation, these kinds of stuff. But for more serious philosophical-minded people, I think there is definitely an urgency to do this kind of philosophical work.

Not simply, as I said, not simply interpreting these topics and subjects in computer science based on pre-existing philosophical concepts, but developing new concepts for them. Adam, any comments? I mean, I agree. There's actually a huge gap, basically. I don't know. The way that...I think there's computer science which is sort of detached in a way. It's detached from a theoretical

in the land, but also academic computer science is sort of detached from software being built in a weird way. Yes, absolutely. Yeah. I think they're actually connected somehow, like because you can't...like this is very Intuitionistic. But the fact that software doesn't connect well to theoretical computer science, software as built, and the fact that theoretical computer science doesn't connect well with the sort of philosophical hinterland is all connected to me. And you can see connections, for instance, in the material that we're going through.

In practice, we have self-driving cars driving around in California already. And that's a process where it's driving around, reacting to events, running continuously with no clear exit point of that program. So that's already detached from a sort of Turing model of computation of here's a program you execute, here's all the inputs, and you spit out an output at the end. Right. And that to me is a way that it's as an example of, well, OK, you can bring in the idea of the game theory aspects

where you're sort of modeling a program as a game, as in a game with its environment that fits into that model, for instance. And I don't know, that disconnection all seems very related to me. If there was some theoretical hinterland that both could relate to, then that would be very powerful and useful as well. Yeah, no, I completely agree to this, that computer science, especially theoretical computer science, is also detached from applied dimensions. But I think there is a reason for it.

I think, and the reason is precisely this whole idea that, first of all, the whole computer science is young, so we can't really bitch about this. That's this whole idea that for decades they were putting, basically they were trying to extract applied dimensions of the classical shared steering theory of computability. And now that they have, they think that there can be done a lot to this paradigm, obviously at some point, maybe not the current figures in theoretical computer science, but they

were students. And already, in fact, if you look at the students of these people who I've been introducing, they are moving toward applied dimensions. But their applied dimensions is not exactly software engineering at this point. more of a, you know, encryption, security, smart contracts, language design, these kinds of stuff. But at some point I think it will definitely go to our network, but I don't think that anytime soon, because still I think the whole idea of theoretical computer science is that it's extremely in a kind of a larval stage.

And as I said, there is no overarching narrative. There is no cohesive narrative that can build a momentum toward the applied dimension. Also, one thing that, again, needs to be pointed out is that so many of the people who are part of this theoretical computer science main debates at present are, in fact, against these applied dimensions of computer science. I don't know why, but part of it is, you know, I think, is dogmatic, and part of it is more

of a cautionary stand. What do you mean against exactly? Exactly. That's the whole idea of, for example, I mean, especially again the Frenchies, which have actually really contributed massively to the theoretical computer science in the past few decades. When you see the French figures, there is precisely because of that idea of computation, digitalism, digitalism being in the service of Silicon Valley and these kinds of chains of reasoning, that they have this kind of, when you see their texts,

there's always one or two comments thrown out of nowhere and making some sort of snide comment about artificial intelligence or software engineering or these kinds of things. Yeah, I mean there's a big gulf sort of at the moment. That's interesting. I guess the other thing that I would bring in actually is, which I think is actually very powerful, is more like computation as a natural phenomenon or as a material phenomenon reflecting some structure in the universe rather than an entirely mathematical sort of theoretical concept.

you're actually the way that computer tation turns off in very fundamental ways in mapping physical systems on and that as a theme all here I which I thought was all the which I thought was powerful and very closely related as well and and again there where you need you need some more sophisticated description of, or some more sophisticated computational tools than you've needed up till now for that. Yeah, yeah, absolutely. And, you know, as you've noticed,

I haven't really talked about this that much. I think that was completely intentional, you know, this whole idea of whether Our physical systems implement computation. That's a whole, I think, a whole gigantic subject. But as you say, and this is precisely the reason that I didn't talk about it, because the whole idea of this kind of physical computationalism is very much founded on this whole kind of, even if not really classing, tiering, chair-tiering

paradigm of computation, but on a kind of paradigms of information processing that they They themselves, I think, are controversial. Nevertheless, they're powerful, this whole idea of natural induction or, you know, computation as basically inductive information processing and stuff. But yeah, I definitely, I think. But another, I think, a thing that needs to be said about physical computationalism and

whether universe at any level implements computation is I think these are extremely tied to traditional philosophical questions. the idea of metaphysical problems, whether the idea of information increase in any system is subjective criteria or an objective one. Can we have, in fact, an objective account of information? That's, I think, one really philosophical question. Not in the sense of philosophy proper, but philosophy of basically information science.

And I think without analyzing carefully these questions, talk of physical computationalism can become extremely convoluted and basically hard to defend. Not that I'm objecting. In fact, I do think that you can, in fact, provide an objective account of information increase information in systems. But there are so many problems and I think a good person to begin with who gets into this at least at the level of natural induction and kind of the Solomanov

of idea of computation. A good person who covers some of these complications and at the end adopts a critical position against this kind of physical computation is Hilary Putnam. He basically started as a functionalist, kind of more of a classical functionalist, with being on the side of this kind of computationalism. But later on during his life, he changed his position completely and gave a really kind

of devastating critique of this kind of physical computationalism showing that what kind of contradictions it basically leads to the kind of fallacies that are behind the central arguments in the universe as computational physical computation of this. Yeah, I mean, if it's too rich and the topic gets away from it, we can sort of put a lid on it. But yeah, Crutchfield was talking about the role of the observer, just not necessarily

a deep way, but he was already introducing that part of the problem, right? Like, what do you call information without an observer? The sort of, the idea that you have information is information to what in that system, right? Is it the scientist making the model of that system and that's the observer? You know, that's where, like, who holds the model, basically? Or in other contexts, you actually have, well, here's some evidence that there's some structure of information that the system itself exploits and takes advantage of. Like some organism sort of takes advantage of that pattern nature of the system for its

own ends. And so the observer is embedded in some larger system, not just sort of the scientist observing in his lab, but the system has this pattern of hierarchy of observers as well. So I'm sure that it's very easy to tie yourself in knots with that sort of layers of observers and basically, where's the meaning coming into the system, and what's preceding what, I'm sure you could very easily get yourself in a mess. But at the same time, it seems, if this computational toolset is so powerful in describing these things,

then that also implies something very strong about the way the universe is behaving, even if the whole, you have to be very careful about like bringing, like what part of the toolset you bring in at what stage, I guess. Yeah, the level of, yeah, I think one of the things that we, I think I talked about this first session about what complexity is not, the idea of methodology and application of the right method to the right level of abstraction. Yeah, definitely.

Other than Crutchfield, I think the best person who has done some really good work on this idea of whether computation is subjective, observer dependent, or it's an observer independent, nevertheless contextual area is Samson Abramsky that I mentioned a number of times. He, you know, Cratchfield basically gives a kind of a Bayesian, Markovian paradigm, very much in line with, you know, Shana and Solomon of Kolmogorov's idea of computation.

But Abramsky is still probabilistic, but based on basically quantum mechanics, Bell inequalities, which is one of the key concepts, key theorems in quantum mechanics. And he is really great. And he has a couple of papers that are quite actually easy to follow because he's very meticulous about the steps that he takes. You can find it on his website, I think. He's a very good one. He's with a number of other people, I think, are the most interesting people who are working

currently in computer science. And you have some extremely sophisticated students who have been, again, who have actually moved to the applied dimension, including DeepMind project and this sort of stuff. Yeah, I mean, it does seem to be, at least my rough reading of it is that big I guess between software and computer science is it's starting to end again. They're starting to be in better communication with each other. Just seeing little signs of that playing together again.

Like, fashion in software engineering and software engineering or programming is weirdly fashion driven. The functional programming languages are suddenly sort of basically hip and useful. I mean, I'm sure they were always useful, but they're suddenly fashionable in a very strong way, which I think it's a socially opportune moment. I'm not sure about the actual deeper reasons for it beyond fashion, but yeah. Well, functional programming actually, yeah, it is it.

And also because of this, I've noticed that so many software engineers hate functional programming and talk against it. But actually, functional programming, the reason is because it is precisely because it's the closest of all programming paradigms to theoretical computer science in recent debates. Yeah, absolutely, absolutely. Yeah, whenever I see software engineers make always that they have to say something really nasty about . Why do we even need to do this? Why is it good for her? Okay. Any discussions from any of you guys?

Anything? Maybe me. So this is a thought I had after the previous session. So there is a movement, I guess, in mathematics towards abstraction and then generality. Yeah, generalization. Yeah, exactly. And I think, I guess, computation grounds mathematics in a way. And also it is maybe, I'm hypothesis-serving, it's the medium of action which is always political. So I'm just throwing this out. Maybe I'm not clear, but I can explain it more.

So... Okay, explain it more. Because yes, okay, I understand that computer science can be understood as a medium of action, But action may be not in the sense that we mean as action, but simply elementary, abstract acts. Yeah, I guess the problem is that mathematics becomes more and more formalist or meaningless in the sense that you talk about. And computation may be also, as you guys talk about applied stuff, computation makes it then condense it into a point of decision, all this very abstract, I guess, theoretical

stuff into a point of decision which is very, in a political point of view, very problematic because you also see politicians who are not able to decide. So you have a decision in algorithms, I guess that's what I'm saying. So decision or action, I'm not sure which is the, I guess those are different things. Yeah, I know what you are saying, but I think... It's I guess, sorry to use the Deleysian term de-territorialization, but if mathematics is in this process of de-territorializing, then computation grounds it,

and also it gives its effects, allows it to have effects in the real world. Well, I think this topic is a little bit more convoluted than it appears to be, because, yes, maybe, And that's the applied dimension of computer science, as we talked about. And that's why so many of the people who are at the center of theoretical computer science are biased toward it or critical of it. But computation as a discipline, as a field, especially computer science, absolutely does not ground mathematics in the sense of negative grounding as opposed to the territorialization

that you are pointing. It actually deepens, further deepens. I missed the last sentence. Oh, I said that computation, yes, from the applied dimension, yes, it can be seen as in par and aligned with technological appropriation and technological capture of this kind of formalism. hence can be understood as a kind of negative grounding. But computation as a concept, as a genuine concept, as something that still needs to be determined what it really is, and especially, particularly by extension,

theoretical computer science does not ground mathematics by any means on any level. it really deepens what you call that de-territorialization force, precisely because it broadens the scope of generalization in mathematics. And that's exactly what we have been talking about. This is the whole idea. Really, I think this is the philosophical significance of that, you know, the Kari-Howard-Lambeck correspondence, or more generally, the correspondences between logics, mathematics, and computation. The holy trinity, that if you make a discovery in one,

it essentially leads you to have development in other fields. And precisely because, you see, mathematics, mathematical objects, can be understood as logical objects. And logical objects and logical behaviors, proofs, namely, can be understood at a deeper, more general level as computational constructs. I think this is the whole thing. But yes, from the applied dimension, it can be seen as an apparatus of capture, in your terms. But then this is precisely because for the moment the applied dimension is very much

tied still to that canonical definition of computation since the time of Church and Turing. Actually, maybe I should use a more precise term which is rationalization. I guess it rationalizes mathematics, because then I guess this is what politics does in a way. It doesn't. You mean computation in general or the applied dimension? I guess I mean the applied, maybe artificial intelligence, the whole. It doesn't actually rationalize. You see, there is no rationalization here. Yes, at some level, yes, they rationalize them,

And precisely, that's the whole idea of application, at the core of the application. But what is mathematics exactly is? That's the whole point. Mathematics is a form of abstraction that is exactly tied to the idea of judgment, forming abstract judgments, judgments being the object of your study. That's proofs. Mathematical objects can be understood at the level of proofs. And what is exactly the behavior that determines this proof? So there is reason and rationality, rationality being not essentially in the sense that we understand it as common understanding of reason

or rationality, but simply making inference. And putting this inference, this inference is not monological, it's dialogical. It's always interactive. So there is a difference. Yes, mathematical is tied to rationality, but not every rationality can be reduced to rationalization. Rationalization happens when there is an excess of rules without you explaining where these rules are coming from. That's the whole point. And that's what really computer science at this moment, theoretical computer science, tries to do. Instead of talking about what is the rules of logic, you know, the kind of procedural

rules or predefined, preexisting methods that you simply need to abide by, move toward, instead of that, moving toward the logic of rules, how rules are constructed in the first because rules are the medium of abstraction, are basically the engines of mathematical novelty. And you can see this in a Brandomian rationalism paradigm that instead of endorsing the dogmatic rationalism that was built on basically norms of the game of rationality moving toward an idea of rationality that is based on game of norms, basically the interactive, how rules,

how norms are constructed in the first place. So this is the ultimate, really the ultimate question, the most significant question, when we are talking about judgment, novelty, mathematical novelty, logical novelty, intelligence, abstraction, so on and so forth. So I think in order for this topic to, you know, doesn't elide, doesn't become, you know, we need to prevent, we need to avoid aligning the distinction between rationalism understood at least in the way that we have been trying to formulate it, in the sense of understanding

how rules are constructed, we need to avoid eliding the distinction between this account of rationality and rationality that has been constructed under rules that have been given. That's in fact not rationality. in fact, if you think it has more common naturalism, bad naturalism than rationality, because rationality is really the medium of the artifice, of artificiality, of you defining the rules and understanding how these rules are, you know, how they interact and how they construct these really complex compositions and constructs. So yes, these two accounts of rationality, These two accounts of rationality, rationality for which rules are not pre-given and rationality

for which rules are given already, we need to avoid aligning the distinction between the two. Because if we align the distinction between these two accounts of rationality, essentially our rationality, as you say, is a form of rationalization. But in the game, there is a moment of decision, I guess. One player needs to do, I'm not sure if it's always like that, but one player needs to do the move. So there is a process of rationalization which condenses into a point of decision in the game, no? Yes, but this decision, first the criteria of these decisions are at least in the idea

of computation as interaction or rationality as being the medium of social interaction. This moment of decision is not decision in the sense that we traditionally understand decision, or even like traditional decision problems in computers, not in church during pieces. It's a different kind of decision. But yes, this decision, yes, so what? Decision simply is an abstract concept for making a move. And this making a move can be understood not as something that you basically rationalize

it, but something that allows you to construct these complex structures out of basically occupying different positions in some sort of abstract construct, abstract structure. So I think, yes, I can understand the connotations of this, but I'm very tentative about this idea that how far we can extend decision in games, the concept of decision in games, making a move, with the idea of decision in common sense, decision that always comes as with

some sort of that implies rationalization, like a rational choice theory. These are, I think, completely different concepts. And yes, they can be connected by making it more restrictive, by putting more rules on the criteria of decision, on the choice. Then it becomes something more of the rational choice theory and classical game theoretic stuff. But precisely, this is not really the case in the way that some people like Brandoom, Sellars, or in theoretical computer science, people like Abramsky, Blass, and Jafaridze, or Girard have been talking about it.

Two different things. They can be equivalent if you put too many restrictions, basically, on this criteria of choice. And precisely we have shown that this idea of decision is simply making a move, and these moves are according to the constraints. And these constraints are not any more rules, but simply building blocks of more construction, namely resources, namely abilities. These are completely abstract stuff that I don't think that we can extrapolate any rationalization from them. Even rationalism or reason, even rationalization in a negative sense, comes from the consequence

of these constructs. But you can't really, I don't think that you can inject these concepts at this level, at this fundamental level of decision, because decision at this level is extremely abstract. It's devoid of those procedural rules and the kind of constraints that make it more of a decision as the concept of decision, something like game theory or rational choice theory or so on and so forth. Adam, any comment on this? on I was just a

and it is not the implications about which a pretty broad it's a liberal critique and by the whole rational law choice but and thread with them so economic and political thinking if you if you want to take it that far right like that whole so the account of rationality and then the things that they they do with that definition of a rational agent? I mean, it seemed, is that, am I picking up the wrong end of the stick there? No, no, no. No, no, that's where I was going, I think. Yeah, but you see, in fact, this is one of the things that even Brandoom talks about

Brandel and McDowell that, in fact, when you look at the principles undergirding rational choice theory, decision, choice, and stuff, rules in these, basically, paradigms have nothing to do with the rules as we understand them in rules as inferences, as simply being logical, computational, linguistic constructs or processes. But the rules, in fact, the rules of rational choice theory have more, are more aligned

with naturalistic accounts of rules, pre-existing, predefined. In fact, the account of agency that rational choice theory gives you is much more tuned with these conservative takes on evolution and biology and human as being given, so on and so forth. But of course, the whole idea of the more restriction, the more rules you add to your system, there is more chance that the final product would resemble something more and

more like a kind of rational choice theory, classical game theory, so on and so forth. Adam, do you have any comment on this decision problem, decisions at the level of the very abstract level of fundamental computer science, the way how it's defined, and decision in the sense of a kind of a rationalization paradigm, that you rationalize if you make a decision. I can focus my question to all of you, maybe. So maybe computation is also about new type of action, which

is not necessarily human, I guess. I can use the term label, but which is more precise and more deals with the artifice you talked about, Trezor. What is action? I don't have a good definition for that. But the problem today also with politics is that politicians can't decide and they can't act in the public sphere anywhere. You could see it with the refugee crisis, I guess, maybe in many... And maybe we need new types of action. And maybe this relation between totally abstract pure mathematics, which is very meaningless, into something more concrete, which is action.

Maybe the medium can be computation. It is the idea hypothesis, maybe. But the problem here, I don't know what I mean really by action. So I used the word decision, which, or move, but I don't know. Yeah. Well, I think the question is a very interesting question. And I think this, you are right, that the concept of action is, first of all, it's very broad. It can mean so many things. But yeah, I mean, isn't it the whole enigma of German idealism, really? What is exactly the philosophy of action?

Because what is action? But it's freedom also, I guess. Yeah, what is action? No one knows what action is. everyone talks about it but no one knows really and yeah I am my intuition is that precisely this deepening of computation and move toward this really computer science can give that's that's really one of my interests other than this whole idea of intelligence defining intelligence and stuff is really because to and this is really the topic of my manuscript upcoming book to understand if we can renegotiate and solve some of the enigmas of German idealism,

namely the connection between philosophy of mind, philosophy of action, philosophy of knowledge, by way of this move toward deeper and deeper generalizations that have been foregrounded by mathematics, logics, and ultimately computer science. Adam, Elton, Stefan, any thoughts? I'm going to, Aaron, do you want to jump in? Go ahead. I want to formulate this. I was going to say it seems very tied to the idea of work

and the ambiguity around the definition of work to me, or that put me in mind of it. That was the first thing that also occurred to me when in the piece that you posted on the classroom, where we have this idea of computational work, and decide the error and it's connected no conflated with this idea of human work are and and it's a little more disconnected from the physical idea of doing work which is about expending energy but the and i i mean it's it's not well clarified what actually means for a program to be doing work and and then

that equivalents of body push it right on and and then is that machine my love and as the whole so the fall well things you know not all with that as well so around yeah that does what I was just gonna throw in cuz sony these questions about choice as well when you make your choice and you're constrained by all sorts of all promises and in sort of doing work. Anyway, seems like there's both a mapping and a bunch of unpacked assumptions there. I wanted to say something.

So where are you getting your use of action from? Are you using like a Hannah Arendt paradigm here with labor and action or where? Yes, yes, yes, exactly. Yes, yes, yes. Hannah Arendt, the human condition I guess, she criticizes Marx there for his not sufficient enough concept of labor. Right? I mean, generally, as a general comment, and not just about this topic, but everything, I think a concept that is too general and bulky that covers a lot of qualitative details,

qualitatively distinct details, is not really a useful concept for critique. Precisely, the idea of action might really make sense to use it in a political context. But once it becomes too general of a concept, it also covers the meticulous details and qualitative traits of action in terms of computation, then it becomes basically not useful anymore. In fact, we need to steer away from it, precisely because it creates these confusions and illusions. And that's, I think, that it is good for making these transference between different qualities

in different methods in different systems from a kind of a metaphoric understanding of thinking, which is, I think, is behind, it's one of the ideas behind the idea of abstract creativity. And when it comes to critique, we need to have particular concepts, particular concepts that cover qualitative distinctions, precisely because actions in the computer and actions in politics, while there are minimal isomorphisms in the sense that they appear to be functioning the same way, but they are qualitatively distinct. At that point we should, I think, avoid the application of the word action as it's meant in politics to some of these really abstract ideas like confrontation of axiomatic acts

like in computation. Because what is really acting computation is not really an action, really. Yeah, that was someone's... I also sort of dislike this kind of conceptual division between labor, work, and action in Arendt. I don't find it that helpful. And while I like what you're doing with trying to look at computation as labor, because I think that works within her paradigm. It doesn't work as work, computation in the same sense, where work is a very, like, Heideggerian phenomenological category of sort of directed activity toward a horizon, like, toward an intentional horizon, whereas computation is labor in the sense

that it's purely sort of mechanistic. And action, I think, is vague and unhelpful, but more thinking I like German idealism better for this and trying to think through freedom but I think her idea of action also as in being able to construct norms to define yourself as a who rather than as a what I don't know the sort of game game philosophy and the ability to construct norms rather than just sort of exist within the narrow paradigms that you're given in sort of economic and rational choice theory. I don't know, I assume that's what we're

doing with a lot of the game syntax we were talking about yesterday, right? Not last week. Yeah, absolutely. So, simulating in a very basic way. Yeah, yeah, yeah. I mean, the whole idea... ...the whole construction works, right? Yeah. I mean, I think computation, the absence can be understood precisely as labor. It's a labor whose products are computational abilities, and at the top of them are cognitive abilities, really, in the sense that those cognitive abilities are the ones that allow

you to not only have action in the sense of political and the German idealism, but you You can be able to make the critique. You can have the cognitive capacities required to make those renegotiations and redefinitions. From that, I think it is a labor, and it's the most fundamental labor, precisely because these cognitive abilities are not given to us. And the norms that drive and produces these further, further, you know, semantic abilities, semantic capacities that apply to judgment, we use them, you know, in terms of judgment, and judgments being basic components of the critique and action and so on and so forth.

We need to see where they are coming from, really. What is, what are the mechanisms that are behind them? This is, I think this is really a kind of extremely important avenue of investigation. Rather than treating human agency, human cognitive ability, that's pre-given, I'm not just talking about norms, I'm talking about even cognitive abilities, see what are really, what kind of labor is behind it, what kind of processes lead to these, you know, the instantiation of these kinds of abilities and capacities, and how they can be extended.

Precisely once we understand the mechanisms, how they function, how they behave, then we are also capable of extending them, implement them, not only in technological artifacts as traditional artificial intelligence, but also implement them in the social domain. So without doing this work, this understanding how cognitive abilities are coming from, we can't really talk about, I mean, we can't talk about it, but it would be extremely restricted

and narrow. We can't talk about how, for example, something like abstraction needs to be rechanneled, how we need to realize cognition in the social domain, so on and so forth. So I'm fine with Ray's idea of the social realization of cognition as completely a political project and really completely a political project and really for the ultimate political project. But that would be extremely, I think, simplistic and narrow if we really don't know the mechanisms underburning cognition.

How cognitive capacities, how semantic abilities, semantic abilities, being behind judgment in action, in critique, and in knowledge accumulation, where they are coming from? What are the mechanisms that are responsible for giving rise to this phenomenon? Can they be diversified? they be realized in other systems that they currently are, you know, implemented. That's why I think for me, you know, artificial intelligence is not an idea that is great in itself, but because it has implications.

And that's, its implications is really the intersection between philosophy of mind, philosophy of action and philosophy of knowledge, but also understanding the very, I think, the basic idea behind artificial intelligence is the differentiation between sapiens as the category, as a qualitative category of rational personhood and sapiens as a biological species. Further, it tries to further asymmetrize between the two, precisely because it tries to understand how these cognitive abilities are generated. Then if they can be generated in this way,

how they can be extended, and how they can be implemented in something that is no longer biological. Precisely, it's the idea of taking thought and all of its fruits, all of its implications beyond its evolutionary heritage. And I guess from the perspective of Dern, idealism, there's this wonderful paradox there, and kind of artificial intelligence at least understood narrowly, right, where if you can build sort of this sense of freedom in a very abstract way, right?

Yeah, yeah, absolutely. That's the question of forming the agency. Agency, in the Kantian sense, is really the index of freedom. And then how you can make a rational person, a person in the way that I use it, a person in a Solarzian sense. A person is not a biological person in the way that we understand. A person is simply an entity that is capable of forming judgments. Why is it a paradox, Alon?

Just in terms of being able to see something, like, causally understand how thought can develop how, like, norm construction and, yeah, what we understand as sort of sapient language processing activity. Understanding it totally causally but then seeing it also normatively and understanding it as sort of adding to, understanding it causally as a way of sort of extending its normative capabilities. And this is sort of traditionally how we've always seen this idea of sort of rationalized totalitarianism and behaviorism dominating humanity, all these sort of bad Adorno-Horkheimer

paradigms of dialectic of enlightenment and... I don't know, basically I think since like German idealism, there's just been this sort of fear of mechanistic behaviorism that German idealism was an attempt to kind of overcome. And artificial intelligence, I think if I understand Reza correctly, is kind of the the way of circling the square here and kind of connecting sapience to sentience in a line where if we can build who's, we can understand how we are, how we have come to be who's and how we can build better who's, how we can be more politically accountable to each other in a way that can complete kind of classical German idealistic political goals like an

and to war or cosmopolitan republicanism and things like that where the normative sphere is really enlarged and strengthened, right? Yeah, I mean, yes. But as I said, when I talk about artificial intelligence, I don't mean it essentially in the sense of that you make a machine or a collection of machines that have cognitive capacities on a human level or beyond, but simply applying the principle of artificial intelligence in that deep sense to be able to model basically social normativity, how we interact with one another at any level, political, economic, ethical, so on and so forth. And I think this whole idea of artificial intelligence, as you say, can be really seen

as the genuine child of German idealism, as being, especially being the extension of Kant's identifying the first task of German idealistic or Kantian critique, is really identifying what Kant calls the conditions necessary for cognition, determining what are the necessary conditions for generating something that we call a judgment, a cognition. So you see that there's a possibility to connect philosophy, and it's quite old philosophy,

with, you know... Yeah, absolutely, yes, I think that's, as I said... You were sceptic about this. No, I wasn't a skeptic. I'm a skeptic of the ones that make these kind of trying to make this connection between extremely superficial understanding of concepts in computer science and also bad sloppy interpretation of philosophical concepts. Yes, I'm completely a skeptic. In fact, I'm not a skeptic. I'm downright against it. But I'm not a skeptic of that we need to bridge between philosophy, politics, and computer science. I absolutely think it's an urgent thing,

and it's extremely consequential. Adam, what are you doing, frowning at this stuff? I'm not sure if I can articulate it well enough. But I'm trying to trace back that part of the conversation and then back to sort of individuals today, right? And you're sort of like, it's sort of like a critique of where there are lack of freedoms or people are constrained in action by a totalitarian

state, for example, you're sort of mapping them back to like a robot, essentially, it it seems to me. Or is that, like maybe it's too crude a characterization, but that was the- A robot is actually quite a, is a proto free agent. Is a proto free agent. You see, we don't- I'm used to thinking of it as a little more deterministic, I guess, but no, you're right. A robot, yeah, you can think of as an AI already, and in that sense, actually- The whole idea, I think, is freedom.

And obviously, again, freedom, the concept, is just too general. And when I usually talk about freedom, I mean positive freedom, rather negative freedom, not freedom from constraints, but freedom that by espousing certain constraints, certain constraints, and type of constraints, you are able to do something more. That's positive freedom, freedom to do something, by espousing certain constraints. And what are these constraints? These constraints are constraints of society, of interaction, which I think, again, that, again, brings back this whole idea of computation, paradigm, of interaction, especially the linguistic instantiation

of this. And these are really, I think, and this why German idealism is so important after Kant, Hegel, because these are basically the main problems that they have been dealing with. And now we are just going deeper level, see what are exactly the minimum requirements for the generation of cognition, for the generation of judgment, not just understanding it as, okay, language is a medium of social discourse and through language we can form concepts and concepts are responsible for our power of judgment so on and so forth. Going deeper level, what is exactly social interaction? What is exactly how concepts are constructed in the first place through the language, with

language itself being a byproduct of some more fundamental processes? OK. Yeah, all right. So the idea of constructing freedom through constraints and that sort of good strapping process there. OK, that seems really rich. I think I'll go do some reading there rather than . I mean, that's an interesting link from Tal as well. Thanks for that. It's from a book called Allies of Your Mind. I think Reza is also participating there by Matteo Paschalini, something like that.

Yes. I haven't read your article, Reza, but I will. Yeah, I have an essay there. It's old. Yeah. No, that book is good. There are a couple of essays that are very good. I mean, but as usual, the majority of essays are just this kind of downright really, sorry to be offensive, which I always try to be offensive when I talk philosophically, downright clueless accounts of AI computation and stuff. And this is, as I said, that's something that I think that's really the plague of and the

main antagonist against, the main obstacle against this genuine bridging of philosophy, politics and computer science, besides these kinds of sloppy interpretations. Okay, I'm going to share the screen. Sean is not here. Sean asked me that diagram that I shared on the classroom page, where are we now? And basically what are we doing? So I'm going to share that screen. We are already shut. It's okay. I will figure it out. We're

I'm already late. So can you guys see this, the diagram? Yeah. OK. We are basically in that gray area. And logic of computability was last session. So what is the significance of this area? Some of the key ideas is one refounding logic and language on proto-logical, i.e. computational processes. seeing and by logic I do not mean it in the classical sense anymore. We ruled out that

classical sense of logic. Logic is a much more fundamental field and language respectively. So it is more like this refounding is more like identifying the necessary conditions for the generation of logical and linguistic constructs and respectively the kind of capacities or cognitive abilities that they provide us with. Two, developing frameworks for studying complex behaviors of computational processes. And notice that we are now dealing with processes and behaviors in the sense that we have been

addressing. Three, understanding the computational structure, namely the geometry underlying logic and language as a first step toward designing new formal languages that one, capture syntactic, semantic and pragmatic aspects of both natural and artificial languages. This, of course, has two immediate implicit dimensions. One is that traditionally formal languages and national languages are opposed to one

another. And in fact, usually the proponents of national language think that formal languages are not rich, and proponents of formal languages think that national language is just too vague to be able to have any powerful traction on, for example, a specialized theoretical data or frameworks. Basically it doesn't, it has new theoretical power. This is especially

a position that's defended by Lorenzo Pantel in his tomb, Structure and Being, which I highly recommended. So this is one and the other one is that national languages have different sets of abilities than those of formal languages. I mean both at the level of syntax, semantics and pragmatics. So with this understanding of computation as interaction and move toward these more fundamental computational behaviors that are responsible in giving rise to something

that we call language, general concepts of the language, then are we able to create formal languages that can capture both the syntactic-semantic-pragmatic aspects of formal languages and syntactic-semantic-pragmatic aspects of natural language. increasing the cognitive abstractive abilities that each of these languages envelop in the

first place. And the other one is advanced strong forms of artificial intelligence with new paradigms of linguistic abstraction or cognitive abilities in general. This is because higher cognitive abilities, mainly semantic capacities, semantic abilities, power of judgments. Judgments in different forms are directly connected to language. And we can understand this in the Szilardian terms that thought is equivalent to language.

there is no such thing as thought as the way that we understand for sapiens without language. So if we can develop these kinds of languages, these new formal languages that capture both natural and formal languages, then what will be the ramifications of this for the project of artificial intelligence, namely giving rise to new forms of agents that basically cover broader range of cognitive abilities capable of qualitatively different forms of judgments than us.

This can be understood as realizing human or sapient intelligence beyond its evolutionary instantiation, further asymmetrizing the qualitative difference between sapient as the category of rational personhood and homo sapient as a biological species. Of course, the whole point is that this idea that we are, basically, we are trying to still founding artificial intelligence on a sapient model, namely a linguistic agent, because

the key role that language plays in coordinating philosophy of knowledge, action, and cognition. So we are still trying to found artificial intelligence on this account of linguistic agent. But by virtue that the framework of the language we are capable of developing would be much more powerful, much more general, covering and generating much broader sets of cognitive abilities, then there is no reason for us to think that the artificial agent,

in the sense of a strong human level artificial intelligence, would be the same as what we currently understand as a sapient agent, namely a human. Four, uncovering deep correspondences between computation, logic, and mathematics in a way that a discovery in one field would have an immediate corresponding development in the other fields. This is, you know, so moving further in this paradigm and this avenue of research further accentuates

the correspondences within logics, mathematics, and computation. That's that whole trinity of computation that I talked about, in which you can have, basically you can generate novelties in one field by looking at its correspondences with the other two fields, whether it's mathematics, logics, or computation. Five, providing models for different semantic levels of information processing in complex natural, social, and technical systems.

This can be understood as working out the level of abstraction criteria, distinguishing different levels of information processing in systems, whether they are natural, social, technical. And with that, we are capable of moving more and more toward the applied dimension of developing ontology in the sense of information science and semantic webs to study these various levels of information processing and how they behave, what are their products and how basically

they are connected with deeper levels or higher levels. So that can be understood as a kind of a hermeneutics of complex systems. And by complex systems, we mean it in a broad sense of not only natural physical complex system, but social and technical complexes. So these are some of the ideas and significant points that this area is covering. Any questions on this? I guess it would be helpful if you talked a little bit more about this idea of like enhanced semantic capabilities? I have a hard time imagining what that would look like.

Yeah, well that's... Yeah, sure. Okay, semantic abilities. What are really semantic abilities? Semantic abilities are, for example, what is the exact semantic complexity? Semantic complexity is because our concepts, the concepts being the rules, can have different, can lead to different, you know, or bring about different cognitive abilities. So what are concepts, for example, doing concepts, at the very most rudimentary, trivial sense, they are labeling

tools, but also they describe. Not only they describe, they also can be used as counterfactuals, allowing us to simulate our environment, ourselves, our actions, our thoughts, using simply counterfactuals, if conditionals. At a higher level, concepts can do more abstract things. They can be modalities, in fact. With modalities, we are capable of developing robust empirical vocabularies. Hence, we are capable of cognitive traction upon

of basically observations, assimilating those observations within conceptual, sophisticated conceptual theoretical frameworks, hence the idea of scientific progress. So these are basically, this is the semantic complexity of cognition that derives from the role of linguistic items and how they are deployed in networks of inferences. So we know that one of the principles that's...

Hello? We know that one of the principles that's responsible for these diverse rules that concepts can take in language is really the idea of linguistic interaction, the idea of the game of assertions, commitments and entitlements, randoms, deonticus, or TP. For every assertion, every assertion, as soon as you deploy an assertion, as soon as you assert a sentence, that assertion

becomes basically disposed to counter-assertions. And that's what is counter-assertions is that we make, we distinguish different roles that the concepts of those linguistic items take in a sentence. And hence, we are capable of diversifying its role, from simple labeling, descriptive, to counterfactuals, to modalities, so on and so forth. Hence, semantic complexity arises with different limits of complexity. What we know that in artificial languages, This idea of interaction, the idea of just two-person player game between assertion and counter-assertion, can be diversified even further by way

of indexing different computational behaviors, different methods of interaction. So these should be able to basically give rise to different concept rules, different moves in the assertion game. hence leading to different levels of semantic complexity, bringing about different types of judgments, different types of cognition, cognition simply being understood in the Kantian sense of basically conceptual judgments. There's one thought I have. is that given a system that could sort of develop these kind of emergent forms of new conceptual use

that, say, you and I simply having a conversation probably wouldn't be able to achieve, would someone still of sort of like a normal human's cognitive capacities be able to simply, having this having been done, be able to grasp a role like that? Or would it be something that we would also need, because it would be a part of an artificial language, would it be a matter of whether that was translatable? Translatable, yeah, okay. This is, I think, a very good question and something that is a conundrum for me too. Of course, this has a ramification. This means that how much, even though human-level AI would be grounded on the paradigm of linguistic

agency, namely sapience, how far can it diverge from its present instantiation? How asymmetrical can it be? And that would be that with a machine that even if has been founded on rational personhood principles, how much does it look like a rational person as we define it? I really don't know to answer this question. I'm really thinking about it. I think there would be some isomorphisms. would be some mapping that we can map some of the behavior precisely because of this linguistics because there is our linguistic behaviors involved but the

form of judgments the form of cognition I think there would be extremely asymmetrical to ours divergence not even the asymmetrical divergence so this is This is one of the things that, you know, this idea that Scott Baker and David Rodin talk about, that people like me and Ray or Pete, that we try to ground artificial intelligence as a principle of human rationality, namely sapience agency. We are basically binding, basically, artificial intelligence. No, there is no such binding at place.

Just because you are founding it on the principle of human rationality doesn't mean the cognitive abilities would be still basically continuous and congruent to our cognitive capacities. No. It's just, in fact, I think that's the principle of unbinding, precisely because language has such capacities, has such an unbinding capacity for cognition. That's really the core of the German idealist philosophy, to show, Kant especially, and later on, no pragmatism, no pragmatism, to show that language can steer things quite

in unanticipated, uncharted territories for the agency. But there's nothing in principle to say that we couldn't do this in English, right? Or? Yes, I think it would be. Because you see, maybe we should say there is nothing in principle to say that we couldn't do this in a language that we can track and we can investigate and study, but not necessarily

English language or for that matter any other natural language. Because natural languages are extremely narrow when it comes to these extremely sophisticated, ramificatory linguistic processes. Yes, they are, but that's one of the things, that they also have powers that formal languages don't. Vagueness. Vagueness is a power. It is a sloppy thing, but once it's tethered to embodiment, especially the idea of gestures, extended cognition, embodied cognition, vagueness can become quite a powerful cognitive tool,

cognitive capacity. So that's why I said that developing this whole idea of interaction, computation as and interaction and this refounding of logic and language and interactive paradigm of computation can lead us to design new formal languages that can capture both the properties and capacity of natural language and formal language. You know, in formal languages we don't have such a thing as metaphor. is strictly of a natural language. And what is really, we can't give in fact a formal description of a metaphor, it's a form of a cohortism. Those of you who are familiar

with the concept of cohortism in mathematics, it's like a blurring of the boundaries, creating compositionality, new constructs. This idea that Chatelet talks about metaphors that are like Trojan horses, to which you smuggle, you import the resources of an existing concept into a new territory, exactly like a Trojan horse. And by virtue of that, you create a site of disturbance, and that site of disturbance creates these unanticipated, unexpected ramifications. That once you navigate these ramifications,

unanticipated branches, then you are coming up, refining not only your new concept, your metaphor, but also capable of developing new concepts and new theoretical framework. So that is really an extremely tied to conceptual novelty and conceptual creativity, which is, and as I said, metaphor is part of natural language. I think that formal languages are not essentially foreclosed to things like vagueness and metaphors. once we try to reformulate formal languages

at the level of intraction, the computational paradigm of intraction. Precisely, intraction, what gives rise to things like metaphor, like vagueness, is radical context sensitivity and diffusibility. That we can update the context of our linguistic items. and ramify their contextuality. And that can only be done by way of at least two people interacting with one another. For example, I will try to talk about this today in terms of ludics, and that's what ludics tries to do. For example, when we are talking, I make an utterance,

and you don't know about, for example, the use of word that I talk about. Then you ask me what you mean, and then I try to refine it. And then you can come with a different, appending a different word to it, and that basically broadens its context. Different contextuality, levels of context, can be built to simply conversations around a meaningless word, simply through interaction. That's really the core idea behind ludics. You don't have any more propositions or formulas where you have falsity and truth already predetermined for these formulas.

All you have is the trace of the sign. What is the trace of the sign? It's the location within the context of interaction between two computational processes, two agents. Thank you.

Can you guys hear me? Now we can. Jessica was trying to speak, but it didn't seem like her microphone was working. No, she, I think, muted me. Jessica, do you have a question? I did, but my connection is very bad,

so I think I'd better not... Okay, you can type your question in the chat box. Sorry, and I can't get the chat box because I'm using my phone. Oh, okay. Any questions from any of you before we move forward? Yeah, I think today's session, you know, we didn't manage to cover the stuff that we supposed to cover, but I think these discussions are basically kind of bringing the whole,

everything that we have been talking about into a kind of a cohesive picture. Why is that these things are significant? What kind of works needs to be done in order for us to actually make any kind of significant philosophical connection? You can go back to the slides, I think, now. Yeah, you want to look at it again? Is it the end of everything? Oh, no, no, no, no, no, no. I'm going to start this session. But that slide was that slide.

That was it. Oh, I see. Stephen, have you had any comments on this stuff? AI, agency, computation, language, the ramifications of these? Let me think. Yeah, but let me, I'll wait until the end. Let's get started. Are you sure? We can, we have spent time on these discussions. So yeah, you can go on, it's OK.

No, I need to formulate it a little bit better. OK, OK. So last session I talked about Georgi Jaffaritze's computability logic, we are really tight on time. What I plan to do is that, as you see in the diagram, we are looking at different developments and revisions done on traditional linear logic. And Jaaparitza was being one of them. I'm not going to go further into computability logic and hold it for the next session when, hopefully, Sean

and the rest of people will be online. And instead, I will move straight into Ludix, and the context from which it emerged, it was developed. And then I make these comparisons, basically studying the differences and similarities between computability, logic, and ludics. And that's where I resume the little bit that was left from the computability logic part. But if you remember the whole point of computability logic,

was to understand game itself, basically a strip of all of its procedural rules, predefined and preexisting rules, the game itself as the ultimate computational object. And in order for us to be capable of understanding game itself as the ultimate computational object, we need to give at least a coherent minimal semantics of game. And that's how computability logic differs from classical game semantics, precisely because

Because it's not founded on syntax as the first level of construction, but a minimal coherent semantics of construction, construction being the ultimate logical mathematical object or in our case, computational object. And this semantic priority or syntax led Jafarize to give a semantic interpretation of operations on a game. What these operations on games were, choice operators, choice operations, resource operations,

negation, reduction, and parallel operations. Whereas we saw that in linear logic, the interpretation of resources and choice do not have any semantic, you know, a strong semantic significance. They are actually, compared to computability logic, they are quite, in fact, naïve. They do not really tell us how resources behave, how choices behave, what consequences they

might have in the construction, the roles they play, the semantics of their instantiation within the medium of interaction. And that's what Japparitze's main critique against traditional linear logic. Now today we are going to look at ludics. This is a framework that Gerard, Jean-Baptiste Jeunet, and Pierre Courienne developed from of traditional linear logic with one of the fundamental discoveries done by

another French magician and mathematician Andrew and really in the it's called focalization we will talk about this but for conversations and they true so they developed ludics from linear logics and ludics then can also be seen as not only a development of further development of linear logic explicitly in track the framework but also revision of some of these you know semantic insufficiencies in linear logic making the interactive side of linear logic more refined and more explicit

So, let me... Can you see the screen? Yes. Okay. So, Girard wrote this manuscript that was never published because it was too eccentric

for academic publishing, but it has influenced a lot in logicians, computer scientists, and mathematicians. It's called Locus Solum. The title is a kind of twist on Raymond Russell, Locus Solus. Locus Solum can be translated to location, is all that matters, or only place matters. And the subtitle of his manuscript is from the rules of logic to the logic of rules. This is, again, brings us back to that idea

that I was talking in reply to Tal about that the rules are no longer predefined, rules of logic and rules of rationality, rules of judgment in the formal sense, but that we We need to study where these rules are coming from. So we need to study the logic of rules, or more accurately, the protologics, the computational behaviors, protological computational behaviors responsible for generating rules at any level in the first place.

So from the logic of rules, there is also a brandomian equivalent of this. Those of you who have read Brandom or Sellars, this can be put in a brandomian sense from norms of the game of rationality to the game of norms. So as we know, removing weakening and contraction gives the space for more logical connectives. This is what we talked about when we looked at how traditional linear logic was developed.

The Siglin calculus has two variants which coincide in the classical frame, the multiplicative and the additive ones, multiplicative connectives and additive connectives. In general, we distinguish between the active formula, the one to which the rule is applied, and the inactive ones, which are its contexts. In an introduction rule for a given connective, a conjunct or a disjunct, on the left or on the right, We may formulate the rule either by mentioning this joint context in the premise or by mentioning identical ones. Because of weakening and contraction, that does not matter.

But in the absence of these structural rules, weakening and contraction, it matters. This is, that was the whole idea of resource sensitivity. And the multiplicative and additive variants are no longer equivalent. we saw that how conjuncts branch into additive conjuncts and multiplicative conjuncts, the same for disjuncts, additive disjuncts and multiplicative disjuncts, with different interpretations of resources and choices. But in the absence of these structural rules, it matters, and the multiplicative and additive variants are no longer equivalent. Therefore, we get multiplicative

conjunction and disjunction, which was symbolized by an invert ampersand or the symbol that's called par in linear logic. An additive conjunction and disjunction. Negation is simply a duality operator. The same thing in compatibility logic. We know that negation in logic is really the function of a more fundamental photological phenomenon, and that's called duality. In a two-person game, it can be formulated as the switch of rules, the interchange of rules between player and the environment, between the falsifier and verifier, proponent and

the opponent. Every formula may change its side in one sequence by being negated. Linear implication is a multiplicative connective. A lollipop B is defined as A orthogonal multiplicative disjunction B. We gave also an interpretation of this in terms of what it really means in terms of resources and the kind of moves being made. It is this connective which expresses resource consumption. Against A, you obtain B. Now, a natural interpretation of linear logic is in terms of processes. The linear

implication gives an illustration of that. When you give A in order to obtain B, there are two entangled processes, one of giving A and one of receiving B in exchange. Therefore, Therefore, the multiplicative disjunction, par, is naturally interpreted as a parallelization of processes, whereas a multiplicative conjunction is interpreted as a sequentialization of processes. A circle product or tensor is either A and then B or the other way around. game semantics interpretation have been provided very early on for linear logic. So it's not

that ludics was the first that developed an interactive framework for linear logic. People like Angrius Blass, Samson Abramsky developed game semantics, an interactive game semantics for linear logic. But of course, we'll see that ludic is different from these game semantic interpretation of linear logic. It's a completely different piece altogether. In computational terms, a type could be regarded as a server from which client can get, in one axis, an element of that type.

The client need not to do anything more than showing up. This kind of type is said to be simple, because the client has nothing to do, but it is also possible to build complex types. In fact, we can understand a, additive conjunction, b, as a choice. The resources you have can provide you with A as well as with B. Therefore, they provide you with a choice between two kinds of data. The complex type may be therefore interpreted as a server from which the client can get either A or B because additive disjunction

has a symmetric law with regard to additive conjunction. It is natural to understand it as a dual choice. The client has nothing to do because the server makes the choice itself. Now, because of De Morgane's laws, negation may be interpreted as an exchange between the two rules, of server and of client. Falsifier, depending on the context of falsifier, verifier, if you are specifically talking about proofs. the constructive account of proofs. Blass still proposes a more elaborate interpretation by means of games. He says, a play of A, multiplicative conjunction B, consists in the interleaved ones of the two constituents,

A and B. Whenever it is the proponent's turn, namely server's turn, to move, he or she must move in the same component in which the opponent, the client last move, while the opponent is free to switch components. Finally, A, multiplicative conjunction B, is a complex game with the impossibility for the proponent to make use of the information obtained from one component while playing the other, while A, multiplicative disjunction B, means such a game where he or she can. This game interpretation is something that we get in the more recent ludics developed by, initially, by Girard, Corian, Poitrini, and Alain Lecomte.

Ludics starts from the observation that proofs can always be represented as alternations of positive and negative steps, a concept developed by French religion Andrioli. Where a negative step is a reversible one, such that we may always make the reverse step because we never lose contextual information when making that step, and a positive one is non-reversible. Seeing attempts to find the proof as such successions of negative and positive steps allows us to see those attempts as gains. where positive steps are moves by the profit and negative ones, namely the steps that you

can basically go back to prior steps precisely because they preserve contextual information. Sorry, I lost my track. Because the roles are proper and an opponent may be exchanged, we see the similar attempt to build a proof exists from the opponent's viewpoint. But his or her attempt to build a proof has its goal, the negative sequence with regard to the sequence defended by the first player. are thus opposed to counter-proofs in a space where both are coexisting, which is called

the space of paraproofs, an orthogonality relation. And we know that an orthogonality relation conveys two things. One, the idea of duality, and another, the idea of convergence, between players, between falsifier and verifier. An orthogonality relation may then be defined in an analogy to vector spaces, a new vector is introduced, which belongs to the proofs as well as the counter-proofs. This paradoxical object is a paralogism that Girard calls the diamond.

more on this later, defining what a daemon is. So the semantics interpretation of linear logic that was given by the likes of Andreas Blass and Samson Abramsky can't be really again understood as explicit, as making explicit the intractive component of proof itself, maybe the construction, computation, depending on the context. But it was more of a later addition, you know, appending interaction to the established context

of linear logic, giving a game interpretation of it. But in ludics, the traditional aspects, kind of like very similar to computability logic, the traditional aspects of linear logic are suspended in favor of making explicit the intractive component itself. Namely, again, the game becomes the ultimate object. The game being simply another name for construction, for intractive construction. how proofs are being constructed, or judgments being constructed, simply through interactions. This interaction itself doesn't need to have any predefined rules, any procedural rules.

Again, like the subtitle of Lukas Salaam, from rules of logic to logic of rules. The morality of this story is that we are led to consider true proofs and false ones, that is, unsuccessful attempts on the same level. What interests us above all is their intraction, also in ludics, but also generally in computer science and logics called normalization process. I will talk about what is normalization. It's normalization when normalization can be understood

depending on the context, as abstract rewriting system, as the very idea of computation, as the idea of cut elimination in sequence calculus. Any of you know what rewriting systems are, abstract rewriting? Adam, any comment on that? Or normalization in general? Yeah, well normalization in general as a process of separating our separate dimensions on to in to separate expression I guess so it's a so we're going to talk about some dollars so

program normalization on and and by me and then you have the idea of normal form which is sort of related where that's, I'm trying to think of a nice definition of it, but again, it's about separating out into different dimensions so that then allows for elegant expression and navigation of the information. Sure. And also another important thing is that this idea of separation or well-formedness, creating well-formed collections, precisely can be understood in terms of a more fundamental phenomenon.

That's why we are capable of doing this. And that's what rewriting systems, abstract rewriting systems try to capture. And this is also what cut elimination really captures, is that we are capable of cutting, simply in the sense of Gensen, the stuff that we have been using, precisely because it's a form of a kind of almost a condensation, a condensation that allow you to, for example, our game to remove those histories and obviously it has computational significance in terms of the resources, in terms of tracking of formulas, cutting those formulas, removing

them and starting new and our proof, so the whole idea is that a proof that has been constructed And via cut elimination procedure, rewriting system, cutting excess of formulas, formulas that are being repeated on the left side and the right side, that proof would be equivalent, equal to a cut-free proof. This cut elimination, proof derived from cut elimination, is equal to proof that it's cut free. We will talk about normalization and what exactly normalization is in terms of these

different contexts abstract rewriting systems, but especially as cut elimination later on and basically you can have also different, based on your framework of interaction, how players play against each other and what happens in the game, basically how the interaction emerges between these players can lead to different types of normalizations.

So the morality of this story is that we are led to consider true proofs and false ones. That is, unsuccessful attempts on the same level. What interests us about all is their interaction called normalization, and not particularly their truth or their falsity. Again, this is in line with the idea that we do not have procedure or rules, nor do Do we have predetermined truth and falsity values of our formulas? All we have is interaction, the game itself. In fact, this is exactly what is needed when we try to isolate various meanings that a

sentence can have. meaning, so that's why also ludics can teach us a lot about natural language, about the question of meaning, and especially the inferentialist account of meaning as used, the pragmatic A meaning is determined by the counter meanings with which it interacts. There is no need to use truth values as primitive objects for representing that, as it suffices to have a formalization of the notion of interaction, something provided by ludics.

And this is following the paradigm that I mentioned last session from denotational semantics, from denotation and model theory of meaning to operational semantics. Meanings are determined by the interaction of meanings and counter meanings. are really proofs. So it would be again the interaction of proof of type A and proof of type not A. Or if you do not have an untyped interaction, again, the proof and discounted

proof, meaning and discounted meaning. And that's how, as we see ludics, semantics, the distinction between semantics and syntax collapses. Any syntactic utterance, any syntactic vocabulary deployed in an interactive framework imminently gives rise to semantic layers, to different contextualities of how that syntax is being used in the context of the game or the interaction, the confrontation between proofs and counter-proofs, meanings and counter-meanings, assertions

and counterinsertions if you are Brandovian. Just before moving to the story about ludics, This whole idea of when people started to apply game semantics, even interaction in the more of a kind of traditional game theoretic sense to natural language, can be traced back to work of Hentika. Hentika as a school gives rise to important notions, like a strategic

meaning, that is the aspect of meaning concerned with a set of decisions we have to take when understanding a discourse in order to respect some coherent properties. According to Hentika, for instance, the meaning of a proper name does not refer to a set of properties, neither does it refer to some original baptismal, but comes from a strategic meaning. If I meet, say, in a novel, a proper name, Flora, for the first time, myself, as a player, chooses an individual as the value of the name, since myself tries to check a sentence S against another player, sometimes named Nature by Hentika. It's exactly like that machine environment, system environment paradigm that we've been talking about.

By leading the semantic game G of S associated with S until an atomic subformula of S is observed to be true, it appears that in a winning strategy, myself will have to choose as the value of the name the real bearer of this name. Hentikov proposes similar theory for anaphoric pronouns. So a few things about this. You see, so in the traditional game, semantic application of the paradigm of interaction to natural language, like linguistic interaction, dialogue, meanings are essentially understood

and investigated through the procedure of decomposition to atomic formulas or propositions, atomic sentences that are self-evidently true or false. This is basically what atomism is, atomistic theory of semantics. Hentycock devises an interactive game, semantic account of his semantic atomism. But in ludics, as we saw, as we very briefly talked about,

there is no such a thing as predetermined truth and falsity. Meanings cannot, no longer be understood and studied through decomposition into propositional formulae-like atoms. Meanings can only be meanings via their interaction with countermeans in a game in which there is no procedural rule nor an account, a predefined account of truth and falsity. within this new dynamic framework, which is ludics, meanings are essentially infinite

objects. You can normalize them. You can determine a meaning. It doesn't mean indeterminacy of meaning. You can determine and test them according to criteria, for example, of convergence between two players, so on and so forth. But you can have infinite context for a given, for example, word or a given sentence, precisely because you can anchor that sentence within different forms of interaction, which each form of interaction leading to a scenario

that might not be essentially convergent, might go infinitely, might contradict. So this is the whole idea that you can have increasing levels of context, semantic context, for a given word. So this is very much ludics in tune with, you know, no pragmatist, post-Wittgenstein of meaning and contextuality as can be found in the works of Sellars and Brando.

Is that even capturing the idea that the meaning of a term can change over time? If you look at the time... In Ludwig there is no such thing as atoms. That's the whole point. And that's what I'm going to talk about. Because atoms essentially is a basic fact, you know, that of course has metaphysical, epistemological, implicit dimensions. But it means that it's something that you can't decompose it further. Hence, it's considered to be self-evidently true or false. But the whole thing is that ludics does not start from atoms, nor it tries to decompose

two atoms, because atoms don't exist anymore, precisely because there are no self-evident truths or falsity. It's just all the game, all the construction, all the logic of rules, rather than the rules of logic that determines an elementary account of truth or falsity. Okay. So ludics is a theory proposed by Girard as a new foundation for logic.

It results from analysis of the concept of proof in linear logic. As was established by Andriol in 1992, every proof in linear logic may be viewed as a process of polarized steps, alternately positive and negative. This process comes from the ability to concentrate several successive positive respectively negative steps, each of which are associated with a positive respectively negative rule into only one big positive respectively negative step, which consists in the application of a so-called synthetic operator. Of course, an infinity of such operator exists. This leads to a more abstract way of seeing a logical system.

Otherwise, because of this feature of any proof, and because we may associate a positive respectively negative step with a positive or negative action of one speaker, a proof may also be seen as a strategy in a game." And the whole idea of construction of proof, determining the meaning, generating semantic contexts for a given sentence and for its linguistic items, can be seen within the medium

of interaction between these strategies, each represented by a player, abstract player, verifier, calcifier, proof and counterproof, meaning and countermeaning. and the one who argues against that assertion, if you are in the context of the game of giving and asking for reasons. We are thus able to reconcile the two aspects of the constructivist project outlined by Brouwer, Heiting, Kolmogorov, Curry, and Howard.

The proof aspect and the game aspect. Various accounts of game semantics have been provided for linear logic, thus making it, as is traditionally the case in logic, a synthetic level, the rules of linear logic, and a semantic one, an interpretation of connective groups in terms of game connections. Ludics, on the other hand, rests on the willingness to collapse the opposition between the two levels, syntax and semantics. The semantic of rules is in the rules themselves, since proofs as syntactic objects may now be viewed as strategies, the interpretive objects at

one unique level. So proofs now can be viewed as confrontation of strategies, interaction of strategies. All right. I skipped this part and we'll come back to it later. So we need to know a few of the objectives and why Ludig's is important and what it is good for. Ludix studies protological computational phenomena at a foundational level, much like

logic of computability proposed by Jabbaritze. Ludix allows one to get rid of a conception of meaning based on model theory, which takes truth denotation and truth conditions for granted, while many approaches to language Peirce, Wittgenstein, Salars, and Brandoom are in favor of a more procedural way of grasping sentences' meanings. Ludwig's can directly be connected to this pragmatic operational semantics account of meanings. A consequence of the previous direction resides in some sense, putting most of semantics into

the domain of pragmatics. The use of words amounts to making actions, which are best depicted as moves in games." But this is, as we'll look at it, just as Brandon and Seller's account of meaning as use is very different from Wittgenstein's meaning as use and her's meaning as use paradigm, Ludix also very different from Brandoom and Sellars. And as I will try to explain in next session, in fact, we can rectify, revise, and further develop

some of the aspects of Brandoom's inadequacies, also some of the good points of Brando's and our system theory of meaning by way of ludics. And just, I will make this more explicit as we move forward, just to make sure, in fact, This can be seen as a computational interpretation of pragmatics, a computational interpretation

of what exactly social interaction is, how social normativity, social game of language determines meaning. We can talk about society, social discourse, social interaction in terms of social discourse and social communication, but those are completely, I think, inadequate way of explaining what exactly the social dimension of pragmatics is. And I think a computational interpretation of what exactly the social is needs to be be given. And this is, I think, ludics is a good candidate for it. Maybe not at this

level, but it really, you know, put forward a kind of convincing and promising direction for this interpretation. Another consequence is that ludics allows one to account for inferentialism, overcoming some of the difficulties encountered by Brandoom's theory and by proof theory. So not only ludics is not really about monological determination of meaning, it's about inferentialist

and dialogical and inferentialist. role a sentence or linguistic items play in the linguistic interactive game among the members of a linguistic community. So ludic is very, you know, is compatible with this view, but also, as I said, it can add further rectifications and makes more developments in explaining what exactly inferentialism

is what is exactly a network of inferences and how can we formalize them, how can we track and observe fundamental behaviors that are responsible for this kind of the emergence and the configuration of this inferentialist network. precisely because we know that in Brandoumi and Salarsian's theory of concepts is that the concept is defined by its content, and its content is determined by the role it plays in a network of inferences.

And these network of inferences cannot no longer be understood monologically. They are dialogically. Hence the semantic holism crosses over to pragmatics, to the social dimension. The content of the content is determined by the role it plays in a network of inferences. And the network of inferences cannot be investigated other by moving toward the pragmatic dimension of inferences, because that pragmatic dimension is what allows this network of inference that

moves between meanings and countermeanings, assertions and counter-assertions, giving and asking for reasons. That pragmatic dimension is what generates the network of inference in the first place, and hence plays a significant, a key, a main role in determining the content in determining the content of the concept and ultimately the cognitive capacities provided by the ability to use concepts in different contexts.

As I was talking to Aaron about not only labeling descriptive, but also context-factuals, modalities, so on and so forth. Now what is probably the most striking is that by delving deeply into the foundations of logic, the Ludix project has shed a new light on the foundations of language. Thus this foundational exploration has given rise to concepts which can be dubbed and proved are logical and are therefore applicable in the field of language as well as the field of logic, thereby going towards common foundation of both. We have only like 20 minutes, so I think we can't go too far because then it will be like

of we have to interrupt the whole argument where it's the most important so maybe we should just get back to our discussion and try to talk a little bit about this and see these things in a broader picture and within that kind of interpretive bridge between philosophy of action, mind, knowledge, computation, language, no pragmatism, neo-rationalism, et cetera, et cetera. What was the last sentence in your slide?

The last sentence in my slide was that the one that I read it or the one that I didn't read it? I'm not sure if you read. No, no, the one that you read. I missed it. Oh, I said that what is probably the most striking is that by delving deeply into the foundations of logic, the Ludix project has shed a new light on the foundations of language. As I said, seeing the language as this vast computational frameworks with different levels of information processing, thus this foundational exploration has given rise to concepts which can be dubbed protological and are therefore applicable in the field of language as well

as in the field of logic, thereby going towards a common foundation of both. So I have one question. Sure, go on. Why is the reversibility thing important? I mean why is he using reversibility and non-reversibility and positive and negative because maybe you don't know the opponent's move or strategy? I'm not sure I got that. Sorry, can you repeat the question? I kind of got cut off. Yes. The reversibility thing, what between steps of the proof, I guess?

Okay, yes. You see, reversibility, we'll go into this much further. Reversibility means that you can single out constants between your moves. And these constants in ludics can be seen as contexts, context, you know, meaning, contextual semantic, contextual meaning of your words that you have deployed. So this reversibility, if you can preserve the information, you can single out constants, invariances, semantic invariances. And basically these are another name for it is the context,

the semantic context of the word that you have deployed. So that's the kind of really beauty about it. That context can be seen as the ability to revise your moves and see what kind of context, see how your context, the word that you use or syntactic utterance that you deployed in your interactive framework can be traced back and you see the steps that you made that allowed you to construct that context, that semantic meaning, semantic context of that syntactic vocabulary you deployed. And in what cases do the context then change? The context can change based on different modes of interaction.

For example, you can have, that's where the idea of interaction as normalization comes to play, that I will talk about it next session. There are different scenarios that two players, at least two players, can interact with one another. It can be seen as different, for example, Hegelian scenarios at the end of dialectics, Whether it's completely the players converge or basically the players, you know, the argument completely unravels. There is no agreement, complete dissensus, or the game moves to infinity.

For example, when there is convergence, a criterion in ludics, that's when new context happens. out of two designs, namely two sets of meanings and counter meanings, you can have, or each representing, for example, progression of contexts, you can have a new context, a new design, a new strategy with new behaviors, hence giving rise to new contexts. And one of the things that I think is extremely, makes ludic very important for any person

who is into, they don't know pragmatism and this, Salars and Brandoom, you know, rationalist paradigm, is that one of the reasons that Salars and Brandoom in different ways, they object against artificial intelligence, at least in the classical sense of artificial intelligence, is that the way that it tries to linguistically capture the machining agent, the abstract machine, is that the linguistic picture of this does not allow for a radical

component of the national language. And what is that? It's the idea of me being capable of updating my commitments, my conceptual commitments, hence giving rise to arriving at new contexts. This radical context sensitivity which is tied to updating my conceptual commitments. For example, if I say, you know, this rose is black, and you counter-assert me that, first of all, this is not a rose, but also it's not black. It's dark red. So this idea that I will lead to this idea of interaction, pragmatic interaction, to

update my judgments, perceptual judgment, conceptual judgment, so on and so forth, is what really makes, has the ramifications in terms of semantic complexity and semantic capacities of an agent. And that's what really traditional linguistic picture of a machine in classical project of artificial intelligence does not have. But ludics allows us to formulate this computation, updating of commitments, revision of context, generation of new contexts. So to put it in ludic terms, an occurrence of irreversibility is when something, I don't

know, like a trauma or something from the outside changes the context. Yes. Does that make sense? Yes. Yeah. Yeah. Yeah, and you see why negative move? There are negative moves are reversible. Because the context construction is always a pragmatic thing, a pragmatic task. It's a public thing. Another person is the one that revises my assertion with a counter-assertion. Yeah.

So is the reversibility necessarily external or the irreversibility? You should be able to have moves which are inherently irreversible, right? Yes, and those are the positive moves, yes. Right, so like, you know, like in chess, there's moves you can't reverse. Like you move a pawn forward and you can't reverse.

It doesn't matter what the opponent does. But then there's other moves where it would depend on the next move of the opponent, whether you can reverse it, for instance. Yes. And then you get the same thing. It's interesting, the chain of reversibility, and you have to carry the history with it. It's very like in a text editor, or like Word, or whatever. It keeps this history of your actions, in fact. And that's how you undo, right? So that's a vision. A good linguistic example of this is the phenomena of anaphora. What is anaphora? Anaphora is that are words that if they don't have a context,

they're purely meaningless. They can mean anything, like he or she. He, when we are talking about gossiping about a person, we use he or she. And this he can, depending on the history of our conversation, might refer to John, Mary, me, you, different people. But we know this precisely captures, the Anafora captures this idea of histories, contextual histories. What is that? What are you thinking about?

JOHN MUELLER- No, so that's powerful to make sense, actually. And it explains a lot about the limits of how you linguistically analyze a sentence. It's actually the conventional sentence level linguistic analysis. Actually, it's quite easy to come up with natural language interactions, which confound it. but it's usually because of some shared history, right? So it's because of the history that you can then, that the people in that interaction can have a meaningful interaction, right? Yes. And in fact, meaning is precisely this. Meaning cannot be divorced from interaction. That's the whole point.

Which is sort of like the flip side of the private language critique, right? So it's interesting where you were saying thought and language, like it doesn't make sense to talk about one without the other, because I was reminded about the private language argument, that it doesn't make sense. Like, this is, in a way, it's trying to, sort of it's a way of solving both to me, right? Because the meaning is coming out of the interaction inherently here, right? Yes. So there is no private language here, because the meaning is entirely... All private language, or put in different ways, private thoughts. Private thoughts are modeled, are possible, but they are intrinsically and inherently

are modeled on public language, namely the interactive dimension. And this is what Selaar's critique of the myth of Jones, he talks about this a lot, and Rosenberg's develops it much, much further in thinking self. or so okay and is lost there so we have these news which are figures is that once it was a little bit irreversible and then there's another sort of news to go well on interest is there that

irreversible it I'll more structural level in a way so I You're talking about this contextual transformations can happen to the meaning of tokens, for instance, so that actually the game itself can be revised to be a different game, right? Yes, I will show you. Let me actually, before... So this whole idea, I will talk about this, elaborate this more, this whole idea of convergence of two strategies to designs leading to a new design which that can account for a new

context is represented by a behavior or an object, a computational or a proteological object called fax in ludics. It basically looks like it functions kind of like a fax machine, a Xerox machine. And Abramsky, in fact, studies this fax phenomenon by way of a more generalized computational model of game called a copycat strategy to show how this works. I mean, I have made a Lego toy universe out of this.

I will share with you one second. Can you guys see this? Yes. Yeah. Okay. So we have player A and player B down the diagram. They are basically, they do not even need to interact. You can simply see them as within the framework of an asynchronous concurrent system.

And each, of course, each player can be represented by its own base. This base, which means that they have their own universe of moves. And if you see, each cell has been labeled. So PA makes that move from going from 1E to 2G, and player B moves from 1A to 2A to 3A. Okay? Now the thing is that the interaction between them, even within the concurrent system, can

be represented by a shady character called the copycat. Now the copycat, how captures the map, the identity map of interaction between these two players to show that if they converge, it gives a completely different set of moves with different behaviors, even if they are isomorphic. So it's like the idea that I said, how to play against two grand chess masters at the same time and always be the winner. So player, the copycat at the top, plays PA the copycat at the top plays PA against PB by copying its moves within its own base,

basically the other bases, the base of the PA, the base of PB. and plays actually, and yeah, playing PB against PA, but with the base of PA, the universe of its own label itself. Now we see the moves that are being basically copycat moves. If we see that, for example, PA made a move with the base XI and PB's original move was

with the base row. Now through this copying strategy, the copycat makes two new designs simply by interacting these two PAs and interacting them with one another. Makes two different new moves that are isomorphic with previous moves but completely are new moves. New basically allows for instantiation of new context. One is the move that isomorphic to PA's move but with the base of rho and another one is a move isomorphic with the move of player B but instead of the base of it being rho,

its base is psi. So this is the whole idea that copycat, which is simply the idea of genuine interaction in the game, and the interaction always gives to, if it's convergent, gives rise to new behaviors, to new designs. It's the idea that copycat does not just copy, it also makes new designs, new moves with new behaviors. in a game, in the interactive framework, in this sense, leads if it is convergent. Can be understood as generation of new behaviors. All you need to know is that this is the function

of the facts. Copy the moves of another player but with a new base. We can see this in, for example a dialogue I have made a question about your holiday how for example did you enjoy your holiday and we talk a little bit so this would be the base of our design in that context and then suddenly we change to talk about this holiday within a different context or move the conversation to a new topic is still congruent to the previous one, changing the basis of the questions and assertions and simply provides further topicalization, diversifying the topics of our conversation.

I will get to all of this stuff, the idea of designs, the strategies, behaviors, the concept of focalization and topicalization, and how they map to a study of natural language next session. Okay, Stephen, your discussion before we wrap up today's session. Hang on, I'm having a problem with the window.

Reza, how does it happen that in a conversation it changes, the context changes? Yes, sometimes, but not all the times. Yes. No, I'm asking, how does it happen, and is it because of that copycat player? Not because of the copycat, but context change is really about how based on if we are moving, we have the same design. What is design? I will talk about this in Ludix. You can see this design as we talk about the same topic in our conversation, okay?

So we have the same bias, the same focus. Now, according to how we interact, and this interaction, again, computationally, pathologically understood, only according to interaction, interaction being another name for normalization of processes, how these processes interact, according to this interaction, the context changes. example, when we converge, usually the context changes. But also, it can happen to deployment

of something that Girard calls a diamond. What is a diamond, really? A diamond is more like termination process or more like when in dialogue I say, OK, I give up. I surrender to your point. These are some of the basically scenarios where the context become disposed to alteration, to change. Questions, thoughts?

Stefan, I think you had a question, no? Oh yes, we are waiting for it. Yeah, no. Go on, don't worry. I'm still trying to think about the best way to handle this, and this might be just a... Well, just move forward. We can talk about it. Maybe a second-hand version of the question I asked a while back, which is, I guess, when we talk about language, how are we understanding the possibility of a distinction between language as a phenomena or like as an utterance maybe or a series of utterances or an interaction as it happens and the capacity for language to abstract beyond

immediate experience in the sense that they have that words have semantic content or that yeah maybe be, yeah, essentially that words have semantic content. Does that make sense? Let me try to, and please correct me if I'm misrepresenting your question. You are saying that, OK, language has these proteological computational behaviors, and that's what Selaar's called the intralinguistic behaviors, right? That's basically the functional core of language as such.

What happens inside language itself? And then there is this idea that language, obviously, other than within its own pragmatic, interactive dimension, also interacts with our perceptual experiences with the world. and hence is kind of constrained by somehow evolutionary restriction on our perceptual experience. Right? I mean, it need not be evolutionary, maybe.

Well, evolutionary, I don't mean just biological, but I mean also social evolution. Yeah. Yeah, I suppose so. I mean, in the sense that, like, in a... The instant of an utterance, or the moment of an utterance, appeals to a linguistic context that is outside of it, but also contains... The instant, I mean, contains the context by which it's capable of doing that. So I guess what I'm... Yes, and that context also, the pragmatic part, is anthropologically constrained. Yeah. Yeah. Yeah, I think this is definitely the case.

And not only that, but also we can see that language, in fact the brain processing of language, puts key constraints on how language functions at the level of natural, ordinary language. all these heuristic, social, anthropological constraints. And yes, I think, and unless, so that's what usually I talk about, why we need to distinguish between the two, and we should, otherwise maybe it's really bad, sloppy theories of meaning, theories of language, and anthropological also claims. While we need to distinguish between the two, we need to understand exactly what are the anthropological or even general broad evolutionary constraints

on this pragmatic dimension. And then determine the extent of these constraints. Are they strong? Are they weak? How they function? I think these are different avenues of research And they haven't been done in this kind of narrative, of course. So yes. But nevertheless, this brings us back to this whole idea of artificial general intelligence. That distinguishing language in terms of interlinguistic behaviors undergirded by fundamental, proto-computation, proto-logical computational processes, allows us to develop

conception of language, frameworks of language, and hence generating levels of semantic complexity of judgments, cognition, so on and so forth, that can no longer be constrained, constrained by the same level or the same type of evolutionary anthropological restrictions that are currently in place. I said the same. This doesn't mean that they won't be constrained by any kind of physical restriction or social restriction. I said the same. They won't be constrained by the same type.

And hence, this is really broadening the concept of human, concept of sapience as a social agent, social linguistic agent. But yes, I think there are constraints. I think at different level, level of brain, level of anthropology, there are constraints. again, this whole idea that what are exactly these constraints? And the extent of these constraints needs to be investigated. All right. I mean, I think I need to think about it a little bit more. But I might have something more constructive by the next time.

OK, good. Good. Looking forward to your comment on this. Because I think it's really like one of those. And it's kind of like a bugbears of this whole idea of, you know, kind of no rationalism, no functionalism, but also some of this stuff about the linguistic core of thinking self or thinking agents usually proposed by people who are talking from not essentially the anthropological dimension but from the biological, technological dimensions of what defines the social pragma,

how the social pragma being constrained by other factors. But definitely I think at this whole idea of constraint, I think we need to also distinguish the type of constraint. constraints are just about the form of the language, not the content of it. You see, the content is strongly determined by those intralinguistic behaviors rather than by these external anthropological, biological, technical factors. It's the form, the form as the kind of like the general framework, how the information is being processed and some of these kinds

of stuff that, yes, I think are constrained by these additional external factors. But moving from content to form, I think, leads to extremely biased positions. Yeah, I think that makes sense. Thank you. But nevertheless, I'm looking forward to your comments.

Think about it. I will think about it too. Okay, guys. Any more questions? If nothing, we can wrap this session. Just a reference question from before. You were mentioning when we were talking about problems with rational choice theory and you were referencing some kind of, it sounded like a discussion or like a back and forth between McDowell and Brandom. Was that a specific text or something like McDowell? Yes, yes. I've forgotten the reference but I can't find it for you because I have that quote. I think McDowell talks about this, that he doesn't really put it in the sense

of rational choice theory, but you can extend it to rational choice theory. It talks about this idea of the people who, for them norms are given, whether it's ethical norms or stuff. And they say that we are rational and normative and these kinds of things. They are not. They In fact, it's much more common to a naturalist, despotic position rather than being a rationalist. Because norms are coming from somewhere, are being generated. They are not naturally given to us. And this whole idea that if you predefine norms, you essentially create a bounded sphere.

And that's where basically all the ideologies can arise. We can see this in the scope of the critique. I mean, isn't it the whole critique is identifying the conditions under which I am capable of making judgments? You know? And if I can't, for some reason, because my norms are forgiven or I haven't gone deep enough, that basically the whole idea of critique falters. So there is no such thing as critique as without identifying, deepening this idea of where rules are coming from, where norms are coming from. Thank you very much.

Thank you very much. Thanks.