I cover a lot of grounds, at least as much as I can, without overloading you today. And then we go to discussions. But any kind of discussion from previous sessions? Also, I would like to answer Steven's question on the classroom page. But in any case, any discussion, any question? I mean, there are some good questions there that I didn't manage to weigh in on during the week. I don't know if you had extra thoughts on it. There was also this interesting question about complexity
when it's used in a more general sense or outside of the direct context. to complexity. Yes. Right. So I thought that was a nice true reason actually, but I wasn't able to weigh in. It seemed like they weren't using it in the sense of complexity science or complexity measures to make. It was more like, have you heard this term about the tendency towards complexity? Sometimes it gets bandied about like... Yeah, it's more of a, I think they are using it more in the sense of dynamic tendency system that we talked about, but also complexification tendency.
But I think, I know that a lot of them talking specifically about the abstract concept of tendency dynamic systems. The thing, I think, you know, yeah, I mean, the whole point is that one needs really to explain why we want to increase complexity, especially if you are using the concepts related
to complexity sciences, specifically things like hierarchy, the statistical stability, complexity measures and stuff. So obviously you are having that kind of complexity in mind rather than the more intuitive idea of complexity. So if that's the case, then why we want to increase complexity? I mean, especially the general idea of basically without any discrimination, we have to amplify all complexities. That just doesn't make sense to me. I think it's, you know, there are so many bunching up together of concepts and assumptions
in this formula, that we ought to increase complexity. I mean, it kind of makes sense to me as a reaction, but I think it's hard to define complexity of that type in a technical way, and that probably points to it not quite being the best term, which I think is where you're going with it, right? Yeah. Obviously, you know, the whole thing really, there are different, I think there are distinctions that need to be made in order for this to go anywhere. One, sociotechnical complexities being increased, increasing of those kinds of complexity, I
not always, but in, you know, from a certain aspect, increase the control, in fact, the control of complexity. So that's, we can call this as a kind of like the functional kinds of pragmatic kind of complexities. That, in fact, they increase the control of the complexity, you know. The other one is the kind of complexity that basically we have been dealing with, the object of complexity sciences. And that's, I mean, it's just why to increase the complexity of, for example, a system,
especially if the increase in the complexity of that system in the second sense leads to basically incapacitation of any kind of long-term schema or even short-term schema of action, thinking, planning, so on and so forth, modeling? I mean, I guess if I try to read it in a more sympathetic way, there's two points of intersection that I see as maybe more productive, at least from my perspective. And the first is the idea of a platform. So there is a bit of a thread about sort of thinking of governmental structures as a platform
or as an emerging platform, sort of like a stack, like a technology stack, which is very, there is a connection there to ideas of hierarchy and complexity theory, which seems to me that might be interesting and productive. Yes, yes, of course, yeah, that is interesting. But, I mean, this is the whole idea, I mean, there are still two, I think, kind of unanswered questions here. One is that there would be extremely narrow sense of what we mean complexity.
We just take the hierarchical platform level question aspect. Yes, which is the whole idea of functional accumulation and structural complexities and stuff. But leaves open, basically, still a whole other kind of concepts. that are fundamental to the idea of complexity, and those are really problematic for these kinds of projects. This is one. The other one, I think this whole idea of platform stack, it is, I think, yeah, it is, I think, important, but then we can't really talk about this in analogy with the idea of
hierarchies in nature or in physical systems. It's modeling on this, but these are two fundamental kinds of forms of complexity. One is completely, basically, involves with kind of like the criteria of cultural evolution, socio-technical control, you know, augmentation of social social cognition, you know, so on and so forth. And the other one, the whole idea of hierarchy when it comes to physical systems doesn't really neatly fit into this formula of platforms.
So I think that, because I'm aware that there are, the majority of like Ben or you know Nick and Alex they talk about platforms they talking about in socio-technical systems but they always make these kind of references to the idea for example hierarchies in nature kind of a structural complexity in that sense but I think this kind of analogy is rather more of a kind of opportunistic theoretical move doesn't really hold that much. Because these are two fundamental forms of system. Well, I mean, the other way that I could try to read it
sympathetically, and maybe I haven't read widely enough in the recent stuff, but is if you think that we are somehow trying to apply too simplistic a set of models or too crude instrument in our current politics, government, whatever, sort of systems to solve these problems. And therefore you're sort of saying, well, you need a more complex model. You need a model that applies something more sophisticated and stuff. More sophisticated model, right? The more complex model, you see? Right. Maybe sophisticated is a better…
start whistling around the boards while they use these weasel, basically, comparisons. I mean, they basically loosen up the scope of the concept of complexity while when people asking them about the theoretical nitty-gritty of the theory, then they make these references to actual complexity sciences. Yeah, I mean, you could sort of argue that in a more local sense, not the complexity in itself is always good, but that a more complex sort of model or solution is required
in the context of the current day with our current systems. and government. Yeah, sure. That might be a more... Yeah, absolutely. I think that is, I mean, from that aspect, you know, this whole idea of, you know, increase of complexity makes sense if we, you know, really tailor it to that specific local and very strict sense of complexity, which basically comes to this whole idea of, you know, understanding in control, broadening the scope of the understanding of how dynamic systems trying to extract their dynamic traits, implement them functionally, pragmatically, so on and so forth. Yeah, that is what I think at the level of theory,
this whole idea that increasing complexity and then you try to make these leaps, theoretical leaps toward actual complexity sciences with those accurate definitions of complexity, that is, I think, very problematic. OK. Hello, Sean, by the way. Okay, before starting, as I said, I'm going to read a lot of stuff, and then hopefully at the end we have some discussion.
But before that, I want to answer Stefan's question, not answering it, at least trying to attempt to put in the right track, so hopefully we can go somewhere with it. The reason that I'm going to start with that, because it ties into what I'm going to talk about, which is at the end, it's the ludical view of language. So, Seven, you were talking about this idea that the distinction between functional structural
aspect of language and speech acts and occurrences, right? Yeah. Yeah. OK. I think, you see, the thing is that definitely on the functional level, but also to an extent on the structural level, we can't really distinguish the functional level of language, especially when it comes to natural language, from speech acts. So what is really the functional core of language? are the concepts. Concepts are rules, are not things. And concepts basically relay or
deploy propositional contents. And these propositional contents, the counters or the entities that deploy these propositional content are sentences. Sentences are these expressions whose unembedded utterance basically gives a category to a speech acts, like making a claim, asking a question, commanding. Without these basically sentential categorical
functionality, there is no such a thing as a speech act. Now, this brings us to the more important question. That the content of the concept, conceptual content, is determined by its role in an inferential network. This is the whole idea of the inferentialism. The content of the concept is nothing but its inferential role. Now, inferential role itself is determined
by how speech acts interact with one another, by the confrontation of the speech acts, precisely in that accurate sense of sentential categories, making the claim, asking the question, commanding, so on and so forth. So this is basically the core idea of Brandon's inferentialism, in which inferential role semantics, how meanings are determined, the conceptual content,
inferential role semantics is inseparable and in fact modeled on speech acts. And speech acts themselves, speech acting, like any kind of those categories of linguistic practices, also are determined by sentential categories within the theological structure. So this is basically this whole idea that we can distinguish at the functional level, especially at the functional level of language. We can, in fact, distinguish that we can separate these two
from one another, speech acts and the functional architecture of language. namely, you know, it's intra-linguistic behavior, inferential processes from one another, I think that's not feasible. Now, the question is then becomes, so if the inferential rule semantics is tied to the pragmatics of speech acts, namely dialogical interaction of how these speech acts confront one another within the dialogical setup.
If that's the case, then according to the concept of game or dialogical framework that we are presenting, basically we can come up with different, both different theories of meaning, namely inferential role semantics, but also we come up with different theories of speech acts. The more sophisticated, I think, the concept of game or the concept of dialogue or dialogical interaction becomes, you know, the better, you know, the more sophisticated
the model, you know, of our speech acts and the more sophisticated of our theory of meaning. But so I wanted to point, and this is really the whole point of Ludix, that there is no such a thing as a speech acts without the functional architecture of language. And there is no functional architecture of language without dialogical interaction of a speech acts. This is, as I said, this sums up in a kind of different way the whole idea of Brandoumian
inferentialism, where inferential rule semantics is tied tightly to basically social pragmatism of speech acts, where speech acts always are presented in a dialogical structure, and that dialogical structure, making a claim, asserting, these are the driving engines, the interactive driving engine of how inferences are made, of how we determine the conceptual content, of how meanings are, of how semantic complexity emerges from more primitive levels.
Comments? Nothing? Nothing? So I guess I'm still curious about this distinction between dialogic interactions and speech events and the models of them. Does that make sense? Yes, okay. So they can't be separated in a way that is, in which one could be determined to itself
be independent from the other, right? Yeah, they are mutually dependent, yes. You can distinguish them, obviously, but they are absolutely dependent on one another. Now, yes, so I will go into this ludical view of language. It will give you a better kind of a grasp of this whole idea. But typically, as I will talk about this in the history of how the first theorists who talked about speech acts and especially categorization of speech events and speech acts were John Austin and John Searle. Searle is the Chinese room argument guy.
The thing is that the theory of the speech acts that they had was based on truth condition, truth-oriented understanding of speech acts. For example, and that's completely a monological idea in the kind of classical sense that analysis of speech acts is based on their truth and falsity. decompose speech acts, basically those elementary components where you can extract the truth or falsity of the statement of speech acts. And of course the categorization of speech acts are also based on these kind of monological
truth oriented approach. Then there is another position that came later in in defining what speech acts are, and that's attributed to Jonathan Ginsberg. Definitely highly recommend him. I think even Brandon has, I haven't seen any reference to him in Brandon's work, but definitely Brandon has been influenced by him. Ginsberg, especially his book Interactive Stance, he has a number of other books too. is, and with his colleague, Gensler, they developed the game view of speech acts. That
we can't talk about truth and falsity of speech acts, because speech acts are completely context-sensitive, radical context sensitivity, context dependency. So when we are going to, we can't really categorize, we can't really analyze the truth and falsity of speech acts unless in a dialogue. That's the whole center core of this whole no pragmatism thing. were the kind of the flaw their system had is that speech acts in their system comes pre-typed. Basically, you have a core of, you know, like the main types of speech acts,
assertion, question, and query. And then according to them, then you have to, you know, subtypes, different kinds of minor categories that emerge as a dialogue moves forward for speech acts. This again, I think, is a flaw, and that's how I think the ludical approach complements it is that the type of speech acts is also determined throughout the interaction, throughout the dialogical interaction. And if a speech act comes pre-type, that restricts this whole idea of determining semantic dimension
or the context or the effect of the speech act. So that also leads to kind of restrictions in the theory of speech acts. But in the Ginsburg system, I will show you the table. speech acts has, is the way that they, and that basically, Ginsburg, one thing that I need to mention, Ginsburg is also considered to be like the forefathers of computational linguistics because he was among the first people who made equivalence class between
speech act theory and function theory in computation, in theory of computability. So the body of speech acts is usually considered to be the function. For example, the effect of the speech act is considered to be the output of a given data the context is, or conditions, considered to be, for example, a given data of a certain type of function, and so on and so forth. So there is this kind of equivalent class. Now, as you see, this whole idea that functions comes typed already in Ginsburg, in the
account of the speech acts is very much in line with the idea of a lambda calculus and the classical views of computation. Whereas ludics, as we talked about, comes untyped. Types are determined throughout the interaction. And that's really the interactive aspect, It's not just restricted game in the sense that everything comes pre-typed. Types themselves are determined as the dialogue being developed. how ludics really bridges between theory of speech acts, between theory of syntax semantics,
We talked about different dimensions of this. Now I'm going to, as I mentioned, Luca has written this really nice paper, Go Back to Anne Fang, which I think the parts that she talks about ludics are very reader friendly and gives a very good introduction to the basic aspects of ludics. So I'm just going to skim over some of her, some portions of her text, and then once we have a kind of intuitive familiarity with the basics of ludics, then I will go into
more formal aspects and then again come back to this idea of the central role of ludics as formalizing the core concepts of inferential rule semantics, no pragmatism, etc. So this is an excerpt from Go Back to that fact. Luca says, logical atoms are analyzable propositions normally indicated by naked letters without any connective, symbols, or grammatical structure. In a sequent calculus proof, one works by decomposing the sequent to be proved,
following the logical rules assigned to each connective, until one reaches atomic propositions. And the proof or analysis terminates. If, at this point, every leaf of the proof theory contains a sequent of the form A, turnstile A, A, implies A, or A, proves A, then the sequent, Adatud is proof. It is a theorem. The notion that every meaningful proposition can ultimately be decomposed into atoms has a long history. This is what we briefly talked about at the end of last session, that one of the main motivations behind development of Ludwig's was subversion of atomism.
with atomism being one of the most dominant logical theories of truth. that in order for us to determine the meaning or the truth or validity of a statement, of a sentence, we should decompose it to atoms, atomic statements, atomic formulas, where
we have, where they are self-evidently true, where we have facts basically, elementary facts. It is one of the fundamental pieces of Leibniz, one with which Hegel broke emphatically, and one reasserted against Hegel by Russell, who took the practical need for atoms in mathematical logic to show that Hegel was mistaken in rejecting semantic and logical atomism. If we do not presuppose the existence of atomic propositions, Russell argued that the acquisition of knowledge has nowhere to begin. Of atoms, however, ludics has none.
At bottom, it does not even operate on propositions and retains only the loci of propositions as its space. We said that that was the hallmark of ludics. In ludics, you do not have formulas. You do not have the salesman. You do not have atoms. All you have are address, the locus of the formula, equivalent to a trace of the sign. Remember when we talked about the idea of the formalism, that Tarski had said the meaningless sign is really the element of a formal language. Now the trace of the sign is
really the sign of its meaninglessness and that has logical computational significance in ludics. Precisely that you can trace the addresses, you can see justifications as traces of the sign within this interactive framework. These are called loci, locus as a place, place of the sign, place of formula. The basic entities of ludic are what Girard calls designs or strategies. They resemble proof trees in the sequence calculate except that while a proof three has a sequence and its root such as where gamma
and delta are sequences of propositions, where gamma turns side delta, where gamma and delta are sequences of propositions, the root of a design is a sequence or a pitchfork of the form a Xi and turnstile Xi with different numerics applied to it. Now Xi, the symbol Xi in ludics denotes a concept that I will talk about later called bias. Bias are, show you the trace of the formula, namely the locus, in a specific design,
in a specific strategy, in how this, for example, the strategy of player versus the opponent falsifier emerges. Also another way of thinking of this whole idea of locus, locus you can think about it as a memory cell. That's also a good intuitive way of thinking about locus or the address. So where gamma and delta are sequence of oppositions, The root of a design is a sequent or pitchfork of the form xi and turnstile xi, which is a relation between a locus, which we can think of as certain actions or gestures,
and collection of several other loci, which we can think of anticipation of certain reactions. So the whole idea that if we just have the trace of the meaningless sign, if we just have the address of the formula, not the formula itself, then how are we going to prove a theorem? That's the whole point of Ludwig's, that every address is recursively determined by its relation to other addresses, other traces. And these traces are determined
by how the opponent and the player, the prover and the falsifier interact with one another. As a result, their strategies emerge in a particular way. In a sequined proof, we would proceed by isolating the main connectives on each side of the sequence. They might be conjunction, disjunction, or whatever, and determining the structure of the immediately upper nodes of the proof tree in accordance with the rules assigned to those connectives. The design has no set of rules to follow. Instead, it is allowed to branch out in any fashion we like, so long as certain rhythm
between positive and negative moves is preserved. But this technically isn't altogether crucial here. Instead of having each proposition branch out into sub-propositions, for example, having gamma, comma, delta turnstile A conjunction B branch into... Let me share this screen with you so you can follow the formulas. Thank you.
into, can you see the screen? Yeah. OK. Branch into gamma turnstile A and delta turnstile B, horizontal line, gamma and delta, turnstile A, conjunct B. We have each locus branch into its subloci. But since we began with bare loci, without any propositional structure imposed on them in advance, there is nothing written at the root of a design that preordains how the design will decompose or ramify. The process of ramification may indeed
carry on infinitely in an infinite analysis of the initial loci actions and anticipations that never encounters a single atom. Since there are no atoms to be found in designs, there are no axioms either. A kernel of what we could call axiomaticity nevertheless persists. It persists in the form of a pure abstract arbitrariness, as pure contingency under the name of the diamond, which I said is a rule in ludics that signifies termination,
or halt, or give up. I give up a statement, such as OK, fine, these kinds of stuff in a dialogue. The diamond, symbolized by the Maltese cross or the obelisk symbol is the rule of ludics that allows any locus whatsoever to be inscribed without justification, without being subject to further inquiries from the opponent. It is the only action by which the branching of a design may be brought to a halt. Formally, it is written horizontal line, cross, turnstile, psi, n. It can be seen as the bare form of the axiom,
purified of all content and every appeal to evidence. It is an interruption of thought or a brute decision. So once you invoke the diamond rule in your proof or in a dialogue, the dialogue comes to an end. As, for example, we have it all the time in our dialogues. For example, you say something, and I halt the conversation with an abrupt OK. OK, I will do it. That's it. Conversation comes to an end. It's invoking the daemon rule halts
all the process of interaction. And this rule, as I will talk about, is tied to normalization, to the process of computation in ludics. Allowing designs to have recourse to the diamond opens the field of logic considerably. Its intervention populates the arena, not only with the locative skeleton of proofs, but also with the bones of para-proofs. Unfinished proofs and Sufisms. These are what occupy the pivot left vacant by functional proof theory and open logic
to complete duality between proofs and tests. Every design has a counter-design against which it should be tested. To give some illustration of the expressive capacities the formalism, we could turn to Miriam Quattrini's recent work where she shows the most of the sophisticated stratagems Schopenhauer catalogs in the art of always being right, the stratagems, which this arch enemy of Hegel like to call dialectical, can be transcribed into ludics with a diamond's aid, diamond's rule. Now, Luca continues, and which you should definitely read the whole essay. But the part
that I wanted to read again is this part that so when in the interaction scenario of ludics when these design or strategies interact with one another we have typically three scenarios And these three scenarios are represented by three designs, or three objects, ludical objects. A proof grasped at first as the tree-like object that the sequent calculus formalization of logic make of it is stripped of all imaginary decoration.
All the imperetriable atoms that the realist, Russell, for example, takes to promise a metaphysically atomistic interpretation in the real and the entire apparatus of pre-formulated rules that refer to the question of how we must proceed to the authority of presupposed forms. What results is what Girard calls a design or a strategy determined in a purely locative fashion. The strategy is not tested against a model. Because in traditional game theoretic logic, the strategies of players, of how they play,
are usually tested against a predetermined model. So you don't have this in ludics. Ludics is purely interaction in that accurate sense that we have been talking about. Everything is determined throughout the interaction, not before it. There is no such a—and that's the whole idea that interaction is the most fundamental object of logic and computation in that proof-theoretic, constructive sense that we have been discussing. The strategy is not tested against a model, a typically infinite construction brought into a more or less external relation with the syntactic proof structure and susceptible
to being ideologically understood as the given reality against which the proof or collection of proof is measured, but against other strategies without any of their correctness or erroneous being determined beforehand in any fashion. The basic unit of these strategies is not any longer a formula or proposition, but a positive or negative volucus, an empty position answering to or making a demand upon its polar counterpart. The relation between a positive volucus and its negative counterparts or vice versa is not a static or extrinsic relation, but immediately a process of interaction. It proceeds like the generalized form of the
cut elimination. We talked about the cut elimination. There is in logics where you have to form your logics, two sides of the sequence. You can cut them. You can remove them. And the The equivalence of this in computer science is abstract rewriting systems. And the whole idea is that cut elimination in ludics is no longer a rule. In Gensen, it's a rule. But cut elimination in ludics is really the process of more fundamental process of computation, normalization, basically. Like a generalized form of the cut elimination algorithm discovered by Gensen, this process
is an effective and concrete process of contradiction, but a form of contradiction that is deeper than and prior to any determination of truth value, anterior to any fixed support for alethic reference to reality. When this takes place, one of the three things may happen, three scenarios, interactive scenarios may happen in Linux. One, the conflict between the strategies goes on endlessly in the sort of badly infinite progression that Hegel took to be the symptom of an unresolved contradiction. In this case, Hegel's diagnosis is at the situations in which interaction diverges are those in which the two designs are locked in the form of
abstract dissensus rather than determinate dissensus, abstract dissensus in a Hegelian sense. It is a form of antagonism on which no propositions can be grounded, a logical phenomenon that has no counterpart on the alethic plane. The name that Girard gives to this outcome, or lack of an outcome, is fit or fidelity. Just also for those of you who want to look more into ludics and start working on the formalisms and work on yourself, The reason designs or objects of ludics are usually written in a fracture font.
So whenever you have this, a fracture name or letter, it's an object really in ludics, usually designs. Two, the conflict converges on a particular design, usually different from the two that enter the interaction. Interaction can therefore be used as a way of transforming one design into another in a concrete and effective fashion. The most methodologically important of this transformation is a procedure called faxing. We talked about this briefly last session.
Faxing has been, is usually generally understood as a copycat strategy, copying the moves of one player and playing it against a player, copying the moves of player one and playing it against player two and copying the moves of player two, playing them against the moves of player one. And this results in moves that are completely different. Copycat does not merely copy moves. It produces new behaviors, new moves. We talked about that Lego diagram last session.
So this is kind of generalization of the idea of fax. It's a design called fax. The most methodologically important of this transformation is a procedure called faxing, which serves to delocate or transpose a design onto a different located base. So it delocalizes in order to move it and make a new move, a new design, which serves to delocate or transpose a design onto a different located base, performing the material labor underlying abstract or a spiritual conception of proof structures mediated by a particular
class of design called FACS. If, for example, we wanted to transpose a design D with the base turnstile xi onto base turnstile rho, we have it interact with FACS design of base xi turnstile rho, a process which converges on a design isomorphic, structurally identical to D but rooted in a turn side row. We saw it in the Lego diagram how it worked. The copycats, the facts itself can be seen as a player who has its own base and player one and player two at the other side of the game or playing with one another. By copying the
moves of one player and playing against it the other player in its own base the copycat delocates the base of one players move and modify it with the base of the other players move. So you get exactly a kind of design facts procedure. Copying of the copycat strategy in game is also a procedure of delocalization. Delocalization in order
to modify and create a new design, create a new old set of moves. Now the third possible outcome is that step by step the opposed loci cancel each other out entirely, collapsing the two trees into a design called die. The empty ground into which the contradiction founders is here, a pure void, the empty pitchfork sequence, summoned up by the daemon that cross. When this takes place, two strategies, called them
X and Y are said to be orthogonal to one another, written X orthogonal sine Y. This is a note, I think, to myself. So just another point deserves attention with regard to normalization. There are many cases where the disrupt disputation does not terminate on a die, but on some reduced net. The two designs are not, in this case, really orthogonal, but neither do they diverge. We are strongly interested in these cases, since it seems that normalization provides side effects we are concerned with. The situation looks like the case of a speech act, where wars are uttered, resulting in side changes of the world seen as a set of pre and post condition of the utterance.
We will get to this later. So this was kind of like a very basic of scenarios that Ludix work with and give a little bit of elaboration on the motivation behind the development of Ludix. So back to Ludix, and I'm going to introduce the basic features of Ludix and give them a little bit of formal treatment. As previously in linear logic, Girard a geometrical point of view of proofs and in turn, long implicit approach of dynamics.
So ludics can be summed up as an explicit intraction theory. The objects of the ludics view are no more formulas and proofs, but they're geometrical representation, seen as an architectural object. what is needed for the interaction is kept. And that's really the address, the locus, the place of the formula. In order to perform this geometrical work, polarized formulas are taken into account. This leads us to create a link between ludics and game semantics, which then is good metaphor for first approach of ludics. The central object of ludics is the design. From the logical point of view, its conceptual
description is radically modest. Syntactically, it can be seen as the architecture of proof, whereas its semantics is the result of its interaction against the other designs." We talked about this, the whole idea of, you know, the controversy of syntax-semantics interface. Elytics tries to collapse the fundamental distinctions by taking a monist syntactical stance, an autonomous minimal syntax, and then shows that once the syntax, this monist
syntactical architecture is taken in an intractive dimension, in an intractive framework. When these syntactic branches interact with one another, then semantics imminently arises from this interaction at the level of syntax. So the so-called fundamental gap between syntax and semantics is being bridged in ludics. Instead of formulas, we find the addresses, namely locus or loci, where formulas and subformulas are stored.
One of its, namely the focus, one of these addresses, namely the focus, represents the logos, where the interaction between design takes place. So the focus in the concept of focus in ludics, represents the place or the logos, where the interaction between designs takes place. Instead of proofs, we find designs which can be seen as trees of addresses with rules for building designs. These rules specify either the offered possibilities in a point to make an action, or the anchorage points that we consider as possible for the reaction. Everything is ready in the view of this interactive stance.
So the basic features of Ludix are one, proofs as processes. Let us start from a particular formulation of linear logic, hyper-sequentialized linear sequence calculus. This formulation elaborates on the fact that linear logic may be polarized. We talked about this, that when you look into how linear logic in traditional framework, classical framework was developed, there was already dualities, polarities, interaction, dynamics implicit in formulas and innovations of linear logic. Implicit. And Ludic tries
to make this explicit. This formulation elaborates on the fact that linear logic may be polarized. we have positive connectives, additive disjunction, multiplicative conjunction, which are also set active in the sense that they make non-reversible choices in the construction of a proof and negative ones, and then par, which don't. By grouping together successive positive, respectively negative steps, it is possible to present proof as an alternation of positive and negative steps. A logic results which has only two logical rules, one positive and
the other negative. It also has a cut rule and axioms. These are the positive and negative The first of these two rules is the negative one, a negative formula, left-hand side of the sequence, all the subformula of which are combined by the positive connectives. If it were on the right-hand side, the connectives would be replaced by par and and, which are negative, happens to be decomposed in a canonical way when applying this rule. There is no particular choice to make. The second one is a positive rule, a positive formula. All the subformula which are combined by positive connectives happens to be decomposed according
to some possible choices. We also have, as usual, in sequence, the cut rule. But I said we don't have it as a rule, really, but as a fundamental process of normalization. And that's the traditional cut elimination rule in sequence calculus. The second feature of ludics is locativity, the idea of locus, the address. A remarkable property of linear logic resides in the ability it provides to present a proof by a graph or a net, simply called proofnet.
Starting from the sequent to demonstrate, we decompose its formulas until we reach atoms and according to the polarity and the types of the links by which their two main subformular are combined, the positive and negative instances of the same atoms are connected, the so-called axiom links. If some geometrical criterion then is satisfied, we are sure that the sequence is proofable. So this is the classical idea of proof theory, which is also connected to that idea of atomism, logical atomism that we talk about. Now, Girard noticed that in fact locations in the net and links between them are sufficient
to identify a proof, exactly as if we were getting rid of formulas altogether. Everything is at work without logic. And that's the whole idea of protologic or prelogic. Ludic's is a protologic. All that matters is the place or the location of the formula. This provides a basis for locativity, which opens the way to ludics. If we ignore formulas, we can only reason on locations, addresses of formulas within an interactive framework.
A logos is a mere address, like a memory cell or like a specific position occupied by a statement in a conversational network. The third feature of ludics are called designs, which I read a little bit through Lucan's text. The design is a central object of ludics. It can be seen as an infinite tree by means of the metaphor of games. A design can be understood as a strategy, upon a strategy, verifier strategy or falsifier strategy system, machine or the environment.
A design can be understood as a strategy. a set of plays. So plays in ludics are called chronicles or views. There is also a formalization for them. Sequences of couples' actions, player, reaction, in the description of a strategy, the point of view of player is taken into account so that every positive move is the possible action of player. And negative moves are anticipations of opponent moves by player.
So you see the whole idea of negative moves in ludics are external. But not in the sense that simply the player is positive and the opponent is called negative. No. The anticipation of the opponent's move by the player who plays the positive moves are called negative moves. So this is the whole idea. Possible actions of players and anticipation of opponent moves by player.
These are the criteria of determining positive actions versus negative actions. We talk that negative actions are the ones that allow for extraction of contextual data. In a dialogue, they determine context. And once you extract the constancy, the invariance of a contextual variation in a dialogue, you You have basically determined the meaning, the contextual semantics of a word or a sentence or a counter, a linguistic counter or a marker in a dialogue. That's how you determine meaning in a dialogue precisely through this game of assertions
an anticipation of counter-assertions by the opponent in a dialogue. I say, for example, the swatch is red. So I have a number of possible moves to make in my linguistic game. I anticipate that the opponent comes up with two questions at least. Why is that I call this a swatch? And is this really red?
So I need to anticipate at least two questions with regard to the name swatch and the name of that color, the swatch is red. So this is kind of a basic game of assertion. We have this anticipation of the counter-assertions or asking about both the name swatch and the name red, the word red, the word swatch, that I need to further justify the use of these and through this interaction it might actually be proved that this is not really a swatch nor this color is red. So through this interaction, through this anticipation of these counter-exertions with
regard to the words swatch and red we can basically arrive at highly context sensitive pieces of dialogue in which we can determine the concept of red and the concept of the words what the meaning of the words watch and the meaning of word read. Basically, we can evaluate the sentence, the swatch is read. And the evaluation, we don't have the evaluation of the sentence unless the dialogue is brought to a halt. Of course, it might not be brought to a halt for a different kind of statement according
those scenarios in ludics. It might infinitely, you know, go on. So in ludics, the nodes of the design seen as three are labeled by the two sets, gamma and delta, of addresses, or loci denoted gamma turnside delta. An address is a finite sequence of integers. For example, xi is star i. I said that xi is called bias. So I will show
So that according to how you put the numbers, 0 and 1, you really determine the location of a formula. Location, or you are able to trace your moves and your opponent's moves in a dialogue, in an interaction. For example, Xi star i. Now, loci are sequences of biases or integers. That's how, as I said, are denoted, xi star i. Roughly speaking, gamma, turnstile delta, is an organization of positions from which the next move can be executed. The root is called the base of the design.
So the base of the design, you can think about this our very elementary statement, dialogue around the elementary statement, the swatch is red. So you can have two different sets of designs, different strategies, or different branches of dialogue according to whether our conversation is going to be around the word red or the word swatch. So these, if the conversation emerges, if we start to talk about whether this is a swatch
or really not, or whether this is red or not, can be understood as two strategies or two conversations that have two different bases, two different rules. The root of one is the topic read and the other one is the topic swatch. So this is the idea of base intuitively understood in Linux. We see that in a very kind of a regular ordinary everyday life dialogue, our conversations have usually ramified with multiple bases precisely because it's kind of an
asynchronic processing in dialogue in conversations that they ramify from a very basic element of conversation. They ramify into new bases, new, hence new topics for conversation, new points of focus, and so on and so forth. The designs are built by means of only three rules and schemes. Two first schemes of rules are issued from logical rules, a positive one and a negative one, and a new one called the daemon, seen as giving up that I mentioned. This rule does not arise from the logic, is needed for taking into account the interaction.
Positive, so these two rules, one positive action, to perform an action, to ask, to answer, which is played by the player. By positive action, the player selects branching locus and opens all his possible loci for continuing the interaction. He chooses to act in the place zai, and he opens to his interlocutor the range of actions. You can, again, intuitively think in terms of dialogue. And so this is the positive rule. By playing an empty ramification,
player prevents opponent from any reaction, and so he blocks the continuation of the interaction. Now, in addition to positive action, positive rule, we have negative action, negative rule. And negative rule, as I said, it's really the idea of anticipating a counter move or reaction by the opponent. It's the idea of to receive opponent's action, to foresee, to forecast. And you see, the whole idea is that context, semantic context, contextual meaning of sentences, are inherently tied to this negative rule or negative action, precisely because there
is no such a thing as the meaning of a statement without not being entered in the game of giving and asking for reasons in the game of assertions, where I make an assertion, I make a commitment to believe that this watch is read, and then I have to justify it, but I can only justify by interacting with opponents, being questioned. So it's like that Brandomian idea that once I make a conceptual commitment, what are commitments? The concept of commitment is the idea that the criterion of intentionality is beliefs. And beliefs are normative entities. And in order for us to have beliefs, we ought to be able to justify them.
So it can be branded and formulated under, again, another game view. It's called deontic score keeping, or the game of giving and asking for reason. It can be seen as a two-player game where by asserting P therefore Q, or for example this swatch is red, I make a commitment, a conceptual commitment. Now this game can be seen that by making this assertion, I have a box or a ledger. I put my commitment inside this box labeled a C directory.
Now the opponent, now every commitment that I make also entitles me to other moves, other commitments. Basically we talked about this in previous sessions, that every conceptual commitment not only is about what it leads to, what other commitment it leads to, but what it presupposes, what it follows, what it leads to and what it follows from. This is the whole idea of the chain of commitments. So the opponent, by making a counter-assertion, might deprive me of my entitlements, about
the idea of that. For example, this is not really direct, this is not really a swatch. So by adding opponent, by adding his own counters, mainly sentences, assertions, he can alter my entitlements to move further within the game of my conceptual commitment. Also, me by using my entitlements, the ramifications of my commitment, I can also alter the set of my own conceptual commitment, but also my opponents. So this is the whole idea of
the very basic formula of deontic and score keeping, which can be seen as really centered around this idea of negative action or anticipations, precisely because the whole idea of justification proceeds by way of interacting with opponent. How every time that I make a commitment, how I play a move in my linguistic game might lead to counter moves by the opponent that
might completely change my linguistic game. Or in the Brandomian sense, my entitlements, the entitlement box, entitlement directory. That's really the whole idea of meaning, context, and judgments are being determined through this confrontation of positive and negative actions.
Reza, can I just check something to get that I've understood it? So when you're talking about the sort of, there's a sort of connection or analogy, maybe not the right word between the daemon where you can make an arbitrary choice and that sort of ends the dialogue, right, to sort of say, okay, you walk away, right? And you sort of made a connection to the role of axioms in a traditional logical system and that there's no further support for an axiom.
It's just sort of a given. And so does that mean, have I got that correctly? Like you could sort of chain dialogues, right, to just sort of have results from previous dialogues to determine the context for later dialogues, right? And now it sort of behaves like premises or axioms, but the difference is that if you trace it back all the way to the start, There's no bootstrap axiom there to get it off the ground, right? Yes, yes. The conversation starts at some point. Is that about right? Yeah, absolutely. There is no axiomatic bootstrapping, really, in ludics.
Yes, it's compositionality, but not the kind of bootstrapping that we see, for example, in other forms of axioms. And that's, if you remember, I talked about, you know, the old classification of axioms. I'm talking about formal languages. I mentioned that, you know, you can have it in the Euclidean sense of axioms or based on intuitions. And then Hilbert, formal and non-formal set theory, axiomatic systems, and then Carnapian predicates. And then in addition, you have again an axiomatic system, which is the whole idea of ludics and game semantics, but it's not really axiomatic in the sense that it's usually understood as a set of self-evident premises.
And hence, the system is not being bootstrapped to the combinatorial or combination of how these axioms are being played. OK. Thanks. Welcome. So. Oops.
Can you see the screen? Yeah. Okay. Sorry, I forgot to scroll the page. I was saying the following rule and then I did show it to you. So formally a negative action specifies the ramification of a directory. In our context we can say that in the place, xy, else after one of my actions I get ready
for receiving reactions of my interlocutor in a list that I have foreseen, or I receive a list of messages sent by my interlocutor. The removal of formulas apparently deprives us of... So I said three rules, two, the positive and negative rules, and also the diamond. The removal of formulas apparently deprives us of rules which make explicit use of formulas. That is mainly the axiom rule and the cut rule. The cut rule is externalized. The cut is simply a coincidence of loci with opposite polarities and identity will be expressed by the so-called facts. In ludics, we make the assumption that the proof attempt may be stopped at any arbitrary stage.
That corresponds to the use of the diamond rule. This rule, of course, is a paralogism when compared with axiom rules in hypersequential by SQL linear logic, since taken literally, it would say that every positive sequence is drivable. But this interpretation is far from now on different. It only means that we don't go further in argumentation. It's basically the equivalent of halt or termination of process or I give up a statement in a dialogue. dialogue. Moreover, the admission of this rule shows the need to embed proofs inside
a more general class of objects, some of which are simply not proofs at all and hence often called power proofs, namely unfinished proofs and sufisms. A design is a tree of forks built by means of these three rules. Its basis is the fork at its bottom, but there is another way to see a design, since a proof process may also be seen as a sequence of negative and positive steps in a game. It is as a set of possible plays. These plays are called chronicles or views. A chronicle may be built from a design according to the previous definition. Starting from the bottom, we record all the branches and their sub-branches.
In order to correspond to a true design, these chronicles must satisfy some conditions, coherence, propagation, positivity, totality, et cetera. Then another basic feature of ludics is really the interaction. This is really the core fundament of ludics. Entering two designs or in a game theoretic view, strategies of bases of different polarities, interaction consists in a coincidence of two loci in dual positions in these bases. This creates a dynamic of rewriting of the cut net made by the design, called normalization.
In linear logic, the interaction is represented by the cut elimination. In ludics, the interaction is meeting between two players' strategies localized in the same locus. You can see it in the dialogue. Or even we can see it as really the evolution of a speech, the linguistic speech. language couldn't really emerge without this idea that two strategies, two syntactic behaviors
cannot lead to semantics unless they are being localized in the same address. You can see it in a kind of very basic way through Cellar's famous essay, Functional Classification of meaning when he talks about chess. And I remember I talked a little bit about this. That's any syntactic utterance, once I deploy syntactic utterance,
if the other player, the other potential speaker does not recognize my syntactic utterance, basically the syntactic utterance can never become part of a dialogue, can never lead to any functional rule within our linguistic game. Hence, it has no meaning whatsoever. Once it's being recognized by the opponent in the sense that the opponent takes my syntactic utterance as the
input for his own move and to yield a different output. and then I recognize his output as the input of my own moves, then that's how a syntactic vocabulary, a syntactic utterance, takes a functional role. We see this in a chess, a pawn. Obviously, we need to recognize pawn. It has basic features. And we can call these syntactic features. Now the functional role of the pawn is when we interact around this basically how I move
my pawn and how you responded to the move that I made by recognizing not only the pawn, my pawn, white pawn, but also recognizing the move that I made. And precisely the moves of the player and opponent are being developed around this syntactic recognition, we can understand it as the same locus, same locus of interaction in the ludical sense, allows
ramification of functional rules. The pawn can make this move, different rules emerge, so on and so forth. And this is really, you can see this in dialogue, but also I think this can be seen as a fundamental a protocol computational process responsible, in fact, for genesis of semantics from primitive syntactic abilities.
The interaction is concretely translated by a coincidence of two loci in dual positions in the basis of two designs. For example, a design of base, sigma turnstile psi, can interact against the design of psi turnstile rho. The dynamics of the interaction is given by a process, normalization in computer science or cut elevation in sequence calculus, which regulates this meeting. At any step, action-reaction of players are put in coincidence until one of the players gives up or until this coincidence being failed or even endlessly continues. Without entering the formalism, we can say that the interaction between design is seen
as a cut net in a proof-theoretic way. An acyclic finite graph of designs pairwise connected by their bases. For example, let us consider the following cut net of the base, sigma turnstile lambda, comma, rho. Those inverted triangle deltas are symbols of design. We don't go into formal details of this procedure here. We just surveyed two views about how it basically behaves, the processing behind this way of
formulating interaction. In this example, the base of the cut net is turnstile. We can observe that in this example the ramification R1 and 3 is in the directory R sets 1, 3, set 2, 3. The first reduction step eliminates dead forks, the branches upon an unanchored node, and produce the following net. After n reduction of steps, there is only three possible configurations that I mentioned
I read in Lukas' text, convergence by giving up diamond, invoking the diamond rule, is one of the design produced by the reduction, then all the net is reduced to dime. Divergence, the ramification R of the positive design, is not in the directory, italic R, like R of the negative design. Divergence, because of an infinite interaction, the exchange makes loops or continues infinitely, that bad infinity or abstract dissensus that Luca was talking about. So the next basic feature of ludics is the concept of orthogonality.
When the normalization between two designs, D and E, respectively, based on turnstile, zi and zi turnstile, succeeds, the designs are said to be orthogonal, and we note d orthogonal of E. In this case, normalization ends up on the particular design diamond. Let D be designed D orthogonal denotes the set of all its orthogonal designs. It is then possible to compare two designs according to their counter designs. Then we have infinite designs.
of the infinite designs is facts that I mentioned. And then we have also the concept of behaviors, very much in line with the idea of behaviors versus functions that we have been talking about in our previous sessions. Behaviors, one of the main virtues of deconstruction is to help us rebuilding logic. And that's what Ludiex or even Javarez's computability logic were all about, rebuilding logic from protological computational processes. Formulas are now some sets of designs. They are exactly those which are closed or stable by interaction.
Technically, they are called behaviors. And behavior is a set of designs or strategies of the same base C, which is equal to its biorthogonal. It's a double linear negation. We remember that double linear negation has a different interpretation in this game semantic framework or in this ludicolor view. It has a very different perception than that of classical logic or even intuitionism, precisely because negations here are now dualities, the whole interchange of roles in the play.
So in classical logic, in classical proof theory, we have formulas and proofs. In ludics we have behaviors and designs. Now with this very, very short and kind of almost crude characterization of ludics and some of its basic concepts. Now we can look at more what I'm going to talk about, its significance for language, how we can model language and study its deep, the proteological
computational processes that are undergirding it through ludics, a ludical framework. Ludics provides a frame in which we can explore the speech acts realized in discourse as really two-faced. This is mainly because in ludics, as a locative framework, makes it possible for two parallel processes to interact, therefore generalizing the well-known dynamics of proofs that we have already in Gensensic will calculate by means of the procedure of cut elimination to the dynamics of par proofs. In such a framework, there is no truth, properly speaking, but
only ways for proof candidate to pass tests which are themselves other proof candidates. And we said that the whole idea is a meaning, is a proof of a statement. The meaning of a statement is proof. And this proof in ludic is testing. In a concrete dialogue situation, In a concrete dialogue situation, our utterance is a proof candidate. It has necessarily to cope with counter-proof candidates, which are either the reactions of the other speaker or some kind of virtual reaction that we have ourselves in mind. This way, our interventions are doubly driven, once by our positive acts, and second, by
the positive actions of the other speaker or of such a virtual partner and by the way we record these reactions. Again, this can be seen as that in the Brandomian framework of commitments and entitlements. With commitments and entitlements can be seen as directories in which we add counters. And what are these counters are linguistic items, sentences. And how my taking up my conceptual commitments and playing them, playing my entitlement,
alter my commitment entitlement directories, but also the other players' counter-assertions to my assertions can again deprive me of my conceptual entitlements, for example, about whether this swatch is red or this color is red, or in fact allow me to preserve my entitlements. So Ludix can really accurately model this score keeping scenarios.
Of course, whereas in a dialogue each participant has to take into consideration the expectations and reactions of the other, in monologues, utterances are co-determined by the speaker herself and by her virtual interlocutor. Again, this can be summed up not at a very trivial sense, but in a deep, proteological, computational sense that private thoughts are all in fact modeled on public linguistic practices. And from that sense, there is no such thing as a private thought or private language.
They are modeled on interactive linguistic moves. It is this interaction which drives the speech until a tacit agreement occurs, either coming directly from the speaker or indirectly via the image she has of her speech. Language is interaction. It can be said that language emerges from human minds interacting with one another. The main interest of ludics for the study of natural language resides in the possibility it offers for expressing this interaction. There are many indices of this interaction in language itself and even in syntax, as
witnessed by the presence of many small words which have essentially a rhetoric or a pragmatic effect or impact, like event, nevertheless, or but. These words cannot be understood simply in truth conditional terms. But is not simply and, for instance, and if, for a truth conditional viewpoint, there is not a big difference between few and a few, it remains that from a pragmatic side it is quite obvious that sentences containing these two words cannot be pursued in the same way. If I say Peter has read a few books by Virginia Woolf, this can be continued by, therefore, he does not know her well as a writer. And if I say Peter has read a few
books by Virginia Woolf, this can be continued by, therefore, he knows her as a writer a little. And the converse discourse cannot be pronounced. This can be interpreted if we assume that the speaker answers an implicit question, which could be, does Peter know Virginia Woolf well as a writer, and that few is a negative item while a few is a positive one. Vague quantifiers like few, a few, many, a lot, denote, as is well known, approximative positions on a scale, but specific vague quantifiers have the property of orienting this scale
in a direction or in another, comparable to the branching of our designs in ludicrous framework. But the word but has a similar property, taking two propositions as inputs. It does not only provide us with the coordination of them, something which can be done by a simple end, it also creates a scale which can be scanned in two opposite directions. One proposition is supposed to be oriented towards one end and the other one towards the other end. The second kind of a semantic ramification of the syntactic deployment of the word but.
This is particularly visible when but is used to coordinate two-quantified expressions, thus requiring they have opposite directions of variation. For example, he has many relatives but few friends versus he has many relatives but many friends. We may also study the phenomenon of presuppositions and see about it that it is as if a dialectical structure was at the stake. If A says to B, I don't regret to have been watching the movie, A not only says something about his or her feelings that she does not regret, but also restricts the ways B can
react to this assertion because B is supposed to know that A went to see the movie, or if she did not know is required to include in her knowledge database that of course A watched the movie. All these facts are well known and they all assume a model of conversation where each speaker takes into account not only the assertions made by the other but also and perhaps mainly the set of expectations or anticipations that each speaker has concerning the reactions of the other. Ludix exactly provides a framework where the actions of one speaker, seen as positive, not only depend on the actions of the other of the same polarity, but also on its expected answers, that is, negative actions.
and misogy semantics or meaning as something built in interactions. There are two ways of looking at meaning, a simple set of justifications, when we take into consideration all the possible objections which can be made to a sentence, or as a behavior, that is a set of all designs which give the same results for all the interactions in terms of convergence, divergent scenarios. And that's the whole idea of contextual invariance that I was talking about. Which of course classic theories of meaning or even classic game views of speech acts cannot really, cannot properly frame precisely because they do not have a way of solidly
framing context dependence. Ludics, on the other hand, is radically context-dependent framework. Complex articulated sentences may be viewed as combinations of more elementary behaviors. Under a completeness theorem, the behaviors generated by such operations are complex in the sense that they contain no other design than those obtained by the operations. Because a behavior is ordered by a relation of refinement, and because behaviors may be ordered by inclusion, it is possible to associate a family of behaviors with a sentence, each
of them reflecting some degree of refinement. for a sentence, there is in principle no end to the process of its examination. There are no atoms, properly speaking. So before I move to more talking about bringing ludics to lay out a framework of a new theory of speech acts and then see the significance of ludics for kind of no pragmatic theories of language like brandons and cellars. I just want to
to very briefly look at how ludics represents language moves. Very kind of like how the formalisms look like, and how those concepts of ludics, basic concepts of ludics, are applied to this linguistic framework. So we have designs, which was the central object of ludics. Let us call language move every move that the speaker makes during a conversation. A positive move consists in an explicit assertion or question.
A negative one consists in a way of collecting the content of the other's utterance, the opponent's utterance, and reacting to it in a purely mental way. If somebody says to me, are you still smoking? I will store in my short-term memory that this is a question and that it is assumed that I was a smoker and even that perhaps I'm still one. I also know, of course, that the speaker who says the question, are you still smoking, some background information about me, and in particular that she knows or believes that I was a smoker. Therefore, when she asked his or her question, she had in mind some
of the states in which I can be. In the absolute, these states are combinations of the following. I was a smoker versus I was not a smoker. I presently smoke versus I don't presently smoke. The point here is that by this question, why are you still smoking? Speaker a priori eliminates two states, those, the common features of which is I was not a smoker. Let us represent the various possible elementary states by integer 0 and 1, which are also called BIOS, which I mentioned.
A move is a sequence of such BIOS. Many exchanges are such that they have only moves of the length one. In such a case, the player who moves either negatively or positively simply adds a BIOS to a previous sequence, which summarizes the history of the exchange in the downline. But sometimes she adds three BIOSes at a time, or even perhaps more. Let us suppose a positive move on player is an elementary question. By asking it, she has a bias. Let us call it zero. So zeros are denoting basically questions,
elementary questions. After this positive move, she makes a negative one, which consists in expecting an answer, zero or one, if there are only two possible answers, like it is the case for dichotonic questions. These are precisely the loci where the other player could play if there would be no presupposition, case of did you ever smoke, for instance. But by asking a complex question, like are you still smoking, Iso-Tel named multiple questions. Two elementary questions are combined, to each of which we assign a bias zero, so that in fact the only loci the speaker provides to his or her opponent are 000 and 0001, and
neither 0100 nor 0101. Let us therefore assume that the speaker starts from scratch, a situation which is in reality never the case. We represent that by the empty locus, by asserting that question, are you still smoking? The speaker directly jumps to a set of possible answers, 0, 0, 0, and 0, 0, 0, 1. If it happens that in reality I never smoke, I have no locus to answer. We say that the conversation locally diverges. Only a metagame allows us to fix the interaction. This metagame uses pieces of interaction which are ready-made. For instance, one of them consists in forcing the speaker to retract one's cell.
This is done by erasing the whole interaction and replacing it by a more fine-grained interaction, according to which, one, the speaker gives at first alternatives 00 and 01, and two, and plans if the other speaker answers by 00 to give another set of alternatives. Now, how does it represent it in a formal way in ludics? For example, this absurdist piece of dialogue. Jody's voice. Is that you, P.D.? Pause. P.D., is that you? Peter. What? Jody's voice. Is that you? Peter. Yes, it's me. Jody. What? Are you back, Peter? Yes. I've got your cornflakes ready.
Here's your cornflakes. Are they nice? a bit, date be nice. You got your paper? Yes. Is it good? Not bad. What does it say? Nothing much. You read me some nice bits yesterday. You read me some nice bits yesterday. Peter. Yes. Well, I haven't finished this one yet. Will you tell me when you come to something good? Peter. Yes. Jody. Have you been working hard this morning? No. Just a stack of the old chairs cleaned up a bit is it nice out very nice so you see this conversation is distinguished by is extremely condensed and compressed but it relates massive amounts of information it's kind
of a qualitative compression of information then that's not the whole idea of language and qualitatively compresses information and allows branching, selection, freedom of selection. There's one whole idea that linguistic conciseness, linguistic qualitative compression allows your development of increasing degrees of freedom, of selection, of how you can move in this basically data structure. And as you see, it starts, is that you, PD, beginning of the conversation, marked by Xi
XI zero. Then she repeats, is that you? Again, XI zero. And yes, it's me. XI zero, one. And then how the conversation emerges. But at some points, as you see, the conversation changes its focus. First it was about the presence of Pete. Then it's about the corn and it's about paper. And as it changes the focus, the base of the design, the base of the strategies and linguistic moves changes from Xi to Sigma, from Sigma to P in this
dialogue. In ludics, there is also another kind of move, the one in which the speaker decides she has got enough information, for instance, by means of an answer from the other speaker which satisfies him or her. There is no bias added in that situation. Only a signal indicating that the exchange is over. And this is where we apply the diamond rule, denoted by a cross symbol, which is a positive
move. Generally, no speaker's viewpoint can end up as an indefinite weight for a positive action. We may represent this interaction in the following way. And in the sense of these 001s are, you know, the biases about questions and answers in in the dialogue that are represented as proof through these or sequence, attractive proof through these in ludics. Where that empty tuple is basically an empty locus.
speaker's viewpoint, my viewpoint, can be represented by either this one or that one structure. This is the case for that very rudimentally multiple question, are you still a smoking one, not the Pete and Joanie's conversation. A third issue is the one for which I object that I never smoked, which would be on my viewpoint represented, again, by this. A's viewpoint is replaced by this or this, where E is
called chronicle, or view. A view is a justified sequence such that no two following moves have the same polarity. For each pair of constructive actions, sigma i, sigma i plus 1, such that lambda of sigma i is positive and lambda of sigma i plus 1 is negative. We have sigma i turns out sigma i plus one. A strategy is a prefix closed set of views, D, such that the following formal properties.
Very intuitive way of seeing this, again, back to our Brandomian commitment, entitlement directories of boxes where we add new counters, namely sentences, and that might alter our directories, update them, either remove a set of previous counters or add or preserve them, is that our basically the whole idea of justification that is central to the game
of giving and asking for reasons or making assertions can be formalized, can be formalized in terms of justified sequences of moves into these elementary acts, positive-negative A great book that goes into details and elaborates the formal aspects of this, but also more concrete examples of dialogues is Alan Lecombe's Meaning Ludics and Dialogue. is a great book because he starts with a history of syntax semantics, theories of meaning and
speech acts, and then he moves gradually to classical game semantics and ultimately ludics. the Alan Lecomte, Marianne Flory, Daniel Pirello, they have made these comparisons between ludics and brandomian inferentialism. So they are really good references if you want to look into this further. Okay, so
The viewpoints in ludics, in the sense that formalized here, is in fact exactly like a strategy that players can have when playing together. Intuitively speaking, designs are sequences of moves, each of which being associated with the application of a rule, positive or negative. They can therefore be seen at the same time as deductions or proofs. The dialectical interaction that we have between a speaker S and his or her co-speaker A may
be seen either as the opposition of two strategies in the game or as a tentative to build a proof against the objections or the counter-proofs of the other speaker. One of the main differences with the usual games lies in the fact that there may be no winner in that kind of game. The goal is not to win against the other speaker, but to reach together a situation in which there is an agreement on expectations. Such a situation is expressed in terms of convergence in ludics. on the contrary, may be assigned to failure, like presuppositional failure. Let us otherwise notice that conceived this way, dialectical exchanges seem to occur not by opposing steps
to steps one by one, but by opposing a whole strategy to another." So global polarities of strategies, global dualities. It is as if each speaker had in his or her own mind a whole plan, or as if she was projecting an entire design. This seems to be in agreement with present views in neuroscience, as attested by the following remarks by Jean-Pierre Changeu. Human communication generally takes place in a well-defined context of knowledge in which speakers are informing each other, aiming at maximizing the efficiency of communication.
Each speaker tries to recognize and to infer the intention of the one who communicates. In other words, when communication begins, each partner has in his or her own mind the whole possible content of the speech, which constitutes a subject of all his or her knowledge on the world. We may think that each speaker constantly tries to project his or her frame of thought into the mind of his or her co-speaker. Now, let's start to wrap up this session and bring it to the final,
that how ludics frames the idea of neopragmatism via complementing the game, the truth-oriented approach to speech acts and game-oriented approach. And by complementing them, it basically can be used as a kind of a very sophisticated model of how to grasp the concepts of no pragmatism and hence rationalism in the sense of Brandomian
inferentialist position. First, a very, very brief introduction on speech acts. Because I said, speech, we do not have such a thing as concepts without the speech act. We do not have something as inferential or semantics without interaction between the speech acts. No, we have speech acts without the categorizing capacity of sentences, making the claim, asking a question, commanding.
First we can observe the foundational remarks about the speech acts and the classical separation between constative and performative assumptions, as put forward in the works of John Ossin and John Searle, opens the way to making a bridge with proof theory. For example, the meaning of a constative sentence, like, the weather is good. A lot of constative sentences are the ones that tell you something is the case.
In the speech act theory, they are distinguished by truth-falsity criteria. For example, the meaning of a constative sentence like the weather is good can be explained in terms of truth and falsity. But in the case of a performative sentence like, I wish you to grow old, we can't say what would be the truth value. We just know that in some cases, depending on the context, the sentence would be understood as a real wish or not. For this reason, we can identify a whole class of natural sentences which are not truth valuable and for whose meaning determination require a contextual analysis.
These utterances convey speech acts, i.e. linguistic objects, which realize some concrete pragmatic action. We suppose that for each meaning M, there exists an expression E which is relevant which is a relevant formulation of M, i.e. E is sufficient, expression is sufficient to transmit the meaning, meanings intention M to the interlocutor. You could define a speech act as a quadruple I gamma B epsilon given by a communicational
intention I, a set of prerequisite condition gamma, a body which concretely realizes the action, B, a set of effects that it produces in the conversation, epsilon. This definition states that speech acts in their purest form, the most disembodied one, as we see in the following example. And the example is, sentences that, for example, we promise something to someone. A speech act S will be considered of the type promise, so, of the type promise, when four conditions are respected. A speaker has the intention of meeting some propositional content P. A speaker wants to
make a commitment to add, to add receive to the interlocutor about P. A speaker really wants to fulfill this commitment. And for a speaker, an addressee, it is an evidence that without this speech act, a speaker would not have done the promised action. Some remarks can be said at this stage. First, we do not know exactly how to consider and take in charge the speaker's intention of communication something, because the speech act is defined as if the intention was totally transparent. So this is the formulation of a speech act in the classical, more classical theories of speech acts. It's the whole idea
that we do not know about the intention part of speech acts. Second, the normativity of speech acts is unclear because it suggests that conditions are fully established before the realization of the speech act. But we know that by convention we intend to justify the fact that the speakers associate linguistic expression with meanings they want to refer. So this is, again, when the idea of normativity in classical speech act theory is pick up is that idea of pre-established normativity, classical normativity, whereas in neopragmatism,
normativity is really embedded in the interaction, is not predefined or pre-determined. Of course, there are other questions that arise in these frameworks. Is the speech act distinct from its effects? Can we in fact talk about speech acts without their effects or their impacts? What difference can we make between the effect and the intention of, related by a specific speech act of a specific type? Considering these critical points, a good theory of a speech act would have then to define conventions and intentions not only as core notions, but evidently as material
objects upon which interaction between agents can be developed. The body of a speech act, i.e. the means which operates an effect, can be seen as a function responding to an expectation. This function, in order to be operational, i.e. to produce some effect, must interact another function with another speech act, some set of data and or contextual elements. We can call this collection of inhomogeneous elements functional environment of speech acts. We can see it in this table. Speech act theory intentions are understood as functions types.
are understood as contextual data required in a given time. The body of the speech act is its function, and its effects are output data produced in a given time. And again, these effects, for example, in Brandoomian sense can be seen as how it alters our entitlement directory. By making a new assertion, I might alter my own entitlements, but also the entitlement of my interlocutor, my opponent. That's how they can be seen as equivalents of type,
outputs, contextual data, and function. A speech act must be seen as actions committed by a speaker and accepted by some addressee, which updates some databases about facts, things to do, and commitments. This mirroring effect can be called the game play. and the sinking effect between players is like a game. We can see the origin of this idea of gameplay in the fact that sentences can produce this symmetrical effect on context. They engage a commitment of the speaker about something and call on the addressee to take in charge
of some counterpart. With these ideas, Jonathan Ginsberg opens the way to the formalization of speech acts as games, i.e. integrating the two players in the analysis. So the notion of commitment is modeled by means of a game board in the Ginsberg model. It generates a source of bookkeeping of actions, very much in tune with Brandon's deontic scorekeeping. randoms, deontic, and scorekeeping. Things to do, shared knowledge, and all the things which must be known for ensuring the practicability of a speech act and or the reliability with
which follows the speech act. In the classical style, we postulate that the speech act is defined by some propositional content associated with an illocutionary force, according to the fact that the content can be affected by the force. For example, 1, 2, 3 have the same propositional content. And what is this content? P is the idea of laughing, we laugh. And three different illocutionary force, respectively, assertion, question, and command. We laugh, are we laughing, let us laugh. The two main problems in this theoretical game, a theoretic account of speech acts,
are the uniformity of the propositional contents transmitted, as if it was the same in all variations, and the bijective relation between clause types and illocutionary forces, as if it was possible to establish a strict and decidable correspondence between them. Ginsberg and Sack are in favor of defining multiple types of propositional content according to types of speech acts. As I said in 57, one of the flaws of this game, the theoretic view as performed by like like Ginsburg sang and gets there is that they try to pre-define types of speech acts,
come up with different categories, multiple types. And that's already put the restrictions. And if the function comes pre-typed in line with the lambda calculus interpretation we have been looking in the second module, then we can't really determine the context, the
effect of speech acts by analyzing their behaviors in an interactive framework. Ludic's interactive frameworks. There is no such a thing as pre-typing, pre-typed function or pre-typed speech acts. Types are being determined throughout interaction. The idea that typing, pre-typed function, pre-typed the speech acts restricts the interactive behavior of speech acts and respectively narrows
the scope, the potential scope of how we can analyze and determine the context, the impact and determine the context, the impact of a certain speech act. If we do not have this pre-typedness, then we don't have restricted behavior, and hence we are capable of coming up with more sophisticated modeling of linguistic practices or speech acts. In the game view, we see that the speech act as a program which operates on private and shared databases. For speech acts, the program updates essentially two types of entries, commitments of the player,
call on its opponents. This model can also be further upgraded by extending the notion of commitment, defining it as a function operating on the environment. In this manner, we can see the following example of the speech act types. And what are these speech act types? They are assertions, questions, and queries. So queries and questions are different in Ginsburg's theory of speech action. Questions that you are asking prima facie is something.
Query is something about anticipation. When you anticipate, expect something to be done. So an actual roadmap of the speech acts theory would be clearly defined by the aim of taking into account the interactivity and the context dependency. First, we have to show that speech acts we are interested in can be seen as collaborative results. For this reason, the function played by the addressee in the felicity of the speech act must attract all our attention. Second, we must restore the dialogical dimension of a speech act, notably in their evaluation.
This point implies to relate the game, concentrating our force on the chaining and the embedding of speech acts. The third objective is about the extension of the notion of commitment, viewing it like an impact on an environment. And then commitments besides that whenever I deploy a commitment in the Diantic scorekeeping game of Brandome, I change something of my entitlement but also the entitlements of my Now we can define commitment as a registration and context modification as transformation
on data structure, like for example a database. So very briefly, the Speech Acts theory classically is divided to two positions. First truth-oriented approach as developed by the likes of Austin and Searle. The second one is the view based on the Speech Acts as games interpretation developed by in the likes of Gansdor and Ginsburg. These two models can be identified in these positions, promoting different means for understanding the speech act situations and effects, which do not focus on the same object. The ludical view of speech acts, on the other hand, constitutes a third option, not rival but complementary.
It focuses on the structural modification in the speech act world and view their speech acts as constrained processes realized in context. So in this table, we saw these distinctions between the classical view, the game view, and the ludical view, how they see as speech acts. In classical view, objects are conditional. In the game view, there are functions. And in ludical view, the object itself is the interaction. Classical view, variabilities.
Expression, express indexes of variability. In the game view, our data. And in ludical view, shared context, which precisely emerge from computing or having dialogue from shared locus in ludics that I mentioned. So in classical view, a speech act type expresses invariance. In game view are inscriptions. In ludical view, there are impacts. The effect of basically a speech acts on the environment in the directory of commitments
and entitlement, in the commitment and entitlement directories. It is evident that with the ludical view, the complexity rides against two other systems. But this complexity is being upset by the way it's being opened up to the formalization of complex and multi-scale architecture of the speech acts elements. For example, in the game view, we got a game designed for speech acts in which we focus on commitments by the way of functions modifying some databases. The use of ludics, however, introduces parallel analysis of speech acts, in which speech acting structures, contexts, and executables
are homogeneously considered and also identified by their polarity. In the ludics approach, as contrasted to the game view, the interaction is taken to a more primitive or deeper level, like a sort of machine language which talks both the language of executables, executable structures, and the contextual structures. So another point of contrast is that inscriptions or counters, when considered in the game view, are notifications in a notebook or a ledger managed by some interacting agent, a score keeping book, a game board. It suggests that commitments are countable, and for each commitment there is almost two
inscriptions in two personal notebooks, you know, opponent and the player, the speaker and the interpreter, or just one inscription in some big shared notebook. This hypothesis holds very well, but in the case of a negative condition, as in the promise, for example, when we have to verify that the speaker is not already committed to do the promised thing, We do not know exactly what could be an inscription of the fact that someone is not committed. A possible approach would define it as the fact that there is no inscription about that in the available notebooks. Agents would have to scan notebooks searching for an inscription, exiting with an error.
In a ludical view, we consider that for a good approximation of the problem, we can define the negative condition as the absence of opposition of the present speaker to the presupposed fact contained in the Speech Act, as if the speaker was saying, I am not actually committed to do anything I want to realize with this promise, and nobody would have neither arguments nor the desire to refute this proposition. The interest in this point is that absence of reaction in a dialogue is itself a procedural definition. And hence it needs to be conceptualized. This is something that also is missing in Brandomian's framework.
The interest in this point is that the absence of reaction in a dialogue is itself a procedural definition because there could be no known reaction at time t and a contra reaction at time t plus one. A speech act evaluation becomes a real-time conceptualization. The model is self-contained. So before moving forward, any questions on this ludical view of speech acts and its possible implications for pragmatism and other kinds of topics?
I guess I'm still kind of just holding on to see where this is going. I could kind of figure that this is probably the richest formal language of logic that we've covered, and it sort of follows this trend or an earlier stream in which we kind of went from sort of simple correspondence up into sort of like
interaction being the most complex form, with an interactive-based formulation of logic. Yeah, I want to see. But can you already kind of guess the how it's tied to really the kind of computational protological structure of natural language, precisely in that semantic pragmatic sense that there is no such thing as semantics without pragmatics and there is no pragmatics without inferential rule semantics.
Yeah, sure. It's trying to capture more or it seems like it has a better facility to decompose positions over time. both kind of like vertical and horizontal because you have all these. You know, axioms are supposed to be like the undefined or the taken for granted. Taken for granted, yes. To reduce the surface area of what you take for granted and capture more of the context. And I get that and I appreciate that. Great. I see how it does that differently than other systems, especially with the logic. Yeah, that's my take on this path that we are on.
But, yeah. What about you, Stefan? Any thoughts about this? Especially because you're still thinking about the speech acts, speech occurrences versus linguistic functions. Yeah, I think I'm still just trying to sort of find the grain of the problem I'm facing. I suppose it's, I mean, without, I guess, undermining the value of the theorization of the speech act, I'm wondering whether the speech act as a concept and the event of an interaction itself need to be theorized in slightly different ways.
Does that make sense? How so? How so? So, I mean, in the sense that the event of speaking happens in space and time in a particular way, sort of, you know, I still think I need to kind of think through what the problem I'm feeling is. but it mostly has to do with the idea of the occurrence of speech being kind of a specific moment in time as opposed to a case of a category of speech acts.
Does that make sense? So it's a distinction between speaking as an instance that can be particularly situated, but maybe isn't commensurate with determinations of the speech act as a class or a category. Yes, but you see that's, again, bringing us back to this whole idea of inferential rule semantics and inferences are all sentential. This is one thing. And this whole inferential structure of sentences that is capable, within the interactive sense, within this interactive framework,
is capable of categorizing or determining the type of a speech act. Now, a speech act within ludics can be seen as not a speech act, that's what I'm going to talk about, as a speech acting, simply an axiomatic elementary act that comes untyped, simply an embedded utterance that once is deployed within the interaction, within the pragmatic dimension, It takes these types. It becomes, you know, it assumes a functional type.
Otherwise, you see, this is in fact in continuity in ludics with this collapsing of the syntax and semantics. And the same thing we have it, speech acts are nothing but utterances that can be deployed. And how they behave against other set of basically deployed utterances determines their type. They become speech acts in the classical sense.
But I wonder, Steven, if you're presupposing sort of like the inherent ordering of the speech acts, and it seems like in Ludix you don't really have time, but you do have sort of like expectations on how other agents are going to respond. So you have speculation that is embedded in Ludix as, what is it called, negative? Yeah, negative. Negative? Yeah, negative. Something like this? So it may not be instant, instantonality may not really be represented in Linux because there isn't any time, but just sort of relative position that makes something either positive
or negative. I don't know if that helps sort of draw out your question. Yeah, no, it does. I think you're right. I think maybe that's the trouble I'm having is finding a lot adequate about ludics in terms of thinking through instances of interaction, but I suppose it's just this difficulty of developing a way to approach the instance with something like ludics that might not theorize it in the way that you're expressing it. Does that make sense? I mean, I think you're right. And I'm not quite sure I've thought through it all the way quite yet. Okay.
So before we move forward with ludical approach to a speech-acted theory, and also in connection with Brandome's no pragmatism, no rationalism, we should justify the relevance of the ludical model of speech acts. To do that, we're going to look at the most important points for our understanding of the ludical or interactive view of speech acts in its most intuitive form. Before going into details of our conceptualization of speech acts, let's introduce some core notions which are imported from ludics. Speech acting, one. While speech acts are viewed as stable structures, the ludical view introduces the concept of
speech acting, where the interaction plays the main part in formulating speech acts. Classical speech acts are presented in a synchronous view, but objectively the procedurality of embodied speech acts oblige us to introduce some complexity. Speech acting is in fact an asynchronous processing. It must be taken into account in the conceptualization of what counts as a speech act. First, we recount the interaction process as a parallel processing processing, realized by two speaking agents, forming their own actions on the basis of
their interlocutors' action. So process one, which denotes or signifies a speaker's actions. Let me share the screen. A speaker proposes a speech act A. It can be seen as a function defined on the context with values in subset of the context containing the commitment
of the interlocutors. The context must satisfy some conditions C1, Cn, and C. So we denote by double struct C a closed set filled with justifications of C. Double struct C will be called a behavior, i.e. a set of designs. As we just defined A, we can write factor A belongs to double-struck C producing some effect E, which means, and that effect is contextual element, really, which means there is a construction called AE,
which transforms the contextual element C obtain contextual element in E. As I said, the whole idea was the idea of transformation on data, data structures. And these transformations, production of effects and impacts are what determine the type of the function, determine the type of the speech act. The speaker thinks that he can access in the open context to some locus in which the condition C is justified by design D, knowing that he is considering a set double-struck C of justifications of C conditions.
This design can be located in a private or a peripherally shared part of the context. Then a speaker feels himself justified to provoke the commitment E, which would be a realize in the context E. Now this was the speaker's action, was process one. As we said, ludical approach to speech act can be seen as parallel computation, parallel processing. Now process two is address's reaction. Address E perceives the speech act. Address E does not have objectively the same view on the context that a speaker had. For example, he
can perceive differently the same situation. The swatch is not red, but just dark brown. Variation of perceptual judgments. For example, he can perceive differently the same situation We can perceive differently the same situation, having more elements in double-struck C, or even possessing arguments which contradicts a condition, double-struck I. For example, we see it constantly like in philosophical argumentation. I know not specifically something to do with perceptual judgment, but basically I know something, I know an argument that refutes your point.
You can also refuse arbitrarily the effectivity of a commitment even if the conditions were filled. For example, in the order, addressee can ignore the authority of the speaker on him. Also add receive response by forecasting the speaker's actions or by acting in some locus or by introducing some elements which were not taken in charge by the design of the speaker. So a key definition, ludical speech acts, as different from the classical speech acts. A ludical speech act is a sequence of reduction by which some executable, called the speech
Act produces an impact when some conditions in the context are fulfilled. A type of ludicrous speech act is a class of executables which produces the same impact in variances in that table that we saw, in variances of impacts. A type of ludicrous speech act is a class of executables which produces the same impact been observed in the same conditions. The speech act is uttered in some determinate context, which contains facts, knowledges, past actions, mental states, etc. Each speaking agent selects the parts of the context he
considers as relevant and acts by reference to its elements. For example, at the utterance a speech act by a speaker, addressee will react by means of parts of the context he perceives and which could be different from those viewed by the speaker. The difference between what views the speaker and what uses addressee plays a huge function in the realization of impacts. As a speaker can feel himself so justified by contextual elements to obtain some effects which are refused by addressee by means of some other contextual elements. In the interaction, these contextual elements take the form of possible actions of the speaking agents in their plans. They are positive when invoked by addressee as context, negatives for speakers, or invoked
by speakers as conditions. They are negative when used by addressee as an action positive for a speaker, or invoked by a speaker as anticipation. So a lyrical speech act is defined by three elements. The speech act, namely some competence of the speaker for impacting the context, considering some actual conditions or anticipated reactions of its interlocutor. This competence is invoked in the situation as a structured system of actions, or elementary axiomatic, elementary acts. The test, the interactive situation by which we oppose the speech act and the complex
structure which plays the role of context mixing contextual data with interlocutors reactions. And finally the impact, which is the result of the interaction, i.e., a modification of the context. In the script you add a counter to your entitlement commitment boxes or you erase them or you repair your previous commitments according to the alterations that just was made. So we can decompose the Speech Act in three levels. The body of the Speech Act, the Speech Act in an interactive situation, i.e. taking into
account the reaction of addressee, and the Achieved Act, main or peripheral effect. In the following design, we assume that the active part takes the form of a function, modifying context to produce an effect, which is the basic form underlying the ludicrous model. So the relation between these elements of speech acts, the speech act, namely the body, context and the impact can be seen as this. And as you see in linear logic and of course
in ludic which is linear logic, this can be seen again as a resource construction, Here's the interpretation of construction. A speech acts being consumed in the process, as we see by, symbolized by linear implication formula. Where A, Fractor A, B, C are some interactive trees called designs, structured interactively by alternation, observation, and action. In the case they are negative, they are passive and represent a contextual structure, knowledge, mental states, facts. When positive, they are active treats and represent the structure of an operation, functions,
transformations, etc. Each design, like C, realizes a behavior here, EF, which is a category possessed by some speaking agents. So we can say that the realization factor C is in the behavior double-struck EF, which modify the structure of trees. The Speech Act is strictly considered, i.e. seen as a program or function, is represented here by design A in the behavior double-struck linear implication E.
E, C being consumed in production of E. More exactly, we would write multiplicative conjunction CI, linear implication double-struck E, where the behavior in multiplicative conjunction C are the conditions associated to the effects multiplicative conjunction E. Now, we recall that the design F in behavior, double-struck A, linear implication double-struck B, is
performing effects somehow as a function f defined in the set A to B. If we present to it a design A belongs to double-struck A, then the intractive situation is normalizing in the design. Fractor B belongs to double-struck E, or either it fails. So this is the kind of formalization that involves at the core of formulating what speech acts are, in fact,
ludics, where the interaction is a primary object, where invariances are seen as constant, constancy of effects of some speech acts in certain condition. And that determines the class or the type of that certain speech acts. As I said, they don't come pre-typed. The
type is being determined. And what determines it is precisely through this interaction and how they produce effects on their environment, the constancy of these effects, the invariancy of these effects. Now, when I was going to the branding part, let me see if I, yeah, I don't need to talk about this more formal stuff. So, OK. As I said, Ludix has been, especially recently, been frequently compared to Brandome sellers
and Brandome's in French journalism. The comparisons being made by a number of people, you can look at their work, Alan Lacombe, I can write his name here, Marion Flory, Daniel Porello that I mentioned a number of times, and other people. So we can talk a little bit about this, how the ludical view can be compared with Brandome's inferentialism, precisely because they both assign significance to the notions of proofs
or inference and game. is less ex...the concept of game, however, in Brandom is less explicit than in Ludix. And this, as I said, Brandom's Deontica scorekeeping is still very much modeled on classical logic, a tool that we said that it really filters out a lot of useful information and kind of waters down the complexity of this whole interactive pragmatic dimension of dialogue. So I think the comparison between the two can be a bit metaphorical precisely because
of how Brandon, you know, models Deontay's core-picking on kind of a classical logic, whereas Ludwig's is, you know, completely proteological theory of interaction. But nevertheless, at a deep, at the level of a concept, I think they can be linked together and it would be, in fact, I think fertile to see the ramification of the Ludic's view for Brandons in Frenchism.
So another point of difference other than this whole idea of being model of classical logic is that when seen from Brandomian inferentialist viewpoint, actions take on different interpretations. Here we move from previous conception according to which positive actions were conceived of as mere interventions in dialogue and negative actions as mere recordings to a new conception,
precise and philosophically richer, where positive actions may be seen as commitments and negative actions as entitlements, in the sense that this is how ludics can be really tied back to Brandomian, Solarism and Brandomian influentialism. Positive actions can be seen as commitments. You add encounter into your directory of entitlements by, for example, coming with an assertion and the swatch is red. And negative actions can be seen as entitlements, precisely because they are bound to the reaction
of the internal locutor in a conversation. In fact, performing a positive action in ludics, distinct from diamond rule, is selecting a positive locutor, as if selecting a token in a game and from it creating any number of negative loci or none, as would be the case in the game that includes a rule explaining the circumstances under which you can move a token from a black square to a white square, to several or to none. We then know that the negative loci or the new tokens or negative squares give rise to potential questions or objections from the other speaker who may ask for reasons to say certain things and that the speaker has to answer those questions and objections. Therefore,
we're performing a positive action which is always followed by a negative action unless it is a diamond or a rule labeled by cross. Every speaker commits herself to providing reason for what she says. On the other hand, by performing a negative action, every speaker limits the type of utterance the other speaker can choose for her to perform. Example, either an answer or a new question. By doing so, every speaker gives entitlements to the other. In what follows, basically, the answer
We can think of a case in which the other speaker, your interlocutor, is fictitious and reacts as a scorekeeper in a game. As I said, private thoughts, private language, is itself implicitly modeled on public pragmatic language, pragmatic dimension of language, precisely because it involves this fictitious scorekeeper, virtual scorekeeper.
In fact, the role of the fictitious scorekeeper is to give entitlements and when acting positively to react to every speaker's commitment either by an acknowledgment, thereby increasing the speaker's score, or by a failure to acknowledge, which occurs when normalization fails. These notions of a score as a scorekeeper are heavily used in Brandon, who, for instance, remarks, understanding a speech act, grasping its discursive significance, is being able to attribute the right commitments and response.
This is knowledge how it changes the score of what the performer and the audience are committed and entitled to. Or when he says, suppose we have a set of counters or markers such that producing or playing one has a social significance of making an assertional move in the game. We can call such counters sentences. And for any player, at any time, there must be a way of partitioning sentences in two classes by distinguishing somehow those that he is disposed or otherwise prepared to assert, perhaps when suitably prompted. These counters, which are distinguished by bearing the player's mark, being on his list,
or being kept in his box, constitute his score. By playing a new counter, making an assertion, one alters one's own score and perhaps that of others. This explanation can be correlated with the rules of ludics. In ludics games, counters are replaced by loci, the addressed. We may consider that selecting one locus has the social significance of making an assertional move. At any time, any player has a way of partitioning loci into two classes, those he is allowed to select and those he is not allowed. This partitioning depends on the moves of the other player.
When acting positively, if he wants to keep convergence, the first player has to select the locus in a range offered by the other one. And thus, if he succeeds, he improves his score as well as the other scores. This shows a difference between ludics and other game semantics. In ludics, convergence gives points to both players. So it is in their interest to cooperate. We can also suggest that it's not only sentences that are counters, but also any part of the speech. You may say that the utterance of the swatches read is not simply submitting a proposition to evaluation by stating a true or false value, but playing it as a token in a game, and knowing
that other players can ask for reasons for this statement, either by challenging the choice of the word swatch or by contesting that it is read. Only after this game has come to an end can the assertion be evaluated. In this setting, assertion may be analyzed by assuming that counters are part of the speech, and that when producing an utterance, such as a swatch is read, the speaker is in dialogue with a scorekeeper, who at first entitles the speaker to choose a theme from a restricted range of topics allowed by the context. After the choice of a theme, the speaker expected to be validated by the scorekeeper in a virtual
positive move, followed by a new series of proposals concerning the predicates which is dependent on the selected theme. The speaker then selects her own predicate from this series, waiting for new validation and perhaps other moves involving assessment of truth, modality, and so on. There are different avenues of correspondence between Brandome's inferentialism and ludics. For example, the idea of assessment of truth in Brandome's framework and normalization in ludics. Or for example, the idea of incompatibility and convergence, incompatibility in Brandoms
and convergence in glutex. I think what makes it significant, Brandom's position as such, is that it's infringing Inferentialism, as opposed to Szilardzian inferentialism, is that, what is Szilardzian inferentialism? Szilardzian inferentialism is mostly, as I said, it's a functional theory of meaning, role semantics that has been motivated by his version of referential theory of meaning.
So for Salars, what is really important is this idea of the inferential theory of meaning as opposed to the inferential theory of meaning. For Brandom, this is not really that much. It is still as, you know, it is still important, this aspect. What is really much more important in Brandoom's inferentialism is that inferentialism allows him to be analyzed as structure of intentionality, simply having beliefs, what it means for a rational agent to have beliefs. Beliefs cannot be understood also respectively the idea of rational agency cannot be understood
underscores this coupling of inferential role semantics, inferential theory of meaning, and pragmatic theory of linguistic practices, interactions, deontical score keeping. So in opposition to those people who think that, in fact, Brandon tries to re-inscribe kind of an enchanted account of rational agency, and again come back to this kind of naive anthropomorphization, is that he in fact tries to conduct a thoroughgoing deconstruction
of intentionality, in fact much more brutal than any naturalist, greedy reductionist philosopher can do, like the likes of, for example, Scott Baker, so on and so forth. Precisely why is it important, is that not, especially this, when I say brutal, precisely once we are capable of analyzing what a belief is and respectively what a rational agency is based on these kinds of formal dimensions of inferential role semantics and pragmatic
linguistic practices, we are already moving toward a kind of irrational disenchancement of what counts as a discursive, a perceptive agency, namely human, in the sapiens, not as a biological species, but in the Kantian sense. But what makes it even more brutal is when we link Brandon's inferentialism to ludics, namely seeing pragmatic linguistic practices as from the lens of deep proteological computational
processes. And that's, I think, that deepens basically the cuts, the construction of intentionality and respectively rational agency. When we no longer talk about what is really the social when we are in the sense that we are talking about social anthropological pragmatic linguistic practices. What we see, what counts as the social in no pragmatism, brand new pragmatism, are these fundamental interactive computational, proteological computational processes.
That from very basic mechanical syntactic components, once our frame this interactive sense, they increasingly give rise to higher levels of semantic complexities, as I said, in the sense that where you have not only words that label things, but concepts that describes, but not only concepts that describe, but also concepts that can be used as counter-factuals. concepts can be used as counterfactuals. And not only concepts are counterfactuals, can be used in order for us to simulate things, imagine things as if they could be otherwise, but also concepts that are modalities. And this is really, I think, the core of Brandon's
book, Between Saying and Doing, to show the fundamental import of modalities as determined determined within the pragmatic dimension of linguistic practices for any empirical sciences. That empirical vocabularies cannot be deployed unless you have modern vocabularies. So these are, I think, really kind of good avenues of research from both the how normative rationality converges on, you know, scientific rationality in modern empirical sciences, but It's also a kind of a more cosmological stance of this deconstruction of what counts as a rational agency in the sense of Kantian discursive, perceptive agent, especially once we see that
agency. For Kant, the agent is really the one who masters the judgment. And judgment is really the idea of the inferential role semantics. Hegel moves it one step further by embedding this within the social interaction, kind of becomes a precursor of pragmatism and no pragmatism. And then Brandoom moves this further by deconstructing the social dimension of the so-called master of judgment, the rational agent. And then we can do it further by taking this into this sphere of
deep proto-linguistic, proto-logical computational processes to see that what counts as social, comes as judgment, as the social that determines the environment of that judgment, the criteria of that judgment, that marks, that characterizes the rational agency, can themselves be seen as semantic levels built upon these deep proteological computational processes. And that, I think, gives us really perspective of what kind of languages can be designed that can capture both the kind of properties of natural language and properties of formal
languages that can engineer a rational agency that can be armed with both the cognitive abilities that natural language enables us with, such as the feasible judgment, for example, but also the kind of cognitive abilities that strictly formal languages are capable of enabling. And those are the ones that we talked about in terms of de-sematification, re-sematification in terms of extended theory of mind and information processing systems. So these are I think all avenues of research to be done before, you know, so
and obviously I, for me it's impossible to cover A lot of the stuff I should have covered, but we didn't have time. So as I said, the whole idea of the course was just give you some very, very small indication of the historical context, of what are the contemporary debates are, and give you, you know, kind of putting you in the right direction of looking at these new fields of research and doing it by yourself. Other than that, yeah, so this has been completely introductory, and we couldn't really get into
the kind of detailed discussions, but other than looking at the specificity of these debates and research fields, I think for bigger philosophical picture, it has these significances. And these are significances that I've made. And I think this, or the whole entire line started with Kant, Hegel, German idealism, moving to person pragmatism, , and all these people, can be seen,
In fact, can be even amplified, can be even talked more consequentially once we deepen the scope of things by going into these kinds of talks of complexity, computational complexity, interactive theory of computation, so on and so forth. So questions, answers, objections, thoughts, Anything.
Discussions? So, I mean, this is more of a technical question, but a lot of the stuff that we've gone over has been fairly new to me, and it's something that I'd really like to integrate into my work in anthropology, but it's exceptionally difficult, just because of, I think, the disciplinary distinction. I'm curious.
I'm planning on going over a lot of this stuff again over the summer, and I'm wondering if the materials will be available and maybe, like, the documents for the slides and stuff that we've used. Sure, sure. I will put... Yeah, I mean, we can keep the class board room open and make you guys feel free to email me. Yes, the new center email is good. I checked that. But feel free to ask any question on the Google Classroom and I get the email and then I will reply. Because the majority of these are extremely difficult, some of them, especially more you move
toward these kind of new logical frameworks. are not kind of easy or even intuitive when you really get into details. So it would be great for us to exchange thoughts and stuff because what I'm doing is really along this line of research, namely starting with German idea of this conception of agency and obviously things that are attached to this, cognitive freedom. And then trying to reformulate it according to these more involved scenarios, but still
because as I said, especially in the last session when we were talking to Aaron, I think There are really massive deep parallel stuff going on between German idealism and these new pragmatism and hence these interactive computational theories of language and thought. Yeah, I thought the class was fantastic in providing a very rough but exciting roadmap
more contemporary research and we kind of skipped along sometimes at quite a pace. But I'm glad that we were able to get to where we arrived. I think I want to take a little bit more time and sort of it would be great if you did fill out all the notes because that's where a lot of the technical parts come from. Also, I should put some of the, we should make a, we have a library already, but I will add some, some text and stuff. Yeah, definitely. But I mean, what I'm really interested in is how this can be integrated in your line
of research. what is the significance of all this for your own projects? Yeah, I guess for me, taking a step back to when we covered Boltzmann, and so what were the sort of, from the perspective of dynamical systems, what kind of tools they were deploying then to provide some reason about the phenomena they were observing, I definitely want to go back there and do some more work on more information theoretic conceptions of complexity. Yeah, trying to tie in sort of uncertainty principles.
I still need to scan those chapters of Berg's book. But it is, I think, it's probably one of the best books that I have read on both sides. But yeah, I thought that in general, providing the roadmap, having little pit stops with certain key authors, that was really informative. But it was a little bit dense. It'll take some time to unpack, at least for me. and stuff I've been going back and fleshing them out. And this new stuff on linear logic and ludics, I thought was quite rich. I would have preferred if the last seminar
introduced new material and we focused entirely on recap and the conclusion you give at the end, which was the last 10 minutes was fantastic. That was the whole three hour session. We just, like 10 minutes of material. Well, we can do that. We can coordinate some sort of a... Yeah, sure. I mean, we can definitely. Yeah, I mean, I would love to talk about, especially the... Because Tal was, last time was saying that I'm skeptical of this making philosophical interpretation of this stuff. No, I'm not skeptical of that. I'm skeptical of this kind of using bad pre-existing philosophical concepts to talk about these things.
But yeah, I think that these are really massive philosophical implications, especially when you think them in that kind of umbrella, huge, gargantuan project of German idealism. Where this, what is this really German idealism? It's German idealism is the point where three lines intersect. Philosophy of mind, namely cognition, philosophy of knowledge, epistemology, and philosophy of action. What counts as practical action? Yeah, I would suggest with these lines, like if you were to put up the texts that we could set up another session maybe,
like at the end of the summer, and then we could all get back together and have... We can, yeah, sure, we can have it. I would say that we can have it not even at the end of the summer. We can have it in the course of a month, so still you guys remembering some stuff, because by the end of the summer, our art is losing. Okay. Sure, yeah. Bye, Sean. Thank you all so much. All right, ciao. Thank you. Yes, definitely. Yeah, we just go over philosophy and how we can use these to reformulate some of the main concerns of pre-neal questions of philosophy, what to think and what to do.
Yeah, what also might be interesting is if we have, like I said, a date for it, we can have, if people want, they can all, like, they can prep, like, 15 minutes to kind of contextualize what they took from it. Yes, that would be great. Yeah, that would be excellent, especially if it is, if they can reintegrate some of the stuff within their own research field and talk it from their own research perspective. Yeah, I think that would be fun. Okay, guys, I will let you go.
You are going to have a good day and you had some use in this whole class because I know some of the stuff are not evidently connected to our philosophical, theoretical, even artistic projects. But nevertheless, I think exciting connections can be made. No, I thought it was awesome. Thank you, Reza, for the extremely informative seminar and for all of your time. Thank you very much.