 So first and foremost, I would like to thank Professor Frugal for his kind invitation, because I'm clearly a non-scholar, a disindicted non-scholar in ideology. So my point is to use, make use of formal systems, formal tools in order to make sense, if any, of the Saptabanghi, especially. Because this is very intriguing. This is a very intriguing system for logicians and Western philosophers, so to say. So my approach is a constructuist one. Constructuist is the term I just borrowed from Professor Basilovic in one of his quotations, according to which, when you are a constructuist, you are opposed to the reductionist approach of Indian systems, for instance. So constructuist is a way to use, to make use of modern tools in order to disambiguate some ancient texts and words and concepts from Indian philosophy, especially. So that's exactly what I want to do right now, if possible. And the reason, the personal reason why I wasn't very interested by Indian logic, especially with Saptabanghi by gene logic, is because it's often referred to multiple values with the Saptabanghi, because seven two values, so to say, and because they're often referred to paracosistency. It's a non-classical system, and two of these words are very frequently referred, mentioned with respect to gene logic. But at the same time, it's very dangerous to use modern systems, because if you want to understand ancient texts or to see ancient texts with modern glasses, of course, the frit of anachronism is very big. And I want to be, just to propose you as a non-scholar, a way to reconstruct or to create a puzzle with different concepts and expressions for gene logic and to have your opinion as chorus about this point. That's the gist, the game, so to say. I have been, I had the pleasure to be mentioned by Professor Balseravitch with this quotation as one of the authors who developed some logical systems, but without paying attention about the real meaning of the text. Of course, I totally agree, because I'm not a scholar in Indian philosophy. So I was, I was the target, so to say, with a gallery of this approach. And I would like to say, to use this 20 minutes in order to defend my case, so to say, to defend my point, if possible. It's not a trial, but it's just a way to say that logic has something to say, modern logic has something to say about Indian logics. So if I want to reproduce different ways that reconstruct logical system from gene logic, the first paper, I followed Ghaneri. Ghaneri, in which we have something like a many-valued system for Saptabangi. We have seven true values, seven logical values, and I propose an existential quasi-true functional view of Saptabangi. I will explain exactly the sort of parents in a couple of minutes. I propose to develop this logical system with a syncretist, a 15-valued version, 15 logical values, because there are two different ways of interpreting Avakthavia. Avakthavia is supposed to be either both asserted and denied, or neither asserted nor denied. So there's two different interpretations of Avakthavia, and if you decide to conflate both interpretations, you obtain 15 logical values, two values, so to say. The point is that, of course, it's a purely formal extension, it's just a game, a formal game with ancient texts. So right now I would like to say, to use these systems to answer to the question how to account for the right gene rational throughout Saptabangi. Right now that's the point of my presentation. So Professor Shin just presented the seven Bangis. So I suppose that you are very familiar with this Bangis, we have seven. The fifth one is just a combination of the fourth and the first. The sixth one is a combination of the fourth and the second and the seventh one is just an addition of the three different Mula Bangis. Mula Bangis, it is a nasty, nasty and Avakthavia. So just something like a combination, combinatorial game with sort of three Mula Bangis as primary Bangis. So if formal logic is supposed to disambiguate ancient expressions, that means that I should be able to give a new, not a new, a clear, precise understanding of a lot of different concepts, including these ones. I just let you read these very famous notions on the Kantavada, Avakthavia, Bangi, Saptabangi. Saptabangi, it's a different, it comes from the Madhavaka tradition, from the Buddhist tradition, that I would like to make a very clear comparison between Avakthavia and Avakthavia, between Saptabangi and Saptabangi in the end of my paper, because they have something very intriguing as a parallelism between both Indian schools. Ayavada, Palamata Satya, sort of truth, Palibasha, two sort of negation, relational negation and non-affirming negation, Pramanya, Saptabangi, Suntayavada, Shat, Shatvada, and so on, okay. So the first point is that I would like to emphasize the one-valued systems I would like to present here, because in 2009, I proposed a seven-valued, but here I'm modest, I proposed a one-valued system. For logicians, it's very strange to have one value. I'll just explain why it's very strange because I have only one logical value. So in this new paper, two different papers, I propose this one-valued and by means of an existential interpretation of Saptabangi because the Shat means that there is one standpoint, such that there is a standpoint means an existential interpretation of Shat. That's all. This interpretation, formal interpretation of the Saptabangi is supposed to superset, replace the fregan true values by new sort of logical values because the logical values I use here are not the fregan true values, it's something else. Non-fregan logical values. And I would like to emphasize that by means of this game, logical game, the import of dialogue is supposed to be rendered by means of a question-answer game because the semantics I propose here is obtained by means of a question-answer game because the dialogue is very important, I think so, in Indian fairies, like Dark Prince. So the name of this formal semantics is a question-answer semantics to account for the gene logic. So we have by means of this question-answer semantics, I propose a discussion about the very meaning of the true values. What's the meaning of a true value? If you are a reader, frega, frega, gotop frega is for the fifth instance, the meaning of the true value is very precise but I'm absolutely not sure that this true value is rendered by a Saptabangi, for instance. So we have to be very cautious when we want to parallel ancient and modern concepts. This non-fragant semantics is used to be so because first the sense of a sentence is another set of questions. You ask questions about the sentence and if you give answers, yes, no answers to these questions you just asked, you obtain the reference. So the reference of a sentence, in this case, is just a set, ordered set of answers to question. Yes, no, yes, et cetera. So the reference of sentences is the logical value, admittedly, but not a true value. It's not a friggin' true value. The logical value of Bangui is a set of answers about semantic predicates. Semantic predicates in the sense that the Bangui are supposed to be statements in which semantic predicates are assigned to sentences. That's the way we construct the very meaning of each Bangui. And especially I wanted to emphasize about this point, by means of question and answer game, I do justice to the bevelance feature of the Sabta Bangui because a plenty of texts say that the Indian scholars of philosophers only refer to true values, truth and falsity. So how could you have seven true values if only two values are mentioned in the text? So it doesn't make sense. So by means of this new form of semantics, you catch the bevelant structure of sentences. So in this case, every statement about a sentence is about the truth of falsity. So you say yes or no for an answer. So if you say yes, we have the value one. If you say no, you have the value zero. So by means of this game, I propose to reconstruct the seven Bangui. So we have third order questions. The first question is about alpha, alpha is a sentence about the pot for instance. You say is alpha assertible? So can you say something justifiably true? The second question is, can you say something about alpha justifiably false? And the third question, the third Bangui is about Avaktavia. It's non-assertible. So is it the case that alpha is non-assertible? I have two disentangles very meaning of non-assertible because it's not clear. I think that it's not very proper to use non-assertible as a way to translate Avaktavia. It's supposed to be sliding. And here are just the seven different Bangui. If you say yes for only the first question and no to the two other ones, you have the first Bangui. The second, the third, the fourth Bangui, and you have the seventh. Why not eight? Because if you have the eighth Bangui, you say no to each of the questions. And the Bangui are always a yes answer to each of the specific Malabangui. You never have only no answers to each of the three Bangui. That's the reason why you have seven and not eight Bangui. The second question is alpha deniable. I take this answer to be something to do with negative assertion. Do you think that this sentence is false? Do you commit in the falsity of the sentence? And that's a very specific meaning of negation to be distinguished by another meaning of negation that we present in the third part. So here we have just a way to have a logical symbolism to the justice to this difference. For instance, if you say that, if you have a yes answer to the first question about the negation of alpha, you have exactly the same as the yes answer for the second question. So you can translate these sort of questions by means of the meaning between yes and no answers. And here we say that the negation proceeds like an answer switcher, is we have two different answers for two questions about justice for the truth and justice for the false. And you just have to switch the two answers in order to make sense of the negation of the sentence. This is a sentential negation. This is a sentential negation. I have to emphasize over this point. So it does make sense. It's very clear. You have modern systems, you have modern glasses and you can read the saptabagi with modern glasses. So far so good. So, why did you decide to reduce from seven to one logical value? Because I have seven first, in the middle I have only four and then only one. No zero, of course, I just decided to stop to one logical value. So Amunabangi is just a statement about the semantic predicate of a given sentence. Truth about the truth or the sentence or the falsity of the sentence or about the Avaktavya state of the sentence. So, for instance, if you want to translate shatasti, this means the same as the sentence alpha is true from some standpoint. The meaning of the second Amunabangi is the same as the sentence non-alpha is true from another standpoint. So you say that it's possible to say that from another standpoint you have the falsity of the one in the same sentence. So it's clear that from this question-answer game, one and two are totally independent. You can have two no-answers, two yes-answers. So there's no implication between both answers, like as the case is in classical logic, for instance. So that's just to explain here by this means. And to the contrary, according to me, non-one sentence and a cantavada means something like you have two yes-answers to the first two mollabangis. Is the sentence true? Yes, is the sentence false? Yes, but from two different standpoints. So you have two yes-answers. That's the gist, according to me, of the point with non-one sentence and a cantavada. So as you can see here, you have two kinds of statements, attitude towards the sentence. We have either a session or denial. Once again, denial in joint philosophy, denial is supposed to be the same as negative assertion. You say yes about the negation of a sentence, or you commit in the true value of the sentence. It's the case that the pot is not such and such. That's a way of commitment. So if I want to make a parallelism between mollabangi and modern logic, I would like to say something like a parallel between mollabangi and Bernapps. Bernapps is a modern logician who proposed the four-value logic about true or thought-false. It's something like a logic of viewpoints, I would say. So for instance, siad asti eva is the same as alpha is thought-true. Siad nasti eva is the same as alpha is thought-false. But from two different standpoints. Different standpoints. So that has to do with the successive denial in a session. Not the simultaneous. In Nagavad-Tavim, the successive. The third, bangi. So a difference is to be made between two versions of inconsistency. What is exactly the meaning of being inconsistent? Because that's a blame currently made to saptabangi. A difference is to be made between avaktavia and the true-fold-yes answer. If you say yes to the true-first questions about the meaning, the true value of the sentence, it's not the same as avaktavia. Because avaktavia, for some logicians, avaktavia is supposed to be something like a strong inconsistency. You have falsity and truth on one and the same standpoint. So for instance, this view has been defended by a priest, current priest, a paraconsistentist, for instance. I propose another view of avaktavia according to which avaktavia means something like a lake of value. It's not both true and false, it's a lake of value. It's a lake of value in the sense that the subject of a sentence that is supposed to be avaktavia is a subject, an extra-mondent subject, like Hartman or Blachman. I have this interpretation. So in this case, it's not a value. Avaktavia is not a value, or an obsessive value. It's different. So we have three grades of inconsistency, because according to the sort of answers we give, you have frontstones, you have a light inconsistency. You just have falsity and truth from two different standpoints. So it's totally trivialized, so to say the inconsistency. Another view of inconsistency is mind inconsistency. In this case, you say yes and no from two different, one at the same standpoint. You say that do we think that this sentence is true from this standpoint? If you say yes from this standpoint and yes from another one, but if you say yes and no for the one at the same standpoint, this is a stronger inconsistency. And strong inconsistency is the case in which we say both yes and no to one at the same question. So we have three different steps, the grades of inconsistency, so to say. So where is Avaktaavia, where is Saptabangi in this case? That's my point, that's my problem. So Anikantavada, according to me, Anikantavada is just a logic of light inconsistency. It just says that you can have truth and falsity for one at the same sentence for different standpoints. Not one is the same, according to me. Those who claim that it's truth and falsity from one at the same context are those who say that Avaktaavia is the case. So I disagree with this point, but it seems to be discussed. Okay, the third part is I would like to make a comparison between Saptabangi and Chattoskoti for the end. It's a long hand, not so long, but I just want to be clear about this. So the first question is why did I choose to use a one-valued logic rather than a two-valued or maybe a seven-valued, as is the beginning, for instance. The inconvenience of such values, of course, nullifies the relation of consequence. Because if you want to construct with monologic system of inference and inferential systems, you have to make a difference between at least two two-values. You have to make a difference between truth and falsity because if everything is true, you cannot make invalid judgments. Everything is valid, so to say. So this logic is trivial in this case. But in order to define this one-valued logic, I would say that I think that inference in the sense of the Chattoskoti in text is not a formal logic. It's a very specificity of general logic is that if you want to talk about inference, like as Marie-Laine, for instance, said this morning, it's something very empirical, informal. So it's not formal. It's not a formal view of inference in this case. So the role of epistemic faculties, for instance, like perception, addiction, the nias, the way to, or the prominence, the way to have a judgment about a sentence, is different from the case of a formal logic. So it is not something to be formalized, according to me. The question-answer semantics insist upon the speech acts because assertion is a speech act. Denial is a speech act. So it's a statement about a sentence. And by means of the question-answers, you do justice to this illocutionary aspect of the statement, the bongi, so to say. So it's a logic only in the sense of a set of rules for the formation of judgments. That is, sub-tabongi is just state, how can we construct a specific set of sentences? So I think that it's very akin to, excuse me, yes. It's very akin to what Aristotle did in the categories, but not in the analytics. So Aristotle learned, for instance, syllogism is something a formal syllogism. It's not something to be related with what we saw this morning, for instance, in the logics. So the advantage of a one-value logic is that QS, so it makes sense of light paracostancy. It explains why we have only two values, but seven different bongis, for instance, and at the same time, why the paracosistant aspect of this logic is very light. It emphasizes upon the role of dialogue, because if we have questions and answers, this is a dialogical game. It overcomes the pitfall of Octavia because Octavia is not the same as both yes and no for one of the same questions, it's something else. And at the same time, it brings out the dual connection between sub-tabongi and chatoskuti. I would like to just finish doing five minutes about this point. So sub-tabongi and chatoskuti has to do with soteriology, something to obtain the salvation of soul. And truth is not the first problem, so to say, in this logics. You have to find a way to save your soul in this religious doctrines. And Matrilal said in one quotation, the following quotation, that Buddhism in Jainism proposed to save the soul by totally opposite means. With Buddhism, you deny everything about the truth and falsity of sentences, whereas with Jainism, you affirm your asset, both the truth and the falsity, from different standpoints, but you deny with Buddhist logic why your asset will join logic. We have something like a duality between the sort of answers you give. So a logic has been constructed for this purpose with two saturated domains of valuation. Saturated means that we have just one more value. We have a set of logical with four different values, but only one is given for the sentence from the sub-tabongi and from the chatoskuti, only one. So maybe you know this, because we have the four koti from chatoskuti, and the point with the Buddhist chatoskuti as Nagarjuna was to deny the four koti. So we say no to each of the four statements. The statements are very akin to the bangis by passing, but the difference is that if you use modern classical logic, it results in inconsistency. You can deny ABCD without having an inconsistent system. So we have to avoid this inconsistency by means of another two value, logical values to say. They're not proposed to say that, for instance, ABCD correspond to four different two values. But the point is that when you deny each of the koti as Nagarjuna did, you don't say it's true or it's false or it's both true, you don't say anything. So priest proposed, grand priest proposed to extend the four-valued system from benap to a five-valued. He said that, for instance, the most obvious way to account for Nagarjuna's stance is to proceed, is to take this possibility as a fifth semantic value. So we had a new value, e, to the existent four systems with false, true, both to reinforce or neither to reinforce. But once again, if you say that Saptabagi, you don't have any reason to say that each of the bangi corresponds to two values, you can't say exactly the same for the koti's. Why do you say that each of the koti's correspond to a specific true value? You don't have any reason to do this. So according to me, the best way to account for the Nagarjuna's stance is to say that he makes use of denial in not in the same sense as a jain. Jain used denial as something like a negative assertion. In this case, you don't have the negative assertion. You have paludasha pratisheida. Paludasha pratisheida is negation for the raist, for the nihaya, but this sort of negation is not the same as the negation Nagarjuna used. Nagarjuna used plasaya pratisheida. Excuse me, sorry for the accent. It's something like an irrecutionary negation in which you don't want to commit in the truth on the falsity of the sentence. And the result of this position is we have just the proper, the specific true value, logical value in order to account for the koti's to koti is a reverse answer. You don't have one, one. We just don't have a yes answer to both questions. You have no answer for both questions. That's the point. According to me, that's the way the Buddhists should answer to the sentence in the status koti. So just a way to summarize the whole. So we have four sublogics. So here we have the answer for the jain. We have the answers for the Buddhists, or for the Madhyamakas. And here we have the doctrinalists. Aristotelian logicians, or maybe the nihayas. They say either yes or no, but not both. Never. So we have things like bilitis, as in Bernab's bilitis, we have both force, only force, only true, and another two not force. Just have a correspondence between this answer and this true value. A subtermongu is supposed to be reduced to one logical value. You say yes to the truth and the versity. So to the koti is supposed to be the opposite value. That's the meaning of duality. You say no to both questions. Why does a subtermongu, the giants, say yes to both questions? And to the end, it seems that we have something like a different classification of logical systems. Nihayas are realists, so they accept bivalent and say that you don't have both no answers or both yes answers, not possible. Giants say yes to both questions, and Buddhists say no to both questions. So just a way to summarize the different point of view by means of my modern classes I just used during this talk. So here we have relativism. Truth is relative to the standpoint. Skepticism, we are not able to access to the truth. And doctrinalism, for each sentence, it's either true or false. There's nothing to say in Latin. So yes, just the reference I used in order to make this formal reconstruction of logic. And I thank you for your attention.