Okay, so I think we are now ready to start the last session of this year's seminar expanter inference So it's our pleasure to have today Bogdan Disher with a researcher at the University of Lisbon He's going to talk about non-foundationalist frameworks for META if French realism for the floor is yours Okay. Thank you. Thank you so much for the invitation and thank you so much for being here You know, particularly since I understand we are streaming I don't know why this happens. It shouldn't The reason we are streaming I should point out the fact that I'm contractually obliged to have some sort of Logos on all my slides. Those are the logos of my of the entity that it's funding me whom shall remain unnamed. I do want you to notice the fact that the logos are there They are very visible as per my contractual obligations That's it Let's let's move on I didn't quite know what sort of an audience to expect So I just sort of thought well, you know, I suppose it's going to be a sort of general audience of competent philosophers I'm fine with you know Philosophers in audience. I'm a bit queasy about the fact that they are competent, but hopefully that won't be too much of a problem Because I sort of decided that you know in various places, I've said various things generally nasty things about other people And I just thought well, let's bring all this together Yeah In a sort of more coherent red about other people And they need a title for this. That's all I call it non-foundationalist frameworks For meta-inferentialism, right? This doesn't mean anything, but I can do a bit better. Okay, so Here's what I want to talk about In a double of joint papers with Francesco Paoli, we've pushed for a sort of understanding of Consequence relations, which we've dubbed meta-inferentialist Without a meta-inferentialist account of logical consequence. Again, I'll explain this in just a bit But then I at least I was a bit Queasy about how much We've said in favor of that position from a sort of grand philosophical perspective So I've tried to work my way from what we believe about consequence to something like a position a philosophical position that you know makes those beliefs about consequence really shine So it's a sort of process of engineering backwards a Grand philosophical view about things And now here comes meta-inferentialism in the form of mark, which is really an acronym for meta-inferentialist account of logical consequence. I am assuming A bit of knowledge of the Of the sequence calculus in the in the background. This is not necessary, but it's sort of convenient For the explanation. If that's a problem, just stop me. I've got a What's his name? A marker and a whiteboard. I can be more clear about all these things. See the traditional story is that Logical consequence is a sort of inferential relation. So it's something like well, you can say that A and B, A and A implied B Have B as a consequence, right? So B is a logical consequence of A conditional that has B as A consequence and A certain formula that that also happens to be The antecedent of that of that consequence. So really when I'm saying that here A follows logically from B or the B follows logically from A or what you are saying is there is A valid inference from a logically valid inference from A To B. This need not be a primitive inference. It need not be a simple one. You get this complex as you want so that What I'm saying it makes sense and really If you look extensionally at the consequence relation, that is really nothing more than the class usually the set of valid inferences of Of a logic and the way you come to know this Extensionally determined class is by knowing things about valid inferences Now this is easier to see in sequence calculator in which Traditionally you have this sort of so as traditionally interpreted sequence calculator are taken to be Expressing a verified valid inferences generally. So if I were to write this in in a sequence calculus I would write this as follows A A implies B some sign which is called a sequence sign B so what's a sequence if you don't know what a sequence is simply take pair of collections of formula Which is usually written By way distinguishing with a sort of left hand side And the right hand side and you can think of what's on the right hand on the sorry on the left hand side as being the premises of your influence and what's on the left hand side the The Conclusion of your of your influence now. Why does this matter? Well, this is sort of nice Because sequence calculator are actually the sort of calculator in which if you are a proof staff You are producing sequence out of sequence, right? So if you have a a proof system, I obviously haven't brought my My what's his name? My charger This this is not what I want. I want power Can you see power? I think it was there But now for the battery before number four On the left Turn this play off after never I think this should do it. Now if I can write good fingers crossed. So What I was saying is that in a sequence calculus If you want to derive things from other things what you're actually doing you are moving between sequence, right? So if I were to try in a sort of vanilla sequence calculus Say for classical or nutritionistic logic to prove that B is a valid consequence of a and a implies b. I would have to apply a rule which What basically looks like this? Which is called the conditional introduction Right, can this make sense any more respondents, which is the rule here is in fact an ordination rule for conditioners Um Okay, that's a crash course In sequence calculus if you have questions ask them Either now or in the qna. Whatever. Whatever you want. I'm fine with being Being interrupted. So that's the sort of spirit in which one traditionally handles Sequence calculate, you know, you take sequence to express right five influences We try after all Nothing more than Specific claims of consequence, right? The sequence says tells you what follows from From what? Okay, so far so good. But of course there's a problem in this because otherwise I wouldn't be talking about it, right? So Here's a sort of range of problems. The first problem is that There's reasons to believe that valid influences or sequence under the term Logics Now this sounds super fancy, but it's actually a very very simple phenomenon We which might already be familiar though not in terms of Consequence relations, but rather in terms of fears So if you are familiar for instance with the logic of paradox grand priests logic of paradox, then you know that This logic has exactly the same theorems as classical logic Although its consequence relation is Completely completely different for instance in classical logic a contradiction entails Everything, right? Whereas that's not the case in in LP the same happens for instance with classical logic and the sentential fragment of a very bizarre Logic called dual intuition is the logic that too happens to be a logic in which A logic which has the same theorems as Classical logic The funny thing is that the same thing can happen with Valid sequence and valid meta sequence now, what's What's a valid meta sequence world or meta sequence in general meta sequence is really what I wrote here So you can think of a meta sequence as an influence between sequence an influence between influences on the Traditional account or in other words a meta inference, which explains the title of the talk meta inferential this Right. I don't like that Tenninology, so I don't like calling meta sequence meta influences mainly because I don't believe that sequence are Influences I I don't buy the traditional interpretation, but it's pretty well entrenched So I'm going to say meta inferential is And meta influences quite quite often meta sequence is equivalent to meta inference Well, I'm never going to the details you have how this happens How is it that you know A certain inference can be valid without the corresponding meta influence Also being valid. I'm going to ask you to take my word On that but if you feel like in the q&a Whenever you can ask and I'll tell you Why this why this happens the the phenomenon for those that know happens with for instance classical logic and something called the logic of paradox, which is Uh something called st logical strict tolerant, which is kind of relative of LPH I believe that it is LP but don't tell that to anyone that it's in writing, so it's fine Okay, that's the first problem a kind of under Determination has been a sort of very mathematically precise as far as problems Go you can pinpoint it Then there's another thing Which I call fragmentation. So you might think that this view or this interpretation of sequence as claims of consequence is actually a kind of analysis of The concept of logical consequence. That's sort of the formal analysis, but nonetheless, you know an analysis of The properties of Of logical consequence. Well, if you think that They never got a bit of problem in the sense that There will be no such thing as a sort of general picture of the properties of the general See like are known as it were properties That a relation must have in order to be A consequence relation why because sequence coming many sorts and many many fashions, right? Some of them require That the left-hand side Contains that the right-hand side contains no more than One formula populace For instance, and that's a That's property of sequence. We should have to understand as a property of consequence relation and The way you do it is a well, okay fine This just means that the consequence relation is single occlusion All right, it might be that my sequence can contain more than one formula or more than one formula Occurrence or whatever and this again is it is a substantive feature of sequence in the sense that methods This constraints matter they will yield different Logics in in many cases And if this is how your sequence look like then it's natural to take Consequences relations to be multiple inclusion For instance, by the way, uh, if you only If you're not the only one Thing here, then you are kind of constructivist Depending on what else is going on Uh going on there, but Really what I'm trying to say is that the difference between say classical logic and Intuitionistic logic for instance books down to how big The left hand the right hand side of the sequence can be so because there's Many logics. I'm not assuming that one or More or none is correct and just sort of you know looking at the world And I say that you know textbooks have Are talking about lots of logics, right? Now if you think that if you if you accept that's a theological phenomenon And you also think that sequence sequence inference is a sort of reasonable analysis of consequence Then at least prima facie you are going to have to say that oh, well, yeah, there's many ways of interpreting consequence and there's many ways of Understanding consequence relations and that might be a problem might not be a problem depending on whether you are a pluralist or Monist or so on and so forth or whether you have a favorite logic Or not The main point is that the decision on that is going to lie outside information about sequence and outside Uh, any sort of information that's carried by this sort of simple equation that says ratified valid influence equals Valid sequence equals a true claim of Of consequence this might be a bit of a a bit of problem There's yet another one which I called indetermination. So remember we had under determination Then we had fragmentation now we have Indetermination and This has to do with the fact that many logics are such that they can be presented by a sequence That have different structural properties, right? So I already mentioned the fact that, you know No cardinality restriction in the succedent on the left hand side Is generally a property associated with classical logic? Oh, well, that's fine because you know classical logic actually has presentation uh that Use only one Formula in the in the succedent I've already also said that oh look, you know, this is generally a mark of intuitionistic logic. Well, yeah, that's actually true but You know, there are also presentations of intuitionistic logic that have more than one formula here. So This means that Because it can happen that the same logic has Structurally different sequence calculi You end up with no determinate answer to the question. Well, is classical Consequence single or multiple conclusion I should add this all these arguments are fairly weak Uh, there's ways of Going around them, but all of these ways are Should very involved. They require a lot more work and a lot more information in order to uh, uh, To get off the ground Right. I'm working under the hypothesis which is not implausible that You know sequence and sequence calculi do provide for a kind of Maybe deflationist in spirit analysis of logical Consequence, I'm gesticulating scare quotes against deflationism All I'm saying I really should be saying lazy rather than deflationist, okay Now if these are problems then obviously a meta inferential account of consequence has to Do away with them, right? I wouldn't be speaking about it. And that's that's what happened. That's what happens. It turns out that if you, uh characterise consequence as a relation As you know, sort of the writer based on feeling if you want on Infances between sequence then you do get a sort of univocal Uh, uh, and perfectly determinate account of The properties of logical Consequence There's some people that disagree with that. They have reasons. They are very complicated reasons But more importantly these people are living in Argentina Argentina is very very far away Uh, therefore I'm not going to get into that but remember this as a as an asterisk and If uh If you want to know more about Don't you can ask me in the in the q and a So I was saying that you do get a sort of uh, uh, non-equivocal determination of consequence relations um in Is a type of there in this form in the form of a task and consequence relation, which is The most familiar Account of consequence. What's the task and consequence relation? Where is not in part sort of a substitution invariant? Break it down because I won't be talking about substitution invariance and what follows So logical Consequence relation is tasky and if it's substitution invariant that accounts for the logical bit The reminder is that follows this relation holds between a set of formula As premises a single formula As conclusion and you can because a single template doesn't really matter and on top of that It's also reflexive. So every formula entails itself is more tonic if I have a entails b then if I chuck in more Premises more things next to a it's still going to be the case that b Follows and it's also transitive right in the simplest case if a entails b and b entails seed and a entails See this is Tansky's account of of consequence And this is what you actually get in the case of sequent Now it's a bit more Here's how you get it. So here's how you have to think if you want To to get it when we are talking about consequence in respect to sequence We are talking about the properties of this single here, right? We are talking about the properties of Consequence in relation to Metasequence we are talking about the properties of this Line here, right? So when I'm saying that this relation is tasky What I'm saying is that this line here It's actually Tansky Has the the Tanskyan properties now there's you know, you you can The properties of consequence are precisely the properties of sequence to sequence That is ability in a In a sequence. I'm going to skip about the footwork Required for this is very elegant. It's not Uh, it's very yeah, it's very elegant and the form of mine Is the work of Glock and Jonson down in the context talking about the algebraic Like that super elegant stuff. We can talk about it. Well, so let's recap because this is just the introduction as it were And I'm already out of time This is the sort of meta inferential account of Consequence relations the view that logics are determined as consequence relations between sequence Rather than as consequence relations between between formulae This has the effect that task that the consequence is tasky and across the board even Importantly even for the so-called substructural logics now Substructural logics Let's simplify things even for Sub tasky and substructural logics and you can think of a Substructural logic as being sub tasky and it has if it has a consequence relation. That's not tasky So for instance, if you don't have Reflexivity if you don't have the rule that says that any formula enters itself then that Logic is going to be Sub tasky because it's going to be a reflection, right? now If you go meta inferential You are going to get The full complement of tasky and properties even for logics that inferentially are Sub tasky and this is where This version of meta inferential is defaced from the one defended by my colleagues and friends in Buenos Aires They think that you can have sort of sub tasky and meta inferential logics. I disagree with that um Okay Comes at cost obviously and most good things even if they're bad come out at the uh at the cost The first is that you can no longer interpret sequence as claims of consequence or as logical influences In the same way you can no longer interpret Structural rules as Stipulating the properties of consequence relations But if you want to know more about what the structural rule is you can ask me It's basically the stuff that I was talking about Before rather special version of the rules than rules and properties that stimulate the properties of of the sequence So this is the problem because These interpretations are if not natural then at least well entrenched. I mean there's a If you if you interpret sequences Influences there's a very very natural Correspondence between sequent calculator for instance and natural reduction Sort of illustrated that but there's also a sort of almost as natural Correspondence or relation between sequent calculator and axiomatic Systems of which I've said nothing before and I won't but if you want to ask Now Alternative interpretations are Available. I should know I'm working on one I like it. It's still not as natural as Or simple as the As the first one again q and a We need to manage this problem and It's not too hard Seeing as a philosopher's therefore we are in the business of inventing problems So it's not too hard to see that this management might be Problematic the first thing that happens Here is that you put some sort of distance considerable as it was consensual distance between logic logical practice logical fear And what I'm calling the phenomenology of vernacular Raising me which I take to be kind of object The target of logical theory is the thing that logical theories are Are about Which some people might argue should be at least an important guide The phenomenology should be at least an important guide in in in logical theorizing If not an outright constraint on it and historically there have been arguments To the extent that the way Seem to us pre theoretically should guide our Theoretical musings, I mean if you know you'll dumb it then you will remember that he goes on for pages in The logical basics of metaphysics saying I'm pleasant means about multiple conclusion logics Basically, this is a sort of generalization of the regular theoretically in view of generalization of the Preformal practice, but it lacks any sort of rational justification sort of basis its part You shouldn't be doing it Etc. If you know you're Genson then you know that you know when Genson touted the virtues of natural reduction One of the things he said is why this is the way mathematicians really think Right, so this this way of presenting logics Against the natural reduction comes as close as possible to the actual reasoning of mathematicians things Do you see in that way and a scary number of People actually take the natural in that in in natural that in a serious way. I just don't understand what that means But these people who apparently do Hopefully not here Right So To make things worse For you better for me because you know i'm talking about most substantive stuff if this is the case You also have this sort of complication that the meta inferential account of consequence while neutral with respect to logic choice Right, we've just seen that there's lots of logic that can fit into that That pattern is actually not a neutral account of the properties of logical consequence, right because it comes with the task in properties So it's again kind of natural to think that Well, if you're learning about such a substantial issue As the properties of a relation that's Presumably the object of your analysis, then you better do some kind of analysis Uh, right of the target system and you know sort of extract those properties on On its basis, but us We haven't said anything to defend Meta inferentialism that would come, you know, anywhere close to being a substantive analysis of Of reasoning Of inferring of correct inference. I mean, what's what's the target of logic? It's it's uh, what what logic is the theory of it is sort of Complicated, maybe we'll talk about it. Um, so this is an extra complication. Now I shall argue that This is a complication only if one is a foundationalist about Uh, about logic. Now you might wonder where it wants to be a foundation list about logic Why not? Because I've got things to say about that. Let's see how fast I can do it. Um So My argument of this is going to be well, you shouldn't be a Foundationalist about logic. I mean if not for any conceptual reasons then because it doesn't match You know with what I'm saying about logic and that would really hurt me I'm Here's what this particular is means is nothing more than a sort of acceptance or adherence to what I call The conjugated cases, which is very simple to do the sort of general broad idea that there is no kind of qualitative gap distance or space if you want between logic And the facts, you know the scapegoats That logic is supposed to account Uh for why the scapegoats because I don't want to do metaphysics. I just use facts in the sort of Vanilla way The things that people take logic to be about and this you know been Quite a lot quite a lot of proposals as to what those facts might be and what logic might be a theory of Williamson says that it's reality after some fashion of course is wrong unless him or his students are In the audience in which case.  I can't remember which version I think is Tyler Uh, but if not stewardship you Talk about mathematical practice All these being things that the logic reportedly Is called to account for Uh, just to simplify my life And to you know, sort of be in the realm of the plausible Keep the discussion in the realm of the plausible. I'm just going to assume that the facts in question Uh are facts about vernacular reasoning That are otherwise manifested in natural language All right, because this way I don't need to worry about Differences between linguistic and the mental and that sort of thing. I won't let alone reality or What not so in this case the continuity this is just because just becomes the view or the claim that Yeah, when you're doing logic Or rather that logic, you know, it's really a sort of enhanced version of reasoning in natural language If you want you know, whatever kind of phenomenon happens In in the vernacular. Well, it's the same type of phenomenon that happens when you are you know doing logical inferences in a formal system What not I mean there's many things That this might mean I'm not going to get into a sort of very precise scholarly Analysis of it. I'm just going to give you a few caring actions of Of the news it is a sort of possible tenets of a foundation These things like you know, logical some more quickly represents Moves already present in the vernacular reasoning Well, this is not precisely what genson said that is not all that far right what from what genson said about Natural deduction and oh right do take isomorphically in the Ethmological sense and having the same form now. Don't ask me what form is I'm a logician I can write books about that, but I still have no idea what it is in this in this set Then you know, you've got views like the criteria for logical correctness are already present in in Vernacular reasoning so on version of either rather set of Gloss on this would be that You know vernacular influences are logically valid or invalid irrespective of any sort of theoretical decision about validity less radically you might take this beauty be something to the extent that well, you know logical validity is to be regulated via our strongest intuitions about correct reasoning Then you might think that you know the the content of the conceptual apparatus That's deployed by logic to analyze Validity is essentially determined again by intuitions about Vernacular reasoning So all these are foundational instances and all of them are I believe to be rejected and I'm going to very briefly sketch two simple but I think compelling arguments against against foundationalism the first is Michael Granzberg's it's a version of the no logic in language argument Which might remember here historically goes back to at least In the fifties the other is a sort of reduction of foundationalism From logical logical nihilism Another ism will Get to that so Granzberg's idea is quite simple, but I think very compelling. He's working in a sort of more the theoretic framework and generally the semantics by way of Roughly tasky and with conditions and he just points out that the semantic analysis of natural language Is not in itself up to support The attribution of logical properties To to natural language. Why because you know logical properties are supposed to be general formal universities around But when you are when you are doing, you know, Davidson's semantic to natural language, you are not doing that So the difference if you want boys down to how you are use this through conditions You know knowing what the cat is on the mat means in English actually means knowing the actual truth Condition of the sentence the cat is on the map That's what you need to know if you're doing natural language if you are doing logic for instance, what you want is relative truth Conditions something like You need an account of what the cat is on the map might mean If say a certain inference is to come out as Valid under every deputation under everything that the cat is on the mat might might mean so Really my first point is that to get to logic you need to abstract and idealize At least and then you know also your entire outlook is going to be quite Quite different right and then there's You should have apparently compelling argument that Contegreaty generates nihilism. So here's what logical nihilism is. There's a few versions of it The one I'm talking about is something that's been investigated It's by Julia. No, I mean she's actually flirting with it enough to take it seriously. I think that's wrong So it's the view that Because logic is general University Validity that is a property that's supposed to be holding of every domain in every domain Domainlessly If you aren't on because there's plausible evidence then one can build counter examples to Pretty much every putative logical law provided that one looks at the right Domain then you know There can be no non-empty logic Right, so for every putative validity you are going to find a counter example. That's the That's the that's the general idea And that actually holds a bit of water If you are a foundationalist if you subscribe to the Contegreaty pieces at least if your domain of facts of relevant facts is natural language All right, there's natural language messy and there's really no reason to believe it is not messy enough To screw up pretty much everything that you might try to do in In your logic Now I actually believe that The problem is not so much that nihilism is wrong, which I think it's obvious, but rather the worrying about nihilism is Is is wrong? simply because it feel This worry is generated by positing that there is no filter No work Going from the vernacular To the logical I mean this is just the Contegreaty This is so you know you start with Contegreaty you end up With nihilism. Now what do you want to do at this point? Well, I suspect that Most of us would agree that the reasonable thing to do is to perform or adopt you and say and we've got to drop Contegreaty I mean otherwise, you know, we're going to be out of a job I guess there is no logic or rather, you know every logic is empty There's a bit more to be said about this. For instance, I very much think that This is that the nihilist conclusion is wrong You know, you don't get to infer that the logical consequence relation is empty So you don't get nihilism what you get is anarchist Which is really the view that material validity and logical validity collapse is such is a lot more Plosive And there's also the fact that, you know This would be a historically inaccurate description of the practice. I mean when people don't have done logic They've understood themselves to be operating with this sort of Sanitized version of the natural language Thing. I mean certainly frege Thought of the pregrif shift as being that you know a sort of replacement of natural language that's apt to support logic and as many other people who Reflectively have pushed for the same same sort of idea of the original taste and sanitization Niceification of this jungle, which is the nuclear reasoning Okay Very quickly fine But if you drop continuity foundationalism, what do you put instead? Well It's not so many options One thing to do one thing you could do is to think a bit more Clearly about why this entire idea of you know, regimenting natural language might Might me and the obvious option here is to sort of think of Whatever it is when you are doing logic or whatever it is when you are using a formal language It's being a kind of modeling process in which you are building Models of a certain phenomenon is to mess it to be Grasp as it is that's fine. You build a sort of simplified model You investigate its properties and then perhaps you can move from those properties to the properties of your Target system and this is the sort of logic as modeling approach which has been Defended by Stuart Shapiro and Roy Cook I don't like it Let's see why so This is an important not merely motivational quote. So I'm going to go through it Completely it says that this PhD thesis in 2001 The philosophical logician in is engaging a April sterile or a scientific enterprise of describing mathematical practice Notice that the facts that Cook's talking about are not even the vernacular in general the problem Logic is a tool not for building foundations, but For constructing models of mathematical practices Uh, the actual day-to-day behavior of the mathematician is something To be considered as a natural phenomenon to be described explained on perhaps predicted and possibly Improved logic is a tool for description not just prescription So this illustrates one way that you can think about this entire modeling modeling business as a kind of descriptive Uh procedure And is this part of it This sort of epistemological descriptive is that I don't quite like At all now, let's see how this works because you know, I have a small question for my face So there's pros prescription That's the same as prescription or does it mean something else? Yeah, it means interdiction. So it's supposed to be a Palm It's not a typo It's not a typo I did if it's typo it's It's Roy's but I think he actually means proscription is prohibition Logic we the thing that there's no reason like that And that actually makes sense because you know one of the one of the trains of the view would be a suit Would be the rejection of revision About logic and ending of revisionism has been you know, sort of a proscriptive not prescriptive and proscriptive Stance So here are here's how things are supposed to work. Oh before that. So notice that this might not mean all that much Because you know for one thing I take this view that logic has a modeling component or dimension to be almost trivial for another there is a very informal use of the word model the that makes Its meaning goes almost indistinguishable from the meaning of theory So, you know often they will say oh, there's just a model of what our meaning is something like that I'm just giving you a theory you know what What the zoologist does some people might describe as being you know a model of tigers in the world Right. That's not a model. That's a full-fledged theory but The epistemological picture which is highly descriptive And which repudies the traditional normative of of logic is quite it's quite prominent Here and I would urge you to keep it to keep it in mind. I'm going to go five minutes of the time I'm afraid. Okay Um So here's how things work. I'm going to skip this part right, so They do in fact, but but Cook and Shapiro end up talking about models in a sort of more substantive sense, you know in the same sense in which tiny car Made for various reasons can be a model of a genuine real Real car. So the way things work is that a model presents you with a sort of dual Dual ontology you've got things that are representatives and things that are In a model. So the representatives are elements of the model that either correspond or are intended to correspond To real aspects of the of the target phenomenon So if you're thinking about logic for instance, and you might think that the potential variables I mean, there's a very obvious On the whiteboard, but think of them as variables That you might think that the potential variables in the potential language are representing natural language sentences for instance Truth bears real truth bears In general So they will make them representatives then of course you've got artifacts Which are sort of weird creatures That only exist in the model that are generated by the model that don't match don't represent don't sort of Reflect in any way Form of shape on the on the target Sees so if you know, this is the example thing it's actually quite Quite good one. I mean they're talking about vague languages But we can simplify things. So think of the fact that they represent the truth values with the one on On the zero and then you know starting from assignments of truth values to The potential variables they actually mathematically compute for instance in the case of possible logic the truth values of the of the Um Complex sentences now the fact that you know, we do some a bit of elementary arithmetic In order to understand the truth value of a complex sentence is Artificial right when you are reasoning about p's and q's and o's and n's and n's Uh, you're really not doing a written thing. I think something else, but you know, we simplified calculations in basic arithmetic we can sort of meaning meaning that Quite successful now this is Very quickly this view. I think it's problematic. So for one thing they they say that the Artificial representative distinction is vague Not just in the sense that I can pick Represents that are quite different from from yours. There's just a sort of inherent pluralism of any sort of modeling enterprise, but really the thing can be vaguely Described as you know both a representative and an artifact. We don't really know which ones which Uh Which Simply brings about the question. Well, why have it? Why why keep it and the only rationale for keeping it is that you sort of want a kind of glue Between your target phenomenon and on your model, but this is really no need To advertise that glue as being, you know, represented Strong when in fact, it's not clear that the representative is not also an artifact I also I'm a bit worry And worried about the fact that the view abandons the traditional Prescript or aspirations of Of logic. I mean sure we get a better understanding if you are doing intuitionistic logic of what intuitionistic mathematicians are Doing fact Mathematicians in general, but intuitionists in particular are weird Nobody should have a better idea of what they are doing. They're just bizarre people I hope there's no that's a joke, by the way Let me clarify that that's a joke. I actually believe that the intuitionism is the one through logic that, you know It's a verification transcendent to prove it This brings about the question of what exactly is the point of having something Like a more abstract model of a practice if that model is merely of descriptive Value and that's a hard question I also have this lingering suspicion that the descriptivist epistemology In a sense renders the view just as foundationalist as safest medical conception of logic Except for being, you know less ambitious because it's descriptivist, right? It's not Nomitivist, right? So instead of using meaning for instance as a guide to your reasoning You know, now I'm just accurately describing what you are meaning and the only Sense in which this can guide your reasoning is sort of accidentally If it still happens that you don't really know your meanings and you need a sort of better grasp of them for these reasons I'm just gonna say pass Yeah, no, this is this is not the kind of view that a meta inferentialist should Induce or should use to bolster the case for mark Do we have An alternative? Yes, we do. It's called constructionism. It's way better name And it's it gives a bit like this Florid, Luciano Floridi in a defense of construction Philosophy as conceptual engineering parentheses, the only part thing about the view Is that it's sort of connected with conceptual engineering Which is a great idea, but if you know the literature or rather the common state of the literature on conceptual engineering Then you know what I mean. I really should not say these things That's I can't help it. It's my nature I hopefully nobody's online, right He's what Florid is says Florid is says knowledge is not about getting the message from the world It is first and foremost about negotiating the right sort of communication With it and if you remember the thing that I most dislike about logic as modeling I it's sort of descriptive Orientation Then you can kind of understand why I'm tempted by By this view, right? He says look, this is not about Getting what's going on in the nuclear reason. That's not what A model for instance should be doing first and foremost Really what the model should be doing is sort of giving you the right tools for interacting With With your target phenomenon and you know, luckily Florid and other people See a bit more About about all this and in fact what I do they give you another sort of model of A model and another model of the sense in which logic my work as a model for the For the nuclear reasoning Which in actual fact might not reject description is But it's not married with it. It's not, you know, intimately connected It it gives you the opportunity the option to step away from a very Descriptionistically involved position so The thought is that one goes on to conceive of logics on the whole as artifacts Of a certain kind and there's a kind of cognitive technologies or tools That are used to improve and correct One's inferential practices now, of course when it comes to you know, the sort of fuel a sort of fuel like meta inferentialism you've got a you know climate Around up the ladder, right because it's not really the actual interaction Practices that are under debate here, but there are the debates about the inferential Uh, uh, uh practices, but that's a sort of minor minor minor difference, right? So The emphasis is on improving and correcting and Generating a better understanding of the phenomena than on describing Anything and you still talk about models. It's just that you talk about models in a sort of different way So here's the architecture of a model And the role of a model in a theory according to florida and Patrick color So if you want to talk about the target system, then you sort of need to decide at what level You want to talk about it? I mean the simple analogy here is you know physics and chemistry Built our concern with atoms for instance The substances et cetera They are not the same. Why because they are sort of operating at different levels of abstraction In a sense Um, so what's the level of abstraction? Well, it's nothing but a collection of observers which you know, you can formalize variables Good let x stand for cats Let those things why from the y category stand for dogs And so on and so forth which is really The stuff you are using to formulate a fear Of the system you are talking About of course, you also need to describe the behavior of these Very of these observables Cats are afraid of dogs or irritated by dogs Dogs chase cats Cats are way cooler than dogs, et cetera And this you can formalize this as a sort of complex predicate In in in your system as important, you know that the observers are not representatives Why there's no sort of assumption that they are intended to stand in any sort of scripted connection with The things in your target phenomenon, because in many cases you may want that so you might as I say moderate them So I have to be realistic for the For the system, right? So this sort of means that You know if I'm If my target system is human behavior Right, then when I'm picking my Observers I'll make sure for instance Not to have things like Measures that are incapable of expressing the acoustic Reception capabilities of humans, right? Because there's wouldn't be useful At all See together the behavior and the observers generate a model which is sort of replacement object for your target target phenomenon and it's An object that can be investigated and that yields a set of properties About the model Importantly which you can in fact attribute to the target target phenomenon and here's how things look Right, you have a level of abstraction that alongside you know a behavior generates A model on the basis of which you identify some properties And this is all theory, right and those properties which are properties of the model Are then being attributed to your target target phenomenon So a model is not going to be conceived as first and foremost an idealized description of a target phenomenon Instead it is to be conceived as an interface I assertive Means of communication between two distinct distinct systems, right the system target phenomenon or This corner of the diagram and the Theoretic system As it works that supplants and replaces Replaces it. I mean, this is just a very nice Metaphore, all right, I've got Okay, so with all this in mind you can sort of See how if I'm a constructionist I can really go the trumpet Of the meta inferentialistic consequence because now I can point to Things like oh, look, this is a very flexible and very powerful interface. It can fit as many logical Lots of logics In it right in a uniform At the same time I had the advantage by being a constructionist and you don't need to worry about The fact that you know I'm representing what appear to be influences between truth bears As a sort of influences between more complex objects that really aren't to be interpreted as Truth bears are your sequence because the nature of the sequence is not that of being, you know True or false or having a truth value in general It can but it's not So this means that we can Enjoy all the theoretical benefits of them of meta inferentialism Without worrying that they are obtained by theft instead of honest on a story and we can also defend it in in a manner We can also defend the fact that it comes with a thick notion of consequence right with a with a fixed set of of properties of the consequence relation in even without presenting that as an analysis Of some target Phenomenon because it doesn't really matter. I mean it doesn't matter whether you're reasoning Whether it's reasoning is tasking Or not what matters is that being in a consequence being tasking is a powerful tool for understanding that reasoning and I sort of venture to say that It's not This thing this the in construction is is not going to mean that we'll have to abandon the familiar tools Of the foundationalist view. I mean that's just because I'm writing a paper on how many which is A very foundationalist thing, but that's why I need that here. Okay, so that's about all. Thank you so much. Sorry for Personally I have a list okay, then who wants to uh wants to start Okay, good night So, uh, thank you for the talk and actually I pretty sure agree With your idea. I mean, it's not so often like I put any From you. Well in my defense, probably not a single one is mine. Not a single idea I guess of course, it's not the only one but I mean, uh, I pretty agree. I just wonder Well, two questions. What kind of logic would be the most appropriate maybe to to start this kind of what you call communication probably communication with molecular Reasoning so do you think the classical logic is the most appropriate or you can make some distinction And also, I wonder if some other model Other than logic can be useful to understand the natural reasoning and what part they have in the process Yeah, okay, so can I please start with with the second question which has a much clear Answer If I'm to take your question seriously, then yes, of course There are other things that can provide a Model of vernacular reasoning But that's not what you want to ask what you want to ask is how good a Model of vernacular reasoning is logic It's terrible. It's a very bad one. It's It has nothing to do with vernacular reasoning. So now let me backtrack Um Because in the paper version of of this, I'm a lot more careful about about this I don't think logic is about vernacular reasoning first and foremost. I think logic is about, you know, the objective conditions for correct inference where inference is not to be thought as a sort of Uh, psychological process if they not as a sort of process that's only open to Human human agents, but rather as a sort of Now I'm going to go a bit circular but Don't worry about that as a sort of mathematically described Transition Between certain certain entities So yes If you are talking about if we are talking about vernacular reasoning definitely, I would say obviously so mainly because logic is it's terrible I'm doing it with the cord out that despite appearances to the contrary. I'm really not interested in vernacular in in in in vernacular reasoning I'm going back to the first question Right classical logic So when I said that I think damn it is what rather than I said that intuition with me is v1 through logic I was obviously killing But uh, I wasn't Misrepresenting my biography uh I still think that There's something that intuitionist ecologic gets right More than there is intuitionist ecologic improves In respect to uh, to classical uh, to classical logic um Of course officially I'm blue-bravest I'm a logical pluralist, so I think that yeah many logics will uh, will serve Yeah, I really don't know how to answer the how to answer the question because it really depends on how much as it was I'm going to take that as an empirical question or a question about an empirical Uh, net And then it all boils down to you know, how how much do you want to invest in in your tools? Classical logic simple Uh, pretty much you are forced to learn it. Uh, I mean there's at least the end of I would think 40 percent of The programs in any decent university will offer you the opportunity to learn classical logic So it's in most cases going to be the best tool you've uh, you've got There's a lot of literature in the wake of wasps and Cart test That actually argues that classical logic stand As a starting guide for Investigating vernacular vernacular reasoning is just a wrong tool. I would give you the reference but Uh Standing is the second quarter So, yeah, it might be that it's just the best and easiest tool to come across Pretty rubbish On on its own Uh, if If I got the questions wrong, yeah, very well, and really I'm not for the The second question so the first one's for I have a quick follow-up I just wonder what is the statue of the legal object according to you? Are you kind of platonist in some way? Yeah, because you you guys you can mean that it exists in some way Independently of a human reasoning. Oh, it's the way Can I take a pass on that? It's I might end up You know, so okay I'm happy to think of them as abstract objects now. I love abstract objects I mean frankly my only friends are abstract objects. Do I think that that's more of a problem than You know problem with myself Do I think that they are objective in some sense? Yes Do I also believe that they exist in a sort of realm Of their own, you know, fragrance Third reality or what not? Yeah So I suppose I would be a sort of Species of realist To the extent that I I believe that, you know, this is These are objects of which objective Truth value wise discourse is possible But I don't think that you know these these have a sort of special ontological Status I think I'm a constructivist Uh Broever thought that you can talk objective here about mathematics, although it's all In your head provided, of course. I mean actually brover thought that it's in his head Yeah Yeah I said in the last like transcendentalism in that sense a lot more which is not related to Human land It was tough. I think peter was next So I'm wondering thanks a lot for presentation Uh, but I was wondering In how far this constructionist thing is very different from Old-fashioned carnappian Explanation, uh, you know It seems very similar and and and for me that always did the drake and I didn't have to go to fancy No, but what is what is added to that? A cool name No, that that's that's not correctly That's not actually true. So From what I've said not much I'm friendly. I don't care about The construction is story in you know beyond Many of the things that one could have recovered out of sort of carnappian Explanation explanation story I've Well in in a sense again And One of the reasons why I wanted to stay away from carnapp apart from the ways that He's getting abused in the conceptual engineering literature is He's sort of overarching conventionalism Which at least when you are talking about logic, you know, it becomes kind of kind of problematic Uh, if not in actuality then at least connotation connotation But Okay, so that's that's one one way of answering If you want the question is the strong similarities between a sort of carnappian explanation project and the sort of Thing you get out of out of construction is Uh You talk again about replay. I mean carnapp is talking about replacing concepts with With better concepts here. You know Sure, the observers are conceptual in the sense that they are not you know as in Empirical science things that you can actually observe in some cases naked Naked eye And there might be some minute sort of differences of architecture of You know the mini the mini projects if you have a sort of project of constructing a modern constructionist or project of providing a carnappian explanation They might they might sort of sort of differ what But to the justice to the constructionists So the tools seem to be a bit more sophisticated. That is when they are self self reflective You know operating in self self reflective mode And Yeah, that's pretty much it I think pilaf is next I don't know if that's just one question or two I was trying to Understand the stitch in between logical smaller and I was trying to Think of a situation. So I guess the logic as model as I understand it if for whatever reason We wouldn't use these junctions and we only use like as normal speakers It's equivalent in a in a conditional for instance the logic as model Have a completely different logic with these junctions and have a A hole in the logic they could be introduced as the equivalent but not Being connected and in the case or what you want to defend is that Even if we don't use these junctions as They are so that wouldn't have any impact on the right logic that we want we would like to Model It's not wrong. I mean, I think I may have given This impression They have slightly more sophisticated that that's a good analogy You know, but I think it'd be Unfair to the logic as modeling People to give the impression that that's all that This is this is all All about because So you might think that you know Given that there's A disjunction natural language then ended up with the formal language that you know, say it's a classical formal language only has conjunction and And negation which is perfectly enough You know the lack of A primitive disjunction is sort of artifactual Right and that's certainly something that they would agree with and You know, it's it's correct as it were But it's very sort of very simple Simple simple case and then things get fluffier or hair If you see the standard If you are looking at, you know more complicated models And the southern example in the literature which was provoked by them has to do with vagueness for instance So suppose that you are operating with a model of vagueness that Uses sort of realism between zero and one as your assignments of value to To sentences containing They predicate Now that's obviously, you know artificial why zero to one rather than 17 to 47 You know, it's the same is the same thing In a sense But there's there's a sort of legitimate worry that even when we are doing that you are still doing something wrong Because you are assigning a precise numerical value Right to something that your intuition tells you should not be precisely Quantifiable right, I mean that's the the whole point of yeah, it's all ish you know If if vagueness is not epistemic for instance then, you know The point of saying that somebody is kind at all is not saying that they have a height below above 0.72 Right And it's not that it's wrong to say that it's more than Assigning a determinate Value is wrong Even if you think of real this was kind of sad That still doesn't cut it because you know every real is going to be a precise set And really you should be thinking in terms of fuzzy sets, but then you know You Which is right, so That's that's the sort of uh, that's the sort of worries that really animate Then but so Going back to the constructionist I think I might have given the impression that this is so that they are freer or significantly freer And in a sense that's true in a sense It's not because if you think in terms of you know setting up a model of a certain phenomenon I mean whether you're a modelist or a Constructionist you are still going to be kind of bound by pre knowledge As it were by Things you know or notice about your target Target phenomenon, you know, if you're talking about language and logic You might think that you know, there's really no need to represent natural language or English using fragrance syndics All right, but you might think at the same time that there's still the need to kind of represent in this Whatever syntax I have Uh the logical uh the logical operations because that's What I think to be the logical operation so Even a constructionist is sort of bound by Information pre theoretical if you want information about the target system I think the the difference is mainly one of sort of emphasis I think then the first folk The model is as it were I'm still paying way too much attention To making sure that the models are accurate. Which is why they're worried about representatives. This is out of it The logical model is it's not linguistics. It's nothing So there is also a normative dimension It's not this is how people reason it's an idealization Of so there is any idealization of this is what people do and then I don't know I'm trying also now to draw distinction between linguistics pure linguistics About even about the the notion of follows from the linguist kind of study and the logical Yeah, well, that's I mean cook at least very very voice vociferously The hints are the fact that in sort of things things of Lord urges us to think of logic the same way one would think about linguistics In a sense, you know, it's being merely discreet if sure it might provide you with more information Right because things are simple, etc. And there's always that impossibly long bloody inference That nobody has ever drawn Or ever will be but that logic, you know, kind of can can handle but that's not to be understood in any sort of normative Normative sense, it's really to be understood as a sort of description of the Of the practice. I mean again, I think calm up comes in here Because for various purposes various models might be better Or worse and if you've got a peak which one then you you are facing a an external question in in karnabs karnab sense, but The better of the logic as modeling view Has to be first and foremost a Descriptively better. So it's you know, that model is the answer you give to the question Which of the two models that I have provides me a more accurate description of the target phenomenon given my interests Right the constructionist is going to give you the sense of the thing. I am model, but it's going to Give that while answering the question which model is going to Give me a more efficient representation Of the problems I want to take and the representation here is non-representation I mean, I don't know if that answers your question Yeah, I want to this is this is good because this is in the same kind of direction But I'm not a logician so I'm going to ask it in a very different way And go kind of sociological So it strikes me that one thing that's interesting about this constructed this view is that it would have an upshot for How we should fight about logic in the literature, right? So if we all become constructivist So today Yeah, just because Sorry. Yes. Thank you. I caught myself when I said it. Yes not constructivist already means something. Um, very else So if we're constructionists, um It seems to me that there should be a healthy genre of papers in the literature where we argue in a kind of Hybrid of logic and pragmatics about this adequacy of our tools to our ends Right, and so I'm wondering if and these so this isn't because of because I'm not a logician I'm actually wondering if Do you think that actually those papers are already there and once you become a constructionist you realize that? Hey, a lot of these fights that we've already been having They're actually exactly this fight about sort of how good is the tool for the job Or do you actually think that like no, this would make logical practice better because like we're not having these arguments And actually we should be having this debate more directly with this sort of Availably pragmatic flair about like are the tools that we're building adequate to do the job that we want them to do Yeah, okay, that's a neat one. Uh Uh Yes and no So there's certainly Almost no literature that's self Consciously Representing itself as being about doubt. Oh look, I I provided with the sort of that Uh, as it was set of tools or whatever That's because we are you know, philosophers.  We just care about you being wrong That's all that matters. I mean, you know All that matters is that somebody else is wrong. Sorry. I'm I'm I don't know Yeah, almost Uh No, so there's very little self representation in that in that respect many of the things that people have said in one way or another You know can't be reinterpreted and as So logically somewhere in this spectrum between philosophy and mathematics Provided as there's a sort of interest in this broad sort of topic of you know Being I think the Italians would say constable A way of what you are doing Uh, the more you move from the philosophy side to the to the Mathematics side the more you're going to find, you know Proposers Advertise something as being a slightly better tool a more efficient Approach to etc Uh, etc. So, you know this this people Which tend to be french which tend to be connected with giard Which tend to be living there for in Marseille or they're about to care a lot about computational complexity right My computational complexity is a very very sort of important instrumental if you want even the philosophers who do that know that they're working on a tool Exactly. Yeah. Yeah. So, yeah wrong now Philosophers will try to make a big facet of failures of or failures I mean insufficiencies in terms of computational complexity The giland's mathematician postdocs just churn out results Sigma pie, etc. I have no idea what I'm talking about but it looks fun On the other hand many of what there is can be approached in in in that sense and there's glimpses of that You know, so for instance, there's people who are saying well, you know Intuitionist Mathematicians or logicians and classical mathematicians. They are arguing about all sorts of things But really they shouldn't be arguing all that much because you can look at the intuitionist as just sort of Being sociopathically interested in in a subclass of results that are Available to the classical mathematicians pie tends to constructively obtain So I guess that leaves open the last little bit. So do you think it's a uh the normative side? So do you think that that is a conclusion of the view that we should be doing more of that kind of stuff like the mathematicians do? more sort of self-avowed tool evaluation kind of stuff You can pass on that. You're allowed to pass on that. I think it all depends on the evolution of the job Sure Let's pray Let's pray Okay, has anyone Does anyone who has not asked a question yet want to ask a question? Okay, then I can ask a question Okay, so thanks a lot great talk. I wanted to push you a little bit more about why not sub-star skin meta inferences uh so Just uh, so as part of motivating my question. So it looks like like so In the determination phenomena I don't know if you agree with that, but I think one could say that Some of the those uh In in determination phenomena are kind of like Not accidental, but I mean so You you can formulate the etiocytic logic in a multiple conclusion sequence, but it will last it will lack some like Natural properties or you can formulate like invertibility or something like that or you can formulate a classical logic in a single conclusion Sequence calculus, but again, you would lose like the elegance of the multiple conclusion So even though you have this indeterminacy That it might be the case that I know it is a case for all the cases of indeterminacy, but in In a lot of salient case, I think it's best to say that it's not completely arbitrary to single out like one most natural candidates as like And the and the sources of indeterminacies are Kind of like some technical accidents, okay? It turns out to be possible to present it in another way and and then It seems like if you accept this kind of indeterminacy as a as a legitimate source of worry or then you you can I mean, it's not like a Necessitation, but you kind of get the same kind of worries If it turns out that you can present Like meta-infringential calculus that are that become like sub-tar skin I mean, I I don't I wouldn't know how to do it technically, but I doubt it's like impossible to to to have the same sort of like Alternative formulations that are tar skin and And then so the the question is like what's wrong with them? Why should we stick to a to tar skin meta-inferences? right See that there's a lot that's going on in in Motivation a lot that I agree with and a lot that actually connects with my Sort of faster this week my taste is within my my top, which it was that you know, these are not very very strong arguments They're just sort of giving you a flavor it's just sort of bait to Pull you on the side of the meta-inferential is rather than you know knock out arguments against the inferential is view So with one of that I'm actually in full In full agreement now sub-tar skin and meta-inferential this is a rather complicated Story on its Actually technical so here here's One way when I'm saying that a certain logic is Reflexive from the meta-inferential standpoint what I'm saying is that this sequence Let me write it as a as an identity sequence. What I'm saying is that this sequence entails itself right The brackets are just for visual Clarification Now entailment semantically this this this relation of entailment here ends up being preservationist a relation in my favorite case is going to be A relation that preserves satisfiability the satisfiability of sequence rather than the Validity so to say that you know a sequence in terms itself means that roughly any valuation that satisfies That sequence in premise position is a valuation that satisfies that same sequence in in Sequence position so basically if you want to think algebraically about it you are in a space in which You have two truth values I'm going to call them six which is satisfied and seven which is unsatisfied Six is designated right Seven is non-designated right And consequence is defined preservationistically Right, it's easy to prove that any relation of this kind Is tasking Right, the only thing that's kind of I might also be a score relation. So I might also be multiple conclusion That's the only thing that's not ruled out for free although it's ruled out in some cases If you go to some valuation Super valuations Okay, so that's sort of the first As it were the script part of the answer namely that the the task and character of the of the relation is sort of unavoidable Because it's just a mathematical property if you want of of the syntax of the sequence on the one In one way or the Of the properties of a logical space in which consequence is preservationist And you are operating with two values Okay, so you want to get you know You want that not to be the case you want that not to happen because you want to go subtle Sometimes what you can do Except the way you do it or the way you need to do it and this is This is stuff that's been done by at one of bio pilots and Damian Snoop, I can't remember how to spell Damian's last name, but if you know this So where's the z it's after s right? I That's that's the I'm sorry Damian if you're anywhere Sorry So How the I mean if you already know the story then why are you asking me because I don't know what they are doing So what they are doing is actually they are sort of breaking down the preservationist dimension of this thing because they are evaluating premise premise position sequence according to one sort of standard of Satisfiabilities, they call it standard alpha and then you know, they are evaluating the second according to a standard that's beta and it which is this thing from From it might be related. They might even be you know, sort of Generated or this generable one from the other which is exactly what happens, but they are nonetheless This now If you are like me once you're going to believe that happens here Is that this is in fact a vocation? And this relation does not say that this sequence entails The same sequence this is going to say that this sequence Mark right In there is this sequence another mark Which is a different relation from the one that you want reflexivity to To be Now I got To bits by a referee Because I said that because the referee said so But you have a definition of what the sequence is a sequence is just a pair of sets of form From a certain from a certain language and if you take that view Then you should be referring papers Ha Sorry, I'm kidding So if you take take that view what I'm saying here about a vocation doesn't Doesn't hold water But You know, this is more than just pure syntax In a weird language is more about you know, how do I the syntactically define? Sequences about what's the sort of information they care And francesca and i we've got a story about what this is The story is Our sequence are in a sense integrity and they mean something It's not something as straightforward as Being an influence, but they mean something and what they mean is strong enough to To support this claim that there is a vocation Going on here. So the the answer to the question is yes, you can go sub task here But you're equivocating when you are saying oh look, this is reflexivity you are wrong right So if you remember the actual example Or rather the simplest example in the Buenos Aires plan What happens here is that this is going to be a non-reflective non-reflexive Logic in which you know a entails a might hold for a particular choice of a but it doesn't Doesn't hold As a rule right whereas this one here Yeah, so this relation is not reflexive and this one is non transitive. I'm saying look This is not I mean I'm saying that this All it's you this does it all you are not saying that It's this sequence that fails straight there's itself what you are saying is that this sequence fails straight there another sequence it is a case of under stone style Heterogeneous and logics rather than a failure of Repetibility but that's not what Federico Just a quick Follow-up, but it's ready for later discussion over here. So it turns out that we with peter and pilar we're interested in Meta synthesis like some kind of Meta inferences you can calculate that are Sub-star skin because the arrow that you have in the middle is supposed to express grounding So that's so you expect it to be non-tar skin and You can represent the ideas to start with particularly like that and then get to the full presentation of Classical logic or any other So do you want to hire a trans-pattern or a grounding? Not Maybe you can talk again later. I don't want to hijack the discussion from our work. It's you are the star here But that's that's kind of where part of the reason why I wanted to know more about There might be other questions. So that's sorry, that's uh, Let me just answer this question. That's perfectly legitimate legitimate move because if that double out of there means something like grounding You know, you're not bound by Anything to do with satisfiability and you can do with preservation of anything you are just sort of You're bounded by those things, but it's even stronger Yeah, okay So it's kind of related to ps question, but uh, do meta inferentialists Need arguments to avoid dropping to meta meta inferentialism and meta meta meta inferentialism Or is it just like can you be just performing that this is a good level of complication of abstraction and we don't So there's two things that can happen here right So you go to the first meta inferential level I apologize to the other people for asking me This discussion doesn't have it doesn't make any sense. I mean once Meta inferences are bad enough when you get to meta meta meta meta inferences you should go home Again, so There's two things that happen once you are the first meta inferential If you stick to the criteria Of validity judgment that we've applied there then everything above Is going to correspond nicely to the first meta inferential So Yes, you can go Why should you because it's just a sort of syntactic translation in an increasingly more complex levels, but they are really compact if you want no point if you want to go in a way that's not 100% Repetri to the first meta inferential level then you need to go Buenos Aires style, which in my book means that you are committing an error because you are Equivocating Many people don't think that you are equivocating for instance. I just don't understand I mean many people who are not important as high So for instance, you know, David is quite adamant that the determination of the standards of goodness for The the meta sequential Influence relation is kind of independent and pretty much available and somehow it still makes sense to So he says, oh look if If you have a standard of satisfiability that applies at level one That doesn't mean that you need to hold on to it at the second At the second level But at the same time you still get to talk about the same And I just Can't wrap my My hair up around that I can see what they're coming from. I just don't see why He doesn't see the obvious How you tell in fact you You come so if you are My kind of meta inferential is that you are going to style yourself as a fine 90s Meta inferential is of the first level that's as far as you need to go because if you go higher you're either wrong Or just taking a stroll in the park, which is very nice. It doesn't solve any problem. That's a bad analogy Maybe because strolling in the park can solve many problems the from a constructionist point of view, I guess is it the stroll in the park Can you exclude it so like if it's No, but Yeah, no, no, I I mean there's nothing wrong with looking at it You know with looking at what what happens at higher meta inferential level. It's just that You know, there's no game And that's enough to not go there. Exactly. So it's not In a sense the problem of whether you need one meta inferential level or 77 meta inferential levels is What's the name? It's debunked. It's It's irrelevant because every higher level is going to behave in the relevant respect as the first level So That's an interesting feature and and it seems like philosophy speaking then what you really are doing is instead of being meta inferentials being Inferentials at all levels higher than the First inferential, I mean, you know, yes, it seems like you're not the right level of Of mobilizing you're doing Constructionism mobilizing Is not only for the but also for Everything more than inferential, you know, yeah, you know that technically they may not make a difference, but If you want to know what you're really talking about may make a difference So, oh, yeah, I see I skipped this because why not? But the official statement of the inferential disposition of the finitism of the inferential disposition is actually the following logic is determined as a consequence relation on sequence As well as any other consequence relation that start that's rocky on some similar to that That relation are problems and similarity here just means that You know the two consequence relations are mutually translatable Consequences so Although I say that consequence is between sequence that doesn't prevent me from seeing Define the same consequence relation between formula for instance provided I can translate my sequence into Into formula, which of course I can And the same happens up the hierarchy if you avoid Buenos Aires style Equivocation, so it's always possible if you stick to That thing there it's always possible to to to show that The consequence relation that you get at level 67, which is a consequence relation between meta-influences of level 66 Is in fact blocky on some similar with the consequence relation that you get at level one and therefore there are one on On the same I think we're out of time so you need to reserve your questions for the peer session Thanks a lot


1. Plots are commonly used to compare sequence sets quickly and provide a synthetic overview of similarity. 2. Dgenies is a standalone and web application that performs large genome alignments using Minimap 2 software and generates interactive dot plots. 3. Dgenies allows users to sort query sequences, zoom in on the plot, download various files, and is an easy-to-install open-source software package developed in Python and JavaScript with source code available at and testing site at. This article was authored by Florio Cabanets and Christoph Klopp.