aboutlogic #10 | Seunghyun Song & Jordi Fairhurst – ABC Conjecture, Epistemic & Linguistic Justice

00:00:00: And that's the imperialism, the epistemic imperialism that Jordy was talking about.

00:00:05: Of course this doesn't just occur because of the ways in which the hormonal resources interact with each other but because of patterns and history of injustices... ...that exist IN THE WORLD!

00:00:19: Which is a non-ideal context where we have to conduct scientific studies.

00:00:29: Hello everybody welcome on our newest episode of About Logic And today we shifted the organization a little bit.

00:00:36: We have two guests and not two moderators, maybe that's more nice way?

00:00:41: Maybe otherwise... ...we had in one episode to comment.

00:00:44: this looks like cross-examination!

00:00:49: But I'm telling you because it is one of many themes.

00:00:52: we will touch on how design things or get everybody to contribute.

00:00:59: But before jumping into the topic, let me first introduce our two guests.

00:01:04: Sangyong Song is a professor at Tilburg University and Jordi Faerst currently visiting the Kaolüven.

00:01:12: but it's normally affiliated with the University of the Balearic Islands in Palma And we know each other for quite awhile.

00:01:21: We did some projects together or met at conferences.

00:01:26: I'm very happy that you joined our little podcast.

00:01:30: Thank you so much, I am very happy to be here!

00:01:33: I hope i will be able to provide you with some nice insights

00:01:38: who are quite positive about that and also about like other perspectives because today is not only Marthe episode but the math will of course still play a role.

00:01:52: yeah let me start two, three sentences what you are normally doing and maybe then also What Are You Doing?

00:02:04: where philosophy of math comes more into play.

00:02:10: So Sangham first maybe

00:02:12: Okay Hello everyone so I'm Sangham Song.

00:02:17: I am based in Tilburg University the Netherlands.

00:02:21: I conduct research In Three broad themes but they're all related.

00:02:27: The First Thing is i do something called theories Of Justice specifically concerns of justice that lasts across generations, so long-standing issues.

00:02:37: And I apply those to two things – one is knowledge which is the reason why i'm here because obviously mathematics and mathematicians at their academic output are related to knowledge making or knowledge production processes And the other one is language, which was also something that I do research quite a bit.

00:03:05: So those two are my field of expertise.

00:03:09: I'm dirty as Dennis mentioned previously.

00:03:11: so first thank you for having us on because it's always very fun and enjoyable to have!

00:03:16: So i primarily work in maybe...I could say three fields?

00:03:23: One is moral philosophy So I was very interested in ethical questions and especially meta-ethical questions.

00:03:31: The other field is social epistemology, which ties into some of the concerns that Senyum raised so... ...the interest not only in knowledge as a form of production but also sort by yes or social activity That has social factors to come into play can transform how certain things occur.

00:03:52: And then the last one ties into this kind of issue.

00:03:55: that's in formal logic, argumentation theory.

00:03:59: Where I'm interested primarily in these agreements where it is the issues were two individuals may lack enough resources to transact arguments and that generates disputes that seem to be long-standing.

00:04:11: so i mean just like The social elements are going to play in these disputes on how we can navigate them.

00:04:18: And that ties into at least a case of mathematics very broadly construed with an interest on the one hand in like social factors that affect mathematical knowledge production and, on the other hand... ...an interesting mathematical disagreements about how to navigate these disputes.

00:04:37: Cool!

00:04:38: So let me pick up this last disagreement word because now at Channel we have a long-running disagreement among all of our guests.

00:04:47: that's constructivism versus classical logic.

00:04:50: but today it started by their disagreement.

00:04:52: But you have a lovely paper about another disagreement in mathematics, which might be even surprising for some people that... People talk about disagreements and math.

00:05:04: Namely one of the ABC conjecture right?

00:05:07: Would you give like rough upshot to those who don't know what happened there.

00:05:13: then follow-up with your take?

00:05:16: Yeah so both Saiyan I've written on a paper that's trying to discuss the matter of deep disagreement in mathematics and trying to break out whether there is anything, uh... ...of profit we can generate with these disputes.

00:05:34: Whether they're worthwhile or should stay away from them.

00:05:38: So In the case of ABC conjecture what were particularly interesting was some sort of case study how we could re-invent history.

00:05:53: I always remember his last name, but it's basically Montezuki had this proposal where he basically claimed that through his theory the ABC conjecture could finally be proved and we were all happy and jolly about the situation.

00:06:10: But then some critics appear saying there was certain faults or errors throughout the proof needed to address and some of the collars.

00:06:20: And that gave rise to this kind of disagreement between both parties.

00:06:25: where Mochizuki was still convinced of the truth, his theory... ...and Charlton Sticks were quite critical of it!

00:06:33: To be critical there we're using sort-of a simplified version of Mochiyuki's theory just because the Intimula... Wait is it Intimulla?

00:06:43: I always forget the second one.

00:06:46: Yeah is quite complex, it's hard to understand.

00:06:49: It's harder to grasp.

00:06:50: so they thought the simplification would make things easier much as Okie had this kind of response where he was saying like on the simplified version.

00:06:59: I agree that there is an issue but my theory is not the simplified versions.

00:07:03: So the objections do not hold.

00:07:06: i still think That My Theory Is Correct.

00:07:08: It Proves What I Wanted To Approve and basically stalemated.

00:07:13: There.

00:07:14: Where We Have One Side We do not think that this is knowledge, and on the other hand another party says I Think this does constitute knowledge.

00:07:23: And it's a published paper as far as i remember.

00:07:28: So technically is within the realm of what we regard there's knowledge.

00:07:31: But it generates its very interesting scenario where?

00:07:34: We have a dispute That we can call deep in the sense that It's irresolvable.

00:07:41: Parties have never bridged the gap between their ways of understanding.

00:07:47: uh, Montezuki's theory.

00:07:50: And what's interesting is that they seem to not even agree on who is a good candidate to resolve the disagreement.

00:07:57: so Montezukie famously said in one of his blogs it's like oh there's.

00:08:01: I think It's Like The Amount Of People That Can Understand Them Properly Evaluate My Theory and The Order Of Ten Which Really Closes In Who Is Part Of The Mathematical Community clearly have a broad understanding of what mathematicians can understand.

00:08:24: So the reason that we chose this case, and then this is when I'll pass it on to Senya now... It's because We have loads of data about their interactions.

00:08:37: So they interacted via blog spots, they interacted by conferences and we had the reports from the conferences so that all this information regarding how they spoke to each other... The ways in which they spoke with one another when communication started breaking down what kind issues held up because sometimes there are disagreements but it's not very transparent where you're going wrong.

00:09:01: This was a different scenario.

00:09:04: What we want to evaluate is whether this dispute could have been carried out differently.

00:09:09: And what kind of social and contextual conditions were required for the dispute to be a fruitful one?

00:09:19: So I generally focus on that epistemological side, which has to do with...what kind of shared knowledge these people require?

00:09:29: Do they need share certain views about who's a good mathematician, for example.

00:09:34: But on the other hand, Sanyan is interested in other issues that come up indeed disagreements and this where I do invent it... Is there social identity side?

00:09:43: So are there issues about attributing credibility to people so-on which as we know important because mathematics is very testimonial ever at space sometimes!

00:09:55: This was when I'll pass the torch over to Sanyang where she can talk how social identities can affect knowledge production and so on.

00:10:08: Yeah, I agree with Jordy that this case is very interesting because we have this understanding especially for hard science and scientific disciplines that purport certain objectivity as mathematics does things such as discrimination or bias, and where prejudices towards certain identities will not exist.

00:10:40: But I think what this case illustrates is that there are surely certain problematic conducts that appear during the process of knowledge production.

00:10:57: So the field that exists within analytic philosophy, really delves deeper into ways in which social identity plays a role.

00:11:09: In knowledge production is called Epistemic Injustice Debate and epistemic injustice debate Just to provide a very brief account, which involves of course for sure simplification.

00:11:30: There is this understanding that when knowledge is produced there are multiple sources one can be reasoning such as induction the other can be testimony and so on.

00:11:44: And within the Episemic Injustice Debate we focus on testimony-based knowledge which relies on interactions with people, who we believe to be credible knowledge givers.

00:12:01: And here what happens is that there's identity at play that contextualizes the interaction between supposed knowledge giver.

00:12:14: and if a Knowledge Giver is contextualized through a specific body.

00:12:20: So they're always embodied, right?

00:12:22: Or they are contextualized by specific culture that they might rely on in order to impart certain knowledges or knowledge.

00:12:33: what happens is the receiver does hearing end must provide justifiable level of credibility.

00:12:44: but sometimes this fails And that's because of the perceived prejudices about The Knowledge-Giver on the basis Of their social identity.

00:12:58: So, That is the whole intuition that Epistemic Injustice debate tries to establish and also of course To explain how this sort of problems can be resolved.

00:13:16: Maybe one tiny little footnote.

00:13:18: I mean the literature is broader, but n equals one.

00:13:24: I Found it astonishing for reflecting myself.

00:13:26: I don't even know what the ABC conjecture says.

00:13:29: I've no idea about it.

00:13:30: I have not even opened a paper.

00:13:33: But when Charles and stick said oh there's an error that at that moment?

00:13:37: I was already convinced right.

00:13:39: so to testimonial side of things It's really more important than we say this ideal of looking into every detail as a rather optimistic one, so to say.

00:13:51: I mean the vast amount of my mathematical knowledge is just from hearsay, so-to speak.

00:13:56: Of course i'm not proper mathematician but even for them because they're narrow field They can understand better than I do.

00:14:04: But even other branches at these days it's.

00:14:10: It's not often the case that a mathematician knows about more than one branch, so to speak.

00:14:15: That is an interesting part I found in myself interestingly.

00:14:23: We do know there are quite a lot of good research showing that testimonial evidence plays very important role in mathematics.

00:14:30: we know that peer review although need not be a determining factor logically when you read the paper and know that it's written by certain person from an institution, then certain evaluations may follow both negative or positive.

00:14:50: And I mean... Not always do we regard this as... A lot of times is purely a pragmatic thing to do with humans.

00:14:57: so if i organise conference and get three hundred submissions then it's likely that I will might prioritize certain institutions over another, just because i know there may be some guarantee of quality and so on.

00:15:13: But what Sanyan and I are very focused is showing these kind of shortcuts we take through identities can sometimes be very detrimental in knowledge production than them?

00:15:28: You already had him as a guest, which is perfect for us because we can really direct people.

00:15:32: So Colin spoke about the case of epistemic injustice.

00:15:35: more generally in mathematics and We see these kind of patterns In science in general with certain Identities are given priorities.

00:15:47: especially white European men have given lot of priority Which means that they're kind of research questions.

00:15:55: Find interest in the kind of projects that we delve into is partly determined by the identity on these people which excludes other perspectives there.

00:16:04: Can be as equally valid.

00:16:06: but i'm not given a voice because it's from an identity that, the right amount of credibility.

00:16:15: And I mean, the ABC conjecture to some extent is that... The reason we listened to Mochizuki was because it's mochizukki!

00:16:24: If there would have been a PhD student who wrote and submitted it It most likely had been discarded immediately Because Of the pretense on trying everything Like how sometimes you see on filled papers for example Some paper by an independent researcher, and it won't be given any kind of time.

00:16:45: So these kinds of issues that generate a lot of injustice to understand how identities shape supposing the objective science is here?

00:16:55: Yes maybe you correct me if I'm phrasing it wrongly... In some sense a lot attention was given in the beginning right we had this four papers which were very weird linking or citing preprints that are unpublished And weird, heuristical elements say.

00:17:15: I think there is some line like the ABC conjecture.

00:17:19: It's the most trivial application of this theory which it not usual right normally would expect to prove other things first that are more easily toy examples and you build up continuously To The Big Theory man here at a very weird situation as we said.

00:17:36: but its this guy who I'm not sure where he did his PhD, which wasn't born or wherever but it's with credentials.

00:17:45: and so we listen first.

00:17:47: And at some point this breaks down as now... We don't listen anymore the communities split.

00:17:56: So there is this lovely saying The theorem holds in Japan and in some parts Edinburgh and a dozen holes elsewhere right?

00:18:06: which is another weird situation so to speak.

00:18:12: So this quite interesting actually, the case that you were just talking about in beginning how these papers garnered much interest might be a case of something called credibility access credibility that is granted to those with certain reliable, say institutional affiliation or authority within the field and so on.

00:18:46: Which like you said might be mitigated through a procedural attempt we can also surmise is that the inverse or opposite could happen, where for instance certain mathematicians because of who they are and in which language they conduct their scientific studies.

00:19:22: They might be provided not credibility excess but the deficit that is playing a role when they enter into global scientific arena.

00:19:34: And what happens, their findings might not receive enough attention or their findings may be sidelined compared to those who come from prestigious situations.

00:19:51: and importantly it's like it's surprisingly very common.

00:20:00: It is a common phenomenon that we experience because as I said, We are talking about knowledge production.

00:20:06: that occurs on the basis of testimonial exchanges and like you say this something happens quite often.

00:20:17: so for instance when we go to conferences We listen to some people who are professors, we've never met them.

00:20:24: We have no means to verify them on the basis of status and in a certain merit that we project onto them.

00:20:47: This happens earlier on, not only at the level of tertiary education but primary and secondary education as well.

00:20:55: And it also happens outside of the educational context where we just go around and interact with people.

00:21:01: for instance if I were to ask you Dennis how old are you?

00:21:05: You will respond in a certain number!

00:21:16: social group about who you are, because you're the most competent knowledge giver.

00:21:21: But sometimes we just don't trust people when they provide whatever-they think is justified belief.

00:21:33: Because for X Y and Z but the problem is Okay this occurs quite frequently.

00:21:40: This occurs at an everyday setting these credibility deficit occurs, it often is patterned.

00:21:51: So they look similar.

00:21:53: or they share certain similar traits Or they share a sort in the similar social context that they often embody.

00:22:00: and The problem is that this sort of patterns also exists at the level of academia.

00:22:08: Yeah That I think the clear is yeah the clearest example.

00:22:12: so In the case of mathematics we have We know there's to some extent, we could call it a culture of mathematics.

00:22:20: So there's certain methods that are prioritized but not only methods of proof which do change over time But rather There's also stylistic elements that come into play and this means if you're all abiding within the given period your work would be accepted.

00:22:37: If you're not role-abiding in those periods You'll likely be excluded from mathematical compensation.

00:22:44: And as Sanyan points out, so we have... I don't want to butcher the name.

00:22:50: So it's Ramanujan who had this situation where he was dealing with problems that mathematicians had.

00:22:58: He dealt with a problem now in quite an outstanding fashion but he was excluded from conversation because not abiding by mathematical culture of time and primarily tied his identity A non-white European, he was basically okay.

00:23:17: You're not doing what we are doing.

00:23:19: you'll saying something weird.

00:23:20: It's even like satirized now to the point of like.

00:23:23: it was revealed to me by God kind of scenarios But his work is a lot more complex than that.

00:23:28: He seemed to get things on the right foot very mess very often.

00:23:32: so We see in these kinds of cases there?

00:23:36: We don't commonly associate him Hard sciences and especially mathematics, but it is an important trait of the field.

00:23:44: And this again I cannot recommend enough Collins podcast on the same kind of issue where they dealt into this scenario more in depth with cases.

00:23:58: It can be very basal things right like not using latech But ascii.

00:24:04: some people are already so known like Friedman.

00:24:08: He writes long ASCII things via an email list, no peer review or nothing.

00:24:15: But we know that person.

00:24:17: so... We listen and otherwise if I get an ASCI e-mail i might be more tempted to ignore it than a proper typeset paper.

00:24:30: And the Ramanujanke is also very interesting because even back then but not entirely sure there were some critics of SOTU to give the story.

00:24:40: then I mean you know it there's this person from India sending letters to the UK huge number theoretical results some new, some reproven and being invited by Hardy to Cambridge.

00:24:57: And Cardi Littlewood two biggest number theorists of that time and Hardy took the put it into this usual corset that even back then some people said you might have destroyed a lot because there was this person with the other standards of rigor, whatever.

00:25:17: It is coming up with a thousand good ideas and now we force them to only come up with one hundred Good Ideas but write them as We would like And its Like A waste Of Resources.

00:25:29: Another Would Say No That Was Exactly Right.

00:25:32: Otherwise This Is Just Garbage very weird situation to be in.

00:25:41: Yeah, I think this ties into something... So there's also- I was actually gonna pass it on to you Sanyin This ties into some thing that Sanyan has with us about.

00:25:50: uh i guess level of like epistemic imperialism?

00:25:54: That is a good bridge and this was something that I was thinking about while listening to Dennis' description.

00:26:02: So one of the things that social epistemology or let's say more closely, epistemic injustice debate what they focus on is how this happens.

00:26:13: Because we cannot always appeal to you know like this idea of prejudice or bias where like lets go a bit inch further and say racism or sexism give credibility to certain knowledge givers is because of these reasons.

00:26:31: Yes, fine this could be the case but it's not always that there are these rotten apples in a whole basket That causes the problem.

00:26:42: Some people say that they're more broader reasons like structural reason behind and made scholars look into not only the testimonial aspect, but also something called a hermeneutical aspect of what it means to build knowledge or produce knowledge.

00:27:02: And basically there are made different camps about this issue.

00:27:07: so some people think that is one shared hermaneutical resource among all not the mainstream anymore because there's a better understanding, but an updated understanding of what it means to participate in knowledge-making process.

00:27:27: And that assumes they're multiple pockets of hermeneutical resources basically which overlaps and kind of merges with each other... ...and the analogy is often provided in order understand how these hormonal resources exist as something akin to clouds.

00:27:47: They are clearly differentiable from each other, but sometimes they overlap and Sometimes it's merged in the sense that you cannot really tell which one switch And can not really tell apart.

00:27:59: In a similar way there are resources out There That we try to make intelligible about The things that We experience About the Things that we want To clarify and mathematics is A great example because what?

00:28:15: basically how the world is spelled, right?

00:28:17: How it's supposed to be communicated with each other.

00:28:20: How we try verify that certain assumptions are true or whatever.

00:28:27: What happens often these one particular hormonal resource among different resources may be exaggerated so that it eclipses all of them and that's the imperialism, the epistemic imperialism that Geordi was talking about.

00:28:48: And of course this doesn't just occur because of the ways in which the hermeneutical resources interact with each other but because of patterns and history of injustices That exist In The World Which is a non-ideal context where we have to conduct scientific studies.

00:29:13: Just as a clarification, by hermeneutical.

00:29:16: I'm talking about meaning-making activities that also for instance constitute very important part of science.

00:29:27: A great example is hardscience which tries to explain why there's speed and what does it mean types of speed and what they try to do is to formalize it, right?

00:29:44: And that's the meaning-making process.

00:29:46: Of course in order make things intelligible to each other What we rely on as a certain language or certain shared conception of what it means to have speed etc.

00:29:56: etc.

00:29:57: etc.

00:30:00: For the case of mathematics yeah with what we see primarily this idea There's certain standards for proof.

00:30:06: There are certain standards what academic writing is, there're certain standards of all these different elements that constitute what makes mathematics in the present time.

00:30:17: So a very clear example.

00:30:19: I think it shows That can be something very complex like mathematical methods.

00:30:25: so method of proof Dennis pointed out very well, like you're forcing somebody to jump into another hermeneutical bubble.

00:30:34: So it's their learning-to-play game.

00:30:36: they've played all their life but with different rules and suddenly becomes really hard.

00:30:40: It's a bit if an English person suddenly bought mainland Europe And then asked to drive everything is upside down.

00:30:49: now I can do this But its harder than what.

00:30:51: it was Quite interesting that this could happen in complex things methods of proof and so on, but it can also happen with very basic things such as language.

00:31:04: So we know that is not uncommon for people to negatively evaluate a paper because the English is not to Oxbridge standards.

00:31:15: basically And that's another situation in which we see certain prejudices can surface.

00:31:21: this perp, I've seen it as a reviewer and i've seen that as an editor.

00:31:26: And I have seen it is an author where you had these comments of like... This paper cannot be evaluated because the English is beyond understanding!

00:31:34: It's generally not the case but clearly understandable.

00:31:37: In mathematics, generally even more understandable Because at least there are shared formal language we can all get along with roughly.

00:31:48: But again those kind of elements were.

00:31:51: if the hermeneutical space of mathematical mainstream, mathematical knowledge is with certain rules and some people can't abide by those laws because of certain past injustices.

00:32:06: And so on or because of social identities in any of these kind of elements then it's... It basically means that we are making a certain mathematics.

00:32:16: it's screwed within perspectives without real justification for Which I think the small clarification that we always have to make.

00:32:24: it doesn't mean that the mathematics that We are making now is path mathematics or its force Mathematics and so on.

00:32:31: It's rather than Its one way of doing mathematics in by prioritizing.

00:32:37: That way if they're mathematics, we can be excluding perspectives that Are equally as right but maybe interesting for other purposes with Other kind of questions other kinds of problems other kind of paths to take.

00:32:51: And I try to, I mean now lowering it down back Western context.

00:32:55: He established proof standards and we have a big disagreement in this podcast one that already came up with an episode.

00:33:05: It's likely published when this comes out With Andre Bauer and Hamkins.

00:33:11: Joel Hamkins who is invited and lovely person will probably join hopefully other as we cut this out.

00:33:19: They disagreed on something and if I butcher it up, Thorsten will kill me.

00:33:24: but let we still try.

00:33:26: There's a logical difference for the intuosynistic mathematician between refutation so i assume A... ...I get to a contradiction.

00:33:36: So I got to non-A.

00:33:38: that cannot be And thats fine with the intuisynist.

00:33:41: What is not fine for him or her Is.. ..I start from Non-A thus a must hold.

00:33:51: This doesn't work for the intuitionist, For classical mathematician same thing potato-potato.

00:34:00: So the classical mathematician just says proof by contradiction while the intuitionists would like to distinguish this because one is valid and other isn't.

00:34:11: And then people got heated as you get in mathematics it's still not politics.

00:34:20: And they said, oh this is wrong.

00:34:22: We should change the Wikipedia.

00:34:23: we don't distinguish that.

00:34:24: and some classical mathematician maybe I singled out Joel Hamkin's head Don't over Embrace This issue.

00:34:36: it's a nuance.

00:34:36: It's correct nuance i'm fine with it But there's no reason to go through The first year BA students and already pushed them too much so To speak and I mean similar only within set theory classical math.

00:34:49: The axiom of choice is a delicate issue and normally we just do the dance once.

00:34:54: We said, oh well here use the axioms of choice And then don't give it damn Just use or not to use.

00:35:00: Who cares?

00:35:00: I dont know.

00:35:03: Maybe you have any strong intuition.

00:35:05: There's no right or wrong here I guess at least.

00:35:08: maybe i'm already butchered for that.

00:35:11: But what your feeling about this issues relevant for you or am I just saying something trivial and missing

00:35:21: the bigger picture.

00:35:21: No, no i think it's very relevant because so that ABC conjectures set theories actually a case we are interested in as well because there has been.

00:35:35: I think it's primarily Andrew Aberdeen and also Deborah Kandt that was on the podcast talking about set theory.

00:35:45: So we do have researchers are working in this kind of disagreement, as you rightly point out seems to be... The closest thing with politics or mathematics where there is very heated disagreements over like.

00:35:59: can i have extra axioms?

00:36:00: Or not?

00:36:01: Can i take these?

00:36:02: And..I think the point your raises actually quite interesting because yeah Like hermeneutical bubbles in the term, In terms of like cultures and societies.

00:36:13: So The hermaneutical bubble Of-of the West is very different to their hermoneutical Bobble off other regions of the world And we should not be exclusionary To other ways of doing things.

00:36:24: A lesson that maybe We would like take from these kind of cases such as set theory Is that at the end of day there are Different Ways of approaching similar problems by acknowledging that there might not be a necessary right choice or the correct one to exclude The other and simply allow both practices to surface into Develop their work in the ways they do.

00:36:51: It might be Yeah, very very very positive for mathematical knowledge In general just means we're generating more things.

00:37:01: it would generate interesting questions That may even overlap.

00:37:04: And another thing We talk about about the case at least of set theory, is that sometimes even having these kind of opposed sides can be very beneficial for the mathematicians themselves.

00:37:20: So the idea is generally if we work within a community where there's just total consensus our knowledge production We will struggle to deal with confirmation bias.

00:37:36: because if I take my paper, To You Dennis and you like it.

00:37:39: And say ah this is great all these little small mistakes or small imprecisions Will never come out?

00:37:47: And we'll just walk together and say oh we both agree on This adamantly!

00:37:51: There's no issue.

00:37:52: but If we do have practices in mathematics where there Is long-standing disagreements then These kind of In positions in the knowledge production will sort of start to be ironed out because we will have somebody on the other side Being very picky about.

00:38:09: well.

00:38:09: No, that's actually not the case.

00:38:11: But I think the line that we need to not transgress is invalidating The way that the other does it?

00:38:17: We can point out hey this has no up-to-the standards I believe and the other person can revise It.

00:38:22: but we need not do that while just silencing perspectives.

00:38:27: But it does bring in something interesting, I think ties well into saying this section on the paper that for these kind of things to happen there needs to be certain individuals need to have an epistemic character in terms of virtues and vices.

00:38:48: so its not merely a matter knowledge but also about how individual approach their practices.

00:38:57: So I don't know if you want to add something about this.

00:39:00: Can i first boil back down to the small knife question now?

00:39:04: You brought it again bigger, to these proper disagreements between let's say classical not classical math because I just really wanted to talk about a very small linguistic point and knowing your work on linguistic injustice maybe this is simply too trivial.

00:39:21: so just...you can reject my question or hurt feelings.

00:39:24: Do you have an intuition there with your side, the minority?

00:39:29: The constructivist who has a right to point out a difference for them?

00:39:35: or is that nothing where we should use the big work of injustice?

00:39:42: and this is just a trivial pragmatic question.

00:39:44: So thank you!

00:39:45: Do you sense to chip in?

00:39:50: Yes so I think it's actually very long-standing inquiry in theories of justice because within our field there is a distinction between wrongs, harms injuries and injustice.

00:40:09: And all these terms denote something different.

00:40:14: Your question was There are two camps in mathematics one that defends ways of understanding, one way you have an understanding and the other one defends otherwise.

00:40:27: And there is a dispute... You know?

00:40:29: And then basically the question is would just say that minorities so constructivists are they facing injustice?

00:40:39: in order to answer this questions either as yes or no what we have to see?

00:40:44: whether it's first sporadic second incidental Whether it's patterned, whether its long-standing etc.

00:40:57: So what happens is that if a harm occurs It's not always a wrong Right?

00:41:08: so A doctor can harm you by cutting off your arm But he's not wronging You.

00:41:14: in the same way and the academic world.

00:41:17: something can occur which can be harmful where we lose out and certain truths, but it may not be wrongful in a sense that it did not harm certain let's say dignity of the scientists involved.

00:41:35: But it could be harmful at the level of the academic collective and so on.

00:41:40: The question you wanted to ask was whether there is an injustice which bit more of a collective level.

00:41:56: If these minorities who are rejected depict certain identity or certain group membership that had a long-standing history of mistreatment, were exclusion from the dominant mathematic field then we can perhaps say This points to something greater.

00:42:29: Just my two cents.

00:42:30: having this refined vocabulary, I think in the past it was easier to see proper injustice there because we have historical case studies of people being excluded systematically not getting positions into a cynistic tendency so i think they're as well documented.

00:42:52: Nowadays, it's a proper empirical question just to see whether this is a brawn because of the epistemic benefits of young learners who shouldn't distinguish too much things or if they are injustice.

00:43:09: Maybe maybe it's an injustice as it reflects and paternalized not looking at constructive distinction.

00:43:18: we will probably not know.

00:43:21: Twitter is dead, but the discussion will continue elsewhere.

00:43:26: Access dead.

00:43:27: maybe I should say that's about twitter anyway.

00:43:30: sorry

00:43:32: What i wanted to achieve was there are certain factors you can consider to judge for yourself whether it isn't injustice or not because of course the crowd will differ right?

00:43:42: Because its already polarized crowd.

00:43:45: But what I can offer These are the normative factors that you can judge to see whether this exclusion is justifiable for consequential reasons or it's not justifiable because it constitutes a certain pattern which might result in an injustice.

00:44:02: Something that had happened in the past, if it resembles in-the present The resemblance itself sometimes gives justification enough to stop that practice Right?

00:44:13: A Nazi salute was used for specific reason this Elon Musk doing it, he shouldn't do it for a reason.

00:44:22: Not because of his ideological tendencies but... Because its just simply symbolic that you should no longer use right?

00:44:30: So yeah anyways You can cut this part out if you want.

00:44:37: Yeah I mean whatever you prefer.

00:44:40: i think you can insist on that and we'll do otherwise.

00:44:44: Okay, yes so sorry for bringing this back to the smaller linguistic question.

00:44:49: I think that helped but let me ask as a final topic because we are already running out of time like is there also positive story?

00:45:03: What can we do?

00:45:04: what can we learn?

00:45:06: Is it with our other ideas yet to develop in particular maybe in this context satiristic disagreement?

00:45:14: Yeah, so the to the paper that we have on deep disagreements.

00:45:20: The whole point about it is to show that when we have these long standing disputes at me be tied to either different ways of doing mathematics whether that'd be within a shared hermeneutical bubble or between different hermaneutical bubbles?

00:45:35: We do like to end this story with some positive treatment of what can't And we talk about the improvements in knowledge that these disagreements have.

00:45:47: So as mentioned earlier, like it allows us to combat confirmation bias sometimes by responding to harsh critics We tend to generate new knowledge.

00:45:57: so if I have an objection That i didn't have previously and i addressed that objection then maybe i'd generate something new?

00:46:04: So imagine if mochizuki instead of saying like our shells and sticks do not understand what i say But rather said, oh okay I'll take this as a real opportunity to improve my theory.

00:46:15: Then we have this very interesting moment that's like now new knowledge is being produced.

00:46:20: This is very Very beneficial to the discipline of the whole.

00:46:25: but our contention Is for these things happen there needs To be certain epistemic attitudes by The people involved and By That We mean If I want a disagreement between set theories to be beneficial, the people involved in this agreement need to act in certain ways that enable these good things to happen.

00:46:49: So one of the clear ones is this idea of epistemic humility and sort-of having a certain awareness about your own ideas on the fact you may be wrong or not have all the truth inside.

00:47:03: so it means in case of set theory What we know that the both sides are very adamant they're right and there fundamentally write about issues at their dealing with.

00:47:13: but.

00:47:14: Our consent would be when you have an agreement somebody on the other side what do need to do is take a step back in say hey maybe I'd be wrong may i'm wrong about this baby uh... different way of doing set theory can be beneficial to me, maybe here in how another person does set theory can be beneficial.

00:47:33: And these kind of interactions will generate something more interesting.

00:47:37: but I also want deposit the same because it's not only about the character regarding your own ideas But also you're character with regards to possible biases which we talked About interacting and how we give testimonial credibility to individuals.

00:47:53: Yeah, so of course.

00:47:57: So what Jordy just talked about is Let's say from the perspective of people who should be granting certain credibility.

00:48:06: But of course there's a other side of the coin where they're people who might be receiving less credibility or those Who?

00:48:18: Might require you know additional Know-how you know, awareness of how to navigate unkind epistemic environments.

00:48:34: And here what I have advocated in the past and that was recently published basically is important for an epistemically responsible agent something called discernment as an epistemic virtue, where you are able to discern whether a circumstance is exploitative or it's in the context when which can really engage and earn us conversation for the betterment of party who may be biased but maybe biased you know, like pervasive and repetitive manner.

00:49:27: So when you're engaging with certain epistemically let's say uncooperative parties You can lend yourself to situations where you know that you will expose yourself epistemally speaking by trying to be a knowledge giver Trying for instance advocate of the mathematical camp belong to, but you sometimes know that the listening party simply will not budge and it's just probing you in order to expand what their thoughts are.

00:50:04: And do not give space To What You Are Thinking In which case I think you should have The Virtue to be able to discern the situation as exploitative and then Simply Walk Away

00:50:19: right?

00:50:19: That is probably good.

00:50:21: They've been thinking about the haymaker debates and the internet, things like that.

00:50:26: Exactly!

00:50:28: And in certain cases if you choose to do this then it could be a really loss of opportunity... ...to form allies or to contest certain assumptions that are scientifically held for the betterment of science right?

00:50:47: So, this is a really important epistemic virtue that I think may allow these difficult epistomic terrains to resolve itself of course at an individual level.

00:51:00: And because it's on the individual level its not the only solution and should not be So, yeah.

00:51:12: It's just but one side of what it means to cultivate a good epithemic environment for science.

00:51:21: That lovely last words because this is exactly what we try to do here right?

00:51:26: To have the nice epistemic environments Hopefully even in the comment section which not often the case on YouTube But so far there was always great many questions some critiques Some euphoric people But that's always fine.

00:51:42: So thank you so much for being here and donating your time to our little podcast about logic.

00:51:47: Thank

00:51:48: very much, Dennis.

00:51:49: This is a wonderful project.

00:51:52: We view it regularly we recommend it again

00:51:55: We are royal followers And I'm very happy and honored to be Here!

00:52:01: Thank You so much For giving us Time & Space.

00:52:04: this Is an important platform.

00:52:08: Yeah, that you are the host because you also have a knack for it.

00:52:12: So that's very nice!

00:52:13: Okay I'm blushing so i should just say we go.

00:52:17: once again thank you and to all other people who follow this podcast by subscribing ringing the bell commenting forwarding it to friends and hyping it whatever that means.

00:52:27: so far...I think nobody did that not sure if we must turn it on but we will figure out.

00:52:33: and uh once again Thank You bye-bye.