aboutlogic #06 | Colin Rittberg – Philosophy & Sociology of Mathematics, Epistemic Injustice

00:00:00: How do you define a mathematician?

00:00:01: Is it somebody who verbs at the math

00:00:03: department?".

00:00:04: That, I guess is a question that doesn't really have an answer.

00:00:08: So i define a mathematician depending on whatever I'm interested in.

00:00:14: Great!

00:00:18: Welcome to our next episode of About Logic and today we have a dear colleague of mine –at least when we're recording because then I am still affiliated with Brussels– Colin Jakob Rittberg who's a post-doc And he's doing something called philosophy of mathematical practice.

00:00:40: That may be already our first question when we're talking here about logic and foundations, but also about philosophy of math?

00:00:47: So would you give our listeners like a very short rundown what's philosophy of Mathematical Practice?

00:00:54: Well I guess philosophy of mathematics practice broadly wants to understand what mathematicians are doing.

00:01:01: So individual activity of mathematicians, the institutions that play a role in mathematical research and mathematical knowledge making.

00:01:12: It's about communal activities.

00:01:14: so understanding kind of mathematics as it is being done...

00:01:22: What exactly?

00:01:24: how do you define a mathematician?

00:01:25: Is somebody who works at a math department...?

00:01:28: That, I guess is a question that doesn't really have an answer.

00:01:32: So i define a mathematician depending on whatever I'm interested in.

00:01:36: so... Okay!

00:01:38: In my usual research I am interested in research mathematics and thinking about mathematicians who tend to work at universities and kind of publish mathematical journals even though they might not be hired as mathematicians right?

00:01:50: There may be computer scientists or there maybe theoretical physicists something like this.

00:01:55: But of course, I mean if you think about mathematics education a mathematician might very well be the fourteen-year old sitting in his classroom and your talking from that perspective.

00:02:05: So i wouldn't want to give clear cut definition on what a mathematician is In philosophy or mathematical practice.

00:02:12: research effort focuses on research mathematics but

00:02:17: not just this lacking And not only done at the mass department, because I mean necessarily.

00:02:28: So my impression... maybe you can tell me more about your research.

00:02:34: but my question is that you're very much about culture of mathematics.

00:02:39: or is this all to say?

00:02:41: No, no.

00:02:42: There's a kind of subfield in the philosophy of mathematical practices called the Mathematical Cultures movement or field or whatever you want to call it.

00:02:51: so where they have their real idea is too focus on cultures.

00:02:55: Of course that raises questions about what exactly is a culture and further issues.

00:03:01: but yeah I mean i'm very happy with that.

00:03:04: So The Mathematica Cultures Movement might be relate the most to in this various different strands all collected under the big heading of philosophy or mathematical practices.

00:03:17: Because I mean since, that I always have this problem Am i a mathematician?

00:03:23: Some people say yes but sometimes they no because im not really into mainstream culture of mathematics, yeah.

00:03:34: And I'm quite sometimes can be quite cynical about it.

00:03:39: not that i think that computer science is all wonderful and better but its different ,and I want to see whether you have got some observation about...I tell you one example.

00:03:49: maybe you can interpret something for me?

00:03:51: Yeah so I mean ...I am sort of an intuitionist like use different foundations, I'll just talk theory if it means anything to you.

00:04:02: But so I'm talking.

00:04:04: we had actually already Kevin buzzard in here and about logic And not at this conversation but previously i talked with him.

00:04:18: So Kevin is interested in formalized mathematics.

00:04:23: he uses his lean system And for me, the lean system on one hand is good because they use type theory.

00:04:29: On the other hand it's a bit disappointing because you're very classical yeah?

00:04:33: So I'm talking to Kevin and say like so why are you trying to convince him that sort of type theoretic principles may be interesting to consider?

00:04:44: Yeah!

00:04:45: I mean i not want turn into an intuitionist but open up intuitionism...and then he says yeah this all very interesting But the field methodists, they wouldn't buy this.

00:04:57: I mean actually... This is quite strange because i want to have a discussion about philosophy yeah?

00:05:03: About what we talk about foundations and he talks about sociology.

00:05:06: Yeah so can you sort of comment?

00:05:09: Can you interpret for

00:05:11: me?

00:05:12: I'm much more for the sociology than then this type of philosophy.

00:05:18: So I guess, so if we're thinking about Kevin's work.

00:05:23: This whole idea of kind of digitalizing mathematics and having some computer verification for mathematical proofs... For this particular issue then we want to capture the logics that are employed in ordinary mathematical proofes ...and run them through a machine to check for correctness?

00:05:43: Okay,

00:05:44: so I think that's not even... Sorry.

00:05:56: Because the nature of construction changes ... Even if you're classical, let's ignore this question!

00:06:07: The nature of mathematical construction changes in a moment when we use the former system.

00:06:12: So it is about just formalizing existing mathematics transforming ideas from existing mathematics, but it makes a difference and also creates different idea.

00:06:23: Different dynamic yeah?

00:06:25: Absolutely!

00:06:26: So no I fully agree with you right this is Lakotosch one-on-one.

00:06:30: so the translation of The Proof As Written into whatever formal system You might use to then assess It.

00:06:38: And i guess that's an issue for kind Of digitalizing Mathematics in This way And I'm with you on that.

00:06:45: Nonetheless, there is a research effort... ...that doesn't fully ignore the problem but the philosophical ramifications of this are considered to be minor or something.

00:06:56: You have an ordinary mathematical proof written in the ordinary style as published in academic journals and computer verification code that you might need to verify them Because what you're referring to correctly point out it's not the same.

00:07:15: You'd be verifying the translation of The Proof, right?

00:07:18: Actually

00:07:19: no even this I don't agree.

00:07:22: Okay sorry.

00:07:23: No go ahead

00:07:24: and say it is rather an opportunity To reinvent a proof And have quite different proofs Have a different perception Of the subject.

00:07:34: So i'm bit... I think when you see digitalization of mathematics that doesn't For me, it's not the right description.

00:07:46: It is a new kind of mathematics which is inspired and related to existing mathematics but also offers really new opportunities with new proofs or ideas.

00:07:59: so its cultural change isn't just digitalizing existing mathematics.

00:08:06: I guess there's a kind of, you know that this is a philosophical question what exactly are doing?

00:08:11: they're right.

00:08:11: And so when i'm thinking about Schultz and the liquid tender

00:08:16: Yes

00:08:17: What was it called?

00:08:18: The Liquid Tender Right.

00:08:21: So then idea to have an ordinary proof and worry about correctness go through the motions of digitalizing it and running at putting in a computer code, having libraries that can support this.

00:08:40: And then check formally kind of computer-aided or computer assisted proof checking.

00:08:45: Now you have

00:08:46: to point out

00:08:47: what your checking is a translation of thing right?

00:08:52: Nonetheless... No!

00:08:56: It's a new think.

00:08:58: First of all, the original proof was actually wrong.

00:09:03: So they created a new thing which is not the translation for an existing thing... ...which is inspired by an existing reasoning or argument on the whiteboard maybe and that's one thing I thought this liquid tender was about.

00:09:22: but it goes further And I don't know a good quote, maybe it was Tao or something where they really discover new mathematics by using a formal system.

00:09:35: So yeah sensitive to saying translation digitalization is really a cultural change.

00:09:48: It's the new kind of mathematics which has created...which is related and inspired to existing mathematics,

00:09:54: and you

00:09:54: would be at translation.

00:09:56: The framing in translations because

00:10:00: the

00:10:00: objects are not closely related enough that you might call one... I mean

00:10:04: they're related!

00:10:05: They're related in a way so one inspires another, certainly related but actually it goes further there now things being created which are not related.

00:10:21: Which I really knew, right?

00:10:24: Because the way to do mathematics changes by getting a computer into the game and...

00:10:35: Sure in many ways!

00:10:37: Not just the kind of verification efforts but The creation rights, collaborative efforts and collaborative practices have changed massively.

00:10:49: Yeah I mean the digital transformations of mathematics are extremely impactful and impact all sorts aspects of mathematics absolutely.

00:10:59: just maybe as a compromise because i think in some sense you agree Because there is this informal math or journal maths let's call it.

00:11:08: And then there is some procedure and we get the formalized math.

00:11:14: This procedure might be called a translation, but you can ask whether it's an adequate one... ...whether something got lost or added?

00:11:22: I think that reply to this is philosophically very laden issue.

00:11:27: There are people nowadays like Yasin Hamami.

00:11:36: It's often sometimes called the standard view even Maybe that's not adequate, but they would say no this is in some sense the very same.

00:11:44: It's just filling in gaps.

00:11:45: it's whatever and there are different conceptions.

00:11:51: I think a lot of people would perceive that as the standard theory.

00:11:58: But then when lots of peoples see never really I mean, one thing which always thought about philosophy of mathematics.

00:12:15: So so i went to some meetings even years ago and uh...and i noticed that a philosopher of mathematics.

00:12:24: they think by observing mathematicians there can find out something on mathematics.

00:12:32: The wrong people.

00:12:34: Don't ask mathematicians about mathematics because they have this really strong cultural bias, yeah?

00:12:41: They have a certain very limited perception of mathematics as well and asking them what is mathematics in my mind the wrong way to go?

00:12:52: or

00:12:52: start the question that you were listening too beacuse.

00:12:55: we can certainly find out certain things about mathematics by talking to mathematicians.

00:13:00: I mean,

00:13:02: some

00:13:03: speaking claims can be counteracted by simply asking mathematician who doesn't agree with the claim.

00:13:10: So if all mathematicians are Platonists and you find a single one that proclaims not to do once... You know so you can find out something.

00:13:19: but of course it's well known in any kind of empirical methodology where you cannot just go to practitioner ask them what their practice is.

00:13:27: because What do you use?

00:13:28: Yeah, that's the case.

00:13:29: Yes!

00:13:36: I mean... So i think about something constructive mathematics and basically they say it is same as what mathematicians are saying.

00:13:46: It doesn't matter.

00:13:48: we have already an old story Hilbert won the Grundlagenstreit.

00:13:56: Who cares?

00:13:57: That's from the past, right and philosophers sort of just I mean not all of them but some of them so have just repeated this perception that what i'm saying is I mean, being an intuitionist.

00:14:24: I'm quite critical about current mathematical practice even though i understand that you should have to be open-minded and so on...I try my best Dennis knows this but..i find it quite shocking the sort of ignorance of mathematicians with respect to constructive methods.

00:14:49: I find this quite shocking.

00:14:50: And then, sometimes met philosophers who don't question it says... I mean you're getting me right!

00:14:59: What i'm asking for?

00:15:00: some awareness of that.

00:15:01: there is still an issue that some people are doing intuitionistic mathematics and mathematicians tend to completely ignore or many of them They just don't really want to know, or they have some misconceptions which are not often interested to overcome.

00:15:24: And I think you wrote something about this kind of things as an open-minded methodological alternatives?

00:15:38: looking at this kind of thing.

00:15:40: Right,

00:15:40: yeah I wrote a paper about humility in mathematics so that was interesting.

00:15:45: to bring virtue epistemology which uses virtual theory to address epistemological issues... ...to the philosophy of mathematics and it was collaborative effort with Fener Tanswell and Andrew Aberdeen.

00:15:59: we've been pushing the idea that you know virtual theory might be of help to engage with issues in the philosophy of maths that otherwise have been left unaddressed or addressed from different angles.

00:16:14: Don't you all think, Emilio, where you say this?

00:16:15: That foundations should be a topic of discussion instead just being assumed but bored out and open?

00:16:28: shouldn't mathematicians be aware of what foundations they're using and what alternatives.

00:16:37: They are not, I would say most of them... Right!

00:16:40: And so one argument and you ...and i'm curious to hear a counter-argument to this.

00:16:46: but one argument might be well it's mathematicians already very busy people just like all academics.

00:16:52: And so to just get a grasp on your field of research, that's already heavy work and then stay up-to-date.

00:17:01: So why worry about other approaches to the very foundations of mathematics?

00:17:08: What are you

00:17:09: thinking... Okay first off I'm not expecting they should learn my area of research but there use certain logical principles and mathematicians often say, logic isn't something they don't consider.

00:17:29: It's not relevant because there are just two mathematics and it doesn't have to reflect on what methods you're using.

00:17:36: And I think a practitioner should always be in some sense reflective.

00:17:41: You do something in mathematics and you should reflect on your doing.

00:17:45: part of this reflection I think is what foundational principles you're using, whether it's set FC with a new choice.

00:17:55: Whether those can be framed constructively and there are other things which interesting yeah?

00:18:04: Whether your very dependent on representations where the presentation independent one.

00:18:08: so these are questions Which i think any practitioner should reflect No matter how busy you are, actually this is important for the development of a subject and also for the communicability.

00:18:26: And my critique on contemporary mathematics that it's very little.

00:18:34: I mean they would rather say okay logic we don't care or want to do anything with us because We know how to do mathematics.

00:18:46: I studied mathematics and when i think back on this, we never had a course in the foundations of maths.

00:18:54: Because i chose mathematical logic which turned into

00:18:57: set theory.

00:18:58: so i saw some set theory but it was also only just set there right?

00:19:01: There were no categories discussed ,there are no institutions in logic But most of my classmates didn't see any foundation.

00:19:12: It was just mathematics is presented as this-is-it and the very foundations of these.

00:19:17: And also, the philosophical foundation that come with it right?

00:19:20: I mean... The whole foundation debate is also a philosophical debate.

00:19:22: none of those were discussed!

00:19:23: And i agree..

00:19:27: That

00:19:28: impoverishes the mathematical research culture so mathematical cultures in general.

00:19:33: Maybe just short remarks on that.

00:19:36: Because we already talked about cultures, there's a weird element concerning foundations in not towards them like your linear algebra course where you say oh... We are now talking about basis of vector spaces and their choice is important.. And we don't even spell out ZFC but talk about choice in particular Models.

00:20:03: and of course, there are some equivocations.

00:20:06: They're about constructive non-constructive.

00:20:08: We don't need to talk about right now.

00:20:11: So there's this cultural not at one hand And then there is on the other end.

00:20:16: There is maybe a division of labor At play nowadays.

00:20:21: so they more extreme.

00:20:24: Example is physics?

00:20:25: They don't care about rigorous math in The journal.

00:20:29: math sense, right?

00:20:30: the smooth thing or not, they just assume that for now and work out their theorems.

00:20:37: Then there's the rigorous math mathematician going over that and finding the right formal apparatus... There is this famous example of the Dirac-Delta function where physicists said don't put it into an unbounded integral when nothing happens.

00:20:54: but if you do get contradictions then we got a proper reconstruction which isn't really.

00:21:02: And then we have the logicians who really care about whether this happened in ZFC or how many Grottendijk universes needed to be added, maybe even piano arithmetic suffices.

00:21:17: We also talked about this with Kevin very shortly that it's kind of open whether Fermat last year needs whatever much they need and his formalization effort will make that clearer at least given up about.

00:21:33: So,

00:21:34: at least in current practice maybe this is how mathematician decided to solve it?

00:21:43: I mean okay i had some hopes that the formalization of mathematics anyway has already affected mathematical culture...in the suspect so very corporalized as a lean system and leanness based on type theory.

00:22:05: Lots of statements in Lien, they are not actually very sex theoretics.

00:22:11: They're really type-theoretic.

00:22:13: Now Lien is a funny thing.

00:22:15: that's the funny mixture... ...of type theory and classical mathematics.

00:22:21: so there are lots of... I mean actually of choice is assumed and then so on.

00:22:29: But still, there is already this different sort of perspective on how you present things.

00:22:35: Which actually in a way... This type theoretic may be much closer to the informal mathematical practice than that theory.

00:22:43: That's certainly an artificial foundation really!

00:22:49: Big discussion

00:22:50: by others would say this iterative conception of set mimics it very well?

00:22:57: phrase it slightly different.

00:22:59: We just have an observation about mathematical practice.

00:23:02: that's clear for all three of us, but maybe wasn't clear to all the listeners.

00:23:07: and thats disagreement on foundations in this case.

00:23:11: now And one of the dominating themes is your research column.

00:23:22: I don't think there is a conflict about so much.

00:23:32: the conflict of foundation says completely ignorance Of foundations.

00:23:36: that was my part, but sorry Colin

00:23:40: Disagreement would be.

00:23:41: some people say we care.

00:23:42: Some people saying we don't care.

00:23:44: Or maybe it's weaker kind of disagreement.

00:23:47: But no back to college

00:23:49: right even though are you know?

00:23:50: I guess i would agree with Thorsten That People Don't Even Say i don't Care They Just engage with the issue.

00:23:58: And I think that's the ignorance you talk about, right?

00:24:03: It is not part of their epistemic life.

00:24:07: but yeah to come back a disagreement point... Disagreement was something that got me into philosophy so i already mentioned it and studied mathematics.

00:24:17: The anecdote goes as follows at some point he wouldn't comes along And he mentions at some point, you know that something implies that V does not equal L which is a set theoretic statement and.

00:24:34: He takes this now as it being true.

00:24:37: but the statement is I mean its not provable from our theory.

00:24:41: so we thought to my mind because i was very naïve at the time in mathematics just again according The statement is neither provable nor disprovable, so it's either true or false.

00:24:57: It isn't decided by the game and that's at end of story.

00:25:00: So how can somebody like Boudin come along to say we know this was wrong?

00:25:07: This statement wasn't right because no one made a mistake.

00:25:13: I went home thinking he doesn't really know and in my kind of juvenile hubris.

00:25:20: Because, he is one the leading mathematicians on this field!

00:25:25: He knows much better than me as a little student... ...and it got me interested and questioning how can mathematicians have different views about the very mathematics that they study from ME?

00:25:39: Because mathematics should be kind of this value free and, you know there shouldn't be any physical basis to any of these.

00:25:46: And then in my master's thesis I actually worked on Hamkins who disagreed with William.

00:25:52: so that is a fundamental disagreement between the two.

00:25:55: Now i did it from a mathematical perspective working out some details of Hamkin stuff.

00:26:05: But now I got interested in this debate that they are having, where all of them are set theorists.

00:26:13: They all agree we should do the classical kind of set theory is what we should be doing.

00:26:20: it's not intuitionist logic or type theory It's just plain old set theory.

00:26:26: Even with a small group of experts there was disagreement about about the very foundations of things.

00:26:34: So Hugh Woodin is what's called a monist, so he believes there are one true state-of affairs... This particular statement this vehicle L statement that I just mentioned.

00:26:47: you know?

00:26:47: That it's just wrong whereas for Hamkins There's a multiverse or he was a pluralist and multiple different universes And in some of them The Statement Is True In Some Of Them It's False.

00:27:00: So here we have two well respected mathematicians in the field, but they disagree about some more or less fundamental issues.

00:27:10: And that got me excited about this agreement and kind of philosophical underpinnings of mathematics?

00:27:18: Yeah!

00:27:18: Can I comment on... so i find it interesting because what these really questions is this idea that mathematics support truth.

00:27:28: alright I mean, this Platonist view.

00:27:34: And i find quite interesting that they sort of... Okay there's questions a little bit.

00:27:41: There is monism versus multiverse but not fundamentally right?

00:27:46: Fundamentally somehow these things are real.

00:27:50: and maybe going one step further intuition means these all construction overhead hence We cannot really talking about the truth is very artificial.

00:28:05: It's a metaphor, not more right?

00:28:09: And this in Grundes ist basic criticism.

00:28:14: from intuitionism I mean that mathematics it´s really mental construction.

00:28:19: its not discovered Its created and because its created has got completely different nature from this.

00:28:26: or we discover and these VOE equals L is must be, they must discover the true nature of sets.

00:28:34: There isn't anything that's a true nature.

00:28:36: set because he created those sets out And then whatever... We are just referring to our intuitions To our intuitive understanding which can communicate and which can be different Which then reflected in formal statements.

00:28:51: So I find it surprising at this point that you didn't buy into intuitionism, to be honest.

00:28:56: Oh I can have a very good explanation for this... I mean ultimately i do not care.

00:29:00: so um ultimately I'm-I am NOT really interested in the metaphysical underpinnings of mathematics!

00:29:05: This is not what I care about.. I care but

00:29:07: sure

00:29:07: about um what mathematicians are doing as basically my big bafflement like what's happening?

00:29:14: Um I find it fascinating and I'd like to understand it and cared about these metaphysical questions only in so far as mathematicians are holding it.

00:29:23: So, right?

00:29:24: And then I worked out and my PhD... ...I worked on how these metaphysical underpinnings of Hamkins' end-of-wooden influence their type of mathematics.

00:29:38: They both stayed flatout.

00:29:39: you know, ''I'm a

00:29:40: Platonist.''.

00:29:41: they don't discuss at any length.

00:29:43: They just say well i'm a platonist.

00:29:45: now let's get on with business And I'm interested.

00:29:50: not as in the question, you know are they right or wrong about this?

00:29:55: That's not a question.

00:29:56: But that was interesting and kind of okay.

00:30:02: so if there is metaphysical underpinnings In mathematics what are all the influences on that?

00:30:07: Right?

00:30:09: Influences type of research at you do with questions You find relevant.

00:30:13: They agree corrective

00:30:14: proofs but disagree

00:30:16: Significance.

00:30:17: They

00:30:21: even published together, right?

00:30:26: I think you mentioned it once to me.

00:30:32: Wooden was the PhD supervisor of Hamkins and they all took us together.

00:30:36: yeah that's true.

00:30:39: we should get those at the podcast as well.

00:30:42: i think it's more likely if we got one of them than the other but let's see what future tells.

00:30:48: You'll see.

00:30:50: Now we add this kind of disagreements, but there are many more types of disagreement right?

00:30:56: Is there any other paper you want to plug in now on the other conceptions?

00:31:05: I mean what's...I moved from the metaphysical disagreements about maths and two broader questions.

00:31:12: What became clear in that is the kind of social structure of mathematics heavily impacts this.

00:31:20: So I wrote a paper about Epistemic Injustice in Mathematics, where the central case study was to work together with Fener Tanswell yet again and John Paul von Wendelheim And The Central Case Study is one about young mathematician at the time PhD or postdoc level.

00:31:40: So there was a proof constructed and submitted to the journal, then rejected on the basis that this is already known.

00:31:51: It's not new enough to be

00:31:52: published.".

00:31:53: And students complained about it saying if you say so show me where?

00:31:59: Show me when these things give any kind of lecture notes mentioned.

00:32:03: some conferences were discussed... ...and reviewers failed to do so!

00:32:08: And because it's a tiny field that this all happened in, you know the author of The Proof was able to actually ask the experts on the fields.

00:32:19: What they said is well we kind-of know.

00:32:23: yes its true but I cannot point you into any publication.

00:32:29: So you have this, that links with the notion of what's called a folk theorem.

00:32:34: So these theorems

00:32:35: are

00:32:36: somehow known by their community but whoever has proven them first is kind lost in time.

00:32:43: What exactly a folk theory means?

00:32:44: That's deep question or probably doesn't have an answer because mathematicians use it more less willy-nilly.

00:32:52: But in the paper we just use ghost theorem instead to make clear, what were talking about?

00:32:59: are theorems that.

00:33:00: The experts on a field claim at least to know but it's not accessible to anybody outside of this very small circle of expert.

00:33:10: and

00:33:11: then... It is a shame!

00:33:12: The word folk theorem is quite

00:33:15: nice no?

00:33:15: I mean its like

00:33:16: a folk song.

00:33:17: Yeah, I mean we set it for ghost theorems because the one literature that we found actually discusses what a folk theorem is was discussing folk theorems in slightly different terms than what we wanted.

00:33:28: So we mentioned that literature and then moved to move to a different term.

00:33:35: anyways... In academic presentation till i give of this i sometimes just talk about folk theoremas.

00:33:41: That's true!

00:33:41: It's

00:33:42: good.

00:33:42: yeah Just redefine the word.

00:33:44: so Yeah.

00:33:46: Why not, right?

00:33:48: So what this shows is that what counts as novel enough to be published depends on and can it depend in some extent on background knowledges of expert communities... Sure!

00:34:01: ...that might not be accessible to others.

00:34:05: Yes

00:34:05: please

00:34:06: very much.

00:34:06: I

00:34:07: mean we discussed this in terms of epistemic injustice with ethical terminology here.

00:34:13: So epistemic injustices are injustice that occur on some epistemological dimensions or have to do with knowledge making.

00:34:20: The classical case is testimonial injustice where a judge doesn't listen to the testimony of somebody because their color skin, something silly like this.

00:34:31: and we then applied that kind of philosophical framework to discuss the cases I've just given And that has sparked.

00:34:41: Well, that has moved my research effort from thinking about disagreements in mathematics to thinking about the entanglement of ethical concerns and mathematical knowledge making.

00:34:52: So I've written a paper on kind of the epistemological relevance of social justice and power relations in mathematics.

00:35:00: so who gets to decide what's get to be published?

00:35:03: What counts as serious enough right...so one case study again a PhD student, who found the floor in fundamental paper of The Field and was able to correct that flaw.

00:35:18: But he then was dissuaded from publishing this because his academic standing wasn't high enough.

00:35:26: so it's very much challenging for him.

00:35:29: as long your proof is correct you will get some credit or something.

00:35:35: That is just not the case, right?

00:35:36: So it's been chipping away at that kind of talk.

00:35:42: By the way I mean obviously what you say... Obviously we always have trouble with reviewer too!

00:35:54: And they're different and actually maybe I don't know whether anybody systematically.

00:35:58: I had recently trouble getting a paper published.

00:36:07: Now it's accepted, but there were more than one repetition in.

00:36:12: that though is very important paper and then It was reviewed by...I think Anurud was ...by a colleague who was culturally in different position, right?

00:36:23: I mean it was a different culture.

00:36:24: And he says oh this word that you're using is not the right words and what your doing sort of doesn't taste right.

00:36:32: on this note... This isn't such kind of theorem as you say yeah!

00:36:37: So basically, I think he's very good guy.

00:36:41: He wasn't completely negative but still rejected to paper.

00:36:44: based on this so cultural bias If you get a reviewer who has got slightly different cultural background, then they may not like what you're doing or there may suggest that he should really do it the way they would have done.

00:37:04: Absolutely and this can also happen in mathematics... That is not obvious to non-mathematicians!

00:37:12: To people who don't publish mathematical journals And many of my philosopher colleagues are very much part of that particular crowd.

00:37:22: So they also do not think about mathematical research being published in this sort of way, right?

00:37:27: In the kind what's a non-ideal epistemology might call the non idealities of mathematical publishing like so you can have the realities off people having different conceptions on how should name your theorem and whether this theorem falls in one book or other what counts as novel, I just mentioned and all these other aspects that are not questions about right or wrong in a mathematical proof.

00:37:53: But you mentioned culture.

00:37:56: so let me use the word cultural dimensions of mathematical activity here.

00:38:02: evaluation for proofs.

00:38:04: So very shortly this remark since Thorsten asked about studies Not aware about people really speaking with reviewers, but there is this study by St.

00:38:13: Greifenhagen About editorial practices.

00:38:16: so speaking to the editors about these things like quick opinions Is it even interesting or not?

00:38:23: And now shameless self-promotion.

00:38:29: Colin and I edited a special issue on disagreement in Axiomata's Global Philosophy On their Benedict Luever published paper modeling disagreement between reviewers, but that's not an empirical study.

00:38:42: So it is just if you are aware of these other dimensions like interestingness even... If we assume correctnesses and stuff like that one should mention that reviewers often don't look at correctness in very detail.

00:38:59: some say this looks kinder right?

00:39:02: Or if this was right then would be a tristing.

00:39:04: And he modeled So it's an interesting paper and should be open access.

00:39:10: We will link that, you know And the very final remark and then we can change the topic if you want.

00:39:17: It's an Interesting fact that in math You Know who are reviewing.

00:39:21: so its single-blinded.

00:39:23: usually The author is known to the reviewers?

00:39:27: so Its impossible In some sense To really blind people because they're only so few experts.

00:39:34: even you have a gist Who might Be the reviewer from like this little text.

00:39:39: So the other way around, it's clear.

00:39:40: and if you really want to nowadays mathematicians in many fields upload their papers at the archive anyway.

00:39:46: so just search for some sentences that can reconstruct... Actually

00:39:51: sorry because I was thinking also about this i was going to pose a question.

00:39:56: uh though i'm not a big fan of double blind reviewing think its computer science is very common.

00:40:04: As you said, first of all it's not really very effective.

00:40:08: And although its a bit artificial because often... You want to understand somebody's work out in the context of their previous work and this attempt to isolate is very artificial!

00:40:24: I doubt that prevents these sort of bias things.

00:40:31: It's in my view entirely negative effect on the practice.

00:40:39: Yeah, reviewing is another huge topic right?

00:40:41: Some people would say abolish reviewing anyway.

00:40:43: just post-publication reviews and something...

00:40:49: There are a few debate about reviewing and the publication crisis.

00:40:53: I see what you mean with the problem for double blinds, but there are also problems of single blind.

00:41:04: There's a problem without reviewing whatsoever... ...I cannot claim to have any kind of good argument over one or another.

00:41:13: I wouldn't

00:41:26: know!

00:41:28: technical terms.

00:41:30: I mean, the worry is that single-blinded review becomes triple blinded review right?

00:41:35: Nobody would ask me to review a paper of most important mathematicians because they will ask more capable people.

00:41:43: but just in theory how could i reject a paper by somebody so much better and trusting them whatever this might be?

00:41:52: Actually,

00:41:54: I don't agree.

00:41:55: I mean... I just learned a conference PC and they said oh yeah you want to make sure that every paper gets an expert reviewer?

00:42:07: And i say i agree.

00:42:08: however!

00:42:09: We also need to be able to make certain papers get non-experts reviewers because while as a non-Expert reviewer You may not be able criticize the results but it makes very much sense and better able to criticize the presentation.

00:42:25: I am not saying which journal said that me, but one editor told me we mostly accept papers with one positive at one negative review because this shows there is something really sad.

00:42:37: Exactly!

00:42:41: That's a nice note... By the way i used this argument in PCs.

00:42:44: We had some papers which were very controversial.

00:42:47: We need to accept this and we have the discussion as a conformance at least.

00:42:51: This is something interesting, yeah?

00:42:53: Exactly this argument here.

00:42:57: Case study too still to be done to look more into the reviewing

00:43:03: practice

00:43:04: of mathematical reviewing.

00:43:05: there's already a lot right.

00:43:06: I mean... Yeah sure!

00:43:09: The whole work of Lina Anderson on Mathematical Reviewing Practices which was kind of empirical study.

00:43:16: Dino was talking to mathematicians, despite your reservation source.

00:43:24: And asking them about how do you review?

00:43:29: The outcomes of this are fascinating!

00:43:33: People report that they would like to adhere... ...to the kind of epistemic ideal where we check every line and make sure everything works out nicely.

00:43:40: but it's not our reviewing ordinarily goals.

00:43:44: There are various kind of heuristics, so these fallible strategies that you might use to check whether something is correct or not.

00:43:52: So maybe it just looks like something that you already know and what you know was correct?

00:43:57: That will probably also be okay!

00:43:59: Or do we just check a couple examples for general claims... there's deference to authority in this argument Dennis made earlier.

00:44:11: You just accept the claim because it's some champion of the field who is making these claims so they will probably know best.

00:44:18: And many more strategies like this that feature in contemporary reviewing practices of mathematics, yeah?

00:44:27: By the way here we need to mention formalization also.

00:44:30: I mean this already very important and computer science said the correctness issue sort of solved saying okay i have a formal proof And the question is as interesting, or it's a presentation good?

00:44:45: and so on.

00:44:46: that correctness can be delegated to formal truth.

00:44:53: And you mean to reopen this translation debate?

00:44:56: The other half which I hadn't mentioned like Fener, Raaf or whoever... I

00:45:04: love them!

00:45:07: They would say, is this even the thing you are claiming?

00:45:10: You have proved.

00:45:13: So Descartes now says there needs to be some soul in that step so it cannot be completely formalized.

00:45:22: whether he really got the right thing

00:45:25: contrasts with

00:45:26: Leibniz...

00:45:28: What's happening here is people give a more humanly visible account and then also submit their finalization.

00:45:36: And the people who hired, apart from reviewers... ...who look at artifacts in particular check whether the artifact actually reflects what's set on paper or those assumptions are made.

00:45:50: so obviously that is important

00:45:53: But when you don't have a full grasp of your set of theorems that it might be problematic.

00:46:01: I think the meetsup project suffered from this in the seventies and later stages, but it simply wasn't clear if these small nuance changes are going quickly towards our informal limit.

00:46:21: so let me maybe ask you to is there anything you would really like to problematize?

00:46:26: another five minutes?

00:46:29: This is the moment.

00:46:31: Me to problematize something

00:46:33: or Torsten if you have still a pressing question, then let us thank for being here

00:46:41: and thank from watching

00:46:42: me.

00:46:43: yeah always.

00:46:45: And Then To The Listeners As Always Subscribe Hype Comment Give A Thumbs Up Or Five Stars Whatever in order to post this upon the pages of more Potentially interest people

00:47:00: and let us know what we should do better.

00:47:03: I mean, that's always the other alternative.

00:47:04: Yeah That maybe will even listen.

00:47:07: now it well But after the first ten episodes which will be recorded at a batch And then released afterwards.

00:47:16: Great!

00:47:16: Then thank you again and see you around.

00:47:19: Thank You bye-bye

00:47:20: Okay Bye.