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Recording and transcript of the "philosophy and inclusive design" presentation I delivered in August 2021.

recording

Acknowledgement of Country

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I began my presentation with an Acknowledgement of Country. For privacy reasons it is not included in the recording.

So I always like to begin with my own acknowledgement of country. We have been presenting from [First Nations Country] and I particularly want to recognise their wealth of mathematical knowledge and practice, that they have preserved for over tens of thousands of years. They are the traditional owners and their land was never ceeded.

And I think in the interest of, you know, public philosophy and inclusion - we are standing on indigenous land that was stolen and that should be informing our thinking. Even if it's unconsciously or subconsciously.

this video makes sense in my head but like WHY DID WE CREATE THIS STUFF

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I played a video uploaded to TikToc by the user @gracie.ham. You can view their original video at:

https://www.tiktok.com/@gracie.ham/video/6864198263063448837

and their follow-up:

https://www.tiktok.com/@gracie.ham/video/6865480616012516614

Introduction

00:00

So that's one of my now most favorite people. Her name is Gracie Cunningham and that video she put it up online - as you saw on TikTok - August of last year and it blew up. It got shared to Twitter, it got shared to Facebook. It was covered on multiple news sites, radios. All the blogs. Everything. She received a lot of hate. People messaged her insulting everything from her looks, to her personality. Some even suggested... Where is it?

[audience member] top right.

"Go jump off a Cliff". Because she posted 52 seconds asking some really important philosophical questions about mathematics.

You can see from some of the headlines that some scientists stepped up and defended her. Took about 24 hours before they got in on the show. Bit longer and some philosophers also stepped up.

Eugenia Cheng is one of my most favorite mathematicians. She wrote a full, two-page document where she took every single question that Gracie asked and she answered them honestly and comprehensively.

So you know she's... if you Google "TikTok math girl" you will find Gracie.

And while this was a great opportunity for public philosophy and for philosophers of mathematics to step up and share their work. It should not have happened in the first place.

You all heard the giggles. I'm not gonna ask who was laughing. But you all heard the giggles. Some of you thought that was really, really funny and I'm going to bet you weren't thinking it was funny for charitable reasons.

You were  probably judging Gracie on her ignorance, her lack of articulation. Maybe you were judging the fact that  she's a 16 year old girl doing her makeup. 'cause we all know how floozy 16 year old girls can be.

Except what she was asking are really important, deeply philosophical questions. And the fact that this happened and she received - and continues to receive - public hate is an  indictment on philosophy and it is an indictment on philosophers.

Philosophy and Inclusive Design.

02:42

Philosophy and Inclusive Design.
Public ignorance is an indictment of philosophy, and the public perception of mathematics is notoriously poor. We  have decades of research, we have our very own special mental illness called math anxiety, all of which is an indictment of philosophy. Yes, philosophy of mathematics, but also philosophy generally.
Mathematics is hard, it's irrelevant. It's innate, but it's abstract. It is unknowable to most people and  comprehendible to only a few.

We call this "the romance of mathematics". It is well documented myth. It is all lies.
Philosophical models of mathematics  that underpin these perceptions and reinforce them throughout the lifecycle  of mathematics education have really significant ethical implications. Our  quality of life today is very strongly  connected to educational achievement  that requires a minimal standard of  mathematical literacy.
I think the philosophical status quo is  not good enough. And that as a   discipline and as individuals, we need  to do more than just respond ad hoc  when something blows up online. We  need to engage more.

So, using philosophy and mathematics  as a case study, I'm going to argue for inclusive design. That is, philosophers  should approach their work via process  that prioritises accessibility  and inclusion of people from diverse  physiologies, psychologies, cultural  backgrounds, and educational  histories. And applying inclusive design in philosophical practice will result in  better philosophy. Philosophy that is  methodologically rigorous, intellectually honest, dynamic, flexible, relevant, and more importantly, engaging.

Here's the plan:
I'll very quickly introduce you to  inclusive design, I'm going to give you  an overview of philosophy of  mathematics. I'm going to describe a  possible, future version of an inclusive  philosophy mathematics. And then I'm  gonna bring it all back together with  inclusive philosophy by design.

Hopefully we'll get there. I apologise if we don't.

Inclusive design

05:26

Inclusive design is... Talk about  inclusive design. I did my PowerPoint  on Mac and this is PC and it stuffed up  my formatting. That is on computer  people not doing proper accessible  design.
That's a lot of words. You know, it's  very old school to go straight to  definitions. Who can be bothered.
There's some quotes. It's still with lot  of words. And you know, inclusive  design as a concept, it's pretty vague. It's pretty nebulous. There's a lot of  different words that are used  interchangeably depending on the field, for example, whether you're in  architecture or web design. Whether  you're working on legislation for  government. Hence accessibility,  usability, design for all, universal  access, inclusive design.
'm using "inclusive design" deliberately because I want to prioritise the explicit  and deliberate engagement with  marginalised groups.
Design is a  process and a  methodology. It is a  perspective, it is a set of principles, and it is a process. There's a lot of different ways of  looking at it. You can look at it as  intersections. You can look at it as  dimensions that relate to each other.  You can look at it as families. You can  look at it as processes. This is one of  my favorites - looking at it as an  ecosystem. And, I just really like this  one. I like the idea that they talk about  amplification, which is actually not  included in a lot of models of inclusive  design, but I like - one of my favorites  because they specifically include  amplification, which in this context  would be public philosophy.

Philosophy of mathematics

07:25

Inclusive design. What does that have to do with philosophy of mathematics?

So let's start with what philosophy of  mathematics is not.
Philosophy of mathematics is not  absolute. It is not universal. It is not  functional. And it is not objective. It is  severely, deeply flawed.
We have a nice map for mathematical  sciences, provided by a university in  Japan. I looked at a lot of different  maps. This one is the prettiest.
There's a lot of different fields. They're  still missing some because this is just  the mathematics that they teach at  their university. And you know there are bigger, more complex maps, but  they're far too messy and not as pretty. But there's a lot there.
As far as philosophy of mathematics  goes, there is no consensus on what  mathematics actually is. In some  philosophies it's all about sets, in  others it's all about numbers. With  some it's all about logic and axioms of  proof.
Often the models are internally inconsistent. And even when you have  different models with the same  assumptions they are between-model  inconsistent. You can't take one model  of sets and another model of numbers  and put them together because they're  inconsistent and they contradict each  other.
There are metaphysical gaps. None of  the current you know, big name  philosophies of mathematics can  properly deal with problems like "what  is infinity?" What does it mean to have  an uninstantiated universal? They don't  know what to do about prime  numbers. Or irrational ones. Infinite  decimals. And they don't know what to  do with mathematical biology.
On the sunflower, seeds are actually  packed according to the Fibonacci  sequence of numbers. Biological  membranes, for example in plant cells,  form what we call triply periodic  minimal surfaces. Which are incredibly  complex 3 dimensional shapes that we  also see in the atomic structures of  crystals. For example, in diamonds: we  also see triply periodic, well they're  not surfaces because they're  lattices, but a triply periodic lattice that  corresponds to a triply periodic surface in a membrane. Philosophy of math  doesn't know what to do with that.
Today, the metaphysics of mathematics is concentrated on realism versus anti-realism. There has being superficial and insufficient engagement with the  epistemology of mathematics. And it  has failed to keep up with the  developments in mathematics. Modern mathematics now includes fields that  depend on assumptions that cannot be claimed as universal. In fact, some you can take or leave it - it doesn't change  mathematics.
Philosophy of mathematics, it's not  universal. It is predominantly dominated by dichotomous thinking. So, when you have the two sides of the debate. This is rooted in the old Greek  tradition of people getting up on the  stage and duking it out. There's  someone "for" and someone "against". And that has flowed through into our  writing and our work, and especially  into our mathematics.
Most of the discussions about different models are critiques. They're not about
"how does this model work on its own  terms?" "How could we possibly  improve it?" "Is there a way that we  could adapt it or transform it, so that it  works with other models that have to  do with other mathematics?"
Most of the work on the epistemology  of mathematics has actually been happening in cognitive science and  mathematics education. And it is super cool! The stuff we know! We can map  areas of the brain that are specifically  involved in numbers and thinking about mathematical problems. We know that  babies as young as 24 hours old can  add and subtract between 1 and 2, and  2 and 3. We know this! Our brains  are born doing mathematics, but our  philosophy takes none of that into  account.
It is not objective. This is quite possibly the biggest sin of them all, I think. Everyone loves to talk about how  objective mathematics is. That's  debatable.
Philosophy of mathematics: not  debatable. It's not objective.
It is explicitly biased against non-symbolic mathematical systems. If  you're a culture that didn't have a  written system, you were deemed non-mathematical. Doesn't matter what you did, what tools you use or how sophisticated your engineering was, you didn't have mathematics.
All of our philosophy, not just the mathematical kind but all of it, is rooted in preservation and survival bias. So,  this graph here: Anthropological Actions that Create Bias in Natural  History Collections.
Most of philosophy is rooted in history.  We rely upon the works and thoughts  of people in the past. And these are all  the ways that their work can acquire  artifacts of transmission. At every  single point, someone's work can be  excluded. It can be changed or revised.
Maybe they literally just burned. How  many times did invading parties burn  down libraries?
It's also not functional.
Philosophy mathematics isn't used by  mathematicians. And vice versa. There  is no mathematics of philosophy,  because philosophy doesn't make  sense and we would rather do  hyperbolic geometry. It's not useful for  mathematics education. There's not, as yet there aren't many models that can  be used to incorporate new  developments.

And it continues to  perpetuate systemic injustice.
What if we created a philosophy of mathematics that wasn't any of that?

Inclusive philosophy of mathematics

14:09

What if we created an inclusive  philosophy of mathematics? What could  it be?
It would be engaging, accessible,  equitable, adaptable, and relevant. It  would be lovely. Might be a pipe dream.
This is one proposal. People who know  cog-sci might recognise this little quartet  in the middle. Anyone know what they  are? Enacted, embodied, embedded, and extended. Anyone? Yeah. Do you know  about it?

[audience member] 4E.

4E? 4E what?
[audience member] Basic cognition.

4Es of cognition! Yes! Thank you! Wow. I was really hoping more people would  know that!
So inclusive philosophy of  mathematics would incorporate the 4Es of cognition, and by doing so  would cover all of those gaps that I  mentioned earlier. So it would look at  ethnomathematics, mathematics and  social practice. It would look at  mathematical objects that exist in the  physical world independent from  humans. It would look at how humans  apply mathematics to our environment  to adapt and alter our environment.  And it would look at how our bodies do mathematics - in our brains, but also in our other physiological systems. By  metabolic processes, by sensory  processes. You know, even... if I  wanted to measure the length of this  room, I could walk and I could count  my steps or count my arm widths.  Once upon a time measurement was, you know, the foot, the length of the  foot of whoever was king at the time.
It wasn't very stable. But we were  using our bodies for math.
An inclusive philosophy of  mathematics would do that.

Inclusive philosophy by design

16:06

So philosophy more generally, what would that look like? How could we do that? Well, we need to start with these  four questions:
Who's philosophy are we doing?
Which epistemologies are we  validating?
Who does our philosophy include,  exclude, marginalise?
And do the ends of our philosophy  justify the means?
And we need to ask these questions  across the philosophical life cycle, which is something I... made up on the  spot. And I like this, you know,  "engagement". I was thinking "public  engagement" and PowerPoint  suggested a ring. So you know, maybe  we need to be going out there and  proposing to the public. We need to  make them a promise that we will  respect and honour them, that we will  value them, that we will treasure them  as partners. Maybe PowerPoint is onto  something.
If I may borrow from my marketing past, this requires us to know our  audience. Who we talking to? When  are we talking to them? How are we  talking to them? And if anybody's ever  done any writing, we need to kill our  darlings. That means we need to get  rid of all the excess, unnecessary  baggage that is weighing us down. All  of those side characters that aren't  contributing anything to the plot. They  need to go! Embrace your inner Joss  Whedon. He killed too many darlings in my opinion, but that's a different story.
This could be what it looks like in research. When we're planning our  projects, are we interrogating our own  unconscious biases? We could all do  to be a little less WEIRD. That's not my  acronym. It was created by a couple of  neuro-scientists analysing psychological literature. They found  that all of the samples came from  populations that were wealthy, educated, from industrialised countries, rich, and democratic. Turns out, we  have very different brains to people  who come from different socio-economic environments. It doesn't  make for good research.
We need to seek out interdisciplinary collaboration. Why are there only  philosophers in this room? Maybe   there are non-philosophers in this  room; they're probably too scared to  point out that they are non-philosopher.
And we need to establish cross-institutional relationships. We need to  work with government. We need to  work with non-government, other  universities, nonprofits, community  groups. The works.
In education, we need to prioritise diversity over canon. Plato and  Aristotle lived two and a half thousand  years ago. They were really not nice  people. Plato was a eugenicist. And  Aristotle was a misogynist.

Maybe  you're a woman, from a  marginalised racial background, and  then you rock up to your "intro to  philosophy" class, and they're like,  here's a dead white guy who lived in a  completely different socio-political and  physical environment. And we're going  to use what they maybe said (because  it was two and a half thousand years  ago, and we're using translations of translations of translations) we're going to use that to talk about our lives today.
Maybe we could look at diversifying our curriculum. Maybe we could just share a bit of context. You know, Heidegger was a Nazi. What does that  mean for his philosophy? What does  that mean when we study his  philosophy? Could he possibly have  some biases sneaking their way in  there?

We need to get out of our classrooms.  And we need to provide alternative assessments - and by that I don't just  mean modified assessments for people with disabilities, I mean something that  isn't writing.
For my unit this semester we are  required to produce a piece of public  philosophy. That is written. This presentation doesn't count. This is just  me doing it for fun. Because I'm... you  know, a sucker for punishment.
I was at a workshop this morning run  by the Public Philosophy Network. I  was up very early because they're running on East Coast time in the States. And we did a little group  exercise where we all posted little  notes on things that we've experienced as students, as educators, as  researchers, as general public, things  that have worked as public philosophy  as... You know, promoting inclusion  and diversity. There's a lot there.
This is - I'm not saying anything new.  Everything I'm saying has already been said before, just most people were screaming into the wilderness and no one was listening.

What do philosophy and statistics have in common?

[text on slide] People like them the  least.
There was a study done in 2019 in the  United States of how people feel about humanities and arts. There's us! Philosophy! Statistics! People like us the least. Science, history, even math  got in there higher than us. What is  going on? I'll tell you what's going on:
People aren't reading. When people, general public, are out there engaging  with humanities and arts, they're not  reading. They're watching videos.  They're doing online searches. Sometimes they pick up a book, but  that's classified as engaging with literature, and it doesn't happen nearly  as much as you think. Usually it's shows with historical content or researching something online. People  like documentaries. So "writing stuff" is not public philosophy. That's just writing stuff - you're like every other  blogger out there.

References

22:39

Those are my references. If anybody wants them.

Audience question no. 1

22:48

[audience member] I think it's rather  hopeless if you want to make the  philosophy of mathematics inclusive. I  think the mathematics itself already is not very inclusive, and if you are talking about the philosophy of mathematics, you will  be doubly handicaped, so that's...

[reply] Yes, because mathematics and  how people perceive it and interact with  it, teach it - everything comes back to the philosophy of it.

[audience member] why?
[reply] All of it.That's what people do.

[audience member] but why? Why is it? Why is philosophy here... say, why not  mathematics itself? I think much of the blame you put to the philosophy of mathematics actually should be laid on the doorstep of mathematics. At least that was my impression.

[reply] Nobody's out there reading Euclid's elements, or at least very few. Most of them are reading what Plato wrote about Euclid's elements.

[audience member] I had geometry, in secondary school that we had to learn all the axioms of Euclid. I think it's no longer done anymore.

[reply] But you need to understand that entire reason Euclid's elements are  written the way they are is because he  was working in very mathematically  hostile environment. Because, you  know, Greek entertainment at the time  was two people getting up on the  stage and having an argument. Zeno's paradoxes were less about mathematics and more to see who  could entertain the general populace. If you look at what the mathematicians  were saying about Euclid's elements,  it's nothing at all what the philosophers were saying. And if you look at  mathematicians in the past - even  Descartes says Aristotelian  philosophers may as well as have not  gone to school.

[MC] let's just squeeze in one more question.

Audience question no. 2

Item Subtitle

[audience member] So who is the blame for the crime? Nah! I was gonna say, what do you think of sacred geometry? I've heard that, you know, I've seen the Fibbonaci sequence and once I figured out you can draw a circle. And then connect another circle part-way through it and it just kind of keeps going inside. I don't know something hold...

[reply] It's cool is what it is. It would be  nice if we could have coherent  conversations about it, you know,  between mathematicians, which we  can't because different mathematicians are working off different foundational  philosophies. And it would be cool if  we could have those conversations  with everybody else. But people are so  scared of mathematics that you can't  even ask them about it without them  going into a state of anxiety. There's a  ton of research on that. Happy to share it.

You know, like in the end, our entire  educational system is based upon  philosophies that are passed down  through generations of Western European and Anglophone people, and most of them, even if they weren't actively philosophers were doing  philosophy and were employing it. You  know, Dewey was revolutionary in the  United States, he had a very significant influence on their educational  practices. Dewey was a philosopher.  But he wasn't as impactful here. And  he wasn't as impactful with Europe.  And so in the end, you know, if  philosophy is the oldest form of human intellectual thought, then everything  comes back to it.
You know, in the end we need to stop  denying our responsibility and start accepting and thinking maybe we can  do something about it. It's not about  blame. It's about: we've got the tools,  we've got the resources. Why not?  What are we scared of?

Acknowledgement of Country
this video makes sense in my head...
Introduction
Philosophy and Inclusive Design
Inclusive design
Philosophy of mathematics
Inclusive philosophy of mathematics
Inclusive philosophy by design
References
Audience question no. 1
Audience question no. 2
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