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?