Connecting Thursdays

A Worrying Lack of Evidence

How can we be certain that we know the true numbers of people suffering from the coronavirus?

Like many people familiar with TOK, I find myself profoundly bemused when someone starts lamenting how difficult it is to “integrate” theory of knowledge within the DP curriculum.   

In an age of increasing pressure to ensure that students learn the required material for their DP courses, I often hear, ruminating on “how we know what we know” is considered something like an intellectual luxury good  – a good idea to indulge in in theory, but in the real world, who has the time to fit such philosophical speculations into a biology or mathematics course? 

Well, sitting in my quarantined house in France, it’s pretty clear that “the real world” has suddenly caught up with all of us with a thud, and navigating the way forwards is going to be nigh on impossible without a clear understanding of core theory of knowledge principles.   

For a good example of what I’m talking about, check out a particularly thoughtful article by Stanford University epidemiologist John Ioannidis called A fiasco in the making? As the coronavirus pandemic takes hold, we are making decisions without reliable data, where he details how major public policy decisions are currently being made in the absence of any solid evidence, warning us that “the data collected so far on how many people are infected and how the epidemic is evolving are utterly unreliable”.   

This article has provoked considerable debate throughout the global health community, but the key point for us is not to directly address its implications for current government policy, but rather to stress that without a rigorous understanding of the true numbers involved it’s impossible to have any real faith in the models being unhesitatingly bandied about in today’s press – a point to most definitely bear in mind the next time you come across an article with eyebrow-raising specifics like, “UK coronavirus crisis to last until spring 2021 and could see 7.9m hospitalised.”

I have never met Dr Ioannidis, and it could well be that he has never heard of “TOK”, let alone the so-called “challenge” of integrating it in today’s Diploma Programme. But it’s hard to think of a stronger argument for its real-world relevance; and I would strongly urge any TOK, biology, business management, chemistry, geography, global politics, mathematics, philosophy, psychology or social and cultural anthropology teachers out there to use this article as a concrete discussion point in their current online teaching.

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Connecting Thursdays

Porous Boundaries

In what ways does historical knowledge progress?

For many people, it’s hard to think of a more static field of endeavour than history.  After all, everything that historians study happened in the past – often in the quite distant past – and the past, famously, doesn’t have the capacity to change. 

Those developing a TOK-related understanding may start to appreciate that things are not quite that black and white, as our current cultural values condition us to look differently at the same historical events than others who possess a different background would likely do.  

But what even a sophisticated TOK-aware person might miss is that some of those very values explicitly include historical categories themselves.  In this clip, Princeton University historian David Cannadine describes how recent historical understanding is beginning to re-assess the views that past historians thought were, well, written in stone.   

It’s worth mentioning that the filter of religious conflict is hardly the only one that Professor Cannadine takes aim at in his work on re-appraising what he calls the “boundaries of identity” as historical justification. In his book, The Undivided Past: Humanity Beyond Our Differences, and virtually all of the associated Ideas Roadshow IBDP videos, he examines no less than six different categories of what he calls “collective identity and collective antagonism” – religion, nation, class, gender, race and civilization – to demonstrate that, properly viewed, a proper historical understanding is invariably vastly more complicated than most people recognize.

Related resources and supporting materials that are part of Ideas Roadshow’s IBDP Portal to explicitly integrate TOK in history:  TOK Connections Guide for History, TOK Connections Guide for English A: Language & Literature, TOK Connections Guide for SCA, Rethinking History (TOK), Towards Better Explanations (TOK), The Historian’s Task (TOK), History TOK Sampler.


Connecting Thursdays

Fake “Fake News”?

How do we know when our collective moral standards are slipping?

Few these days would argue with the claim that we are currently wading through one of the most morally challenging moments in modern times: from the American impeachment proceedings to never-ending Brexit diatribes to the all-pervasive spectre of “fake news”, the world seems to be ever-increasingly polarized into rancorous tribes loudly decrying the unparallelled depths of moral turpitude displayed by their unconscionably brazen opponents.  

But is that, in fact, true? 

Renowned UC Berkeley intellectual historian Martin Jay’s careful, studied reflections gives us pause. Watch the video called Decline? featuring Prof. Jay.

Professor Jay, I am quite confident, would hardly claim that all ages are inherently identical or that we should necessarily be complacent in the current social and political climate, only that we stop for a moment to indulge in some careful, historically informed comparisons before rushing off to the land of hyperbolic judgements about the unprecedented moral decline we are living through.  

Such talk might well make for popular television.  But that hardly makes it true.  

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Connecting Thursdays

Pondering Proof

How do we know when we’ve proved something?

For most people, it’s hard to think of something more black and white than mathematics, a domain that, with its celebrated distinction between “right answers” and “wrong answers” is often invoked as nothing less than the acme, in some cases even the very definition itself, of objective tests of knowledge. 

And yet, it is not always quite as simple as that.   

You might be relieved to learn that this piece will not try to convince you that claims such as 2+2=4 are merely experientially-determined subjective opinions, but rather explore something somewhat more nuanced: the very notion of mathematical proof itself.   How do we know, in short, when something has been mathematically proven?

If you talk to a mathematician, more often than not this question won’t seem any more profound than asking her what 2+2 is, as she will unthinkingly rattle off a list of the various long-established techniques for mathematical proof that everyone agrees on: deduction, induction, contradiction, and so forth.  

But what about if I do something different from all of that?  What if, as the philosopher of science James Robert Brown suggests, I rely upon a picture instead as proof of my claim?

Well, it’s one thing to discuss these things in the abstract, but quite another to grapple directly with a concrete example, and the one that Professor Brown highlights in the associated video clip Proof by Picture on Ideas Roadshow’s IBDP Portal will, I’m quite certain, make you agree with him: a careful examination of the diagram he provides will convince you, just as much as any other “established” mathematical technique, that the theorem he states at the outset is successfully proven.   

And suddenly, our answer to the question of “how do we know we’ve proved something?” is much less obvious.   Because now we’re aware – at least sometimes and in some cases – that there might be additional ways, much less easy to objectively quantify and assess, that can somehow provide us with that very same sense of certainty that our established mathematical toolkit of proofs does. And suddenly, instead of being in possession of a clear, objective decision procedure for mathematical certainty, our gut feelings have begun to play a curiously significant role in our convictions of what is true. 

For additional examples of how TOK overlaps with mathematics, see Ideas Roadshow’s TOK Connections Guide for Mathematics which you can find in the Teacher Resources section and the Student TOK section of Ideas Roadshow’s IBDP Portal.

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