One thing I love to do is browse different sections at bookstores and see what I find. About ten years ago, while browsing the philosophy section I found a small, unassuming pink book named Epistemetrics by Nicholas Rescher:
Epistemetrics is a scholarly discipline waiting to be born. With regard to scientific information there is the discipline of scientometrics, represented by a journal of that name. Science, however does not have a monopoly on knowledge; although it is one of our most important cognitive resources, it is not our only one.
Epistemology, if you’re not too familiar, is the philosophical study of knowledge, and Rescher here is proposing the birth of a subfield of epistemology aiming to make knowledge measurable and quantifiable.
The entire book is great, it’s only 105 pages long and it’s a fascinating consolidation of well-known and lesser known ideas in epistemology - tying these ideas together with the common goal of making these ideas quantifiable.
I’m interested in writing more about this book at a later point, but for this post I wanted to zoom in to the first chapter. This chapter had me fascinated 10 years ago, and it has continued to resurface at least once a month in all kinds of unexpected and unrelated scenarios.
Asking for More Than Truth
Duhem’s Law of Cognitive Complementarity
Many mathematical laws describe something so simple and so elemental that it is hard to un-see after you’ve been exposed to them. This is equally so the case with Duhem’s Law of Cognitive Complementarity.
It’s hard to do Rescher’s writing justice, since every single paragraph is both dense and precise. Here goes.
In our everyday usage of the word knowledge, it is clearly distinct from information. What makes knowledge so different? Rescher claims that certainty is one aspect that makes knowledge knowledge. This is not so hard to imagine - imagine going hiking and you see a mountain in the distance. You say “I think the mountain is about 80km away”, your hiking friend says, “You’re way off, it’s actually 187.5km away.”.
You open your phone, find the mountain and see that it’s 187km and 650 meters away. Note what has happened here, not only were you wrong, you were also less detailed about your prediction.
Rescher states there are two aspects to knowledge that stand in relation to one another when it comes to certainty. There is the detail of a claim, and there is the security of a claim. Now, these two words are simple but surprisingly difficult to grasp precisely due to their overloaded meanings.
The detail of a claim is relatively straightforward, especially if you are able to express this claim claim numerically.
I found that security is more difficult to grasp, it may mean how “sure” you are about your prediction. When making the claim about the distance to the mountain, you implied some uncertainty “I think…”, whereas your friend claimed greater certainty “You’re way off, it’s actually …“.
Rescher identified that the physicist and philosopher of science Pierre Duhem made a strong claim about how these two aspects of claims stand in relation to one another. You are always able to trade certainty for detail.
Imagine having to make a claim about the mountain, but you’re challenged to phrase it in such a manner to say something you are 100% certain about. You could say “I’m absolutely certain it’s less than 10.000km away”. The utility of such a statement is questionable, but you wouldn’t experience the slightest of doubt making such a claim. Similarly, how about “I’m very certain it’s less than 1.000km away”? Going on, “I’m quite sure it’s less than 250km away”; “I think it’s less than 100km away”.
You are actively trading certainty for detail.
Rescher took Duhem’s tradeoff and formalised it with a remarkably simple equation
Where the product of , security and , detail is lesser than or equal to a constant. He named this law Duhem’s Law of Cognitive Complementarity.
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I have to end this post for now, as I have been writing for long enough for now. I will certainly revisit the topic at a later point in time and dive deeper into the fascinating topic of this deceptively simple tradeoff in the novel field of epistemetrics.
But for now, please entertain yourself with the amazing interactive graph above and make sure to get yourself a copy of Rescher’s Epistemetrics.
Stay tuned for more.
~ Laura