Inferring What We Don't Know: A Taxonomy of Paradox
I identify six themes among paradoxes with six different ways that we reorganize thoughts. Paradox is inherent in the gap that arises when we reorganize our thoughts. It is the gap between signifier and signified, as characterized by six equivalences which yield six qualities of signs. Our minds leverage the tensions in these equivalences to shift our attention from what we know to what we don't know. We thus variously clarify what we don't know.
In 1998, I was intrigued by educator Kestas Augutis's vision that every high school student write three books (a chronicle, a thesaurus, and an encyclopedia) so as to master three kinds of thinking (sequential, hierarchical, and network). I thus collected dozens of examples of how we organize our thoughts. Surprisingly, we never use sequences, hierarchies or networks in isolation. Instead, we use them in pairs:
In general, a first, large, unified, comprehensive structure grows so robust that we restructure it with a second, smaller, different structure of multiple vantage points. In 2012, I analyzed and grouped all of the paradoxes listed in Wikipedia. This yielded the following six themes:
Each type of paradox brings to light the essential gap between the (seemingly infinite) primary comprehensive structure and the (manifestly finite) secondary structure which organizes our vantage points. Our mind visualizes a qualitative but illusory relationship between the primary and secondary structures. Upon closer inspection it becomes apparent that there is no definitive way to match up the two structures. However, these six mental illusions do allow our minds to make tangible that gap, which is to say, that which we do not know. This may be considered as the gap between signified and signifier. Consider four levels of knowledge (whether, what, how, why) in terms of Peirce's types of signs (the thing itself, icon, index, symbol). Then pairs of these four levels yield six qualities of signs. A sign can be:
Paradoxes thus heighten and reveal six ways that our minds foster our mental freedom, ever shifting from the structures we know to that gap which models what we don't know.