I’ve found it useful to think in terms of known / understood / intelligible. Each of these has three states:
- Known, not known, not knowable
- Understood, not understood, not understandable
- Intelligible, not intelligible, not intelligibuble
Some things are not knowable, in terms of a given system of thought. For example, Heisenberg’s uncertainty principle in quantum mechanics states that increasing the measurement accuracy of a particle’s position increases the uncertainty of a simultaneous measurement of its momentum. If its position is exactly known, its momentum is unknowable.
Something is not understood when there isn’t a compelling answer to a “Why question.” When an explanation is persuasive, a phenomenon is deemed to be understood. We understand why the sun moves through the sky because we accept an explanation about planetary motion that involves Newtonian mechanics and a disposition of the sun and the earth. Understanding is a matter of argumentation; it’s subjective. At least one human is necessarily involved, and usually a community decides whether it understands a process, that is, whether the explanation meets the standards of that community.
When the terms of an explanation exceed one’s grasp, something is not understandable. Religious mysteries fall into this category; the Holy Trinity is not understandable in logical terms. A more mundane version occurs when an individual or group doesn’t have the contextual knowledge that supports an explanation; string theory is not really understandable to those without the requisite knowledge of advanced mathematics. However, I will place such cases in the category “not intelligible.” (Agreed, this taxonomy isn’t water-tight.)
By intelligible I mean something that can be apprehended in general terms. One may not grasp all the steps of an explanation, but the overall shape is familiar. Any book written in English is to some extent intelligible to an English speaker. (Translations of French postmodernists don’t count.) If something is not intelligible, not only do you not understand it – you’re not even sure what the topic of discussion is. Many intellectuals might find it unintelligible that Francis Collins, leader of the human genome project, is both a devout Christian and a scientist.
When there is no possibility of making something intelligible, it’s “not intelligibuble”. Philosopher of mind Thomas Nagel famously argued that because consciousness has an irreducibly subjective component, we will never know what it’s like to be a bat. That experience is not intelligibuble to a human.