One last post on understanding

1. Both intuitionistic logic and classical logic are understood.
2. It is not the case that both intuitionistic logic and classical logic are sound.
3. Hence, there is something that is understood which is not true.

More on whether understanding requires knowledge

In the last post I suggested that understanding needn't be factive, and hence isn't a species of knowledge.  I also suspect that understanding needn't be doxastic (viz. doesn't require belief).  Take for instance a historian of science who understands phlogiston theory, but doesn't take it to be true.  There's a retort here: sure enough the historian of science doesn't believe phlogiston theory, but there is something she is required to believe about phlogiston theory in order to have understanding; i.e. that such and such is what people took phlogiston theory to be, that "phlogiston theory" denotes such and such propositions, or whatever.  Certainly, in most ordinary cases of understanding, beliefs of this sort will be involved, but these might only be a contingent feature of ordinary cases of understanding, not essential to understanding itself.  Imagine a whimsical wizard implants in a person S's mind a grasp of some such theory $\Gamma$.  This person, being epistemically cautious, whilst having a conceptual grasp of $\Gamma$, forms no beliefs about its origin, its truth, whether anyone else believes $\Gamma$, or whatever.  It seems coherent to imagine someone who understands $\Gamma$ without having any beliefs about it (other than trivial ones such as "I grasp $\Gamma$").

Is Misunderstanding a Species of Understanding?

I take it that something of the sort Kvanvig says about understanding is correct:

The central feature of understanding, it seems to me, is in the neighborhood of what internalist coherence theories say about justification. Understanding requires the grasping of explanatory and other coherence-making relationships in a large and comprehensive body of information. One can know many unrelated pieces of information, but understanding is achieved only when informational items are pieced together by the subject in question.  [Kvanvig, The Value of Knowledge and the Pursuit of Understanding: 192]

and

[U]nderstanding requires, and knowledge does not, an internal grasping or appreciation of how the various elements in a body of information are related to each other in terms of explanatory, logical, probabilistic, and other kinds of relations that coherentists have thought constitutive of justification. [ibid.: 192-3]

(My own view actually differs slightly from Kvanvig's in that I want to take understanding as fundamental and explain explanation in terms of it, rather than the other way around, but this is tangential to what I'm talking about here.) So, for example, someone who misunderstands evolutionary theory might think that humans evolved from chimpanzees, while someone who understands evolutionary theory will hold that both humans and chimps evolved from a common hominid ancestor. Broadly speaking then we might think that there are four states a person can be in: (i) understanding; (ii) misunderstanding; (iii) befuddlement (when a person's beliefs in a particular domain are largely incoherent); and (iv) simple non-understanding (when a person doesn't have any beliefs about a particular domain, coherent or otherwise). In this case, it seems that misunderstanding is a species of understanding: the person who beliefs that humans evolved from chimps grasps coherence-making relationships between a body of propositions. Now, a dissenter might just define understanding as the factive kind, but at the very least, misunderstanding shares all the distinctive features of understanding, while lacking factivity, and so the two are naturally grouped together as cognate phenomenon. If this is right, understanding is not a species of knowledge because truth is not a necessary condition for understanding.