(This is the online equivalent for thinking aloud. I suppose the problem with this is that while if I say something stupid I can just pretend I never said it, there is actually greater proof of my ignorance when I actually write it down and push ‘publish’ on my blog program!)
I (still) want to claim that an ability to explain is a requirement for understanding. If you’re unable to offer appropriate explanations, then that inability indicates a lack of understanding (to the extent that you’re unable to offer an explanation).
When one offers an explanation, there must be some expectation of success, mustn’t there? But what are those success conditions? Explanations are, at the very least, bits of information that is being conveyed. And when information is conveyed, do we say it is successfully conveyed when it is received and comprehended? It seems so. When someone is trying to give me their phone number, that information is successfully conveyed when I’ve received and comprehended what they are doing.
Explanations aren’t just conveyances of information, though, but rather specific sorts of conveyances. An explanation is not just conveying any old information but specific sort of information in a specific manner or structure. (I realize that there is a lot of scholarship about the nature of explanation that I’ve not read. That I should read.) And so what does it mean to have offered a successful explanation?
At first glance it seems that successful explanation requires that the recipient of the explanation must at the very least comprehend that explanation and that explanation should aid in the understanding of the recipient of the explanation. But there’s something far more complicated about the picture than this. The onus isn’t just on the explainer but the recipient of the explanation. If I’m trying to explain modus tollens to a student and, despite my best attempts at explanation the student simply did not get it, I’d hesitate to say that the failure of explanation was my fault. Indeed, I might say that this wasn’t a failure of explanation as much as a failure to comprehend that (perfectly good) explanation. I wouldn’t expect a mathematician to be able to successfully explain Godel’s incompleteness theorem to an 8 year old such that the child would be able to comprehend and even come to have greater understanding as a result of the explanation. The mathematicians failure to succeed in this instance is not (it seems) a failure to explain but rather this is a case of the child failing to comprehend.
But we can’t let the explainer off that easily. Clearly there is some success condition for explanation, though, and a crucial component of that success condition is successful conveyance of information plus something important (increased understanding? An appropriate answer to a certain sort of question?). But how shall we explicate this idea of successful conveyance such that we can determine that the blame lies with the explainer instead of the recipient of the explanation? Maybe there’s some counterfactual move that could/should be made here. If recipient R is capable of comprehending explanation E, then person P can be said to successfully explain E if P can explain E to R in such a way that R can comprehend R (and something else. Maybe ‘and, through comprehending R come to have a greater understanding of R’ or something of that sort.). Thus the mathematician will be said to have successfully explained Godel’s inompleteness theorem if he explains the theorem to an individual who is capable of comprehending it.
I still think the account is a bit more complicated. Well…maybe. There are levels of explanation. We wouldn’t expect the mathematician to explain Godel’s theorem to both fellow mathematicians and undergraduate students at the same level. But in the case of the mathematician who fails to explain Godel’s theorem to undergraduates on account of presenting that explanation on the same level as she would explain it to her fellow mathematicians (thus talking over the head of the undergraduates)…where would we say that the blame for the failure to explain /comprehension lies? It doesn’t seem to lie with the mathematician. There are individuals who could comprehend (and come to better understand) Godel’s theorem as a result of the explanation given.
A related thought: consider two mathematicians who can offer successful explanations of Godel’s theorem to fellow mathematicians. Only one of those mathematicians can successfully explain Godel’s theorem to undergraduates. Would we say that one has better understanding because she has a better ability to explain (to more people)? It doesn’t seem so. But the mathematician who is able to explain the matter to undergraduates (and thus, I take it, distill the complexity of the matter to a great degree) is able to do something important that the other mathematician is not. I wonder what this is and/or what it reflects about the capacities of that mathematician (as compared to the other).
(Tie back to Ancient philosophy (because there always is one!): At Republic 533a Socrates tells Glaucon that Glaucon won’t be able to follow him any longer because Socrates would be giving him explanations that Glaucon wouldn’t be able to understand. (Well…Socrates actually says that they’d be looking at the truth itself rather than at images. But the thought is the same.) Does this indicate that Socrates simply isn’t able to offer adequate explanations? (Richard Robinson hints at this on pg 70 of Plato’s Earlier Dialectic.). Does this just mean that despite Socrates ability to explain, Glaucon lacks the ability to understand the explanations given? (This is what Cross and Woozley suggest on pg 257 of Plato’s Republic: A Philosophic Commentary.) This is actually rather important in the context of Platonic epistemology in that Plato says that one must be able to give an account in order to be said to have knowledge. There is, then, this question of how we judge whether one has given an adequate/successful account and whether the explanation that Socrates may or may not be able to give about dialectic at Republic 533a indicates a lack of knowledge on his part or simply a lack of an ability to offer an explanation to one not capable of comprehending it.)
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Interesting post!
“Would we say that one has better understanding because she has a better ability to explain (to more people)? It doesn‚Äôt seem so.”
I have a different intuition here. It seems to me that the mathematician who can explain the concept clearly even to undergraduates has, in that respect, a better understanding of the concept. She understands it well enough that she can distill and simplify it down to its essence, which is more than the other mathematician can do. The other therefore lacks this dimension of understanding.
“how shall we explicate this idea of successful conveyance such that we can determine that the blame lies with the explainer instead of the recipient of the explanation?”
Perhaps one could appeal to the notion of what a reasonable/competent member of the target audience would understand. Person P offers a good explanation E if the hypothetical competant target H would comprehend E. Insofar as the actual recipient R is less competant than H (i.e. less competant than what it would be reasonable for P to assume they are), blame for the failure of a “good explanation” rests with R rather than P. But if both R and H would fail to comprehend E, then it is not a good explanation — the blame for its failure rests with P.
How does that sound? I think it gives good results in our two test cases:
1) When an 8-year old fails to understand an explanation targeted at undergrads, it correctly yields the result that the explanation’s failure is no fault of the lecturer.
2) When none of the competant undergrads are able to follow the lecturer’s explanation, which was supposed to be aimed at them, then this *is* the fault of the lecturer.
Concerning the question of judging an account:
Try looking at something. Then, make a logos to describe it, as best you can. Return to that something later and double-check your logos. Perhaps you will see something different, or something new.
Consider the end of Book VI. Glaucon seems to do well here. At 511b and 511c Glaucon responses begin with “I understand” (though they are modified as well).
Then, take a look at his various responses throughout Book VII. How strong or weak are they? Are they sensible? Etc.
This may help us think about what it means to follow Socrates.
Hi Richard,
Thanks for the comments! I really like how you’ve drawn out how we might be able to tell whether the blame for the failure to comprehend the given explanation rests with the explainer or the explainee. I think that something like that is right. And then it’s probably an empirical matter (or, at least, a further investigation) to determine just what do count as appropriate explanations for target audiences.
There’s the extra question about whether a failure by the lecturer to explain a case to the undergraduates indicates a failure by the lecturer to properly understand the material or just a failure by the lecturer to properly simplify (I don’t like that word, but I can’t think of a better at the moment!) the explanation such that the undergraduates can comprehend it.
About the case of the mathematician who has the ability to explain to undergraduates vs. the one who isn’t able to…I find my intuitions going back and forth here. I do think that the one who is able to successfully explain to undergraduates has something important that the one who is unable to explain to undergraduates lacks. Is that understanding, though, or some ability to simplify and, well, explain? Of course, one might say (and I find myself wanting to say, sometimes!) that a crucial component of understanding is seeing how everything fits together in an abstract, holistic, and perhaps simplified, manner. Thus the mathematician who is able to offer explanations to undergraduates might be demonstrating this very ability (to see things holistically and in a simplified manner) and thus also demonstrating a better understanding than the one who is unable to offer such explanations. But my intuitions also go another way – there is a skill of teaching and being able to break down complex ideas into more simple ideas and not everybody has it. I don’t think we should say that because one lacks this ability to teach or break down complex ideas that she lacks understanding or, perhaps, does not have as much understanding as someone who is able to do this. As I said above and before, I do think that this extra ability – to break down complex ideas to their essence and explain them clearly – is an important ability and one that we should strive to have. But I’m still up in the air about whether that ability demonstrates greater understanding of the material or whether it demonstrates something else. (But I see your point and at least half of the time I completely agree with it!)
Hi Pilgrim,
Thanks for the comments…and my apologies for not responding sooner.
I think how you’ve described judging an account is one important way to look at it – you’ve got to offer an explanation and then go back and make certain that the explanation accurately describes/explains whatever it is you’re giving a logos of. But there’s more to it than that…we see in the Meno that Socrates says that this is an ‘account of the reason why’ (well…an ‘aitios logismos’) and then in the Phaedo and the Republic he mentions the need to be able to defend that account against questions/criticisms. (More explicitly in the Republic…but I think it’s there in the Phaedo, too.) So in order to develop the proper account you’ve got to engage in dialectic/question and answer and you’ve got to properly address the questions that are asked of you about the thing you’re claiming to know. But what happens if your interlocutor is unable to understand the explanations that you give (which I take to be what happens at 532e-533a where Glaucon asks Socrates to explain dialectic and Socrates says that Glaucon wouldn’t understand what Socrates would say)? Is that a failure to properly engage in dialectic? If so, does that indicate a lack of episteme?
Thanks, too, for pointing to bits of the Republic where Glaucon says that he understands. I actually do think that’s important – because Glaucon is demonstrating that he’s at least following what Socrates is saying sometimes. There are other bits where Glaucon says (roughly) ‘I get it sort of’ or ‘I agree insofar as I understand’ (see 534a-b for an example) where Glaucon is indicating a lack of complete understanding.
Thanks Michelle. I see now that the issue (of skill in explanation as reflecting understanding vs. something-else) is more difficult than I had previously recognized. I still lean towards the ‘understanding’ option, but I can feel the tug in the other direction too…
I’m inclined to agree with Richard’s initial intuitions. It reminds me of something a professor of mine once said in introducing us to formal logic. For relatively simple arguments, most of us can evaluate them without using formal tools. Yet breaking down simple arguments into even simpler ones, using logic, demonstrates a deeper understanding of the argument, not just the formal system.
It’s true, as Michelle points out, that there is a skill in teaching. But I think that skill has more to do with choice of language, patience, and tact than it does with genuine understanding the material.
“But what happens if your interlocutor is unable to understand the explanations that you give (which I take to be what happens at 532e-533a where Glaucon asks Socrates to explain dialectic and Socrates says that Glaucon wouldn‚Äôt understand what Socrates would say)? Is that a failure to properly engage in dialectic?”
Hi again,
I very much agree with your statement, “There’s more to it than that.” It seems when we talk about something, we are both looking at that something, and perhaps others see more. Maybe 532a6’s “dialegesthai” can help (I am thinking of Bloom’s translation of this as “discussion.”)
Now, Glaucon tells Socrates to convey what is the power of dialectic. This doesn’t look like discussion to me. Glaucon is eager to hear Socrates’ opinion.
Consider 506c, between Socrates and Adeimantus. Adeimantus appears to me to demand Socrates’ opinion. The latter’s response is: “‘What?’ I said. ‘Haven’t you noticed that all opinions without knowledge are ugly? The best of them are blind.’”
Glaucon would be following an image (533a). Perhaps Socrates would rather have Glaucon be beautiful than ugly, for to have opinion without knowledge is ugly.
It is amazing to see how full of opinion we are concerning all things! I have attempted to see this once or twice and made progress.