Book VII of Plato’s Republic begins with this conversation between Socrates and Glaucon:
And now, I said, let me show in a figure how far our nature is enlightened or unenlightened: –Behold! human beings living in a underground den, which has a mouth open towards the light and reaching all along the den; here they have been from their childhood, and have their legs and necks chained so that they cannot move, and can only see before them, being prevented by the chains from turning round their heads. Above and behind them a fire is blazing at a distance, and between the fire and the prisoners there is a raised way; and you will see, if you look, a low wall built along the way, like the screen which marionette players have in front of them, over which they show the puppets.
And do you see, I said, men passing along the wall carrying all sorts of vessels, and statues and figures of animals made of wood and stone and various materials, which appear over the wall? Some of them are talking, others silent.
You have shown me a strange image, and they are strange prisoners.
Like ourselves, I replied; and they see only their own shadows, or the shadows of one another, which the fire throws on the opposite wall of the cave?
True, he said; how could they see anything but the shadows if they were never allowed to move their heads?
And of the objects which are being carried in like manner they would only see the shadows?
Yes, he said.
And if they were able to converse with one another, would they not suppose that they were naming what was actually before them?
And suppose further that the prison had an echo which came from the other side, would they not be sure to fancy when one of the passers-by spoke that the voice which they heard came from the passing shadow?
No question, he replied.
To them, I said, the truth would be literally nothing but the shadows of the images.
That is certain.
The human situation with respect to truth is somewhat like Plato’s cave dwellers. I argued in the previous post that all human knowledge is imperfect and vague. A more precise argument to the same effect would be the following.
There are two basic ways that we can learn the meaning of words. In one way, by having the meaning of the word explained to us. This requires the knowledge of other words. In another way, by learning the contexts in which the word is used. This does not necessarily require the previous knowledge of other words. Thus for example we learn the meaning of the word “red” by seeing it used in reference to red things, without a necessity of explaining the idea of red using other words. Third, we might learn the meaning of some words by a combination of the above methods.
Defining a word by other words cannot lead to an absolutely precise meaning unless the other words that are used have an absolutely precise meaning, so such a definition cannot be a source of absolute precision. And unless one points to all possible cases in which a word might be used, which is a physical impossibility, experiencing the contexts in which a word is used will also never lead to an absolutely precise meaning. It is consequently unlikely that you can arrive at an absolutely precise meaning by any combination of these methods, and consequently unlikely that you can arrive at such absolute precision in any way.
Language and thought are very closely connected. There are perhaps not many real cases of feral children, but the experience we do have of such situations suggests that someone who does not learn a language is basically unable to think. This is perhaps not true absolutely, but it is surely true that such a child cannot think clearly. Clear thinking requires language. This at least suggests that perfectly clear thinking would require perfectly clear language. But this is impossible, by the above argument. Consequently perfectly clear thinking is impossible for human beings.
This argument does not refute itself. It it of course impossible to have a proof that there are no proofs. Likewise, if absolute subjective certainty is impossible, as I have suggested, then it is impossible to have such certainty about this very fact. There is no inconsistency here. Likewise, if all thoughts and all arguments are vague, then these very thoughts and this very argument is vague. There is no inconsistency here.