There's some discussion going around about the number line and innate intuition. This is a good time to talk about Meno's Paradox!
The paradox is raised by the sophist Meno as Socrates attempts to engage him in some philosophical inquiry. Meno wonders how we could possibly inquire into anything without already knowing the subject we are inquiring in to. Here's the official statement of the paradox from Plato's dialogue:
Meno: And how will you enquire, Socrates, into that which you do not know? What will you put forth as the subject of enquiry? And if you find what you want, how will you ever know that this is the thing which you did not know?
Socrates: I know, Meno, what you mean; but just see what a tiresome dispute you are introducing. You argue that man cannot enquire either about that which he knows, or about that which he does not know; for if he knows, he has no need to enquire; and if not, he cannot; for he does not know the, very subject about which he is to enquire.
Socrates rejects the paradox immediately. Instead, he cites "priests and priestesses" who discuss something like reincarnation of the soul. Socrates says that if the soul is reincarnated, then we never really learn anything new. Instead, we simply recall things we've already experienced before. He says:
"The soul, then, as being immortal, and having been born again many times, rand having seen all things that exist, whether in this world or in the world below, has knowledge of them all; and it is no wonder that she should be able to call to remembrance all that she ever knew about virtue, and about everything; for as all nature is akin, and the soul has learned all things; there is no difficulty in her eliciting or as men say learning, out of a single recollection -all the rest, if a man is strenuous and does not faint; for all enquiry and all learning is but recollection. And therefore we ought not to listen to this sophistical argument about the impossibility of enquiry: for it will make us idle; and is sweet only to the sluggard; but the other saying will make us active and inquisitive. In that confiding, I will gladly enquire with you into the nature of virtue."
Ignore the stuff about immortality for the moment. We can treat Socrates' argument as a defense of innate intuition. Instead of thinking about my own soul surviving over and over, we might think instead about my genes passing down generation to generation by fit members of the species. Innate intuitions, my so-called "instincts", are presumably the things my genes have already learned how to do through the successes of my ancestors, and aren't things I need to learn today. My innate intuitions are the things that we might call "hardwired" into my operation as a biological system, as if I already know them.
That's Socrates' theory: learning is really a sophisticated form of remembering from previous lives or incarnations. Interestingly, instead of giving an argument, Socrates devises something of an empirical experiment to demonstrate his conclusions. Socrates calls over one of Meno's slave boy attendants, who is entirely uneducated in mathematics and geometry. Socrates' goal is to see what the boy "innately" understands about mathematics before any formal education.
Socrates poses a geometry problem for the slave boy, demonstrated in the picture below. The problem is to draw a square with exactly twice the area of the original square. After some discussion, the boy figures out how to double the area, by first quadrupling the area and taking the internal diagonals, as the diagram demonstrates. It's not that hard of a problem, and the boy comes to the correct solution after a bit of guidance from Socrates. Socrates takes this to be evidence that the capacity to reason about geometry is innate in all human minds, including the minds that lack formal education. In fact, Socrates later describes the educational process itself as merely a sophisticated act of helping one remember what one already knows.
Anyone who has taught math knows how hard it is to teach the most basic concepts of mathematics; at some point, it feels like either you get it or you don't. If you don't already get it, there's not much anyone can do but to just point out the obvious: here are two apples, and here are three apples, and now we have 5 apples. In fact, we usually teach children math by this kind of demonstration, and we know that no matter how many times we demonstrate the same things to, say, a cat, the cat will never pick up on the basic mathematical principles at work.
Socrates concludes that the ability to understand geometric reasoning is available in all rational thinkers, even if those abilities haven't been well developed through education and training. The discovery that the number line is not an innate intuition doesn't quite refute Socrates' theory, since we might still be able to teach the number line even to those we were not exposed to the model before, in which case the ability to learn the number line depends on some deeper innate abilities.
Clearly Socrates' views can't apply to all knowledge. But is it a good model for some knowledge? Does it resolve Meno's paradox? What do you think?
You can read the full dialogue between Socrates, Meno, and the slave boy here:
You can read more background on Plato's Meno and its philosophical importance at the links below:
#philosophy #meno #plato #paradox #socrates