Plato’s Cave: Lost in the symbolic system

Plato’s Cave

More than two thousand years ago, philosopher Plato, came up with an idea that the human knowledge system was based on unreal, imaginary observation of the actual world. In his book, The Republic, he explained the idea with an metaphor.

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.

The discussion above, however, is not the most horror thing of the metaphor, but the following.

And now look again, and see what will naturally follow if the prisoners are released and disabused of their error. At first, when any of them is liberated and compelled suddenly to stand up and turn his neck round and walk and look towards the light, he will suffer sharp pains; the glare will distress him, and he will be unable to see the realities of which in his former state he had seen the shadows; and then conceive some one saying to him, that what he saw before was an illusion, but that now, when he is approaching nearer to being and his eye is turned towards more real existence, he has a clearer vision, -what will be his reply? And you may further imagine that his instructor is pointing to the objects as they pass and requiring him to name them, — will he not be perplexed? Will he not fancy that the shadows which he formerly saw are truer than the objects which are now shown to him?

From ancient times, our ancestors gradually found out our brain were not able to process far too complex data. So we started to analyze things and construct models for those in the natural world.

We started to define everything in a simple way. We thought of the edges of everything as lines, which formed shapes, solids and so on. Then we found that our natural language system was not accurate enough to power the logical and abstract thinking, therefore we built a new symbolic system called mathematics.

Is this a gate to heaven, or the abyss to the hell?

The modern logistics point out that our mathematics is essentially a first-order predicate logic, which defines symbols and axiomatize their algorithms. For example, in the N set, we define ‘a+b‘ as outputing the next bth number of a, but why don’t we define as others? The answer is clear – the original definition is ACTUAL.

There’s always a question that why math can describe the real world so accurately. There’s no other reasons but because it’s a enough complete system – Godel’s completeness theorem works well on it – and it’s based on ACTUAL axioms. Any natural language can describe the cosmos accurately as well.

Any natural language can describe the cosmos accurately as well.

Perhaps, I wonder, everything we have done on math, from calculus to linear algebra, from logic to group theory, is not the true answer to the world. Like the answer 42 after thousands of millions of years’ calculation, maybe in the end, we draw water with a sieve.