Thursday, 6 July 2017

Plato and Socrates, on Data Science versus Inferential Statistics

The other day I was listening to the podcast “The History of Philosophy Without Any Gaps” (a nice way to catch up on the subject while exercising), an episode which talked about the Dialogue “Meno”. This is the dialogue where Socrates (or Plato, depending on your perspective) discusses Virtue with one of his interlocutors (or victims, depending on your perspective).

Socrates speaks on virtue, but he makes it plain that he thinks the key to virtue is knowledge – as I understand it, he believes that a person with knowledge will always want to do the right thing.

Leaving that aside, he also speaks of “true opinion” or “true belief” versus “knowledge”. True belief can lead people to perform the correct actions, but it inferior to knowledge, as true belief can be possessed without understanding. In other words, we might know something is correct, but not know why it is correct.

Here’s a quotation from Plato’s Meno, to show what Socrates is getting at:

Socrates. You would not wonder if you had ever observed the images of Daedalus; but perhaps you have not got them in your country?

Meno. What have they to do with the question?

Socrates. Because they require to be fastened in order to keep them, and if they are not fastened they will play truant and run away. (Bloggers’ note: it was said that the statues Daedalus made were so realistic that they had to be chained to keep them from running away).

Meno. Well. what of that?

Socrates. I mean to say that they are not very valuable possessions if they are at liberty, for they will walk off like runaway slaves; but when fastened, they are of great value, for they are really beautiful works of art. Now this is an illustration of the nature of true opinions: while they abide with us they are beautiful and fruitful, but they run away out of the human soul, and do not remain long, and therefore they are not of much value until they are fastened by the tie of the cause; and this fastening of them, friend Meno, is recollection, as you and I have agreed to call it. But when they are bound, in the first place, they have the nature of knowledge; and, in the second place, they are abiding. And this is why knowledge is more honourable and excellent than true opinion, because fastened by a chain.

Meno. What you are saying, Socrates, seems to be very like the truth.

Socrates. I too speak rather in ignorance; I only conjecture. And yet that knowledge differs from true opinion is no matter of conjecture with me. There are not many things which I profess to know, but this is most certainly one of them.

So, Socrates insists that the elements of true knowledge “are fastened by the tie of the cause”, while true opinions, though they are often “beautiful and fruitful”, can “run away”, since they are not “fastened by a chain” (i.e. through understanding via a chain of causation) .

This reminds me of the debate between new data science methods and the more traditional model driven statistical methods. Many of the newer methods, especially in the category of predictive analytics, don’t supply much understanding of the causal structures behind data, whereas the major techniques of the older style did. The older methods provide such information as which variables are statistically significant in predicting the outcome variable, what the comparative strengths of these variables are, and so on. However, these methods make many assumptions about the data, and the models are sometimes difficult to build and interpret.

The newer methods often make few assumptions about the data and are quite robust in that regard. However, they generally don’t give much in the way of helping to understand the causal structure behind the data – neural nets, for example, are generally thought of as black box solutions. Frequently, however, they can do better than the older techniques when it comes to predicting relevant outcomes for new cases or new datasets (assuming that the researcher has been careful in the use of test data, holdout data, etc., and that the underlying conditions relevant to the analysis haven’t changed much).

So, if we could get into a Tardis and whisk Socrates into the present day, he might say that the newer methods are good at generating “true belief”, but the older methods are better at generating “knowledge”. But in the current context, that would be considered heresy, so he would probably be put on trial by powerful elements of the data science community…and you know where that leads.

Sources

https://historyofphilosophy.net/

Plato. Plato: The Complete Works (31 Books) (Kindle Locations 8919-8930). Titan Read Classics. Kindle Edition.

http://www.encyclopedia.com/literature-and-arts/classical-literature-mythology-and-folklore/folklore-and-mythology/daedalus

And here’s a modern Socrates, the XKCD creator, Randall Munroe, on the subject:

Now that we have contemplated the mysteries of knowledge versus true belief, you should read a short story on the subject, whereby a gambler can’t be sure whether his winning streak is due to knowledge, or just true belief given to him by something diabolical.

A Dark Horse

Just what might a gambler give up, to go on the winning streak of his life? Even he can't know for sure. Christopher Marlowe's Doctor Faustus legend is given a Damon Runyon spin, in this short story.