Simplify Complex Problems Like Descartes

Ever Feel Stupid?

Many of us wish we were smarter than we are. Rene Descartes even felt this way:  

“For myself, I have never fancied my mind to be in any respect more perfect than those of the generality; on the contrary, I have often wished that I were equal to some others in promptitude of thought, or in clearness and distinctness of imagination, or in fullness and readiness of memory…I will not hesitate, however, to avow my belief that it has been my singular good fortune to have very early in life fallen in with certain tracks which have conducted me to considerations and maxims, of which I have formed a method that gives me the means, as I think, of gradually augmenting my knowledge, and of raising it by little and little to the highest point which the mediocrity of my talents and the brief duration of my life will permit me to reach.”

So, though he felt less clever than many others, he was able, by his estimation to increase in knowledge and mental ability over time because of a method of thinking which he came upon at a young age. And while we shouldn’t fool ourselves, his IQ has apparently been estimated to be around 162, his methods may yet help us. He made important contributions to philosophy, intellectual method, (for better or for worse) to anthropology with his dualism, and to theological proofs. Even Hume claimed to be convinced by Descartes’ proofs of God’s existence.

The Method

Let’s assume, for a moment, that Descartes really did improve his mind with his method. Don’t we sometimes face relationship problems, philosophical questions, difficult assignments, or some other such issue that makes us freeze or look for distractions? Descartes did too, but he used this method:

1. The first [rule] was never to accept anything for true which I did not clearly know to be such; that is to say, carefully to avoid precipitancy and prejudice, and to comprise nothing more in my judgement than what was presented to my mind so clearly and distinctly as to exclude all ground of doubt.
2. The second, to divide each of the difficulties under examination into as many parts as possible, and as might be necessary for its adequate solution.
3. The third, to conduct my thoughts in such order that, by commencing with objects the simplest and easiest to know, I might ascend by little and little, and, as it were, step by step, to the knowledge of the more complex; assigning in thought a certain order even to those objects which in their own nature do not stand in a relation of antecedence and sequence.
4. And the last, in every case to make enumerations so complete, and reviews so general, that I might be assured that nothing was omitted.¹

A Paraphrase

Did you get that?

Here’s my paraphrase:

1. Start with what you know. Ask these questions, “What do I know? What can I figure out? What is the problem I am facing? What facts are present? What knowledge do I have that is less certain?”
2. Break the problem down into smaller pieces. For example, when trying to solve a relationship problem find answers to questions like, “How do I feel? Is this feeling based on selfishness or a genuine offense? Do I need to apologize for anything? Who wronged me? What did they do?” In a mathematics problem break the problem down into smaller steps. Try to discover which equations apply through trial and error, find out precisely which unknowns/variables you must discover, look at mathematical expressions in terms of discrete steps like in the classical order of operations (PEMDAS). 
3. Then start solving it. Answer from the simplest and easiest questions first. Then move toward the hardest and most complex synthesized answers. Just because you do not know the solution to a problem does not mean that it is not available. 
4. Through the whole process, take notes. Write everything down, the human mind is fallible, forgetful, and is jogged quickly by lists, diagrams, and graphical representations. Write what you know, write the smaller problems and questions, write the solutions to them and the steps, then finally bring it all to a conclusion. 

Good philosophy is the art of asking and answering the biggest and smallest questions of our existence. 

References

¹Rene Descartes, Discourse on Method, (Electronic Edition), 2.7