1.2.1.2 Descartes’ Systematic Doubt

Version 1.0 July 2016                                     (Previous Version)

The French philosopher and mathematician René Descartes (1596 - 1650) was a smart fellow.  He invented coordinates systems (like the x and y coordinates in graphs) for the first time providing a quantitative frame for geometry.  From that beginning he invented analytic geometry, a prerequisite for the eventual development of infinitesimal calculus by Newton, Leibnitz and others.  

Descartes went on to conclude many other things that we now know to be wrong.  For instance, he proposed that the pineal gland connected our physical brains to the supernatural world of ideas.  But his idea of systematic doubt is a good start.

Descartes’ method of systematic doubt is that we should doubt everything that is uncertain.  He concluded that we can doubt everything but our own existence: I think therefore I am (in Latin, cogito ergo sum).  I can doubt simple things like my perceptions, more complicated things like my knowledge of what is happening in the world, people I learn from, and even my memories.

●   Can I doubt the colour of my desk?  Yes of course.  If we shine different coloured lights on the desk it has a different colour.  If it is completely dark, then the desk has no colour.  The colour is apparently not a property of the desk but of the light, and it is not constant.

●   Can I doubt that the sun will rise tomorrow? Certainly!  The sun has apparently risen every morning for thousands of years, even if we can't see it through clouds at the time.  So most people have no doubt the sun will also rise tomorrow.  Close to the North and South Poles once the sun rises it stays up for about 6 months, then sinks below the horizon for the other six months of a year.  But even if we stay in “normalâ€� latitudes, there might be some catastrophic event that destroys the Earth overnight.  If the Earth blows up, then the sun won't rise tomorrow at this place on Earth.

●   How do I know the sun has risen every day for thousands of years?  No-one has lived that long.  The writings I refer to or the people I talk to could be lying or simply mistaken.  Perhaps I misremembered what they said.

●   Indeed I can doubt all my memories.  The memories I think I have don't always correspond to other people's memories of the same events.  Either my memory or their memory or both memories must be wrong.  I can certainly doubt my memory: why would mine be accurate, and others’ not?  Perhaps some strange God created a small universe just moments ago with me in it, adding false memories of the past to my memory banks.  How could I possibly demonstrate this didn’t happen?