Probably a lot less than you think. Today, we'll look at the thoughts of René Descartes', a French philosopher who lived in the early 1600s and went to extreme lengths to answer this question. He was interested in finding out what beliefs are truly undoubtable because philosophical reasoning, just like mathematics, is built on foundational beliefs. These beliefs are those that are self-evidently true, so they are the only sure points of thought that we can construct the rest of our beliefs on. For example, if it's self-evidently true needless suffering is bad, then that belief could function as a starting point to construct the rest of our beliefs around, and if there were other self-evident truths, then we could construct even more beliefs around those as well. The idea is that if you use rigorous logical reasoning in constructing your other beliefs from the most fundamental truths, then all of your conclusions are definitely true. And because your conclusions are true, then you can find out even more true things from those conclusions. If you repeat this over and over, you can come to discover many truths about reality. This method is called deductive reasoning. Descartes agreed that this is how we determine what is true or false, but he felt that philosophers of previous generations held beliefs in things that wouldn't hold up under intense scrutiny, and if their most fundamental beliefs weren't true, then how could he trust that their conclusions were true? Troubled by this, he wrote a book called "Meditations on First Philosophy," where he inquired about everything he couldn't be absolutely certain of.
By everything, I mean absolutely everything.
We might think we are justified in believing that there are rocks and trees outside, but then again, our senses are open to deception at any time. How can you be absolutely sure that you weren't drugged earlier on in the day? Even things like sounds, colors, and shapes are things that we couldn't be absolutely certain of while under the influence. Descartes decided that he couldn't be certain in believing that anything in the external world exists, not even the people he talks to, because there is always the possibility that he is dreaming. We've all probably had a dream so vivid that it felt real, only to wake up in a shock because we thought we didn't experience anything that was actually real. In our dream, we thought we were living in the real world, that the objects and even people we talked to were real, but as it turned out, we were walking on a ground that didn't exist and talking to people that didn't exist either. If your dream world seemed like the real world, how could you be sure that you find yourself in the real world right now? Ultimately, Descartes believed that we have absolutely no way to be certain that the external world exists at all.
...But he wasn't quite satisfied with that. He felt that we could doubt even more things besides the external world: mathematical truths. He thought that, even in a dream, mathematical propositions (statements about whether something is true or false) are self-evidently true. That is, there is no way to reason that 1+1 equals anything besides 2 when we are dreaming because that's a proposition nearly fundamental to mathematical thinking--how could 1+1 equal anything else? Descartes wondered if there were any way that we could be wrong about what mathematical truths exist, and as a result created one of philosophy's most iconic thought experiments: Descartes' evil demon. I've reproduced a translation of parts of it below:
"...I shall then suppose... some evil genius not less powerful than deceitful, has employed his whole energies in deceiving me; I shall consider that the heavens, the earth, colours, figures, sound, and all other external things are naught but the illusions and dreams of which this genius has availed himself in order to lay traps for my credulity; I shall consider myself as having no hands, no eyes, no flesh, no blood, nor any senses, yet falsely believing myself to possess all these things..."
This is the pinnacle of Descartes' skepticism. Through his evil Demon, Descartes found that we cannot be certain of not only the external world, but also mathematical truths. How? Descartes reasons that the evil demon can actively inhibit his mind's ability to perform truly rational thought. So, whenever we prove something in mathematics, there is actually a mistake in our line of thought because the evil demon is messing with us, rendering all of our results false. 1+1 could very well equal 5 or 10 or even pi. There's no way to be absolutely sure.
At this point, Descartes had doubted everything except one thing: his own existence. He realized that doubting his own existence was self-defeating because the act of doubting requires someone to do the doubting. Even if he were locked in an eternal struggle with an evil demon, he could never doubt that he himself is able to doubt, so he must exist. At the end of his ruthless skepticism, Descartes had finally found one belief that was surely undoubtable and truly foundational. This is where we get the famous quote "I think, therefore I am," which more accurately should be "I doubt, therefore I think, therefore I am". Through this thought experiment, Descartes had begun to lay the foundation for epistemology, one of philosophy's most important fields. Over the next couple centuries, many philosophers debated over the question of what is the nature of truth and how we can come to discover those truths, and in science, epistemology helped formulate and define the limits of the scientific method.
That's going to wrap it up for this week. If you haven't already, make sure to read last week's post about if it's reasonable to fear your own death. Next week's might have something to do with applied ethics.