Descartes’ famous line from ‘Meditations’ is exactly what it sounds: a proof that we exist. Furthermore, this isn’t an ‘assumption’ per se, it’s irrefutable fact. For further explanation, I suggest you go pick up the book ‘Meditations’ from a library.
Okay, I can’t disprove that we’re all secretly part of ‘The Matrix’ and that the world as we experience is merely an illusion. I simply can’t. However, if we take Occam’s Razor into account, we can assume it. Occam’s razor states that the simplest explanation is most likely the correct one. To put it another way, entities should not be multiplied beyond necessity. If we apply that principle toward existence, it is overwhelmingly more probable that the world as we experience it exists, as do the laws that govern it. Since any ‘illusion’ theories require many assumptions in order to believe them, we can largely disregard them.
Anything that happens does so for a definite reason. To put it another way (in the words of wikipedia):for every entity x, if x exists, there is a sufficient explanation why x exists
For those of you who are reading this and thinking, “Well what about miracles? Those don’t need any explanation!” Well sidestepping the whole argument as to whether or not miracles occur, I can say to any one who believes in them that miracles happen for a reason: God made it happen. God wanted so-and-so to live or win, so he (or she) made it happen. That’s as much a cause as anything else.
By assuming (2), we are judging scientific law to be true. And assuming that, we cannot discredit the overwhelming amount of scientific research in support of Darwin’s theory of evolution. I don’t want to get into the nuances of this argument; it’s a waste of time. You’re either reading this and agreeing with me, or reading it and disagreeing with me. No amount of ‘deductive reasoning’ will sway any opinions, so I’m not going to bother.