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Everyone has, does, and will disagree with someone because everyone has a different opinion about what's true. The fact that everyone argues demonstrates that everyone, even the staunchest existentialist, does believe that they exist within an immediate reality where some things are true and others are not.
We have tools to help us see the truth more clearly. Even, the extreme existentialist, though he may not be confident of his own existence, is very confident in his methods of inquiry. He only questions his corporeal experience because the axioms and rules of classical logic he chooses to accept do not enable him to prove even the simplest facts that humans typically take for granted. That is to say, classical logic is a powerful tool to understand many truths, but, contrary to what the Greek thinkers believed, it cannot prove, create, or discover all truth.
Math, for example, is a numerical abstraction for a small subset of classical logic. Like any other art form, math can generate patterns that are fun to look at and a pleasure to contemplate. But, just like other art forms, the applicability of math comes from its descriptive correspondence to objects and events in the real, physical, observable world. For centuries now, most mathematical inquiry is conceived and laid to rest on the basis of its descriptive power and the limits of its correlation to physical reality. Math is a powerful tool to describe many truths, but, contrary to what many academicians believe, it cannot prove, create, or discover any truth.
Just like any other virtual reality, it is a self-contained, abstract universe that is accepted or rejected based on its relationship to actual reality. When I throw a ball, it will move through space, time, and whatever other dimensions as it so pleases with no regard for the latest mathematical theory. Mathematics doesn't create the ball or its trajectory. It simply tries to describe those physical phenomena, and does so as imperfectly as trying to measure the circumference of a can with a straightedge.
I'm a scientist, not a philosopher or mathematician. This means that I'm concerned with the kind of truth that says, “That happens because this happens.” Recognizing this kind of truth helps to advance and ease our progress through life. Just like a mathematician, I scramble to use my abstract tools to describe and simplify actual phenomena in such a way that they become comprehensible to the human mind. I try to use numbers and narratives to describe things that the early philosophers took as “self-evident” or “natural.” I use both philosophy and mathematics to contextualize, describe, and create comprehensible abstractions of the truths I uncover. I use the mathematicians' and philosophers' cold and artificial vocabularies to describe things that are blatantly obvious: “When I let go of something, it falls.” “When the conditions for life aren't met, people die.” “When I push something, it moves.”
We scientists often fool ourselves into believing that we are able to use our methods to draw lines between what is true and what is not, in the same way that a mathematician may fool himself into believing that mathematics has any concrete ties to reality, or a philosopher might fool himself into believing he is an independent ego observing his own imagination as a disinterested third party.
My entire generation is infatuated with the falsehood that the scientific systems we've made for ourselves will enable us to discover or even generate truth. In fact, they often go so far as to say that the scientific method, if applied consistently and for long enough time, would be able to describe everything that happens in the universe. This extreme naturalism assumes that science, a system built to describe the arbitrary experiences of the hairless apes living on a speck of dust in a minor corner of the universe, is somehow connected to the ultimate truths of the universe in a way that the truths will reveal themselves as long as the apes perform the correct ritual of, “Form a hypothesis, test the hypothesis, observe the results, form a new hypothesis…” This is no different from so-called “primitive” beliefs that promised the favor of the gods or spirits in exchange for rituals and offerings. For the naturalists, nature is their god, science is their religion, and scientists are their priests.
The naturalist may call us to “trust the science,” or “listen to the scientists” in the same way a faithful parishioner might say, “have faith in God,” or “the pastor knows best.” The naturalist holds scientists and their words in the same venerable light as the religious do for their religion. All of us hope that our respective priests have access to the truth, and we put our faith in them, because we trust their methods.