“The most pervasive falsehoods are the hardest to see.”
If faith is belief in what cannot be proven, then all human endeavor rests on faith. This is as true for science, mathematics, and every aspect of our personal lives as it is for philosophies and religions. Schools of thought, bodies of knowledge and everything we do from the moment we get up and brush our teeth in the morning, all rise up from and depend upon an assembly of beliefs accepted on faith. Whether you are Christian, Muslim, Hindu or atheist, faith is the bedrock of your reality.
It’s easy to see that religions are based on a set of beliefs subject to question by those who do not believe. Indeed, one of the admirable aspects of religions is their honesty about the role of faith as a foundation for everything they claim. We also accept that people have philosophical beliefs upon which they may base their actions or entire lives. We don’t see as clearly, however, that mathematics, science and our daily existence are all likewise based on unprovable beliefs. This has been widely affirmed over the centuries by wisdom traditions of all stripes. It’s a central principle of Buddhism, in Christ’s message, in Socrates’s probing approach to philosophy and in what quantum physicists have discovered about the nature of reality on a fundamental level. We would be better served were we daily more mindful of the ground of belief upon which we walk, and through which we experience what we call reality.
Take mathematics, a field we think of—when we are forced to think of it all—as logically airtight and having no truck with faith whatsoever. For mathematics is based on proofs. A mathematician only accepts into the canon of his field a “truth” that can be proven, at which point this truth becomes a “theorem.” But what are used to prove theorems? Other theorems! Clearly, though, this can’t go on forever. Eventually the most fundamental theorems have to come from somewhere else. Eventually something has to provide a foundation for the theorems. And so it is. Mathematicians call these “somethings” axioms. But we can call them beliefs.
Why? Because axioms aren’t proven. An axiom (also known as a “postulate”) is a statement taken at face value. It’s a statement mathematicians—who are human beings, I hasten to add (despite common misconception)—have agreed to accept as obvious. An example of an axiom in geometry is “the unique line assumption,” which says that through any two points there can be drawn exactly one line. Part of the wikipedia definition of an axiom is that its “truth is taken for granted, and serves as a starting point for deducing and inferring other truths.”So it seems that, just as is the case for religion, the foundation for mathematics are also truths that are “taken for granted.”
Now you are doubtless thinking, “Hold on, brother. If the ‘unique line assumption’ is anything to go by, these mathematical beliefs are a lot more obvious than religious beliefs. Surely mathematical axioms are no-brainers—only a crazy person would doubt their truth.” Indeed, this seems true, but as I’ll later explore in more detail, many things once thought self-evident have turned out to be false. For now, let’s move on to see how science is also based on unprovable beliefs.
How does science rest on faith in the same way that religion and mathematics do? You could say that the business of science is to explain phenomena. To explain something, we depend on the concept of cause and effect: “A causes B and B causes C” and so on. However, as the Scottish philosopher David Hume pointed out around 1740, the very concept of cause and effect is actually a belief. There may be no such thing.
Think about it. When a pool stick hits a billiard ball and it rolls, there is no way to prove that the stick caused the ball to roll. All you can say is that in every case up till now, when someone has hit a billiard ball with a pool stick, the billiard ball has rolled. The past being all we have to go on, you can only say that in the past we have always observed the two activities occurring together in sequence. The concept that the stick caused the ball to roll is a belief we impose on the events. Perhaps in the future one might push a billiard ball and the ball might not move, or might roll up the stick, or jump around and whistle dixie. One cannot prove otherwise. As Hume put it in his Treatise on Human Nature: “[cause and effect]… are… qualities of perceptions, not of objects… felt by the soul and not perceived externally in bodies.” We believe in cause and effect. It’s not a fact.
Now let’s address the objection that the truths taken for granted in math and science are a lot more obvious and universally accepted than those taken for granted by religions—that one would have to be practically insane not to believe them, whereas religious beliefs are clearly open to question. The belief that two points determine exactly one line is a far cry from the belief that Jesus Christ was the only son of God. True enough. But they are beliefs nonetheless. And even beliefs considered obvious are not necessarily true. The earth certainly seemed flat until we discovered the truth. Indeed, the greatest breakthroughs in human progress have occurred when some genius—or is that “insane person?”—questioned widely-accepted beliefs.
Take our concept of time. Before Einstein, it seemed apparent that time marches at a steady rate for everyone everywhere. In 1905, though, Einstein contended that time moves at different speeds depending on how fast we’re traveling and on the force of gravity. Even more than a hundred years later this idea seems at the very least bizarre if not downright crazy. And yet it has been borne out by experiments. Given this capsizing of accepted wisdom with regard to the nature of time, it is not completely bonkers to imagine a similar assault on the concept of cause and effect. Actually, this assault has already begun, as observations in the tiny world of quantum physics appear to challenge our notions of cause and effect (one example being that Newton’s third law of physics—”for every action there is an equal and opposite reaction”—doesn’t always seem to apply down there).
Just as our notion of cause and effect is suspect, so too may be the “common sense” belief in the separation between matter and “spirit,” which we could also call energy. Since the Enlightenment, science has operated on the assumption that matter is “dead,” in other words there is no animating spirit or consciousness in matter. We tend to think this way in our everyday lives: there are forces on the one hand and stuff that gets pushed around by these forces on the other. But this belief has been challenged by quantum physics ever since 1905 when Einstein sprung his famous equation E = mc2 on the world. E stands for energy, m for matter. The equation states mathematically that energy equals matter (after the amount of matter is multiplied by the speed of light squared). They’re actually the same thing! As such, they can theoretically be converted back and forth. We don’t know how to turn any matter into energy but physicists have since shown that energy can “pop out of nowhere” as a particle, and a particle can “disappear” into pure energy. Matter is only inert in our minds.
You might agree that scientific ideas are always open to challenge and revision, but surely our mathematical axioms are completely obvious and safe from attack? Well, maybe. But it turns out that at least in the world of geometry there are theoretically infinite different sets of axioms upon which different systems of geometry could be based. Each set of axioms leads to a different geometrical system that is internally consistent and therefore “logical” on its own terms. The type of geometry we learned in high school was Euclidean. It’s quite handy for flat situations like paper. You could say “it believes in flatness,” for it rests on a foundation of assumed flatness. But another thing Einstein showed is that space itself is not Euclidean but curved. Therefore a different geometry, based on “curvedness” and using different axioms is needed for calculations involving curved space.
The beliefs most fundamental to a way of thinking become second nature. Through long habit, they are ingrained, taken for granted and unquestioned. But a fresh, active mind explores beliefs. It probes and tests them and is willing to discard dry, cob-webbed beliefs in favor of those more vital, supple or nuanced. This is called being re-born. This is called life in the most vigorous and broad meaning of that word. This is what Socrates meant by “The unexamined life is not worth living,” and why he, and Christ, walked around questioning the accepted wisdom of their day.
Our most fundamental beliefs about ourselves and the world are like a pair of colored glasses we wear all the time. If they are yellow glasses, all we ever see are yellow things. Most never realize they can take the glasses off and try another pair. Most never realize the profundity of the bumper sticker that reads “Don’t trust everything you think.” Most never realize that they can be the Einsteins of their own lives.