I have found a few simple insights whose truth I believe to be obvious, self-evident and undeniable which have helped shaped my thoughts and allowed me to see many of the insights I am sharing on this site. I could call these my "axioms," though this word gets misused and I hesitate to use it here myself. In mathematics, a axiom is part of a definition, a condition which the thing in question must fulfill before it gets the name we are defining. In the precise realm of mathematics, axioms are not not merely statements which we assert to be true without justification, which seems to be what most people mean by "axiom." Here, I am asserting that the following statements are true and I am giving such arguments as I feel are warranted. I shall use these Truths as fundamental facts in most of my further writings. (Note that when a statement here is an imperative (such as the first two), the statement being asserted is "You should ..."). My first axiom is so obvious that it shouldn't really have to be stated, but to be complete and because there are those who don't understand its importance, here it is: 0. Be completely honest with yourself. Shakespeare put it this way: "This above all: To thine own self be true." The fact is, lying to yourself is never a good thing. If you repeat a lie to yourself often enough, you will eventually start to believe it simply because of Pavlov-type conditioning. However, believing something and making it true are very different things; you cannot make something true simply by repeating it or making yourself believe it. Despite the fact that we can convince ourselves of something simply by repeating it enough, the truth remains true and falsehoods remain false, so by lying to oneself all that is accomplished is distortion of one's view of the world. Those who lie to themselves eventually insure that they make bad decisions, decisions based on delusions and lies rather than accurate knowledge. It is crucial that we should be fully honest with ourselves about everything, even those things which make us uncomfortable; indeed, it is especially important that we should be strictly honest with ourselves about things we don't like or aren't comfortable with, for these are the things which we are most often tempted to lie to ourselves about. Self-honesty and self-knowledge are the first steps toward gaining greater knowledge and pursuing the Truth. We have basic tools for distinguishing truth from falsehoods, namely observation and careful thought. In order to learn the Truth, we must: 1. Question Everything. The Truth will stand up to being questioned. It is a good thing to question, to doubt, to hesitate to accept the truth of a claim simply on the authority of some other person, for the simple reason that it is only by questioning and careful thought that we can tell the difference between truth and falsehood. Obviously, others can choose to lie to us for one reason or another, but even those who don't intend to lie can still be mistaken in the things they say; even experts and authorities are wrong from time to time. The fact that someone sincerely believes something she or he says does not make it true. There are some schools of thought which hold that questioning is bad or even sinful, that we should suppress our natural tendency to question and simply accept their words on faith. This strikes me as highly suspicious: if indeed their claims are true, then by questioning we will only verify the truth of what they say, so what are they afraid of? If we question and think carefully and critically, we will eventually find the Truth, so there is no need to fear questioning if it is indeed truth that we are after. Certainly the person doing the questioning need not fear, for by thinking critically she or he is simply protecting her/himself from being misled. Indeed, it is only by doubting and questioning that we can ever hope to sort out truth from falsehoods. Further, those whose claims are being questioned should have nothing to fear, unless they are intentionally misleading us and trying to keep us from knowing the Truth. The Truth is still true whether we believe it or not, whether our faith is strong or weak, well-placed or misplaced, and if we look to see whether some claim is true we can weed out mistakes and falsehoods and, eventually, find the Truth. Perhaps those who would discourage our independent questioning are only afraid that we will "lack faith;" but questioning and finding truth replaces mere belief with knowledge, which is much stronger. Having faith in an untrue idea is of dubious value at best; I assert that it is not desirable at all. The only value I can think of in beliveing a false idea is the possible peace of mind that might come from believing a comforting lie rather than seeking the (possibly) painful truth. Yet believing lies is dangerous, and I suggest that we are better off seeking the truth even at the cost of personal comfort. Anyone who suggests that it's "wrong," "bad" or "sinful" to question is acting suspiciously, demonstrating more concern with her/his control over the beliefs of others than with their knowing the Truth, and such a person is certainly not acting in our best interests. There have always been (and hopefully will continue to be) a few of us who are not content to simply accept the wisdom of the past without question. These people recognize the fact that even though the great visionaries of the past are worthy of our respect and have much to teach us, they didn't know everything that can be known. In particular, it is not disrespectful to the great masters of the past for us to look for our own answers. Indeed, if we are to follow in the footsteps of people such as Jesus, the Buddha, Mohammed, Einstein, and many others, we must do as they did: think for ourselves. We must not simply accept the words of our elders on no other grounds than that they were our elders. Rather, we must examine the facts for ourselves and come to our own conclusions. Sometimes our conclusions will agree with those of people before us; sometimes we will find that the truth is a refinement of ideas from the past; sometimes we will notice things that those before us had overlooked or didn't have access to and hence discover entirely new answers to old questions. The visionaries of the past all understood perhaps the most important insight I have recorded in this site, namely: the Truth will stand up to questioning. If we honestly and carefully examine the world, we can find the Truth. Of course, a key word here is "carefully"; far too many people are not sufficiently careful in the way they look at the world. Indeed, many people choose what to believe based not on what they actually observe to be true, but rather based on what they want to be true. This leads me to another major insight: 2. It is far better to know a disturbing truth than to believe a comforting lie. To those who disagree with this statement, those who would rather believe a comforting lie than know a disturbing truth: Get Ye hence! This page is not for you. Often the Truth is other than we would like it to be, and many people prefer not to think about it and just hold on to their comforting lies rather than face the Truth. Such people perpetuate ignorance and hold back the advance of Human Knowledge. Ignorance may be "bliss," but it is a very cheap sort of bliss, especially given that the ignorant are easily manipulated and exploited by those who aren't afraid to learn a little Truth. To stubbornly hold on to comforting lies is perhaps the most childish possible way of reacting to a discomforting insight; yet many people simply ignore disturbing ideas, choosing instead to lie to themselves and pretend that their cherished falsehood is true, believing their "faith" in their belief more valuable than knowledge of the truth. In the end, though, refusing to face the truth inevitably leads to problems, and any short term gain in comfort is ultimately far outweighed by the consequences of living a lie. The simple fact is, the Truth is still true whether we believe it or not; to refuse to face the truth and choose instead to believe a lie can obviously lead to problems, not just for the self-deluded one but for all other affected by her/his actions. Indeed, to persist in refusing to face the Truth and instead choose to believe a lie is an act of selfishness, to choose one's personal comfort at the cost of misleading and often endangering others. Sadly enough, choosing comfort over Truth is the exact reason that many people refuse to question the teachings of the past; they fear that they will not like what they see. Someone once told me that "there are things that Man is not meant [by God] to know"; if this were indeed the case, then why did God give us brains and make us curious? An intelligent God would simply make those things He didn't want us to know completely invisible and unaccessible to us, just as an intelligent parent keeps dangerous substances out of reach of children; it is indeed a foolish parent who places dangerous things where a child can reach them and then simply tells the child to leave them alone. Provided that God has at least a minimal level of intellect and competence (which I think we can easily grant :), we should have no fear of questioning and searching for knowledge; those who tell us that any form of knowledge is "forbidden" are simply trying to prevent us from finding the Truth. Yet, organized religions often discourage questioning, instead charging us to simply accept what they tell us on faith; in the past those who dared to think independently and question were condemned as heretics and often executed for the "crime" of looking for the Truth. What were these "pious" church officials afraid of? Sadly, an answer presents itself readily: they were more concerned with political power than with Spiritual Truth. The sad fact is, it is much easier to control people who take your word as "gospel truth" than it is to control those who think for themselves. Many examples of this sort of placing politics over Truth are still with us today; totalitarian regimes invariably control the press and discourage independent thought. Unfortunately, it is simply easier to control ignorant people who have absolute faith in your words than it is to control thinking individuals who might question your decisions; given this, it's not to hard to see why certain people and groups discourage questioning. Another problem, in one sense the opposite of the above and yet in another sense simply a disguised version of the same, occurs when people are too eager to believe a particular idea and decide to accept it without being sufficiently critical or careful in their thoughts. In many cases certain ideas are adopted because they are fashionable or because they are expressed by a persuasive speaker. The fact is, the Truth is still true whether it is fashionable or not, no matter how eloquently it (or its opposite) may be phrased. An example of this is the current fascination of Americans with UFOs, the idea that we are being visited by extraterrestrial beings. It has become fashionable in the US to express frustration with the government by asserting belief in UFO/conspiracy theories, even in the absence of real evidence and despite considerable evidence to the contrary. To critically consider such ideas is one thing, but to simply accept them as "truth" on such weak evidence is very sloppy reasoning at best. Sloppy reasoning does not lead us to truth, just as sloppy craftsmanship does not lead to quality products. Another example is how certain members of the scientific community sometimes simply dismiss ideas which don't fit into their wold view in the name of Skepticism. This attitude is just as unscientific as the attitude of immediate acceptance of far-out ideas. For those who aren't familiar with it, let me explain the Scientific Method: In Science, we start by making observations of the phenomena around us. We then devise theories or models explaining what we think is going on; these theories have consequences, i.e. they make predictions about what the outcome of certain experiments should be. We then carry out the experiments and observe the results, which then help us to refine our theories. Indeed, we sometimes have to discard our original ideas altogether in favor of completely new ideas. Our theories may be supported by our observations or they may be disproved by observations which contradict the predictions of the theory. A theory can be disproved by making observations which directly contradict it, but a theory can never be proven, only (at best) supported by evidence. This is simply because observations cannot distinguish between two different theories which make the same predictions. At most, we can say that our theories are consistent with our observations, but never "proven true" by them. This shows us that theories should be thought of like maps: it is a silly mistake to confuse a map for the terrain it represents. Our theories are just road maps, containing some information about the world but never all of it. It is not scientific to simply disregard observations which do not fit in with our expectations. It is not scientific to start with a conclusion and then try to fit the evidence to a favorite theory; this is the central problem with so-called "creation science," which is unwilling to accept any conclusion other than one particular favorite theory and hence fails to be an any way scientific. In Science, we must be willing to throw out even the most cherished theory if evidence is discovered which contradicts it, and nothing less than this level of willingness to question is acceptable if we really want to find the truth. It is absolutely against everything that science is and stands for to dismiss an observation as "impossible" because it disagrees with current scientific thought; this is like telling someone that a certain tree doesn't exist because it's not listed on the map. Yet many so-called scientists who should know better do precisely this all the time, simply refusing to even contemplate the possibility that part of their cherished world view might be wrong, and worse yet they try to justify this unscientific attitude in the name of Skepticism! Indeed, many people make the mistake of simply denying the possibility of anything which doesn't fit their world view. We might hear things like "it's been scientifically proven that there are no such things as ghosts," or similar statements, when all that should really be said is "the existence of ghosts is incompatible with our current materialist world-view, which so far has been well supported by evidence but is not 'proven' true." The "accepted" views of science have changed radically in the past many times before: it used to be thought that meteorites were rocks picked up from the Earth by storms which later fall to the ground, simply because the idea of "rocks in the sky" did not fit well with the ideas which were accepted and "established" at the time. This leads me to another major insight: 3. Many Truths are counter-intuitive, i.e., there are truths which contradict our intuition. Anyone who doubts the existence of counterintuitive truths is naive and undereducated. A little thought shows us clearly that we should expect at least some truths to be counterintuitive; after all, our sense of intuition has been developed over millennia for surviving on a small part of the surface of one planet, at one particular scale, within a relatively small temperature range, etc. In other words, our intuition has been developed in order to deal with certain very specific situations which are rare in the universe as a whole. This is not an attack on intuition; indeed, intuition is generally a good guide and a valuable tool in our quest for truth. Yet we must understand that our intuition only prepares us for the kinds of situations it has been developed for over the last several hundred thousand years; it should not come as a surprise, then, that when we investigate the subatomic world, observe the behavior of objects in outer space such as black holes, contemplate traveling close to the speed of light, or investigate many other realms and scales far removed from everyday experience, our intuition falls a bit short. Intuition can guide us so far, but at after a certain point we must rely on our much stronger tools: logic and the scientific method. Further, it is not only in the exotic situations of abstract mathematics and quantum physics where we shouldn't rely on intuition alone; as we may learn from Sherlock Holmes, logic is just as useful for just trying to understand daily life as it is for doing astrophysics. This is where critical thinking becomes very important. As a Mathematician, I am familiar with the kinds of precise language and strict logic (known as "mathematical rigor") which are necessary in order to achieve the kind of Absolute Truth which are found in the theorems of mathematics. (A "theorem" is a statement which has been proven true by the use of a rigorous logical argument called a "proof;" once proven, a theorem is no longer subject to doubt, but has been shown to be absolutely true. To deny the truth of a theorem is to misunderstand what the theorem says. Do not confuse theorems with theories, which are scientific models or guesses as to what we think might be happening behind the scenes in some physical real-world scenario; we know the truth of our theorems, but we can (at most) believe in the truth of our theories.) One does not need to be a mathematician in order to benefit from this kind of precise and careful thought; anyone who is interested in the Truth must be equally thorough and rigorous in her or his thoughts. If we are to find the truth, we must be careful to make our statements say exactly what they mean; no more, no less. This is very different from ordinary language, where we often say more than we mean, relying on the listener to filter our intended meaning from what we said, and where we equally often say less than we mean, relying on the listener to fill in the details; indeed, some of us manage to do both simultaneously, saying both more and less than we mean at the same time! This kind of imprecision in our language makes it easy to misunderstand others and to be misunderstood ourselves. In order to discover the Truth (and especially those counterintuitive truths), we cannot afford the luxury of such sloppiness. Thus we must examine carefully the ideas we are trying to evaluate, rephrase them so that they say exactly what they mean ("analyze" the ideas), and then use careful logic (making sure that each statement we make really follows from the previous one) to eventually come to a conclusion. Note that this often entails "analyzing" compound statements to separate out all of the claims being made. Perhaps the most common kind of error in logic (or "fallacy") is to leap to a conclusion, to skip over "obvious" intermediate steps and go right to the desired conclusion. A simple example: certain thinkers argue that abortion is murder, reasoning as follows: Human life begins at conception, so to abort a fetus is to kill a human being and therefore is an act of murder, which is obviously immoral. The usual attack on this argument is to deny the initial claim, i.e. that a fetus is a human being, instead making a distinction between actual and potential human beings. Notice, however, that on closer inspection, one doesn't need to take this route, for the argument already has a critical flaw: the argument takes "abortion kills a human being" and concludes "abortion is murder." Here is the flaw: killing is not necessarily murder. There are many instances in which a person is killed by another but not murdered: instances of self-defense (which can well be the case in abortion), accidents, times of war (which is not the case in abortion), etc. Note that I am not making any claims here about whether abortion is actually right or wrong; this is just an example of how easy it is to make errors in logic when we are not sufficiently careful. Of course, many questions cannot be easily answered, and indeed there may be some questions which we cannot answer at all, though I personally feel that we can eventually answer any question, given enough time. There are many questions which are still open, still being investigated and as yet unanswered. If we are to have a chance of finding Truth, we must be willing to question everything, and in our process of questioning we must be exceedingly careful in the way we think and proceed in order to avoid making errors. Here is a fourth Important Insight: 4. What we call "The Universe" is really only the span of our senses. This means that when we investigate the Universe, we're not seeing everything that's there, only part of it. As with our intuition, our physical senses have developed with the specific purpose of helping us survive on the surface of the Earth. There is no reason in the world to suppose that we are capable of sensing everything that there is; we could be surrounded by things which we cannot perceive with our senses simply because these things have not been relevant enough to our survival long enough for us to have developed senses to detect them. Indeed, we know that we are surrounded by such things constantly: for example, X-rays, radio waves and various other forms of electromagnetic radiation are really colors of light which our eyes can't see, largely because seeing them would not be particularly useful to us, Superman's "X-ray vision" notwithstanding. "Now wait," a reader thinking critically might respond, "just because we don't directly sense something doesn't mean we can't find out about it; after all, we know about X-Rays and such even though we can't see them." This is what I meant by saying the "span" of our senses. We can often deduce the presence of and certain properties of things which we cannot directly perceive by observing their effects on things we can directly perceive; this allows us to extend our senses, for example by using a telescope or an electron microscope or any one of the myriad other instruments we have invented. Nonetheless, there is no reason why everything that there is should be perceptible to our extended senses any more than to our original senses. Indeed, cosmologists have found good reasons think that up to 90% of the mass in the universe has yet to be discovered; this is the hypothetical "dark matter" which is being sought actively by modern physics. Given this, it is an act of arrogance to insist that "you can't have seen what you said you saw" to someone who reports an observation which does not fit in with our theoretical roadmap. What we think we "know" from our theoretical physics and our various other useful theories is really only a working model of a part of the potential span of our senses; it is not the same as reality and never really can be. Of course, to be fair, it is entirely possible to misinterpret things we think we have seen or experiences we have had. Skepticism requires that we withhold our judgment until we can make a "sufficiently strong" case for one theory or another; it neither requires nor condones the outright dismissal of observations which we don't happen to like. In truth, we should never accept a theory as "fact"; instead we must always be ready to replace our old ideas if better ones come along. Indeed, many so-called "skeptics" are often guilty of the same mistake they criticize the "believers" for. 5. Science is NOT a religion, despite claims to the contrary. I have often heard the charge leveled against science that "it's just as much of a 'religion' as anything else" and that science "requires faith just like a religion does." These claims demonstrate a fundamental ignorance of what science is and how it is done. Unfortunately, there is an element of truth to the above claims, and I will explain what that is just after explaining why they are not true. Science does not ask anyone to have faith in any particular ideas, doctrines, dogma or beliefs. Indeed, if anything, science requires skepticism and thoroughly critical thought; even those ideas and theories which pass the tests scientists devise must be thrown out without hesitation if a better idea comes along. A properly scientific attitude requires that we never place our belief in any theory, only a kind of tacit acceptance while we continue to refine our theories, for belief kills questioning since we treat the problem as solved and stop investigating it once we decide to believe something. Even the greatest scientists are still human beings, though, and in practice some scientists forget the strict logical discipline they are supposed to adhere to. Indeed, many scientists actually do believe that their theories are true, confusing the road maps for the roads; some even stoop to primate-level politics to try to promote their pet theories without regard to finding the real truth. These problems are further compounded by very real concerns of funding and satisfying political requirements, all of which can get in the way of the Quest for the Truth. Scientists who treat their theories like religious beliefs do a great disservice to both themselves and indeed to mankind as a whole, for such a view of a scientific idea leads to both refusal to accept or even consider new ideas and clinging to the old idea like the above-mentioned comforting lies. In fact, science is not a religion, but there are some people who erroneously treat it as such. 6. Science and Religion do not conflict. For ages there has been a perceived conflict between science and religion which has had great cost in the form of lost knowledge kept secret for fear of persecution and indeed in the form of actual persecution of people who dared to question the wisdom of their elders. The greatest irony is that this whole perceived conflict is completely an illusion. Science and religion are not, as is commonly thought by some, mutually contradictory world views. Indeed, they cannot contradict each other at all, for when we understand them for what they are, we see that science and religion address entirely different questions. Science seeks the literal truth about the world. Science asks "what?" and "how?", whereas religion asks "why?". Science cannot approach the question of why the world is, for no experiment can reveal purposes to us, only the way that things are. Religion seeks to answer our questions about where we fit in in the universe, what life is about and what it means, why things are the way they are. Yet just as scientists can be prone to treating their science like religion, so too many religious people treat their religion like science, often entirely missing the point of parables and other metaphorical stories and instead treating them like news reports, stripping the stories of the profound insights they are meant to express and then criticizing others for not believing the story "literally." The truth is, religion and science cannot conflict even if they want to, since they exist in entirely different realms. The Bible, the Koran, the Tao Te Ching and other religious works are no more history books than they are physics texts or auto repair manuals. To treat these works of profound wisdom as if they were merely newspapers is the worst form of sacrilege. When Jesus spoke in parables, he wasn't reporting on actual events which really happened; he was telling fictional stories intended to express moral messages and insights; the same holds true for ancient Greeks who wrote myths about the exploits of their gods. Science deals in and searches for literal truth whereas religion expresses mystical and profound insights through metaphor. It is not hard to see why this distinction can and does confuse some people; yet the distinction is there whether we all see it or not.

Back