Defying Logic

Hi Glenn,

Which assumption is one violating if they decide to ignore the rules of disciplined math and science?




Good question. I guess that “the rules of disciplined math and science” are exactly what makes each branch of knowledge a “discipline.” Undisciplined thinkers tend to be “illogical,” that is, their conclusions do not follow from their assumptions. The violated assumption is INTERCONNECTION, which, in this case, demands that there be minimal contradiction between assumptions and conclusions. With its opposite, disconnection, indeterminists are not bothered by contradiction, either because they fail to see it or because they have been accepting great contradictions throughout their lives. Of course, the clearest thinkers carefully state their beginning assumptions and definitions so that their interpretations of data will have minimum contradiction. This tendency is not specific to math and science, as there are many religious folks (e.g., the Templeton Foundation) who seek the same thing. Of course, the Ninth Assumption of Science, RELATIVISM (All things have characteristics that make them similar to all other things as well as characteristics that make them dissimilar to all other things), assures us that the transition from assumption to conclusion is never without at least minor contradiction. How can we ever know that a particular conclusion is warranted from a particular assumption? Only science can answer this question correctly, because it begins with the First Assumption of Science, MATERIALISM, which essentially states that truth is determined through agreement between the internal and external world. Ultimately, this univironmental occurrence is necessary for survival. As an example, a predator, such as the red fox, assumes that the rabbit he is about to catch will be just as tasty as his previous quarry. Reasoning by analogy, he assumes that all rabbits are alike. A successful test of the external world allows him to survive yet another day.

Math and religion have no such requirement. In each case, one can imagine all sorts of things unprovable in the external world. Contradictions appear for the more outlandish ideas only when they confront the external world in spite of themselves. The “logic” of a particular mathematical derivation or religious idea may have little or no contradiction within itself, but may not survive for a second in the external world. Thus, I am not “defying logic” to think that I can walk on water as long as that is where I leave it. I would be “defying logic” only if I tried to test that idea in the external world.

Nonetheless, neither math nor religion can escape the external world once it becomes the property of more than one person. In math, it is the duty of one’s colleagues to point out errors—the annoying but essential disease common among academics. In religion, logical errors regularly are overlooked in order to foster loyalty, which is the far more important evolutionary purpose of religion.

So logic occurs in a particular context replete with contradictions large and small. In any particular logical analysis we always choose the analogies and disparities that we are most familiar with. We tend to ignore “outlier” data that doesn’t fit the dominant trend or what we already know to be true (probably through decades within the discipline). Outlier data derived from the real world always exist because the universe is infinite. We see this in the Second Assumption of Science, CAUSALITY (All effects have an infinite number of material causes) and its cohort, the Third Assumption of Science, UNCERTAINTY (It is impossible to know everything about anything, but it is possible to know more about anything). The “rules of disciplined science,” therefore, never lead directly from assumption to conclusion in the same way they often do in mathematics. The “fuzziness” we encounter in measurements of the real world usually does not exist in math. To do math at all, we must reduce an infinite number of causes to a few that we actually can work with. Thus it is perfectly logical that 1 + 1 = 2. What we are really saying, however, is that the idea of 1 + the idea of 1 is the same as the idea of 2. But what is “1” in reality? Am I “one” person? Well, not quite—I have lost some stuff over the years (hair, teeth, maybe some brain cells). So pardon me if I don’t consider myself a complete “1”. If I am involved, maybe the equation should be 1 + 0.99 = 1.99.

It is clear that the disciplined rules of math, which do not demand an encounter with the external world, have a much better chance of not being violated than those of science, which do. Those who appear to “defy logic” in coming to conclusions in science or religion usually hold erroneous assumptions and/or emphasize the wrong data, as judged by those making that claim.

On the other hand, no one really can “defy logic” in the same way that no one really can have “free will.” This is because the nexus of assumptions used for each conclusion includes many that are subconscious presuppositions, which when included in the analysis, make the operation perfectly logical. This follows from the “Principle of Least Effort,” which states that all microcosms, including humans, will always exhibit the least amount of motion for the univironment. In other words, the object moving under Newton’s First Law of Motion will not increase its velocity on its own. Thus, if you really believe someone is violating the Principle of Least Effort by “defying logic,” then you have not included some of the important microcosmic or macrocosmic causes in your analysis. For instance, you may think that your failure to advance within a corporation is illogical because your qualifications and achievements are vastly superior to those of your office mate. But “qualifications and achievements” are not the only criteria for advancement, especially when your office mate is the boss’s son. If we want to understand the world around us, we must include as many important causes in our univironmental analysis as possible.

Thus the logic that gives us the Big Bang Theory, likewise, is perfect—providing that we are aware of all the ingredients necessary for its production. After all, most folks do not view the BBT as an absurdity. The theory follows from all that went before, including the equally absurd assumptions hidden and not so hidden. So how do we get rid of this insult to intelligence? We do it the same way that we always have: point out its contradictions, often and loudly. I have done my part with TTAOS and TSW, following suggestions of Kuhn and Collingwood that a major paradigm shift cannot occur without a change in fundamental assumptions. Nonetheless, the opposing assumptions are replete throughout society. The decline of their influence and the demise of cosmogony awaits the financial turmoil of the next four decades.


Unknown said...

Hi Glenn,

Thanks for the thoughtful answer. You’ve raised several good points. One area I want to explore is the distinction between a rule and an assumption. An assumption is something that one believes is true, but that one may not be able to show as true when starting a proof or examination. A rule is something that follows a logical flow of steps, starting with an accepted and preexisting “accepted truth” (in a given discipline), to arrive at a particular conclusion. The challenge isn’t the distinction between a rule and an assumption (which is in-and-of-itself an important distinction). Rather, the challenge is in recognizing when a rule has been violated, followed by our subsequent choice to ignore that violation; a violation of which would otherwise be cause for the proof or examination to fail.

In order to consider a (very hard to spot) mistake in Einstein’s 1905 work, let’s look at a specific example. The equation x^2+y^2=r^2 is that for a circle. When given a collection of points that satisfy this equation, we can say we have a circle. This suggests the basis for a rule:

“That when given a collection of points that adhere to the equation x^2+y^2=r^2 we will always have a circle.”

We have reliably used this rule in many disciplines for eons. Now we ask, “does this rule always work”?

No. Unfortunately, this rule is incomplete, not because of an assumption, but because it fails to capture all of the requirements for a circle. Missing is the requirement that every point in that collection have the same radius from the center of the circle. So, when given a collection of points (as x,y,r values), we will find cases where the equation is always adhered to, which would lead us to conclude we have a valid circle: When, in reality, we do not have a circle because the radius is changing. This subtlety is introduced when we allow variables on both sides of the equal sign to vary, as is the case in Einstein’s derivation. This error cannot be found simply by examining the equation. Its detection requires an additional math test – one that validates that the radius is not changing. This is a mistake that Einstein has made in his 1905 work and also explains why we have had a hard time finding it. Most people do not see anything wrong with the rule until it is pointed out that the equation alone is not sufficient - that we also need to check for an unchanging radius.

As you’ve stated, some have trouble accepting this finding because it would introduce a contradiction to their existing, century old, belief system that says that Einstein’s derivation is mathematically correct. So people have a choice: They can choose to accept the validity of the math rules for a circle (and reject their belief in Relativity), or they can choose to accept the validity of Einstein’s derivation (and reject their belief in math). Rather than accept a mistake in Einstein’s work or reject what it means to be a circle, they select a third option; they change their view of what Einstein says! Specifically, they choose to ignore Einstein’s statement of the shape he says is formed. They say that he “meant” to say a different shape, regardless of the fact that the math for the two shapes isn’t similar and has its own mistakes. This, however, enables them to continue to hold on to their belief in Einstein’s derivation and also hold on to their belief in the math rules for a circle. In other words, they avoid the conflict by choosing to ignore things that contradict their beliefs and they will rewrite the theory to make it fit their beliefs. This allows them to continue living in a contradiction free world. At this point, however, as you have pointed out, it means that the theory is no longer in the realm of science, but now falls into the realm of religion.

Steven Bryant

Glenn Borchardt said...


You are welcome.

Your example is excellent in that it clearly shows how folks treat contradiction through ignorance or “ignore ance,” that is, by looking the other way. Although often characteristic, I doubt that activity is especially religious.

I have to admit that I was involved in a similar situation involving a practical incident in which termites were attacking my house. I had noticed a tiny, 1-mm hole in the plaster about head high along the north wall of a downstairs bedroom. There were a few winged termites by the window. I chose to ignore these telltale signs for several months, being very busy with other activities. I wasn’t much concerned about this particular contradiction to household integrity. After all, the bedroom wall looked perfectly good except for that tiny hole. Finally, I happened to see one of the winged critters emerging from the hole. I made the hole bigger, only to find more and more live termites. By the time I was done, I had to replace the entire north wall of the bedroom.

The theory of relatively has similar contradictory characteristics that were present, as you point out, from the very beginning in 1905. Folks could look the other way because Einstein’s result favored their indeterministic point of view. Religion had just suffered four decades of damage due to the materialistic theories of Darwin, Marx, and many others. Why be concerned about varying radii and a little “time dilation” among friends? This is a great lesson for the strict mathematicians among us. The ultimate collapse of relativity and the BBT will not depend solely on mathematics or even on fundamental assumptions, but on the public’s desire for a global philosophical shift. We need mathematicians and univironmental determinists to point out that a circle needs to have a constant radius and that time, being motion and not matter, cannot dilate. With so much “ignorance” around, the educational field is wide open.