





[Theoreticians must always examine their premises, for they deal with what is, not what might be. Mathematics cannot probe the axioms it begins with, because the given is not susceptible to the method it makes available. The given is the axiom upon which that method relies, and as such, lies beyond analysis.]
This essay shows that there are limits to mathematics; in fact, there are limits to human reasoning itself. What are those limits: the boundary of what is intelligible.
Physics is a science; it deals with what is, and the explanation of what is through abstraction and theorizing methods of analysis, which enable the production of the future state of what is. Thus the verification of these future states through experimentation allows the necessary connections between things to be probed; and, what is hidden, made known. But mathematics must have a body of knowledge upon which it rests; a set of axioms from which it begins to make its deductions. This set of axioms is given; not itself provable. As in Euclid’s axioms, taken from experience, they are usually the obvious or perceptible features of the world. They represent the boundary of what is intelligible; for beyond the intelligible there is no necessary connection to be probed, because this boundary is this set of axioms upon which all analysis rests.
The beginning of the universe is such an axiom. It is not analyzable because it is a given without a necessary connection (a cause). “Big Bang” theory leads us to this exact situation. There are two possibilities for the conclusion of what “Big Bang” theory theorizes:
(a) The existence of a state which has always existed, or,
(b) The production of such a state from nothing.
Both (a) and (b) are beyond human intelligibility, in other words, they exist outside the possibility of causality as we know it, and are instead beyond the boundary of human intelligibility, where science has no relevance whatsoever.
In fact, when theory reaches such a state (one that defies causality, as the above does), then this signals the crossing of the boundary of intelligibility itself, since the resultant has crossed over the human sensory boundary, and presumed knowledge outside the realm of the knowable; let alone the verifiable. “Big Bang” theory has entered this region in its postulation of the ‘singularity’; With only two possibilities for this entity: (a) or (b), as above mentioned. Neither of these support human experience, which is the material, the methodology of science studies. In this case, science has gone beyond human perception, and into what may be considered the ‘mystical.’
In fact, this is a proof that all reasoning, logic and mathematics can only soundly probe beyond the unproven premises they must accept as their beginning points – the boundary of human perception itself.
What, in effect, I am saying is that the value of the “Big Bang” theory lies in the theoretical fallacy it hypothesizes: a state outside of causal connection. In realizing this, we realize that we have crossed over the perceptual boundary into a theory that takes as its premise a mystical state, which never had a causal beginning, and therefore is essentially unknowable. We can almost say that this theory leads us to something that can only have the properties of a God. Does science now assume the mystical in its realm? Does it presume to take God as its ultimate premise?
No, what science has forgotten, in this case, is that reasoning, logic and mathematics are open ended methods that can examine anything within the realm of human perception – human experience. They always assume an unproven beginning point from which all else is deducted through the necessary causal chain ^{1} . The ultimate beginning state (the axiom or postulate) must be assumed as unproven. If we assume something that has always existed, or something that can be produced from nothing, then we are outside of any existing human experience, as such, since the human perceptual apparatus cannot deal with it. In this case science, cannot deal with it, and must assume a fallacy in its reasoning.
The human is the most versatile of living creatures, since through its reasoning it can probe all experience as such by using an equally versatile reasoning process, which through abstraction can produce consistent premises through which the world can be probed. But these premises are always assumed, and their experiential replication assumed; in other words they are in the realm of human experience. “Big Bang’s” singularity is not. And its unverifiableness (as an irreproducible state) puts it in the realm of belief not science.
Another point is that mathematics is used to create models of physical change, not the other way around. The equations are modeled to the phenomenon, not the phenomenon to the equations. The characteristics of the approximating equations are not the phenomena they model; they, merely, give an approximation to the change the phenomena produce. Equations use infinity and mathematical functions that follow their own rules, the rules of mathematical manipulation, not the rules of nature. The phenomena are abstracted or limited to an extent that allows them to be modeled by the mathematical equations used to predict the movement from one state to another; if, under certain conditions, the equations confirm the phenomena, there is no certainty that they will conform under other conditions, because the phenomena follow the laws of Nature, not the laws of mathematics. And the premises assumed for the equations need not be the premises Nature presents at all times. If Mother Nature has expanded the universe, as the “Big Bang” states, there is no reason for her not to also change the rules of the universe ^{2} , for reasons we can’t even imagine with our meager tools that barely penetrate the tip of the celestial iceberg, let alone the far greater mass beneath. The premises we set up in our mathematical laws of Nature, are meager, as far as the premises Mother Nature has set for the universe we model; for the complexity of natural phenomena is phenomenal in comparison to the complexity of the causes we assume in our axioms.
Science is not about the mystical, but the provable, or verifiable: the realm of causation, as the human knows it ^{3} .
1 This was shown in nonEuclidean geometries, where a geometry could be formed from any consistent set of axioms.
2 These are The Laws of Physics (the laws of the natural phenomena physics has studied).
3 See my essay: “Speculations Into The Origins Of Reason”







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