Image Alt
Earth Science Limitations of Human Logic

Limitations of Human Logic

From William C. Mitchell Bye Bye Big Bang p. 254, those who reject the many errors of present day cosmology, that is based on theoretical innovation that lacks the support of experimental data, have some very good company.

Willam MacMillan, believed the universe to be Newtonian and rejected Einstein’s relativity as outside of common sense, said (in 1927), “The exclusive use of mathematics is a dangerous thing,” and Arthur Eddington wrote (in 1928), “As a scientist I simply do not believe that the Universe began with a bang.” Astronomer and physicist, and president of the Royal Astronomical Society from 1951 to 1953, Herbert Dingle (in 1961) declared that mathematical physicist, “have simply lost the power of understanding of what they are doing…(and) have substituted mathematics for reasoning.”

Big Bang (BB) cosmologist Michael Rowan-Robertson admitted in his university text (in 1977), Cosmology, “most of the models of the universe described in this (his) book are based on general relativity, which cannot be said to rest on a very solid experimental basis.”

British astronomer Fred Hoyle wrote (in 1982) concerning cosmology, “Over the past seventeen years astronomers and physicists the world over have made numerous investigations with the outcome essentially nil. It has been a fruitless churning of mathematical symbols, exactly the hallmark of an incorrect theory.”

According to Lerner, the BB fails scientifically because it seeks to derive the present historically formed universe from a hypothetical perfection in the past. All the contradictions with observation stem from this fundamental flaw. According to Alfven “I have always believed that astrophysics should be the extrapolation of laboratory physics, that we must begin from the present universe and work our way backward to progressively more remote and uncertain epochs.” (1) Mitchell, makes the simple statement; “the scientific method goes out the window”.

It can be seen that BB cosmology does not begin with observations but with assumptions. Mathematical equations are then postulated to try and account for the assumptions. When observations do not line up with the equations, rather than throw the theory out, new concepts are added to the previous assumptions and new equations are devised to try and account for the new concepts. What we end up with is a lot of mathematics having its foundations in nothing but “guesses” at something that is not able to be seen or measured in reality. Mathematics can describe some aspects of nature, but has its limitations in regard to the true reality behind appearances. Anyone can dream a dream, create a reality in their minds, throw in some equations, and presto, announce to the world that this is how everything came to be. This is the present day state of cosmological understanding. Is it a house of cards ready to collapse? Nigel Brush has written a book entitled The Limitations of Scientific Truth – P. Kregel Publications 2005 relates the following section includes substantial quotes from his book. Limitations of Mathematics in the search for absolute truth. One would, perhaps believe, that anything (such as a scientific theorem) that could be proven mathematically would be the purest form of truth, due in part to the accuracy of mathematics itself. However there are weak links in mathematical methodology and processes. These weak links were first discovered by the Austrian mathematician Kurt Godel (1906-1977). If mathematics was to be the final arbiter of scientific truth, Godel and other scientists wanted to prove that mathematical systems are themselves “complete” – that is, every true statement of number theory can be derived from within the system itself – and “consistent” – that is, mathematical statements contain no contradictions. (2)

Godel made the startling discovery that all formal mathematical systems are both incomplete– in that mathematics would not be able to prove all possible truths – and inconsistent – in that, mathematical theories could not even prove themselves. In 1931, Godel published his findings in a seminal paper on the consistency and completeness of mathematics titled “On Formally Un-decidable Propositions of Principia Mathematica and Related Systems I.” What Godel’s First Incompleteness Theorem did was to show that all mathematical systems are incomplete because they are unable to encompass every possible truth. In other words, some things exist that we absolutely know to be true but cannot prove through the use of any mathematical system.

Godel was also able to show that all mathematical systems are inconsistent in that they contain contradictions. By substituting the idea of “proof” for “truth”, Godel was able to introduce into mathematics the famous Epimenides Paradox. Epimenides was a sixth-century B.C. poet from Crete who made the paradoxical statement, “All Cretans are liars.” The Epimenides Paradox forever trapped philosophers in a strange loop because they could never determine whether Epimenides’ statement, was true or false. Epimendes was a Cretan, so he must be lying. If he was lying, however the statement “All Cretans are liars,” must be true. Godel took the core out of the Epimenides Paradox – “This statement of number theory does not have any proof”. By doing so, Godel was able to show that mathematical systems can contain contradictions and are therefore inconsistent. (This contradiction is true only of theories or systems, not of mathematical givens such as 2+2 = 4.) Therefore, how can mathematics be used to validate the empirical observations of scientists if it cannot be used even to validate its own consistency? In plain language, it cannot. (3) Based, then, on the work of both Hume and Godel, the conclusion is inescapable that absolute truth cannot be confined within the bounds of logical (inductive) or mathematical (probabilistic) systems. At best, all that can be done with induction or mathematics is to apprehend a part of the larger truth that is out there; the systems being used are simply not robust enough to capture the entirety of this truth. (4)

What can we assume about assumptions?

Quoting from Dismantling the Big Bang by Alex Williams p. 72 William of Occam, a British monk who studied and taught at Oxford University in the 14th century, put forward a very reasonable solution to this problem of assumptions. It has come to be known as “Occam’s Razor.” This principle says that assumptions should not be multiplied without necessity. In practical terms, it means that if explanation A requires 3 assumptions, and explanation B requires 5 assumptions, then explanation A is preferred on the grounds of economy.

As we consider the number of assumptions inherent in the BB theory, we should be alerted to the preposterous level of doubt we should have about the possibilities of it being anywhere near the truth.

Since we understand that there are several dozen models for the universe, we must conclude that it isn’t an easy process to construct a cosmological model from our observations. Is it comparative to ten people observing an accident? Do we not often get ten different renditions of what happened? How much more difficult is it for ten scientists to look into the cosmos and tell us what happened after the fact. More accurately, these ten people are trying to describe an event that happened on the next street over, and no one was there to see it.

Observations can be explained in many different ways, but the observations being made are not complete in themselves, but lack the elements of observation over the entire time period and difficult to verify. There is the assumption of an application of local physics to conditions “out there” where perhaps that physics doesn’t apply. We had an earlier discussion regarding quantum theory where it appears that that concept has merit. There is the assumption that what we observe is the same no matter where in the universe we make our observations from. Do we occupy a “typical” position in the universe or might our reference point be very atypical? How time and motion are not constants in our universe create assumptions about how things really work out there.

Fundamentally, there are only two scenarios out of dozens that most scientists wish to hang their hat on – the big-bang model and the steady state model. The steady state model is presently in disrepute so our only alternative is the big-bang. Professor Joseph Silk, head of astrophysics at Oxford University has this to say about why this is erroneous thinking: “Because there is essentially no direct and unambiguous experi-mental consequence of our assumptions about the first seconds in the big bang, we may question the model of a simple, uniform and isotropic big bang. Surely, the metaphysical conjecture continues, a highly irregular and chaotic beginning seems the most likely of the infinite set of possible models of the early universe. The one constraint is that such models must eventually decay, to a uniform state of expansion to provide an adequate description of the currently observed universe.” (5)

Silk is saying that there is an “infinite set of possible models of the early universe.” Also; what is a “metaphysical conjecture”? A conjecture is “the formation of conclusions from incomplete evidence; or a guess.” Metaphysics is “the branch of philosophy that deals with first principles, especially of being and knowing.” So a metaphysical conjecture about what happened in the beginning is a philosophical guess. One guess is as good as another. (6)

Verifiability – Can you prove it?

Most basic assumptions in cosmology are unverifiable. Oldershaw distinguishes between two types of un-testability: 1. Un-testability of the First Kind: A theory that is untestable because it cannot generate definitive testable predictions or whose predictions are impossible to test is inherently untestable. Un-testability of the Second Kind: A theory that has many adjustable parameters or is in general modifiable in an ad hoc manner is effectively untestable.

Many of the basic features of big-bang cosmology are inherently untestable. The most critical events of the BB theory are not available to us. The latest inflationary big-bang models are heavily dependent upon particle physics, which in turn involves more unverifiable theoretical entities. The standard model of particle physics has more than twenty parameters (such as particle masses and coupling strengths of the forces) that cannot be uniquely derived and are thus freely adjustable. Many of the problems in particle physics are ‘solved’ ad hoc by inventing new concepts. (7)

By 1934, Karl Popper (1902-1994) had concluded that the mathematical probability of all scientific theories was zero. In his work, The Logic of Scientific Discovery, Popper stated, “My own view is that the various difficulties of inductive logic here sketched are insurmountable. So also, I fear, are those inherent in the doctrine, so widely current today, that inductive inference, although not ‘strictly valid’, can attain some degree of ‘reliability’ or of ‘probability’.” (8)

Popper’s second major breakthrough was his recognition of the “asymmetry between verifiability and falsifiability”. For example – based on a casual observation of swans, one might easily formulate the hypothesis, “All swans are white.” The only way, of course, to verify this statement would be to examine every swan in the universe to be absolutely certain that all swans are, indeed white. Popper, however, pointed out that an infinite number of observations would not be necessary to prove that this statement is false. A single observation of a black swan would be sufficient to falsify the statement, “All swans are white”. Popper showed, that while it is forever beyond our ability to prove absolutely (verify) a universal statement; it is well within our means to disprove (falsify) such a statement. All truly scientific statements must be written such that they can be falsified – not verified. As Popper stated, “the criterion of the scientific status of a theory is its falsifiability, or refutability, or testability”. In a perfect world, scientists might be willing to open up their work to criticism by pointing out the weak parts of their theories; under ideal conditions, scientists might willingly abandon pet theories as soon as they found them to be false. But in the real world things are quite different. Is Popper’s falsifiability criterion the solution to the problem of demarcating science from pseudo-science? No. For Popper’s criterion ignores the remarkable tenacity of scientific theories. Scientists have thick skins. They do not abandon a theory merely because facts contradict it. They normally invent some rescue hypothesis to explain what they then call a mere anomaly or, if they cannot explain the anomaly, they ignore it, and direct their attention to other problems. Popper’s principle of falsification fails to set science apart from pseudo-science. Scientists, naturally having a vested interest in the outcome of their work, are far more prone to justify than to falsify their theories. If neither induction, empiricism, verification, mathematical probability, nor falsification, can be used to separate scientific truth from religious or metaphysical truth, what can? (9)

Paul Feyerabend, philosopher of science (1924-1994) – came to the long-overdue conclusion that, in reality, there is no difference between scientific, religious, and metaphysical truth. Truth is truth no matter where you find it; it is the one immutable object in the universe. As Albert Einstein concluded, “All religions, arts, and sciences are branches of the same tree”. Science itself, concluded Feyerabend, is a religion. Moreover, in the search for truth, because no preferred or superior methodology exists, the human mind should simply make use of every pathway that it finds available. (10)

We are lead to believe that astronomers are observing the past, but this is not true under further consideration. What they see is “coming from the past”, but the actual observations are being done “in the present”. We are told that these observations are “in a historical sense”, what was happening billions of years ago, but what is omitted are the events that affected those observations over the time period from “then” until “now”. This takes us directly into what assumptions will be applied to the activity of that light over billions of years. It is important to be clear on this issue. What people see, or think, or what they think they see, and then what is reported, leaves much to the imagination.

The observer is operating within a “paradigm”. Paradigms’ are ways in which people think about things, and ways in which ideas and theories are communicated. They are always an approximation of the truth. At a future time, the paradigm may hold up or will be discarded. Today, we are waiting patiently for someone to come along with another paradigm that explains the universe. One aspect of paradigms is the tenacity with which one holds on to the constructs within the paradigm. It almost seems that a paradigm becomes part of one’s personality or identity. To give it up is like becoming another person. Usually the main scientists promoting this way of thinking have to die out before any new paradigms can take hold.

Isn’t it All Just Storytelling? Stephen J. Gould notes in an essay titled “Literary Bias on the Slippery Slope,” relates the following; So much of science proceeds by telling stories – and especially vulnerable to constraints of this medium because we so rarely recognize what we are doing. We think that we are reading nature by applying rules of logic and laws of matter to our observations. But we are often telling stories – in the good sense, but stories nonetheless.

The story of human evolution has great literary appeal because we’ve been telling stories to our children for generations. The usual basic plots are found in folktales around the world. The appearance of common story motifs and plots in scientific accounts of human evolution should warn us that we are not being given “just the facts.” The “facts” in evolutionary reconstructions have been selected and standardized from a much larger body of data and have been organized in such a way that they tell a logical, pleasing story. Discrepancies or missing data are often ignored in the interest of telling a story that is complete and the flows smoothly from one point to the next. Such it is with the BB theory. (11)

Problems with Interpreting

The idea that the universe, the galaxy, the solar system, the earth, life upon the earth, and the human mind, all arose by random chance and therefore have no real meaning staggers the human imagination – at least some human imaginations. Many ideas are initially appealing to the human mind simply because they are so foreign to common sense. Nevertheless, many scientists have prided themselves in believing the unbelievable and condemning the rest of society for not placidly following their example. As the White Queen boasted to Alice in Lewis Carroll’s Through the Looking Glass, “Why, sometimes I’ve believed as many as six impossible things before breakfast”.

In his book The Creator and the Cosmos (1993), Hugh Ross identifies no less than twenty-six physical parameters that must fall within extremely limited ranges in order for life to exist anywhere within the universe. He identifies another thirty-three parameters that must be precisely set for life to be possible on the earth. Science has found repeatedly that the statistical probabilities for life arising by chance in the universe are ridiculously low. Many scientists have looked at the evidence and have not missed the implications inherent in the fine-tuning of the universe, while others have dismissed it as “illusory.”

(12) Science is but one manifestation of humanity’s quest for absolute truth – not the ultimate acquisition of absolute truth. Because scientific truth is constantly changing, it cannot be absolute truth. Because modern science is not absolute truth, it must contain a mixture of truths and non-truths. Whether science can someday overcome these limitations and arrive at absolute truth is certainly open to debate. What cannot be debated is the current incomplete (non-absolute) state of current scientific understanding. (13)

Searching for truth is like a coin. It has two sides. Scientists today are looking at only one side of the coin and refuse to turn it over and observe what information can be attained on the other side. One side of the coin has a great deal of information, but it is incomplete. In order to understand everything there is to know about our coin we must turn it over. When I turn over my coin, I can find another potential solution to understanding the purpose and value inherent in the coin. Most importantly, I can read the words, “In God We Trust”. Perhaps the coin of the universe has been turned over and other motivations, personal or otherwise, cause one to turn the coin back over and hide its relevancy.


1. Lerner, p. 40
2. Brush, p. 68
3. Ibid., p. 70
4. Ibid., p. 71
5. Williams et al., p. 55
6. Ibid., p. 55
7. Byl, pp. 71-72
8. Brush, p. 73
9. Ibid., pp. 74-81
10. Ibid., pp. 82-83, 85
11. Ibid., pp. 107-108
12. Ibid., pp. 211-213
13. Ibid., pp. 248, 254