6.5 John Oakes’ Assumptions of Science

These ideas were aggregated from a series of presentations that can be found at http://www.grossmont.edu/johnoakes/, the website for John Oakes at Grossmont College in El Cajon, California. He, I am sure, is not the originator of this list. But he did a very good job of compiling them into a single presentation which I summarize here. In his view, they express the core set of basic assumptions that both science and rational empiricism embrace:

• The rules of logic are valid tools for learning and understanding.
• The world is real. The physical universe exists.
• Human senses are reliable.
• The real world is knowable and comprehensible.
• There are laws that govern the real world. The universe is orderly, having regularity, pattern, and structure. Laws of nature describe that order.
• Those laws are knowable and comprehensible. The principles that define the functioning of the universe can be discovered. Nature is understandable.
• Those laws don't radically change according to place or time, since the early stages of the big bang. They are universal.
• All phenomena have natural causes. Scientific explanation of human behavior opposes religious, spiritualistic, and magical explanations.
• Language is adequate to describe the natural realm
• Mathematical rules are descriptive for the physical world
• Unexplained things can be used to explain other phenomenon (e.g. gravity is thus far unexplained but it is used to explain the movement of planets and the bending of light)
• Observable phenomena can provide information and knowledge about unobservable phenomena (induction)
• All ideas are tentative, potentially changed by new information. This harkens back to Newton's fourth of his Rules of Reasoning in Natural Philosophy :

"Propositions deduced from observation of phenomena should be viewed as accurate until other phenomena contradict them.” Unless proven otherwise, the best theory that successfully explains the facts should be accepted, keeping in mind that all theories are provisional, subject to revision given new evidence.

• Nothing is self evident. Truth claims must be demonstrated objectively.
• Knowledge is derived from acquisition of experience, empirically, through senses directly or indirectly.

6.6 Norm Levan Panel on Intelligent Design

When you compare the list in the previous section to this next one, you will notice quite a lot of overlap. Even after examining the assumptions presented in just these two sections, one can see a common thread emerge: With the use of empiricism, informed by logic and rational thought there appear to be few if any blocks to acquiring an understanding of the universe. The Norm Levan Panel is part of a secular humanist research facility based in Bakersfield CA. It investigates issues related to Intelligent Design, Evolution, and the conflict between religion and science. These assumptions were presented during a forum held at Bakersfield College on April 21, 2006:

• There is a reality independent of us or our viewpoint
• Nature follows fundamental rules and laws
• Humans have the ability to figure out rules of nature
• Peer review is critical to filtering out human biases
• Objective observational experiences are necessary for advancing knowledge of reality
• Scientific method combines rationalism's deductive logic with empiricist's inductive logic based on observational experience
• Invoking the supernatural is dead-end to further inquiry. Science cannot test supernatural explanations, since they are unfalsifiable, unverifiable, and can be altered to fit any situation post-hoc.

I cannot completely agree with the last of the bulleted items. There is nothing inherently untestable about supernatural claims. What is untestable are supernatural causes if they are presented as being immune from being disproved. Claims of ESP or faith healing, which rely on supernatural powers, can certainly be tested. But supernatural causes that can transform to fit any outcome, which elude falsification, or defy testing are, by definition, unscientific and fall outside the realm of the scientific method. They may be true or not true, but science is not equipped to find that out.

So, the elements in these catalogs of assumptions underlying the scientific method and empirical inquiry revolve around assertions that reality is objective and consistent, that humans have the capacity to perceive reality accurately, and that rational explanations exist for elements of the real world. These assumptions are based in naturalism, logic, and empiricism, which provide a framework within which science can be performed.

Biologist Stephen J. Gould included two additions that augment these lists: 1) Uniformity of law and 2) uniformity of processes across time and space--must first be assumed before you can proceed as a scientist doing science.

6.4 Falsifiability vs Verifiability

Karl Popper, the well-known modern critic of Logical Positivism, wrote The Logic of Scientific Discovery in the 1930's. In it he promoted the revolutionary idea that the Logical Positivists' requirement of verifiability was too strong a criterion for science, and should be replaced by a criterion of falsifiability. The Positivists held that statements about the world are meaningless and unscientific if they cannot be verified.

To the Logical Positivist, the technical term, "Verification", has a very precise meaning (though different Positivists have had slightly different definitions of it). Generally it indicates that a statement is meaningful only if it is either empirically verifiable or else tautological (i.e., such that its truth arises entirely from the meanings of its terms). "Verifiability" requires that a statement be logically entailed by some finite set of observation reports. Later Positivists, having abandoned this view, required of a verifiable statement only that it be made evident or supported or rendered probable by the relevant set of observations.

Popper, on the other hand, argued that verifiability was more a requirement for "meaning" rather than science. He explained that there exist meaningful theories that are not scientific, and that a criterion of meaningfulness is not the same as a criterion for demarcation between science and non-science. Popper proposed that that falsifiability was the correct rule for this use because it did not invite the philosophical problems inherent in verifying via induction. It allowed for statements from the physical sciences which seemed scientific but which did not meet the more stringent verification criterion. In other words, it is more difficult to construct strictly verifiable hypotheses than it is to devise falsifiable ones, and for this reason, the criterion of verifiability excludes much of what we would consider to be real science. If verifiability were the criterion, then the targets which science could address would be far more constrained.

One of the main criticisms of logical positivism was that its own principle of verification, which held that a statement is only meaningful if it can be empirically verified, was self-defeating. The Positivist "Verification Principle" was central to the Positivist project of demarcating scientific knowledge from non-scientific or metaphysical claims. The problem with the Verification Principle is that it cannot be empirically verified itself. This means that the principle fails its own test for meaning and is thus rendered meaningless according to the Positivist's own criteria. This problem is known as the "verification principle's self-refutation" and was pointed out by several philosophers, including Popper and Quine, who argued that the principle was either trivially true or not at all true.

This critique undermined the Positivist's claim to have found a solid foundation for scientific knowledge and contributed to the decline of the movement. However, it is important to note that this was not the only reason for the demise of logical positivism. Other factors, such as the emergence of new scientific theories, critiques of the positivist's understanding of language and meaning, the emergences of Quantum Theory (and the "Uncertainty Principle"), and the social and political changes of the time, also played a role.

To be clear, just because something is "falsifiable" does not mean it is false. Rather, it means that if it is false, then this can be shown by observation or experiment. Popper used falsification as a criterion of "demarcation" to draw a sharp line between those theories that are scientific and those that are unscientific or pseudo-scientific. He was motivated by a frustration with what he considered to be some unscientific theories that were popular at the time - Marxism and Freudianism, and his great admiration of Relativity Theory. He saw the one set of theories as qualitatively different than the second. Marx and Freud were making claims that were fundamentally incapable of being disproved, while Einstein's claims were very clearly capable of disproof. This difference is the essence of Falsifiability. It is useful to know if a statement or theory is falsifiable, if for no other reason than that it provides us with an understanding of the ways in which one might assess and test the theory. One might at the least be saved from attempting to falsify a non-falsifiable theory, or come to see an unfalsifiable theory as unsupportable.

Popper claimed that, if a theory is falsifiable, then it is scientific; if it is not falsifiable, then it is not open to falsification and therefore not a meaningful scientific issue. This puts most (but interestingly, not all) questions regarding God and religion outside the domain of science. Falsifiability also circumvents the debate over whether the domain of science only encompasses the "natural world" as opposed to the "supernatural". Instead it frames science within the bounds of a methodology - science deals with hypotheses that can be falsified.

Falsifiability certainly ranks as one of the most important elements in the modern conduct of science. Its superiority to verifiability results from fact that no number of positive experimental outcomes can ever absolutely confirm a scientific theory. But a single counter-example is decisive. It shows that the theory being tested is false, or at least incomplete. Instead of saddling scientists with the impossible task of providing absolute proof, a theory was considered to be tentatively “true” if ample opportunity and means were proposed to disprove it, but no one was able to do so.

Popper demonstrated his position with an example of the rising sun. Although there is no way to prove that the sun will rise every morning, we can hypothesize that it will do so. If only on a single morning it failed to rise, the theory would be disproved. Barring that, it is considered to be provisionally true. The longer a theory retains this provisional status, and the more attempts are made to test it, the greater its claim to firm truth. The “sun-will-rise” theory has been well tested many billions of times, and we have no reason to anticipate that circumstances will cause it to stop happening. So we have a very good reason to believe that this theory represents reality. This argument has some weaknesses (primarily that it is not deductively ironclad). But because no stronger proof suggests itself, it is consistent with other information we have, and it is pragmatically useful, it remains a very good operating theory.

However, critics have legitimately pointed out practical problems with the straightforward use of falsifiability to test theories. The basic idea that Popper proposed is that a scientist proposes a theory, and researchers test the theory in an attempt to find confirming and/or contradictory evidence. If it can be falsified by reliable and reproducible experimental results, that theory must be abandoned.

Thomas Kuhn argued that the actual practice of science doesn't follow this type of pattern at all. He pointed out that in the history of science, there have been several famously incorrect conclusions reached by applying this standard. For example, when it was discovered that the orbit of the planet, Uranus, did not follow the path predicted by Newtonian mechanics, it appeared to falsify Newton. However, the desire to retain Newton's laws was so strong (after all, it was coherent with so many other theories), that post hoc explanations were introduced to save it - in this case another planet was posited even further out than Uranus. This actually turned out to be the case (Neptune was discovered some years later). But it is considered a weakness in a theory to have to postulate ad hoc changes simply to save it from the facts.

A similar problem was encountered by Lord Kelvin in his attempt to falsify claims of great antiquity for the Earth's age. He was a devout Christian who objected to Darwin's new Theory of Evolution, and was very motivated to demonstrate that not enough time had passed for evolution to have occurred. He calculated the rate at which the Earth has probably cooled since its early (assumed) molten state. This number (about 20 to 100 million years or so) happened to agree very well with his other calculation for the age of the sun. Our planet could certainly not be older than the sun. And he thought that if the sun were made of even the highest grade coal, it could have been burning at its current rate for only a few thousand years. He added in gravitational contraction as an alternate source of heat, and arrived at the same age - 20 to 100 million years. Thus, he believed he had falsified the Theory of Evolution, which requires much more time than that. Of course, if we altered the assumption concerning the source of heat for the sun (e.g. from coal to fusion), it would allow a far greater age for both it and the Earth. To Kelvin's credit, he did recognize this when he wrote,

"inhabitants of the earth cannot continue to enjoy the light and heat essential to their life for many million years longer unless sources now unknown to us are prepared in the great storehouse of creation."

Another great example is the Theory of Evolution. The current "Modern Synthesis" Theory is quite different from the version first proposed by Darwin, though it shares many of the basic fundamentals. It has incorporated Mendelian genetics over Darwin's version of inheritance, and was improved by our increased understanding of DNA and molecular biology. The theory has changed over time in the face of new information that showed limitations, weaknesses, and actual errors in the original theory. It was not discarded, but improved.

The question is, though, how many times are we allowed to move the goalposts and alter theories, and the background assumptions of those theories, after they have failed? The addition of ad hoc, "auxiliary propositions" can weaken the original theory by erecting a shaky scaffold of special cases around it. But even Popper admitted that the "naïve falsification" he proposed has to be flexible enough to bend with necessity:

"Some genuinely testable theories, when found to be false, are still upheld by their admirers—for example by introducing ad hoc some auxiliary assumption, or by reinterpreting the theory ad hoc in such a way that it escapes refutation. Such a procedure is always possible, but it rescues the theory from refutation only at the price of destroying, or at least lowering, its scientific status."

I question his assertion that introduction of ad hoc assumptions inevitably weakens or lower the status of the theory. In the examples above involving Uranus, the sun's age, and the Theory of Evolution, the addition of new considerations into the theories enriched them and eventually led to a clearer understanding of the solar system and life. Similarly, the history of Quantum Physics over more than a century has demonstrated how experimental results required modification of the Standard Model. Unexplainable results related to Blackbody Radiation, Quantum Entanglement, Neutrino Mass, and many other experimental observations required changes to the underlying theory. In all these cases, the modified theories were actually stronger than the original ones.

As attractive and seemingly fail-safe as Popper's Falsifiability Theory may have seemed, especially when contrasted with the most competitive alternative of the time - the Logical Positivist's Verifiability technique - it is clearly not a panacea. We see that it has some serious limitations and weaknesses. Popper's theory was basically that no amount of data could ever completely prove a theory, but that even a single piece of counter-evidence is sufficient to disprove it. It is a wonderful guideline, like Occam's Razor or "measure twice cut once", but it is not useful in all scientific endeavors. Although the naïve initial temptation upon learning about it is to apply it indiscriminately, it turns out that it is not universally applicable.

The first problem concerns the assertion that no amount of data can confirm a theory. This is simply not how science is actually practiced. Overwhelming and consistently supportive data boosts confidence in a theory to the point where it is accepted as a practical fact; that to dispute it would be contrary and perverse. No one seriously disbelieves in the law of gravity (e.g., that apples may start falling upward tomorrow). Scientists usually don't need to confirm a theory one hundred percent in order to trust and use it as if it were true.

As Kuhn described in his work, scientists do not discard a theory as soon as an experimental observation contradicts the theory. That contrary evidence would need to be reproduced several times, and other similar experiments would need to be done to probe the potential weakness and boundaries of the problem area. There could have been flaws in the experimental methodology or the analysis of results, or maybe the theory just needs a minor adjustment to accommodate the new data.

Another reason why the importance of falsification has declined is because much of modern science is model-based rather than hypothesis and theory-based. Doing science using models rather than theories doesn't really lend itself to falsification, since there are no experiments being conducted to isolate behaviors that will yield evidence supporting or contradicting a hypothesis. Of course models are incomplete and simplistic (compared to the complex physical process they are modeling). There are bound to be errors in them. Data that conflicts with the model doesn't necessarily imply that the model should be discarded, but more likely that the model needs additional refinement to address aspects of reality that were left out of it or incorrectly dealt with in the model. In fact, discovering and repairing flaws in the models adds deeper understanding of the real-world phenomena the model attempts to replicate. Climate and weather models, molecular models, economic models, cosmological models, and the rest are not always thrown out when reality conflicts with them - instead they are usually enhanced or modified to incorporate the new information, making the models stronger and more accurate and representative. Sometimes older models become so ragged and jury-rigged that it makes more sense to discard them and begin again with a new approach.

One last problem with falsification is that much of science does not involve establishing the correctness of theories - they are not tests of theories. Materials science, chemistry, biology, computer science, and others involve activities that don't involve falsification or verification - they are making things like new materials, molecules, pharmaceuticals, software solutions, and devices. There is nothing to falsify - so Popper's method is simply irrelevant in these legitimate sciences.

Duhem-Quine Thesis

The Duhem-Quine thesis adds another objection to Popper's criterion of falsifiability (sad to say). Falsifiability works well in so many cases, but it does, unfortunately have at least one fatal flaw, which Duhem and Quine identified. They assert that no hypothesis entails predictions about an empirical observation alone, because that hypothesis is always associated with a large collection of supporting assumptions, theories, and auxiliary hypotheses. This thesis states that it is impossible to test a hypothesis in complete isolation, because an empirical test of the hypothesis requires one or more of these background assumptions, the ultimate background assumption being that we can even rely on the rules of logic. The hypothesis being tested cannot be completely segregated from the assumptions that support it. Instead, the consequences of the hypothesis rest on background information, and that information must itself be tested and proven (or at least shown not to be false) - they must be accounted for. And those background assumptions, themselves may depend on other background assumptions, practically ad infinitum. If your experiment on the primary hypothesis generates a negative result (i.e., according to Popper, you have falsified the hypothesis), but you have not accounted for all background assumptions (ad infinitum), you really can't draw any conclusion. Your hypothesis may indeed be wrong, or the background assumptions may have problems which invalidate the falsification. The case involving the age of the Sun (above) is an actual example of this - the background assumption about the source of heat in the sun was wrong, as was Kelvin's additional assumption about the rate of the Earth's cooling. So, although Kelvin thought he had falsified evolution, he had done nothing of the sort. Further, a discrepancy between what a hypthesis predicts and the actual observed data does not necessarily falsify the hypothesis because there may have been flaws in how the data, itself, was collected or measured.

The thesis can be expressed using symbolic logic:

H → E

This says that "If H, then E", where H is the hypothesis and E is evidence, or an observation expected if the hypothesis is true. That is, if the hypothesis is true then we should see the evidence. By the logical rule of modus tollens,

¬E → ¬H

This says that if we do not observe E, then H is false. In other words, if we don't observe the evidence when running an experiment, then the hypothesis has been falsified. For example, say that H is the hypothesis that water boils at 100°. You have a pot of water you intend to boil. If you heat the water past this temperature and it does not boil, then you have falsified the hypothesis. But this assumes quite a lot, for example it assumes that you are at one atmosphere of air pressure, and that the water is pure and unadulterated. But what if you are at two atmospheres of pressure, or what if the water has a contaminant, such as antifreeze, in it that raises the boiling point? The background assumptions have been violated. So a better expression of the experiment is:

(H & A) → E

This means that H, along with some background assumptions imply E. So, if you don't observe E, then (H&A) are false

¬E → ¬(H & A)

This says that the combination of H and the its background assumptions, A, is false. A is not just a single assumption, but many (such as we are at one atmosphere, that the water is pure, that the thermometer is well calibrated, etc). So, A is really (A1 & A2 & A3 & ... & An), where each of the A's is a different background assumption. So now we have:

(H & (A1 & A2 & A3 & ... & An)) → E

and also:

¬E → ¬(H & (A1 & A2 & A3 & ... & An))

The above expression, ¬(H & (A1 & A2 & A3 & ... &An)), is the same as any of these:

¬H | ¬(A1 & A2 & A3 & ... &An)
¬H | (¬A1 | ¬A2 | ¬A3 | ... | ¬An)
¬H | ¬A1 | ¬A2 | ¬A3 | ... | ¬An

This means that if you don't observe E, then either the hypothesis, H, is wrong, or one of the background assumptions, (A1, A2, A3, ..., An), are wrong, or some combination of H and one more of An is wrong.

So, as frequently as the idol of "falsifiability" is honored in the context of science, a "naïve falsification" approach truly is insufficient. Serious researchers must also take background assumptions into account to ensure that they, too, have strong support. But all is not lost. Obviously, science still occurs, experiments are run, hypotheses are falsified, and progress is still made. Overall, this critique of Popper's method been healthy for science. Researchers are forced to take less for granted in their assumptions, do a thorough job of supporting their underlying assumptions, and check their experimental methods to buttress against possible errors in auxiliary assumptions. The reliance on background assumptions cannot be eliminated, but their destabilizing influence can be minimized to, hopefully, manageable levels. The process of justifying beliefs and assumptions can only begin once a number of precursors assumption are independently justified. Some of these fundamental assumptions must be accepted as self-evident if they cannot be justified because they comprise the frame in which justification takes place.

6.3 Ockham’s razor and the Law of Parsimony

I have made several appeals to Ockham's razor so far in this paper. It is one of the most widely referenced basic principles of science, empiricism, and reason, being one of the few that people who don't actually study this field are familiar with. It is a heuristic principle that has been shown to be immensely valuable in the long history of science, as well as in everyday living. Also called the "Law of Parsimony", it is succinctly expressed as "entities should not be multiplied beyond necessity". In modern English, "the simplest explanation tends to be the correct one". This is not a mystical revelation, but is a guideline that has been borne out in case after case. Simply stated, nature tends to solve problems using the least energy and complexity that will suffice, taking the shortest and most direct path available. Just as water flows downhill, and Uranium splits into new atoms that have the lowest stable energy level, all physical systems trend to the state of lowest energy following the path of least resistance. All of these phenomena, summed up, seem to promote the overall tendency of nature to "prefer" (pardon my anthropomorphizing) the simplest course to an outcome.

Ockham's razor is not a scientific theory, nor is it a law of nature. It is a guideline - a rule of thumb. It is a pattern that frequently fits the turn of events. However, things don't always work out according to it. It does not compel us to always choose a particular explanation over another. And there have been many cases where the more complicated explanation was correct. The mind boggling number of subatomic particles is by no means a simple explanation for the existence of matter. It is a far more complex theory that simple atomic theory that required only protons, neutrons, and electrons. Mendeleev's periodic table with its dozens of elements is much more complicated than Aristotle's five elements (earth, air, fire, water, either). The theory of evolution is far more complex than "god just created everything as you see it today". In each of these cases, a more complex theory turned out to be correct.

But in most cases, the simpler explanation does tend to be the right one. Example: If a dog owner comes home to the trash can tipped over and trash scattered on the floor, two possible explanations are that the dog tipped over the trash or someone broke into the house and sorted through it, or that a poltergeist was responsible. Most of the time, blaming the dog would be the correct choice. This guideline has been stated in many ways by many different people in different times and places. Aristotle wrote in one of his essays:

"We may assume the superiority "ceteris paribus" (i.e., all things being equal) of the demonstration which derives from fewer postulates or hypotheses."

John Duns Scotus preceded Ockham in proposing this rule in the late 1200's:

"Plurality is not to be posited without necessity. What can be done with fewer would in vain be done with more."

Thomas Aquinas, also in the late 1200's, wrote:

"If a thing can be done adequately by means of one, it is superfluous to do it by means of several; for we observe that nature does not employ two instruments where one suffices."

Galileo, in the course of making a detailed comparison of the Ptolemaic and Copernican models of the solar system, maintained that

“Nature does not multiply things unnecessarily; that she makes use of the easiest and simplest means for producing her effects; that she does nothing in vain, and the like”

Isaac Newton proposed his four “Rules of Reasoning in Philosophy”, the first of which dealt directly with Ockham's Razor, though not by that name. This is his somewhat anthropomorphized, teleological version of Ockham’s Razor:

"We are to admit no more causes of natural things such as are both true and sufficient to explain their appearances. To this purpose the philosophers say, that Nature does nothing in vain, and more is in vain, when less will serve; for Nature is pleased with simplicity, and affects not the pomp of superfluous causes.”

The name of this guideline is (most agree) incorrectly attributed to William of Ockham, a 14th century Franciscan friar. Whether or not he actually said anything resembling the rule that bears his name, the words he supposedly said were:

"Entia non sunt multiplicanda praeter necessitatem" (entities must not be multiplied beyond necessity),

Bertrand Russell, much later in the 20th century offered a version:

"Whenever possible, substitute constructions out of known entities for inferences to unknown entities."

Kant, in the Critique of Pure Reason, proposed his version:

“Rudiments or principles must not be unnecessarily multiplied (entia praeter necessitatem non esse multiplicanda).”

He argued that this is a regulative idea of pure reason which underlies scientists' theorizing about nature. This common-sense mindset appears and reappears multiple times thoughout western thought. It probably also occurred to Oriental and Arabic scholars, though I have found no references to such independent origins. In any case, its wide distribution and persistent popularity testify to its enduring value. Although our explanations sometimes run counter to Ockham's Razor, it is a valuable rule to keep in mind. It can help bring us back to reality when tempted to engage in complex flights of fancy when faced with confusing situations. It probably leads us in the right direction more often than not. But, as noted, we should not be enslaved by it, but should use it as one of our tools for problem solving in the real world.

6.2 Aristotle’s Laws of Thought

Aristotle's "Laws of Thought" date back to the earliest days of Western Philosophy. They shape the basic structure of western thought, science, and its overall worldview - the worldview that can so puzzle many non-Westerners. Many philosophers (and mathematicians) who followed Aristotle such as Locke, Leibnitz, Schopenhauer, and Boole, have modified and enhanced his principles. However, the initial intent has remained the same even if the laws, themselves, get reformulated. These laws are fundamental logical rules, with a long tradition in the history of western philosophy, which together define how a rational mind must think. To break any of the laws of thought (for example, to contradict oneself) is to be irrational by definition. These three classic laws of thought were fundamental to the development of classical logic. They are:

• Law of Identity - an object is the same as itself:
  A ⇔ A
• Law of Noncontradiction - contradictory statements cannot both at the same time be true, e.g. the two propositions "A is B" and "A is not B" are mutually exclusive:
  ¬(A ∧ ¬A)
• Law of the Excluded Middle - Everything (that is, every proposition) must either be true or not true. There is no in-between:
  A ∨ ¬A

Actually, with just a little logical manipulation, I think I can show that the Law of Noncontradiction is the same as the Law of the Excluded Middle. There is a rule in logic called De Morgan's Law. It has several representations, but one of them is:
    ¬(P ∧ Q) ⇔ ¬P ∨ ¬Q
If we let P = A, and Q = ¬A, then
    ¬(A ∧ ¬A) ⇔ ¬A ∨ ¬¬A,
which is the same as:
    ¬(A ∧ ¬A) ⇔ ¬A ∨ A
The left hand side is the Law of Noncontradiction, and the right hand side is the Law of the Excluded Middle.

These are self-evident logical principles - fundamental axioms that cannot be proved (or disproved), but must be accepted (or rejected) a priori. In other words, there is nothing "under" them - they cannot be decomposed into more basic principles. They are similar, conceptually, to the axioms in Euclidean Geometry (e.g. the famous "Parallel Postulate"). Other types of geometry are possible, but if you begin with certain postulates you get Euclidean geometry. Other postulates generate other geometries. In logic, other postulates could be substituted for the Laws of Thought, and in fact have been in other traditions such as Buddhism, which celebrates contradiction. Paraconsistent logic (a type of logic that deals with contradictions differently than classical logic) does not depend on the Law of Noncontradiction. Even Greek philosophy before Aristotle (and Parmenides, who proposed similar laws) did not always embrace these concepts. But practically everything we know of traditional Western Philosophy and Logic embodies these principles. Preceding Aristotle by over a century, Heraclitus believed that contradictions were necessary - that their existence was essential to a thing's identity:

"Not only could it be stated that identity is the strife of oppositions but that there could be no identity without such strife within the entity."

He argued that because all things change, they must have already had in them "that which they were not". Only the existence of such contradictions could account for the change we see in the world. For example,

"Cold things grow warm; warm grows cold; wet grows dry; parched grows moist."

The defenders of Aristotle’s three laws of thought quickly learned that they had to establish the context for the application of these laws, because they were frequently assailed with counter-examples that seemed to violate them. It became clear that the laws could not be employed loosely or in poorly defined conditions. So, they began to require a “definite logic” model. In this model, the terms and the expressions formed from these terms must be clearly definable and knowable. But this ideal is rarely achieved in the real world, and we are forced to make assertions about things in less than precise, fuzzy terms. Not until the creation of Mathematical Logic by Boole in the 19th century, and later Russell and others, was logic able to refine its expression with mathematical, perfectly clear terms and operations.

This development in logic admirably suited the predispositions of the Western mind, and certainly helped shape it. Western philosophy to a very large extent has been founded upon the Laws of Thought and similar ground rules. We believe that our thinking should strive to eliminate ideas that are vague, contradictory, or ambiguous, and the best way to accomplish this, and thereby ground our thinking in clear and distinct ideas, is to strictly follow laws of thought.

But are these laws simply axioms, or can the be proved? It doesn't appear that there is a direct proof, but to some degree they must be accepted a priori. However, Aristotle pointed out attempts to logically justify these axioms were unnecessary. He held that the axioms of classical logic are self evident because 1) all syllogisms rely on them, and 2) because they can be defended through retortion.

A defense through retortion occurs whenever an argument must rely upon the very principle it seeks to challenge or overturn. Any attempt to form a syllogism to refute the Laws of Thought will have to rely on the very axioms it seeks to overturn, leading to an implicit reliance on the axioms, which is a self refutation (i.e., the "Stolen Concept fallacy"). In other words, it is impossible for the laws of logic to not be correct. If I were to say, "the Law of Non-Contradiction is false", this presupposes the Law of Non-Contradiction itself, because I am simultaneously intending to convey, "It is not true that the Law of Identity is true".

In spite of how dominant these laws of thought have been, they have not been without their critics, and philosophers from Heraclitus to Hegel have leveled powerful arguments against them. But the issue does not seem to be whether the laws are applicable or not, but where and when are they applicable. Certainly, the laws of thought have a place, but what is that place? As Walt Whitman wrote in “Song of Myself”:

"Do I contradict myself?
Very well, then, I contradict myself.
(I am large, I contain multitudes.)"

Also as Nagarjuna, one of the fathers of Buddhism, wrote in "Verses on the Middle Way":

"Everything is real and not real.
Both real and not real.
Neither real nor not real.
That is Lord Buddha's teaching."

The time to abandon strict laws of thought arises when we are beyond the realm to which ordinary logic applies, or as when “the sphere of thought has ceased, the nameable ceases” (Nāgārjuna). A similar sentiment is expressed by Wittgenstein's assertion in the Tractatus,

"what can be said at all can be said clearly, and what we cannot talk about we must pass over in silence"

Many people who value rational thought, objectivity, and clear, precise thinking have no doubt been frustrated while engaging in fruitless debates with those who abandon the Rules of Thought. Anyone who has had to counter statements like, "your truth is not the same as my truth", "everything is relative", "what is proof for you is not proof for me", "your facts are just your opinion" has dealt with this first-hand. I have been frustrated in my conversations with relativists, sophists, self-styled mystics, and post-modernists who toyed with words and meanings simply for the pleasure of being evasive and derailing rational discourse. They equivocate on the important concepts like truth, meaning, free will, reality, faith, belief, trust, experience, existence, good, bad, etc. When they sense they are being pinned down in a logical contradiction, they do an end-run around logic and question the very premises of rationality (for example, the Laws of Thought), subverting the entire effort. They redefine important terms, frequently in mid-discussion, using them in varying ways that suit their desired outcome (note - it is always important to define terms up front to make sure you are not talking at cross purposes with someone!) There doesn't appear to be a sincere desire to arrive at a clear conclusion, but more a desire to put the person promoting the rational world-view off balance, questioning the very premises needed for an exchange of ideas, throwing logic out the window, and wallowing in mystical babble simply for the fun of it.

The Persian philosopher, Avicenna (also known as Ibn Sina) has a famous quote about how to deal with those who disregard the Law of Noncontradiction:

"Anyone who denies the Law of Noncontradiction should be beaten and burned until he admits that to be beaten is not the same as not to be beaten, and to be burned is not the same as not to be burned."

Of course I don't recommend that, but it definitely shows that even great minds can become a little peeved with intransigent illogical thinking.

Philosophical naturalists and realists attempt to understand the world using a reason and evidence-based approach. They employ logic and empiricism, filtered through external review and correction, iterative refinement, and ultimately balanced by informed judgment which also has to take unknowns and risk into account. Experience has shown this to bear the greatest fruit if the goal is truly to understand the world.

Those who approach these questions from a religious or mystical point of view, will achieve an outcome which embodies whatever results they feel are enlightening, thrilling, comforting, uplifting, or that allow them to persist in their irrational (by definition) and incoherent (i.e., disorganized and internally inconsistent) mystically-based world view. To allow the introduction of multiple, inconsistent concepts during an exchange causes confusion because of the impreciseness (and even trickery) of language. The epistemologies feeding our different world views (science/evidence/reason/naturalism vs mystical/religious/irrational/revelatory) differ. The irrational approach is based on revelation/inspiration/emotion/myth/sacred texts, and the scientific world view is based on observation/experiment/measurement/evidence/theory/methodology/coherence/critique. It is difficult, probably impossible, to bridge the gap between these diametrically opposite positions.

However, the irrational does have its place in our world. Humans are not robots, but are primarily emotional beings with a veneer of rationality laid on top. Not everything is best dealt with through a reductionist, rational approach. We would lead a very narrow existence, indeed, as well as barren and joyless, to try to apply these or similar laws to every human experience. Of what use is it to be entirely reason-based when enjoying the beauty of nature, the joy of your pet, or the laughter of friends and relatives. However, in the focused realm of science, whose goal is merely to explain how things work and of what they are made, this type of restricted and disciplined thought is a perfect fit.

6 Assumptions of Science

None of the philosophical questions we have explored are resolved, or else (obviously) they would not still be considered philosophical questions. The controversies and different points of view surrounding the nature of reality, the problem of induction, and the necessary assumption of a uniform universe still stir debate as to what scientific naturalism represents, what are its limits, and how well man can actually know the world. Having said all that I can on the subject, I must now leave it and bubble up one level to describe assumptions that science makes based on these convincing, but admittedly unresolved, principles.

6.1 Rejection of Magic

No one has addressed primitive beliefs in magic and superstition as well as Sir James Frazer, author of The Golden Bough. This was the first definitive description of the myriad explanatory techniques and coping mechanisms that pre-scientific people used to make sense of their world. Rather than using empirical methods of observation, hypothesis, test, and measurement, the long standing unsophisticated, intuitive methods they used to explain how the universe worked invoked what would today be called magic. These people found patterns in the world based on associations of ideas in the mind, either through similarity or proximity. According to Frazer, “the order on which magic reckons is merely an extension, by false analogy, of the order in which ideas present themselves to our minds.” Primitive societies, succumbing to this way of reasoning, relied on what he called “sympathetic magic” to explain events in the world. Two sub-categories of these phenomena subsumed the bulk of primitive magical thought:

• Law of Similarity (“like” produces “like”). This is the basis of voodoo, images, effigies, idols, and holy statues. Charms based on the Law of Similarity may be called Homeopathic of Imitative Magic. The Mandrake root, which resembles a man's form, is supposed to have magical properties. Rhinoceros horn, which bears a striking resemblance to a body part of virile male, is used as an aphrodisiac. Primitive cave paintings depicting of successful hunting scenes were thought to insure a successful outcome to the real hunt. Mistletoe was used in pre-modern times as a cure for epilepsy. It does not fall to the ground because it is rooted on the branch of a tree. It would seem to follow as a consequence that an epileptic cannot fall down as long as he carries a piece of mistletoe. Such a train of reasoning would probably be regard even now as reasonable by a large portion of humanity.


• Law of Contact (or Contagion) is based on the idea in which things that have once been in contact with each other continue to act on each other at a distance after the physical contact has been severed. Charms based on the Laws of Contact are called Contagious magic. Our abhorrence at the idea of wearing a piece of clothing previously worn by a mass murderer, or receiving a blood transfusion from a violent criminal are demonstrations of this law at work. Relics of saints, or fragments from the “true cross” can supposedly transfer spiritual energy. A lucky shirt or lucky ritual such as crossing your fingers invoke the Law of Contact. Charms made from fingernail clippings, hair and other discards from a target of magic are frequently used.

Magic is a spurious system of natural law as well as a fallacious guide of conduct. It is more akin to a false science than a false religion. Magical systems attempt to express, explain, and exploit causality through an association of ideas – the first through similarity in form, the second in similarity of position. Magical thinking commits the mistake of assuming that things which resemble or were near each other are somehow the same or have some unseen but real connection and causal relationship. The magician believes he can produce an effect merely by imitating it (law of similarity), or that whatever he does to a material object will affect equally the person with whom the object was once in contact (law of contact).

There are countless examples of sympathetic magic in primitive and not-so-primitive societies – far too many to list here. But here is a sampling from The Golden Bough:

Among the Esquimaux boys are forbidden to play cat’s cradle, because if they did so their fingers might in later life become entangled in the harpoon-line... Here the taboo is obviously an application of the law of similarity... as the child’s fingers are entangled by the string in playing cat’s cradle, so they will be entangled by the harpoon line when he is a man and hunts whales. Again, among the Huzuls of the Carpathian Mountains the wife of a hunter may not spin while her husband is eating, or the game will turn and wind like the spindle, and the hunter will be unable to hit it. Here again the taboo is clearly derived from the law of similarity… In some of the East Indian islands any one who comes to the house of a hunter must walk straight in; he may not loiter at the door, for were he to do so, the game would in like manner stop in front of the hunter’s snares and then turn back, instead of being caught in the trap. For a similar reason it is a rule with the Toradjas of Central Celebes that no one may stand or loiter on the ladder of a house where there is a pregnant woman, for such delay would retard the birth of the child ... Malays engaged in the search for camphor eat their food dry and take care not to pound their salt fine. The reason is that the camphor occurs in the form of small grains deposited in the cracks of the trunk of the camphor tree. Accordingly it seems plain to the Malay that if, while seeking for camphor, he were to eat his salt finely ground, the camphor would be found also in fine grains; whereas by eating his salt coarse he ensures that the grains of the camphor will also be large … The chief product of some parts of Laos, a province of Siam, is lac. This is a resinous gum exuded by a red insect on the young branches of trees, to which the little creatures have to be attached by hand. All who engage in the business of gathering the gum abstain from washing themselves and especially from cleansing their heads, lest by removing the parasites from their hair they should detach the other insects from the boughs. Again, a Blackfoot Indian who has set a trap for eagles, and is watching it, would not eat rosebuds on any account; for he argues that if he did so, and an eagle alighted near the trap, the rosebuds in his own stomach would make the bird itch, with the result that instead of swallowing the bait the eagle would merely sit and scratch himself

The list of examples goes on and on. In Cormac McCarthy's Blood Meridian, there is a scene where one of the soldiers objects to having his drawn likeness captured in a sketchbook. He rejects being compared to a superstitious native, but cannot otherwise account for his extreme reluctance. The implication is that, like the "savages" they are pursuing, he feels danger from sympathetic magic associated with a book containing his picture over which he has no control.

In our own lives, we subscribe to many superstitions and magical belief systems. Recently, the system called “The Law of Attraction”, popularized in the motion picture, “The Secret” encouraged visualization of desired outcomes to cause the outcomes to occur. This is more than just positive thinking – it is literally magic. The Law of Similarity, again, is at work here: a mental image of a thing is somehow similar to the thing itself. Also, we use homeopathic medicine when we believe water retains a “memory” of a curative agent that once was in it - this is the Law of Contact at work. And how many of us, normally rational in most of our decisions, continue to take large varieties of supplements and herbal remedies based on a recommendation or foggy personal recollection, and refuse to stop taking it in the face of proof that they don't work?

Science avoids magical explanations in favor of empirical observations, hypotheses, and experimentation. But we all seem to have weak areas where we let primitive magic drive our decisions.

5.3 Is Nature Uniform and Predictable?

The previous chapter, How can we have confidence in our inferences, investigated Inference and the Problem of Induction. Predictability and continuity from past to future, from the known to the unknown, from the small to the large, and from the near to the distant underlie our ability to make meaningful statements about the world. Out of necessity we assume that our knowledge about that which we can access tells us something useful about that which we cannot access due to distance, time, speed, size, or practicality.

But can we really make these assumptions? The principles of uniformity, homogeneity, and isotrophism (for which we have no deductive proof) are foundational principles underlying our ability to make warranted and defensible universal statements about nature. Without them, we can only talk about what we directly experience, and must leave as utterly unknown and unknowable that which we have not yet experienced.

As we have seen, there appears to be no deductive proof of uniformity or for the inferential process which requires it, and it goes without saying that you can't use induction to prove itself. But for all the reasons presented so far, the existance of a uniform and predictable universe is very likely to be the case - so likely that any other possibility is vanishingly small. Whether we choose to defend this assertion with foundational axioms, coherent and mutually supportive lines of evidence, acceptance of an infinite series of increasingly more subtle explanations, relaxing of the requirement for a firm deductive proof, probabilistic methods (such as Bayes Theorem), relying on the "Criteria Of Adequacy", or inference to the best explanation, rejecting the basic principle of uniformity and the inductive method which assumes it requires a far greater effort than accepting it. This would indicate that we should probably cultivate a tolerance for uncertainty (since we seem to be stuck with it), and an understanding that absolute certainty about phenomena in the world is probably not possible.

Uniformitarianism is the principle and belief that the natural processes operating in the past are the same as those that can be observed operating in the present, and by extension, the same as those operating throughout the universe. This principle postulates that laws of nature that apply on Earth function the same throughout the universe. Its methodological significance can be summarized in the statement: "The present is the key to the past." This concept was introduced into modern thinking by Charles Lyell, James Hutton, and centuries before, by Avicenna and others. Although Lyell, Hutton, and Avicenna restricted their argument for uniformitarianism to geology, it quickly found application throughout all of natural philosophy. James Hutton wrote,

“If the stone, for example, which fell today, were to rise again tomorrow, there would be an end of natural philosophy, our principles would fail, and we would no longer investigate the rules of nature from our observations.”

This means that for us to be able to draw conclusions about the past, we must assume the invariance of the natural laws we see in operation in the present. Mere position in space or time cannot by themselves be relevant to whether some phenomenon occurs or not.

We start from the premise that the universe is homogeneous and isotropic, meaning that it is the same everywhere and of roughly the same distribution. At all times and everywhere, the laws of the universe behave exactly the same. Every observation ever made supports it, and none refute it. The light we see in our homes is the same as that we see from distant stars (as in Newton's “the light of our culinary fire and of the sun” from his Rules of Reasoning). We have measured light generated billions of light years away, and it is the same as the light generated by our refrigerator bulb. Countless observations support uniformity of the laws of nature across the universe. We see stars and galaxies just like our own as far as the universe stretches. We have recently discovered extra-solar planets with atmospheres circling some of those distant suns not dissimilar from our own. We see light, gravity, physics, and chemistry behave just as it does on Earth no matter where (or when) we look. I say “when” because much of what we see happening in distant space happened billions of years ago. Despite centuries of looking out into space since Galileo first viewed the moons of Jupiter, there is no evidence to support an argument against natural uniformity. Instead, there is overwhelming evidence in its favor. The standard caveats regarding physics at the boundaries of our experience (at the sub atomic level and at the galactic level) apply. The laws of nature at the human level do differ in kind from those we have discovered at these two extremes. But that is not an indictment of uniformity. Instead it is simply a widening of our understanding at these two scales. It is true that the behavior of quarks and leptons, and of dark matter and black holes, differ from what we experience in our daily lives. But we have strong reason to believe that these behaviors are retained at these levels no matter where (or when) in the universe we look.

Uniformitarianism was such a successful paradigm that, not surprisingly, it was eventually overplayed. It received such wide acceptance as a result of Hutton's influence that legitimate catastrophic theories such as volcanic eruptions, climatic changes, asteroid impacts causing mass extinctions, and of plate tectonics were rejected as being contrary to these principles. It got in the way of the acceptance of quantum physics, and erected barriers to the possibility of undiscovered dimensions and the possible infinity of time and space. These misapplications of the principle of Uniformity help us realize that it is a guideline, not a universal law. Uniformity was not “discovered” as the speed of light or the mass of a star can be discovered. It is a generally good assumption that allows us to make inferences about the parts of the universe we don't have immediate access to. But it is not always proper to employ it. It cannot be dogmatically and mindlessly applied.

Isotrophism and Homogeneity are concepts often paired with Uniformitarianism. They are the two legs of the Cosmological Principle which says that no matter where we look in the universe, we will see the same types and distributions of objects. Bound up in this principle is the idea that the shape, substance, and consistency of the universe in our local area is roughly the same as elsewhere. There is nothing priviledged about our frame of reference, as both Galelio and later Einstein showed. There is nothing unique about “here“ vs. “there“, no matter how distant. This is a truth that man has come more and more to realize. In pre-history, each tribe probably considered itself at the center of the universe (as they knew it). Among Earth's major historic cultures existed the symbol of the Axis Mundi, or “axis of the earth” which expressed their view that they inhabited a unique place at the hub of the universe. The Copernican revolution and expanding exploration of the Earth's surface literally widened Man's horizons, showing both that Europe was not at the center of civilization, and that our planet was not at the center of anything, but one of several planets (and a minor one, at that) in the solar system. Our universe grew even larger when Galileo's telescope showed there to be countless thousands of other stars like our own in our island universe, the Milky Way. In the 1700's Herschel added shape and texture to this fact by constructing the first accurate model of our galaxy. The next step came with Hubble's proof that Andromeda was not just another nebula, but a sister galaxy to our own. During the following years, many other galaxy's were discovered. It is currently estimated that there are about as many galaxies in the visible universe as there are stars within our own galaxy. Further, there may be much more to the universe than the mere 13.7 billion light years worth of stars that we are able to see – the universe may be expanding faster than its light can reach us.

As far as we can tell, the universe is both homogeneous (has similar structure everywhere) and isotrophic (has a similar appearance in all directions). On the small scale, we don't have homogenieity – the universe is full of “clumps”. Earth differs from Mars, our sun differs from other stars, the our galaxy differs from the surrounding magellenic clouds and the other galaxies in our local cluster. Our local cluster differs from other galactic clusters. However, on a large enough scale, even larger than this, you do get homogeniety. An analogy would be a sponge cake filled with raisens. If you stick a pin into the cake, you may pull out nothing, or you might get a raisen. On the scale of a pinhead, the cake is not homogeneous. But on the scale of a slice of cake, you always get roughly homegeneous slices with about the same amount of cake and raisins in each slice. On the scale a billion of light years, we observe homogeneous structure in the universe.

But for the purposes of understanding the universe we live in, there is no need to go that far to look for similar structure. The structure of the objects and phenomena that scientists study in their laboratories have the same structure, consistency, and substance of similar structures and phenomena we know exist outside the lab. There is no need to go to the ends of the universe to be able to make that assertion.

In the chapter, Isaac Newton's Rules Of Reasoning, two of Isaac Newton's four "Rules of Reasoning in Natural Philosophy" deal explicitly with the Principle of Uniformity.

1. To the same natural effects we must, as far as possible, assign the same causes. As to respiration in a man, and in a beast; the descent of stones in Europe and in America; the light of our culinary fire and of the sun; the reflection of light in the earth, and in the planets.
2. Qualities of bodies are to be esteemed the universal qualities of all bodies whatsoever.

So, along with Hume, Lyell, Hutton, and countless others, Newton advances this principle. Although impossible to prove, it is the only explanation that would allow our experiences in the universe to make sense. If every seemingly similar phenomenon in every region of the world was the result of completely different causes, our science, and our common sense would be completely useless and would not work. The fact that both do work is evidence enough that, as Newton says, "to the same natural effects we must, as far as possible, assign the same causes".

5.2.8 Denying the consequent

There is a valid form of logical reasoning called “denying the consequent” (aka “modus tollens”) which can be used to show that induction is a valid and fully warranted methodology that we may rely upon. The form of the argument is:

If P, then Q.
Q is false.
Therefore P is false.

Following this logical form, the use of inference from real world experience is justified by the following sequence:

• If (P) induction from sense experience to make inferences about the world is invalid and unjustifiable, then (Q) science (which relies on inference) has no hope of working.


• However, (Q is false) science does work! There are countless examples of the progress that it has introduced, discoveries that it has made, and new technologies it has spawned. There are no counter examples to its success.


• Therefore, (P is false) our inferences from the real world ARE justified and valid.

Obviously if there was significant evidence in support of the claim that drawing conclusions through the scientific approach was invalid, then opponents would have a case. But such evidence is entirely absent, and there is overwhelming counter-evidence. Nor is there any competing theory as to why science tends to produce correct, useful, consistent, predictive, and informative results. Barring the existence of a competing explanation that accounts for its success (trickery by Satan to test our faith is one such untestable explanation, as is Solipsism), it’s plain, obvious, common sense to accept as fact that inference from the real world is valid. It would require agonizing logical contortions to explain away the falseness of statement “Q” above (i.e., “science has no hope of working”) using some other argument. The rule of Parsimony would indicate that the obvious explanation, above, is the correct one.

We should not become over excited by the fact that an established formal argument supports the use of induction. Language can be slippery, and we have seen earlier in this document a case where the cousin of modus tollens, modus ponens, was used to prove both that reality IS an illusion and later that reality IS NOT an illusion. So be careful with these simple techniques, they can be misused.