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 Evolution, the addition of new considerations into the theories enriched them and eventually led to a clearer understanding of the solar system and life. 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 so 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. If your experiment on the primary hypothesis generates a negative result (i.e., 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 his 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.