The logic of science-8: The power of universal claims in science

(For previous posts in this series, see here.)

In the previous post in this series, I argued that in the case of an existence claim, the burden of proof is upon the person making the assertion. In the absence of a preponderance of evidence in its favor, the claim can be dismissed. As has often been said, “What can be asserted without proof can be dismissed without proof”. The basis for this stance is the practical one that proving the non-existence of an entity (except in very limited circumstances) is impossible. Hence if we do NOT have a preponderance of evidence in favor of the existence of an entity, we conclude that it is not there.

In the case of a universal claim, however, the situation is reversed and the default position is that the claim is assumed to be true unless evidence is provided that refutes it. So in this case, the burden of proof is on the person disputing the assertion, again for eminently practical reasons.

As an example, the universal claim that all electrons have identical masses and charges can never be proven to be true with just supporting evidence because we cannot measure the properties of every electron in the universe. But once a few of them have been shown to have the same mass and charge, the universal claim that all of them do is presumed to be true unless someone comes up with evidence that disputes it. This is why the proposition “All electrons have the same mass and charge and behave identically in interactions with other particles” is believed to be a true proposition. In this case, absence of evidence (against the universal proposition) can be taken as evidence of absence that such evidence exists at all.

In science, negative evidence can be powerful in the same way that it can be in the legal setting, as in the famous Sherlock Holmes story of the inferences that can be drawn from the dog that did not bark in the night. Since there is a belief that dogs always bark when unexpected events occur in the night, we can infer from a silent dog that nothing untoward happened. In science, we believe that natural laws are invariably followed without exception. For example, the strongly held scientific belief that there exist only two kinds of electric charge is based entirely on this argument, because there has been no evidence produced that we need a third kind of electric charge. Similarly, any universal claim about the properties of an entity whose existence has already been established are taken to be true unless evidence is provided that contradicts the claim.

The laws of science are (as far as I am aware) always phrased as universal claims. There are a number of such laws such as energy, momentum, and angular momentum conservation, baryon number conservation, and CPT conservation (where C stands for ‘charge conjugation’, P stands for ‘parity’, and T for ‘time reversal) all of which are believed to be true purely because no violations have been observed. Anyone who challenges the validity of those laws has the burden of proof to provide evidence of such violation. This approach is so routine in science that no one even bothers to state it explicitly

The contradiction of a universal claim is done by means of an existence claim. For example, it used to be considered that something called CP was also conserved in every reaction. Why did we believe this universal claim? Because no reaction violating it had ever been seen. But some scientists suspected that it might be violated under certain conditions. Postulating such a reaction constituted a new existence claim. This was not initially accepted since no one had seen a violation of CP. But then one rare reaction was detected that did violate CP and this was confirmed in subsequent experiments. It was only then that the universal claim that CP was never violated was accepted as not being true, because some researchers produced evidence in support of their existence claim of such violations. Now, without further evidence, we are justified in believing the universal claim that this same reaction will violate CP every time it happens, until someone finds evidence for the claim that on occasion it does not.

So in science this interplay of existence and universal claims, and the different ways they are established, goes on all the time and forms an integral part of the way that scientific knowledge is constructed.

‘God exists’ is an existence claim and the burden of proof lies with those who assert it. In the absence of such evidence, the scientific conclusion is that god does not exist. Similarly, ‘god does not exist’ is a universal claim and the burden of proof lies with those who deny it and they must again provide evidence that god exists. Since they have not produced any such evidence, the scientific conclusion is that ‘god does not exist’ is a true statement.

It necessarily follows from the above discussion that in science the word ‘true’ is used provisionally and not absolutely. In the case of an existence claim, ‘true’ is taken to mean that it is supported by a preponderance of evidence. In the case of universal claims, ‘true’ is used as an abbreviation for ‘not yet shown to be contradicted by evidence’. It is always within the realm of possibility that someone might come along with data that suggests that there exists a particle that seems to behave identically as the electron but has (say) a different mass. In fact, that has actually happened. The scientific community responded with further experimentation that confirmed the existence of this new particle, now called the muon, and it is now considered a true proposition that muons exist and all have the same mass and charge and behave just like electrons except that their mass differs from that of electrons.

Maybe one day there will be a preponderance of evidence for the existence of god. But until such time, a perfectly valid scientific conclusion is that god does not exist.

Next: Proofs as used in science

The logic of science-7: The burden of proof in science

(For previous posts in this series, see here.)

The logic used in arriving at scientific conclusions closely tracks the legal maxim that ‘the burden of proof rests on who asserts’. It should be noted that the word proof used here does not correspond the way it is used in mathematics, but more along the lines used in law. As commenter Eric pointed out in response to the previous post in this series, in the legal arena there are two standards for proof. In criminal cases, there is the higher bar of proving beyond a reasonable doubt, but in civil cases the standard is one based on the preponderance of evidence. So if the preponderance of evidence is in favor of one position, it is assumed to be true even if it has not been proven beyond a reasonable doubt. Scientific propositions are judged to be true not because they have been proven to be logically and incontrovertibly true (which is impossible to do) or because they have been established by knowledgeable judges to be beyond a reasonable doubt (which is not impossible but is too high a bar to result in productive science), but because the preponderance of evidence favors them. Evidence plays a crucial role here as it does in legal cases.

Scientific claims can be both existence claims and universal claims, and these two types of propositions are proved in different ways. In science the burden of proof in existence claims lies, as in legal claims, with those who make the claim. If they cannot meet the standard of proof, the claim is presumed to be false. With universal claims however (once at least some positive evidence has been provided in support of existence), the burden of proof lies with those trying to show that it is false. In the legal context, a witness who swears to tell the truth is assumed to be always telling the truth, a universal claim. A lawyer who wishes to make the point that a witness is not truthful is the one who is assumed to making an assertion and thus has the burden of proof to show that the witness has lied.

For an example of proof of an existence claim in science, the claim that an entity called an electron exists has to be supported by evidence that shows that an entity with the postulated properties of an electron (such as its mass and charge) has been, or at least can be, detected in experiments. The reason that I say ‘can be’ is that in some cases if there is strong circumstantial evidence in favor of the existence of an entity, a provisional verdict in favor of existence may be granted, pending more direct confirmation. The most famous case of this may the ‘ether’, which was postulated to exist on the basis of circumstantial evidence that it should exist, until it was shown that the theory of relativity undermined all that evidence in its favor and its existence was rejected. The neutrino is example of something that was granted provisional existence and was later directly detected.

The reason for these rules about how to judge the truth of existence and universal claims is simply because without them science would be unworkable. In most cases of scientific interest, it is impossible to prove that an existence claim is false and without these rules we would be swamped with existence claims for non-existent entities. The film Avatar, for example, postulated the existence of a valuable mineral called Unobtainium on another planet called Pandora somewhere in the universe. How could one possibly prove that such a mineral (or even the planet) does not exist? One cannot. Thus originates the scientific rule that to establish that a proposition of existence is true, one has to provide positive evidence in support of it. In the absence of such evidence, a perfectly justifiable scientific conclusion is that the proposition is false and that it does not exist.

This rule is hardly controversial. It is used in everyday life by everyone because would be impossible to live otherwise. To not have such a rule is to open oneself to an infinite number of mythical entities. To allow for the existence of something in the absence of a preponderance of evidence in support of its existence means believing in the existence of unicorns, leprechauns, pixies, dragons, centaurs, mermaids, fairies, demons, vampires, and werewolves.

This is why it is perfectly valid to conclude that there is no god. ‘There is a god’ is an existence claim and the burden of proof lies with those making the claim. Since no one has produced a preponderance of evidence in support of it, the claim is not to be taken seriously. Religious apologists who try to argue that god exists using logic alone without producing a preponderance of evidence in its favor are not being scientific and have entered the evidence-free realm of theology, in which one starts with whatever one wants to believe and then manufactures reasons for believing in it, even if that same reasoning is not applied to any other sphere of life.

Religious ‘logic’ is beautifully illustrated by this cartoon.


Next in the series: The power of universal claims in science

The logic of science-6: The burden of proof in law

(For previous posts in this series, see here.)

For a long time, religion claimed to reveal eternal truths. No one except true believers seriously says that anymore because science has become the source of reliable knowledge while religion is increasingly seen as being based on evidence-free assertions. So some believers tend to try and devalue the insights science provides by elevating what we can call truth to only those statements that reach the level of mathematical proof, because such a high bar can rarely be attained and thus everything else becomes a matter of opinion. They can then claim that scientific statements and religious statements merely reflect the speaker’s opinion, nothing more.

But science uses criteria other than proof for making judgments about truth. In making such judgments, scientists act more like judges in legal cases than mathematicians deriving proofs. For example, in legal proceedings, the usual practice is to follow the legal principle ei incumbit probatio qui dicit, non qui negat, which I am told (not knowing Latin myself) translates as “the burden of proof rests on who asserts, not on who denies”, where the assertion is of a positive nature and not a negative one. So if someone is accused of committing a crime, the burden of proof is on the accuser and not the defendant. This principle is more popularly stated in English as that a person is presumed innocent until proven guilty beyond a reasonable doubt.

This principle is considered such a fundamental aspect of a civilized society that it is enshrined in Article 11 of the Universal Declaration of Human Rights which states that: “Everyone charged with a penal offence has the right to be presumed innocent until proved guilty according to law in a public trial at which they have had all the guarantees necessary for their defence.” Of course many countries (including the US) routinely violate this principle when it suits them, while still smugly claiming to uphold the basic principles of human rights.

A point to note is that technically the only outcomes in a legal proceeding are “guilty” (i.e., proved beyond a reasonable doubt) and “not guilty” (not proved beyond a reasonable doubt). The defendant is never proven to be innocent, and has no obligation to do so. Indeed the defendant is not even obliged to provide any kind of defense at all. This can of course lead to undesirable situations where the jury can suspect that a defendant is indeed guilty of the crime but feels obliged to bring in a verdict of not guilty if the case has not met the ‘proved beyond the reasonable doubt’ standard which is why the ‘proven innocent’ phrasing is not appropriate for not guilty verdicts. But this kind of undesirable outcome is the price we pay for trying to have the fairest possible system, even if it should lead to public outcries of the sort seen following the not guilty verdicts in the O. J Simpson and Casey Anthony murder trials which were mistakenly interpreted by the public as statements that innocence had been proven when all it meant was that the presumption of innocence had not been contradicted.

One could have an alternative system in which a person is presumed guilty until proven innocent, shifting the entire burden of proof onto the defendant. There is nothing logically wrong with such system but in practice it would be unworkable since there are many more people who are innocent of a crime than there are those who are guilty. Furthermore it is often difficult, if not impossible, to prove innocence. For example, if I am asleep alone at home, it would be very difficult for me to prove that I was not robbing a nearby convenient store at that time, which is why the ‘presumed innocent until proven guilty’ standard seems to be a better one. So there are good reasons for having the burden of proof be on the person who asserts a positive claim and not on the person who denies as the method of arriving at legal verdicts or ‘truths’.

Unless one agrees on which of the two frameworks (presumed innocent until proven guilty beyond a reasonable doubt or presumed guilty until proven innocent) to use in making legal judgments, it may be impossible to agree on a verdict. But whatever system one chooses, the basic structure is that there is a default position that is assumed to be true unless shown otherwise, so that proof of only one position is required.

Similar considerations apply in arriving at scientific truths.

Next: The burden of proof in science

The logic of science-5: The problem of incompleteness

(For previous posts in this series, see here.)

As I discussed in the previous post in this series, our inability to show that an axiomatic system is consistent (i.e., free of contradictions as would be evidenced by the ability to prove two theorems each of which contradicted the other) is not the only problem. Godel also showed that such systems are also necessarily incomplete. In other words, for all systems of interest, there will always be some truths of that system that cannot be proven as theorems using only the axioms and rules of that system. So the tantalizing goal that one day we might be able to develop a system in which every true statement can be proven to be true also turns out to be a mirage. Neither completeness nor consistency is attainable.

Belief in god depends upon ignorance for its very existence and some religious people have seized on Godel’s theorem to try and argue that ‘god exists’ is one of these true statements that cannot be proved. This is a misunderstanding of what Godel proved but is typical of attempts by religious people who seize upon and use important results in science and mathematics (especially those that impose some limits to knowledge, such as the uncertainty principle) to justify the unjustifiable.

The fact is that you cannot simply assert that any proposition you choose belongs in that niche that Godel discovered. The true yet unprovable statements have to be constructed within that particular system to meet certain criteria and are thus dependent on the axioms used, and a statement that is true but unprovable in one system need not be so in another one. Simply by adding a single new axiom to a system, statements that were formerly unprovable cease to be so while new true but unprovable statements emerge. Whenever religious people invoke Godel’s theorem (or the uncertainty principle or information theory) in support of their beliefs, you should be on your guard and investigate if what they say is actually what the science says.

So what can we do in the face of Godel’s implacable conclusion that we cannot construct an axiomatic system in which the theorems are both complete and consistent? At this point, pure mathematicians and scientists part company. The former have basically decided that they are not concerned with the truth or falsity of their theorems (and hence of the axioms) but only with whether the conclusions they arrive at (the theorems) are the necessary logical conclusions of their chosen axioms and rules of logic. Even a statement such as ‘2+2=4’, which most people might regard as a universal truth that cannot be denied, is seen by them as merely the consequence of certain starting assumptions, and one cannot assign any absolute truth value to it. So pure mathematicians concern themselves with the rigor of proofs, not with whether the theorems resulting from them have any meaning that could be related to truth in the empirical world. Mathematical proofs have become disconnected from absolute truth claims.

For the scientist dealing with the empirical world, however, questions of truth remain paramount. It matters greatly to them whether some result or conclusion is true or not. While the methods of proofs that have been developed in mathematics are used extensively in science, scientists have had to look elsewhere other than proofs to try and establish the truth or falsity of propositions. And that ‘elsewhere’ lies with empirical data or the ‘real world’ as some like to call it. This is where the notion of evidence plays an essential role in science. So in mathematics while the statement ‘2+2=4’ is simply a theorem based on a particular set of axioms, in science its empirical truth or falsity of it has to be judged by how well real objects (apples, chairs, etc.) conform to it.

This dependence on data raises a problem similar to that of the consistency problem in mathematics that Godel highlighted. We can see if ‘2+2=4’ is true for many sets of objects by bringing the actual objects in and counting them but we obviously cannot do so for everything in the universe. So how can we know that this result holds all the time, that it is a universal truth? Such a concern may well seem manifestly overblown for a simple and transparent assertion like ‘2+2=4’ but many (if not most) results in science are not obviously and universally true and so they can be challenged. For example, for a long time the tobacco industry challenged the conclusion that smoking causes cancer by pointing out that there exist some smokers who do not get cancer.

So however much the data we obtain supports some proposition, how can we be sure that there does not exist some undiscovered data that will refute it? This does not mean that we cannot be definitive in science. But the justification of scientific conclusions depends upon a line of reasoning that is different from those involving direct proofs, as will be seen in subsequent posts.

Next: The logic of science and the logic of law

The logic of science-4: Truth and proof in mathematics

(For previous posts in this series, see here.)

Within mathematics, Euclidean geometry is the prototypical system that demonstrates the power of proof and serves as a model for all axiomatic systems of logic. In such systems, we start with a set of axioms (i.e., basic assumptions) and a set of logical rules, both of which seem to be self-evidently true. By applying the rules of logic to the axioms, we arrive at certain conclusions. i.e., we prove what are called theorems. Using those theorems we can prove yet more theorems, creating a hierarchy of theorems, all ultimately resting on the underlying axioms and the rules of logic. Do these theorems correspond to true statements? Yes, but only if the axioms with which we started out are true and the rules of logic that we used are valid. Those two necessary conditions have to be established independently.

So how does one do that? While we may all be able to agree on the validity of the rules of logic if they are transparent, simple, and straightforward (though there are subtle pitfalls even there) establishing the truth of the axioms is not always easy because things that seem to be obviously true may turn out to be not so.

Furthermore, even assuming for the moment that one knows that the axioms are true and the rules of logic are valid, there are still problems. For example, how can we know that all the theorems that we can prove correspond exactly to all the true statements that exist? Is it possible that there could be true statements that can never be reached however much we may grow the tree of theorems? This is known as the problem of completeness.

There is also another problem known as the problem of consistency. Since the process of proving theorems is open-ended in that there is no limit to how many we can potentially prove, how can we be sure that if keep going and prove more and more theorems we won’t eventually prove a new theorem that directly contradicts one that we proved earlier, thus resulting in the absurdity that a statement and its negation have both been proven?

To address this, we rely upon a fundamental principle of logic that ‘truth cannot contradict truth’, and thus we believe that it can never happen that two true statements contradict each other. Thus establishing the truth of the axioms and using valid rules of logic guarantees that the system is consistent, since any theorem that is based on them must be true and thus no two theorems can contradict each other. Conversely, if we ever find that we can prove as theorems both a statement and its negation, then the entire system is inconsistent and this implies that at least one of the axioms must be false or a rule of logic is invalid.

There is usually little doubt about the validity of the rules of logic that are applicable in a mathematical system (if they are simple and transparent enough) and thus a true set of axioms implies a consistent system of theorems and vice versa. Hence we can at least solve the problem of consistency if we can establish the truth of the axioms, though the completeness problem remains open.

(Those who are familiar with these issues will recognize that we are approaching the terrain known as Godel’s theorem. While I will discuss its main results, for those seeking to understand it in more depth I can strongly recommend an excellent little monograph Godel’s Proof by Ernest Nagel and James R. Newman, and the clever and entertaining (but much longer) Godel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter.)

So how do we establish the truth of the axioms? If the system we are dealing with consists of a finite number of objects, we may be able to prove the axioms to be true by seeing if every one of the objects in the system satisfy the axioms by exhaustively applying all the axioms to all the objects and seeing if they hold true in every case. Even if the axioms do not relate to a set of objects, we may be able to construct a model system of objects in which the elements of the model correspond to the elements in the axioms and thus repeat the above process. So, for example, we can take the axioms involving points and lines and so forth in Euclidean geometry (which are abstractions that have purely mathematical relationships with each other) and build a model system of real objects (such as points and lines in space that can be drawn on paper) and see if the axioms apply to the properties of such real objects in real space. Similarly, we can see if the abstract rules for adding numbers correspond to what we get if we add up real objects together.

The catch is that for most systems of interest (such as points and lines in geometry and the integers in number theory), the number of elements in the system is infinite and it is not possible to exhaustively check if (for example) every point and every line that can be drawn in space satisfy the axioms. So then how can we know if the axioms are true? It is not enough that the axioms may look so simple and intuitive that they can be declared to be ‘obviously’ true. It has been shown that even the most seemingly simple and straightforward mathematical concept, such as that of a ‘set’, can produce contradictions that destroy the idea that a system is consistent, so we have to be wary of using simplicity and transparency as our sole guide in determining the truth of axioms.

One might wonder why we are so dependent on such a pedestrian method as applying each axiom to every element of the system to establish the truth of axioms and the consistency of systems. Surely we can apply more powerful methods of reasoning to show whether a set of axioms is true even if they involve an infinite number of elements? One would think so except that Godel proved that this could not be done except for very simple systems that do not cover the areas of most interest to mathematicians. Godel “proved that it is impossible to establish the internal logical consistency of a very large class of deductive systems – number theory, for example – unless one adopts principles of reasoning so complex that their internal consistency is as open to doubt as that of the systems themselves.” (Nagel and Newman, p. 5, my italics.)

In other words, the price we pay for using more powerful reasoning methods to prove the consistency of some axiomatic system is that we lose transparency and simplicity in the rules of logic used in constructing those very methods and now they cannot be assumed or shown to be valid. As the old saying goes, what we gain on the swings, we lose on the roundabouts. As a result, we arrive at Godel’s melancholy conclusion that Nagel and Newman state as “no absolutely impeccable guarantee can be given that many significant branches of mathematical thought are entirely free of internal contradiction.” In other words, Godel proved that the goal of proving consistency cannot be achieved even in principle.

This is quite a blow to the idea of determining absolute truth because if we cannot show that a system is consistent, how can we depend upon its results?

Next in the series: The problem of incompleteness

The logic of science-3: The demise of infallibility

(For previous posts in this series, see here.)

The idea of scientific infallibility, that the knowledge generated by science should be true and unchanging, suffered a series of blows in the late 19th and early 20th centuries that saw the repeated overthrow of seemingly well-established scientific theories with new ones. Even the venerable Newtonian mechanics, long thought to be unchallengeable, was a casualty of this progress. Aristotle’s idea that scientific truths were infallible, universal, and timeless, fell by the wayside, to be replaced with the idea that they were provisional truths, the best we had at the current time, and assumed to be true only until something better came along.

But despite that reduction in status, it is important to realize that for the practicing scientist, the question of ‘truth’ remains paramount. But what the word ‘true’ means depends on the context.

One form that this commitment to truth takes is that it requires scientists to be truthful when reporting the results of their work, because others depend upon it. The whole structure of scientific knowledge is created cumulatively, each person building on the work of others, and this requires trust in the work of other people because it is not always feasible to independently verify every claim of other scientists. Because scientific knowledge is so interdependent, falsehoods in one area can do serious damage to that structure.

This does not mean that scientists are more truthful as persons. But it does mean that being dishonest is not a good career strategy because you will likely be found out, especially if your work has important consequences. Scientists are not usually suspicious of the work of other scientists and do not reflexively check their work. But the interdependence of knowledge means that a falsehood or error in one area will eventually be detected because people will try to use that knowledge in new areas and will encounter inexplicable results. When the sources of the error are investigated, it will eventually be traced back to the original perpetrator. This is almost always how scientific errors and frauds are discovered.

As a minor example, in my own research experience I once uncovered an error published by others years before because I could not agreement with data when I used their results. Similarly a published error of my own was discovered by others after a lapse of time, for the same reason. It is because of this kind interdependence that science is largely, but not invariably, self-correcting. This is also why in academia, where the search for true knowledge is the prime mission, people who knowingly publish or otherwise propagate falsehoods or commit many errors, suffer serious harm to their reputations and are either marginalized or drummed out of the profession. Some recent spectacular cases of deliberate fraud are those of Jan Hendrik Schon and Woo Suk Hwang . So in the search for knowledge, accurately reporting honestly obtained data and making true statements about one’s work is a prime requirement.

But there is another, more philosophically elusive, search for truth that is also important, and that is determining the truth of scientific theories. It matters greatly whether the theory of special relativity is true or not or whether some chemical is a carcinogen or not. To get those things wrong can have serious consequences extending far beyond any individual scientist. But it is important to realize that in such cases, truth is always a provisional inference made on the basis of evidence, similar to the verdict arrived at in a legal case. And just as a legal judgment can be overturned on the basis of new evidence, so can such scientific truths be overturned, thus eliminating the idea of infallibility.

So how does one arrive at provisional truths in science? In establishing the truth of a scientific proposition, scientists use reasoning and logical arguments that are closely similar to, but not identical with, mathematical and legal reasoning. Being aware of the similarities and distinctions is important to avoid claiming scientific justification for claims that are not valid, as often happens when religious people try to co-opt science in support of their beliefs in god and the afterlife.

The first issue that I would like to discuss is the relationship between truth and proof, because in everyday language truth and proof are considered to be almost synonymous. The idea of ‘proof’ plays an important role in establishing truth because most of us associate the word proof as being conclusive, and it is always more authoritative if we are able to say that we have proven something to be true or false.

The gold standard of proof comes from mathematics and much of our intuitive notions of proof come from that field so it is worthwhile to see how proof works there, what its limitations are when applied even within mathematics, and what further limitations arise when we attempt to transfer those ideas into science.

Next: Truth and proof in mathematics

The logic of science-2: Determining what is true

(For previous posts in this series, see here.)

An important question in any area of knowledge is being able to identify what is true and what is false. The search for what is true and the ability to know when we have discovered truth is, after all, the Holy Grail of epistemology, because we believe that those things that are true are of lasting value while false statements are ephemeral, usually a waste of time and at worst harmful and dangerous.

Aristotle tried to make a clear distinction between those things that we feel we know for certain and are thus unchanging, and those things that are subject to change. The two categories were variously distinguished as knowledge versus opinion, reality versus appearance, or truth versus error. Aristotle made the crucial identification that true knowledge consisted of scientific knowledge, and his close association of scientific knowledge with truth has persisted through the ages. It also made the ability to distinguish between scientific knowledge and other forms of knowledge, now known as the demarcation problem, into an important question since this presumably also demarcates truth from error. (This brief summary of this history is taken from the essay The Demise of the Demarcation Problem by Larry Laudan which should be referred to for a fuller treatment.)

Aristotle said that scientific knowledge was based on foundations that were certain and thus was infallible. Since he identified scientific knowledge with true knowledge, it followed that scientific knowledge had to be unchanging because how could truth ever become false?

The second characteristic of scientific (and hence true) knowledge was that it should consist of not just ‘know-how’ but also of ‘know-why’. ‘Know-how’ knowledge was considered to be the domain of craftsmen and engineers. Such people can (and do) successfully build boats, bridges, houses, and all manner of valuable and important things without needing an understanding of the underlying theoretical principles on which they work. The electrician I call to identify and fix problems in my house has plenty of know-how and does his work quickly and efficiently without having to understand, or even know about, Maxwell’s laws of electrodynamics (the know-why), whereas any scientist would claim that the latter was essential for really understanding the nature of electricity.

It is for this reason that Ptolemaic and early Copernican astronomy were not considered scientific during their time even though they made highly accurate predictions of planetary motions. Their work was not based on an understanding of the laws that governed the motion of objects but on purely empirical correlations, and thus lacked ‘know-why’. If, for example, a new planet were to have been discovered, existing knowledge would not have been of much help to them in predicting its motion. Hence astronomy was considered to be merely know-how and astronomers to be a species of craftsmen.

The arrival of Isaac Newton and his laws of motion provided the underlying principles that governed the motion of planets. These laws not only explained the existing extensive body of data on planetary motions, they would also be able to predict the motion of any newly discovered planet and even led to the prediction of the existence of an actual new planet (Pluto Neptune) and where it would be located. Newton’s theories provided the ‘know-why’ that shifted astronomy into the realm of science.

It was thought that it was this know-why element that made us confident that scientific knowledge was true and based on certain foundations. After all, even if a boat builder finds that all the wood he has encountered floats in water, this does not mean that the proposition that all wood will always float is necessarily true since it is conceivable that some new wood might turn up that sinks. But the scientific principle that all objects with a lower density than water will float while those with a higher density will sink seems to be on a much firmer footing since that knowledge penetrates to the core of the phenomenon of sinking and floating and gets at its root cause. It seems to have certain foundations.

As a consequence of the appreciation that ‘know-why’ knowledge has greater value, science now largely deals with abstract laws, principles, causes, and logical arguments. Empirical data is still essential, of course, but mainly as a means of testing and validating those ideas. Many of these basic ideas are somewhat removed from direct empirical test and thus determining if they are true requires considerably more effort. For example, I can easily determine if the pen lying on my desk will float or sink in water by just dropping it in a bucket. But establishing the truth of a scientific proposition, say about the role that relative densities play in sinking and floating, is not that easy.

So given the primacy of scientific principles and laws in epistemology, and since the discovery of eternal truths is to be always preferred over falsehood, an elaborate structure has grown around the whole exercise of how to establish the truth and falsity of scientific propositions, often requiring the construction of expensive and specialized equipment to determine the empirical facts relating to those propositions, and extensive long-term study of esoteric subjects to relate the propositions to the data.

Next in the series: The demise of infallibility

The logic of science-1: The basic ideas

In the course of writing these blog posts, especially those dealing with religion, atheism, science, and philosophy, I have often appealed to the way that principles of logic are used in science in making my points. But these are scattered over many posts and I thought that I should collect and archive the ideas into one set of posts (despite the risk of some repetition) for easy reference and clarity. Besides, I haven’t had a multi-part series of posts in a long time, so I am due.

Learning about the principles of logic in science is important because you need a common framework in order to adjudicate disagreements. A big step towards in resolving arguments can be taken by either agreeing to a common framework or deciding that one cannot agree and that further discussion is pointless. Either outcome is more desirable than going around in circles endlessly, not realizing what the ultimate source of the disagreement is.

When people seek definite knowledge, they turn to science, not religion. For all its claims of revealing timeless truths, religion completely fails to deliver the goods. Nobody except religious fanatics seek answers to empirical questions in their religious texts, whereas the power and reliability of science is such that people accept completely counter-intuitive things as true, as long as a scientific consensus can be invoked in support of it. For example, the idea that stars are flaming hot gases is by no means self-evident, and yet everyone now accepts it. The idea that entire continents move is also accepted even though we cannot sense it directly. How does science get such persuasive authority? In this series of posts, I will examine how it can be so successful.

A good example of how the logic of science works is to see how the advance of science has made it quite obvious that there is no god. But it is important to be clear about how that conclusion is reached. Science has not proved that there is no god, can never prove that there is no god, and does not need to prove that there is no god. So why is it that so many scientists are so confident that god does not exist? It is really very simple. While the logic of science is such that it can never prove the non-existence of whatever entity that one might like to postulate, what it has shown is that god is an unnecessary explanatory concept for anything. It is just like the ether or caloric or phlogiston, scientific concepts that ceased to be necessary explanatory concepts, making them effectively non-existent. God has joined the ether, caloric, and phlogiston in the trash heap of discarded knowledge.

You would think that this simple point would be easy to understand. But as the cartoon below by Jesus and Mo shows, religious people somehow don’t seem to get this simple point, perhaps because it throws their own arguments for a loop. They seem to willfully misunderstand it, perhaps so that they can continue to argue against straw men. So let me repeat it for emphasis: Science has not proved, and can never prove, that there is no god. Science is not in the business of proving and disproving things. What it has shown is that god is an unnecessary explanatory concept.


A big source of confusion about the logic of science comes from religious believers in their efforts to create some wiggle room for them to claim that believing in god is rational. What they try to argue is that even if there is no evidence for god, it is still reasonable to believe in he/she/it. Some religious people claim that since we cannot logically or empirically prove that god exists or does not exist, taking either point of view is an act of faith on an equal footing.

This is flat-out wrong because the logic of science is different from the logic of mathematics or the logic of philosophy because evidence is an essential ingredient in science. In science, logic does not remain in the abstract but is applied to data. When it comes to empirical questions such as whether any entity (including god) exists, the role of logic is to draw inferences from evidence. In the absence of evidence in favor of existence, the presumption is nonexistence.

We believe in the existence of horses because there is evidence for them. We do not believe in the existence of unicorns (or leprechauns, pixies, dragons, centaurs, mermaids, fairies, demons, vampires, werewolves) because there is no evidence for them even though we cannot logically prove they do not exist. It really is that simple. Anyone who argues that it is as reasonable to believe in god as it is to not believe in god is forced, by their own logic, to assert that it is as rational to believe in the existence of unicorns, etc. as it is to not believe in them.

The only time one encounters this type of ‘logic’ is from people who are defending god, the afterlife, and all the other forms of magical thinking that they cannot bear to give up and cannot defend in any other way.

So what follows in this series of posts is my attempt to clarify some of the underlying logical principles on which science functions and why one can confidently say that, applying the logic of science, the only reasonable conclusion has to be that god does not exist. I have few illusions that it will persuade religious people to give up belief. As the TV character House said, “Rational arguments don’t usually work on religious people. Otherwise there would be no religious people.”

My goals are more limited and that is to enable atheists to more effectively expose the fallacious arguments of religious believers and to facilitate more meaningful discussions about the role of science in arriving at firm conclusions about things. Over time, as religious believers find their assertions firmly challenged by others in every sphere of life, we will see an accelerating erosion of belief.

Next in the series: Determining truth