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The Nature of the Logic of Confirmation in Science
by Rick Garlikov

Many science textbooks say, as many scientists themselves often say, that scientific theories are confirmed (i.e., not necessarily proved, but shown to be "probable") by the fact that their predicted consequences are demonstrated to occur. So if theory T predicts some phenomena will be observed, that observation of the phenomena's actually occurring is said to be evidence for T's being correct. 

However, it is a logical fallacy to affirm any statement by merely showing that its consequences are true, because the truth of any consequence never shows that the statement it derives from is true. Take a simple case: what would be a consequence of its having recently rained outside? The sidewalk would be wet. Suppose then you wake up from a nap and see that the sidewalk outside the window over your sofa is wet. Is it safe to deduce that it rained? Of course not, because it could be that your spouse washed the car or watered the lawn, that the kids have been playing in the sprinklers, that a nearby water main broke, etc. Any of a number of theories or ideas would explain or account for how the sidewalk became wet other than that it rained. Many different, even incompatible, theories might have the same consequences, and observing those consequences cannot then confirm all of them to be true or probable. How then can science (supposedly) confirm theories by looking to see whether their consequences occur or not? That is the issue this essay will discuss. 

A scientific theory is an "in principle" testable explanation, in statement form, of observed phenomena or laws. [Laws are simply descriptions of the regularly occurring, invariable, and (often) universal properties of nature, sometimes described under ideal or idealized conditions, conditions not subject to interfering influences. (For example, laws about the nature of the acceleration of falling bodies due to gravity describe that acceleration in a vacuum where air resistance will not affect it; under those conditions, a feather and a stone will fall at equal acceleration and velocities).]

Since a theory is in statement form, it (or its individual statements) are either true or false, though they may be difficult to disprove or impossible to prove. [Remember, something's being true, and anyone's knowing that it is true are two different things. If they were not different things, the easiest way to keep from getting pregnant would be to stay away from doctors who conduct tests that tell you that you are.] As I will explain later, in some cases -- those of theories involving unobservable entities or ideas -- disproof of a false theory (that is, proving it false) may be possible, but proof of a true theory may be impossible to attain. Instead probability of its being true will be increased. In some cases -- where a theory postulates or supposes observable, but yet undiscovered phenomena -- either proof or disproof are each possible and the theory can be in principle demonstrated either to be true or to be false. 

"Testable in principle" simply refers to the notion that a test could be conceived which would confirm or disconfirm the theory, not that such a test could necessarily be practically carried out at some specific time. Sometimes technology or natural circumstances are not available to test a theory; nevertheless the point is that technology or circumstances are conceivable which would allow a test of the theory. If there is nothing, under any circumstances, that would or could count for or against the theory, the theory is not in principle testable and is not a scientific one, and perhaps not a reasonable one of any sort. [I think an example of a theory of this sort is the view that all people act selfishly or in their own perceived best interest, usually expressed by college freshmen as the view that people act in ways that they think will make them happiest. Whatever initial plausibility this view may have, with just a little reflection, some fairly obvious counterexamples arise. What about people who give to charity, sacrifice for their children, keep promises at personal cost, dive on hand grenades to save their buddies, or who simply commit suicide? The theorist then replies that people who commit suicide think they would be happier dead (or no longer as unhappy as they are alive); and continues that people give to charity, keep promises, sacrifice for their children, and dive on hand grenades so that they will not feel guilty for not doing it or so that they will feel better about themselves for doing it, or that they do it to have a good reputation, which is more important to them than whatever they sacrifice for it. If time permitted there would be much one could say in response to this, but my point here is that what is really going on is that the theorist will simply not let any evidence count against his theory, not because there isn't any such evidence, but because he will not let it count, and will "explain it away". He is using the word selfish in a peculiar way, a way in which it in effect does not have the opposite, unselfish. On his account giving candy to a baby is no different in morality or motivation than taking candy from a baby. He does not really have a theory or a testable theory at all because nothing can count as evidence for or against it. The "theorist" no longer understands the normal distinction between selfish and unselfish acts, no longer understands the normal sense of what is an unselfish act, and therefore no longer is using the word selfish in a normal way.]

Unintelligible Theories

Unfortunately not everyone who formulates theories formulates them or their parts clearly and understandably, and some of the most difficult work in trying to test a theory is first trying to understand exactly what the author is saying in a way that is clear and precise. Some of the worst theories are the most obscure. Often just providing all the possible clear, unambiguous interpretations of them will show them easily capable of being proved false or inadequate. Any time you are confronted with a particularly unintelligible argument, try to put it in as clear and simple language as possible, with clear cut examples, in order to see what it says and what merit it might have. For example, in political science one might want to understand and test Marx's seemingly poetic dictum that "man creates himself through his work"? If it were meant literally, it would obviously be false, since no one can be biologically parented by himself or herself. Marx certainly knew that, so the question is what he did mean; and is there anything he probably meant by it that might be true or reasonable. It might mean a person's personality is determined by his work, that a person's self-esteem depends in some way on his work, that his abilities are increased or decreased by the kind of work he does, etc., etc. These kinds of statements may be tested for their truth; "man creates himself through his work" cannot be tested. 

Ambiguous Theories or Interpretations

Seemingly clear but actually ambiguous or vague theories are often more difficult to discover flawed because they may sound plausible by confusing various notions that make sense in one context, but not in the context they are crucially used. For example, a view about when punishment should be administered to criminals may rightly hold that people who were not responsible for their actions should not be punished, giving as examples such cases as people acting under the influences of drugs someone else had secretly spiked their punch with or under the influences that were the accidental result of combining different medications, extreme cases of compulsive behavior a person did not want to do but was unable to keep himself from doing, etc. But then the view might confuse such non-responsible behavior with irresponsible (meaning reckless and/or inconsiderate) behavior and hold that no one who commits a crime irresponsibly should then be punished. And since many crimes are irresponsible (though not necessarily non-responsible) acts, the view would then go on to argue mistakenly for the elimination of most punishment. Theories about intelligence may start out clearly defining intelligence as a certain score on a certain test manipulated in some particular mathematical manner, but end up making totally unsupported conclusions about our normal, vague, imprecise and common understanding of intelligence. Supposedly this is exactly the case in racially or sexually biased IQ tests whose interpretations then give the impression that women or blacks are not as intelligent as white males, when, in reality, given their backgrounds, they are just not able to do as well on the particular (unfair) tests as white males. Confusing IQ or IQ scores with intelligence is the mistake. Teacher competency tests are also probably misnamed since they seem to inquire about (some) things you might or might not know instead of what things you can or cannot teach. 

Though sometimes it may seem an author is being intentionally obscure or vague in order to keep from being proved wrong, more than likely he or she is probably victim to, instead of perpetrator of, his or her own ambiguity, vagueness, or obscurity. Further, many ambiguities do not show themselves easily, and until a difference of opinion arises or until some circumstance occurs that causes a difference of opinion, the ambiguity may not become evident. Even then, insight may be required to recognize it. 

Philosopher and psychologist William James tells the story of having gone for a solitary walk while on a picnic with friends and returning to the group to find them evenly divided in an argument about the following: one of them had spotted a squirrel part way up the opposite side of a tree trunk and had circled around the tree to get a better look at it. As he did, the squirrel, as squirrels do, had circled around the trunk in the same direction to keep from being seen. The man, about 10 feet from the tree, was obviously going around the tree, as was the squirrel; the argument had arisen about whether the man was going around the squirrel; half the group thought he obviously was; the other half thought he obviously was not. They wanted James to tell them who was right. James said they were arguing about two different interpretations of the ambiguous notion of "going around". He explained that going around something could mean going from the east to the north to the west to the south, and then back to the east of something, in which case the man was going around the squirrel. But going around also meant going from the front to the side to the back to the other side, and then around to the front of something again, in which case the man was not going around the squirrel, since the squirrel always kept his belly toward the man. James said there was no exclusive "right" answer because the phrase "going around" meant both things. It was not usually a problem or even noticeably ambiguous because usually when you went around something in one sense you also did it in the other sense. [There is more to this than what James thought -- relative radius lengths from center of circles, movement of the squirrel within the area of its circle -- but his explanation is essentially correct; it simply needs to be expanded to take into account the other conditions that are usually simultaneously involved in one thing "going around" another.] Many concepts have multiple features like these that, unless explicated clearly, often lead to confusion in one's own thinking as well as in communication to others. It is often very difficult to make certain you, or you and others, are attending to the same feature when you discuss a particular concept and its import. 


Theories are explanations of how and why observable phenomena are as they are. Some theories involve ideas about, or the postulation or supposition of, the existence of "underlying" phenomena which are not themselves observable. (This is not always the case, as there may be a theory explaining a variance in planetary orbits by hypothesizing a yet undiscovered planet, its required size, and location. Such a planet may then be sought and found, or shown not to exist, by astronomic or space exploration.) When theories involve unobservable "entities" or properties, they are testable by means of those logically implied consequences of them which are in principle observable. For example, one of Einstein's theories implied that large masses would bend light rays by gravitational pull. When photographs of a particular solar eclipse were taken to test this particular implication of the theory, study of them confirmed the light rays were in fact bent by the implied prescribed amount. 

Theories are both explanatory and predicting; they explain what is already known and they predict (and explain) what has not yet been discovered or observed. Their predicting nature is what makes them testable. And it is also what makes them particularly useful, for they are most useful when they predict particularly useful consequences which, though they are (in principle) observable, are not necessarily ones likely to be discovered on their own, or by accident. If, for example, some theory of learning implied that learning would occur ten times faster and be of twenty times longer duration under a relaxed hypnotic state, that would not only be testable, but if confirmed, might greatly influence practical educational practice. 

There are principles of logic that apply to the confirmation or disconfirmation of theories. I believe actually that the tasks are done by just one principle of logic (or two related and very similar ones). The principle is that a known false statement shows to be false any statement which implies it. Consider the following two cases: 
If Jones has been murdered, he is dead.
Jones is not dead.
Therefore Jones has not been murdered.

Theory A implies consequence B.
Consequence B does not occur.
Therefore Theory A is false. 

The second case is sometimes also stated: 

If Theory A is true, consequence B will be observed under certain conditions.
Consequence B is not observed under those conditions.
Therefore Theory A is not true.
These valid arguments involve the same form and the same valid principle just stated, that of disproving the "antecedent" (implying part) by showing the "consequent" (implied part) to be false. This is the form of argument that disconfirms or disproves a theory. 

[In practice it has somewhat limited success because the proponents of theories can sometimes make reasonable modifications in their theories to save them from such otherwise devastating results. Whether such modifications can be made while still retaining essentially the original theory depends on how central or essential the consequence is that is disproved. And, of course, the new, modified theory must also be testable in principle.]

Now although proving an antecedent of a true hypothetical does prove a consequent, it does not work the other way around. Consider first the valid argument ("valid" meaning that the conclusion does follow from the premises, or put another way, that if the premises are true, the conclusion must be true): 

If Jones is murdered, he is dead. 
Jones is murdered.
Therefore Jones is dead.

Proving a consequent of a true hypothetical does not prove an antecedent. The following variation of the above argument is an invalid argument -- meaning that the conclusion does not follow from the premises, and may not be true even when the premises are true: 

If Jones is murdered, he is dead.
Jones is dead.
Therefore Jones has been murdered.

Even if the first two statements are true, they do not imply the truth of the third. The third statement is independent of the first two and may be true or may be false when the first two are true. 

Hence, though it appears to, and though some writer's believe it does, science cannot (and does not) adequately confirm its theories by the following kind of (invalid) argument:

If Theory A is true, consequences B are true. 
Consequences B are true.
Therefore Theory A is true.
For even if the first two statements are true, they do not imply the truth of the third, which is independent of them. 

I think theories are confirmed by the following kind of argument, again disproving the antecedent by disproving the consequent:

S1: If Theory A is false, we are not likely to observe the consequences B that it implies.(1)
S2: We do observe consequences B
S3: Therefore Theory A is likely to be true.
This is of the form: 
T1: C implies D is probably true.
T2: D is not true.
T3: C is probably not true.
The degree of probability is the same in T1 and T3. 

(If you do not see how S1, S2, and S3 are related to T1, T2, and T3, let me rephrase T1, T2, and T3 in the following way: 

T1: C <Theory A's being false> implies D is probably true <consequences B will not be observed> .
T2: D <That consequences B are not observed> is not true.(I.e., consequences B are observed.)
T3: C <Theory A's being false> is probably not true. (I.e., theory A is probably true.)

This would explain why the particular predicted consequences of a theory that are used to test it must be previously (in some important sense(2)) unknown or undiscovered phenomena, since otherwise Statement S1 would not be true; if those consequences are already known, they would be (likely) observable. It also explains why science can only confirm and not prove (that is, it can only show probable and not certain) its theories that involve phenomena or "entities" that are not themselves directly observable. And it explains why the more improbable or surprising the predicted consequences are, the more spectacularly demonstrated and more probable the theory seems to be when those consequences are indeed found to occur. 

Hence, in an area of study where much is already known about the observable phenomena already occurring in it, it is more difficult to develop a scientific or testable theory because it is difficult to predict something that is not already known to occur, especially something as spectacularly "surprising" as atomic bombs, space-walking, gene splicing, etc. I suspect this is almost as great a difficulty of confirming any theory in a social science as is trying to conduct an experiment in it that truly excludes, isolates, or takes into account all the various influences that might effect the results. 

Richard Garlikov

This work is available here free, so that those who cannot afford it can still have access to it, and so that no one has to pay before they read something that might not be what they really are seeking.  But if you find it meaningful and helpful and would like to contribute whatever easily affordable amount you feel it is worth, please do do.  I will appreciate it. The button to the right will take you to PayPal where you can make any size donation (of 25 cents or more) you wish, using either your PayPal account or a credit card without a PayPal account.


1. There was a great movie scene that turned on the point of this premise, and that then utilized this whole argument. In the movie Support Your Local Sheriff, James Garner reluctantly says he will take the job of sheriff which no one else wants. The town council, meeting in the hardware store owned by one of their members, asks him whether he can shoot a gun. He says "Yes" and reaches for the badge. They tell him that even though they desperately need a sheriff and have no other candidates, he will still have to prove to them that he can shoot. So he goes over to one of the hardware bins and pulls out a steel washer, has one of them throw it up in the air, and he shoots at it. When it comes down, he shows them the washer and says "See the bullet went clean through the center of the hole, not leaving a mark on the washer at all." He reaches for the badge. The councilmen look at each other. Then one of them takes the washer and puts a piece of masking tape over the hole, and says they need to see this again (because, of course, the consequences they observed --the metal part of the washer's not being hit by the bullet -- is not only an unlikely consequence of his not being able to shoot well; it is also a more likely consequence of his not being able to shoot well, and of his missing the whole thing altogether). He demurs, saying that he has already put one bullet hole in the ceiling of the store. But they insist, and so he does it again, putting a bullet clean through the masking tape without touching the edges of the washer. They apologize and beg not to have offended him. (But now they have a consequence that truly was extremely unlikely if he could NOT shoot really well; so it is evidence that he most probably can shoot really well.) (Return to text.)


2. the "important sense" is somewhat difficult to explain. The point is made because some theories about things such as history may entail consequences which were once known but which have been so lost for so long that re-discovering them counts as evidence for the theory. It is not clear to me how convincing or unconvincing evidence would be or should be that involves consequences already known by some members of an inquiring community, but not known by the person or people originating the theory. (Return to text.)

I do not know how to compute this probability, and it may be that it is only an intuitive form of probability, rather than something that can be specifically calculated in regard to scientific theories.  The problem in making the calculation is that there may be a great many (perhaps even an infinite number of)  reasonable theories from among the potentially infinite possible theories that would predict the correct results.  We do not know their number. Nor do we know how many reasonable explanations there might be for seeing disconfirming results.  So we cannot really calculate how likely or unlikely it is to observe the predicted results. So we cannot really know how likely or unlikely it is that if our current hypothesis or theory is false, we will not observe the predicted phenomenon. Yet there is some intuitive sense of likelihood we go by, whether there is real justification in that or not. 

Pasteur "demonstrated" the effectiveness of his anthrax vaccine by injecting it into two of four sheep that were then exposed to anthrax.  The two vaccinated sheep did not die from anthrax but the two that were not vaccinated did.  That surprised sufficient people that they accepted the effectiveness of the vaccine, but that trial was not really large enough to have seriously eliminated "chance" from the possible explanations. 

Suppose we are trying to find our keys and after a long search, we seem to remember putting them in a sweater pocket we had worn when we last had them.  Suppose we look there and find them.  That seems to confirm the memory was correct. 

But it may be that memory was from a different time, and suppose our spouse found the keys somewhere else before we had noticed them gone, and had put them in the sweater so that we would find them there when we put it on to go outside. (Maybe the sweater had been lying on the couch, and the keys you had laid on the couch had fallen onto the floor, and your spouse figured they had fallen out of the sweater pocket and put them back in it.) Or perhaps our spouse had used the keys and then put them in the sweater pocket and told us that is where they were, and we forgot about that communication, but it was that which made us think they were in the sweater rather than our supposed memory of having put them in the sweater ourselves. Or it is theoretically possible (but not reasonable), that a squirrel found the keys outside and carried them into your house and put them in the pocket of that sweater.  Or one of our kids may have worn the sweater when s/he last borrowed the keys. 

At any rate, there are a host of possible explanations for the keys being in the sweater pocket, some of which are more far-fetched than others or that  would require a greater number of coincidences or strange, unlikely phenomena.  And the problem is we cannot calculate how many theories of that sort there are or how much each of them is to likely to be true. 

Or, what happens in science sometimes, is that a theory accounts for all known phenomena of the sort in question, but that new phenomena appear that the theory cannot explain.  Eventually a more inclusive (or an entirely different) theory is proposed and confirmed.  That second theory would have been confirmed by the same experiment that confirmed the first theory, but it wasn't -- either because it was not thought of or because even if it had, it would have been eliminated by Occam's Razor, which essentially tells us to accept the simplest explanation when there are different explanations for the same phenomena.  But since we do not even know what all the relevant phenomena might even be, or what percentage of it we have discovered so far, there is no reason to believe that the simplest explanation of known phenomena is the correct one.  (Return to text.)


Reset June 21, 2000