Orthodontics and Philosophy

 

Mark Lowey MSc FDS BDS MOrth DOrth LDS RCS (Eng.) MNTF

KARL POPPER philosophical thought applied to orthodontics. Part IV.

 

 

Theories that are of use to mankind are of value.

The more valuable theories are those that appear “truest” under the most circumstances.

The longer it takes to disprove or falsify a theory the more useful it is to mankind.

However it should always be remembered that any theory is manmade and should never be expected to function perfectly for ever under all circumstances. At some point the theory will break down so should not be given religious importance.

Scientists can build a reputation on any specific theory.

The good scientist will state along with the theory under what circumstances the scientist would reject their own theory.

Once falsified the poor scientist will try and justify the theory with exceptions and qualifications rather than reject the theory.

Once a theory has been rejected the good scientist starts working on the next theory.

 

 (Lowey’s summarisation of Popper )

 

Popper uses falsification as a criterion of demarcation to draw a sharp line between those theories that are scientific and those that are unscientific. 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 the theory. For example if I expressed the theory that the “Loweyanotor”  adjusted posture and tongue position to prevent a class 2 div 1 malocclusion developing. This theory may or may not be true. 

 

If it was stated that without this appliance 80 % of any given population would develop an Overjet of between 6-14 mm by the age of 11. This can be tested. If further stated  that following use of this appliance only 2% of any given population would have an overjet greater than 2mm and none would have an overjet of 4mm; That measurement error was 0.25mm +/- 0.002mm for 1 standard deviation ( i.e. 0.006mm for 3 standard deviations 95% confidence limits ) This can also be tested.

 

If however Once the effects were found by others to be no better than placebo and that only 50% of a population were affected and that the changes produced a reduction of Overjet only 1-2mm. Also that by age 11 50% still had overjets in the range 6-12mm and further that measurement error itself was of the order of +/- 2mm for 1 standard deviation (i.e. +/- 6mm for 3 standard deviations or 95% confidence limits ) then the theory whether it is a bit right or not is of limited use to humans.

 

The good scientist would reject the original theory based on these findings.

The good scientist would then attempt to find a better appliance or a more useful theory for more people. Alternatively accept that the marginal variations were much greater than the theory predicted and therefore the theory is less useful than expected and wait for better measurement techniques or experiments to test the theory.

 

The poor scientist would try to produce exceptions and qualifications to the theory. If only I had undertaken the treatment. That case was a very high angle case so the theory should not have been applied. The others sample was biased, the measurement technique was undertaken incorrectly. If only my laboratory had made the appliance.etc. All of which may or may not be true but it is still of limited use to mankind.

 

If completely vindicated and the all the results had proved correct for the proposed theory for 50 years in all populations then  the good scientist would still predict that at some point the theory would not be valid.

 

E does equal mc². It doesn’t equal 1/2mc² on a wet Wednesday and sometimes on a Saturday when there is an r in the month 1/2 e =mc² . However even this well known exact and illustrious theorem does break down at some point.

 

For example Mass–energy equivalence does not imply that mass may be "converted" to energy, but it allows for matter to be converted to energy. Through all such conversions, mass remains conserved, since it is a property of matter and any type of energy. In physics, mass must be differentiated from matter.

 

 

Falsifiability

 

 

Are all swans white?

Falsifiability or refutability of an assertion, hypothesis or theory is the logical possibility that it can be contradicted by an observation or the outcome of a physical experiment. That something is "falsifiable" does not mean it is false; rather, that if it is false, then some observation or experiment will produce a reproducible result that is in conflict with it.

For example, the assertion that "all swans are white" is falsifiable, because it is empirically verifiable that there are swans that are not white. However, not all statements that are falsifiable in principle are falsifiable in practice. For example, "it will be raining here in one million years" is theoretically falsifiable, but not practically so.

This concept was made popular by Karl Popper, who concluded that a hypothesis, proposition, or theory talks about the observable only if it is falsifiable.

The classical view of the philosophy of science is that it is the goal of science to prove hypotheses like "All swans are white" or to induce the conclusion from observational data. Popper argued that this would require the inference of a general rule from a number of individual cases, which is inadmissible in deductive logic. However, if one finds one single black swan, deductive logic admits the conclusion that the statement that all swans are white is false.

 

Falsificationism thus strives for questioning, for falsification, of hypotheses instead of proving them.

For a statement to be questioned using observation, it needs to be at least theoretically possible that it can come in conflict with observation.

For example, the statement "All swans are white" is falsifiable, because it can come into conflict with the observation "this swan is black". In contrast, the statement "White swans do exist" is not falsifiable, since no counter-example is logically possible.

Popper stressed that unfalsifiable statements are important in science. For example, while "all men are mortal" is unfalsifiable, it is a logical consequence of the falsifiable theory that "every man dies before he reaches the age of 150 years" Popper claimed that falsifiability is merely a special case of the more general notion of criticizability, even though he admitted that empirical refutation is one of the most effective methods by which theories can be criticized.

 

Naïve falsification

Some Philosophical definitions and statements are rather turgid. This tends to reflect the limitations of meaning to actual words. Sometimes you must follow the journey read between the words then arrive at the destination understanding the thoughts behind them.

In the 1930s, Popper gave falsifiability a renewed emphasis as a criterion of empirical statements in science.Two types of statements: observational and categorical

He noticed that some types of statements are of particular value to scientists. "all swans are white". Logicians call these statements universal. They are usually parsed in the form: For all x, if x is a swan, then x is white. Scientific laws are commonly supposed to be of this type. One difficult question in the methodology of science is: How does one move from observations to laws? How can one validly infer a universal statement from any number of existential statements?

 

Inductivist methodology supposed that one can somehow move from a series of singular existential statements to a universal statement. That is, that one can move from 'this is a white swan', 'that is a white swan', and so on, to a universal statement such as 'all swans are white'. This method is clearly deductively invalid, since it is always possible that there may be a non-white swan that has eluded observation (and, in fact, the discovery of the Australian black swan demonstrated the deductive invalidity of this particular statement).

 

Induction and Inference.

Popper held that science could not be grounded on invalid inference. He proposed falsification as a solution to the problem of induction. Popper noticed that although a singular statement such as 'there is a white swan' cannot be used to affirm a universal statement, it can be used to show that one is false: the singular observation of a black swan serves to show that the universal statement 'all swans are white' is false—in logic this is called modus tollens.

 

This leads the thoughtful into intellectual summersaults:

 'There is a black swan' implies 'there is a non-white swan,'

which, in turn, implies 'there is something that is a swan and that is not white',

hence 'all swans are white' is false, because that is the same as 'there is nothing that is a swan and that is not white'.

 

One notices a white swan. From this one can conclude:

At least one swan is white.

From this, one may wish to conjecture:

All swans are white.

It is impractical to observe all the swans in the world to verify that they are all white.

Even so, the statement all swans are white is testable by being falsifiable. For, if in testing many swans, the researcher finds a single black swan, then the statement all swans are white would be falsified by the counterexample of the single black swan.

 

One important Popperian observation is however also this.

If nothing other than white swans had ever been observed for 1000 years and the theory that “All swans are white” was about to be engraved on the walls of St Peter’s in Rome in Latin as a declaration of its religious importance a good scientist must be most on guard. It must be remembered that while the theory appears valid and has served mankind for many years it is after all only man made and at some point is likely to break down. A mutation or the discovery of an Australian black swan could undo the theory instantly. The good scientist would look then for a better theory whether he owned the first theory and had built his lifetime’s reputation on it or not. The poor scientist would qualify the discovery and maintain the theory.

 

Deductive falsification

 Deductive falsification is different from an absence of verification. The falsification of statements occurs through modus tollens, via some observation. Suppose some universal statement U forbids some observation Observation O, however, is made: So by “modus tollens”, universal statement U is false.

Nearly any statement can be made to fit the data, so long as one makes the requisite 'compensatory adjustments'. Popper drew attention to these limitations in The Logic of Scientific Discovery in response to criticism from Pierre Duhem. W. V. Quine expounded this argument in detail, calling it confirmation holism. To logically falsify a universal, one must find a true falsifying singular statement. But Popper pointed out that it is always possible to change the universal statement or the existential statement so that falsification does not occur.

 

On hearing that a black swan has been observed in Australia, one might introduce the ad hoc hypothesis, 'all swans are white except those found in Australia'; or one might adopt another, more cynical view about some observers, 'Australian bird watchers are incompetent'.

 

So dental malocclusion may be caused by tongue posture but that does not automatically mean that all Orthodontists are incompetent or indeed that the Loweyonator is the only way to treat every malocclusion.

 

Thus, naïve falsification ought to, but does not, supply a way of handling competing hypotheses for many subject controversies (for instance conspiracy theories and urban legends). People arguing that there is no support for such an observation may argue that there is nothing to see, that all is normal, or that the differences or appearances are too small to be statistically significant. On the other side are those who concede that an observation has occurred and that a universal statement has been falsified as a consequence. Therefore, naïve falsification does not enable scientists, who rely on objective criteria, to present a definitive falsification of universal statements.

 

Sophisticated methodological falsification, on the other hand, is a prescription of a way in which scientists ought to behave as a matter of choice. The object of this is to arrive at an evolutionary process whereby theories become less bad.

 

Naïve falsification considers scientific statements individually. Scientific theories are formed from groups of these sorts of statements, and it is these groups that must be accepted or rejected by scientists. Scientific theories can always be defended by the addition of ad hoc hypotheses. As Popper put it, a decision is required on the part of the scientist to accept or reject the statements that go to make up a theory or that might falsify it. At some point, the weight of the ad hoc hypotheses and disregarded falsifying observations will become so great that it becomes unreasonable to support the base theory any longer, and a decision will be made to reject it.

 

Instead of naïve falsification, Popper envisioned science as evolving by the successive rejection of falsified theories, rather than falsified statements. Falsified theories are to be replaced by theories that can account for the phenomena that falsified the prior theory, that is, with greater explanatory power.

 

The world of Physics presents one of the best examples of this:

 

“ Aristotelian mechanics explained observations of everyday situations, but were falsified by Galileo’s experiments, and were replaced by Newtonian mechanics, which accounted for the phenomena noted by Galileo (and others). Newtonian mechanics' reach included the observed motion of the planets and the mechanics of gases. The Youngian wave theory of light (i.e., waves carried by the luminiferous aether) replaced Newton's (and many of the Classical Greeks') particles of light but in turn was falsified by the Michelson-Morley experiment and was superseded by Maxwell's electrodynamics and Einstein's special relativity, which did account for the newly observed phenomena. Furthermore, Newtonian mechanics applied to the atomic scale was replaced with quantum mechanics, when the old theory could not provide an answer to the ultraviolet catastrophe, the Gibbs paradox, or how electron orbits could exist without the particles radiating away their energy and spiraling towards the centre. Thus the new theory had to posit the existence of unintuitive concepts such as energy levels, quanta and Heisenberg's uncertainty principle.”

 

At each stage, experimental observation made a theory untenable (i.e., falsified it) and a new theory was found that had greater explanatory power (i.e., could account for the previously unexplained phenomena), and as a result, provided greater opportunity for its own falsification.

 

The criterion of demarcation

 

Popper claimed that, if a theory is falsifiable, then it is scientific. This leaves us with the Duhemian problem of what constitutes a 'whole theory' as well as the problem of what makes a statement 'meaningful'. Popper's own falsificationism, thus, is not only an alternative to verificationism, it is also an acknowledgement of the conceptual distinction that previous theories had ignored.

 

Verificationism (also known as the verifiability theory of meaning) holds that a statement must, in principle, be empirically verifiable for it to be both meaningful and scientific. This was an essential feature of the logical positivism of the so-called Vienna Circle that included such philosophers as Moritz Schlick, Rudolf Carnap,Otto Neurath, the Berlin philosopher Hans Reichenbach, and the logical empiricism of A.J. Ayer.

 

Popper noticed that the philosophers of the Vienna Circle had mixed two different problems, that of meaning and that of demarcation. Popper emphasized that there are meaningful theories that are not scientific, and that, accordingly, a criterion of meaningfulness does not coincide with a criterion of demarcation.

 

So Popper urged that verifiability be replaced with falsifiability as the criterion of demarcation.

 

Use in the Law Courts.

 

Falsifiability was one of the criteria used by Judge William Overton in the McLean v. Arkansas ruling to determine that 'creation science' was not scientific and should not be taught in Arkansas public schools as such (it can be taught as religion). In his conclusion related to this criterion he stated that:

 

 "While anybody is free to approach a scientific inquiry in any fashion they choose, they cannot properly describe the methodology as scientific, if they start with the conclusion and refuse to change it regardless of the evidence developed during the course of the investigation."^[8]

 

It was also enshrined in United States law as part of the Daubert Standard set by the Supreme Court for whether scientific evidence is admissible in a jury trial.

 

Criticisms by Contemporary philosophers

 

Popper is not without his critics I have however included these as a foot note. The arguments can be turgid reading even for the interested. [i]

 

They argue that falsifiability cannot distinguish between astrology and astronomy, as both make technical predictions that are sometimes incorrect.

 

David Miller, a contemporary philosopher of critical rationalism, has attempted to defend Popper against these claims. Miller argues that astrology does not lay itself open to falsification, while astronomy does, and this is the litmus test for science.

 

The same statements can be made with respect to theories regarding tongue posture and breathing in relation to development of malocclusion. Examining these examples shows the usefulness of falsifiability by showing us where to look when attempting to criticise a theory.

 

For example when asked what hypothetical evidence could disprove evolution, J.B.S. Haldane, replied  "fossil rabbits in the Precambrian era” Richard Dawkins adds that any other modern animals, such as a hippo, would suffice.

Karl Popper at first spoke against the testability of natural selection but later recanted, "I have changed my mind about the testability and logical status of the theory of natural selection, and I am glad to have the opportunity to make a recantation."

 

Critical rationalists hold that scientific theories, and any other claims to knowledge, can and should be rationally criticized, and (if they have empirical content) can and should be subjected to tests which may falsify them. Thus claims to knowledge may be evaluated. They are either falsifiable and thus empirical (in a very broad sense), or not falsifiable and thus non-empirical. Those claims to knowledge that are potentially falsifiable can then be admitted to the body of empirical science, and then further differentiated according to whether they are (so far) retained or indeed are actually falsified.

If retained, yet further differentiation may be made on the basis of how much subjection to criticism they have received, how severe such criticism has been, and how probable the theory is, with the least probable theory that still withstands attempts to falsify it being the one to be preferred. The least probable theory is the one with the highest information content and most open to future falsification.

 

Critical rationalism has it that knowledge is objective (in the sense of being embodied in various substrates and in the sense of not being reducible to what humans individually "know"), and also that truth is objective (exists independently of social mediation or individual perception, but is "really real").

 

Popper notes that this "may illustrate Schopenhauer's remark that the solution of a problem often first looks like a paradox and later like a truism". Even a highly unlikely theory that conflicts current observation and is therefore falsifiable  "all swans are white"  must be considered to be better than one which fits observations perfectly, but is highly probable "all swans have a colour".

 

This insight is the crucial difference between naive falsificationism and critical rationalism. The lower probability theory is favoured by critical rationalism because the higher the informative content of a theory the lower will be its probability, for the more information a statement contains, the greater will be the number of ways in which it may turn out to be false.

So from an Orthodontic perspective, the Loweyonator which is designed to affect tongue position and posture and carries with it claims of so doing must have considerable informative content before it should be accepted as either preferable to existing forms of treatment and/or  confirmation of the theory supporting it.

 

The rationale behind this is simply to make it as easy as possible to find out whether the theory is false so that it can be replaced by one that is closer to the truth.

Justificationism is what Popper called a "subjectivist" view of truth, in which the question of whether some statement is true, is confused with the question of whether it can be justified (established, proven, verified, warranted, made well-founded, made reliable, grounded, supported, legitimated, based on evidence) in some way.

They are naïve rationalists, and thinking that their knowledge can indeed be founded, in principle, it may be deemed certain to some degree, and rational.

Knowledge and truth still exist, just not in the way we thought.

 

The pit falls of justificationism and positivism

 

 

The naïve empiricism of induction was shown to be illogical by Hume. A thousand observations of some event A coinciding with some event B does not allow one to logically infer that all A's coincide with B's.  So for example “I have examined 1000 patients who have had teeth removed and they therefore have a click in their joints.” This statement can be falsified by examining a single patient who has had extractions but no click in their joint. A statement such as  “ I have had orthodontic braces and therefore I have a pain in my joint.”  are no truer than “ Caesar was the emperor of Rome. My dog is named Caesar therefore my Dog was the emperor of Rome.”

If we were really "inducting" theories from particulars, it would be inductively logical to claim that the sun sets because I get up in the morning, or that all buses must have drivers in them (if you've never seen an empty bus). So equally all malocclusions are caused because of posture and tongue position. Or all patients mouths must have a Loweyonator  in them ( if you’ve never seen an empty mouth).

 

Popper and David Miller showed in 1983, that evidence supposed to partly support a hypothesis can, in fact, only be neutral to, or even counter-support to the hypothesis. David Miller, attacks the use of "good reasons" in general Miller calls "tediously familiar", is that all arguments purporting to give valid support for a claim are either circular or question-begging.

Albert Einstein is reported to have said:

”No amount of experimentation can ever prove me right; a single experiment can prove me wrong.”

In relation to Orthodontics some of the current theories of beauty are falsifiably incorrect with respect to the Golden proportion, symmetry and averageness. Some of the theories regarding “stability” and Cephalometric measurements with or without extractions have been shown to be of limited use to mankind. Some of the theories regarding tongue position and posture with respect to malocclusion have insufficient informative content to make them of benefit to mankind.

 

 

Popper, Karl (2002) [1959]. The Logic of Scientific Discovery (2nd English ed.).

The criterion of the scientific status of a theory is its falsifiability, or refutability, or testability. — Karl Popper, (Popper, CR, 36)