Lesson 32.   Logic and the progress of science

 According to the majority science is knowledge that proceeds via endless accumulation.   We can be proud, Gentlemen, that we now know more than those before us!   We pile up knowledge and new theories as we would bricks for a construction and thus the monument of Science is built.  Hence many people imagine scientific knowledge to be the sum of certainties accumulated by generations of scientists, and pride themselves that scientific discoveries and current advances allow them to dismiss the need for religion, something earlier generations could not do.   While they, men of the past, relied on superstitions, we, men of today, rely on facts and certainty!


 Yet does science progress in a linear fashion?  Is scientific knowledge the result of an accumulation?  Does the advance of knowledge really bring certitude?  Does science never question its own theories?  If so can we still say that knowledge is cumulative?  Science does not bring old discoveries up to date.  Rather it is a radical remake that can alter former beliefs to the core of their very principles.  But on the other hand the expansion of what we know also widens the field of our growing ignorance.  What then becomes of the idea of scientific progress?  More radically we need to question the process of the development of science.  In one word: is there a logic of scientific development? 

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A. The idea of progress applied to Science

    Progress means more than just change.  A change is a neutral modification, while progress is a modification which, with respect to a former state, consists in a genuine ‘plus’, a ‘betterment’, an amelioration.  It is not enough for a tendency to be continuous in order for there to be progress.  That is, any progression is not a progress.  The progression of rabies in Europe or the SARS epidemic is not a progress.  The idea of progress receives its full meaning when it includes at once a tendency following in a constant way a certain logic as well as an unquestionable amelioration.  In fact our model of progress is not one we find in science but in technology.  Our current means of locomotion and communication from a distance are so different from those of our ancestors and represent a succession of such undisputable ameliorations that no one can deny the existence of a technical progress, in the sense of the indefinite improvement of its realisations.  When applied to the sciences, these prerequisites raise several questions:

    1) can one speak of a logic – some kind of regularity - of scientific discovery? 2) Does science progress through adding knowledge to knowledge?  3) If this is not the case, had we not rather say that science undergoes a constant revolution than pretend that it is progressing?

       It is correct that during the Renascence the West invested extraordinary hope in science.  Philosophy of History has taken over the argument of the history of science as an adventure in order to justify the promise of a better world, built on the foundations prepared by the new science.  Hence minds were divided in Ancients and Moderns: the former defended classical culture (Greece, Rome) while the latter the new philosophers formed on the bench of scientific method and discoveries.  Modern science has stirred an immense enthusiasm for progress, one extending to the beginnings of the 20th century.  It enabled one to take over an idea of progress stemming from religion, that of a linear time and the arrival at the end of some sort of paradise, yet replacing religious content with one confined to the anticipated results of pragmatic science.  Thus one can preserve the idea that Time flows along a straight line and in lieu of the stages laid out by Bible inspired creation, those of the apparition of Christ and the Martyrs to save humanity, and of the emergence of celestial Jerusalem, one substitutes, like Auguste Comte, the “stages” of emergence of society.  At first there was the “theological age”, the time of Homer and the Greek gods.  Then came a “metaphysical age”, that of the Greek philosophers, Plato and Aristotle.  Finally mankind emancipated out of all forms of superstition and entered the “positive age”, the one of the undivided reign of Science.  This stage was thought to bring a progress beyond anything found in the former stages.  When explained to pupils and students of today, this theory of History still arouses fascination of some sort.  It justifies the faith and hope one puts in Science.  It nourishes a deep need, the one to believe in an evolution.  And since we don’t know what drives this evolution, we take it to be the result of science for want of anything better.



                                                     This is the myth of progress resonating in our Western minds even to this day. For long we have needed to think of History as the golden way of human accomplishment and redemption, and this is why the oldest myths of progress keep recurring in such different forms. Stephan Zweig writes in Yesterday’s World : « with its liberal idealism the 19th century was sincerely convinced that it found itself on the road that would take it straight to the ‘best possible world’.  One looked upon former times with contempt for their wars, their periods of starvation and rebellions, one took it that humanity, for not being enlightened enough, had not yet reached manhood…  This faith in an inescapable and continous “Progress” had in those days all the force of a religion.  One already believed more in this “Progress” than in the Bible and this gospel appeared irrefutably demonstrated by the ever-renewed marvels of Science and Technology”.


    What has happened since for us to speak now of the faith in progress in the past tense?  In our post-modern world we have lost faith in the myth of scientific progress.  Wars and human violence have continued, ever more brutal, lack of education, injustice and inequalities are still here, and we have in addition reaped the harvest of ecological problems stemming from the application of science and technology.  Science has completely changed the world, it has enabled considerable transformations to take place, yet it would seem that man has stayed the same!  There has been no progress of inner man.  The only important change, the one the siècle des Lumières believed in, the change of man’s consciousness, is one we have not seen.  We now know that it is vain to expect from science what it could never give.  Science is not a religion, it is not an ideology, nor wisdom or even philosophy.  Science is objective knowledge, and hope in progress is something altogether different.  It is not contradictory to imagine an over-developed techno-science in a world that is morally barbaric and ignorant.

   The only valid idea about science, as regards its progress, is that of a progress of knowledge independently of any mythology.  This is the kind of progress we are witnessing.  No one contests that science has come a long way since Antiquity.  Yet is there progress in this logical progression?

   B.  Audacious conjectures, severe refutations.


For knowledge to progress is must conform to a constant logic that should be clearly visible.  We have seen that the core of science is its theories. If scientific knowledge is progressing would that not be the result of a continuous application of a certain logic of theoretical discovery? 

  British empiricism has often viewed the logic of scientific research as the application of a method said to be  « inductive ».   The scientist is supposed to make observations and then to draw generalisations from these observations.  In order to account for a scientist’s ability to find an explanatory hypothesis, Claude Bernard said that “the fact suggests the idea”.  This presupposes that the repeated observation of the same fact enables the mind to induce, that is to amplify a generalisation that one will subsequently want to convert into a law of Physics within a theory.  Newton’s motto was ‘I feign no hypotheses’.  Yet does the generalisation of the observation of a fact have any logical rigour? Does it comport any necessity?

        Were it the case that I once, twice, a hundred times have seen a white swan, does this entitle me to derive a law from this according to which all swans are white?  No.  A single counter-example is sufficient to overturn inductivism.  “No matter how many swans have been observed, it still does not justify the conclusion that all swans are white.”  Induction has no logical rigour.  The conceptual work of science is not the result of induction, and experimental induction is an epistemological myth that does not correspond to the Logic of Scientific Discovery.

But this does not mean that scientific method would not be logical, only that the logic of scientific thinking should be looked for in the deductive demands imposed on any theory and not in the process of induction.  This means that what matters above all in science is first, to examine the internal coherence of the theory, then the manner in which the theory is confronted to facts, and finally the relation between theories.

     Science cannot accept a theory that includes internal contradictions.  The logical coherence of a new theory must be tried.  Even though it breaks the easy representation of ordinary space and time, the theory of relativity is consistent.  In addition, when compared to Newton’s celestial mechanics, it appears as scientific progress.  Within the framework of the theory of relativity, Newton’s theory seems a particular case, one adapted to the scale of human perception.  It is surpassed without being rejected; therefore it would appear as an approximation to a description that is more accomplished in the logical system of relativity.  Finally and most important is that we wan draw consequences and find concrete applications that can test it.

Viewed in this light, the logic of scientific discovery entitles one to think  that it would be merely deductive and not inductive; since science’s moment of invention is more than anything the hypothesis, Karl Popper retains that it is among other things an audacious conjecture.  A new scientific hypothesis is indeed a parry, a bet, a theoretical audacity.  Yet, since we are talking about science and not about religion or ideology, this audacity, this freedom to invent, has the logical obligation to undergo the test of facts.  No audacious conjecture without severe refutations.  From this we conclude that the progress of scientific knowledge is situated in the dialectics proceeding from audacious conjecture to severe refutations in a continuous way as scientific theories succeed one another.  The trial of a theory is a deductive process.  It operates by deducing from the fundamental hypotheses of this theory certain predictions that are then subjected to a protocol of experimentation or observation.  If the result is positive, that is “if the particular conclusions show themselves to be acceptable or verified, then the theory has provisionally passed the test; we will not have found any reason to reject it”.  Yet this does not rule out that an observation or an experiment might one day find it inadequate.  In the meantime we say that a theory has “been tried”or that it is “corroborated”.  (Popper, The Logic of Scientific Discovery)

On the contrary, when a prediction is refuted by facts then we are obliged to consider that its conclusions have been falsified.  Since the procedure is that of deductive logic, the falsification of the conclusion leads to the falsification of the principles and therefore of the theory itself: “this falsification also falsifies the theory from which it was logically derived”.

For instance the astronomical observation of the perihelion of Mercury gives a counter-example with respect to the calculations of Newton’s theory of gravity.  The planet Mercury reaches the point nearest to the Sun in noticeably shorter a time than that predicted by Newton’s celestial mechanics.  Here is a fact that is not consistent with Newton’s theory.  For a while this fact is an unexplained oddity, yet it is also pregnant with polemics.  But later a new theory, that of relativity, appears and this theory arrives with more precise explanations.  Now there is no more room for doubt.  Newton’s mechanics has revealed its approximate character and been falsified.  With the new theory we have a point of view that embraces the precedent one and that also has a better explanatory fecundity and improved precision.

The passage from one theory to the next is a progress, but it comes at quite heavy a price: it obliges us to recognise that a scientific theory is just as mortal as it is provisory.  A scientific theory is only valid for as long as one has not found a better one.  A scientific theory is mortal because it is scientific.  Recalling the metaphor of the net and the fish we can say that the first theory did catch fish, but that its too wide mesh allowed too many to sip through.  The second theory has tighter mesh, so it is more satisfactory.  But this does not prevent the other theory from catching fish!  In other words it is possible that polemic facts are observed that are not consistent with what one would be allowed to expect.  In Physics, as regards relativity, such facts are already there.  One is awaiting another that will be able to construe a satisfactory synthesis between the theory of relativity and the new quantum mechanics, two sorts of physics that have very different viewpoints.  We must be aware of the relative character of our current knowledge.  Our grandchildren may well smile at today’s textbooks: “in those days, one still believed that…”

Thus we better understand what might be the logical relation between one scientific theory to another and thereby what might be the logic of scientific discovery.  Science evolves when one realises that discoveries can be made which challenge existing explanations.  Yet this logic is a polemical one that appears relentless, an endless striving towards an ideal of total knowledge that one never reaches, receding as one advances.  Popper’s analyses also allow one to trace a borderline between what is scientific theory and what is not.  Scientific theory can be falsified, non-scientific theories cannot.  There is no way to show the falsity of non-scientific theory, it stays out of the dynamics of the theoretical development of science.  This is the status of psychoanalysis and Marxism: “Marxism and Psychoanalysis are outside science precisely in that and because of the very structure of their theories they are irrefutable.”

C.  Scientific Revolutions.


However there is another remarkable aspect of the making of scientific theories : they depend more on sociological than on logical conditions.  What makes the dynamic of scientific revolutions is not just the relation of theories and facts, or the relation of theories to other theories, but it is the reign of successive paradigms in scientific thought.  A paradigm is an explanatory model that is installed inside the collective consciousness of the scientists at a given time and becomes common reference.  The Greek words means “example”: a paradigm is an exemplary explanation.  Finalism is a paradigm of Greek physics that we find in Aristotle and the Stoics.  It is expressed in the image of Mother Nature who provides for the need of all things.  “Mechanism” is a paradigm of classical physics that we find in Descartes.  It is expressed in the image of the clockwork of the universe.

It takes a certain time for a paradigm to win recognition.  Once it is shared by the scientific community, a period of normal science is installed.  “ Normal science designates the research solidly anchored in one or many past scientific achievements that a certain group of scientists regard as sufficient to be the starting point of other works”.   Normal science develops inside textbooks and classes that are taught to students. 

Universities teach first of all normal science.  This allows for a tradition to be transmitted and extended.  It is the study of paradigms that enable a student to feel he belongs to a scientific community.  But this is also what enables research to not only draw from common acquisitions, but to challenge the work of colleagues on fundamental points when it becomes clear that a paradigm has become insufficient.  Science is practiced in a collective manner and by groups who are attached to the dominant paradigm at any given time and who do not wish to change school or scientific environment.  Science also has its chapels!  It has its own conservatism once a paradigm is finally installed in the scientific collective consciousness.

     This conservatism functions only until the time when brilliant minds can deal very hard blows to the ruling paradigm.  And this can only take place when objections have accumulated, objections that are in contradiction with the ruling paradigm, and that generate unsolved problems.  Then science enters a period of crisis.  Normal science does not represent novation but a very cumulative activity that amounts to exploiting paradigms without questioning their fundamental hypotheses.  Scientific genius inaugurates a break.  These crises of knowledge are the condition of apparition of new theories.

Ptolemy’s paradigm, elaborated in the third century BC ended up in crisis because of its imperfect and approximate results.  The system of Copernicus breaks away from a certain representation of the world through a change of paradigm.  In other words the Copernican paradigm succeeds to that of Ptolemy in order to solve the crisis.

This too is the case in the passage from Newton’s celestial mechanics to Einstein’s relativity.  Facts that refused to agree with Newton’s conception were accumulating and gave rise to polemics.

It is on the verge of crisis that a mind of genius has a great idea that will first be thought of as heretical with respect to the science of his time.  Yet beware, this does not always say that a new idea is absolutely new!  It may be forcefully exposed at this moment in time, but may well have been thought of before without at that stage being able to break through.  The Greek Aristarch of Samos had already thought of heliocentrism, a view that had been present for millennia in Indian astronomy, as well as a very accurate dating of the age of the Earth.  But this was not the West.  What matters  is that an idea be taken over by the scientific community.

This odd fact questions the very notion of scientific progress.  A scientific revolution is the overthrow, the passage from an old to a new paradigm which, far from taking place in an innocuous continuity, does on the contrary occur during a difficult breach that forces one to radically revise what happened before in order to recover reliable foundations.  “The passage from a paradigm in crisis to a new paradigm that might generate a new scientific tradition is far from being a cumulative process that could have been drawn from variants or an extension of the old paradigm.  Rather it is a reconstruction of a whole sector on new foundations.”(Kuhn, The Structure of Scientific Revolutions).

     A change of paradigm inaugurates a new way of thinking about old problems.  For a while, because of the conservatism of normal science, many explanatory theoretical models will be competing, each of them claiming to be the explanation of certain facts and the solution to certain problems, without any real overlapping.  “During the transition period there will be some overlapping, important perhaps, never complete, between problems that can be resolved by both the old and the new paradigm.  But there are also crucial differences.”  Hence, once the transition is complete, specialists will look upon their own field with very new eyes.  Think for instance of the earthquake provoked by the appearance of the theory of relativity in the old Newtonian Physics and you will get some idea of what is meant by a change of model.  Instead of speaking of the evolution of scientific representation, we ought to speak of a scientific revolution with all the subversion and polemics that this implies.  Kuhn makes a comparison with political revolutions and says that in the same way that a revolution arises from the feeling that the old institution have ceased to “adequately respond to problems”, scientific revolutions have one feel that the old vision of science is obsolete in the face of the new.  It is no longer possible to believe, as one did before, in a theory one can see bursting at the seams and that must urgently be replaced.  A science in crisis presupposes the apparition of doubt and questioning.  It generates the idea that the old science is merely imperfect knowledge, approximate and incomplete.  Conversely the new theory gives rise to hope and enthusiasm for a complete renewal of perspective.  On the one hand science made, on the other hand science in the making.  On the one hand science slumbering inside a tradition that repeats hackneyed ideas, on the other a science that is more awake, inventive, creative and revolutionary.   Thus, as it is pressurizing for the elaboration of a more complex theory, the crisis of science is not only destructive, but also instructive.  Through supplanting the Newtonian paradigm the theory of Relativity allowed one to resolve unfinished work and anomalies that it was impossible to integrate in the old physics.  One came to think that the old laws of Mechanics were not as universal as one had thought.  The domain of their validity was retrained and did not extend to the galaxy taken as a whole or to the domain of the finest particles.


Given its superior range and power of prediction, one could expect it that the new model would take over fairly quickly.  Yet this never happens.  The problem is that one cannot grasp the exact point of view of the new theory as long as one has not given up the old one.  The new idea requires a leap of the intuition and the new perspective imposes a deep reshuffle that scientists who have been schooled on the bench of normal science are rarely able to make.  Those who have been fruitful inside the old paradigm are attached to it by habit.  Even confronted to the evident they may obstinately hang on to an erroneous but familiar conception, while the new paradigm is gaining more and more influence.  A new generation ends up reversing this and make a new idea acceptable.  Once a sufficient number of scientists have embraced the new perspective, a consensus is formed and this is the beginning of a new period of normal science.  And the whole process starts again!  There will always be some lucid minds who perceive that the new paradigm is itself unsatisfactory in many ways.


Kuhn’s analysis has the merit of showing us a process of scientific revolution and the resistance it gives rise to.  It also has the merit to show that science is a collective undertaking.  It is the collective consciousness of scientists that structure the consensus which a certain generation will call objective truth and scientific knowledge.

  Leaving aside for the time being some objections, we may sum up the foregoing analyses in a table that will put together the points made by Kuhn and Popper.



1 

2 

3 

4 

Theory 1 :

Audacious Conjecture

Challenging facts

severe Refutation

Theory 2

Audacious Conjecture

Challenging facts

severe Refutation

Deductions of facts


Deduction of facts


Consistence of a system

Apparition of inconsistencies

Consistency of a new system

Apparition of inconsistencies

Ex : Newton’ Mechanics


Ex : Einstein’ relativity


Theory tested by time


Theory 1 is outperformed but kept


Normal science = textbook

Science in crisis = uncertainties

Normal science = textbook

Science in crisis = uncertainties

Paradigm 1


Paradigm 2


Consensus of the scientists of a certain time

Critical discussions

Consensus of the scientists of a certain time

Critical discussions


If so, how can we then distinguish between a theory that is scientific, because considered such, and one that is not scientific, because it is not accepted by the scientific community of its time?  Is this not an ideological combat?  And is not the very wish to separate science and non-science also ideological? Reversals in the history of science and the scandal that always surrounds new theories ought to remind us to be cautious.


What is clear is that the notion of scientific progress does not rest on a cumulative process.  Were we to stick to what most people think we might imagine that pupils at school and then university would move from certainty to more certainty. Yet what is taking place is the very opposite. Even the foundations he believed to be so firmly established are the topic of bitter debates.  We must be aware that all advance of knowledge takes place inside the field of the unknown that it tries to conquer. This also means that the roads to knowledge multiply.  We may liken this to what happens to a speleologist as he discovers the entry to a cave. In the beginning he may be proud of his discovery.  His pride is abashed when he realises that the first hall opens up to five others that themselves have many entrances.  It is only the beginning!  What remains to be discovered is even more vast that what is known now.  Let us take the example of the knowledge of the brain.  Those who first discovered that there are regions in the brain can be proud.  Yet this was only a first step giving a tiny glimpse of the immensities that remain to be explored.  In this sense the more science moves forward the more ignorance progresses!


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We can no longer feel as proud of « scientific progress » as we did in the past.  We have to learn humility and modesty.  The history of contemporary science is thus shown to be a time of uncertainties because man has become aware of its complexity, something 18th men did not suspect. 

We must understand that a scientific explanation must always be thought of as something taking place inside our current knowledge and is now the best explanation that we can give.  We know that science is in the making.  Knowledge accepted at one time is an inter-subjective fabric and a common pool of certainties.  Inside this one we attempt to select away whatever is not consonant with accepted ideas or theories.  Yet we must take care that this demarcation does not turn ideological.  What science makes possible is to extend and share our knowledge about the world.  Without being open in this way it might easily become sclerotic.


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