Galileo’s second important successor Newton was closer to him in the sense that
he is also a member of the mixed tradition. He tried to keep a proper balance between
an unlimited confidence in mathematics unchecked by experience, and mere experimenting
unaccompanied by mathematical analysis and demonstration.28
His statements on method, therefore, sounded much like Galileo. He gave his method more experimental coloring than Galileo had done, for the latter did not feel the need to check by observation mathematically deduced consequences. For Newton the logical inclusion of a proposition within a deductive system was not a sufficient proof of its ‘truth’. As rightly pointed out by Randall, the experimental analysis of instances in nature forms a part not only of the method of discovery
but also of the verification.29
27
Laudan 1981, p. 29. The quotation in the last sentence is from: R. Descartes, Oeuvres (ed. Adam and Tannery), Paris, 1897-1957, vol.2, p. 199. Italics are original.
28
Randall Jr.1962op.cit. p. 576.
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58 Chapter 2. The Marriage of Mathematics and Natural Science
In the Opticks appears Newton’s classic statement of the joint method of analysis
and synthesis, with its experimental fervor.
As in mathematics, so in natural philosophy, the investigation of difficult things by the method of analysis, ought ever to precede the method of composition. This analysis consists in making experiments and observations, and in drawing several conclusions from them by induction, and admitting of no objections against the conclusions, but such as are taken from experiments, or other certain truths, for hypotheses are not to be regarded in experimental philosophy. And although the arguing from experiments and observations by induction be no demonstration of general conclusions; yet it is the best way of arguing which the nature of things admits of, and may be looked upon as so much stronger, by how much the induc- tion is more general. And if no exception occur from phenomena, the conclusion may be pronounced generally. But if at any time afterwards any exception shall occur from experiments, it may then begin to be pronounced from compounds to ingredients, and from motions to the forces producing them; and in general, from effects to their causes, and from particular causes to more general ones, till the argument end in the most general. This is the method of analysis: and the synthesis consists in assuming the causes discovered, and established as principles, and by them explaining the phenomena proceeding from them, and proving the
explanations.30
It may be noted that the term ‘analysis’ is used to refer to the experimental and empirical context, unlike the modern usage of the term to the logical and deductive context. Accord- ingly the term ‘synthesis’ refers to deductive proof. The terms are used to refer to the same contexts as in the Aristotelians of the School of Padua at Italy, as elaborated above. This terminological inversion, as indicated above, must be due to the later linguistic orientation of philosophers, specially after Kant. It is typical, for Aristotelians, to consider the effects or phenomena as complex, therefore to be analyzed until they reach the causes, which are regarded as simple. The later modern philosophers use the term ‘analysis’ mostly to denote the logical movement from the more general statements to the more specific statements, while inductive movement from specific to general statements is regarded as synthetic. This inver- sion of terms demands historico-philosophical explanation. Again, we are afraid, we cannot meet the demand here, but must remain content with the observation.
The events mentioned in the method of synthesis, though include induction, are not mere simple unidirectional inductive movements. But it is characterized as dialectical, i.e., checking errors and collecting instances, ultimately arriving at the general. It is the well known view of Newton that in this context hypotheses should not be brought in. So much has been written, which is ridden with confusion regarding Newton’s cryptic views on the role of
30
hypotheses, we shall not add anymore to it. However, it should be noted, that it is typical of the scholars of that period to believe in only those postulates that are ‘deducible’ from given experience. If Descartes allowed in the last resort some room for hypotheses, it is not because it is desirable to have them, but because we have nothing better than them. However the difference between Newton and Descartes should be noted. Newton wanted that the principles be ‘induced’ experimentally, while Descartes’ earlier program was to deduce them from the clear and distinct principles. Thus the nature of the kind of reason they have envisaged is qualitatively different. Now for Galileo, as elaborated above, the first step was to construct the definitions, and then the hypotheses. Considering the deficiencies of both inductive and hypothetico-deductive methodologies that developed, it is Galileo’s position that needs to be reconsidered. In the view that we are going to defend, constructing definitions will be considered the first step in the context of discovery.
Chapter 3
The Rise of Consequentialism
3.1
New Objects of Scientific Knowledge
It is usual to contrast Bacon with Descartes, the former being seen as an empiricist, and the latter as a rationalist. Bacon’s name has become synonymous with inductivism, and has met with much criticism from various quarters. A quotation from Jevons would tell how Bacon has come to be regarded:
The value of this method [Bacon’s] may be estimated historically by the fact that it has not been followed by any of the great masters of science. Whether we look to Galileo, who preceded Bacon, to Gilbert, his contemporary, or to Newton, Descartes, Leibniz and Huyghens, his successors, we find that discovery
was achieved by the opposite method to that advocated by Bacon.1
Bacon was very popular with the English scholars, even among those who took mathematics very seriously, such as Newton. Though Bacon opposed decadent scholasticism and barren belief in the authority of science, he continued to believe in the Aristotelian objects of knowl- edge, which consists in qualitative understanding of the nature or essence of things. Ideas about the nature of science that followed after Bacon, however, did not entertain Aristotelian objects of science, but undertook to probe for invariant antecedents.
In fact much before Galileo, the new objects of knowledge were developed in the school of Alexandria by Archimedes, but it took many centuries to apply similar methods to other physical problems such as motion. Some explanation as to why Archimedean methods did not take off immediately has been attempted in the case studies. Here we find it necessary to clarify the nature of knowledge that developed after Bacon, which was already available in the works of Archimedes. This partially explains why Bacon’s inductive method failed.
1
Take Archimedes’ law of the lever: When a two armed-lever is in equilibrium, the attached weights are inversely proportional to their respective distances from the ‘fulcrum’. Thus, if one side of the lever is ten times as long as the other, a weight attached to that side will balance another weight ten times as heavy when placed on the other side of the lever. Here no reference is being made to “inherent qualities” or Aristotelian essences to describe thesystem. Neither is there any talk of any metaphysical ‘force’.
It [The law] expresses a mutual dependency of quantities and nothing more. Even the distinction between independent and dependent variables is obliterated, and the relationship which the law defines is completely reversible. In other words, the law expresses a type of dependency for which the mathematical notion of
“function” has furnished the pattern.2
It should be noted that the pattern of relationship is symmetrical, because of which it is reversible. In fact we cannot say, except arbitrarily, which is the cause and which is the
effect. What emerges here is aninvariant, symmetric, relational, and functional form. This,
we claim, is the character of the objects of scientific knowledge of not only Archimedean science, but also the science whose development we continue to watch even today. More examples of this pattern will be presented in the case studies.
Another example from Newton again suggested by Werkmeister in the same context, is equally telling. The form that emerges from Newton’s law of gravitation expresses mutual dependency of two masses each one attracting the other. For example, in the case of a falling stone, the earth attracts the stone, and also the stone attracts the earth.
Gravitation cannot even be defined without reference to at least two bodies. The attractive “force” is in every case proportional to the masses of the bodies and inversely proportional to the square of their distances. If this means anything at all, it must mean that the “force” of gravitation is not “inherent” in any one thing, but is essentially a relation between things. The “immanent” forces of
metaphysics disappear, and there is left only mathematical proportionality.3
Therefore the new objects of scientific knowledge are based on relational invariance, and is undoubtedly non-Aristotelian. This knowledge is necessarily not obtained by Baconian in- ductive methods, for it involves creative abstraction. The role of abstraction is mostly in creating an affine space in which mathematical knowledge can find application and where induction has no place. It is in this context, we claim that inversion plays its crucial role
2
Werkmeister, W. H. 1940, p. 40. Werkmeister makes these observations in the context of explicating the functional notion of force that Kepler and latter scientific tradition adapted. We are using his observations for the general objects of knowledge that science has adapted ever since.
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62 Chapter 3. The Rise of Consequentialism
and induction fails miserably. If there is one singular achievement of philosophical reflec- tion on scientific method so far, it is, we think, the limitation of the inductive method in understanding scientific knowledge.
The Baconian method would have worked if the objects of knowledge were Aris- totelian, but since the new objects of science contained functional relations inductive method failed. Thus if Bacon’s methods did not find application in science it is due to the new face that science took after Bacon.
The nature of the change, as we understand it, consists in realizing newer objects of knowledge that are not solely based on the thematic division of universals and particulars.
We have noted above that for both Plato and Aristotle episteme constitutes the knowledge
of the universals. We have also observed that the ‘discovery’ of universals can be understood as a requirement to meet the Sophists’ challenge. Now, the new object of scientific knowl- edge is not merely a relation between universals, but between two measurable parameters of a physical phenomenon. Before Plato, and even after him, only unchanging objects were thought to be measurable, and mathematics was conceived as a science of such objects alone. Even the Archimedean science (statics) had this limitation of not being able to mathematize a physical phenomenon that has the character of necessary change, such as motion. However, after Galileo, it is realized that even changing phenomena can be mathematically understood. Galileo demonstrated this possibility with epistemological and methodological support. The discovery of Galilean relativity is indeed the first outcome of the new forms of knowledge.
The character of this new knowledge is to capture theinvariance of variable phenomena. It
is no longer statics. Dynamics is the hallmark of the new science.
Earlier, after Plato, the changing objects of knowledge were regarded as a threat to
understand the world around. If it is possible to show thatchange itself can have a pattern,
change becomes a knowable object. It is in this sense that this new development can be regarded as an answer to the problem of knowledge that the Sophists raised. This is how we interpret the nature of the transformation that took place in the 17th century revolution in science. We will argue below that this change is impossible without inverse reason. The claim, that this newer form of invariance is not solely based on the relation between universals and particulars will become clear in Part-II.
After this transformation in science the discussion on whether scientific methodology should be Baconian or Cartesian (empiricist or rationalist) continued for a long period. We cannot go into the details of the events that followed after the 17th century. However we find it necessary to discuss the general nature of the interesting and highly significant changes
that took place after the 17th century. Since we are not in agreement with the historico- philosophical observations of Karl Popper, Imre Lakatos, and Larry Laudan on the history of methodology after 17th century, we shall present below a critical discussion, which will also contextualize the problem of the thesis. The general theme of all the three philosophers is the rise of consequentialism, and the fall of infallibilism.