Question 5

Q. Theories in Science can not be inferred inductively. Do you agree? Exemplify.

Posted by Shraddha

Theories in science cannot be inferred inductively, scientific theories are more of a deduction based ones.

Aristotle- an individual science is a deductively organised group of statements

Although Aristotle did not specify a criterion of the “essential” attribution of a predicate to a subject class, he did insist that each particular science has a distinctive subject genus and a set of predicates. The subject genus of physics, for example, is the class of cases in which bodies change their locations in space. Among the predicates which are proper to this science are “position”, “spped”, and “resistance”. Aristotle emphasized that a satisfactory explanation of a phenomenon must utilize the predicates of that science to which the phenomenon belongs. It would be inappropriate , for instance, to explain the motion of a projectile in terms of such distinctively biological predicates as “growth” and “development”.

Aristotle held that an individual science is a deductively organised group of statements.

At the highest level of generality are the first principles of all demonstration- the Principles of Identity, Non-contradiction, and the Excluded Middle. These are principles applicable to all deductive arguments. At the next higher level of generality are the first principles and definitions of the particular science. The first principles of physics, for example, would include:

All motion is either natural or violent.

All natural motion is motion towards a natural place

e.g. Solid objects move by nature toward the centre of the earth.

Violent motion is caused by the continuing action of an agent. (action at-a-distance is impossible)

a vacuum is impossible

The first principles of a science are not subject to deduction from the more basic principles. They are the most general true statements that can be made about the predicates proper to a science. As such, the first principles are the starting-points of all demonstration within the science. They function as premises for the deduction of those correlations which are found at lower levels of generality.

The ideal of deductive systematization

Euclid (300 B.C), Archimedes (287-212 B.C)

Many writers in late Antiquity believed that the ideal of deductive systematization had been realized in the geometry of Euclid and the statics of Archimedes.

Euclid and Archimedes had formulated systems of statements- comprising axioms, definitions, and theorems -organised so that the truth of the theorems follows from the assumed truth of the axioms. For example, Euclid proved that his axioms, together with definitions of such terms as “angle” and “triangle”, imply that the sum of the angles of triangle is equal to two right angles. And Archimedes proved that his axioms on the lever that two unequal weights balance at distances from the fulcrum that are inversely proportional to their weights.

Three aspects of the ideal of deductive systematization are:

1. that the axioms and theorems are deductively related

2. that the axioms themselves are self-evident truths

3. that the theorems agree with observations.

   Philosophers and scientists have taken different positions on the second and third aspects, but there has been general agreement on the first.

One cannot subscribe to the deductive ideal without accepting the requirement that theorems be related deductively to axioms. Euclid and Archimedes utilised two important techniques tom prove theorems from their axioms: reudctio ad absurdum arguments, and a method of exhaustion.

The reductio ad absurdum technique of proving theorem “T” is to assume that “not T” is true and then to deduce from “not T' and the axioms of the system both a statement and its negation. If two contradictory statements can be deduced in this way, and if the axioms of the system are true, then “T” must be true as well.

The method of exhaustion is an extension of the reductio ad absurdum technique. It consists of showing that each possible contrary of a theorem has consequences that are inconsistent with the axioms of the system.

Euclid's geometry was deficient with regard to the requirement of deductive relations between axioms and theorems and was later reacted into rigorous deductive form by David Hilbert in he latter part of the nineteenth century.

Descartes- ideal of deductive hierarchy of propositions

Descartes agreed within Bacon that the highest achievement of science is a pyramid of propositions, with the most general principles at the apex. But he, unlike Bacon, was commited to the Archimedian ideal of deductive hierarchy of propositions.

Descartes vision of science combined the Archimedian, the Pythagorean and the atomists points of view. For Descartes the ideal of science is a deductive hierarchy of propositions, the descriptive terms of which refer to the strictly quantifiable aspects of reality, often at a sub macroscopic level. He was influenced to accept this ideal by his early success in formulating analytic geometry. Descartes called for a universal mathematics to unlock the secrets of the universe, much as his analytic geometry had reduced the properties of geometrical surfaces to algebraic equations.

From a more general principle of motion (all motion is a cyclical rearrangement of the bodies, if one body changes its location, a simultaneous displacement of other bodies is necessary to prevent a vacuum),Descartes derived other 3 laws. He then deduced from these laws seven rules of impact for specific kinds of collisions. These rules are incorrect , largely because Descartes took size rather than weight, to be determining factor in collisions. He claimed that the scientific laws he had elaborated were deductive consequences of the philosophical principles.

Descartes recognised that a statement about a type of phenomena be deduced from more than one set of explanatory premises E.g:

laws of nature

                                  statement of relevant circumstances

                                                   hypothesis 1

THEREFORE,

                                                         E

                                                laws of nature

                                 statement of relevant circumstances

                                                hypothesis 1

THEREFORE,

                                                      E

In such cases, Descartes specified that other effects be sought, such as are deducible from premises that include hypothesis 1, but are not deducible from premises that include hypothesis 2 (or vice versa).

Mill's Hypothetico-deductive model

John Stuart Mill's inductive methods were found unavailing in cases of the composition of causes- one cannot proceed inductively from knowledge that a resultant effect has occured to knowledge of its component causes. For this reason he recommended that a deductive method be employed in the investigation of composite causation.

Mill outlined a three stage deductive method:

1 the formulation of a set of laws

2 the deduction of a statement of the resultant effect from a particular combination of these laws

3 verification

Mill preferred that each law be induced from a study of the relevant cause acting separately, but he allowed the use of hypotheses not induced from phenomena. Hypotheses are suppositions about the causes which may be entertained by scientist in cases where it is nor practical to induce separate laws. He demanded of a verified hypothesis, not only that its deductive consequences agree with the observations, but also that no other hypotheses imply the facts to be explained. e.g Newton's hypotheses of an inverse-square central force between the sun and the planets. Mill claimed that Newton had shown, not only that the deductive consequences of this hypotheses were in agreement with the observed motions of the planets, but also no other force law could account for these motions.

Mill attributed to the deductive method an important role in scientific discovery. Jevons rejected Mill's claim that the justification of hypotheses is by satisfaction of inductive schema. In doing so, Jevons reaffirmed the emphasis placed on deductive testing by Aristotle, Galileo, Newton, Herschel, and many others.

References: A Historical Introduction to the Philosophy of Science by John Losee

Submitted by Ranjana

Inductive inference: It goes from particular to general. To be more specific, for eg. in inductive generalisation, all members of a class K have property P from the evidence that all the members of K have P, and observed members of an unlimited class are only some of its members. Certain forms of syllogistic inference, the kind of inference investigated and formulated by Aristotle, can be argued to proceed from the general to the particular. “All men are mortal, Socrates is a man, therefore Socrates is mortal” or “No men are immortal, Socrates is a man, therefore Socrates is not immortal” applies geaneral rule here, the major premise to a particular case. Ironically, this piece of reasoning, which clearly illustrates reasoning “from general to the particular,” would have been excluded by Aristotle from the domain of scientific knowledge, because he held that only species, not particulars are subject- matters of science.

Theories of science cannot be inferred inductively. The answer to this question is yes- because as we know induction is from detailed information to generalised form which is not always true in scientific theories. When a scientist tests a theory, he deduces from it observation statements; after verification of the later he proposes the theory, which means that it is more probable now. How much more depends on the various factors whose study must defered until reaches to the elements of the calculus of the probability . For example- Neptune confirmed Newton's theory of gravitation, for the existence of this planet a specified place in the solar system had been deduced from that theory.