What is Science 2
On the other hand, deductions in rationalism in Western
Knowledge make use of rules of inference, which are obtained through induction.
The rule if a=c and b=c, then a=b is nothing but a
generalization from limited observations such as if two people are equal in
height to a third person, then the two people concerned are themselves equal in
height to one another. The rule if a=b then b=a, or the
rule a=a are rules of inference obtained through induction by observing
a limited number of cases. These rules are not God given. Reasoning which
depends on rules of inference, obtained by induction cannot be justified
without induction that does not come under logic.
These rules of inference are static in the
sense “change” has been ignored. The
rule a=a is valid only if a does not change. If a changes
then what is identified as a does not exist as it is not the same a
that is encountered. To say that a= a, one needs to consider a as
an object that does not change. This is generalized from the observation of
“non-changing” properties of objects.
Change itself is a property that cannot be
deduced using two valued two-fold logic as exemplified by Zeno’s arrow.
However, we shall not discuss it here as it is beyond the scope of this essay.
If one considers a finite population,
makes a limited number of observations of a certain property of members of the
population and then extend the observations for the unobserved as well, it may
be called a concrete induction. However, if the population is infinite then the
induction is abstract as the conclusion cannot be grasped through the senses or
even imagined.
What we have tried to explain so far is
that empiricism and rationalism do not belong to water tight compartments but
depend on each other. Some people without being aware of it call themselves
both empiricists and rationalists, which seems to be correct even though
according to strict dualities in Western Chinthanaya, an empiricist cannot be
considered as a rationalist as well. What is discussed here is not related to
the so-called Copernican Revolution of Kant.
In western science, very often with or
without experiments observations are made (In Astronomy no experiments as such are
designed). Most of these observations depend on some basic knowledge that has
been acquired by the observers (experimenters as the case may be) through
concepts and “axioms”.
The observations are very often limited to
samples of population, and induction is called into play in arriving at an
“axiom” whether concrete or abstract. These inductive “axioms” could be tested
by considering other members of the population, but until a member is found to
the contrary the “axiom” is held to be valid. As Hume has observed people have
a tendency to come to conclusions by induction.
Learning Process
People and animals learn by trial and
error if left to themselves. It is revealed by experiments done with mice when
they are left to find their way through a mesh with blocks and openings. They
try one path, if they do not succeed they try another path and so on, until
they find their way out. Children left on their own follow the same method of
trial and error.
In western science scientists who want to
“explain” nature adopt the same method in arriving at “axioms” that “explain”
observations with respect to a property of the members of the population. This
method is known as abduction after the American Philosopher and Logician
Charles Sanders Peirce (1839 -1914). Abduction, though in the earlier
formulations of Peirce had similarities with induction, is entirely different
from induction. In abduction, in order to explain a set of observations a
hypothesis, an “axiom” is guessed. If the “axiom” does not lead up to the set
of observations, then the particular “axiom” is dropped and a different “axiom”
is introduced. The process is repeated until a satisfactory “axiom” is
obtained. The “axiom” if satisfactory, is sometimes called a theory. This is
what happens in abduction but it has to be elaborated in comparison with
induction and deduction. It has to be emphasized that satisfactory does not
mean true or correct.
We shall first discuss briefly deduction,
induction and abduction.
Deduction
In deduction there are definitions,
“axioms” and rules of inference in a given population. We restrict ourselves to the use of the word
inference only with respect to deduction. Depending on the population, we
identify either concrete deductions or abstract deductions. The population has
to be identified first, followed with definitions and “axioms”.
Consider first, a concrete example. Let
the population be a box of toys. It has to be understood that box, colour,
white and toy have been defined in a larger context, in a larger population.
Consider the property of colour of the toys. Let us begin with the “axiom” ‘All
toys are white’.
Deductions are made using rules of
inference. The rules of inference as shown above are arrived at by induction.
It has to be emphasized that the “axioms” are mere statements unless they had
been deduced in a different context. In any event the very first “axioms” are
not deduced, and are mere statements. Thus, reasoning alone leads us nowhere,
though many people have a kind of faith in the process. These people do not
believe in a God, after life, but believe in reason. Can they show that reason
is not a belief?
We shall consider two deductions one in a
finite population and the other in an infinite population.
Syllogism is a rule of inference obtained
by induction. If the objects in a population have the same property, then we
know that any object of the population must have that property. It can be
generalized as, if all M are P, all S are M, then all S are P. Applying this
syllogism to the toys in the box we deduce that since all toys are white, and
if some toys are selected from the bag, then the selected toys are white.
Let us now consider the case of the
population of straight lines. This is a population of infinite number of
members. Then starting with some of the definitions and axioms and theorems in
Euclidean Geometry, and the rule of inference if a+b=a+c, then b=c, it can be
shown that when any two straight lines intersect each other the alternate
angles are equal. (It is easy to see that the rule of inference if a+b=a+c,
then b=c, is also obtained by induction).
In deduction whether in a population of
finite number of members or of infinite members one starts with definitions and
“axioms” and conclusions are arrived at using rules of inference.
Induction
Induction as mentioned before is
generalization of a property of a sample(s) of members of the population to the
entire population. When the population is finite it is called concrete
induction, whereas, when the population is infinite it is called abstract
induction. The result by induction could be tested by considering members of
the population, other than in the sample(s).
Suppose we take a box of toys and select a
few members and find them to be white. Then by induction, we may say that all
the toys in the box are white. If we come across even one toy in the box, which
is not white, then our statement obtained from induction becomes invalid. Thus,
induction can also be taken as a test for the statement arrived at. Though this
is a population of finite members by considering the more famous examples such
as all swans are white or all crows are black we can say abstract induction can
be considered as a test as well.
Abduction
Abduction was introduced by Pierce, though
at first he himself could not see the difference between abduction and induction.
Abduction is guessing of an “explanation” (reason) of an observed property of
the members of a population.
Let us consider the case of falling
apples. One has to give a reason for the falling of the apples. One could say
that there is an affinity for the apples to fall to the earth, with heavy
apples having a strong affinity. However, apples come down with the same
acceleration, and one gives up one’s guess. Newton comes and guesses something
else, which happens to work, may be under certain conditions. Newton’s guess is
taken as the “reason” for the falling of the apples.