PROBLEMS OF INDUCTIVE LOGIC
OUTLINES
1.0 INTRODUCTION
2.0 DEFINITION OF INDUCTIVE LOGIC
2.1 TYPES OF INDUCTIVE LOGIC
3.0 PROBLEMS OF INDUCTIVE LOGIC
3.1 DAVID HUME'S VIEW
3.1.2 KARL POPPER'S VIEW
3.2 WESLEY C. SALMON'S VIEW
4.0 CONCLUSION
BIBILOGRAPHY
1.0 INTRODUCTION
Logic or argumentation is a process to look for
reasons. logic uses arguments which are sets of statements or propositions each
consists of premises and conclusion. Conclusions are derived from the
statements (premises).
Logic can either
be deductive (deduction) or it can be inductive (induction). In an argument,
for the assumption that the premises is true and it is impossible that the
conclusion is false, the argument is deductive, but if the truth of conclusion
is presumable then it is inductive argument. One can believe the conclusion if
the premises are justified and there is a proper connection between the
premises and conclusion of the argument . The connection between the conclusion
and the premises is very important, because, otherwise, the reasoning will lead
us to a false conclusion.
v
For example, if we say: Mr. Ogunbure a logician , has been teaching
us Logic for the last two years.
Therefore We will become medical
doctors. This does not make sense,
because being student of a logic for long period, one may become a logician or
a critical thinker for example, but not, a medical doctor.
The problem of
induction is among one of the problems being faced which needs major studies.
Before going deeper into the problem of
Inductive reasoning Although inductive reasoning exists everywhere in
science but it is philosophically controversial. There are problems to describe
the general principles to follow in inductive reasoning or argument, problem of
describing and to justify the inferences or conclusions problem of induction
. induction we need to define and
explain inductive logic.
To repeat, inductive reasoning never conclusively supports
a conclusion. It is always subject to
the degrees of confidence that range from the credible to the probable.
2.0
INDUCTION OR INDUCTIVE LOGIC
An
inductive argument is one in which there is no claim of conclusiveness, in an
inductive argument the premise provide partial support to the conclusion [1]an
inductive argument takes a very different claim not that the premises gives
conclusive ground for the truth of its conclusion but only that its premise
provide some support for the conclusion
inductive argument therefore cannot be valid or invalid as of deductive.
Inductive argument can be evaluated as strong
or weak base on the support it receive from the conclusion in an inductive argument even when the
premise are true the conclusion will be false the[2]
difference between inductive and deductive argument is that deductive inference
move from general to particular why inductive infrences moves from particular
to genaral
Induction" as reasoning from the specific to the
general. These definitions are outdated and inaccurate. For example, according
to the more modern definitions given above, the following argument from the
specific to general is deductive, not inductive, because the truth of the
premises guarantees the truth of the conclusion:
v
The members of the Dominican family are
Sampana Eric and Godwin. Sampana wears
glasses. Eric wears glasses. Godwin wears glasses. Therefore, all members
of the Dominican family wear glasses. Moreover, the following argument, even
though it reasons from the general to specific, is inductive:
v
It has rained in Ibadan every December in
recorded history. Therefore, it will rain in Ibadan this coming December.
An inductive argument is an argument that is intended by
the arguer merely to establish or increase the probability of its conclusion.
In an inductive argument, the premises are intended only to be so strong that,
if they were true, then it would be unlikely that the conclusion is false.
There is no standard term for a successful inductive argument. But its success
or strength is a matter of degree.
Inductive
arguments can take very wide ranging forms. Inductive arguments might conclude
with some claim about a group based only on information from a sample of that
group. Other inductive arguments draw conclusions by appeal to evidence or
authority or causal relationships. Here is a some what strong inductive
argument based on authority:
v
The police said Seun committed the murder. So,
Seun committed the murder. Here is an inductive argument based
on evidence: Two independent witnesses claimed Seun committed the murder.
Seun's fingerprints are the only ones on the murder weapon. Seun confessed to
the crime. So, Seun committed the murder.
This last argument is no doubt good enough for a jury to
convict Seun, but none of these three arguments about Seun committing the
murder is strong enough to be called valid. At least it is not valid in
the technical sense of 'deductively valid'. However, some lawyers will
tell their juries that these are valid arguments, so we critical thinkers need
to be on the alart as at how people around us use the term
Inductive
reasoning or induction is the process of reasoning in which it is believed that
the premises of an argument support the truth of conclusion, but they don’t
ensure its truth. It is true even for a good argument, where it is quite
possible that there will be false conclusion even if the premise is true. An
inference is said to be inductive inference if it passes from singular
statements to universal statements or theories. That is to say that induction
leads from specific truth to general truth (knowledge expanding). Inductive
inferences that we draw from true premises are not 100% reliable, because they
may take us to the false result from true premises. Induction takes individual
instances and based on those instances, some generalization is made. For
example:
v
Students A, B, and C in Dominican are
Seminarians. Based on the above premise,
a general conclusion is drawn as following.
All the students in Dominican are Seminarians.
Many scholars,
historically like, David Hume, Karl Popper and David Miller have discouraged
inductive reasoning. They have rejected and disputed its existence. Inductive reasoning has been divided in two
categories based on the strength of its effect; strong induction and weak
induction.
2.1 TYPES OF INDUCTIVE LOGIC
In strong inductive logic the truth
of a premise would make the truth of a conclusion probable, but not confirmed.
In other words, the truth of a premise can make the conclusion more likely to
be true, but it can’t guarantee its 100% truth. Consider the argument:
v
All observed people in Bodija are
literate. Therefore All people in Bodija are literate.
v
All Dominican brothers wear there harbit to
class therefore all Dominican student were harbit to class.
Here we actually
induce the general or the universe from the particular or individual. But the
conclusion is not certain. The result above may be false. There may be
illiterate people in Bodija. It can be certain if, by some means, the statement
„there is at least one illiterate person in Bodija‟ is proved false. This is a
proof by falsification.
2.2 WEAK INDUCTIVE LOGIC
Weak induction,
on the other hand, induce conclusion from the premise, but it is not the
correct one. There is no proper link between the premise and the conclusion.
Like:
v
I always put the book on table. Therefore
All the books are on the table.
You may be in the
library studying introduction to logic of Science book and then you put it on
the table after reading it. Based on this premise, you draw a conclusion that
all the books are on the table just because you have put the book on table.
This will lead to generalization based on the certainty of premise. This
conclusion will be wrong. This does not make sense to link the conclusion with the
premise. The link between the two is very weak. If we use our knowledge from
other sources, we can see that the conclusion drawn is wrong. There is no
guarantee that all other students put their books on the table in the library
after reading. They might return the book to the librarian, who put the books
in the book boxes in the library, or the students borrow the books and put it
in their bags (instead on table), or they put the book on table outside the
library, and so on. Only you put the book on the table but most of the books
are already in the vertical cupboards of the library, some are with students
for reading, and so on. The conclusions drawn overgeneralizations by this way
are actually Scientific laws and theories are actually universal generalization
which surpasses the finite number of observations and experiments, on which the
theory is based, by a great margin. These theories are confirmed by evidence
using induction. This confirmation makes these scientific theories reliable,
trustworthy and justifies our belief on theories. If there was no inductive
confirmation, science would be just like a „blind guess‟. Induction leads to
creative inference where new theories are formulated from the evidence (logic
of discovery). After the new theories are formulated, then induction does
confirmation by connecting evidence to those theories logic of
justification.
THE PROBLEMS OF INDUCTIVE LOGIC
As mentioned earlier, induction leads
to a universal or general truth from specific truth. There is no reason or
obvious justification to predict universal truth from specific truth. A
conclusion drawn in this way may always be false. Now the question arises known
as the problem of induction, is that whether inductive inferences are
justified? If yes, under what conditions? Put this question in another way. Is
the induction indeed justified? If yes how?
Consider the arguments:
v Introduction to Logic
class will start at time 10:15 am.
Because It has been starting at
time 10:15am for the last two months.
And the well known Newton’s
Third Law of motion For every action
there is an opposite and equal reaction.
Can we believe on the conclusions drawn from the premises in the above
arguments? Is it possible for scientists to test/have tested each and every
action and found and judged the reaction? Also, is it possible for them to
verify that the actions for all those reactions are opposite and equal? Should
we trust today that “the Introduction to logic class will start at time
10:15am”? The scientists may have tested hundreds of actions/reactions where
they were equal and in opposite direction. But how can one be sure that the
ball will reflect back (in opposite direction) with the same (equal) velocity
after we throw it over the wall, considering the factors like speed of air and
wall resistance and so on as stated by the theory? We drew conclusion based on
induction. We can not use deduction, a logical movement, in all cases to
conclude from premises, if there is no syllogism to allow us for such movement.
Syllogism is a logical argument in which one argument is inferred from two
others of a certain form. So relying on induction could be a solution. In
induction, just we believe that if a situation holds in all observed cases
(tests the scientists carried out in the above example), then that will be true
for all other cases (the Newton’s Third Law) . Many scholars have different
ideas about the problem of induction. We present views of few philosophers.
DAVID HUME’S VIEW
According to Hume we can’t show that
induction is either reliable or reasonable. If some information about initial
conditions and rules or principles does not ensure a unique result or solution,
then that result or solution is said to be under determined. Beginning with
under determination, David Hume says that our observations do not necessitate
our predictions. He further suggests that the principles we use for our
inductive inferences are based on the uniformity of nature. Where we believe
that the things which are unobserved but are observable are quite similar to
the things we have observed. As a result, if we use the concept of uniformity
of nature as a basis for the inferences then the conclusion drawn by this way
will automatically be justified, if it is shown that the nature is really
uniform. But it can`t be deduced from what we have observed using uniformity
because uniformity itself is based on prediction. To reason to support
uniformity, we have the only one option of inductive argument, which in turn
will be dependent on uniformity leaving the problem unsolvable. He concludes
that the past history of induction can not be used to justify induction. The
successes in the past can not justify the success in the future.
Hume argues that
there is not. He believes that any inductive or empirical argument that we
would ordinarily take to be good is of the same kind as the argument that we
are worrying about ,and so cannot be used to justify that argument on pain of
circularity:
1. If the principle of the uniformity of nature is
justified, then it is justified either by deductive [2]reasoning or by
inductive reasoning. 2. The principle of the uniformity of nature is not
justified by deductive reasoning. 3. The principle of the uniformity of nature
is not justified by inductive reasoning. Thus, 4. The principle of the
uniformity of nature
The justification for (1) is plainly that all reasoning is
either deductive or inductive. This will depend upon what one means with the word
“inductive”. In older times, when people spoke of “induction” they just meant
what is today called “enumerative induction”. Enumerative induction is
inference of the form (or similar forms) 1. Hume have observed many times that
things of the type A are also things of the type B. Thus, 2. All A's are B's.
Today “inductive” means something like “not deductive” and so it would include
abductive reasoning as well. However, it is not really the case that the
difference between deductive and inductive arguments is well-define. The
justification for (2) is that all things justified by deductive reasoning
(alone) are necessary truths, and the principle of the uniformity of nature is
not a necessary truth, and thus, it is not justified by deductive reasoning. The
justification for (3) is that all inductive reasoning 'presupposes' or
'presumes' (obscure but insufficient space to clarify) the principle, and thus
to attempt to justifiy the principle would be using the very same principle and
thus be circular reasoning. The typical exposition ends here, but it really
needs a last step before it works. The last step being that all circular
reasoning is bad and gives no justification. We'll return to this later. The
inference (4) is plainly valid as the argument form is just denying the
consequent with the consequent having the form of a disjunction, and the denial
of the disjuncts being divide premises.
HUME AND INDUCTIVE GENERALIZATIONS
While all of the preceding forms
of arguments indicate specific forms of inductive reasoning, inductive
generalizations are a bit more generic. Inductive generalizations are basically
those forms of reasoning that take a small sample and try to create a larger
“truth” out of it. Put another way, “in inductive generalization, an inference
is made from a subset of a population, called a sample, to the whole of the
population. A sample may consist of people, objects, events, or processes,
about which something is observed. The results of the observation are
generalized to the larger group or population. This form of reasoning is
pervasive in our everyday lives. The easiest example so point to are poll
results. News organizations and independent organizations invest enormous sums
of money in this form of reasoning when conducting research on questions
ranging from the President’s job approval rating to the kinds of coffee that
consumers prefer most. In each case, the polling organization tries to compile
a representative sample, to ask its respondents targeted questions, and to
predict the answers of a larger sample. So, for example,[3]
pollsters knew before the 2000 election that Florida would probably decide the
election. They also knew that it would depend on voter turnout. Statistically
speaking, Florida was a tie. However, we also know that inductive
generalizations can fail given the problems with the predictions of these
models. In short, the mathematical
models that were used to declare Al Gore the winner of the state did not match
the reality of the situation (well, maybe it did but that is another story for
another day). Regardless, the exit polls in the more Democratic areas did not
accurately predict the margin of victory for Gore. Again, there are other
examples besides polls, but they are the clearest example of this form of
reasoning.
Evaluating
Inductive Hume is not just saying that we can never be certain about inductive
inferences (i.e., we can never be 100% certain that all ravens are black). This would be uncontentious: Most people would agree that there’s always
room for error in making an inductive inference. However, most people would at the same time
claim that we are justified in making (some) inductive inferences, even though
they aren’t 100% guaranteed to work (i.e., we think there are standards by
which we can judge good inductive inferences from bad ones). Hume is saying
that this is wrong: we are not reasonable
in believing any type of inductive inference..
Rationalism, on the other hand, claims that some matters of fact can be
known a priori (without recourse to experience). So a Rationalist can block Hume’s argument,
for Hume, to justify a method of inference requires knowing with confidence that
it works. There are weaker philosophy of
justification.
KARL POPPER’S VIEW ON INDUCTION
Karl Popper
agrees with Hume. We can relate our example of Newton’s Third Law of motion
with Karl [4]Popper’s
view about induction. According to Popper’s view, as the scientists have tested
hundreds of cases of actions/reactions where the actions and the analogous reactions
were equal and opposite to each other, does not mean that the feedback of an
action will be equal to that action and opposite next time as well. There is no
way to prove it rationally that the law will be fulfilled in next time as well
just because it got satisfied many times in the past. He thinks one can not justify the induction.
He supports his arguments by offering a deductive approach falsification. In
one of his book Objective Knowledge, [5]Karl
Popper presents his views about the problem of induction in the statement “I think that I have solved a major
philosophy problem: the problem of induction…. This solution has been particularly
fruitful, and it has enabled me to solve a good number of other philosophical
problems” In his solution to the problem
of induction, he completely rejects induction. Popper in another place
addresses the problem of induction with more tight hold . This leads us to the workable
problems of induction, which to start with, might organize thus: (a) Upon which theory should we rely for
practical action, from a rational point of view? (b) Which theory should we prefer for
practical action, from a rational point of view (a) is: from a „rational‟ point
of view, we should not rely on any theory, karl popper says no theory has been
shown to be true, or can be shown to be true (or „reliable‟). My answer to (b) is: we should prefer the
best tested theory as a basis for action.
In other words, there is no „absolute reliance but since we have to
choose, it will be „rational‟ to choose the best tested theory. This will be
„rational in the most noticeable sense of word known to me: the bestand I do
not know of anything more „rational than a well conducted critical
discussion" It is clear from the
above discussion that Popper doesn’t trust on any theory, because, in his
opinion, no one has either shown a theory to be true or can show it to be
reliable. He argues that as there is no theory which is reliable and can be
trusted, so one should select only the best tested theory
. A theory is
considered to be "the best tested so far", only if it is ranked “the
best tested theory” by the " essential
discussion”. He also doesn’t agree with
the concept to pleasure the inductive inference as some degree of “reliability”
or of “probability”. According to the “probability" concept, the
scientific statements can’t reach either truth or falsity. They can only get
“probable” values. If, according to the principle of induction, the statements
don’t get the values as “true” and get the label as “probable”, then nothing is
gained from those scientific statements.
The problem of induction may also He formulated as the
question of how to establish the truth [3]of universal statements which are
based on experience, such as the theory and theoretical systems of the
empirical sciences. For many people believe that the truth of these universal
statements is 'known by experience'; yet it is clear that an account of an
experience or of an observation or the result of an experiment can in the first
place be only a singular statement and not a universal one. Accordingly, people
who say of a universal statement that we know its truth from experience usually
mean that the truth of this universal statement can somehow be reduced to the
truth of singular ones, and that these singular ones are known by experience to
be true; which amounts to saying that the universal statement is based on
inductive inference. Thus to ask whether there are natural laws known to be
true appears to be only another way of asking whether inductive inferences are
logically justified.
WESLEY C. SALMON’S VIEW
Wesley Salmon
do not agree with Poppers views about problem of induction. According to
Salmon[6],
if a theory is considered to be the best tested theory so far, then best for
what? It can be best either for “theoretical explanation” or for “practical
prediction”. Salmon argues that as it is “the best tested theory” as a result
of “critical discussion” and from some other Poppers statements, so it is “the
best tested theory” for “theoretical explanation”. He doesn't agree that it can
be “the best tested theory” for “practical calculation” because Popper has not
provided any reason for that. Salmon mentions two reasons to use induction.
According to him, we use induction to predict the future so to remove our
intellectual curiosity and to take a decision of some importance about the
future events. He finally, reaches his end point about the problem that if we
want to make a practical decision then using only deduction is not suitable for
the problem of rational prediction. He suggests that it may be possible to
remove out the “inductive ingredients” from science, but it would make the
science a “bird without wings.
CONCLUSION
Inductive reasoning or induction plays a vital
role in scientific research. In this paper we have concisely exposed induction
and its problems both by David Hume and other philosophers. According to Hume
trying to justify induction poses a philosophical problem just as trying to
deduce an unanimous definition for philosophy is. Different scholars have different views about
induction. Wesley C. Salmon, favoring induction, thinks that induction is
necessary for science both in the case of intellectual inquisitiveness and practical
prediction. Karl Popper and David Hume both have concepts against of induction.
According to them, there is no reason to rely on the conclusions drawn using
induction. Karl Popper is also not in the favour of “probable” concept of
inductive conclusion. There is no single
point for all the scholars to arrive at. If we analyze the views of all the
philosophers, one can reach to the
point that conclusions by induction are not some thing to
put outside or inside of a “sharp” boundary using a “isolation” rule. Induction
gives conclusion which may lie on the wide band of border between true and
false, giving a probability based conclusion. So, dealing induction in a
“probable” manner, unlike the strict rule of “rejecting” or “accepting”
induction, is a reasonable solution to the problem which more likely favours
the views of Salmon.
Ø
REFERENCES
ü
[1] mr ogunbure note on logic
"definition of inductive logic
ü
[2] Peter Lipton, “Induction”, Philosophy of
Science
ü
[3] Wikipedia; the free encyclopedia,
“Inductive Reasoning”,
ü
[4] 4
See, for example, Popper's essay, ','Science: Conjectures and
Refutations," in his book, Conjectures and Refutations (New York and
London: Basic Books, 1962).
ü
5 Karl Popper,
"Philosophy of Science: A Personal Report," British Philosophy in the
Mid-Century, ed. C. A. Mace (London: Allen and Unwin, 1957), pp. 155- 91,
quotation from p. 181.
ü
6 Popper, "Philosophy of
Science," p. 183.
ü
[5]
Karl Popper, “Science: Conjectures and Refutations”, Philosophy of
Science: The Central. [6] Martin Curd and J. A. Cover, “Philosophy of
Science: The Central Issues.
ü
[7]
Wikipedia; the free encyclopedia, “Philosophy of Science.
ü
[8]
Wesley C. Salmon, “Relational Prediction”, Philosophy of Science:
ü [9] , ‘‘An Essay Towards Solving a Problems of inductive logic Dr. S. Radhakrishnan,Indian Philosophy Vol I,
pg 279
ü S.
Dasgupta - A history of Indian philosophy, Vol III. pg 53
ü Franco, Eli, 1987, Perception, Knowledge and Disbelief:
A Study of Jayarāśi's Scepticism
Franklin, J. (2001),The Science
of Conjecture: Evidence and Probability Before Pascal (Baltimore: Johns
Hopkins University Press), 232-3, 241.
ü Duns
Scotus: Philosophical Writings, trans. A. Wolter (Edinburgh:, 1962),
109-10; Franklin, Science of
Conjecture, 206.
ü Franklin, Science of Conjecture, 223-4.
[1] Mr Ogungbure definition inductive
logic logic note book
[2] Introduction to logic 8th
ediction by Irving M copi
[4] Karl popper on problems of
induction
[6] problems of induction by wesley
.c. salmon
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