Jay asked:

What is the difference between inductive and deductive reasoning? Would you give an example of
each?

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A deductive argument's premises strictly entail its conclusion: that conclusion cannot be false ifthe
premises are true. In the case of an inductive argument, however, the conclusion is only probable in
the light of the premises: the conclusion might be false even if the premises are true.

Here's an example of a deductive argument:

"Premise 1: All human beings are mortal

Premise 2: Socrates was a human being

Conclusion: Socrates was mortal."

Socrates cannot — logically cannot — be immortal if all men are mortal and Socrates is a man. To
deny the conclusion while affirming the premises would be to contradict oneself. But how might we
know whether Premises 1 and 2 are true?

Unfortunately (at least for those insist that deductive arguments alone are the royal road to
knowledge), only inductive arguments can incline us to accept those premises. The reader, for all any
one knows, may never die, which would falsify Premise 1. Future historical research may undermine
the historicity of Socrates, thereby falsifying Premise 2. Both "mays," however, are only "theoretical,"
not sufficient reasons to doubt the premises, let alone regard them as false.

"The sun has always arisen in the past, therefore it will rise tomorrow," expresses an inductive
argument: the conclusion does not strictly follow from the premise, but the premise inclines one
strongly in favor of the conclusion. By the norms of deductive reasoning, an inductive argument is a
fallacy. ("Attempts to justify inductive reasoning by deductive norms have failed in the past; therefore,
so will future such attempts," is also an inductive argument. Perhaps the reader will succeed where
others have failed.)

In courts of law, juries are required to arrive at verdicts that they believe the evidence warrants
"beyond a reasonable doubt," but not beyond theoretical doubt. To deny a jury verdict while affirming
the evidence that jury assessed would notbe to contradict oneself. The history of overturned verdicts
is not a history of formal contradictions. Juries may deduce their verdicts unerringly, but the evidence
from which they deduce them is arrived at only inductively.

Tony Flood

An interesting question. Some regard this as an unbridgeable gulf, others regard one as derivative
from the other.

Deduction, classically, is the process of analysis, in which one finds properties that are inherent in
something. If all men are mortal, and Socrates is a man, then we deducethat Socrates must be
mortal. Induction, classically, is the process of synthesis or extrapolation, in which one infers
properties of things one has not encountered. Thus, if the first three crows you see are black, then
you inducethat all crows are black.

C.S. Peirce analyzed logical thought this way:

Roughly speaking, according to Peirce (e.g., Peirce, 1992, pp. 188-189; Peirce, 1998, p. 95), there
are three basic types of logic, derived from the three-part syllogism. This syllogism consists of R, a
rule: (the beans in this bag are white), C, a case of the rule: (these particular beans are from the bag),
E, a result: (these beans are white)

By altering the order of the elements in this expression, Peirce realized that one could symbolize
entirely different types of thinking. Thus, deduction consists of statements in the above order: (1) R,
C, E; induction in the order (2) C, E, R; and hypothesis construction (also termed "abduction"), the
order (3) R, E, C.

Peirce, C. S. (1992). "Deduction, induction, and hypothesis" in N. Houser & C. Kloesel (Eds.), The
essential Peirce: selected philosophical writings(Vol. I, pp. 186-199). Bloomington, IN: Indiana
University Press.

Peirce, C. S. (1998) "On the logic of drawing history from ancient documents, especially from
testimonies" in N. Houser & A. De Tienne & J. R. Eller & C. L. Clark & A. C. Lewis & D. B. Davis
(Eds.), The essential Peirce: selected philosophical writings(Vol. II, pp. 75-114). Bloomington, IN:
Indiana University Press.

Steven Ravett Brown

Inductive reasoning involves inferring from a number of previously observed cases that the next case
will follow the same general pattern. For example, all the bread I've eaten in the past has been
nutritious and not poisonous. So when I buy another loaf of bread in Sainsbury's I assume that this
loaf of bread is nutritious and not poisonous! So inductive inferences usually have the following form:

All, or most, observed Fs are Gs

This is an F

Therefore this must be a G

We can substitute different variables for F and G to form many different inductive arguments. So in
the example given above, F is a loaf of bread, and G is nutritious, not poisonous. Bernard Williams
gives an example of inductive inference made by a chicken! The chicken has observed on a number
of occasions that when the farmer's wife comes out in the morning, she feeds him. So when the
chicken sees the farmer's wife come out again it assumes that it will be fed. However, this time it is
killed instead. This example shows that inductive arguments can only give you conclusions that are
probably true.Inductive arguments can provide good evidence for a conclusion but this is not enough
to provide us with certainty.

In contrast, deductive reasoning can provide us with valid arguments that logically entail the truth of
their conclusions i.e. they enable us to prove that something must be the case. An argument is
deductively validif and only if it is impossible for the premises to be true and the conclusion false i.e.
an argument is valid if it is inconsistent to assert the premises and to deny the conclusion, as the
conclusion is a logical consequence of the premises. An example of a simple deductive argument can
be given as follows:

All men are mortal

Socrates is a man

Therefore, Socrates is mortal

If Socrates is a man then he must be mortal because all men are mortal.

So the main difference between deductive and inductive arguments is that valid deductive arguments
give us conclusions that must be true, whilst inductive arguments give us conclusions that are
probably true.However, this does not mean that inductive arguments are the only good ones. In
everyday life we rely heavily on inductive inferences, as the example of the loaf of bread given above
indicates!

Samantha Solomons