Analogy
Analogical reasoning is used when there are two items, X and Y, that a similar
in some way. Analogy involves arguing
from
the known similarities between
two things, X and Y, to the existence of further similarities between them. That
is, one thing is inferred to be similar to another thing in a certain respect, on the
basis of the known similarity between the things in other respects. This can be
expressed in a diagram:
Premise 1
Rule R says: “X has attribute A”.
Premise 2
X is similar to Y
Conclusion 1
Rule R says: “Y has attribute A”.
Conclusion 2
Rule R says: “Both X and Y have attribute A”.
Figure 4.4 Form of Analogy
Probability
Probability performs two functions. One is a descriptive function. It describes
how certain we are about the truth of something. For example, when we
require reassurance about something we ask: “Are you 100% sure?” If we
choose to bet on a horse race the bookmaker will give us odds based on
probability. Odds of nine to one mean that the horse as nine chances of losing
compared to one chance of winning. In other words it has a 10% chance of
winning.
A second function of probability is derivative. When one or more probabilities
are known and quantified further probabilities can be derived by rules based
on deduction. For example, if there is a 60% chance that an event will happen
we can use the complementarity rule to devise the probability that the event will
not happen. The probability of an event not happening is the complement of
the probability that it will happen. In the example the probability of the event
not happening is (100-60)% namely 40%.
To give another example, assume that the probability of our winning a
guessing competition is 1 in 10, namely 10%. Assume that the probability of
our football team winning a difficult match is 2 in 10 namely 20%. Given that
these events are independent the probability of two happy outcomes –
our
winning the guessing competition and our team winning the match – is derived
by the multiplication rule. We multiply the two probabilities. Doing this (1/10 x
2/10) gives us 2/100 which is 2%.
Comparison
It is useful to compare four of the forms of logical reasoning namely
deduction, induction, abduction and analogy. To compare these means of
reasoning, we start with two events, A and B, and a rule, Rule R. Rule R says
A causes B so that where there is A there will be B. When Rule R is
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