| Analogy Essay, Research Paper
analogy
Similarity in several respects between discrete cases. A logical argument
by analogy relies upon an inductive inference from the supposition that things
are similar is certain known respects to the likelihood that they are also similar in
some further unknown respect.
Example: “Jennifer enjoys listening to the music of Beethoven,
Mahler, and Bartok. Susan and Harold also like Beethoven, Mahler, and
Bartok. Chris enjoys listening to Beethoven and Mahler. Therefore, Chris
would probably like the music of Bartok, too.”
The degree of reliability achieved by such an argument depends upon the
extent and nature of the similarities that hold between the instances in its
premises and the new case in its conclusion.
Also see DPM, Keith J. Holyoak and Paul Thagard, Allison Barnes and
Paul Thagard, and Am?lie Frost Benedikt.
Analogical Reasoning
The simplest variety of inductive reasoning is argument by analogy, which takes note
of the fact that two or more things are similar in some respects and concludes that they are
probably also similar in some further respect. Not every analogy is an argument; we
frequently use such comparisons simply to explain or illustrate what we mean. But
arguments by analogy are common, too.
Suppose, for example, that I am thinking about buying a new car. I’m very likely to
speak with other people who have recently bought new cars, noting their experiences with
various makes, models, and dealers. If I discover that three of my friends have recently
bought Geo Prizms from Burg and that all three have been delighted with their purchases,
then I will conclude by analogy that if I buy a Geo Prizm from Burg, I will be delighted, too.
Evaluating Analogies
Of course, this argument is not deductively valid; it is always possible that my new car
may turn out to be an exception. But there are several considerations that clearly matter in
determining the relative strength or weakness of my inductive inference:
1.Number of instances. If five friends instead of three report their satisfaction with
the model I intend to buy, that tends to make it even more likely that I will be satisfied,
too. In general, more instances strengthen an analogy; fewer weaken it.
2.Instance variety. If my three friends bought their Prizms from three different
dealers but were all delighted, then my conclusion is somewhat more likely to be true,
no matter where I decide to buy mine. In general, the more variety there is among the
instances, the stronger the analogical argument becomes.
3.Number of similarities. If my new purchase is not only the same make and model
from the same dealer but also has the same engine, then my conclusion is more likely
to be true. In general, the more similarities there are between the instances and my
conclusion, the better for the analogical argument.
4.Relevance. Of course, the criteria we’re considering apply only if the matters with
which they are concerned are relevant to the argument. Ordinarily, for example, we
would assume that the day of the week on which a car was purchased is irrelevant to
a buyer’s satisfaction with it. But relevance is not something about which we can be
terribly precise; it is always possible in principle to tell a story in the context of which
anything may turn out to be relevant. So we just have to use our best judgment in
deciding whether or not some respect deserves to be considered.
5.Number of dissimilarities. If my friends all bought Geos with automatic
transmissions and I plan to buy a Geo with a standard transmission, then the
conclusion that I will be delighted with my purchase is a little less likely to be true. In
general, the fewer dissimilarities between instances and conclusion, the better an
analogical argument is.
6.Modesty of conclusion. If all three of my friends were delighted with their auto
purchases but I conclude only that I will be satisfied with mine, then this relatively
modest conclusion is more likely to be true. In general, arguments by analogy are
improved when their conclusions are modest with respect to their premises.
?1997, 1998, 1999 Garth Kemerling.
Questions, comments, and suggestions may be sent to:
gkemerling@delphi.com
Inductive Inferences
When an argument claims merely that the truth of its premises make it likely or
probable that its conclusion is also true, it is said to involve an inductive inference. The
standard of correctness for inductive reasoning is much more flexible. An inductive
argument succeeds if its premises provide some legitimate evidence or support for the truth
of its conclusion. Although it is therefore reasonable to accept the truth of that conclusion, it
would not be completely inconsistent to withhold judgment or even to deny it.
Inductive arguments, then, may meet their standard to a greater or to a lesser degree,
depending upon the amount of support they supply. No inductive argument is absolutely
perfect or entirely useless, although one may be said to be relatively better or worse than
another in the sense that it recommends its conclusion with a higher or lower degree of
probability. In such cases, relevant additional information often affects the reliability of an
inductive argument by providing other evidence of the likelihood of the conclusion.
It should be possible to differentiate arguments of these two sorts with some accuracy
already. Remember that deductive arguments claim to guarantee their conclusions, while
inductive arguments merely recommend theirs. Or ask yourself whether the introduction of
any additional information, without changing or denying any of the premises, could make the
conclusion seem more or less likely; if so, the pattern of reasoning is inductive.
Truth and Validity
Since deductive reasoning requires such a strong relationship between premises and
conclusion, we will spend the majority of this survey studying various patterns of deductive
inference. It is therefore worthwhile to consider the standard of correctness for deductive
arguments in some detail.
A deductive argument is valid when the inference from premises to conclusion is
perfect:
If the premises of a valid argument are true, then its conclusion must also be true.
It is impossible for the conclusion of a valid argument to be false while its premises
are true.
(Considering the premises as a set of propositions, we will say that the premises are true
only when each and every one of those propositions is true.) Any deductive argument that is
not valid is invalid: it is possible for its conclusion to be false while its premises are true, so
even if the premises are true, the conclusion may be either true or false.
Notice that the validity of the inference of a deductive argument is independent of the
truth of its premises; both conditions must be met in order to be sure of the truth of the
conclusion. Out of eight distinct possible combinations here, only one is ruled out:
Premises
Inference
Conclusion
True
Valid
True
XXXX
Invalid
True
False
False
Valid
True
False
Invalid
True
False
The only thing that cannot happen is for a deductive argument to have true premises and a
valid inference but a false conclusion.
Some logicians designate the combination of true premises and a valid inference as a
sound argument; it is a piece of reasoning whose conclusion must be true. The trouble with
every other case, in which either one of the premises is false or the inference is invalid or
both, is that it gets us nowhere. The conclusions of such arguments may be either true or
false, so they are entirely useless in any effort to gain new information.
?1997, 1998, 1999 Garth Kemerling.
Questions, comments, and suggestions may be sent to:
gkemerling@delphi.com
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