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MICHAEL
LEVIN
A
LITTLE ABOUT LOGIC
Logic.is the abstractstudy of
argument.
Since philosophy is both highly
abstract and concerned with arguments, philosophers take a keen interest in
this subject.
The best approach to logic is to reflect that arguments may be criticized
in two ways. Sometimes when we say "That's a bad argument," wc mean
that one or more of its premises arc incorrect. Should someone reason that
Nebraska has a major canal because the Panama Canal is in Nebraska, you
would probably say, "That's ridiculous  the Panama Canal is not in
Nebraska."
An argument can go wrong in another way, however. Its premises may
be impeccable, but the reasoning by which they (allegedly) lead to the
conclusion is faulty. For instance:
P(remise). Bram Stoker's novel Dracula is contains a great deal of
vampire lore.
Therefore,
C(onclusion). Bram Stoker must have been a vampire.
The premise is true; Dracula does contain a lot about vampires.
However, it is a mistake, or fallacy, to infer from this that its author must
have been a vampire; after all, Moby Dick contains a great deal about
whales, but Herman Melville was not a whale. Or else, someone might
reason this way:
.
,
t
PI .
All fishermen are liars.
P2 .
John is a lim',
Therefore,
C.
John is a fisherman.
You might at first see nothing wrong with this inference, hut a moment's
reflection shows that C docs not follow from P I and P2 Even if all
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fishermen are liars, there may be other liars as well, for instance golfers. "PI
and P2 are consistent with lohn being a mendacious golfer rather than a
fisherman. Some fallacies arc so easily identified they have acquired names:
the one just illustrated is calling affirming the consequent.
Formal logic identifies patterns of reasoning that reliably lead from
premises to conclusion. We arc all familiar with such patterns, which are
readily recognizable when laid out, For instance,
if
X, Y, Z,
...
stand for
any sentences whatever, it is clear that the pattern
of reasoning called
hypothetical syllogism, namely
PI.
If
X then Y.
P2.
If Y then Z.
Therefore,
C.
If X then Z.
is good reasoning. To say this reasoning is "good" means that, if premises
P I and P2 are both true, the conclusion must be true. It is impossible for
both "If X then Y" and "If Y then Z" to be true, yet
"If X then Z" be false.
Another pattern with this agreeable property is the disjunctive syllogism:
PI . X or Y.
P2. Not X.
Therefore,
c.Y.
Once again,
it is impossible for both premises to be true while the
conclusion is false. If the alternatives are X and Y, and X is ruled out, only
Y
remains.
The property illustrated by hypothetical syllogism and disjunctive
syllogism is called validity: A pattern is valid when, given that all its
premises arc true, its conclusion must be
true. Particular arguments arc
valid when their patterns are valid. Thus
P I.
Manitoba is either in the US or Canada.
P2.
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 Spring '09
 Silverman
 Dracula

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