Edward W. Porter wrote:
So is the following understanding correct?
If you have two statements
Fred is a human
Fred is an animal
And assuming you know nothing more about any of the three
terms in both these statements, then each of the following
would be an appropriate induction
A human is an animal
An animal is a human
A human and an animal are similar
It would only then be from further information that you
would find the first of these two inductions has a larger
truth value than the second and that the third probably
has a larger truth value than the second..
Edward W. Porter
Porter & Associates
24 String Bridge S12
Exeter, NH 03833
(617) 494-1722
Fax (617) 494-1822
[EMAIL PROTECTED]
Actually, you know less than you have implied.
You know that there exists an entity referred to as Fred, and that this
entity is a member of both the set human and the set animal. You aren't
justified in concluding that any other member of the set human is also a
member of the set animal. And conversely. And the only argument for
similarity is that the intersection isn't empty.
E.g.:
Fred is a possessor of purple hair. (He dyed his hair)
Fred is a possessor of jellyfish DNA. (He was a subject in a molecular
biology experiment. His skin would glow green under proper stimulation.)
Now admittedly these sentences would usually be said in a different form
(i.e., "Fred has green hair"), but they are reasonable translations of
an equivalent sentence ("Fred is a member of the set of people with
green hair").
You REALLY can't do good reasoning using formal logic in natural
language...at least in English. That's why the invention of symbolic
logic was so important.
If you want to use the old form of syllogism, then at least one of the
sentences needs to have either an existential or universal quantifier.
Otherwise it isn't a syllogism, but just a pair of statements. And all
that you can conclude from them is that they have been asserted. (If
they're directly contradictory, then you may question the reliability of
the asserter...but that's tricky, as often things that appear to be
contradictions actually aren't.)
Of course, what this really means is that logic is unsuited for
conversation... but it also implies that you shouldn't program your
rule-sets in natural language. You'll almost certainly either get them
wrong or be ambiguous. (Ambiguity is more common, but it's not
exclusive of wrong.)
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