Logic -- Juvenile literature; Logic, Symbolic and mathematical
The other kind of Fallacy--'Fallacious Conclusion'--you will not
detect till you have marked BOTH Diagrams, and have read off the
correct Conclusion, and have compared it with the Conclusion which
the writer has drawn.
But mind, you mustn't say "FALLACIOUS Conclusion," simply because
it is not IDENTICAL with the correct one: it may be a PART of the
correct Conclusion, and so be quite correct, AS FAR AS IT GOES. In
this case you would merely remark, with a pitying smile, "DEFECTIVE
Conclusion!" Suppose, of example, you were to meet with this
Syllogism:--
"All unselfish people are generous;
No misers are generous.
&there4 No misers are unselfish."
the Premisses of which might be thus expressed in letters:--
"All x' are m;
No y are m."
Here the correct Conclusion would be "All x' are y'" (that is,
"All unselfish people are not misers"), while the Conclusion, drawn
by the writer, is "No y are x'," (which is the same as "No x' are
y," and so is PART of "All x' are y'.") Here you would simply say
"DEFECTIVE Conclusion!" The same thing would happen, if you were
in a confectioner's shop, and if a little boy were to come in, put
down twopence, and march off triumphantly with a single penny-bun.
You would shake your head mournfully, and would remark "Defective
Conclusion! Poor little chap!" And perhaps you would ask the
young lady behind the counter whether she would let YOU eat the
bun, which the little boy had paid for and left behind him: and
perhaps SHE would reply "Sha'n't!"
But if, in the above example, the writer had drawn the Conclusion
"All misers are selfish" (that is, "All y are x"), this would
be going BEYOND his legitimate rights (since it would assert the
EXISTENCE of y, which is not contained in the Premisses), and you
would very properly say "Fallacious Conclusion!"
Now, when you read other treatises on Logic, you will meet with
various kinds of (so-called) 'Fallacies' which are by no means
ALWAYS so. For example, if you were to put before one of these
Logicians the Pair of Premisses
"No honest men cheat;
No dishonest men are trustworthy."
and were to ask him what Conclusion followed, he would probably say
"None at all! Your Premisses offend against TWO distinct Rules, and
are as fallacious as they can well be!" Then suppose you were bold
enough to say "The Conclusion is 'No men who cheat are trustworthy',"
I fear your Logical friend would turn away hastily--perhaps angry,
perhaps only scornful: in any case, the result would be unpleasant.
I ADVISE YOU NOT TO TRY THE EXPERIMENT!
"But why is this?" you will say. "Do you mean to tell us that all
these Logicians are wrong?" Far from it, dear Reader! From THEIR
point of view, they are perfectly right. But they do not include,
in their system, anything like ALL the possible forms of Syllogisms.
Public-domain text, read in full here on John Shaqi.
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