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The Categorical Converter: Why I Constructed It There are two major reasons why I constructed the Categorical Converter, one practical and one perverse.
In 1989 I was given the task of teaching first year logic students. In particular, I had to teach them the rules of contradiction, conversion, and the rest. The rules as represented on the Square of Opposition were easy to teach; students to easily see which rule or sequence of rules would lead from premise to conclusion. However, once we got to obversion, conversion and transposition, it got a lot harder.
In particular, the following question perplexed
both myself and my students:
I began by tracing the routes from
The rule for selecting which rule to start with
which emerged was the following: Now why couldn't any of the dozens of logic texts I consulted say that? I ask you!
Stripped of all words - including such suggestive
words as Or - as I picture it - it is a map without any place names.
When viewed that way, it is The arrangement of the lines seems entirely arbitrary.
Even if we use
The reason why the lines are where they are,
of course, is that inferences from one proposition
to another should be
In the Categorical Converter, however, truth
is introduced by means of the
But even
Such
a system would be
The only reason we use the structure we actually
use is that the So: my perverse reason is that this is one more way of showing that logic does not represent a priori necessary truth. Rather, logic follows from emprical observation. Logic works the way it does because the world works the way it does, and not the other way around. This ends my explanation of why I created the categorical Converter. From here you may view the Converter, learn how to use it, or learn how to construct one.
For Educators Stephen Downes Guide to the Logical Fallacies Copyright © Stephen Downes, 1995-2001 stephen.downes@ualberta.ca |