Section 36:
Choosing the Right Form
, Barker, pp. 218220.
***Read the section, then the following additional comments.
Please note that for the rest of this course we are not following the order of the textbook
directly.
In this lesson we want to bring together some of the principles from the first part of the course.
More specifically, we are pulling together a few of the ideas involved in deductive reasoning into
a more practical setting.
The point is this:
very rarely do people innately follow the standard
forms of deductive logic.
And even less likely are they going to say, “I am now expressing my
point in terms of quantificational form,” or, “I will now give you a categorical syllogism.”
Thus, if I am a logician, and I need to analyze someone else’s arguments, one of the first things I
need to do is to decide,
which is the best logical form to understand the argument?
We are limiting our discussion for now to deductive arguments.
In the next two lessons we will
also look at inductive arguments, but their situation is sufficiently different to put them aside for
the time being.
These are the options from this course for deductive arguments:
1.
categorical logic;
2.
truthfunctional logic;
3.
quantificational logic.
Now, as we have seen, quantificational logic is the most powerful method of the three; it
combines categorical and truthfunctional principles.
In fact, categorical logic is only a small
subset of quantification, and truthfunctional logic is incorporated into quantification.
Thus,
theoretically, it could always be the method of choice to evaluate an argument.
However, quantificational logic can also be the most cumbersome of the three, precisely because
it is so much more comprehensive.
There is no need to make things harder on ourselves than is
absolutely necessary.
Thus, it is much better to let the given argument give us sufficient clues to
decide which form to choose.
On the whole, the rule of thumb has to be:
the more
straightforward, the better.
Here are the telltale signs to look for.
1
LESSON 11
Applying Principles
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If the argument contains
1.
sentences connected with the truthfunctional
operators:
“and,” “or,” “ifthen,” etc.
2.
classes of things potentially connected with a form
of “to be,” without truthfunctional operators, such
as “or,” or “ifthen”
3.
Combinations of 1. and 2.
choose
1.
truthfunctional logic
2.
categorical logic
3.
quantificational logic
A second important question is by what method to evaluate an argument.
The danger in
assessing whether any argument is valid or not is that
a)
we might have used the wrong method;
b)
we might have used the right method in a wrong way.
After all, human beings are fallible, and taking a course in logic does not guarantee that we will
be perfect thinkers from now on.
So, we must always be careful how we proceed.
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 Spring '11
 BrentKelly
 Logic, Barker

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