Material covered in this chapter
·
1.1 Two
Conventions for Standardizing
·
1.2 Five
argument Types

1.1
Two Conventions for
Standardizing
To standardize an argument is to
break it down into its components in a manner that shows
the logical relationships between the parts. An
argument, in our technical sense, is a reason or reasons
offered in support of a conclusion. So, for anything to
qualify as an argument it must have two components: at
least one reason and one conclusion. Standardizing
involves identifying these component parts. Thus with
respect to example 1.1:
Example 1.1: A simple argument

John is over two
meters tall, so he is tall.

The conclusion is "he is tall", and the reason to
believe the conclusion is "John is over 2 meters tall".
If all arguments were as
elementary as example 1.1, there would be little call to
develop standardization conventions, but arguments can
be quite complex, and so we need to develop some
notation to keep track of everything. One variant,
'standard notation', designates reasons or premises with
a 'P' and an associated numeral, and a conclusion or
conclusions with a 'C' and an associated numeral. Thus,
example 1.1 in standard notation would be presented as
follows:
Example 1.2: A simple argument in standard
notation

P1: John is over two
meters tall.
C: John is tall.

The premise, 'P1', is offered in
support of the conclusion, 'C'. A second convention
involves diagramming. We can insert numerals into 1.1
like so:
Example 1.3: A simple argument with numerals
inserted

[1] John is over two
meters tall, [2] so he is tall.

The associated diagram is given
in 1.4:
We read diagrams from
the bottom up, with each arrow representing
'therefore'. In other words, we read 1.3 as 1,
therefore 2, and substitute in the propositions
for 1 and 2, that is, [1] John is over two
meters tall, therefore [2] John is tall.

1.2
Five Argument Types
The arguments we will discuss in
this work are either one of the five types given in
example 1.5, or a combination of two or more of these
five argument types.
We have seen a simple argument above (example 1.1). Here
are examples of the remaining four:
Notice that the numbers function merely like
names, their order or size make no difference.
We could have just as easily written '157' as
opposed to '1'. Also, look at 1 in the argument.
It is a main premise because it supports the
main conclusion, but 1 is also a conclusion,
since 2 supports it. We will term this a
'subconclusion'. Something that is both a
conclusion and a premise for a further
conclusion is a subconclusion. 2 is a
subpremise, since it supports a subconclusion,
not the main conclusion.
In other
words, any premise that does not directly
support a main conclusion is a subpremise.
Notice how
in a linked argument the premises
must work together to support the
conclusion. [3] on its own does not
support the conclusion without the
knowledge that Lassie is a dog, and
[2] does not support the conclusion
without the knowledge that dogs are
mammals. So, [2] and [3] need each
other to provide any reason to
believe the conclusion.
Notice that
both [2] and [3] on their own
provide some reason to believe the
conclusion. The two independent
reasons converge on the same
conclusion.

Premise [1] is offered
in support of two distinct conclusions: [2] and
[3]. o:p>
You may want to try the
chapter exercises above.


