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Critical Thinking By Example

 Chapter 1: Elementary Standardizing
  Quiz 1.1 Quiz 1.2 Quiz 1.3 Quiz 1.4 Quiz 1.5

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.

 
   
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