Extracting arguments with multiple inferences
Objectives
- Identify the difference between the conclusion of an argument and an inference made as a premise
- Be able to extract complicated arguments into standard form
In section two I covered the basics of extracting arguments into standard form. You may have noticed however that the arguments we extracted were rather simple. Arguments get complicated and it is thus important to make sure that we can extract complicated arguments. One way that arguments can get complicated is by having multiple inferences.
An inference is made when a set of propositions is used to imply some other proposition. For example:
- Cats are blue
- All things that are blue are dogs
- Thus, cats are dogs
Premises 1) and 2) have been used to imply 3), thus an inference has been made. In section two we only covered arguments that make one inference; however, there can be multiple inferences made in an argument. For example:
- Cats are blue
- All things that are blue are dogs
- Thus, cats are dogs (4, 5)
- All things that are dogs are horses
- Thus, cats are horses (6, 7)
Notice that 4) and 5) imply 6) while 6) and 7) imply 8). Furthermore, notice that 6) includes the conclusion indicator ‘thus’ even though it is not the conclusion. Thus, it seems like conclusion indicators can help you find any inference (not just conclusions), and we should thus describe them as inference indicators.
Also, notice that I labeled which premises a specific inference was made from by listing the numbers of those premises in parenthesis at the end of the written inferred proposition.
When you are extracting an argument, you will want to figure out which inference is the conclusion of the argument and which inferences are mere premises. To do this you ultimately need to ask yourself, “what is the ultimate goal of this argument?” Or “what is the arguer trying to convince me of?” The answer to that question will likely be your conclusion.
Furthermore, you can often tell by considering the logic of the argument. Consider this argument:
- Cats are blue
- All things that are blue are dogs
- Thus, cats are dogs (9, 10)
- All things that are dogs are horses
- Thus, cats are horses (11, 12)
The argument above would not make sense if 11) and 13) swapped places. If they did then it would clearly be an illogical argument, so you can thus determine that 11) probably comes before 13).
