Subset Arguments
Subset Arguments are a type of deductive argument that involves a specific logical structure. An argument is valid if the conclusion follows the premises. Here’s a breakdown.
- All A are B
- All B are C
- Therefore, All A are C
We can express the Subset Argument in the form of the following Vein Diagram.
In natural language, an example of subset argument is
- All women are humans
- All humans are mammals
- Therefore, all women are mammals
It can be seen from the Venn Diagram that if the premises are correct, the conclusion can’t be false. However, if we are not careful, we may make errors in the argument and reach the wrong conclusion. For instance, the following shall be an invalid argument
Invalid Argument
- All A are B
- All C are B
- Hence, all A are C
The Venn Diagram of the above argument can be shown as following.
In natural language, the argument can be presented as follows.
Invalid Argument
- All men are humans
- All women are humans
- Hence, all men are women
The above argument is clearly invalid as the premises do not lead to the conclusion that all men are women. However, this invalid logic won’t qualify as a logical fallacy since no man can be a woman; hence, the probability of this statement being true is zero. An invalid argument can be considered a fallacy only if there is some probability that an invalid statement is true. Hence, this statement can’t be said to be a logical fallacy, though it is invalid.
Now consider the following argument.
- All good people fight when they face injustice.
- All just people fight when they face injustice.
- Hence, all good people are just.
In this case, the logic is still invalid, yet the argument would seem convincing to many people because both good and just words are ambiguous and overlap each other at some point. Hence, many people would be willing to accept this logic, even though it is invalid. For instance, some good people would like to forgive the person rather than punish the person for imparting justice. Conversely, eye-for-eye is just but not a policy to be followed by good people; it may spread hatred and make the whole world blind. Hence, if a person chooses to follow the policy of offer-your-other-cheek, he would be considered to be good, though he is not just.
