In propositional logic, when two propositions are connected with “or”, a disjunctive syllogism is formed. When we don’t use this syllogism carefully, we fall prey to the affirming a disjunct fallacy.
Fallacy example 1:
“Tom either likes blondes or brunettes”
Possible conclusion: If Tom likes blondes, he doesn’t like brunettes.
Fallacy example 2:
“You either believe in ghosts or dragons”
Possible conclusion: If you believe in dragons, you don’t believe in ghosts.
It doesn’t take a professor of logic to notice that the sentences are fallacious. We know that it’s perfectly possible for Tom to like both blondes and brunettes. Also, believing in ghosts doesn’t exclude the option of believing in dragons. This fallacy we call, affirming a disjunct.
Example 1 corrected:
“Tom likes blondes or brunettes”
Example 2 corrected:
“You believe in ghosts or dragons”
As you can see from the corrected examples, the fallacy has something to do with “either”. The fallacy does not occur when we don’t use “either” to combine the two possibilities. In order to make this clearer, we need to dig deeper into disjunctive syllogisms.
There are two kinds of disjunctive syllogism, an inclusive disjunction, and an exclusive disjunction. Both use “or” for combining propositions but an exclusive disjunction is also accompanied by “either”. Affirming a disjunct fallacy occurs when an inclusive disjunction is mistaken for an exclusive one.
Inclusive disjunction example:
“God is drinking beer(A) or whiskey(B)”
Here’s the logic:
- If A is true, the statement is true.
- If B is true, the statement is true.
- If both A and B are true, the statement is true.
- The statement is false only when both A and B are false.
Exclusive disjunction example:
“A man is either free(A) or a slave(B)”
Here’s the logic:
- If A is true, the statement is true.
- If B is true, the statement is true.
- If both A and B are true, the statement is false.
- If both A and B are false, the statement is false.
As you can see, using either in a disjunction makes it exclusive. More so, the possibilities you’re naming are mutually exclusive. That means that while one possibility is true the other cannot be also true. In the example above, the terms used, free(freedom) and slave(slavery) are opposites, that’s why the example is not fallacious.
Conclusion
In conclusion, affirming a disjunct fallacy occurs when we use an exclusive disjunction instead of an inclusive one. Sometimes, we don’t realize that there is a third option where both possibilities can be true.
More information: Affirming a disjunct fallacy can be made intentionally. Not everyone agrees that some terms are mutually exclusive and the other way around. For instance, some people will argue that a man can be simultaneously good and bad. Also, some people will argue that a man that likes blondes cannot like brunettes. Whatever the case may be, the statements are still logically flawed.