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Confusing \"if\" with \"if and only if\"


Formal Logical Fallacy of Confusing "if" with "if and only if"

Confusing "if" with "if and only if" is a formal fallacy that covers up the problem when reasoning is based on one of the three fallacies of Agrippa's trilemma. Whenever a logical fallacy is committed, the fallacy has its roots in Agrippa's trilemma. All human thought (without Divine revelation) is based on one of three unhappy possibilities. These three possibilities are infinite regress, circular reasoning, or axiomatic thinking. This problem is known as Agrippa's trilemma. Some have claimed that only logic and math can be known without Divine revelation; however, that is not true. There is no reason to trust either logic or math without Divine revelation. Science is also limited to the pragmatic because of the weakness on human reasoning, which is known as Agrippa's trilemma.

The Formal Logical Fallacy of Confusing "if" with "if and only if" occurs when, during the course of reasoning, an "if" changes its meaning to "if and only if." A conditional statement can be made to claim that one thing is true/false if a second thing is true/false. The form would be, “If A, then B.” This is different from saying that one thing is true/false if, and only if, a second thing is true/false. The form would be, “If A, then B, but if not A, then not B." which is equivalent to "If, and only if, A, then B."

INVALID FORM

“If A, then B. Not A.
Therefore, not B.”

The problem is that we don’t know that B is not true from this logic.

Examples of the Formal Logical Fallacy of Confusing "if" with "if and only if"

“If I heard God leading me, and He would give me anything I asked for when I pray, then I could know that God exists. I have never heard God’s Voice, nor do I get what I pray for. Therefore, God doesn’t exist.”

Of course, the most deceptive fallacy here is the false statement that this person has never heard God’s Voice. The difference is between hearing and ignoring or hearing and acknowledging/obeying. Getting back to this particular fallacy, the statement would have to be “If and only if” to support this conclusion.


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