The Logic of the Conditional Apology

Any apology in conditional form expresses a relationship of necessity and sufficiency with respect to antecedent and consequent claims. In the conditional apology the apology itself is the necessary consequent of some antecedent which suffices for an apology.

Valid forms of the Conditional Apology are:

Affirming the Antecedent

P1. If you are offended, then I am sorry.
P2. You are offended.
      Therefore,
C. I am sorry.

Denying the Consequent

P1. If you are offended, then I am sorry.
P2. I am not sorry.
      Therefore,
C. You are not offended.

Invalid forms of the Conditional Apology are:

Denying the Antecedent

P1. If you are offended, then I am sorry.
P2. You are not offended.
      Therefore,
C. I am not sorry

Affirming the Consequent

P1. If you are offended, then I am sorry.
P2. I am sorry.
      Therefore,
C. You are offended

The rarely used Biconditional Apology is also an option:

      “I am sorry if and only if you are offended”