# Structure of "affirming the consequent fallacy"

The formal structure of affirming the consequent fallacy is,

``````P1 - If A is true, then B is true
P2 - B is true
---------------------------------
C - Therefore, A is true
``````

Now if I give another similar example like, (with a B negation)

``````P1 - If A is true, then B is true
P2 - B is not true
---------------------------------
C - Therefore, A is not true
``````

Will it still be called affirming the consequent fallacy or is there any special name?

• This is not Burger King where you can have it your way and do whatever you like. The two arguments forms are not identical in your question. You have no justification for transforming one form into the other form. The first form is a fallacy affirming the consequent but the second is called Modus Tollendo Tollens which is not a fallacy. Why you are confusing the two visually different forms is the better question all readers should ask you. Perhaps you are reasoning like most people depending on the topic. This is case by case basis thinking. Deductive is a higher way to reason all together. Commented May 11, 2021 at 21:40
• @Logikal, I used the term transform mistakenly. I have updated the post. I did not mean two arguments are identical but the structure seems to have similarities except with a negation. Anyway, Double Knots answer solved my confusion. Thanks. Commented May 11, 2021 at 23:35
• In the second example, we have "B is not true". Thus, why do you believe that we are affirming B? Commented May 12, 2021 at 15:03
• @MauroALLEGRANZA I was thinking like, Not B is true. Commented May 12, 2021 at 16:17

This is just normal Modus_tollens or called denying the consequent of classic logic of syllogism

The form of a modus tollens argument resembles a syllogism, with two premises and a conclusion:

If P, then Q. Not Q. Therefore, not P.

The first premise is a conditional ("if-then") claim, such as P implies Q. The second premise is an assertion that Q, the consequent of the conditional claim, is not the case. From these two premises it can be logically concluded that P, the antecedent of the conditional claim, is also not the case.

• Denying the consequence is not same as modus tollens. it is `If P, then Q. Not P. Therefore, not Q.`. Could you please recheck. Commented May 11, 2021 at 19:26
• @SazzadHissainKhan seems u get confused by MT, see my reference, it specifically says If P, then Q. Not Q. Therefore, not P. Or maybe your question has typo? If you meant not P, then no formal fallacy at all since this can be interpreted as material implication, a false premise can logically imply either true or false consequent of the original condition... Commented May 11, 2021 at 19:40
• I understood, So it won't be a fallacy right? Commented May 11, 2021 at 19:59
• @SazzadHissainKhan your original question is not a fallacy (opposite it's sound) and also btw ~Q -> P is logically valid (T in truth table). I think this question is related to your other cigarette -> cancer question... Commented May 11, 2021 at 20:07
• @SazzadHissainKhan That obviously has fallacy as I've completed an answer there, u may check... Commented May 11, 2021 at 20:16

That's not a fallacy at all, but a deductive argument form, aka modus tollens.

• This is of course a fallacy. There can be other cause for B. Commented May 11, 2021 at 19:17
• First, causation is not an issue here, and second, I was (answering your question) referring to the second argument form, obviously. Commented May 11, 2021 at 19:24
• I am talking about second argument actually. `If A, then B` does not necessarily mean A is the only cause of B. So, one cannot deduce `^A` from `^B` and thus causation matters here and it is a fallacy. Isn't it? Commented May 11, 2021 at 19:29
• Think again. If it is true that "If A, then B, but not B" then A cannot be the case, for, as stated, if A then B. Commented May 11, 2021 at 19:35
• @SazzadHissainKhan what do you mean by "cause" in the context of propositional logic? "If A, then B" does not mean that A causes B; it means that knowing A is true is sufficient to know that B is true, regardless of any other relationship between A and B. Commented May 11, 2021 at 19:36

Since any conditional is equivalent to its contrapositive, P1 is equivalent to "If B is not true, then A is not true." In this form, it should be clear "A is not true" is a valid conclusion, so this is not a fallacy.