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“If you don’t go to the doctor tomorrow, you won’t get better. You will go to the doctor tomorrow. So, you will get better.”
What kind of fallacy does this argument fall under? I have a suspicion it’s one of the formal fallacies; however, the negations in the first premise throw me off.
It's denying the antecedent. The premise 'if P then Q' only tells you what follows from P. It doesn't tell you what follows from not-P. So you cannot infer not-Q from that.
In this case, P = you won't go to the doctor tomorrow; Q = you won't get better. Note that the conclusion can be false even if the two premises are true: perhaps you will never get better -- that's consistent with the assumptions. If the conclusion can be false when the premises are true the argument is invalid.
