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have recently been studying the philosophy of reasoning and have thought of these questions that I am having a bit of trouble answering.

If an argument commits a fallacy, it is invalid. That is true, however, if an argument is invalid, does it commit a fallacy?

Also, if an argument commits a fallacy, must the conclusion be false?

Thanks

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    All fallacies create invalid arguments. Not all invalid arguments are fallacies. Invalid arguments tell you nothing about the truth value of their conclusion. That's the problem.
    – Dan Bron
    Commented Dec 23, 2016 at 6:12
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    The issue is not very clear-cut; see Fallcy : "Fallacies are commonly divided into "formal" and "informal". A formal fallacy can be expressed neatly in a standard system of logic, such as propositional logic". If so, the fallacy e.g. of Denying the antecedent : "If P, then Q. Therefore, if not P, then not Q" is simply an invalid argument.
    – Mauro ALLEGRANZA
    Commented Dec 23, 2016 at 7:13
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    In genersal, an invalid argument may have a true conclusion; the issue is that the conclusion is not "guaranteed" by the premises (this is the lack of validity of the argument).
    – Mauro ALLEGRANZA
    Commented Dec 23, 2016 at 7:16
  • If an argument is invalid, does it commit a fallacy? Nanhee Byrnes PhD states that If an argument is invalid, then it must commit a formal fallacy. Also, that an argument can be logically valid if it commits an informal fallacy. ![enter image description here](i.sstatic.net/mhQwT.jpg) Therefore, the direct short answer (YES/NO) to the original question is YES. Please comment accordingly.
    – Carpenoctem
    Commented Jan 5, 2019 at 3:22

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To understand the relationship between fallacies and validity, you need to first understand the fact that an argument (a pair set of premises and a conclusion) has form and content. The form is concerned with the logical schema between the conclusion and premises; the content is concerned with the reasonable support (or persuasion) of the conclusion by the premises. The two are generally studied independently: the form, in logic; the content, in rhetoric.

A fallacy is a defect in the argument. The defect can happen in form or in content. When the form is defective, the argument is called as committing a formal fallacy. Affirming the Consequent or Denying the Antecedent are examples of the formal fallacy. Committing formal fallacies always produce invalid arguments. When the content is defective, the argument is called as committing an informal fallacy. Committing informal fallacies, however, can be logically valid as in circular reasoning (petitio principii) since the conclusion is already contained in the premises. enter image description here

Based on this understanding, let's examine the three questions (or statements) of yours.

  1. If an argument commits a fallacy, it is invalid.

No, If an argument commits an informal fallacy, it can be valid. e.g., petitio principii

  1. If an argument is invalid, does it commit a fallacy?

If an argument is invalid, then it must commit a formal fallacy.

  1. If an argument commits a fallacy, must the conclusion be false?

The conclusion of an argument that commits formal and/or informal fallacies can be still true.

Example: Denying the Antecedent (formal fallacy)

If I am God, I can eliminate all sufferings.

I am not God.

Therefore I cannot eliminate all sufferings. (True concision)

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