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I am presented with an argument of form:

If p, then q. If q, then r. Therefore, if r, then p.

Does this structure have a specific title? I know that it is invalid, and am assuming that "reverse hypothetical syllogism" is nowhere near correct.

I've looked online to no avail, so any help is appreciated.

Thanks!

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    Edit: This almost seems like a two-stage version of affirming the consequent. Is that a possibility? – Ben Sep 23 '17 at 0:40
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    Syllogisms have premises in the form "all M is P", "some M is P" or "no M is P", so what you have are not syllogisms. If we convert "if p then q" into "all p is q" then your inference is a combination of Barbara with affirming the consequent. It does not have a special name, there are too many possible combinations to name them all. What exactly do you need the name for? – Conifold Sep 23 '17 at 1:26
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    It is not a syllogism. It is a fallacious argument, very similar to Affirming the consequent. – Mauro ALLEGRANZA Sep 23 '17 at 8:24
  • If this were a longer chain, it might be a form of circular argument. – barrycarter Sep 23 '17 at 16:10
  • Can one explain how this form is not a hypothical syllogism as in the inference rule? The form is not a standard categorical syllogism. – Logikal Oct 27 '17 at 1:54
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One name that would work for this fallacy is "affirming the consequent" although we are doing it twice.

The Internet Encyclopedia of Philosophy defines this fallacy as:

If you have enough evidence to affirm the consequent of a conditional and then suppose that as a result you have sufficient reason for affirming the antecedent, your reasoning contains the Fallacy of Affirming the Consequent.

To see how this might be an appropriate name consider the situation.

If p, then q. If q, then r. Therefore, if r, then p.

When one assumes r hoping to derive p in the above example, one could interpret that as using the fallacy of affirming the consequent twice.

First we firm the consequent, r, to obtain the antecedent q given the conditional, "if q then r".

Second, q is the consequent of "if p then q". By using the fallacy of affirming the consequent again, we may try to obtain p as a result.

These two uses of the fallacy of affirming the consequent give us the formally fallacious result desired.


Reference

Bradley Dowden, "Fallacies" Internet Encyclopedia of Philosophy. <https://www.iep.utm.edu/fallacy/>

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If you had "if p, then r", then following that with "r, therefore p" would be affirming the consequent. You don't explicitly have "if p, then r", but it is implicit due to the transitive nature of implication.

Also, "if r, then p" is known as the "converse" of "if p, then r".

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If p, then q. If q, then r. Therefore, if r, then p.

The problem is called illicit minor. If the minor term is distributed in the conclusion, it must be distributed in the premises. This rule of a valid syllogism is violated here.

The question says: All P are Q; All Q are R; Thus All R are P. The minor term R is distributed in the conclusion, but not in the minor premise. In effect, there is no statement here that the quality R applies to every P; for that reason the syllogism fails.

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You are speaking of a Hypothetical syllogism. This is a valid rule of inference. Hypothetical syllogism is not to be confused with a traditional or classical syllogism. The inference you wrote is valid not invalid. Hypothetical syllogism is symbolic whereas a traditional syllogism is not symbolic and there is stuff lost in translation. Hence why the rules differ. You can try to make them say the same thing and you may discover there is something wrong. You would have to know why there is a difference.

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