A friend challenged me with a statement
A1: If there is no Jesus, why are there churches?
Which rules of reasoning does it break? Is there a name for statements like that?
The presented statement seems to assume that:
A2: If there is Jesus, it follows that there are churches.
which can be written as
There is no Jesus OR there are churches.
The existence of churches in a universe without Jesus is presented as contradiction to A2. Which prooves by contradiction, that there is Jesus.
If your formalization is correct, then your friend is affirming the consequent as you describe, per the following structure:
Formalized:
But before we assume that's what's happening there's two issues worth mentioning. First, many normal language expressions can be formalized in multiple ways, and it's not immediately clear that this is exactly the argument your friend means to offer. This ties into the second issue: the principle of charity, which at its simplest is the idea that one should take one's interlocutor's arguments and put them in the best possible light rather than the worst possible one.
To give a better reconstruction:
Now, the reconstruction is not as strong as the initial construction you gave in that it (a) lacks the deductive form which can be truth-preserving and (b) it's openly probabilistic.
... But all of that to say, "fallacies" in natural language arguments and especially informal fallacies involve judgment calls about the validity of certain moves.
Perhaps your friend is arguing as follows:
1. If Jesus did not exist, then churches would not exist.
2. Churches exist.
3. Therefore, Jesus existed.
This line of reasoning denies the consequent and is valid. However, your friend's task is not finished. They still have to show the validity of the premise, "If not J, then not C." There could be many explanations why churches did not exist even if Jesus did.
I think it is a case of argumentum ad populum. If so many people believe in Jesus, to the point that they take the time to build churches in his honour, then Jesus must "exist" (whatever "exist" may mean, from an unusually wise carpenter in Galilea to one of the three constitutive parts of the Godhead).
The main problem is rather the method: this is old school syllogisms, especially since mathematical notation and Venn's diagrams have made it easier to find flaws in those forms of reasoning.
Basically, these propositions are largely undecidable, for lack of formality. The obvious objection is, of course, that there might be churches that don't trace to Jesus (actually predated him, this violates the principle of time anteriority of the cause); and therefore that Jesus may not be a cause of all churches.
Hence the first task would be to give a formal answer to this question: how do you define your set of "churches"?
Also, in the end, ** the most beautiful or authoritative syllogisms are useless if they are not applicable to "nature" "experiment" or "experience" ** (see Feyman's quip about this).
What should be clearer, is what problem you are both trying to solve. I hope the ultimate purpose is not to "prove" divergent philosophies on dualism versus monism with syllogisms. That's because trying to "prove" one or the other might turn to be the actual fallacy (since axioms are starting points and one doesn't "prove" them). Since they are mutually exclusive axioms, you might have a better go at discussing how useful or applicable these two sets of axioms are to "life, the universe and everything".
This is a spurious relationship. They are not causally connected: the existence of churches doesn't prove the existence of Jesus. Spurious relationships sound like a cause-consequence, but they are not. It's just a wordplay.
An equivalent would be saying "If it's not tasty, why do flies eat garbage?". There is no causality relation between both facts, but the wording seems to be a cause and consequence. The fact that flies feed with things on the garbage does not imply at all that garbage is tasty.
"A1: If there is no Jesus, why are there churches?"
Answer: Churches exist because people believe that there is a Jesus. But people who believe that there is a Jesus is not a proof that there is a Jesus.
Due to popular demand... I edit:
FIRST :
You say :
"The presented statement seems to assume that:
A2: If there is Jesus, it follows that there are churches."
While I agree I prefer to translate the A1 question with this statement:
A2-alternative: If there are churches, it follows that there is Jesus."
SECOND :
I see it just an obvious wrong assumption. I choose to transpose the logic part of this sentence to a simpler, more obvious model for easier comprehension:
"If children writes letters to Santa (If there are churches), it follows that there is Santa (Jesus)."
And here I can be wrong but I don't feel the need of an "adlatina" sentence to describe it.
But... What's make the question interesting is not the logical part of the fallacy.
In this sentence there is a very pragmatic part.
It does work on peoples.
Such an argument could definitely be accepted and even firmly defended with billions of logical fallacies by a deeply religious person!
I think the logic of the question is evaluated only because there is "Jesus". Without beliefs (religious, political, etc...) the logical part is naked. What's disturbofascinating is the idea that still, it could easily work with some believers.
