# Set theoretic examinations of fallacies of division + composition

#### bahen

I am curious to know whether there is a set theoretic proof for the fallacies of division and composition. The former holds when one claims that something true for the whole must also be true of all or some of its parts. The latter holds when one infers that something is true of the whole from the fact that it is true of some part of the whole (or even of every proper part).

The query arises out of the fact that they are informal fallacies, meaning that their flaws are about content and not structure. If this is true, then I wonder whether a formal set theoretic proof is possible.

#### Plato

MHF Helper
I am curious to know whether there is a set theoretic proof for the fallacies of division and composition. The former holds when one claims that something true for the whole must also be true of all or some of its parts. The latter holds when one infers that something is true of the whole from the fact that it is true of some part of the whole (or even of every proper part).

The query arises out of the fact that they are informal fallacies, meaning that their flaws are about content and not structure. If this is true, then I wonder whether a formal set theoretic proof is possible.
If there were a formal set theoretic proof is possible, then would they be informal?

#### bahen

Hi Plato. Sometimes it is possible to produce formal proofs of informal statements if the informal statements allow of formal proofs. So the answer to your question is yes. I was wondering whether such proofs are possible for the two informal fallacies under discussion.

#### Plato

MHF Helper
Hi Plato. Sometimes it is possible to produce formal proofs of informal statements if the informal statements allow of formal proofs. So the answer to your question is yes. I was wondering whether such proofs are possible for the two informal fallacies under discussion.
Give us an example of such a proof. If you can then you must have a different of the word informal than many.

#### bahen

Perhaps you're right. So here is an example of an informal statement for which a proof is possible: John can't drive to the shop and not drive to the shop at the same time. The informal aspect of the statement is its content: John, driving, shops, temporality, ability, sameness, etc. The statement can also be formalized in many ways which subsequently allow of proof. For example, with the principles of non-contradiction, excluded middle, etc.