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What is the correct scientific term for the - erroneous - inversion of cause and effect?

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According to a dictionary of psychology this is simply called "reverse causality"

In attempting to understand the relationship between cause and effect, a tendency to attribute what is actually the cause to the effect. For example, does the ingestion of lead paint cause a lower intelligence quotient (IQ) or is it that children with lower IQs tend to eat lead paint?

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Would the concept of contraposition from the world of mathematical logic work for you?

From the Wikipedia explanation of contraposition:

The contrapositive of a statement has its antecedent and consequent inverted and flipped. For instance, the contrapositive of the conditional statement "If it is raining, then I wear my coat" is the statement "If I don't wear my coat, then it isn't raining."

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  • $\begingroup$ The logical error I am looking for, is "I am wearing my coat, therefore it is raining" - to use the example. $\endgroup$ – user1934212 Dec 15 '20 at 17:21
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Given your comment to the first answer...

The logical error I am looking for, is "I am wearing my coat, therefore it is raining"

...I think you are referring to deductive arguments. A deductive argument (definition taken from Mark Storey, Bellevue College):

...claims (explicitly or implicitly) that if the premises all are true, then the conclusion must be true

Valid examples are (taken from the linked document from Mark Storey)

  • All bats are cute animals. No cute animals are mean. So, certainly, no bats are mean.
  • Joan is Lauren’s mother. Therefore, Joan must be older than Lauren.
  • Nobody knows Ned. Therefore, it must be that Ned does not know himself.
  • Some cats are pets. Thus, some pets must be cats.

A familiar invalid example is the following (taken from memory on my own Philosophy class, a long, long time ago):

All cows have 4 legs. It has 4 legs, thus it must be a cow.

Your question proper states that it should be related to cause and effect. In terms of deductive reasoning, however, it is based on premises and conclusions. Quoting Mark Storey again:

[T]he argument may fail in its aim; what makes the argument deductive is that it is the kind of argument that—if it were successful—would have the premises absolutely guarantee the conclusion to be true.

I think what you are after are examples where the premises do not guarantee the conclusion to be true. This is different from causes and effects, though.

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