Equivocation

From FreeThoughtPedia

Equivocation is the fallacy of using one word in two of its equally legitimate definitions, but presenting them as being interchangeable. For example:

A mouse is an animal; therefore a large mouse is a large animal.

We have a right to believe in a religion; we have a duty to do what is right; therefore we have a duty to believe in a religion.

Jesus was the son of God; historians agree that Jesus existed; no son can exist without a father; therefore, God exists.

The first is a fallacy because large takes on meanings from two different things, a mouse and other animals, and so is not the same in those two senses. The second uses "right" as something we are entitled to do and also as something morally good. This could be better illustrated as fallacious by substituting another right in the place of the one cited, for instance:

We have a right to believe Elvis is alive; we have a duty to do what is right; therefore we have a duty to believe Elvis is alive.

The last fallacy concerning Jesus confuses the Biblical Jesus with the historical Jesus, assuming they are the same when in fact the historical Jesus is not necessarily divine and the Biblical Jesus is.