What's the word when someone tries to change the meaning of a statement by using different definitions for specific words?

Question

For example the second amendment in the American constitution "the right of the people to keep and bear Arms" and someone argues that arms here means limbs when it clearly means guns. I remember a word similar to overstretch or overreach was used in that case.

Answer 1

This is an informal fallacy called equivocation (Wikipedia, RationalWiki). The latter defines it as

a logical fallacy that relies on implicitly alternating between the different meanings a single word can have in different contexts.

Texas State University Department of Philosophy has a page on equivocation, which says

The fallacy of equivocation occurs when a key term or phrase in an argument is used in an ambiguous way, with one meaning in one portion of the argument and then another meaning in another portion of the argument

One common example mentioned in RationalWiki is when creationists argue that the theory evolution isn't true because it's only a theory. In science, a theory is (according to a quote in Wikipedia) "a well-substantiated explanation of some aspect of the natural world, based on a body of facts that have been repeatedly confirmed through observation and experiment" but one of the dictionary definitions of theory is "an unproved assumption" (Merriam-Webster). So the theory of evolution is an unproved assumption. This is an example of equivocation.

Texas State gives as an example:

The laws imply lawgivers. There are laws in nature. Therefore there must be a cosmic lawgiver.

Here the concept of a law of nature is confused with a law in the legal system.

Answer 2

This is an example of the Logical Fallacy of Re-Definition, where an original statement of fact is disputed by re-defining the terms of reference.

Logical Fallacy : Redefinition

Redefinition Fallacy

Answer 3

I would use the word "wrest"--especially if it were done intentionally. A similar word would be "twist" or "distort."

For example:

"He wrested the meaning of the statement, turning it into something altogether different than originally intended."

Apple's Dictionary (from Oxford Dictionaries) claims this usage is archaic, but its usage of "distort" is not a perfect replacement. "Wrest" implies intent; "distort" is more neutral, and could as easily include an accidental misusage or misunderstanding of something.

Here is the dictionary entry.

wrest | rest |
verb [with object]
forcibly pull (something) from a person's grasp: Leila tried to wrest her arm from his hold.

• take (something, especially power or control) from someone or something else after considerable effort or difficulty: they wanted to allow people to wrest control of their lives from impersonal bureaucracies.
• archaic distort the meaning or interpretation of (something) to suit one's own interests or views: you appear convinced of my guilt, and wrest every reply I have made.

noun archaic a key for tuning a harp or piano.