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So far I could not find any reasonable translation for "sledgehammer argument". Automatic translations spit out "argumento de mazo." However, everything indicates to me this is just one of those totally non-idiomatic automatic translations that make no sense.
Alternative English expressions from Wikipedia are: "thought-terminating cliché" (also known as a semantic stop-sign, a thought-stopper, bumper sticker logic, or cliché thinking)"
To my ear
a sledge-hammer argument
is best translated as
un argumento demoledor
Since the verb demoler means to demolish, to knock-down
Del lat. demolīri.
Conjug. c. mover.
- tr. Deshacer, derribar, arruinar.
We are talking about something that "beats" a discussion in a way in which "eliminates all opposition". Note that sledge-hammers "are most useful for demolishing work"
(..) they are perfect to use for demolition work, driving large things like stakes into the ground and for breaking through hard materials
I initially also thought of the word contundente (see lat contundere to crush, to beat, to pound to pieces) since in that word Spanish also holds a direct meaning associated with arguments.
To add more punch the expression could optionally carry the adjective "devastador*, or the adverb "devastadoramente" since devastar means to destroy, reduce something into pieces or ashes)
You can use argumento irrebatible:
- adj. Que no se puede rebatir o refutar.
or argumento irrefutable:
- adj. Que no se puede refutar.
where refutar means
- tr. Contradecir o impugnar con argumentos o razones lo que otros dicen.
Comparing these suggestions to the ones in RubioRic's answer, Google has 166000 results for "argumento decisivo", 36400 results for "argumento irrefutable", 13400 results for "argumento irrebatible", and 793 results for "argumento terminante".
I think that the adjective - equivalent to sledge-hammer in this context - that you are looking for is terminante. You gave me the idea with "though-terminating cliché"
According to the Free Dictionary a sledge-hammer argument is
A strong argument that eliminates all opposition
According to the DLE
terminante
2. adj. Categórico, concluyente, que hace imposible cualquier insistencia o discusión sobre la cosa de que se trata.
The highlighted text is almost a direct translation of the idiom definition provided by the Free Dictionary, it says that "terminante" means that something makes impossible to continue insisting or discussing.
Another option is decisivo
DLE
decisivo
1.adj. Que decide o resuelve.
Oxford Dictionary
decisive
2. Having or showing the ability to make decisions quickly and effectively.
un argumento contundente
Contundente literally means "blunt" and conveys, somewhat, the same kind of image that sledgehammer does. It's rarely used with argumento, but it can be used this way.
