Did you see the example above? “Reductio ad absurdum” literally translates to “reduction to the absurd”. You are literally reducing someone’s argument (and/or their justification for an argument) down to it’s bare logic and simply applying it to a specific case.
If you were talking to someone and he said “all people who go by the name ‘Stephen’ should be shot in the face.” (Granted, this doesn’t have to be reduced very far, as it can be seen absurd on it’s face, but we’ll go there just to make the point.) It would be nonsensical for you to say “that’s like saying I should be shot in the face.” No, that’s not “like” what he’s saying…he is saying you should be shot in the face. You along with anyone else who goes by that name. (I of course have to assume you’re not simply trying to claim it’s “not what he’s saying” because he literally didn’t utter those specific words.)
Now, if you wanted to make an analogous statement (i.e. one in which you could use your phrase “that’s like saying…”) you would reply with something like: “You think everyone who goes by a certain name should be shot? That’s like saying everyone who was born on a Tuesday should be shot. It’s completely arbitrary.”
Do you see the difference? With reductio you are reducing the argument—the content of the literal words the person actually stated—down to its logic, and simply applying that logic to a specific case (usually an absurd case), for the purpose of illustrating the fallacy in the logic…logic which was used to form an argument or the justification for an argument. You are quite literally taking the arument as it is stated and reducing it to its logical base…essentially getting at the root of what someone is actually saying (or at least providing an illustration of it).
In a “that’s like saying” situation, you are doing nothing of the sort. You are simply presenting an analogous argument to make a comment about the actual argument being made. In the above case, you weren’t trying to illustrate anything about the logic the person was using, or the implications of their statement. You were simply trying to make your own comment about the statement itself…namely, that it was arbitrary.
So for another example, suppose someone said: “We should raise taxes. Raising taxes always results in increased tax revenue.” A reductio ad absurdum might be: “So you’re saying if we increased the tax rate to 100% across the board, the revenue from taxes would be higher than it is now?”
Your response here would be: “No he didn’t say that. Why are you putting words in his mouth?”
But obviously no one put any words in his mouth. The first guy literally said “raising taxes always results in increased tax revenue”. All the second guy did was take that logic and apply it to a specific case…as, if what the first guy said is true, then a 100% tax rate should yield higher revenue. Your next response might be: “But that’s not what he meant! His argument was just that we should raise taxes! He didn’t say the rate should be 100%! You’re reducing it to absurdity!”
Exactly.