devilsadvocate
New Member
While I was reading the "William Craig debunk" thread, I started thinking about the widespread claim, "You can't prove a (universal) negative", and whether there's any truth to that. I posted this elsewhere, but I thought it could be good to have it here as well for criticism (does it make any sense, in fact?) and discussion . So here are my quick thoughts:
I didn't talk about analytic truths in my original post because in the context it wasn't needed, so consider this paragraph a quick preface: You can certainly prove an analytic universal negative. This is trivial because in analytic statements the subject already contains the predicate, and as such the claim is true by definition. "No bachelors are married", is an example of that. Also deductive logic can be used for synthetic truths, but since those arguments usually fail or persuade depending on the truth of the premises, whose acceptance almost always depends, in turn, on inductive reasoning, I didn't feel worthwhile to consider those. To the actual post then:
First of all, if you can't prove universal negative, you cannot prove universal affirmative. The claim,
"No swans are black" is equivalent to "All swans are non-black" via simple inference. Or more generally "No S are P",> "All S are non-P".
Second, most people do not understand what universal claim means in logic. "Universal" simply means "all of S" instead of the particular, "some of S". The subject, "the S", can be as well-defined as one wants, and, in fact, the claim, "Santa Claus is not real", is a universal affirmative claim about a singular (There is only one possible Santa Claus that fits the definition). Predicate can be as well-defined as we want, as well. For example, "No mice are in my closet", where the predicate, "in my closet", limits the scope of the argument.
So to try to keep it short: Negative and affirmative claims are inferred trivially between each other, and the scope of the argument does not need to be high for a "universal" claim. When it is said, "universal negatives cannot be proved", more often than not what is really targeted are claims where the field of knowledge required for the claim to be proven false is absurdly high. This is of course valid objection when burden of proof is made lopsided, "A bearded, jolly, fat man who owns flying reindeers exists somewhere in the universe. Prove I'm WRONG on that!". But it isn't valid because "You can't prove a negative."
I didn't talk about analytic truths in my original post because in the context it wasn't needed, so consider this paragraph a quick preface: You can certainly prove an analytic universal negative. This is trivial because in analytic statements the subject already contains the predicate, and as such the claim is true by definition. "No bachelors are married", is an example of that. Also deductive logic can be used for synthetic truths, but since those arguments usually fail or persuade depending on the truth of the premises, whose acceptance almost always depends, in turn, on inductive reasoning, I didn't feel worthwhile to consider those. To the actual post then:
First of all, if you can't prove universal negative, you cannot prove universal affirmative. The claim,
"No swans are black" is equivalent to "All swans are non-black" via simple inference. Or more generally "No S are P",> "All S are non-P".
Second, most people do not understand what universal claim means in logic. "Universal" simply means "all of S" instead of the particular, "some of S". The subject, "the S", can be as well-defined as one wants, and, in fact, the claim, "Santa Claus is not real", is a universal affirmative claim about a singular (There is only one possible Santa Claus that fits the definition). Predicate can be as well-defined as we want, as well. For example, "No mice are in my closet", where the predicate, "in my closet", limits the scope of the argument.
So to try to keep it short: Negative and affirmative claims are inferred trivially between each other, and the scope of the argument does not need to be high for a "universal" claim. When it is said, "universal negatives cannot be proved", more often than not what is really targeted are claims where the field of knowledge required for the claim to be proven false is absurdly high. This is of course valid objection when burden of proof is made lopsided, "A bearded, jolly, fat man who owns flying reindeers exists somewhere in the universe. Prove I'm WRONG on that!". But it isn't valid because "You can't prove a negative."
