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I recently came across the fallous reasoning that "if a is the opposite of b, then a must have all the opposite properties of b"
That is:

My dog is the opposite of my cat, and my cat has fur and is black, so my dog must have no fur and be white

What is the term for this?

  • The problem here is not with the reasoning but with the premise, "my dog is the opposite of my cat" makes no sense on the usual understanding of "opposite". In fact, "my cat has fur and is black, and my dog has no fur and is white" could be offered as one way of explaining what the "opposite" as (ab)used here might mean. This could be a case of equivocation but in it the two occurrences of the same word are usually supposed to make sense independently, or rather two different senses. – Conifold Dec 1 '16 at 1:22
  • @Conifold That's just a simplified example I came up with. But of course, no two (real) objects or even concepts can be exact opposites of each other, so I suppose the overall reasoning is still fallous. – cat40 Dec 1 '16 at 1:24
  • @cat40:"if a is the opposite of b, then a must have all the opposite properties of b": Can we imagine anything (a thing or an idea) in this category? If 'yes', 'a' and 'b' are imaginable. Then this won't seem to satisfy your condition. I believe we can't even imagine such thing. What we call 'opposite' is opposite up to certain level only. – SonOfThought Dec 11 '16 at 7:13
  • (I don't know whether) That opposite word needs to kill all the properties of 'a' without leaving out anything. I think Philosophy can nothing to do with this matter. If so, a 'true-nullifier' might incarnate in english.stackexchange.com. So, for an apt word, IMHO, you'd better migrate to that site. – SonOfThought Dec 14 '16 at 13:51
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Dogs and cats are often mentioned together, as are knives and forks; in that context opposite simply means the other of a pair; but more, it means the other of a complement.

Knives and forks are used together in eating a sit-down meal at a table; they complement each other.

Cats and dogs are both domestic pets that people keep, and also are the most common pet; the sense of complement here is quite a bit weaker though than in the first example.

Here, opposite is not used in the mathematical sense of inverse; where properties of an inverse are inverse to the properties of the original object.

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I believe the closest term is "false equivalence."
Just because some component of B might not be in A, it does not mean that all components of B must not be in A.
For example: If we define, a solid(S) is not a liquid(L), S -> ~L. It does not follow that a solid(S) is now excluded from having any of the other properties of a liquid(L). Both could be green, have the same temperature, same volume, etc.

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