# Where is the fallacy here?

Where is the fallacy here:

1. whatever is natural is not unnatural

2. whatever is unnatural is not natural

3. the phenomenon of cats being born into this world is natural

4. the phenomenon of rabbits being born into this world is not the phenomenon in point 3

Conclusion: the phenomenon of rabbits being born into this world is unnatural

• Obviously not all cats are normal. Mar 5, 2019 at 0:23
• Assuming cats are normal: rabbits can also be normal without being cats. Mar 5, 2019 at 1:40
• @Bread - I did some edits. Mar 5, 2019 at 1:41
• @brilliant My answer responds to your original post. I do not think that the edits change my answer. Mar 5, 2019 at 1:58
• It is classically known as 'affirming the consequent'. It involves following an implication backward, or negating both sides of an implication and assuming the result is true. (The former form is 'arguing from the converse', this is the the second form 'arguing from the inverse'.) Even though "an A is an X" implies "any property P of an X is also that of an A', it does not mean that "an A is not an X" implies "any property P of X is not that of an A". Negation does not carry over that way.
– user9166
Mar 5, 2019 at 2:38

When you say "the phenomenon of cats being born into this world is natural," what that means is, "the phenomenon of cats being born into this world is part of the set of natural phenomena." In other words, "is" here indicates belonging to a particular set, as it often does when there is only a predicate adjective. There is more than one element in this set (i.e. cats being born into this world is not the only natural phenomenon). Therefore, the fact that "the phenomenon of rabbits being born into this world is not the phenomenon in point 3" does not prevent the phenomenon of rabbits being born into this world from also belonging to this set.

It's the same situation as saying, "An orange is a fruit. A grape is not an orange. Therefore a grape is not a fruit," which is obviously incorrect, because there can be more than one type of fruit.

In cases where the set does only contain one element, such reasoning can hold, but it requires the explicit specification that the set the object belongs to is a singleton. For example, "I am green-skinned. There is only one green-skinned person in the world. You are not me. Therefore, you are not green-skinned."

Here is the argument:

1. No N is not-N.

2. No not-N is N.

3. All C are N.

4. No R are C.

Thus: No R are N.

The syllogism is invalid for two reasons. First, the third premise denies the antecedent (cats) of the fourth. There can be other animals that are normal. Wikipedia: Denying the antecedent; Formal fallacy.

Second, a term that is distributed in the conclusion (normal) is not distributed in the major premise (all cats are normal). Wikipedia: Illicit major.

The first two premises are not needed except as definitions. The second two, about cats and rabbits, state actual relationships between categories,

• Thank you. I guess your answer is fully applicable to the latest edits in my question, too, right? Mar 5, 2019 at 2:10
• @brilliant Yes. See my comment to your original question. Mar 5, 2019 at 4:53
• Seems like in addition to denying the antecedent, it's a form of equivocating as it makes use of the ambiguous mean of "is". Where in the first 2 statements it uses "is" to mean "has the property of". And then in 3, 4, and the conclusions tries to use that same "is" in the sense of equality. Mar 5, 2019 at 4:57
• "...are not needed except as definitions." You say that as though definitions are not vital. In formal logic, they're crucial. Mar 6, 2019 at 18:12
• If 3. had said "Cats being born in the wild is the ONLY thing that is natural" then your conclusion would be true. Mar 7, 2019 at 10:24

It appears that you are treating "is" as an equality operator. There are contexts where "is" denotes equality ("one plus one is two"), but in other cases where it denotes something else, such as subset ("cats are mammals") or attribute ("cats are furry"). If we replace "cats being born in the world" with "A", "natural" with "B", and "rabbits being born in the world" with "B", then your argument is "A is B, C is not A, therefore C is not B." If "is" is denoting equality, then this would be a valid argument. But the first and last "is" are denoting attribute. The argument "Cats are furry, dogs are not cats, therefore dogs are not furry" would be a shorter version of this fallacy. Or "five is prime, seven is not five, therefore seven is not prime".

This can be seen as an equivocation fallacy (using "is" in different sense), denying the antecedent (we have the true statement "if C were A, then C would be B", and you're denying the antecedent "C is A" to negate the conclusion), false dichotomy (the argument boils down to claiming that everything is either A or not B).

• This type of pun is common to many trick questions and other nonsense, e.g. "No man is an island. Time waits for no man. Therefore, time waits for an island". Mar 5, 2019 at 17:23
• @Barmar : and "One cat has one more tail than no cat. No cat has 8 tails. So a cat has nine tails".
– vsz
Mar 6, 2019 at 5:30
• Suggestion: right after "... are denoting attribute", you could mention that this is a set operation. I.e., the "set of all things that are furry", then "X is in this set, Y is also in this set" does not lead to "X=Y". Without this, your train of thought (or rather the tone of the answer) seems to abruptly stop/change at that point.
– AnoE
Mar 6, 2019 at 10:15
• What this really all comes down to is that human languages have ambiguities that are resolved using common sense and conventions, and you can create fallacies if you try to translate it literally into logic. Mar 6, 2019 at 16:04
• In the immortal words of Bill Clinton, it depends upon what the meaning of the word 'is' is.
– BenM
Mar 6, 2019 at 21:07

The argument is basically the fallacy of Denying the Antecedant. `~C, C → N |- ~N`

• RabbitBirths are not CatBirths,
• CatBirths are NaturalPhenomena,
• therefore RabbitBirths are not NaturalPhenomena.

`R → ~C , C → N |- R → ~N`

You imply in point 3 that all cats are normal. I don't know the specific name of the fallacy, but your argument is invalid because you didn't state that all things normal are cats, only that all cats are normal.

• I am not sure that point 3 is "all" cats are normal or "some" cats are normal. Mar 5, 2019 at 1:24
• By "cats are normal" I meant to say that it is absolutely normal that cats are born into and exist in this world, whatever condition some cats may be born in (blind, no limbs, etc.) Mar 5, 2019 at 1:34
• I did some editing to my question. Mar 5, 2019 at 1:42
• But the general point is that says "cats being born is normal" does not mean "cats being born is the only normal phenomenon". Mar 5, 2019 at 17:24

Your error here is defining "normal" as a single set of things to which something either belongs or doesn't. That's not a useful (or normal) definition. Things are only normal or abnormal in context, compared to others of their kind. Are they a common or typical example of that kind, or are they an unusual or rare example? Normal cats have long tails (Manx cats might be considered abnormal). But a cat would be, say, a very abnormal voter, or an abnormal vehicle (more typical voters being human and more typical vehicles being machines). A perfectly normal person, likewise, would be an abnormal meal (cannibalism being rare), and a perfectly ordinary vehicle (say a bicycle) would be an unusual piece of art to hang on a wall.

You then make a second error in assuming that the statement "cats are normal" is equating the set of cats with the set of normal things. That's not what "are" means in this context. A more appropriate reading of that sentence would be to make cats a subset of normal things.

• I did some editing to my question. Mar 5, 2019 at 1:42
• Your edited question only makes the second error--assuming that "is" means equivalence and not subset. "Cats are carnivores", for example, clearly means that cats are a subset of carnivores, not an identical set. Mar 5, 2019 at 2:37
• This is the same error, not the second one. Mar 5, 2019 at 2:40

The conclusion reads #3 as "Only the phenomenon of cats being born into this world is natural".

Alternatively "is" in this case means "has the attribute of being" or "is a type of", not "is equal to".

The fallacy is called a non-sequitur. It essentially means that even if you accept the premises of the argument you still would not have to accept the conclusion. In other words, the conclusion does not logically follow from the premises.

The question has been answered but I thought a self-evident example would still help:

1. Whatever is alive is not dead.
2. Whatever is dead is not alive.
3. I am alive.
4. You are not me.

This obviously isn't the case. Why not? Well, simply put: just because I am alive (3), does not mean that I am the only one who is alive.

This defeats the conclusion that anyone who is not me must invariably be dead.

I am one of the creatures who are alive. I am not (conclusively proven to be) the only one.

Similarly, the phenomenon of cats being born into this world is one of the things that are natural. It is not (conclusively proven to be) the only natural thing in this world.

This defeats the conclusion that anything other than the phenomenon of cats being born must invariably be unnatural.

• This example only shows the presence of fallacy; however, it does zero in showing where exactly it is. Mar 6, 2019 at 15:56
• @brilliant: Fair point but it was only intended as a simple example to supplement the given answers which are all correct. Nonetheless, I've expanded the answer. Mar 6, 2019 at 18:14

Set logic:

• catbirths are a subset of natural
• rabbitbirths are a subset of natural
• there need not be an intersection between catbirths and rabbitbirths

The fallacy is a false exclusionary disjunct. The point (4) does not deny point (3). It is different, but is not a denial, does not exclude it.

Your conclusion is equivalent to "since rabbits are not cats, then rabbits are not animals".