h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

From the past comes this application of symbolic logic:
1. No cat has 8 tails. (Experimentally true)
2. Every cat has one more tail as no cat (seemes just as true)
As both propositions are true, this implies of course:
3. Every cat has 9 tails.

These cats have been observed, mostly on ships and used by officers agains sailors who tried to discuss logically about how things should be done.

In the last century another form of these special cats was discovered by Erwin Schroedinger ('oe' should be an 'o' with two dots on it).
In this case it seemed to be impossible to decide if the proposition "This cat is dead, it has ceased to be, ......" was true or not.

1. No cat has 8 tails. (Experimentally true)
2. Every cat has one more tail as no cat (seemes just as true)
As both propositions are true, this implies of course:
3. Every cat has 9 tails.

OK, let's take a look at this.

Statement 1. concerns the proposition (P) "All cats have 8 tails," and says "Not P," i.e., "It is not the case that (All cats have 8 tails.)" This statement is taken as true.

Statement 2. is then seen to be nonsense, because it assumes that 1 is a statement concerning an entity named as "no cat," wheras in fact it's a true statement concerning the falsity of the proposition "All cats have 8 tails." Statement 2 seems true only because it depends upon the fact that the truth of 1 hasn't been properly formulated.
When 1 is given as "It is not the case that all cats have 8 tails,"
it's far more difficult to make any kind of statement like 2 depend upon it.

Cheers,
Jon.

Yes, Jon, but that isn't what 1) means.

"No cat has 8 tails" is not equivalent to "it is not the case that all cats have 8 tails".

The original statement means "there is not an x such that x is a cat and x has eight tails".

A statement such as this cannot be proved to be true deductively unless your definition of "cat" excludes any animal with 8 tails. I don't think that is the case, and the proposition can only be presented as true inductively, (or experimentally) as the original poster correctly states.

However the second statement "Every cat has one more tail as no cat" is not true. It can only be true if the definiton of cat includes "has one tail", which it doesn't because:
1. It is possible to perceive of something correctly defined as a cat which has more than one tail and
2. There are actually cats with no tail (Manx cats)

So.. statement 2 is false and the syllogism fails.

Sorry.

Don't be sorry.
The fun in this kind of crooked logic is that everybody knows it cannot be true, while it seems logically true. Mostly the problem lies in the language. In this case, both sentences contain "no cat", so it is logically to assume these have the same meaning. Of course they are completely different.
Dovedale gave a perfect explanation of the first, the second could be something like: "a space containing one cat also contains one tail, a space without cat contains no tail".
The fact that Manx cats exist (and probable siam-twin cats with two tails) just complicates it.
So both statements are completely independent and that makes the conclusion in error.

Hi Dovedale,
I take your point on statement 1, and not going through the route of "all" which isn't implied. (I see that now!) I'm just an amateur where logic is concerned, but it's something I'm developing a fascination for.

Don't apologise, serves me right for trying to sound like I know what I'm talking about!

Cheers,
Jon.

Just in case anyone's still paying attention...

Let's examine the term "no cat". In statement 1, "no cat" refers to not any cat, that is that there is, in fact, no cat in existance with such a trait (though there is, but we can ignore them and refer only to the others). But then "no cat" has any number of tails other than one. In statement 2, "no cat" refers to a lack of cat, and hence of tail. That means tat suddenly "no cat" as specifically *no* tails. Therefor "no cat" cannot have 8 tails, for the tails must have a cat. QED.

-Spike A.

P.S., Jon: a great way to sound like you know what you're talking about is to add "QED" to the end of anything logical you say. Works for me!

Gosh, jolly well wish i could add some logic of my own, but i can't!! Sorry if this is not as intellectually stimulating as the rest of the replies but i found the whole discussion facinating!! As i have only just got into the site (last few days ) and am new to all the discussions i have found this one of the most confusing!! Have decided to read it all again and try to make more sense of it!! All the explanations seem confusing to such an amateur!!

But what fun .............. look forward to joining you all again when i have something constructive (or even clever) to offer you!!

Jules x

A cat has nine tails it’s a whip that was used on ships.
But the feline has only one tail, unless it is a type that lives in the middle of a jungle and has yet to be discovered by mankind, or an feline type of alien that is yet to visit.
No cats have no tails as there is no cats to have any tails.

Timeagian

i understand a cat of this description has been seen on the outskirts of chernoble,it is rumoured to have been of japannese decendents,family recently migrated from hiroshima area .
i would also add the octopussy was omited from the origanal calculation haveing eight such appendeges that serve all the required
requisites of a tail

Cats without tails are an officially accepted race.
As they come from island of Man they are called Manx cats.