## Formal Logic double negatives

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gregl

Posts: 1
Joined: Thu Aug 22, 2013 4:28 pm

### Formal Logic double negatives

Hi,

I have a question regarding formal logic questions involving double negative i.e. if no x, then no y. I know if you have a questions stating

if no x are y (if there are no puppies, there are kittens) you turn it into if x, then no y (if there are puppies, then there are no kittens).

But when you come across a No X, then No Y situation (when there are no puppies, there are no kittens) do you turn it into an If x, then y situation (if there are puppies, there are kittens)? Or can you leave the No X, then no Y situation alone and use it to from a correct contrapositive?

I'd appreciate any input anyone could provide me with.

Thanks!

lsathelper

Posts: 4
Joined: Wed Aug 21, 2013 10:38 pm

### Re: Formal Logic double negatives

deleted

KingofSplitters55

Posts: 139
Joined: Sun May 13, 2012 7:40 pm

### Re: Formal Logic double negatives

Indeed the double negatives can often be a huge source of confusion due to their inherently confusing syntax.

In this case I believe it would be: (the statement "No X, then No Y")

-X -> -Y (Contra: Y -> X)

X appears to be a necessary condition for the existence of Y. Namely, using your example, when there are kittens (Y), that is sufficient to indicate that there must also be puppies (X).

P.S.: I also believe that technically this is conditional logic/reasoning, as the formal logic encountered in the LSAT is in regards to when the quantitative modifiers are linked together in chain (such as most X are Y, and most X are Z, therefore some Y are also Z and vice-versa).

P.S. 2: The "X -> Y" would be a mistaken reversal. Just because X exists doesn't automatically mean Y would exist, at least based on the "No X, then No Y" statement alone. However when Y exists, then X exists, because if X didn't exist then according to your original statement there could be no Y.

bp shinners

Posts: 3086
Joined: Wed Mar 16, 2011 7:05 pm

### Re: Formal Logic double negatives

gregl wrote:if no x are y (if there are no puppies, there are kittens) you turn it into if x, then no y (if there are puppies, then there are no kittens).

You're off here. The original, "No X are Y", is different than your example, "If there are no puppies, then there are kittens".

The former would be diagrammed as: if you are a puppy then you're not a kitten.
The latter would be diagrammed as: if no puppies, then kittens.

The problem here is that when you wrote it out in the parentheses the first time, it wasn't a direct translation of the sentence. However when you said you turn it into something else, that would only apply to the situation that I denoted as the former. In the former, "No" is the key word; in the latter, "if" is the keyword.

But when you come across a No X, then No Y situation (when there are no puppies, there are no kittens) do you turn it into an If x, then y situation (if there are puppies, there are kittens)? Or can you leave the No X, then no Y situation alone and use it to from a correct contrapositive?

Nope, you don't turn into that for similar reasons as above. So you would have, "if there are no puppies, then there are no kittens" and the contrapositive, "if there are kittens, then there are puppies".

I think the problem here is that you're confusing a conditional if then statement with negations with a quantified statement that uses "No" as a quantifier to mean none of a certain group. Those are two importantly different ideas and it's important to keep them separate in your head.