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I posted the following question a few days ago but I couldn't have a reply. But it's still on my mind.
So please let me ask the same question one more time.

Are the meanings of the following sentences the same?

You can't have your cake and eat it.
You can't have your cake and you can't eat it.
You can't have your cake and eat it(,) too.
You can't have your cake and you can't eat it(,) too.

In the following description, I put the meanings inside the quatation marks.

I think the first and the second sentences have the same two meanings, meaning 1 and meaning2.

Meaning 1. "You can't have your cake. You can't eat it." You can't have your cake. has nothing to do with You can't eat it. So the firt and the second sentences are just stating two dirrerent things. One thing is You can't have your cake. and the other is You can't eat it.

Meaning 2. "You can't have your cake and eat it(,) too. " "You can either have your cake or eat it." You can't have your cake. is closely connected to You can't eat it. So the firt and the second sentences are stating only one thing.

I think the third and the fourth sentences have the same one meaning and it's the same as meaning 2 above.
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Comments  
Only these are acceptable:

You can't have your cake and eat it.
You can't have your cake and eat it, too
.

The other two are grammatically correct but carry no useful meaning-- obviously, if you don't have something, you can do nothing with it.
northwind Are the meanings of the following sentences the same? No.

You can't have your cake and eat it.
You can't have your cake and you can't eat it.
You can't have your cake and eat it(,) too.
You can't have your cake and you can't eat it(,) too.

The first and third mean that you can't do both.
The second and fourth mean that you can't do either.



In the following description, I put the meanings inside the quatation marks.

I think the first and the second sentences have the same two meanings, meaning 1 and meaning2.

Meaning 1. "You can't have your cake. You can't eat it." You can't have your cake. has nothing to do with You can't eat it. So the firt and the second sentences are just stating two dirrerent things. One thing is You can't have your cake. and the other is You can't eat it.

How about this variation?
George Bush can't walk and chew gum at the same time.
I'm sure you would agree that I may not rephrase this as
George Bush can't walk, and, at the same time, George Bush can't chew gum.

How about,

George Bush can't walk and chew gum. (Native speakers will assume this to mean "at the same time.")
Similarly, your first and third examples would be taken by native speakers to mean "within the same scenario."
In both cases, the operative word is "and." You would like us to ignore the "and." Sorry, no deal.

Perhaps the reason you're having trouble with this is that you're a mathmetician. We get into this mess about whether "not' is distributive, or some such bull. (not A and B means not A and not B) Sorry, it doesn't. (actually, not A and B means not both) You can have one or the other but not both. You can't solve this problem with math. The rules are different.

Meaning 2. "You can't have your cake and eat it(,) too. " "You can either have your cake or eat it." You can't have your cake. is closely connected to You can't eat it. So the firt and the second sentences are stating only one thing.

The business about having and eating being closely connected or not closely connected is going right over the top of my head. I have no idea what you mean. Sorry. You come out with the exact opposite conclusion from what a native speaker would reach. The key is the clause, not closeness. In your second version, you have two independent clauses, each of which is a negative statement. One does not effect the other. Your sentence says (not A and not B.) This is the meaning you attribute to your first version. You have everything ass-backwards, as my mother used to say.

I think the third and the fourth sentences have the same one meaning and it's the same as meaning 2 above. No, no, no, and no. One and three are the same. Two and four are the same. Emotion: noddingEmotion: shakeEmotion: noddingEmotion: shake
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Oh dear! How much more can be beat this dead horse? MM already concluded this question with 2 examples which most native would agree using. In a nut shall, it means one can't have it both ways, like ordering your breakfast eggs over-easy scrambled. Well, you know the picture.

If there is still confusion with this proverb. This should clear it up:

http://www.wsu.edu/~brians/errors/eatcake.html

YOU CAN’T EAT YOUR CAKE AND HAVE IT TOO



The most popular form of this saying—“You can’t have your cake and eat it too”— confuses many people because they mistakenly suppose the word “have” means “eat,” as in “Have a piece of cake for dessert.” A more logical version of this saying is “You can’t eat your cake and have it too,” meaning that if you eat your cake you won’t have it any more. The point is that if you eat your cake right now you won’t have it to eat later. “Have” means “possess” in this context, not “eat.”
Since the horse is dead, you're welcome to join the party. Emotion: smile
Wow, wow, wow!
I have been in a mess.
But now I'm OK.

Gotcha!!

Thanks!!

But, ...can I ask one more?

What do the following senences mean?
Tom can walk and chew gum.
Tom can ride on a bike and drive a car.

Do they mean the same as the followings?
Tom can walk and chew gum at the same time.
Tom can ride on a bike and drive a car at the same time.

Sorry, but I'm so serious.
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We need to use another example besides the "walk and chew gum" one because that's an idiom almost always used with a negative feel (can't walk and chew gum at the same time, can barely walk and chew gum) and the clear implication is that the person is not very skilled at much.

If you say "Jane has many talents. She can bake a delicious pie and build a treehouse. She can change a flat tire and sew an evening gown" there is NO implication that she does those things at the same time. In fact, to imply that she does these things at the same time is ridiculous.

If you say "Tom can ride a bike and drive a car" there is no implication he does both at the same time.

Oddly, saying "ride on a bike and drive a car" does carry the implication you mean "at the same time" even though doing both of those things at once is impossible.

If you say "The clown can ride on a bike and juggle chainsaws" then you can get an image of those two activities occurring at the same time.
northwindTom can walk and chew gum at the same time.

I think you're getting lost in the details. The point of this particular saying is that someone can successfully do more than one thing at a time. Given that understanding it should be obvious that the "bike/car" example is irrelevant. It is, after all, physically impossible to ride a bike and drive a car at the same time.
RayH It is, after all, physically impossible to ride a bike and drive a car at the same time.
Unless it is one of those
Human powered taxis!
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