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I have the following statement:

All the actors are girls. All the girls are beautiful.

The conclusions are given below:

Conclusions:

1)All the actors are beautiful.

2)Some girls are actors.

My text book says that Both (1) and (2) conclusions follow's from the given statement. There is no doubt in (1) conclusion. But how come the second conclusion will become true. If it's become true then it indicates that if a statement is given in form All X are Y. Then Some Y is X is true. Is it so?

In what all cases does this contradicts?

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Depends on the logic you are using. I think this belongs on SE.philosophy. – TimLymington Sep 18 '11 at 9:37
so i should close this, and post it in philosophy ? – Ant's Sep 18 '11 at 9:40
It depends. Are you asking the question of what those statements mean in terms of English grammar? If so, the question belongs here. If not, then ask in philosophy. – David Schwartz Sep 18 '11 at 9:42
I asked the q in terms of english ;0 – Ant's Sep 18 '11 at 9:49
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The second conclusion (that some girls are actors) only follows from the original statement if there are some actors. (See my comment to rems's answer.) – John Y Sep 18 '11 at 11:03

closed as off topic by TimLymington, RegDwighт♦ Sep 18 '11 at 11:37

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2 Answers

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In formal logic, some means "there is at least one".

They even have a formal notation: character "∀" (inverted "A") means "All"; character "∃" (inverted "E") means "Exist" (there exists at least one).

∀ actor: Girl(actor) means "all the actors are girls".

∃ actor: Girl(actor) means there is at least one actor such that Girl(actor) is true.

The first statement obviously implies the second one (assuming that there exists at least one actor): if all actors are girls then there is at least one actor who is a girl.

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Not quite. The first implies the second only if there is at least one actor. If there are no actors, then any proposition that applies to "all actors" is true, in formal logic. – John Y Sep 18 '11 at 10:58
@John That's a good point. Updated the answer. – rems Sep 18 '11 at 11:35
up vote -2 down vote

In ordinary English grammar, vacuously true statements are not allowed. They're permissible in formal logic, but in English, they're only used as jokes. You cannot say, "Here's an argument that's persuaded every atheist I've ever met" if you never met an atheist.

There are many examples of English statements that have a different meaning from what you get when you parse the words with formal logic. For example, "My cousin doesn't believe President Obama is doing a good job of running the country". You cannot say this if your cousin is newborn. In ordinary common English, "I don't believe X" usually means "I believe not-X" (absent convincing context suggesting otherwise).

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-1: grammar does not impose what one is allowed to mean with his/her sentences... The sentence about your cousin is grammatically correct whether you have a cousin or not, and whatever his age may be. It may be logically flawed, but that is no matter of grammar. – nico Sep 18 '11 at 9:57
@nico: Grammar: The whole system and structure of a language or of languages in general, usually taken as consisting of syntax and morphology (including inflections) and sometimes also phonology and semantics. – David Schwartz Sep 18 '11 at 10:22
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exactly. So... logic or truth is not part of grammar. The sentence Elephants like to spend winter on the Moon. is grammatically correct. – nico Sep 18 '11 at 12:20
It is also grammar that dictates what conceptual relationship that sentence represents. (That is, what must be the case for it to be factually correct.) Since my answer is about what conceptual relationships sentence structures can represent, is it about the rules of grammar. – David Schwartz Sep 18 '11 at 16:12
Let me explain this another way, since I'm not quite sure I got this out. Meaning is about what concept a word names. Grammar is about which relationships among words are legal and what corresponding relationships with their concepts those words form. In this case, we aren't talking about which concepts any of the words name. The question of what "I don't think X" means isn't about what "I" means or what "don't" means. It's a question about what relationship among the concepts the words made, not which concepts it relates. So it's about grammar, not word meaning. – David Schwartz Sep 19 '11 at 8:16
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