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defense

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Are Some Statements Reversible
« on: March 11, 2007, 04:39:36 PM »
If a statement reads "some red plants are tall plants" can you also say that "Some Tall Plants are red plants."

In other words can "RP some TP" be flipped to read "TP some RP."

theo

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Re: Are Some Statements Reversible
« Reply #1 on: March 11, 2007, 05:28:23 PM »
If a statement reads "some red plants are tall plants" can you also say that "Some Tall Plants are red plants."

In other words can "RP some TP" be flipped to read "TP some RP."


Yes, 'Some' statements are always reversible.


If

"some birds fly",

then

"some things-that-fly are birds"
quid leges sine moribus vanae proficiunt?

theo

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Re: Are Some Statements Reversible
« Reply #2 on: March 11, 2007, 05:32:24 PM »
If a statement reads "some red plants are tall plants" can you also say that "Some Tall Plants are red plants."

In other words can "RP some TP" be flipped to read "TP some RP."
If a statement reads "some red plants are tall plants" can you also say that "Some Tall Plants are red plants."

In other words can "RP some TP" be flipped to read "TP some RP."

Yes.

The word some establishes that there is at least one that exists.

Saying some red plants are tall plants establishes that at least one red plant exists and that it is a tall plant

This also establishes that at least one tall plant exists because the statement establishes that at least one red one is also tall. 

Since there is at least one plant that is both red and tall it is also established that some tall plants are red plants, so the reverse of the statement also holds true.

A tricky part of dealing with the reversibility of some statements is when a negative is involved.  For example: some green trees are not tall trees .  You cannot simply reverse the items in this statement and have it necessarily hold true. 

Reversing it into some tall trees are not green trees is not something that is guaranteed by the original statement because in this case it is not guaranteed that any tall trees exist, unlike a some statement where both items are stated in the positive




The trick is to keep the negation with the term that was originally negated:

"some birds do not fly"

reverses to:

"some things-that-don't-fly are birds"

NOT

"some things that fly are not birds"
quid leges sine moribus vanae proficiunt?

bubDread

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Re: Are Some Statements Reversible
« Reply #3 on: March 11, 2007, 06:30:52 PM »
all of these statements are very insightful.

also remember that "most x are y" does not imply hat "most y are x"

bubDread

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Re: Are Some Statements Reversible
« Reply #4 on: March 12, 2007, 10:12:42 PM »
some statements are reversible, but are all reversible statements some statements?

theo

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Re: Are Some Statements Reversible
« Reply #5 on: March 12, 2007, 11:30:34 PM »
some statements are reversible, but are all reversible statements some statements?


'No' statements are also reversible.

"No man is an island" = "No island is a man"
quid leges sine moribus vanae proficiunt?

bubDread

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Re: Are Some Statements Reversible
« Reply #6 on: March 13, 2007, 07:25:23 AM »
So it makes no sense to ask, "for whom the bell tolls?"

LizPendens™

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Re: Are Some Statements Reversible
« Reply #7 on: March 13, 2007, 08:38:14 PM »
So it makes no sense to ask, "for whom the bell tolls?"

Right, because it's a fragment.   :D

in any case, it tolls for thee.
There foam'd rebellious Logic, gagg'd and bound.                           
            -  Charles Dodgson,  "Lewis Carroll"                               
                         "The Game of Logic"

LizPendens™

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Re: Are Some Statements Reversible
« Reply #8 on: March 13, 2007, 09:27:48 PM »
if it doesn't toll, it is not for thee.
There foam'd rebellious Logic, gagg'd and bound.                           
            -  Charles Dodgson,  "Lewis Carroll"                               
                         "The Game of Logic"

LizPendens™

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Re: Are Some Statements Reversible
« Reply #9 on: March 13, 2007, 09:31:44 PM »
it does not toll unless it is for thee.
There foam'd rebellious Logic, gagg'd and bound.                           
            -  Charles Dodgson,  "Lewis Carroll"                               
                         "The Game of Logic"