Rewriting a logical statement
$begingroup$
Only lakers are irrational people.
I believe it technically should be translated as:
All irrational people are lakers.
Is there is any way at all to rewrite the above statement to mean the following and be logically correct:
All lakers are irrational people.
How would you justify it? (If it is possible)
logic logic-translation
asked Nov 26 '18 at 17:42
PhillipPhillip
112
$endgroup$
add a comment |
$begingroup$
Only lakers are irrational people.
I believe it technically should be translated as:
All irrational people are lakers.
Is there is any way at all to rewrite the above statement to mean the following and be logically correct:
All lakers are irrational people.
How would you justify it? (If it is possible)
logic logic-translation
asked Nov 26 '18 at 17:42
PhillipPhillip
112
$endgroup$
add a comment |
$begingroup$
Only lakers are irrational people.
I believe it technically should be translated as:
All irrational people are lakers.
Is there is any way at all to rewrite the above statement to mean the following and be logically correct:
All lakers are irrational people.
How would you justify it? (If it is possible)
logic logic-translation
asked Nov 26 '18 at 17:42
PhillipPhillip
112
$endgroup$
Only lakers are irrational people.
I believe it technically should be translated as:
All irrational people are lakers.
Is there is any way at all to rewrite the above statement to mean the following and be logically correct:
All lakers are irrational people.
How would you justify it? (If it is possible)
logic logic-translation
logic logic-translation
asked Nov 26 '18 at 17:42
PhillipPhillip
112
asked Nov 26 '18 at 17:42
PhillipPhillip
112
asked Nov 26 '18 at 17:42
PhillipPhillip
112
asked Nov 26 '18 at 17:42
PhillipPhillip
112
asked Nov 26 '18 at 17:42
PhillipPhillip
112
112
add a comment |
add a comment |
3 Answers
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$begingroup$
Indicating with $L$ the set of lakers $l$ and with $Pi$ the set of irrational people $pi$, the first statement is equivalent to
$$forall piin Pi quad piin L$$
the second one is
$$forall lin Lquad lin Pi $$
which is not equivalent to the first one, indeed from this last one we could also have $pi not in L$ for aome $pi$.
answered Nov 26 '18 at 17:49
gimusigimusi
92.8k84494
$endgroup$
add a comment |
$begingroup$
All rational people are not lakers.
The opposite converse is equally valid.
The converse that you posit is not equally valid.
answered Nov 26 '18 at 17:46
John L WintersJohn L Winters
829
$endgroup$
add a comment |
$begingroup$
Your initial translation is correct, though in standard form I would write
All non-rational people are lakers.
This is an Aristotelian A type statement, and A type statements have valid obverses and valid contrapositives. They do not have valid converses.
Obverse: No non-rational people are non-lakers.
Contrapositive: All non-lakers are rational people.
So the ultimate answer to your question is no, because you are trying to get the converse of an A statement to be true, which does not happen in general.
If you had an E or I statement, the converse would be valid.
answered Nov 26 '18 at 17:51
Adrian KeisterAdrian Keister
4,90261933
$endgroup$
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3 Answers
3
active
oldest
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3 Answers
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active
oldest
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active
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active
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$begingroup$
Indicating with $L$ the set of lakers $l$ and with $Pi$ the set of irrational people $pi$, the first statement is equivalent to
$$forall piin Pi quad piin L$$
the second one is
$$forall lin Lquad lin Pi $$
which is not equivalent to the first one, indeed from this last one we could also have $pi not in L$ for aome $pi$.
answered Nov 26 '18 at 17:49
gimusigimusi
92.8k84494
$endgroup$
add a comment |
$begingroup$
Indicating with $L$ the set of lakers $l$ and with $Pi$ the set of irrational people $pi$, the first statement is equivalent to
$$forall piin Pi quad piin L$$
the second one is
$$forall lin Lquad lin Pi $$
which is not equivalent to the first one, indeed from this last one we could also have $pi not in L$ for aome $pi$.
answered Nov 26 '18 at 17:49
gimusigimusi
92.8k84494
$endgroup$
add a comment |
$begingroup$
Indicating with $L$ the set of lakers $l$ and with $Pi$ the set of irrational people $pi$, the first statement is equivalent to
$$forall piin Pi quad piin L$$
the second one is
$$forall lin Lquad lin Pi $$
which is not equivalent to the first one, indeed from this last one we could also have $pi not in L$ for aome $pi$.
answered Nov 26 '18 at 17:49
gimusigimusi
92.8k84494
$endgroup$
Indicating with $L$ the set of lakers $l$ and with $Pi$ the set of irrational people $pi$, the first statement is equivalent to
$$forall piin Pi quad piin L$$
the second one is
$$forall lin Lquad lin Pi $$
which is not equivalent to the first one, indeed from this last one we could also have $pi not in L$ for aome $pi$.
answered Nov 26 '18 at 17:49
gimusigimusi
92.8k84494
answered Nov 26 '18 at 17:49
gimusigimusi
92.8k84494
answered Nov 26 '18 at 17:49
gimusigimusi
92.8k84494
answered Nov 26 '18 at 17:49
gimusigimusi
92.8k84494
92.8k84494
add a comment |
add a comment |
$begingroup$
All rational people are not lakers.
The opposite converse is equally valid.
The converse that you posit is not equally valid.
answered Nov 26 '18 at 17:46
John L WintersJohn L Winters
829
$endgroup$
add a comment |
$begingroup$
All rational people are not lakers.
The opposite converse is equally valid.
The converse that you posit is not equally valid.
answered Nov 26 '18 at 17:46
John L WintersJohn L Winters
829
$endgroup$
add a comment |
$begingroup$
All rational people are not lakers.
The opposite converse is equally valid.
The converse that you posit is not equally valid.
answered Nov 26 '18 at 17:46
John L WintersJohn L Winters
829
$endgroup$
All rational people are not lakers.
The opposite converse is equally valid.
The converse that you posit is not equally valid.
answered Nov 26 '18 at 17:46
John L WintersJohn L Winters
829
answered Nov 26 '18 at 17:46
John L WintersJohn L Winters
829
answered Nov 26 '18 at 17:46
John L WintersJohn L Winters
829
answered Nov 26 '18 at 17:46
John L WintersJohn L Winters
829
829
add a comment |
add a comment |
$begingroup$
Your initial translation is correct, though in standard form I would write
All non-rational people are lakers.
This is an Aristotelian A type statement, and A type statements have valid obverses and valid contrapositives. They do not have valid converses.
Obverse: No non-rational people are non-lakers.
Contrapositive: All non-lakers are rational people.
So the ultimate answer to your question is no, because you are trying to get the converse of an A statement to be true, which does not happen in general.
If you had an E or I statement, the converse would be valid.
answered Nov 26 '18 at 17:51
Adrian KeisterAdrian Keister
4,90261933
$endgroup$
add a comment |
$begingroup$
Your initial translation is correct, though in standard form I would write
All non-rational people are lakers.
This is an Aristotelian A type statement, and A type statements have valid obverses and valid contrapositives. They do not have valid converses.
Obverse: No non-rational people are non-lakers.
Contrapositive: All non-lakers are rational people.
So the ultimate answer to your question is no, because you are trying to get the converse of an A statement to be true, which does not happen in general.
If you had an E or I statement, the converse would be valid.
answered Nov 26 '18 at 17:51
Adrian KeisterAdrian Keister
4,90261933
$endgroup$
add a comment |
$begingroup$
Your initial translation is correct, though in standard form I would write
All non-rational people are lakers.
This is an Aristotelian A type statement, and A type statements have valid obverses and valid contrapositives. They do not have valid converses.
Obverse: No non-rational people are non-lakers.
Contrapositive: All non-lakers are rational people.
So the ultimate answer to your question is no, because you are trying to get the converse of an A statement to be true, which does not happen in general.
If you had an E or I statement, the converse would be valid.
answered Nov 26 '18 at 17:51
Adrian KeisterAdrian Keister
4,90261933
$endgroup$
Your initial translation is correct, though in standard form I would write
All non-rational people are lakers.
This is an Aristotelian A type statement, and A type statements have valid obverses and valid contrapositives. They do not have valid converses.
Obverse: No non-rational people are non-lakers.
Contrapositive: All non-lakers are rational people.
So the ultimate answer to your question is no, because you are trying to get the converse of an A statement to be true, which does not happen in general.
If you had an E or I statement, the converse would be valid.
answered Nov 26 '18 at 17:51
Adrian KeisterAdrian Keister
4,90261933
answered Nov 26 '18 at 17:51
Adrian KeisterAdrian Keister
4,90261933
answered Nov 26 '18 at 17:51
Adrian KeisterAdrian Keister
4,90261933
answered Nov 26 '18 at 17:51
Adrian KeisterAdrian Keister
4,90261933
4,90261933
add a comment |
add a comment |
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