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In predicate logic, does existential quantification (∃) include universal quantification (∀), i.e. can 'some' imply 'all'?
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In predicate logic, does existential quantification (∃) include universal quantification (∀), i.e. can 'some' imply 'all'?
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)
Which kinds of Philosophy.SE questions should be taken from (or tolerated in)…Can someone clear up this semantic proof of quantification logic?How is First Order Logic complete but not decidable?A question about statements and conclusionWhat does the truth-value of a material implication represent?Why is this Statement correct: G implies ¬Contradiction?Russell's Paradox and the Law of Non-ContradictionIf an argument can be valid in one logical system, but invalid in another, are logical arguments “meaningful”?Predicate Logic - Existential EliminationPredicate Logic - Universal IntroductionIs Ross' paradox really a paradox?
I am having a discussion wether 'some' can also imply 'all'. The definition for some, 'an unspecified number or amount of people or things' seems to leave room for this interpretation.
Discussion follows on the following statements:
1. All newspaper readers are reasonable people.
2. Some newspaper readers are criminal.
The question is whether or not the statement:
Not all reasonable people are criminal
Is valid...
logic quantification
edited 1 hour ago
Eliran
4,90231433
asked 1 hour ago
6thsense6thsense
404
add a comment |
I am having a discussion wether 'some' can also imply 'all'. The definition for some, 'an unspecified number or amount of people or things' seems to leave room for this interpretation.
Discussion follows on the following statements:
1. All newspaper readers are reasonable people.
2. Some newspaper readers are criminal.
The question is whether or not the statement:
Not all reasonable people are criminal
Is valid...
logic quantification
edited 1 hour ago
Eliran
4,90231433
asked 1 hour ago
6thsense6thsense
404
add a comment |
I am having a discussion wether 'some' can also imply 'all'. The definition for some, 'an unspecified number or amount of people or things' seems to leave room for this interpretation.
Discussion follows on the following statements:
1. All newspaper readers are reasonable people.
2. Some newspaper readers are criminal.
The question is whether or not the statement:
Not all reasonable people are criminal
Is valid...
logic quantification
edited 1 hour ago
Eliran
4,90231433
asked 1 hour ago
6thsense6thsense
404
I am having a discussion wether 'some' can also imply 'all'. The definition for some, 'an unspecified number or amount of people or things' seems to leave room for this interpretation.
Discussion follows on the following statements:
1. All newspaper readers are reasonable people.
2. Some newspaper readers are criminal.
The question is whether or not the statement:
Not all reasonable people are criminal
Is valid...
logic quantification
logic quantification
edited 1 hour ago
Eliran
4,90231433
asked 1 hour ago
6thsense6thsense
404
edited 1 hour ago
Eliran
4,90231433
asked 1 hour ago
6thsense6thsense
404
edited 1 hour ago
Eliran
4,90231433
edited 1 hour ago
Eliran
4,90231433
edited 1 hour ago
Eliran
4,90231433
4,90231433
asked 1 hour ago
6thsense6thsense
404
asked 1 hour ago
6thsense6thsense
404
asked 1 hour ago
6thsense6thsense
404
404
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
"Some" does not exclude "all", but you cannot deduce "all" from "some".
Having said that, the above argument is not valid.
From premises 1 and 2 we can derive :
Some reasonable people are criminal
that is equivalent to : Not all reasonable people are not criminal.
answered 1 hour ago
Mauro ALLEGRANZAMauro ALLEGRANZA
29.8k22065
add a comment |
Rewrite the phrases in a more formal-like manner as
1. For all x, N(x) implies R(x)
2. There exists x, N(x) and C(x)
And notice these do imply there are reasonable criminals, ie,
There exists x, R(x) and C(x)
Now, "Not all reasonable people are criminal" would be
Not for all x, R(x) implies C(x)
which is (classically) equivalent to
There exists x, R(x) and not C(x)
But it's easy to see one can construct a model with a single individual possessing the three predicates N, R and C, which satisfies the first three phrases, but not the last two
answered 1 hour ago
alkchfalkchf
1913
New contributor
alkchf is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
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2 Answers
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active
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2 Answers
2
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"Some" does not exclude "all", but you cannot deduce "all" from "some".
Having said that, the above argument is not valid.
From premises 1 and 2 we can derive :
Some reasonable people are criminal
that is equivalent to : Not all reasonable people are not criminal.
answered 1 hour ago
Mauro ALLEGRANZAMauro ALLEGRANZA
29.8k22065
add a comment |
"Some" does not exclude "all", but you cannot deduce "all" from "some".
Having said that, the above argument is not valid.
From premises 1 and 2 we can derive :
Some reasonable people are criminal
that is equivalent to : Not all reasonable people are not criminal.
answered 1 hour ago
Mauro ALLEGRANZAMauro ALLEGRANZA
29.8k22065
add a comment |
"Some" does not exclude "all", but you cannot deduce "all" from "some".
Having said that, the above argument is not valid.
From premises 1 and 2 we can derive :
Some reasonable people are criminal
that is equivalent to : Not all reasonable people are not criminal.
answered 1 hour ago
Mauro ALLEGRANZAMauro ALLEGRANZA
29.8k22065
"Some" does not exclude "all", but you cannot deduce "all" from "some".
Having said that, the above argument is not valid.
From premises 1 and 2 we can derive :
Some reasonable people are criminal
that is equivalent to : Not all reasonable people are not criminal.
answered 1 hour ago
Mauro ALLEGRANZAMauro ALLEGRANZA
29.8k22065
answered 1 hour ago
Mauro ALLEGRANZAMauro ALLEGRANZA
29.8k22065
answered 1 hour ago
Mauro ALLEGRANZAMauro ALLEGRANZA
29.8k22065
answered 1 hour ago
Mauro ALLEGRANZAMauro ALLEGRANZA
29.8k22065
29.8k22065
add a comment |
add a comment |
Rewrite the phrases in a more formal-like manner as
1. For all x, N(x) implies R(x)
2. There exists x, N(x) and C(x)
And notice these do imply there are reasonable criminals, ie,
There exists x, R(x) and C(x)
Now, "Not all reasonable people are criminal" would be
Not for all x, R(x) implies C(x)
which is (classically) equivalent to
There exists x, R(x) and not C(x)
But it's easy to see one can construct a model with a single individual possessing the three predicates N, R and C, which satisfies the first three phrases, but not the last two
answered 1 hour ago
alkchfalkchf
1913
New contributor
alkchf is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
Rewrite the phrases in a more formal-like manner as
1. For all x, N(x) implies R(x)
2. There exists x, N(x) and C(x)
And notice these do imply there are reasonable criminals, ie,
There exists x, R(x) and C(x)
Now, "Not all reasonable people are criminal" would be
Not for all x, R(x) implies C(x)
which is (classically) equivalent to
There exists x, R(x) and not C(x)
But it's easy to see one can construct a model with a single individual possessing the three predicates N, R and C, which satisfies the first three phrases, but not the last two
answered 1 hour ago
alkchfalkchf
1913
New contributor
alkchf is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
Rewrite the phrases in a more formal-like manner as
1. For all x, N(x) implies R(x)
2. There exists x, N(x) and C(x)
And notice these do imply there are reasonable criminals, ie,
There exists x, R(x) and C(x)
Now, "Not all reasonable people are criminal" would be
Not for all x, R(x) implies C(x)
which is (classically) equivalent to
There exists x, R(x) and not C(x)
But it's easy to see one can construct a model with a single individual possessing the three predicates N, R and C, which satisfies the first three phrases, but not the last two
answered 1 hour ago
alkchfalkchf
1913
New contributor
alkchf is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Rewrite the phrases in a more formal-like manner as
1. For all x, N(x) implies R(x)
2. There exists x, N(x) and C(x)
And notice these do imply there are reasonable criminals, ie,
There exists x, R(x) and C(x)
Now, "Not all reasonable people are criminal" would be
Not for all x, R(x) implies C(x)
which is (classically) equivalent to
There exists x, R(x) and not C(x)
But it's easy to see one can construct a model with a single individual possessing the three predicates N, R and C, which satisfies the first three phrases, but not the last two
answered 1 hour ago
alkchfalkchf
1913
New contributor
alkchf is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 1 hour ago
alkchfalkchf
1913
New contributor
alkchf is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 1 hour ago
alkchfalkchf
1913
answered 1 hour ago
alkchfalkchf
1913
1913
New contributor
alkchf is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
alkchf is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
alkchf is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
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