I have trouble understanding this fallacy: “If A, then B. Therefore if not-B, then not-A.”Why do...
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I have trouble understanding this fallacy: "If A, then B. Therefore if not-B, then not-A."
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I have trouble understanding this fallacy: “If A, then B. Therefore if not-B, then not-A.”
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About "If A, then B. Therefore, if not-B, then not-A":
From what I understand the conclusion is wrong, because it is not said that A is a sufficient condition for B, (and there may be other conditions required for B, so if they are not present B won't be the case, even if A is the case.).
But I have trouble finding a real life example to this and I'm not sure if it is the consept that I don't understand or it is just the way we express ourselves in natural language that causes the confusion.
Here is an example I could think of, in natural language: "In order to have internet (B), the router must be on (A). So, if there is no internet (not-B), that means the router is not on (not-A)" (Which is not true because there may be a problem with the providers, for example.)
So turning the router on is a necessary condition for having internet but can you then say: "If you turn the router on (A), there will be internet (B)." Saying that is just is not true. So is it just that we don't have a good way to express sufficient conditions (in comparison to necessary conditions) or is it that I just don't understanding some fundamental concept (or both)?
logic fallacies
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About "If A, then B. Therefore, if not-B, then not-A":
From what I understand the conclusion is wrong, because it is not said that A is a sufficient condition for B, (and there may be other conditions required for B, so if they are not present B won't be the case, even if A is the case.).
But I have trouble finding a real life example to this and I'm not sure if it is the consept that I don't understand or it is just the way we express ourselves in natural language that causes the confusion.
Here is an example I could think of, in natural language: "In order to have internet (B), the router must be on (A). So, if there is no internet (not-B), that means the router is not on (not-A)" (Which is not true because there may be a problem with the providers, for example.)
So turning the router on is a necessary condition for having internet but can you then say: "If you turn the router on (A), there will be internet (B)." Saying that is just is not true. So is it just that we don't have a good way to express sufficient conditions (in comparison to necessary conditions) or is it that I just don't understanding some fundamental concept (or both)?
logic fallacies
asked 2 hours ago
user18894user18894
61
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user18894 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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1
Not completely following the example you raise, butIf A, then B. Therefore, if not-B, then not-Ais not a fallacy. This is contraposition( en.wikipedia.org/wiki/Contraposition) and it's always valid...
– virmaior
2 hours ago
This is the contrapositive of the afirmation A => B, i.e., it is logically equivalent, not a fallacy. Maybe the fallacy that could happen is ~A => ~B (where ~ = not).
– LAU
37 mins ago
add a comment |
About "If A, then B. Therefore, if not-B, then not-A":
From what I understand the conclusion is wrong, because it is not said that A is a sufficient condition for B, (and there may be other conditions required for B, so if they are not present B won't be the case, even if A is the case.).
But I have trouble finding a real life example to this and I'm not sure if it is the consept that I don't understand or it is just the way we express ourselves in natural language that causes the confusion.
Here is an example I could think of, in natural language: "In order to have internet (B), the router must be on (A). So, if there is no internet (not-B), that means the router is not on (not-A)" (Which is not true because there may be a problem with the providers, for example.)
So turning the router on is a necessary condition for having internet but can you then say: "If you turn the router on (A), there will be internet (B)." Saying that is just is not true. So is it just that we don't have a good way to express sufficient conditions (in comparison to necessary conditions) or is it that I just don't understanding some fundamental concept (or both)?
logic fallacies
asked 2 hours ago
user18894user18894
61
New contributor
user18894 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
About "If A, then B. Therefore, if not-B, then not-A":
From what I understand the conclusion is wrong, because it is not said that A is a sufficient condition for B, (and there may be other conditions required for B, so if they are not present B won't be the case, even if A is the case.).
But I have trouble finding a real life example to this and I'm not sure if it is the consept that I don't understand or it is just the way we express ourselves in natural language that causes the confusion.
Here is an example I could think of, in natural language: "In order to have internet (B), the router must be on (A). So, if there is no internet (not-B), that means the router is not on (not-A)" (Which is not true because there may be a problem with the providers, for example.)
So turning the router on is a necessary condition for having internet but can you then say: "If you turn the router on (A), there will be internet (B)." Saying that is just is not true. So is it just that we don't have a good way to express sufficient conditions (in comparison to necessary conditions) or is it that I just don't understanding some fundamental concept (or both)?
logic fallacies
logic fallacies
asked 2 hours ago
user18894user18894
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asked 2 hours ago
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asked 2 hours ago
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1
Not completely following the example you raise, butIf A, then B. Therefore, if not-B, then not-Ais not a fallacy. This is contraposition( en.wikipedia.org/wiki/Contraposition) and it's always valid...
– virmaior
2 hours ago
This is the contrapositive of the afirmation A => B, i.e., it is logically equivalent, not a fallacy. Maybe the fallacy that could happen is ~A => ~B (where ~ = not).
– LAU
37 mins ago
add a comment |
1
Not completely following the example you raise, butIf A, then B. Therefore, if not-B, then not-Ais not a fallacy. This is contraposition( en.wikipedia.org/wiki/Contraposition) and it's always valid...
– virmaior
2 hours ago
This is the contrapositive of the afirmation A => B, i.e., it is logically equivalent, not a fallacy. Maybe the fallacy that could happen is ~A => ~B (where ~ = not).
– LAU
37 mins ago
1
1
Not completely following the example you raise, but
If A, then B. Therefore, if not-B, then not-A is not a fallacy. This is contraposition( en.wikipedia.org/wiki/Contraposition) and it's always valid...– virmaior
2 hours ago
Not completely following the example you raise, but
If A, then B. Therefore, if not-B, then not-A is not a fallacy. This is contraposition( en.wikipedia.org/wiki/Contraposition) and it's always valid...– virmaior
2 hours ago
This is the contrapositive of the afirmation A => B, i.e., it is logically equivalent, not a fallacy. Maybe the fallacy that could happen is ~A => ~B (where ~ = not).
– LAU
37 mins ago
This is the contrapositive of the afirmation A => B, i.e., it is logically equivalent, not a fallacy. Maybe the fallacy that could happen is ~A => ~B (where ~ = not).
– LAU
37 mins ago
add a comment |
2 Answers
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No fallacy
Router necessary for internet
Can be restated
Internet sufficient for router
Let's restate the second more elaborately
Internet (found to be) working is sufficient (evidence)
that the router (has to be) working
In addition to contrapositive suggested by @virmalor you may like to see also modus tollens
answered 1 hour ago
RusiRusi
562
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‘If not B then not A’ is the contrapositive of ‘If A then B’ and is logically valid.
By saying ‘if A then B’, the author is saying that whenever A happens, B will definitely happen. Hence, if B does not happen, it is clear that A did not happen (if not B then not A).
answered 36 mins ago
danielloiddanielloid
101
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2 Answers
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2 Answers
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No fallacy
Router necessary for internet
Can be restated
Internet sufficient for router
Let's restate the second more elaborately
Internet (found to be) working is sufficient (evidence)
that the router (has to be) working
In addition to contrapositive suggested by @virmalor you may like to see also modus tollens
answered 1 hour ago
RusiRusi
562
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No fallacy
Router necessary for internet
Can be restated
Internet sufficient for router
Let's restate the second more elaborately
Internet (found to be) working is sufficient (evidence)
that the router (has to be) working
In addition to contrapositive suggested by @virmalor you may like to see also modus tollens
answered 1 hour ago
RusiRusi
562
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Rusi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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add a comment |
No fallacy
Router necessary for internet
Can be restated
Internet sufficient for router
Let's restate the second more elaborately
Internet (found to be) working is sufficient (evidence)
that the router (has to be) working
In addition to contrapositive suggested by @virmalor you may like to see also modus tollens
answered 1 hour ago
RusiRusi
562
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Rusi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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No fallacy
Router necessary for internet
Can be restated
Internet sufficient for router
Let's restate the second more elaborately
Internet (found to be) working is sufficient (evidence)
that the router (has to be) working
In addition to contrapositive suggested by @virmalor you may like to see also modus tollens
answered 1 hour ago
RusiRusi
562
New contributor
Rusi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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edited 1 hour ago
answered 1 hour ago
RusiRusi
562
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answered 1 hour ago
RusiRusi
562
answered 1 hour ago
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‘If not B then not A’ is the contrapositive of ‘If A then B’ and is logically valid.
By saying ‘if A then B’, the author is saying that whenever A happens, B will definitely happen. Hence, if B does not happen, it is clear that A did not happen (if not B then not A).
answered 36 mins ago
danielloiddanielloid
101
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‘If not B then not A’ is the contrapositive of ‘If A then B’ and is logically valid.
By saying ‘if A then B’, the author is saying that whenever A happens, B will definitely happen. Hence, if B does not happen, it is clear that A did not happen (if not B then not A).
answered 36 mins ago
danielloiddanielloid
101
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‘If not B then not A’ is the contrapositive of ‘If A then B’ and is logically valid.
By saying ‘if A then B’, the author is saying that whenever A happens, B will definitely happen. Hence, if B does not happen, it is clear that A did not happen (if not B then not A).
answered 36 mins ago
danielloiddanielloid
101
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‘If not B then not A’ is the contrapositive of ‘If A then B’ and is logically valid.
By saying ‘if A then B’, the author is saying that whenever A happens, B will definitely happen. Hence, if B does not happen, it is clear that A did not happen (if not B then not A).
answered 36 mins ago
danielloiddanielloid
101
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answered 36 mins ago
danielloiddanielloid
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answered 36 mins ago
danielloiddanielloid
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answered 36 mins ago
danielloiddanielloid
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1
Not completely following the example you raise, but
If A, then B. Therefore, if not-B, then not-Ais not a fallacy. This is contraposition( en.wikipedia.org/wiki/Contraposition) and it's always valid...– virmaior
2 hours ago
This is the contrapositive of the afirmation A => B, i.e., it is logically equivalent, not a fallacy. Maybe the fallacy that could happen is ~A => ~B (where ~ = not).
– LAU
37 mins ago