How is the claim “I am in New York only if I am in America” the same as "If I am in New York, then I am...
It makes absolutely zero sense to me.
It would make sense if "I am in America" is the antecedent and the consequent is the former.
Even though it wouldn't be sound, it would make logical sense.
I hope someone could explain it in a way someone would to a beginner in logic.
Thanks
logic
New contributor
|
show 4 more comments
It makes absolutely zero sense to me.
It would make sense if "I am in America" is the antecedent and the consequent is the former.
Even though it wouldn't be sound, it would make logical sense.
I hope someone could explain it in a way someone would to a beginner in logic.
Thanks
logic
New contributor
2
Already discussed many times on this site; see e.g. what-is-the-difference-between-necessary-and-sufficient as well as what-are-the-truth-tables-for-necessary-and-sufficient
– Mauro ALLEGRANZA
12 hours ago
I made an edit which you may roll back or further edit.
– Frank Hubeny
11 hours ago
12
Are you perhaps interpreting the word "only" to be qualifying New York? A comma would help to clarify, as would an appropriate pause in the spoken sentence. In other words, do you understand this sentence to be "I am in New York, only if I am in America" or "I am in New York only, if I am in America." If you understood it to be the latter, then I agree that it is illogical. If you understood it to be the former, then hopefully the existing answers have helped you.
– Richard II
9 hours ago
Technically if you were in New York you might be in a foreign embassy and not in "America"
– Mark Schultheiss
5 hours ago
@MarkSchultheiss To take your technicality futher, are you still in new york if you are in an embassy? Is yes, then you are also in america (as you are saying the politics are irrelevant). If no, then you are also NOT in america
– user34150
5 hours ago
|
show 4 more comments
It makes absolutely zero sense to me.
It would make sense if "I am in America" is the antecedent and the consequent is the former.
Even though it wouldn't be sound, it would make logical sense.
I hope someone could explain it in a way someone would to a beginner in logic.
Thanks
logic
New contributor
It makes absolutely zero sense to me.
It would make sense if "I am in America" is the antecedent and the consequent is the former.
Even though it wouldn't be sound, it would make logical sense.
I hope someone could explain it in a way someone would to a beginner in logic.
Thanks
logic
logic
New contributor
New contributor
edited 11 hours ago
Frank Hubeny
9,90251555
9,90251555
New contributor
asked 13 hours ago
MinigameZ moreMinigameZ more
8615
8615
New contributor
New contributor
2
Already discussed many times on this site; see e.g. what-is-the-difference-between-necessary-and-sufficient as well as what-are-the-truth-tables-for-necessary-and-sufficient
– Mauro ALLEGRANZA
12 hours ago
I made an edit which you may roll back or further edit.
– Frank Hubeny
11 hours ago
12
Are you perhaps interpreting the word "only" to be qualifying New York? A comma would help to clarify, as would an appropriate pause in the spoken sentence. In other words, do you understand this sentence to be "I am in New York, only if I am in America" or "I am in New York only, if I am in America." If you understood it to be the latter, then I agree that it is illogical. If you understood it to be the former, then hopefully the existing answers have helped you.
– Richard II
9 hours ago
Technically if you were in New York you might be in a foreign embassy and not in "America"
– Mark Schultheiss
5 hours ago
@MarkSchultheiss To take your technicality futher, are you still in new york if you are in an embassy? Is yes, then you are also in america (as you are saying the politics are irrelevant). If no, then you are also NOT in america
– user34150
5 hours ago
|
show 4 more comments
2
Already discussed many times on this site; see e.g. what-is-the-difference-between-necessary-and-sufficient as well as what-are-the-truth-tables-for-necessary-and-sufficient
– Mauro ALLEGRANZA
12 hours ago
I made an edit which you may roll back or further edit.
– Frank Hubeny
11 hours ago
12
Are you perhaps interpreting the word "only" to be qualifying New York? A comma would help to clarify, as would an appropriate pause in the spoken sentence. In other words, do you understand this sentence to be "I am in New York, only if I am in America" or "I am in New York only, if I am in America." If you understood it to be the latter, then I agree that it is illogical. If you understood it to be the former, then hopefully the existing answers have helped you.
– Richard II
9 hours ago
Technically if you were in New York you might be in a foreign embassy and not in "America"
– Mark Schultheiss
5 hours ago
@MarkSchultheiss To take your technicality futher, are you still in new york if you are in an embassy? Is yes, then you are also in america (as you are saying the politics are irrelevant). If no, then you are also NOT in america
– user34150
5 hours ago
2
2
Already discussed many times on this site; see e.g. what-is-the-difference-between-necessary-and-sufficient as well as what-are-the-truth-tables-for-necessary-and-sufficient
– Mauro ALLEGRANZA
12 hours ago
Already discussed many times on this site; see e.g. what-is-the-difference-between-necessary-and-sufficient as well as what-are-the-truth-tables-for-necessary-and-sufficient
– Mauro ALLEGRANZA
12 hours ago
I made an edit which you may roll back or further edit.
– Frank Hubeny
11 hours ago
I made an edit which you may roll back or further edit.
– Frank Hubeny
11 hours ago
12
12
Are you perhaps interpreting the word "only" to be qualifying New York? A comma would help to clarify, as would an appropriate pause in the spoken sentence. In other words, do you understand this sentence to be "I am in New York, only if I am in America" or "I am in New York only, if I am in America." If you understood it to be the latter, then I agree that it is illogical. If you understood it to be the former, then hopefully the existing answers have helped you.
– Richard II
9 hours ago
Are you perhaps interpreting the word "only" to be qualifying New York? A comma would help to clarify, as would an appropriate pause in the spoken sentence. In other words, do you understand this sentence to be "I am in New York, only if I am in America" or "I am in New York only, if I am in America." If you understood it to be the latter, then I agree that it is illogical. If you understood it to be the former, then hopefully the existing answers have helped you.
– Richard II
9 hours ago
Technically if you were in New York you might be in a foreign embassy and not in "America"
– Mark Schultheiss
5 hours ago
Technically if you were in New York you might be in a foreign embassy and not in "America"
– Mark Schultheiss
5 hours ago
@MarkSchultheiss To take your technicality futher, are you still in new york if you are in an embassy? Is yes, then you are also in america (as you are saying the politics are irrelevant). If no, then you are also NOT in america
– user34150
5 hours ago
@MarkSchultheiss To take your technicality futher, are you still in new york if you are in an embassy? Is yes, then you are also in america (as you are saying the politics are irrelevant). If no, then you are also NOT in america
– user34150
5 hours ago
|
show 4 more comments
8 Answers
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votes
Consider the sentence:
If I am in America then I am in New York.
One could make the antecedent, "I am in America", true by being in Chicago. But then the consequent, "I am in New York", would be false. So this conditional would be false unless we are given other information, such as travel plans, in addition to knowing that I am in America.
However, consider this sentence:
If I am in New York then I am in America.
Now whenever the antecedent, "I am in New York", is true, then so is the consequent, "I am in America". I don't need any additional information for that conditional to be true.
It would be similar for the following sentence:
I am in New York only if I am in America.
Here we are given that "I am in New York" and conclude that "I am in America". Except for English style this means the same as the previous sentence.
The authors of forall x provide a similar example using Paris and France in section "5.4 Condititional". They also provide this symbolization rule:
A sentence can be symbolized as A → B if it can be
paraphrased in English as ‘If A, then B’ or ‘A only if B’.
P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Fall 2018 bis. http://forallx.openlogicproject.org/
This way of converting the sentence to logic does not do justice to the sentence's implications in English. The "only" version of the sentence could easily be read as "if and only if" (that is, a two-way implication).
– Brilliand
4 hours ago
1
I'd read "I am in New York only if I am in America" as "I cannot be in New York if I am not in America", which is (more or less) the contrapositive of "If I am in New York, then I am in America", and therefore (more or less) logically equivalent to it. The pragmatic content might differ but as a native English speaker I wouldn't consider the "if and only if" reading natural.
– Unrelated String
1 hour ago
add a comment |
This is an example of the confusion inherent in switching between a natural language like English, and a formal language of logic.
The formulation
X only if Y
is rare in spoken English, but perfectly grammatical, and it typically has a logical meaning equivalent to
If X then Y
Both statements are saying you can't ever have X without Y. However, at first glance it looks closer to
If Y then X
which is entirely different. This represents how English has many different ways of saying the same thing (with incidental connotations and subtleties of meaning that are completely stripped out when you translate to a formal language).
I understand the logic arguments. And I concur that TECHNICALLY the logic of the two would be the same. However, in common usage, the phrasing of the 2nd clause, using "only" would be interpreted by US English speakers as defining oneself as being in New York because they are in America. Which is obviously not true. Regardless, the "only" usage would be widely misunderstood, whereas the "if . . .then" construction would be interpreted correctly. I suspect there is an error somewhere in interpreting the logic of the two to be the same. But said error is beyond me.
– Corvus B
46 mins ago
@CorvusB, huh. Now that you point it out, I can see superficially similar constructions such as "I will eat only if I am given yoghurt" that would indeed in common usage mean "if I am given youghurt, I will eat". But I can't make my brain see the sentence in the OP with anything other than its intended meaning, and I'm not sure why.
– Harry Johnston
34 mins ago
@HarryJohnston. Yes - you've brought an excellent example. I am pretty sure the first interpretation most Americans would give the "only" example would be "If I am in America, I am in New York". It might get marked incorrect on a test, but that is more like how people would "hear" the "only" statement.
– Corvus B
9 mins ago
add a comment |
"A only if B" and "if A, then B" mean the same.
The truth-condition for "if A, then B" excludes the case when A is True and B is False.
"A only if B" means that we cannot have A without B.
The two are equivalent.
See necessary and sufficient.
add a comment |
I see two interpretations of the sentence here. They mean logically different things. In both cases "only" is interpreted as "must be true and cannot be false".
I am in New York (only if I am in America).
If I am in New York, it can only be true that I am in America.
New York => America.
This is the interpretation everyone else is responding to. It is logically true.
I can be in (New York only) if I am in America.
If I am in America, then it can only be true that I am in New York.
America => New York.
This one is not logically true, you could be in Iowa.
New contributor
My reading of the OP's first sentence could be paraphrased as "I am in New York, unless I am not in America". It's logically equivalent to your second version, I think, although reads like a statement about a particular person rather than a general statement about everyone.
– Brilliand
4 hours ago
add a comment |
The contrapositive of both statements is :
If I am not in America, then I cannot be in New York.
A conditional statement is logically equivalent to its contrapositive. It means both your statements are equivalent since they have the same contrapositive.
1
I think this answer is correct.
– Mark Andrews
3 hours ago
add a comment |
These claims have distinctly different connotations. From a pure formal-logic perspective, the "X only if Y" is equivalent to "Y or not X" which is the same as "X implies Y", which is the same as "if X then Y". However, natural language carries more information than its simple-minded reduction to predicate logic.
The second formulation "If I am in NY then I am in USA" sounds like a simple statement of a containment relationship: it implies that "I" am an unbound variable and informs the listener that NY is within the USA.
The first formulation connotes something about the speaker's mental state: he entertains the possibility (perhaps even likelihood) of being outside the USA in a place confusingly-similar to NY.
New contributor
add a comment |
LOL - The two statements are not equivalent.
You could be in New York - Lazio - Italy
New contributor
1
That means that "If I'm in New York then I'm in America" is false, but it doesn't mean that it's not equivalent to "I'm in New York only if I'm in America".
– Eliran
4 hours ago
While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. - From Review
– Mark Andrews
2 hours ago
add a comment |
One way of analyzing the statements is to look at a truth table. Let's make the following definitions:
A := "I am in New York"
B := "I am in America".
X := "I am in New York only if I am in America"
Y := "If I am in New York, then I am in America"
If both A and B are true, then X is true. We can write that as X(TT) = T. We have X(TF) = F (If you are in New York but not in America, then the statement "I am in New York only if I am in America" must be false). X(FT) = T and X(FF) = T; X makes a statement about what has to be true when you're in New York, so if you're not in New York, then X isn't telling you anything so it can't be proven wrong.
If you analyze Y, you'll find that all the values are the same:
X(TT) = Y(TT) = T
X(TF) = Y(TF) = F
X(FT) = Y(FT) = T
X(FF) = Y(FF) = T
Since no matter the truth values of A and B, X has the same truth value as Y, X and Y are equivalent; if you have two statements such that it's not possible for one to be true and the other false, then the two statements are saying essentially the same thing.
One thing to keep in mind is that in Formal Logic, statements of the form "If S1 then S2" are considered true any time S1 is false; that is, "If S1 then S2" is interpreted as meaning "Whenever S1 is true, S2 is also true". Because of this, "If S1 then S2" is equivalent to "Either S1 is false, or S2 is true" (if S1 is false, then the statement is automatically true, because it doesn't say anything about the situation of S1 being true). And "S1 only if S2 " is also equivalent to "Either S1 is false, or S2 is true".
add a comment |
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8 Answers
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Consider the sentence:
If I am in America then I am in New York.
One could make the antecedent, "I am in America", true by being in Chicago. But then the consequent, "I am in New York", would be false. So this conditional would be false unless we are given other information, such as travel plans, in addition to knowing that I am in America.
However, consider this sentence:
If I am in New York then I am in America.
Now whenever the antecedent, "I am in New York", is true, then so is the consequent, "I am in America". I don't need any additional information for that conditional to be true.
It would be similar for the following sentence:
I am in New York only if I am in America.
Here we are given that "I am in New York" and conclude that "I am in America". Except for English style this means the same as the previous sentence.
The authors of forall x provide a similar example using Paris and France in section "5.4 Condititional". They also provide this symbolization rule:
A sentence can be symbolized as A → B if it can be
paraphrased in English as ‘If A, then B’ or ‘A only if B’.
P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Fall 2018 bis. http://forallx.openlogicproject.org/
This way of converting the sentence to logic does not do justice to the sentence's implications in English. The "only" version of the sentence could easily be read as "if and only if" (that is, a two-way implication).
– Brilliand
4 hours ago
1
I'd read "I am in New York only if I am in America" as "I cannot be in New York if I am not in America", which is (more or less) the contrapositive of "If I am in New York, then I am in America", and therefore (more or less) logically equivalent to it. The pragmatic content might differ but as a native English speaker I wouldn't consider the "if and only if" reading natural.
– Unrelated String
1 hour ago
add a comment |
Consider the sentence:
If I am in America then I am in New York.
One could make the antecedent, "I am in America", true by being in Chicago. But then the consequent, "I am in New York", would be false. So this conditional would be false unless we are given other information, such as travel plans, in addition to knowing that I am in America.
However, consider this sentence:
If I am in New York then I am in America.
Now whenever the antecedent, "I am in New York", is true, then so is the consequent, "I am in America". I don't need any additional information for that conditional to be true.
It would be similar for the following sentence:
I am in New York only if I am in America.
Here we are given that "I am in New York" and conclude that "I am in America". Except for English style this means the same as the previous sentence.
The authors of forall x provide a similar example using Paris and France in section "5.4 Condititional". They also provide this symbolization rule:
A sentence can be symbolized as A → B if it can be
paraphrased in English as ‘If A, then B’ or ‘A only if B’.
P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Fall 2018 bis. http://forallx.openlogicproject.org/
This way of converting the sentence to logic does not do justice to the sentence's implications in English. The "only" version of the sentence could easily be read as "if and only if" (that is, a two-way implication).
– Brilliand
4 hours ago
1
I'd read "I am in New York only if I am in America" as "I cannot be in New York if I am not in America", which is (more or less) the contrapositive of "If I am in New York, then I am in America", and therefore (more or less) logically equivalent to it. The pragmatic content might differ but as a native English speaker I wouldn't consider the "if and only if" reading natural.
– Unrelated String
1 hour ago
add a comment |
Consider the sentence:
If I am in America then I am in New York.
One could make the antecedent, "I am in America", true by being in Chicago. But then the consequent, "I am in New York", would be false. So this conditional would be false unless we are given other information, such as travel plans, in addition to knowing that I am in America.
However, consider this sentence:
If I am in New York then I am in America.
Now whenever the antecedent, "I am in New York", is true, then so is the consequent, "I am in America". I don't need any additional information for that conditional to be true.
It would be similar for the following sentence:
I am in New York only if I am in America.
Here we are given that "I am in New York" and conclude that "I am in America". Except for English style this means the same as the previous sentence.
The authors of forall x provide a similar example using Paris and France in section "5.4 Condititional". They also provide this symbolization rule:
A sentence can be symbolized as A → B if it can be
paraphrased in English as ‘If A, then B’ or ‘A only if B’.
P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Fall 2018 bis. http://forallx.openlogicproject.org/
Consider the sentence:
If I am in America then I am in New York.
One could make the antecedent, "I am in America", true by being in Chicago. But then the consequent, "I am in New York", would be false. So this conditional would be false unless we are given other information, such as travel plans, in addition to knowing that I am in America.
However, consider this sentence:
If I am in New York then I am in America.
Now whenever the antecedent, "I am in New York", is true, then so is the consequent, "I am in America". I don't need any additional information for that conditional to be true.
It would be similar for the following sentence:
I am in New York only if I am in America.
Here we are given that "I am in New York" and conclude that "I am in America". Except for English style this means the same as the previous sentence.
The authors of forall x provide a similar example using Paris and France in section "5.4 Condititional". They also provide this symbolization rule:
A sentence can be symbolized as A → B if it can be
paraphrased in English as ‘If A, then B’ or ‘A only if B’.
P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Fall 2018 bis. http://forallx.openlogicproject.org/
answered 11 hours ago
Frank HubenyFrank Hubeny
9,90251555
9,90251555
This way of converting the sentence to logic does not do justice to the sentence's implications in English. The "only" version of the sentence could easily be read as "if and only if" (that is, a two-way implication).
– Brilliand
4 hours ago
1
I'd read "I am in New York only if I am in America" as "I cannot be in New York if I am not in America", which is (more or less) the contrapositive of "If I am in New York, then I am in America", and therefore (more or less) logically equivalent to it. The pragmatic content might differ but as a native English speaker I wouldn't consider the "if and only if" reading natural.
– Unrelated String
1 hour ago
add a comment |
This way of converting the sentence to logic does not do justice to the sentence's implications in English. The "only" version of the sentence could easily be read as "if and only if" (that is, a two-way implication).
– Brilliand
4 hours ago
1
I'd read "I am in New York only if I am in America" as "I cannot be in New York if I am not in America", which is (more or less) the contrapositive of "If I am in New York, then I am in America", and therefore (more or less) logically equivalent to it. The pragmatic content might differ but as a native English speaker I wouldn't consider the "if and only if" reading natural.
– Unrelated String
1 hour ago
This way of converting the sentence to logic does not do justice to the sentence's implications in English. The "only" version of the sentence could easily be read as "if and only if" (that is, a two-way implication).
– Brilliand
4 hours ago
This way of converting the sentence to logic does not do justice to the sentence's implications in English. The "only" version of the sentence could easily be read as "if and only if" (that is, a two-way implication).
– Brilliand
4 hours ago
1
1
I'd read "I am in New York only if I am in America" as "I cannot be in New York if I am not in America", which is (more or less) the contrapositive of "If I am in New York, then I am in America", and therefore (more or less) logically equivalent to it. The pragmatic content might differ but as a native English speaker I wouldn't consider the "if and only if" reading natural.
– Unrelated String
1 hour ago
I'd read "I am in New York only if I am in America" as "I cannot be in New York if I am not in America", which is (more or less) the contrapositive of "If I am in New York, then I am in America", and therefore (more or less) logically equivalent to it. The pragmatic content might differ but as a native English speaker I wouldn't consider the "if and only if" reading natural.
– Unrelated String
1 hour ago
add a comment |
This is an example of the confusion inherent in switching between a natural language like English, and a formal language of logic.
The formulation
X only if Y
is rare in spoken English, but perfectly grammatical, and it typically has a logical meaning equivalent to
If X then Y
Both statements are saying you can't ever have X without Y. However, at first glance it looks closer to
If Y then X
which is entirely different. This represents how English has many different ways of saying the same thing (with incidental connotations and subtleties of meaning that are completely stripped out when you translate to a formal language).
I understand the logic arguments. And I concur that TECHNICALLY the logic of the two would be the same. However, in common usage, the phrasing of the 2nd clause, using "only" would be interpreted by US English speakers as defining oneself as being in New York because they are in America. Which is obviously not true. Regardless, the "only" usage would be widely misunderstood, whereas the "if . . .then" construction would be interpreted correctly. I suspect there is an error somewhere in interpreting the logic of the two to be the same. But said error is beyond me.
– Corvus B
46 mins ago
@CorvusB, huh. Now that you point it out, I can see superficially similar constructions such as "I will eat only if I am given yoghurt" that would indeed in common usage mean "if I am given youghurt, I will eat". But I can't make my brain see the sentence in the OP with anything other than its intended meaning, and I'm not sure why.
– Harry Johnston
34 mins ago
@HarryJohnston. Yes - you've brought an excellent example. I am pretty sure the first interpretation most Americans would give the "only" example would be "If I am in America, I am in New York". It might get marked incorrect on a test, but that is more like how people would "hear" the "only" statement.
– Corvus B
9 mins ago
add a comment |
This is an example of the confusion inherent in switching between a natural language like English, and a formal language of logic.
The formulation
X only if Y
is rare in spoken English, but perfectly grammatical, and it typically has a logical meaning equivalent to
If X then Y
Both statements are saying you can't ever have X without Y. However, at first glance it looks closer to
If Y then X
which is entirely different. This represents how English has many different ways of saying the same thing (with incidental connotations and subtleties of meaning that are completely stripped out when you translate to a formal language).
I understand the logic arguments. And I concur that TECHNICALLY the logic of the two would be the same. However, in common usage, the phrasing of the 2nd clause, using "only" would be interpreted by US English speakers as defining oneself as being in New York because they are in America. Which is obviously not true. Regardless, the "only" usage would be widely misunderstood, whereas the "if . . .then" construction would be interpreted correctly. I suspect there is an error somewhere in interpreting the logic of the two to be the same. But said error is beyond me.
– Corvus B
46 mins ago
@CorvusB, huh. Now that you point it out, I can see superficially similar constructions such as "I will eat only if I am given yoghurt" that would indeed in common usage mean "if I am given youghurt, I will eat". But I can't make my brain see the sentence in the OP with anything other than its intended meaning, and I'm not sure why.
– Harry Johnston
34 mins ago
@HarryJohnston. Yes - you've brought an excellent example. I am pretty sure the first interpretation most Americans would give the "only" example would be "If I am in America, I am in New York". It might get marked incorrect on a test, but that is more like how people would "hear" the "only" statement.
– Corvus B
9 mins ago
add a comment |
This is an example of the confusion inherent in switching between a natural language like English, and a formal language of logic.
The formulation
X only if Y
is rare in spoken English, but perfectly grammatical, and it typically has a logical meaning equivalent to
If X then Y
Both statements are saying you can't ever have X without Y. However, at first glance it looks closer to
If Y then X
which is entirely different. This represents how English has many different ways of saying the same thing (with incidental connotations and subtleties of meaning that are completely stripped out when you translate to a formal language).
This is an example of the confusion inherent in switching between a natural language like English, and a formal language of logic.
The formulation
X only if Y
is rare in spoken English, but perfectly grammatical, and it typically has a logical meaning equivalent to
If X then Y
Both statements are saying you can't ever have X without Y. However, at first glance it looks closer to
If Y then X
which is entirely different. This represents how English has many different ways of saying the same thing (with incidental connotations and subtleties of meaning that are completely stripped out when you translate to a formal language).
answered 10 hours ago
Chris SunamiChris Sunami
21.2k12964
21.2k12964
I understand the logic arguments. And I concur that TECHNICALLY the logic of the two would be the same. However, in common usage, the phrasing of the 2nd clause, using "only" would be interpreted by US English speakers as defining oneself as being in New York because they are in America. Which is obviously not true. Regardless, the "only" usage would be widely misunderstood, whereas the "if . . .then" construction would be interpreted correctly. I suspect there is an error somewhere in interpreting the logic of the two to be the same. But said error is beyond me.
– Corvus B
46 mins ago
@CorvusB, huh. Now that you point it out, I can see superficially similar constructions such as "I will eat only if I am given yoghurt" that would indeed in common usage mean "if I am given youghurt, I will eat". But I can't make my brain see the sentence in the OP with anything other than its intended meaning, and I'm not sure why.
– Harry Johnston
34 mins ago
@HarryJohnston. Yes - you've brought an excellent example. I am pretty sure the first interpretation most Americans would give the "only" example would be "If I am in America, I am in New York". It might get marked incorrect on a test, but that is more like how people would "hear" the "only" statement.
– Corvus B
9 mins ago
add a comment |
I understand the logic arguments. And I concur that TECHNICALLY the logic of the two would be the same. However, in common usage, the phrasing of the 2nd clause, using "only" would be interpreted by US English speakers as defining oneself as being in New York because they are in America. Which is obviously not true. Regardless, the "only" usage would be widely misunderstood, whereas the "if . . .then" construction would be interpreted correctly. I suspect there is an error somewhere in interpreting the logic of the two to be the same. But said error is beyond me.
– Corvus B
46 mins ago
@CorvusB, huh. Now that you point it out, I can see superficially similar constructions such as "I will eat only if I am given yoghurt" that would indeed in common usage mean "if I am given youghurt, I will eat". But I can't make my brain see the sentence in the OP with anything other than its intended meaning, and I'm not sure why.
– Harry Johnston
34 mins ago
@HarryJohnston. Yes - you've brought an excellent example. I am pretty sure the first interpretation most Americans would give the "only" example would be "If I am in America, I am in New York". It might get marked incorrect on a test, but that is more like how people would "hear" the "only" statement.
– Corvus B
9 mins ago
I understand the logic arguments. And I concur that TECHNICALLY the logic of the two would be the same. However, in common usage, the phrasing of the 2nd clause, using "only" would be interpreted by US English speakers as defining oneself as being in New York because they are in America. Which is obviously not true. Regardless, the "only" usage would be widely misunderstood, whereas the "if . . .then" construction would be interpreted correctly. I suspect there is an error somewhere in interpreting the logic of the two to be the same. But said error is beyond me.
– Corvus B
46 mins ago
I understand the logic arguments. And I concur that TECHNICALLY the logic of the two would be the same. However, in common usage, the phrasing of the 2nd clause, using "only" would be interpreted by US English speakers as defining oneself as being in New York because they are in America. Which is obviously not true. Regardless, the "only" usage would be widely misunderstood, whereas the "if . . .then" construction would be interpreted correctly. I suspect there is an error somewhere in interpreting the logic of the two to be the same. But said error is beyond me.
– Corvus B
46 mins ago
@CorvusB, huh. Now that you point it out, I can see superficially similar constructions such as "I will eat only if I am given yoghurt" that would indeed in common usage mean "if I am given youghurt, I will eat". But I can't make my brain see the sentence in the OP with anything other than its intended meaning, and I'm not sure why.
– Harry Johnston
34 mins ago
@CorvusB, huh. Now that you point it out, I can see superficially similar constructions such as "I will eat only if I am given yoghurt" that would indeed in common usage mean "if I am given youghurt, I will eat". But I can't make my brain see the sentence in the OP with anything other than its intended meaning, and I'm not sure why.
– Harry Johnston
34 mins ago
@HarryJohnston. Yes - you've brought an excellent example. I am pretty sure the first interpretation most Americans would give the "only" example would be "If I am in America, I am in New York". It might get marked incorrect on a test, but that is more like how people would "hear" the "only" statement.
– Corvus B
9 mins ago
@HarryJohnston. Yes - you've brought an excellent example. I am pretty sure the first interpretation most Americans would give the "only" example would be "If I am in America, I am in New York". It might get marked incorrect on a test, but that is more like how people would "hear" the "only" statement.
– Corvus B
9 mins ago
add a comment |
"A only if B" and "if A, then B" mean the same.
The truth-condition for "if A, then B" excludes the case when A is True and B is False.
"A only if B" means that we cannot have A without B.
The two are equivalent.
See necessary and sufficient.
add a comment |
"A only if B" and "if A, then B" mean the same.
The truth-condition for "if A, then B" excludes the case when A is True and B is False.
"A only if B" means that we cannot have A without B.
The two are equivalent.
See necessary and sufficient.
add a comment |
"A only if B" and "if A, then B" mean the same.
The truth-condition for "if A, then B" excludes the case when A is True and B is False.
"A only if B" means that we cannot have A without B.
The two are equivalent.
See necessary and sufficient.
"A only if B" and "if A, then B" mean the same.
The truth-condition for "if A, then B" excludes the case when A is True and B is False.
"A only if B" means that we cannot have A without B.
The two are equivalent.
See necessary and sufficient.
edited 10 hours ago
answered 12 hours ago
Mauro ALLEGRANZAMauro ALLEGRANZA
29.5k22065
29.5k22065
add a comment |
add a comment |
I see two interpretations of the sentence here. They mean logically different things. In both cases "only" is interpreted as "must be true and cannot be false".
I am in New York (only if I am in America).
If I am in New York, it can only be true that I am in America.
New York => America.
This is the interpretation everyone else is responding to. It is logically true.
I can be in (New York only) if I am in America.
If I am in America, then it can only be true that I am in New York.
America => New York.
This one is not logically true, you could be in Iowa.
New contributor
My reading of the OP's first sentence could be paraphrased as "I am in New York, unless I am not in America". It's logically equivalent to your second version, I think, although reads like a statement about a particular person rather than a general statement about everyone.
– Brilliand
4 hours ago
add a comment |
I see two interpretations of the sentence here. They mean logically different things. In both cases "only" is interpreted as "must be true and cannot be false".
I am in New York (only if I am in America).
If I am in New York, it can only be true that I am in America.
New York => America.
This is the interpretation everyone else is responding to. It is logically true.
I can be in (New York only) if I am in America.
If I am in America, then it can only be true that I am in New York.
America => New York.
This one is not logically true, you could be in Iowa.
New contributor
My reading of the OP's first sentence could be paraphrased as "I am in New York, unless I am not in America". It's logically equivalent to your second version, I think, although reads like a statement about a particular person rather than a general statement about everyone.
– Brilliand
4 hours ago
add a comment |
I see two interpretations of the sentence here. They mean logically different things. In both cases "only" is interpreted as "must be true and cannot be false".
I am in New York (only if I am in America).
If I am in New York, it can only be true that I am in America.
New York => America.
This is the interpretation everyone else is responding to. It is logically true.
I can be in (New York only) if I am in America.
If I am in America, then it can only be true that I am in New York.
America => New York.
This one is not logically true, you could be in Iowa.
New contributor
I see two interpretations of the sentence here. They mean logically different things. In both cases "only" is interpreted as "must be true and cannot be false".
I am in New York (only if I am in America).
If I am in New York, it can only be true that I am in America.
New York => America.
This is the interpretation everyone else is responding to. It is logically true.
I can be in (New York only) if I am in America.
If I am in America, then it can only be true that I am in New York.
America => New York.
This one is not logically true, you could be in Iowa.
New contributor
New contributor
answered 8 hours ago
usulusul
1312
1312
New contributor
New contributor
My reading of the OP's first sentence could be paraphrased as "I am in New York, unless I am not in America". It's logically equivalent to your second version, I think, although reads like a statement about a particular person rather than a general statement about everyone.
– Brilliand
4 hours ago
add a comment |
My reading of the OP's first sentence could be paraphrased as "I am in New York, unless I am not in America". It's logically equivalent to your second version, I think, although reads like a statement about a particular person rather than a general statement about everyone.
– Brilliand
4 hours ago
My reading of the OP's first sentence could be paraphrased as "I am in New York, unless I am not in America". It's logically equivalent to your second version, I think, although reads like a statement about a particular person rather than a general statement about everyone.
– Brilliand
4 hours ago
My reading of the OP's first sentence could be paraphrased as "I am in New York, unless I am not in America". It's logically equivalent to your second version, I think, although reads like a statement about a particular person rather than a general statement about everyone.
– Brilliand
4 hours ago
add a comment |
The contrapositive of both statements is :
If I am not in America, then I cannot be in New York.
A conditional statement is logically equivalent to its contrapositive. It means both your statements are equivalent since they have the same contrapositive.
1
I think this answer is correct.
– Mark Andrews
3 hours ago
add a comment |
The contrapositive of both statements is :
If I am not in America, then I cannot be in New York.
A conditional statement is logically equivalent to its contrapositive. It means both your statements are equivalent since they have the same contrapositive.
1
I think this answer is correct.
– Mark Andrews
3 hours ago
add a comment |
The contrapositive of both statements is :
If I am not in America, then I cannot be in New York.
A conditional statement is logically equivalent to its contrapositive. It means both your statements are equivalent since they have the same contrapositive.
The contrapositive of both statements is :
If I am not in America, then I cannot be in New York.
A conditional statement is logically equivalent to its contrapositive. It means both your statements are equivalent since they have the same contrapositive.
answered 4 hours ago
Eric DuminilEric Duminil
92649
92649
1
I think this answer is correct.
– Mark Andrews
3 hours ago
add a comment |
1
I think this answer is correct.
– Mark Andrews
3 hours ago
1
1
I think this answer is correct.
– Mark Andrews
3 hours ago
I think this answer is correct.
– Mark Andrews
3 hours ago
add a comment |
These claims have distinctly different connotations. From a pure formal-logic perspective, the "X only if Y" is equivalent to "Y or not X" which is the same as "X implies Y", which is the same as "if X then Y". However, natural language carries more information than its simple-minded reduction to predicate logic.
The second formulation "If I am in NY then I am in USA" sounds like a simple statement of a containment relationship: it implies that "I" am an unbound variable and informs the listener that NY is within the USA.
The first formulation connotes something about the speaker's mental state: he entertains the possibility (perhaps even likelihood) of being outside the USA in a place confusingly-similar to NY.
New contributor
add a comment |
These claims have distinctly different connotations. From a pure formal-logic perspective, the "X only if Y" is equivalent to "Y or not X" which is the same as "X implies Y", which is the same as "if X then Y". However, natural language carries more information than its simple-minded reduction to predicate logic.
The second formulation "If I am in NY then I am in USA" sounds like a simple statement of a containment relationship: it implies that "I" am an unbound variable and informs the listener that NY is within the USA.
The first formulation connotes something about the speaker's mental state: he entertains the possibility (perhaps even likelihood) of being outside the USA in a place confusingly-similar to NY.
New contributor
add a comment |
These claims have distinctly different connotations. From a pure formal-logic perspective, the "X only if Y" is equivalent to "Y or not X" which is the same as "X implies Y", which is the same as "if X then Y". However, natural language carries more information than its simple-minded reduction to predicate logic.
The second formulation "If I am in NY then I am in USA" sounds like a simple statement of a containment relationship: it implies that "I" am an unbound variable and informs the listener that NY is within the USA.
The first formulation connotes something about the speaker's mental state: he entertains the possibility (perhaps even likelihood) of being outside the USA in a place confusingly-similar to NY.
New contributor
These claims have distinctly different connotations. From a pure formal-logic perspective, the "X only if Y" is equivalent to "Y or not X" which is the same as "X implies Y", which is the same as "if X then Y". However, natural language carries more information than its simple-minded reduction to predicate logic.
The second formulation "If I am in NY then I am in USA" sounds like a simple statement of a containment relationship: it implies that "I" am an unbound variable and informs the listener that NY is within the USA.
The first formulation connotes something about the speaker's mental state: he entertains the possibility (perhaps even likelihood) of being outside the USA in a place confusingly-similar to NY.
New contributor
New contributor
answered 5 hours ago
IanIan
1212
1212
New contributor
New contributor
add a comment |
add a comment |
LOL - The two statements are not equivalent.
You could be in New York - Lazio - Italy
New contributor
1
That means that "If I'm in New York then I'm in America" is false, but it doesn't mean that it's not equivalent to "I'm in New York only if I'm in America".
– Eliran
4 hours ago
While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. - From Review
– Mark Andrews
2 hours ago
add a comment |
LOL - The two statements are not equivalent.
You could be in New York - Lazio - Italy
New contributor
1
That means that "If I'm in New York then I'm in America" is false, but it doesn't mean that it's not equivalent to "I'm in New York only if I'm in America".
– Eliran
4 hours ago
While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. - From Review
– Mark Andrews
2 hours ago
add a comment |
LOL - The two statements are not equivalent.
You could be in New York - Lazio - Italy
New contributor
LOL - The two statements are not equivalent.
You could be in New York - Lazio - Italy
New contributor
New contributor
answered 4 hours ago
MaxWMaxW
291
291
New contributor
New contributor
1
That means that "If I'm in New York then I'm in America" is false, but it doesn't mean that it's not equivalent to "I'm in New York only if I'm in America".
– Eliran
4 hours ago
While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. - From Review
– Mark Andrews
2 hours ago
add a comment |
1
That means that "If I'm in New York then I'm in America" is false, but it doesn't mean that it's not equivalent to "I'm in New York only if I'm in America".
– Eliran
4 hours ago
While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. - From Review
– Mark Andrews
2 hours ago
1
1
That means that "If I'm in New York then I'm in America" is false, but it doesn't mean that it's not equivalent to "I'm in New York only if I'm in America".
– Eliran
4 hours ago
That means that "If I'm in New York then I'm in America" is false, but it doesn't mean that it's not equivalent to "I'm in New York only if I'm in America".
– Eliran
4 hours ago
While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. - From Review
– Mark Andrews
2 hours ago
While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. - From Review
– Mark Andrews
2 hours ago
add a comment |
One way of analyzing the statements is to look at a truth table. Let's make the following definitions:
A := "I am in New York"
B := "I am in America".
X := "I am in New York only if I am in America"
Y := "If I am in New York, then I am in America"
If both A and B are true, then X is true. We can write that as X(TT) = T. We have X(TF) = F (If you are in New York but not in America, then the statement "I am in New York only if I am in America" must be false). X(FT) = T and X(FF) = T; X makes a statement about what has to be true when you're in New York, so if you're not in New York, then X isn't telling you anything so it can't be proven wrong.
If you analyze Y, you'll find that all the values are the same:
X(TT) = Y(TT) = T
X(TF) = Y(TF) = F
X(FT) = Y(FT) = T
X(FF) = Y(FF) = T
Since no matter the truth values of A and B, X has the same truth value as Y, X and Y are equivalent; if you have two statements such that it's not possible for one to be true and the other false, then the two statements are saying essentially the same thing.
One thing to keep in mind is that in Formal Logic, statements of the form "If S1 then S2" are considered true any time S1 is false; that is, "If S1 then S2" is interpreted as meaning "Whenever S1 is true, S2 is also true". Because of this, "If S1 then S2" is equivalent to "Either S1 is false, or S2 is true" (if S1 is false, then the statement is automatically true, because it doesn't say anything about the situation of S1 being true). And "S1 only if S2 " is also equivalent to "Either S1 is false, or S2 is true".
add a comment |
One way of analyzing the statements is to look at a truth table. Let's make the following definitions:
A := "I am in New York"
B := "I am in America".
X := "I am in New York only if I am in America"
Y := "If I am in New York, then I am in America"
If both A and B are true, then X is true. We can write that as X(TT) = T. We have X(TF) = F (If you are in New York but not in America, then the statement "I am in New York only if I am in America" must be false). X(FT) = T and X(FF) = T; X makes a statement about what has to be true when you're in New York, so if you're not in New York, then X isn't telling you anything so it can't be proven wrong.
If you analyze Y, you'll find that all the values are the same:
X(TT) = Y(TT) = T
X(TF) = Y(TF) = F
X(FT) = Y(FT) = T
X(FF) = Y(FF) = T
Since no matter the truth values of A and B, X has the same truth value as Y, X and Y are equivalent; if you have two statements such that it's not possible for one to be true and the other false, then the two statements are saying essentially the same thing.
One thing to keep in mind is that in Formal Logic, statements of the form "If S1 then S2" are considered true any time S1 is false; that is, "If S1 then S2" is interpreted as meaning "Whenever S1 is true, S2 is also true". Because of this, "If S1 then S2" is equivalent to "Either S1 is false, or S2 is true" (if S1 is false, then the statement is automatically true, because it doesn't say anything about the situation of S1 being true). And "S1 only if S2 " is also equivalent to "Either S1 is false, or S2 is true".
add a comment |
One way of analyzing the statements is to look at a truth table. Let's make the following definitions:
A := "I am in New York"
B := "I am in America".
X := "I am in New York only if I am in America"
Y := "If I am in New York, then I am in America"
If both A and B are true, then X is true. We can write that as X(TT) = T. We have X(TF) = F (If you are in New York but not in America, then the statement "I am in New York only if I am in America" must be false). X(FT) = T and X(FF) = T; X makes a statement about what has to be true when you're in New York, so if you're not in New York, then X isn't telling you anything so it can't be proven wrong.
If you analyze Y, you'll find that all the values are the same:
X(TT) = Y(TT) = T
X(TF) = Y(TF) = F
X(FT) = Y(FT) = T
X(FF) = Y(FF) = T
Since no matter the truth values of A and B, X has the same truth value as Y, X and Y are equivalent; if you have two statements such that it's not possible for one to be true and the other false, then the two statements are saying essentially the same thing.
One thing to keep in mind is that in Formal Logic, statements of the form "If S1 then S2" are considered true any time S1 is false; that is, "If S1 then S2" is interpreted as meaning "Whenever S1 is true, S2 is also true". Because of this, "If S1 then S2" is equivalent to "Either S1 is false, or S2 is true" (if S1 is false, then the statement is automatically true, because it doesn't say anything about the situation of S1 being true). And "S1 only if S2 " is also equivalent to "Either S1 is false, or S2 is true".
One way of analyzing the statements is to look at a truth table. Let's make the following definitions:
A := "I am in New York"
B := "I am in America".
X := "I am in New York only if I am in America"
Y := "If I am in New York, then I am in America"
If both A and B are true, then X is true. We can write that as X(TT) = T. We have X(TF) = F (If you are in New York but not in America, then the statement "I am in New York only if I am in America" must be false). X(FT) = T and X(FF) = T; X makes a statement about what has to be true when you're in New York, so if you're not in New York, then X isn't telling you anything so it can't be proven wrong.
If you analyze Y, you'll find that all the values are the same:
X(TT) = Y(TT) = T
X(TF) = Y(TF) = F
X(FT) = Y(FT) = T
X(FF) = Y(FF) = T
Since no matter the truth values of A and B, X has the same truth value as Y, X and Y are equivalent; if you have two statements such that it's not possible for one to be true and the other false, then the two statements are saying essentially the same thing.
One thing to keep in mind is that in Formal Logic, statements of the form "If S1 then S2" are considered true any time S1 is false; that is, "If S1 then S2" is interpreted as meaning "Whenever S1 is true, S2 is also true". Because of this, "If S1 then S2" is equivalent to "Either S1 is false, or S2 is true" (if S1 is false, then the statement is automatically true, because it doesn't say anything about the situation of S1 being true). And "S1 only if S2 " is also equivalent to "Either S1 is false, or S2 is true".
answered 3 hours ago
AcccumulationAcccumulation
812110
812110
add a comment |
add a comment |
MinigameZ more is a new contributor. Be nice, and check out our Code of Conduct.
MinigameZ more is a new contributor. Be nice, and check out our Code of Conduct.
MinigameZ more is a new contributor. Be nice, and check out our Code of Conduct.
MinigameZ more is a new contributor. Be nice, and check out our Code of Conduct.
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2
Already discussed many times on this site; see e.g. what-is-the-difference-between-necessary-and-sufficient as well as what-are-the-truth-tables-for-necessary-and-sufficient
– Mauro ALLEGRANZA
12 hours ago
I made an edit which you may roll back or further edit.
– Frank Hubeny
11 hours ago
12
Are you perhaps interpreting the word "only" to be qualifying New York? A comma would help to clarify, as would an appropriate pause in the spoken sentence. In other words, do you understand this sentence to be "I am in New York, only if I am in America" or "I am in New York only, if I am in America." If you understood it to be the latter, then I agree that it is illogical. If you understood it to be the former, then hopefully the existing answers have helped you.
– Richard II
9 hours ago
Technically if you were in New York you might be in a foreign embassy and not in "America"
– Mark Schultheiss
5 hours ago
@MarkSchultheiss To take your technicality futher, are you still in new york if you are in an embassy? Is yes, then you are also in america (as you are saying the politics are irrelevant). If no, then you are also NOT in america
– user34150
5 hours ago