Language, Proof & Logic 9.17 (9) Exercise
$begingroup$
The exercise 9.17 of Language, Proof and Logic course goes like this:
Start a new sentence file, and enter translations of the following sentences. This time each translation will contain exactly one $forall$ and no $exists$.
All dodecahedra are not small [Note: Most people find this sentence ambiguous. Can you find both readings? One starts with $forall$, the other with $neg$. Use the former, the one that means all the dodecahedra are either medium and large.]
I have passed the assignment successfully and my translation was:
$$
forall x (Dodec(x) rightarrow neg Small(x))
$$
My question is what is the other ambiguous interpretation for that English language sentence that authors hint on (the one that starts from $neg$).
first-order-logic
asked Oct 26 '18 at 11:09
Andrey SurovtsevAndrey Surovtsev
835
$endgroup$
add a comment |
$begingroup$
The exercise 9.17 of Language, Proof and Logic course goes like this:
Start a new sentence file, and enter translations of the following sentences. This time each translation will contain exactly one $forall$ and no $exists$.
All dodecahedra are not small [Note: Most people find this sentence ambiguous. Can you find both readings? One starts with $forall$, the other with $neg$. Use the former, the one that means all the dodecahedra are either medium and large.]
I have passed the assignment successfully and my translation was:
$$
forall x (Dodec(x) rightarrow neg Small(x))
$$
My question is what is the other ambiguous interpretation for that English language sentence that authors hint on (the one that starts from $neg$).
first-order-logic
asked Oct 26 '18 at 11:09
Andrey SurovtsevAndrey Surovtsev
835
$endgroup$
2
$begingroup$
The other interpretation is what would be more properly formulated as "Not all dodecahedra are small", I suppose. Personally, I would never interprete the given sentence this way.
$endgroup$
– Hagen von Eitzen
Oct 26 '18 at 11:12
$begingroup$
@HagenvonEitzen Thanks, it seems likely to be what they intended! Neither would I though! The statement of yours seems to be very fitting, but when I compare it with the original English sentence (even knowing the answer, presumably), seeing one as an interpretation of another still feels counterintuitive.
$endgroup$
– Andrey Surovtsev
Oct 27 '18 at 7:30
add a comment |
$begingroup$
The exercise 9.17 of Language, Proof and Logic course goes like this:
Start a new sentence file, and enter translations of the following sentences. This time each translation will contain exactly one $forall$ and no $exists$.
All dodecahedra are not small [Note: Most people find this sentence ambiguous. Can you find both readings? One starts with $forall$, the other with $neg$. Use the former, the one that means all the dodecahedra are either medium and large.]
I have passed the assignment successfully and my translation was:
$$
forall x (Dodec(x) rightarrow neg Small(x))
$$
My question is what is the other ambiguous interpretation for that English language sentence that authors hint on (the one that starts from $neg$).
first-order-logic
asked Oct 26 '18 at 11:09
Andrey SurovtsevAndrey Surovtsev
835
$endgroup$
The exercise 9.17 of Language, Proof and Logic course goes like this:
Start a new sentence file, and enter translations of the following sentences. This time each translation will contain exactly one $forall$ and no $exists$.
All dodecahedra are not small [Note: Most people find this sentence ambiguous. Can you find both readings? One starts with $forall$, the other with $neg$. Use the former, the one that means all the dodecahedra are either medium and large.]
I have passed the assignment successfully and my translation was:
$$
forall x (Dodec(x) rightarrow neg Small(x))
$$
My question is what is the other ambiguous interpretation for that English language sentence that authors hint on (the one that starts from $neg$).
first-order-logic
first-order-logic
asked Oct 26 '18 at 11:09
Andrey SurovtsevAndrey Surovtsev
835
asked Oct 26 '18 at 11:09
Andrey SurovtsevAndrey Surovtsev
835
asked Oct 26 '18 at 11:09
Andrey SurovtsevAndrey Surovtsev
835
asked Oct 26 '18 at 11:09
Andrey SurovtsevAndrey Surovtsev
835
asked Oct 26 '18 at 11:09
Andrey SurovtsevAndrey Surovtsev
835
835
2
$begingroup$
The other interpretation is what would be more properly formulated as "Not all dodecahedra are small", I suppose. Personally, I would never interprete the given sentence this way.
$endgroup$
– Hagen von Eitzen
Oct 26 '18 at 11:12
$begingroup$
@HagenvonEitzen Thanks, it seems likely to be what they intended! Neither would I though! The statement of yours seems to be very fitting, but when I compare it with the original English sentence (even knowing the answer, presumably), seeing one as an interpretation of another still feels counterintuitive.
$endgroup$
– Andrey Surovtsev
Oct 27 '18 at 7:30
add a comment |
2
$begingroup$
The other interpretation is what would be more properly formulated as "Not all dodecahedra are small", I suppose. Personally, I would never interprete the given sentence this way.
$endgroup$
– Hagen von Eitzen
Oct 26 '18 at 11:12
$begingroup$
@HagenvonEitzen Thanks, it seems likely to be what they intended! Neither would I though! The statement of yours seems to be very fitting, but when I compare it with the original English sentence (even knowing the answer, presumably), seeing one as an interpretation of another still feels counterintuitive.
$endgroup$
– Andrey Surovtsev
Oct 27 '18 at 7:30
2
2
$begingroup$
The other interpretation is what would be more properly formulated as "Not all dodecahedra are small", I suppose. Personally, I would never interprete the given sentence this way.
$endgroup$
– Hagen von Eitzen
Oct 26 '18 at 11:12
$begingroup$
The other interpretation is what would be more properly formulated as "Not all dodecahedra are small", I suppose. Personally, I would never interprete the given sentence this way.
$endgroup$
– Hagen von Eitzen
Oct 26 '18 at 11:12
$begingroup$
@HagenvonEitzen Thanks, it seems likely to be what they intended! Neither would I though! The statement of yours seems to be very fitting, but when I compare it with the original English sentence (even knowing the answer, presumably), seeing one as an interpretation of another still feels counterintuitive.
$endgroup$
– Andrey Surovtsev
Oct 27 '18 at 7:30
$begingroup$
@HagenvonEitzen Thanks, it seems likely to be what they intended! Neither would I though! The statement of yours seems to be very fitting, but when I compare it with the original English sentence (even knowing the answer, presumably), seeing one as an interpretation of another still feels counterintuitive.
$endgroup$
– Andrey Surovtsev
Oct 27 '18 at 7:30
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
There is a well-known saying "All that glitters is not gold"
The literal translation of this would be:
$$forall x(Glitters(x) rightarrow neg Gold(x))$$
but it is clear that what this saying really means is:
$$neg forall x(Glitters(x) rightarrow Gold(x))$$
Maybe that's the 'ambiguity' they are referring to? Though I must say, I think the only reasonable interpretation of "All dodecahedra are not small" is what you have, and "All that glitters is not gold" is just a very poor way of saying "Not all that glitters is gold"
answered Dec 23 '18 at 15:46
Bram28Bram28
61.9k44793
$endgroup$
add a comment |
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$begingroup$
There is a well-known saying "All that glitters is not gold"
The literal translation of this would be:
$$forall x(Glitters(x) rightarrow neg Gold(x))$$
but it is clear that what this saying really means is:
$$neg forall x(Glitters(x) rightarrow Gold(x))$$
Maybe that's the 'ambiguity' they are referring to? Though I must say, I think the only reasonable interpretation of "All dodecahedra are not small" is what you have, and "All that glitters is not gold" is just a very poor way of saying "Not all that glitters is gold"
answered Dec 23 '18 at 15:46
Bram28Bram28
61.9k44793
$endgroup$
add a comment |
$begingroup$
There is a well-known saying "All that glitters is not gold"
The literal translation of this would be:
$$forall x(Glitters(x) rightarrow neg Gold(x))$$
but it is clear that what this saying really means is:
$$neg forall x(Glitters(x) rightarrow Gold(x))$$
Maybe that's the 'ambiguity' they are referring to? Though I must say, I think the only reasonable interpretation of "All dodecahedra are not small" is what you have, and "All that glitters is not gold" is just a very poor way of saying "Not all that glitters is gold"
answered Dec 23 '18 at 15:46
Bram28Bram28
61.9k44793
$endgroup$
add a comment |
$begingroup$
There is a well-known saying "All that glitters is not gold"
The literal translation of this would be:
$$forall x(Glitters(x) rightarrow neg Gold(x))$$
but it is clear that what this saying really means is:
$$neg forall x(Glitters(x) rightarrow Gold(x))$$
Maybe that's the 'ambiguity' they are referring to? Though I must say, I think the only reasonable interpretation of "All dodecahedra are not small" is what you have, and "All that glitters is not gold" is just a very poor way of saying "Not all that glitters is gold"
answered Dec 23 '18 at 15:46
Bram28Bram28
61.9k44793
$endgroup$
There is a well-known saying "All that glitters is not gold"
The literal translation of this would be:
$$forall x(Glitters(x) rightarrow neg Gold(x))$$
but it is clear that what this saying really means is:
$$neg forall x(Glitters(x) rightarrow Gold(x))$$
Maybe that's the 'ambiguity' they are referring to? Though I must say, I think the only reasonable interpretation of "All dodecahedra are not small" is what you have, and "All that glitters is not gold" is just a very poor way of saying "Not all that glitters is gold"
answered Dec 23 '18 at 15:46
Bram28Bram28
61.9k44793
answered Dec 23 '18 at 15:46
Bram28Bram28
61.9k44793
answered Dec 23 '18 at 15:46
Bram28Bram28
61.9k44793
answered Dec 23 '18 at 15:46
Bram28Bram28
61.9k44793
61.9k44793
add a comment |
add a comment |
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$begingroup$
The other interpretation is what would be more properly formulated as "Not all dodecahedra are small", I suppose. Personally, I would never interprete the given sentence this way.
$endgroup$
– Hagen von Eitzen
Oct 26 '18 at 11:12
$begingroup$
@HagenvonEitzen Thanks, it seems likely to be what they intended! Neither would I though! The statement of yours seems to be very fitting, but when I compare it with the original English sentence (even knowing the answer, presumably), seeing one as an interpretation of another still feels counterintuitive.
$endgroup$
– Andrey Surovtsev
Oct 27 '18 at 7:30