A Puzzle of Language

[Orange Seeds]

A story:

For my symbolic logic class, students are required to answer simple quizzes online and submit the quizzes for grades. When we submit the quizzes we get to see what we got wrong. Simple.

So one set of quizzes had four options for answers, and we were tasked to pick all the correct answers. One of the answers is:

4. These are not semantically equivalent in the TARSKI blocks language on every interpretation of the non-logical symbols, whether the standard interpretation or a nonstandard one

which can be shortened without relevant loss to:

not semantically equivalent on every interpretation

I somehow got it into my head that this was a highly ambiguous answer. It could mean two separate things. Accusing a logic professor of ambiguous language is pretty much an accusation of complete vocational incompetence; not realizing this, I went and asked my prof about it. He laughed, gave a simple(/insufficient) explanation and stormed off.

Me being myself, can't rest until someone convinces me that it is not ambiguous. So answer me:
Is

not semantically equivalent on every interpretation

ambiguous?

Spoiler :

It seems to me that it can mean:
1. Equivalent on no interpretation
-or-
2. There is some interpretation that it is not equivalent

 

[warpus]

I am pretty sure it means 1. (Equivalent to no interpretation)

 

[Ayn Rand]

I'm not sure it's even ambiguous. I'd suggest 2. There is some interpretation that it is not equivalent, [and also some interpretation that is equivalent]


Poor use of a prepositional clause - is English his first language?

http://en.wikipedia.org/wiki/Adpositional_phrase
http://en.wikipedia.org/wiki/Adverbial_clause

Difference is between "not every" and "not any".

Chimney's are not on every house
Chimney's are not on any house

As the clause essentially states "Not A on every B"

Alternatively, he could have written "Not A, on every B"

 

[Orange Seeds]

I'm not sure it's even ambiguous. I'd suggest 2. There is some interpretation that it is not equivalent, [and also some interpretation that is equivalent]


Poor use of a prepositional clause - is English his first language?

http://en.wikipedia.org/wiki/Adpositional_phrase
http://en.wikipedia.org/wiki/Adverbial_clause

Difference is between "not every" and "not any".

Chimney's are not on every house
Chimney's are not on any house

As the clause essentially states "Not A on every B"

Alternatively, he could have written "Not A, on every B"

Excellent. My inquiries on various avenues are leading me to the strong conclusion that I am correct.

English is his first language, but his attempt to use an FOL syntax failed in his English sentence translation.
ie. option 3 is:

3. These are semantically equivalent in the TARSKI blocks language on every interpretation of the non-logical symbols, whether the standard interpretation or a nonstandard one

or more briefly:

semantically equivalent on every interpretation

He wanted to say the negation:

¬ (semantically equivalent on every interpretation)

Thus the poorly phrased:

not semantically equivalent on every interpretation