An English sentence which cannot be represented in First Order Logic
I was trying to find some English sentences which cannot be represented in FOL. I tried different ones but I always ended up converting them to FOL.
Is there any English sentence which cannot be represented in First-Order Logic, can someone give me a real sentence as an example?
logic logical-operators
asked Nov 13 '18 at 16:58
Ardit ShalaArdit Shala
36
add a comment |
I was trying to find some English sentences which cannot be represented in FOL. I tried different ones but I always ended up converting them to FOL.
Is there any English sentence which cannot be represented in First-Order Logic, can someone give me a real sentence as an example?
logic logical-operators
asked Nov 13 '18 at 16:58
Ardit ShalaArdit Shala
36
add a comment |
I was trying to find some English sentences which cannot be represented in FOL. I tried different ones but I always ended up converting them to FOL.
Is there any English sentence which cannot be represented in First-Order Logic, can someone give me a real sentence as an example?
logic logical-operators
asked Nov 13 '18 at 16:58
Ardit ShalaArdit Shala
36
I was trying to find some English sentences which cannot be represented in FOL. I tried different ones but I always ended up converting them to FOL.
Is there any English sentence which cannot be represented in First-Order Logic, can someone give me a real sentence as an example?
logic logical-operators
logic logical-operators
asked Nov 13 '18 at 16:58
Ardit ShalaArdit Shala
36
asked Nov 13 '18 at 16:58
Ardit ShalaArdit Shala
36
asked Nov 13 '18 at 16:58
Ardit ShalaArdit Shala
36
asked Nov 13 '18 at 16:58
Ardit ShalaArdit Shala
36
asked Nov 13 '18 at 16:58
Ardit ShalaArdit Shala
36
36
add a comment |
add a comment |
1 Answer
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One of the major issues with translating into FOL actually arises from the other branches of philosophy rather than logic itself. The first thing that came to mind when reading your question was the issue of non-existent objects.
For example; 'John fears Pegasus' could be translated easily into FOL (just give two objects the predicates of 'John-izes' and 'Pegasus-izes', and a two-place predicate stating that one fears the other). You have immediately generated an issue, however; there is no object such that that object Pegasus-izes. Pegasus is not real. So, the statements
'John fears Pegasus' and
'John fears Bigfoot'
ought to be logically equivalent. We as English speakers know that this is not true (John in fact loves Bigfoot). Thus, while the sentences are perfectly translatable into FOL, the system lacks the complexity needed to distinguish between the two statements without incurring some tremendous difficulties. Can the sentences be represented? Yes. Are those representations useful? Well...
Not sure it's quite the answer you were looking for, but hopefully it's some food for thought nonetheless. Might also be worth looking into problems with the material conditional - the logical "if-then" and the English "if-then" don't always play nicely together.
answered Dec 12 '18 at 6:24
G. CorkeryG. Corkery
1
add a comment |
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1 Answer
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1 Answer
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active
oldest
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One of the major issues with translating into FOL actually arises from the other branches of philosophy rather than logic itself. The first thing that came to mind when reading your question was the issue of non-existent objects.
For example; 'John fears Pegasus' could be translated easily into FOL (just give two objects the predicates of 'John-izes' and 'Pegasus-izes', and a two-place predicate stating that one fears the other). You have immediately generated an issue, however; there is no object such that that object Pegasus-izes. Pegasus is not real. So, the statements
'John fears Pegasus' and
'John fears Bigfoot'
ought to be logically equivalent. We as English speakers know that this is not true (John in fact loves Bigfoot). Thus, while the sentences are perfectly translatable into FOL, the system lacks the complexity needed to distinguish between the two statements without incurring some tremendous difficulties. Can the sentences be represented? Yes. Are those representations useful? Well...
Not sure it's quite the answer you were looking for, but hopefully it's some food for thought nonetheless. Might also be worth looking into problems with the material conditional - the logical "if-then" and the English "if-then" don't always play nicely together.
answered Dec 12 '18 at 6:24
G. CorkeryG. Corkery
1
add a comment |
One of the major issues with translating into FOL actually arises from the other branches of philosophy rather than logic itself. The first thing that came to mind when reading your question was the issue of non-existent objects.
For example; 'John fears Pegasus' could be translated easily into FOL (just give two objects the predicates of 'John-izes' and 'Pegasus-izes', and a two-place predicate stating that one fears the other). You have immediately generated an issue, however; there is no object such that that object Pegasus-izes. Pegasus is not real. So, the statements
'John fears Pegasus' and
'John fears Bigfoot'
ought to be logically equivalent. We as English speakers know that this is not true (John in fact loves Bigfoot). Thus, while the sentences are perfectly translatable into FOL, the system lacks the complexity needed to distinguish between the two statements without incurring some tremendous difficulties. Can the sentences be represented? Yes. Are those representations useful? Well...
Not sure it's quite the answer you were looking for, but hopefully it's some food for thought nonetheless. Might also be worth looking into problems with the material conditional - the logical "if-then" and the English "if-then" don't always play nicely together.
answered Dec 12 '18 at 6:24
G. CorkeryG. Corkery
1
add a comment |
One of the major issues with translating into FOL actually arises from the other branches of philosophy rather than logic itself. The first thing that came to mind when reading your question was the issue of non-existent objects.
For example; 'John fears Pegasus' could be translated easily into FOL (just give two objects the predicates of 'John-izes' and 'Pegasus-izes', and a two-place predicate stating that one fears the other). You have immediately generated an issue, however; there is no object such that that object Pegasus-izes. Pegasus is not real. So, the statements
'John fears Pegasus' and
'John fears Bigfoot'
ought to be logically equivalent. We as English speakers know that this is not true (John in fact loves Bigfoot). Thus, while the sentences are perfectly translatable into FOL, the system lacks the complexity needed to distinguish between the two statements without incurring some tremendous difficulties. Can the sentences be represented? Yes. Are those representations useful? Well...
Not sure it's quite the answer you were looking for, but hopefully it's some food for thought nonetheless. Might also be worth looking into problems with the material conditional - the logical "if-then" and the English "if-then" don't always play nicely together.
answered Dec 12 '18 at 6:24
G. CorkeryG. Corkery
1
One of the major issues with translating into FOL actually arises from the other branches of philosophy rather than logic itself. The first thing that came to mind when reading your question was the issue of non-existent objects.
For example; 'John fears Pegasus' could be translated easily into FOL (just give two objects the predicates of 'John-izes' and 'Pegasus-izes', and a two-place predicate stating that one fears the other). You have immediately generated an issue, however; there is no object such that that object Pegasus-izes. Pegasus is not real. So, the statements
'John fears Pegasus' and
'John fears Bigfoot'
ought to be logically equivalent. We as English speakers know that this is not true (John in fact loves Bigfoot). Thus, while the sentences are perfectly translatable into FOL, the system lacks the complexity needed to distinguish between the two statements without incurring some tremendous difficulties. Can the sentences be represented? Yes. Are those representations useful? Well...
Not sure it's quite the answer you were looking for, but hopefully it's some food for thought nonetheless. Might also be worth looking into problems with the material conditional - the logical "if-then" and the English "if-then" don't always play nicely together.
answered Dec 12 '18 at 6:24
G. CorkeryG. Corkery
1
answered Dec 12 '18 at 6:24
G. CorkeryG. Corkery
1
answered Dec 12 '18 at 6:24
G. CorkeryG. Corkery
1
answered Dec 12 '18 at 6:24
G. CorkeryG. Corkery
1
1
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