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The origin of a particular self-reference paradox
Is it possible to determine an object's nonexistence?How to be a good critic?How to understand numbers that become really large?What is the analytic-synthetic dilemma concerning existence?The paradox of onenessAre there Decision Trees for Identifying Fallacies?Omnipotence Paradox Defense and Meinongianism/Neo-MeinongianismRigorous, modern introductions to informal reasoning and critical thinking?A difficulty I've had with this “This sentence is false” and Russell's ParadoxAre there philosophers who argue for a close connection between consciousness and existence?
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This is a simple reference request, for the origin of a particular type of paradoxical statement. The example I remember is
Roger Penrose can't consistently claim this statement to be true.
It's a true statement, but if you happen to be Roger Penrose you can't say so without contradicting yourself. I have a feeling it might be due to (or popularised by) Douglas Hofstadter, but I'm not sure.
Note: it's a different statement from
Roger Penrose can't consistently believe this statement to be true.
It would be helpful to know the origin of both statements, but I'm particularly interested in the first, in which the target person can know the statement to be true but can't consistently say so.
reference-request paradox goedel self-reference
edited 7 hours ago
Mauro ALLEGRANZA
28.6k2 gold badges20 silver badges68 bronze badges
asked 12 hours ago
NathanielNathaniel
3572 silver badges10 bronze badges
add a comment |
This is a simple reference request, for the origin of a particular type of paradoxical statement. The example I remember is
Roger Penrose can't consistently claim this statement to be true.
It's a true statement, but if you happen to be Roger Penrose you can't say so without contradicting yourself. I have a feeling it might be due to (or popularised by) Douglas Hofstadter, but I'm not sure.
Note: it's a different statement from
Roger Penrose can't consistently believe this statement to be true.
It would be helpful to know the origin of both statements, but I'm particularly interested in the first, in which the target person can know the statement to be true but can't consistently say so.
reference-request paradox goedel self-reference
edited 7 hours ago
Mauro ALLEGRANZA
28.6k2 gold badges20 silver badges68 bronze badges
asked 12 hours ago
NathanielNathaniel
3572 silver badges10 bronze badges
1
Sure feels like a GEB-ism 😆
– Rusi
12 hours ago
What the above formulation adds to the "usual" Liar paradox?
– Mauro ALLEGRANZA
11 hours ago
@MauroALLEGRANZA it's quite different. The statement in the liar paradox doesn't have a well defined truth value, but this one does. Try this: "Mauro Allegranza can't consistently claim this statement to be true." Is it a true statement? Can you consistently claim it?
– Nathaniel
11 hours ago
@MauroALLEGRANZA the statement is self-referential in either case, since it refers to itself. But yes, it becomes a version of the liar paradox if you utter it but not if I utter it, this is correct. (But note, even if you do utter it, it's still definitely true!) The question is only about who first formulated this example.
– Nathaniel
10 hours ago
1
@MauroALLEGRANZA perfect, yes, that seems very likely to be it. (Most likely my memory interchanged Lucas and Penrose in the example, as their arguments are quite similar.) Feel free to post that as an answer, if you care about points.
– Nathaniel
9 hours ago
add a comment |
This is a simple reference request, for the origin of a particular type of paradoxical statement. The example I remember is
Roger Penrose can't consistently claim this statement to be true.
It's a true statement, but if you happen to be Roger Penrose you can't say so without contradicting yourself. I have a feeling it might be due to (or popularised by) Douglas Hofstadter, but I'm not sure.
Note: it's a different statement from
Roger Penrose can't consistently believe this statement to be true.
It would be helpful to know the origin of both statements, but I'm particularly interested in the first, in which the target person can know the statement to be true but can't consistently say so.
reference-request paradox goedel self-reference
edited 7 hours ago
Mauro ALLEGRANZA
28.6k2 gold badges20 silver badges68 bronze badges
asked 12 hours ago
NathanielNathaniel
3572 silver badges10 bronze badges
This is a simple reference request, for the origin of a particular type of paradoxical statement. The example I remember is
Roger Penrose can't consistently claim this statement to be true.
It's a true statement, but if you happen to be Roger Penrose you can't say so without contradicting yourself. I have a feeling it might be due to (or popularised by) Douglas Hofstadter, but I'm not sure.
Note: it's a different statement from
Roger Penrose can't consistently believe this statement to be true.
It would be helpful to know the origin of both statements, but I'm particularly interested in the first, in which the target person can know the statement to be true but can't consistently say so.
reference-request paradox goedel self-reference
reference-request paradox goedel self-reference
edited 7 hours ago
Mauro ALLEGRANZA
28.6k2 gold badges20 silver badges68 bronze badges
asked 12 hours ago
NathanielNathaniel
3572 silver badges10 bronze badges
edited 7 hours ago
Mauro ALLEGRANZA
28.6k2 gold badges20 silver badges68 bronze badges
asked 12 hours ago
NathanielNathaniel
3572 silver badges10 bronze badges
edited 7 hours ago
Mauro ALLEGRANZA
28.6k2 gold badges20 silver badges68 bronze badges
edited 7 hours ago
Mauro ALLEGRANZA
28.6k2 gold badges20 silver badges68 bronze badges
edited 7 hours ago
Mauro ALLEGRANZA
28.6k2 gold badges20 silver badges68 bronze badges
28.6k2 gold badges20 silver badges68 bronze badges
asked 12 hours ago
NathanielNathaniel
3572 silver badges10 bronze badges
asked 12 hours ago
NathanielNathaniel
3572 silver badges10 bronze badges
asked 12 hours ago
NathanielNathaniel
3572 silver badges10 bronze badges
3572 silver badges10 bronze badges
1
Sure feels like a GEB-ism 😆
– Rusi
12 hours ago
What the above formulation adds to the "usual" Liar paradox?
– Mauro ALLEGRANZA
11 hours ago
@MauroALLEGRANZA it's quite different. The statement in the liar paradox doesn't have a well defined truth value, but this one does. Try this: "Mauro Allegranza can't consistently claim this statement to be true." Is it a true statement? Can you consistently claim it?
– Nathaniel
11 hours ago
@MauroALLEGRANZA the statement is self-referential in either case, since it refers to itself. But yes, it becomes a version of the liar paradox if you utter it but not if I utter it, this is correct. (But note, even if you do utter it, it's still definitely true!) The question is only about who first formulated this example.
– Nathaniel
10 hours ago
1
@MauroALLEGRANZA perfect, yes, that seems very likely to be it. (Most likely my memory interchanged Lucas and Penrose in the example, as their arguments are quite similar.) Feel free to post that as an answer, if you care about points.
– Nathaniel
9 hours ago
add a comment |
1
Sure feels like a GEB-ism 😆
– Rusi
12 hours ago
What the above formulation adds to the "usual" Liar paradox?
– Mauro ALLEGRANZA
11 hours ago
@MauroALLEGRANZA it's quite different. The statement in the liar paradox doesn't have a well defined truth value, but this one does. Try this: "Mauro Allegranza can't consistently claim this statement to be true." Is it a true statement? Can you consistently claim it?
– Nathaniel
11 hours ago
@MauroALLEGRANZA the statement is self-referential in either case, since it refers to itself. But yes, it becomes a version of the liar paradox if you utter it but not if I utter it, this is correct. (But note, even if you do utter it, it's still definitely true!) The question is only about who first formulated this example.
– Nathaniel
10 hours ago
1
@MauroALLEGRANZA perfect, yes, that seems very likely to be it. (Most likely my memory interchanged Lucas and Penrose in the example, as their arguments are quite similar.) Feel free to post that as an answer, if you care about points.
– Nathaniel
9 hours ago
1
1
Sure feels like a GEB-ism 😆
– Rusi
12 hours ago
Sure feels like a GEB-ism 😆
– Rusi
12 hours ago
What the above formulation adds to the "usual" Liar paradox?
– Mauro ALLEGRANZA
11 hours ago
What the above formulation adds to the "usual" Liar paradox?
– Mauro ALLEGRANZA
11 hours ago
@MauroALLEGRANZA it's quite different. The statement in the liar paradox doesn't have a well defined truth value, but this one does. Try this: "Mauro Allegranza can't consistently claim this statement to be true." Is it a true statement? Can you consistently claim it?
– Nathaniel
11 hours ago
@MauroALLEGRANZA it's quite different. The statement in the liar paradox doesn't have a well defined truth value, but this one does. Try this: "Mauro Allegranza can't consistently claim this statement to be true." Is it a true statement? Can you consistently claim it?
– Nathaniel
11 hours ago
@MauroALLEGRANZA the statement is self-referential in either case, since it refers to itself. But yes, it becomes a version of the liar paradox if you utter it but not if I utter it, this is correct. (But note, even if you do utter it, it's still definitely true!) The question is only about who first formulated this example.
– Nathaniel
10 hours ago
@MauroALLEGRANZA the statement is self-referential in either case, since it refers to itself. But yes, it becomes a version of the liar paradox if you utter it but not if I utter it, this is correct. (But note, even if you do utter it, it's still definitely true!) The question is only about who first formulated this example.
– Nathaniel
10 hours ago
1
1
@MauroALLEGRANZA perfect, yes, that seems very likely to be it. (Most likely my memory interchanged Lucas and Penrose in the example, as their arguments are quite similar.) Feel free to post that as an answer, if you care about points.
– Nathaniel
9 hours ago
@MauroALLEGRANZA perfect, yes, that seems very likely to be it. (Most likely my memory interchanged Lucas and Penrose in the example, as their arguments are quite similar.) Feel free to post that as an answer, if you care about points.
– Nathaniel
9 hours ago
add a comment |
1 Answer
1
active
oldest
votes
The origin is with the so-called Whiteley Sentence.
See C.Whiteley, “Minds, Machines and Gödel: A Reply to Mr. Lucas (1962)”, Philosophy 37:61-62 :
It is possible to devise a formula which will trap a human mind —say, Mr Lucas's— in the same way that his application of Gödel traps the machine. Take, for instance, the formula
'This formula cannot be consistently asserted by Lucas'.
answered 7 hours ago
Mauro ALLEGRANZAMauro ALLEGRANZA
28.6k2 gold badges20 silver badges68 bronze badges
add a comment |
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votes
The origin is with the so-called Whiteley Sentence.
See C.Whiteley, “Minds, Machines and Gödel: A Reply to Mr. Lucas (1962)”, Philosophy 37:61-62 :
It is possible to devise a formula which will trap a human mind —say, Mr Lucas's— in the same way that his application of Gödel traps the machine. Take, for instance, the formula
'This formula cannot be consistently asserted by Lucas'.
answered 7 hours ago
Mauro ALLEGRANZAMauro ALLEGRANZA
28.6k2 gold badges20 silver badges68 bronze badges
add a comment |
The origin is with the so-called Whiteley Sentence.
See C.Whiteley, “Minds, Machines and Gödel: A Reply to Mr. Lucas (1962)”, Philosophy 37:61-62 :
It is possible to devise a formula which will trap a human mind —say, Mr Lucas's— in the same way that his application of Gödel traps the machine. Take, for instance, the formula
'This formula cannot be consistently asserted by Lucas'.
answered 7 hours ago
Mauro ALLEGRANZAMauro ALLEGRANZA
28.6k2 gold badges20 silver badges68 bronze badges
add a comment |
The origin is with the so-called Whiteley Sentence.
See C.Whiteley, “Minds, Machines and Gödel: A Reply to Mr. Lucas (1962)”, Philosophy 37:61-62 :
It is possible to devise a formula which will trap a human mind —say, Mr Lucas's— in the same way that his application of Gödel traps the machine. Take, for instance, the formula
'This formula cannot be consistently asserted by Lucas'.
answered 7 hours ago
Mauro ALLEGRANZAMauro ALLEGRANZA
28.6k2 gold badges20 silver badges68 bronze badges
The origin is with the so-called Whiteley Sentence.
See C.Whiteley, “Minds, Machines and Gödel: A Reply to Mr. Lucas (1962)”, Philosophy 37:61-62 :
It is possible to devise a formula which will trap a human mind —say, Mr Lucas's— in the same way that his application of Gödel traps the machine. Take, for instance, the formula
'This formula cannot be consistently asserted by Lucas'.
answered 7 hours ago
Mauro ALLEGRANZAMauro ALLEGRANZA
28.6k2 gold badges20 silver badges68 bronze badges
answered 7 hours ago
Mauro ALLEGRANZAMauro ALLEGRANZA
28.6k2 gold badges20 silver badges68 bronze badges
answered 7 hours ago
Mauro ALLEGRANZAMauro ALLEGRANZA
28.6k2 gold badges20 silver badges68 bronze badges
answered 7 hours ago
Mauro ALLEGRANZAMauro ALLEGRANZA
28.6k2 gold badges20 silver badges68 bronze badges
28.6k2 gold badges20 silver badges68 bronze badges
add a comment |
add a comment |
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1
Sure feels like a GEB-ism 😆
– Rusi
12 hours ago
What the above formulation adds to the "usual" Liar paradox?
– Mauro ALLEGRANZA
11 hours ago
@MauroALLEGRANZA it's quite different. The statement in the liar paradox doesn't have a well defined truth value, but this one does. Try this: "Mauro Allegranza can't consistently claim this statement to be true." Is it a true statement? Can you consistently claim it?
– Nathaniel
11 hours ago
@MauroALLEGRANZA the statement is self-referential in either case, since it refers to itself. But yes, it becomes a version of the liar paradox if you utter it but not if I utter it, this is correct. (But note, even if you do utter it, it's still definitely true!) The question is only about who first formulated this example.
– Nathaniel
10 hours ago
1
@MauroALLEGRANZA perfect, yes, that seems very likely to be it. (Most likely my memory interchanged Lucas and Penrose in the example, as their arguments are quite similar.) Feel free to post that as an answer, if you care about points.
– Nathaniel
9 hours ago