theory scope and proof [closed]
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I am looking for the proposition which states that a theory rules scope cannot defined all versions of a proposition because it is kind of creating a circle.
Forgive my french.. And approximation.
Could anybody point me in the direction.. Preferably not the door.
Edit : upon an old reading (more than 10 years ago, sorry I'm an old guy), I was trying to recall why a theory needed external rules to be complete or valid and couldn't hold all the terms to its own validation/invalidation. @Dave pointed me on the right track, even if I'd like to expand this concept to a more generic one, philosophically speaking.
Now, I really don't know (and humbly speaking) how to precise something that I don't know : I started the readings that @Dave gave me, maybe I will be more able to narrow. Until then, I will gladly submit to your enlightened advice.
proof-theory
asked Dec 8 '18 at 15:03
John DoeJohn Doe
1064
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closed as unclear what you're asking by Peter Smith, Lord Shark the Unknown, user10354138, Cesareo, Rebellos Dec 9 '18 at 10:21
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
I am looking for the proposition which states that a theory rules scope cannot defined all versions of a proposition because it is kind of creating a circle.
Forgive my french.. And approximation.
Could anybody point me in the direction.. Preferably not the door.
Edit : upon an old reading (more than 10 years ago, sorry I'm an old guy), I was trying to recall why a theory needed external rules to be complete or valid and couldn't hold all the terms to its own validation/invalidation. @Dave pointed me on the right track, even if I'd like to expand this concept to a more generic one, philosophically speaking.
Now, I really don't know (and humbly speaking) how to precise something that I don't know : I started the readings that @Dave gave me, maybe I will be more able to narrow. Until then, I will gladly submit to your enlightened advice.
proof-theory
asked Dec 8 '18 at 15:03
John DoeJohn Doe
1064
$endgroup$
closed as unclear what you're asking by Peter Smith, Lord Shark the Unknown, user10354138, Cesareo, Rebellos Dec 9 '18 at 10:21
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
downvote without explanation is not use at all : at least tell me what I could do better. ;)
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– John Doe
Dec 8 '18 at 15:32
1
$begingroup$
It would help to give some indication of your background level. Given what you've written, I don't know if you're asking about the basic philosophical principal (of which I don't know whether has a name) that axioms are needed to get anywhere, or whether you're talking about some issue related to Gödel's incompleteness theorems. Or something else . . .
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– Dave L. Renfro
Dec 8 '18 at 17:24
$begingroup$
Thanks. My background is a collective few readings.. So basic. But I do remember now (thanks to you) when I read about that, that Gödel was quoted. So I went to WIkipedia and found happiness in one of the consistency definition : for a set of rules inside a theory ~ "no rules combination could lead to prove p and non-p". In laymans terms, could you please explain why and point me to some more formal explanation ?
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– John Doe
Dec 8 '18 at 17:46
1
$begingroup$
A good place to begin is Gödel's Proof by Ernest Nagel and James R. Newman (1958). A bit more advanced is Gödel's Theorem by Torkel Franzén (2005; review).
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– Dave L. Renfro
Dec 8 '18 at 18:19
$begingroup$
Thanks. If you put your comment in answer, I will accept it.
$endgroup$
– John Doe
Dec 8 '18 at 18:58
add a comment |
$begingroup$
I am looking for the proposition which states that a theory rules scope cannot defined all versions of a proposition because it is kind of creating a circle.
Forgive my french.. And approximation.
Could anybody point me in the direction.. Preferably not the door.
Edit : upon an old reading (more than 10 years ago, sorry I'm an old guy), I was trying to recall why a theory needed external rules to be complete or valid and couldn't hold all the terms to its own validation/invalidation. @Dave pointed me on the right track, even if I'd like to expand this concept to a more generic one, philosophically speaking.
Now, I really don't know (and humbly speaking) how to precise something that I don't know : I started the readings that @Dave gave me, maybe I will be more able to narrow. Until then, I will gladly submit to your enlightened advice.
proof-theory
asked Dec 8 '18 at 15:03
John DoeJohn Doe
1064
$endgroup$
I am looking for the proposition which states that a theory rules scope cannot defined all versions of a proposition because it is kind of creating a circle.
Forgive my french.. And approximation.
Could anybody point me in the direction.. Preferably not the door.
Edit : upon an old reading (more than 10 years ago, sorry I'm an old guy), I was trying to recall why a theory needed external rules to be complete or valid and couldn't hold all the terms to its own validation/invalidation. @Dave pointed me on the right track, even if I'd like to expand this concept to a more generic one, philosophically speaking.
Now, I really don't know (and humbly speaking) how to precise something that I don't know : I started the readings that @Dave gave me, maybe I will be more able to narrow. Until then, I will gladly submit to your enlightened advice.
proof-theory
proof-theory
asked Dec 8 '18 at 15:03
John DoeJohn Doe
1064
asked Dec 8 '18 at 15:03
John DoeJohn Doe
1064
edited Dec 9 '18 at 18:41
John Doe
asked Dec 8 '18 at 15:03
John DoeJohn Doe
1064
asked Dec 8 '18 at 15:03
John DoeJohn Doe
1064
asked Dec 8 '18 at 15:03
John DoeJohn Doe
1064
1064
closed as unclear what you're asking by Peter Smith, Lord Shark the Unknown, user10354138, Cesareo, Rebellos Dec 9 '18 at 10:21
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as unclear what you're asking by Peter Smith, Lord Shark the Unknown, user10354138, Cesareo, Rebellos Dec 9 '18 at 10:21
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
$begingroup$
downvote without explanation is not use at all : at least tell me what I could do better. ;)
$endgroup$
– John Doe
Dec 8 '18 at 15:32
1
$begingroup$
It would help to give some indication of your background level. Given what you've written, I don't know if you're asking about the basic philosophical principal (of which I don't know whether has a name) that axioms are needed to get anywhere, or whether you're talking about some issue related to Gödel's incompleteness theorems. Or something else . . .
$endgroup$
– Dave L. Renfro
Dec 8 '18 at 17:24
$begingroup$
Thanks. My background is a collective few readings.. So basic. But I do remember now (thanks to you) when I read about that, that Gödel was quoted. So I went to WIkipedia and found happiness in one of the consistency definition : for a set of rules inside a theory ~ "no rules combination could lead to prove p and non-p". In laymans terms, could you please explain why and point me to some more formal explanation ?
$endgroup$
– John Doe
Dec 8 '18 at 17:46
1
$begingroup$
A good place to begin is Gödel's Proof by Ernest Nagel and James R. Newman (1958). A bit more advanced is Gödel's Theorem by Torkel Franzén (2005; review).
$endgroup$
– Dave L. Renfro
Dec 8 '18 at 18:19
$begingroup$
Thanks. If you put your comment in answer, I will accept it.
$endgroup$
– John Doe
Dec 8 '18 at 18:58
add a comment |
$begingroup$
downvote without explanation is not use at all : at least tell me what I could do better. ;)
$endgroup$
– John Doe
Dec 8 '18 at 15:32
1
$begingroup$
It would help to give some indication of your background level. Given what you've written, I don't know if you're asking about the basic philosophical principal (of which I don't know whether has a name) that axioms are needed to get anywhere, or whether you're talking about some issue related to Gödel's incompleteness theorems. Or something else . . .
$endgroup$
– Dave L. Renfro
Dec 8 '18 at 17:24
$begingroup$
Thanks. My background is a collective few readings.. So basic. But I do remember now (thanks to you) when I read about that, that Gödel was quoted. So I went to WIkipedia and found happiness in one of the consistency definition : for a set of rules inside a theory ~ "no rules combination could lead to prove p and non-p". In laymans terms, could you please explain why and point me to some more formal explanation ?
$endgroup$
– John Doe
Dec 8 '18 at 17:46
1
$begingroup$
A good place to begin is Gödel's Proof by Ernest Nagel and James R. Newman (1958). A bit more advanced is Gödel's Theorem by Torkel Franzén (2005; review).
$endgroup$
– Dave L. Renfro
Dec 8 '18 at 18:19
$begingroup$
Thanks. If you put your comment in answer, I will accept it.
$endgroup$
– John Doe
Dec 8 '18 at 18:58
$begingroup$
downvote without explanation is not use at all : at least tell me what I could do better. ;)
$endgroup$
– John Doe
Dec 8 '18 at 15:32
$begingroup$
downvote without explanation is not use at all : at least tell me what I could do better. ;)
$endgroup$
– John Doe
Dec 8 '18 at 15:32
1
1
$begingroup$
It would help to give some indication of your background level. Given what you've written, I don't know if you're asking about the basic philosophical principal (of which I don't know whether has a name) that axioms are needed to get anywhere, or whether you're talking about some issue related to Gödel's incompleteness theorems. Or something else . . .
$endgroup$
– Dave L. Renfro
Dec 8 '18 at 17:24
$begingroup$
It would help to give some indication of your background level. Given what you've written, I don't know if you're asking about the basic philosophical principal (of which I don't know whether has a name) that axioms are needed to get anywhere, or whether you're talking about some issue related to Gödel's incompleteness theorems. Or something else . . .
$endgroup$
– Dave L. Renfro
Dec 8 '18 at 17:24
$begingroup$
Thanks. My background is a collective few readings.. So basic. But I do remember now (thanks to you) when I read about that, that Gödel was quoted. So I went to WIkipedia and found happiness in one of the consistency definition : for a set of rules inside a theory ~ "no rules combination could lead to prove p and non-p". In laymans terms, could you please explain why and point me to some more formal explanation ?
$endgroup$
– John Doe
Dec 8 '18 at 17:46
$begingroup$
Thanks. My background is a collective few readings.. So basic. But I do remember now (thanks to you) when I read about that, that Gödel was quoted. So I went to WIkipedia and found happiness in one of the consistency definition : for a set of rules inside a theory ~ "no rules combination could lead to prove p and non-p". In laymans terms, could you please explain why and point me to some more formal explanation ?
$endgroup$
– John Doe
Dec 8 '18 at 17:46
1
1
$begingroup$
A good place to begin is Gödel's Proof by Ernest Nagel and James R. Newman (1958). A bit more advanced is Gödel's Theorem by Torkel Franzén (2005; review).
$endgroup$
– Dave L. Renfro
Dec 8 '18 at 18:19
$begingroup$
A good place to begin is Gödel's Proof by Ernest Nagel and James R. Newman (1958). A bit more advanced is Gödel's Theorem by Torkel Franzén (2005; review).
$endgroup$
– Dave L. Renfro
Dec 8 '18 at 18:19
$begingroup$
Thanks. If you put your comment in answer, I will accept it.
$endgroup$
– John Doe
Dec 8 '18 at 18:58
$begingroup$
Thanks. If you put your comment in answer, I will accept it.
$endgroup$
– John Doe
Dec 8 '18 at 18:58
add a comment |
1 Answer
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A good place to begin is Gödel's Proof by Ernest Nagel and James R. Newman (1958; freely available).
A bit more advanced is Gödel's Theorem by Torkel Franzén (2005; review).
(ADDED 9 DAYS LATER) The following book gives a super-gentle introduction to this general topic. I don't know how I forgot about this book --- it was all the rage towards the end of my undergraduate studies (I remember reading about, and sometimes even overhearing discussions about, courses being based on it), it won both the Pulitzer Prize for general non-fiction and the [USA] National Book Award for Science, and it launched the career of Hofstadter as one of the few mathematicians/physicists (his Ph.D. was in physics) whose celebrity has reached the general public.
Gödel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter (originally published in 1979)
answered Dec 8 '18 at 19:56
Dave L. RenfroDave L. Renfro
24.6k33981
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add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
A good place to begin is Gödel's Proof by Ernest Nagel and James R. Newman (1958; freely available).
A bit more advanced is Gödel's Theorem by Torkel Franzén (2005; review).
(ADDED 9 DAYS LATER) The following book gives a super-gentle introduction to this general topic. I don't know how I forgot about this book --- it was all the rage towards the end of my undergraduate studies (I remember reading about, and sometimes even overhearing discussions about, courses being based on it), it won both the Pulitzer Prize for general non-fiction and the [USA] National Book Award for Science, and it launched the career of Hofstadter as one of the few mathematicians/physicists (his Ph.D. was in physics) whose celebrity has reached the general public.
Gödel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter (originally published in 1979)
answered Dec 8 '18 at 19:56
Dave L. RenfroDave L. Renfro
24.6k33981
$endgroup$
add a comment |
$begingroup$
A good place to begin is Gödel's Proof by Ernest Nagel and James R. Newman (1958; freely available).
A bit more advanced is Gödel's Theorem by Torkel Franzén (2005; review).
(ADDED 9 DAYS LATER) The following book gives a super-gentle introduction to this general topic. I don't know how I forgot about this book --- it was all the rage towards the end of my undergraduate studies (I remember reading about, and sometimes even overhearing discussions about, courses being based on it), it won both the Pulitzer Prize for general non-fiction and the [USA] National Book Award for Science, and it launched the career of Hofstadter as one of the few mathematicians/physicists (his Ph.D. was in physics) whose celebrity has reached the general public.
Gödel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter (originally published in 1979)
answered Dec 8 '18 at 19:56
Dave L. RenfroDave L. Renfro
24.6k33981
$endgroup$
add a comment |
$begingroup$
A good place to begin is Gödel's Proof by Ernest Nagel and James R. Newman (1958; freely available).
A bit more advanced is Gödel's Theorem by Torkel Franzén (2005; review).
(ADDED 9 DAYS LATER) The following book gives a super-gentle introduction to this general topic. I don't know how I forgot about this book --- it was all the rage towards the end of my undergraduate studies (I remember reading about, and sometimes even overhearing discussions about, courses being based on it), it won both the Pulitzer Prize for general non-fiction and the [USA] National Book Award for Science, and it launched the career of Hofstadter as one of the few mathematicians/physicists (his Ph.D. was in physics) whose celebrity has reached the general public.
Gödel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter (originally published in 1979)
answered Dec 8 '18 at 19:56
Dave L. RenfroDave L. Renfro
24.6k33981
$endgroup$
A good place to begin is Gödel's Proof by Ernest Nagel and James R. Newman (1958; freely available).
A bit more advanced is Gödel's Theorem by Torkel Franzén (2005; review).
(ADDED 9 DAYS LATER) The following book gives a super-gentle introduction to this general topic. I don't know how I forgot about this book --- it was all the rage towards the end of my undergraduate studies (I remember reading about, and sometimes even overhearing discussions about, courses being based on it), it won both the Pulitzer Prize for general non-fiction and the [USA] National Book Award for Science, and it launched the career of Hofstadter as one of the few mathematicians/physicists (his Ph.D. was in physics) whose celebrity has reached the general public.
Gödel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter (originally published in 1979)
answered Dec 8 '18 at 19:56
Dave L. RenfroDave L. Renfro
24.6k33981
edited Dec 17 '18 at 9:34
answered Dec 8 '18 at 19:56
Dave L. RenfroDave L. Renfro
24.6k33981
answered Dec 8 '18 at 19:56
Dave L. RenfroDave L. Renfro
24.6k33981
answered Dec 8 '18 at 19:56
Dave L. RenfroDave L. Renfro
24.6k33981
24.6k33981
add a comment |
add a comment |
$begingroup$
downvote without explanation is not use at all : at least tell me what I could do better. ;)
$endgroup$
– John Doe
Dec 8 '18 at 15:32
1
$begingroup$
It would help to give some indication of your background level. Given what you've written, I don't know if you're asking about the basic philosophical principal (of which I don't know whether has a name) that axioms are needed to get anywhere, or whether you're talking about some issue related to Gödel's incompleteness theorems. Or something else . . .
$endgroup$
– Dave L. Renfro
Dec 8 '18 at 17:24
$begingroup$
Thanks. My background is a collective few readings.. So basic. But I do remember now (thanks to you) when I read about that, that Gödel was quoted. So I went to WIkipedia and found happiness in one of the consistency definition : for a set of rules inside a theory ~ "no rules combination could lead to prove p and non-p". In laymans terms, could you please explain why and point me to some more formal explanation ?
$endgroup$
– John Doe
Dec 8 '18 at 17:46
1
$begingroup$
A good place to begin is Gödel's Proof by Ernest Nagel and James R. Newman (1958). A bit more advanced is Gödel's Theorem by Torkel Franzén (2005; review).
$endgroup$
– Dave L. Renfro
Dec 8 '18 at 18:19
$begingroup$
Thanks. If you put your comment in answer, I will accept it.
$endgroup$
– John Doe
Dec 8 '18 at 18:58