Mixing
Is $1=1$ tautology?
Clash Royale CLAN TAG#URR8PPP
up vote
0
down vote
favorite
Is "1=1" tautology ?
In this case, "1" means multiplicative identity of real number.
If we treat "1=1" as a simple proposition p , we will get p is not tautology.
But p is always true because it denotes "1=1" which is always true
Can we say that "1=1" is tautology?
logic propositional-calculus
edited Jul 31 at 6:53
Gonzalo Benavides
566217
asked Jul 31 at 5:45
Bless
1,330413
add a comment |Â
up vote
0
down vote
favorite
Is "1=1" tautology ?
In this case, "1" means multiplicative identity of real number.
If we treat "1=1" as a simple proposition p , we will get p is not tautology.
But p is always true because it denotes "1=1" which is always true
Can we say that "1=1" is tautology?
logic propositional-calculus
edited Jul 31 at 6:53
Gonzalo Benavides
566217
asked Jul 31 at 5:45
Bless
1,330413
7
Define a tautology.
– Kenny Lau
Jul 31 at 5:47
1
Define "simple proposition"
– Morgan Rodgers
Jul 31 at 6:03
In most developments of first order logic $x=x$ is a theorem for any $x$. But as Kenny says, it depends on what you mean by tautology. In the sense that any formula having the same arrangement of truth functional operators is true, then clearly not. In the sense that it's true regardless of any extralogical axioms, sure.
– Malice Vidrine
Jul 31 at 6:27
3
See tautology (logic) : "In logic, a tautology is a formula or assertion that is true in every possible interpretation. A formula of propositional logic is a tautology if the formula itself is always true regardless of which valuation is used for the propositional variables." Thus, you have two possible readings: the narrow one, restricting the use of the term to propositional logic, and the wider one, regarding logic in general. According to the wider reading, it is a tautology, because it is an instance of the valid FOL formula: $x=x$.
– Mauro ALLEGRANZA
Jul 31 at 6:45
In classical logic, it is a tautology, but there may be some logics where it's not (actually, there are - but are they interesting ?)
– Max
Jul 31 at 9:57
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Is "1=1" tautology ?
In this case, "1" means multiplicative identity of real number.
If we treat "1=1" as a simple proposition p , we will get p is not tautology.
But p is always true because it denotes "1=1" which is always true
Can we say that "1=1" is tautology?
logic propositional-calculus
edited Jul 31 at 6:53
Gonzalo Benavides
566217
asked Jul 31 at 5:45
Bless
1,330413
Is "1=1" tautology ?
In this case, "1" means multiplicative identity of real number.
If we treat "1=1" as a simple proposition p , we will get p is not tautology.
But p is always true because it denotes "1=1" which is always true
Can we say that "1=1" is tautology?
logic propositional-calculus
edited Jul 31 at 6:53
Gonzalo Benavides
566217
asked Jul 31 at 5:45
Bless
1,330413
edited Jul 31 at 6:53
Gonzalo Benavides
566217
edited Jul 31 at 6:53
Gonzalo Benavides
566217
edited Jul 31 at 6:53
Gonzalo Benavides
566217
566217
asked Jul 31 at 5:45
Bless
1,330413
asked Jul 31 at 5:45
Bless
1,330413
asked Jul 31 at 5:45
Bless
1,330413
1,330413
7
Define a tautology.
– Kenny Lau
Jul 31 at 5:47
1
Define "simple proposition"
– Morgan Rodgers
Jul 31 at 6:03
In most developments of first order logic $x=x$ is a theorem for any $x$. But as Kenny says, it depends on what you mean by tautology. In the sense that any formula having the same arrangement of truth functional operators is true, then clearly not. In the sense that it's true regardless of any extralogical axioms, sure.
– Malice Vidrine
Jul 31 at 6:27
3
See tautology (logic) : "In logic, a tautology is a formula or assertion that is true in every possible interpretation. A formula of propositional logic is a tautology if the formula itself is always true regardless of which valuation is used for the propositional variables." Thus, you have two possible readings: the narrow one, restricting the use of the term to propositional logic, and the wider one, regarding logic in general. According to the wider reading, it is a tautology, because it is an instance of the valid FOL formula: $x=x$.
– Mauro ALLEGRANZA
Jul 31 at 6:45
In classical logic, it is a tautology, but there may be some logics where it's not (actually, there are - but are they interesting ?)
– Max
Jul 31 at 9:57
add a comment |Â
7
Define a tautology.
– Kenny Lau
Jul 31 at 5:47
1
Define "simple proposition"
– Morgan Rodgers
Jul 31 at 6:03
In most developments of first order logic $x=x$ is a theorem for any $x$. But as Kenny says, it depends on what you mean by tautology. In the sense that any formula having the same arrangement of truth functional operators is true, then clearly not. In the sense that it's true regardless of any extralogical axioms, sure.
– Malice Vidrine
Jul 31 at 6:27
3
See tautology (logic) : "In logic, a tautology is a formula or assertion that is true in every possible interpretation. A formula of propositional logic is a tautology if the formula itself is always true regardless of which valuation is used for the propositional variables." Thus, you have two possible readings: the narrow one, restricting the use of the term to propositional logic, and the wider one, regarding logic in general. According to the wider reading, it is a tautology, because it is an instance of the valid FOL formula: $x=x$.
– Mauro ALLEGRANZA
Jul 31 at 6:45
In classical logic, it is a tautology, but there may be some logics where it's not (actually, there are - but are they interesting ?)
– Max
Jul 31 at 9:57
7
7
Define a tautology.
– Kenny Lau
Jul 31 at 5:47
Define a tautology.
– Kenny Lau
Jul 31 at 5:47
1
1
Define "simple proposition"
– Morgan Rodgers
Jul 31 at 6:03
Define "simple proposition"
– Morgan Rodgers
Jul 31 at 6:03
In most developments of first order logic $x=x$ is a theorem for any $x$. But as Kenny says, it depends on what you mean by tautology. In the sense that any formula having the same arrangement of truth functional operators is true, then clearly not. In the sense that it's true regardless of any extralogical axioms, sure.
– Malice Vidrine
Jul 31 at 6:27
In most developments of first order logic $x=x$ is a theorem for any $x$. But as Kenny says, it depends on what you mean by tautology. In the sense that any formula having the same arrangement of truth functional operators is true, then clearly not. In the sense that it's true regardless of any extralogical axioms, sure.
– Malice Vidrine
Jul 31 at 6:27
3
3
See tautology (logic) : "In logic, a tautology is a formula or assertion that is true in every possible interpretation. A formula of propositional logic is a tautology if the formula itself is always true regardless of which valuation is used for the propositional variables." Thus, you have two possible readings: the narrow one, restricting the use of the term to propositional logic, and the wider one, regarding logic in general. According to the wider reading, it is a tautology, because it is an instance of the valid FOL formula: $x=x$.
– Mauro ALLEGRANZA
Jul 31 at 6:45
See tautology (logic) : "In logic, a tautology is a formula or assertion that is true in every possible interpretation. A formula of propositional logic is a tautology if the formula itself is always true regardless of which valuation is used for the propositional variables." Thus, you have two possible readings: the narrow one, restricting the use of the term to propositional logic, and the wider one, regarding logic in general. According to the wider reading, it is a tautology, because it is an instance of the valid FOL formula: $x=x$.
– Mauro ALLEGRANZA
Jul 31 at 6:45
In classical logic, it is a tautology, but there may be some logics where it's not (actually, there are - but are they interesting ?)
– Max
Jul 31 at 9:57
In classical logic, it is a tautology, but there may be some logics where it's not (actually, there are - but are they interesting ?)
– Max
Jul 31 at 9:57
add a comment |Â
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Â
draft saved
draft discarded
Â
draft saved
draft discarded
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2867706%2fis-1-1-tautology%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
7
Define a tautology.
– Kenny Lau
Jul 31 at 5:47
1
Define "simple proposition"
– Morgan Rodgers
Jul 31 at 6:03
In most developments of first order logic $x=x$ is a theorem for any $x$. But as Kenny says, it depends on what you mean by tautology. In the sense that any formula having the same arrangement of truth functional operators is true, then clearly not. In the sense that it's true regardless of any extralogical axioms, sure.
– Malice Vidrine
Jul 31 at 6:27
3
See tautology (logic) : "In logic, a tautology is a formula or assertion that is true in every possible interpretation. A formula of propositional logic is a tautology if the formula itself is always true regardless of which valuation is used for the propositional variables." Thus, you have two possible readings: the narrow one, restricting the use of the term to propositional logic, and the wider one, regarding logic in general. According to the wider reading, it is a tautology, because it is an instance of the valid FOL formula: $x=x$.
– Mauro ALLEGRANZA
Jul 31 at 6:45
In classical logic, it is a tautology, but there may be some logics where it's not (actually, there are - but are they interesting ?)
– Max
Jul 31 at 9:57