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#26 2013-10-15 07:38:28

atran
Member
Registered: 2013-07-12
Posts: 91

Re: What's the difference between a statement and a boolean expression?

Thank you. So, is it safe to say that a boolean expression is a mathematical statement?

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#27 2013-10-15 18:42:36

bob bundy
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Registered: 2010-06-20
Posts: 6,121

Re: What's the difference between a statement and a boolean expression?

hi atran,

Yes.   smile

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#28 2013-10-15 18:49:12

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,121

Re: What's the difference between a statement and a boolean expression?

hi Stefy,

I think the Prior argument is clever and interesting but I think it's a fiddle.  The argument appears to confuse "TRUE" and "This is TRUE" as the same and so leads to an erroneous result.  (Notice that the Wiki writer expresses the point as if it is not generally accepted.)

It is a requirement that the truth state of mathematical statements is never in doubt.  I don't think "This is FALSE" fits this requirement, therefore it isn't a mathematical statement.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#29 2013-10-15 20:57:27

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,845

Re: What's the difference between a statement and a boolean expression?

As I said, I do not think it confuses true and "this us true". Can you explain to me why you think your case (iv) lead to a paradix? (Or as the Daleks woukd say simply: "EXPLAIN! EXPLAIN! EXPLAAAIN!" smile )


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#30 2013-10-15 22:17:14

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,121

Re: What's the difference between a statement and a boolean expression?

hi Stefy,

I thought I had done that already in an earlier post but I'm happy to do it again.  I'm assuming that Wiki have correctly stated the argument.

.... every statement includes an implicit assertion of its own truth. Thus, for example, the statement, "It is true that two plus two equals four", contains no more information than the statement "two plus two equals four", because the phrase "it is true that..." is always implicitly there.

It is unclear whether that means

TRUE AND A = A

OR

"A is TRUE AND A = A

so I explored both.

The first diagram below shows the truth table for the first possibility and the third diagram shows the other.

I accept the first as the truth tables are the same.

I do not accept the second as the truth tables are different.

The argument then uses the second interpretation to generate an expression that is shown in my second (and fourth) truth table.

I accept that this statement is FALSE.  But I do not accept that the statement is equivalent to the statement "this statement is false".

So I do not think this argument clears up the problem.

Furthermore, let's pretend it does and see where it leads.

We are being asked to accept that

"This statement is true and this statement is false" is FALSE and also that

"This statement is false" is equivalent to "This statement is true and this statement is false".

using substitution that means that

"This statement is false" is FALSE.

This means that "This statement is TRUE" and we are back to the paradox.  smile

Bob

View Image: prior.gif View Image: prior2.gif

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#31 2013-10-18 02:29:35

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,371
Website

Re: What's the difference between a statement and a boolean expression?

Hi Bob,

Do you agree with Arthur's resolution? Yes / No?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#32 2013-10-18 07:48:10

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,121

Re: What's the difference between a statement and a boolean expression?

hi Agnishom,

YES/NO is not possible.

Firstly, some assumptions:

(i) Wiki has correctly given the 'proof'.

(ii) By Arthur's resolution you mean Prior's proof that there is no paradox, but rather the statement is FALSE.

On that basis here's what I think:

(iii) A = "TRUE" AND A     ... tick

(iv) A = "This is TRUE" AND A   .... X

(iii) and (iv) are not the same thing.

(v)  "This is TRUE" AND "This is FALSE" is a FALSE statement    .....tick

(vi) There is no paradox ......X

Summary answer =  NO

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#33 2013-10-18 10:02:12

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,845

Re: What's the difference between a statement and a boolean expression?

bob bundy wrote:

hi Agnishom,

YES/NO is not possible.

Firstly, some assumptions:

(i) Wiki has correctly given the 'proof'.

(ii) By Arthur's resolution you mean Prior's proof that there is no paradox, but rather the statement is FALSE.

On that basis here's what I think:

(iii) A = "TRUE" AND A     ... tick

(iv) A = "This is TRUE" AND A   .... X

(iii) and (iv) are not the same thing.

(v)  "This is TRUE" AND "This is FALSE" is a FALSE statement    .....tick

(vi) There is no paradox ......X

Summary answer =  NO

Bob

I disagree on iv)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#34 2013-10-18 17:55:37

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,371
Website

Re: What's the difference between a statement and a boolean expression?

Hmm, I see


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#35 2013-10-18 22:30:29

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,121

Re: What's the difference between a statement and a boolean expression?

Stefy wrote:

I disagree on iv)

Explain! Explain! Explaaain!  smile

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#36 2013-10-18 23:49:42

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,371
Website

Re: What's the difference between a statement and a boolean expression?

Maybe, stefy will tell that This is True is always true


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#37 2013-10-19 00:00:27

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,845

Re: What's the difference between a statement and a boolean expression?

No, I will say that "This is true" always has the value of A.

To Bob:

I can't wait for November 23rd!


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#38 2013-10-19 18:34:26

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,371
Website

Re: What's the difference between a statement and a boolean expression?

To anonimnystefy:

Of which year?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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