Originally posted by Atlantis001
How does "This statement is false. " committ the the logical fallacy Affirming the Consequent ?
There is not a need that logic should never fail, as there is a theorem which implies that there are questions that cannot be answered by logic.
I illustrated this to you already. If presented as a set of conditional statements, "This statement is false," would be, "If A, then B; B; Therefore, A." Any argument following this form is invalid because it committs the logic fallacy of Affirming the Consequent.
There are arguments that defy logic:
[list][*]John wishes to speak to whoever is in charge.
[*]The person in charge is Steve.
[*]Therefore John wishes to speak to Steve.[/list]
However, John may have a conflicting goal of avoiding Steve, meaning that the reasoned answer may be inapplicable to real life.
Arguments to which logic may not apply typically involve human behavior.
Originally posted by Adam_PoE
The statements, "Everything in this circle is a lie," and "This statement is false," committ the logic fallacy of Affirming the Consequent.If presented as a set of conditional statements, the argument would be, "If A, then B; B; Therefore, A." Any argument following this form is invalid.
so there was no answer to the 2 "statements" like I thought eh?
Originally posted by Adam_PoE
I illustrated this to you already. If presented as a set of conditional statements, "This statement is false," would be, "If A, then B; B; Therefore, A." Any argument following this form is invalid because it committs the logic fallacy of Affirming the Consequent.There are arguments that defy logic:
[list][*]John wishes to speak to whoever is in charge.
[*]The person in charge is Steve.
[*]Therefore John wishes to speak to Steve.[/list]
However, John may have a conflicting goal of avoiding Steve, meaning that the reasoned answer may be inapplicable to real life.
Arguments to which logic may not apply typically involve human behavior.
I didn´t meant "What is the definition of Affirming the consequent ", but how does that statement is a "Afirmation" of the consequent. For example try to write it as "If A, then B; B; Therefore, A.", and show the paradox. Like in:
- All humans are mortal.
- Socrates is a mortal.
- Therefore Socrates is a human.
Socrates does not necessarily need to be a human.
Actually, as I said there is a theorem called "Godel´s imcompleteness theorem", which implies that there could be questions without answers, speaking in a less formal way. In other words, its not necessary that logic doesn´t fail, and it can´t be both consistent, and complete at all. Because of this type of paradox, it was created a new type of logic, called "paraconsistent logic" which tries to avoid these contradictions.
Originally posted by Atlantis001
I didn´t meant "What is the definition of Affirming the consequent ", but how does that statement is a "Afirmation" of the consequent. For example try to write it as "If A, then B; B; Therefore, A.", and show the paradox. Like in:- All humans are mortal.
- Socrates is a mortal.
- Therefore Socrates is a human.Socrates does not necessarily need to be a human.
If (A) this statement is false, then (B) it is a true statement; (B) This is a true statement; Therefore, (A) this statement is false.
Originally posted by Adam_PoE
If (A) this statement is false, then (B) it is a true statement; (B) This is a true statement; Therefore, (A) this statement is false.
A statement does not need to be true. In your first sentence you wrote " If this statement is false, then it is a true statement ", but I wrote "This statement is false. " You judged the wrong sentence.
Anyway, the Affirming the consequent fallacy, means that from a sentence in the form " If A, then B.", one cannot conclude " B. Therefore A. " If you write the statement like that, what would be :
- This statement(A) is false(B).
- Something is false(B).
- Therefore, its a statement(A).
But its not necessarily true, that "something" is a statement.
Anyway, that does not solve the problem. To solve the problem means you have to conclude in someway that the statement "This statement is false. " is true, or false. By using the 'Affirming the consequent' argument we just created other sentences which are fallacies, but they do not imply the truthhood or the falsehood of my first sentence.
But no problem its all confusing anyway, some mathematicians from the past thought it was not a paradox too. I just got it because I had logic at university, being physics my course. If this was not a true paradox, there would be no reason to create paraconsistent logic.
Originally posted by Atlantis001
A statement does not need to be true. In your first sentence you wrote " If this statement is false, then it is a true statement ", but I wrote "This statement is false. " You judged the wrong sentence.Anyway, the Affirming the consequent fallacy, means that from a sentence in the form " If A, then B.", one cannot conclude " B. Therefore A. " If you write the statement like that, what would be :
- This statement(A) is false(B).
- Something is false(B).
- Therefore, its a statement(A).But its not necessarily true, that "something" is a statement.
Anyway, that does not solve the problem. To solve the problem means you have to conclude in someway that the statement "This statement is false. " is true, or false. By using the 'Affirming the consequent' argument we just created other sentences which are fallacies, but they do not imply the truthhood or the falsehood of my first sentence.
But no problem its all confusing anyway, some mathematicians from the past thought it was not a paradox too. I just got it because I had logic at university, being physics my course. If this was not a true paradox, there would be no reason to create paraconsistent logic.
I did not judge the wrong statement. "This statement is false," makes three separate claims:
[list=1][*]This is a statement.
[*]This is a false statement.
[*]By nature of being false, it is also true.[/list]
Before one can evaluate the truth or falsity of the premises, he must first determine whether or not the argument is valid. If the argument is not valid, the premises do not logically support the conclusion, making the truth value of the premises irrelevant.
Originally posted by Adam_PoE
I did not judge the wrong statement. "This statement is false," makes three separate claims:[list=1][*]This is a statement.
[*]This is a false statement.
[*]By nature of being false, it is also true.[/list]
Before one can evaluate the truth or falsity of the premises, he must first determine whether or not the argument is valid. If the argument is not valid, the premises do not logically support the conclusion, making the truth value of the premises irrelevant.
In logic everyone is free to make any statement he wants, a statement does not assume that it is true like you said. A statement is something that can be true or false. If in logic is assumed that anything must be true or false, so this statement must be true or false. What it is ? True or false ?
Originally posted by Atlantis001
In logic everyone is free to make any statement he wants, a statement does not assume that it is true like you said. A statement is something that can be true or false. If in logic is assumed that anything must be true or false, so this statement must be true or false. What it is ? True or false ?
Again, it is pointless to determine the truth value of an argument if the the argument is not valid; if the argument is not valid, the truth of the premises do not logically support the conclusion.
Originally posted by Adam_PoE
Again, it is pointless to determine the truth value of an argument if the the argument is not valid; if the argument is not valid, the truth of the premises do not logically support the conclusion.
A statement or proposition is not true or false, I never said that its "true" that "This statement is false." I just said " This statement is false. " Your 2sc and 3rd claims are equivalent.
In logic there is something called, principle of bivalence which states ; " For ANY proposition A, either A is true or A is false. " What my proposition is, true or false ? I must remember that is for ANY proposition.
Originally posted by Atlantis001
A statement or proposition is not true or false, I never said that its "true" that "This statement is false." I just said " This statement is false. " Your 2sc and 3rd claims are equivalent.In logic there is something called, principle of bivalence which states ; " For ANY proposition A, either A is true or A is false. " What my proposition is, true or false ? I must remember that is for ANY proposition.
The Principle of Bivalence is not universally applicable; sometimes the truth value of a proposition cannot be determined, and other times a propositon may have an indeterminate truth value.
Originally posted by Atlantis001
It is valid for all propositions. It states that : " For ANY proposition A, either A is true or A is false. " Thats the very basis of classical logic, and you are denying it !? You will just keep avoiding, won´t you
You are asking me to determine whether or not, "This statement is false," is a true or false proposition. You assume however, that all propositions are either true or false, when in fact, some propositons have an indeterminate truth value. This is why the Principle of Bivalence is not universally applicable.
That's not a paradox, it is just semantics and a relative meaning of the term 'failure'- that what is failure for some is success from the point of view of others.
The actual process is as simple as this- if you wanted outcome A and got outcome B, you failed. That by other criteria it could be seen as a success is not relevant.
Regarding failing at failing, it depends. If a student tries to fail at a math test and fails, then he has succeeded at failing the math test and failed the math test; no contradiction. If you say he tries to fail in some generic sense, it's a gibberish question. You can't define whether somebody has failed or succeeded unless you have some parameters to measure it by.
The below sentence is true.The above sentence is false.
Well, here's how I see it: we have two statements; we can rephrase it as, "The second part of this statement is true, and the first part of this statement is false"
(2nd true) ^ (1st false)
Assume that this is a true statement; then the second statement is true, the first statement is false, and the second statement is false.
So if (2nd true) ^ (1st false), then (2nd true) ^ -(2nd true).
Statements of the form A ^ -A are false.
So if (2nd true) ^ (1st false) is true, a false statement is also true; therefore it is not true that (2nd true) ^ (1st false), and
"The below sentence is true.
The above sentence is false."
simply describes a situation that is by its nature impossible, like "It is raining and it is not raining." I don't see the problem; so "The below statement is true" and "The above statement is false" are mutually contradictory; that doesn't make it a paradox, it makes it false, in the same way that "It is raining and it is not raining" is false.