# Logic Lovers

Hint # 1

On what premise is logic based?

its true because your saying if 1 is true then 2 is false, lets look at one it says: the following statement is true, (if this is true) then the second statement says: the previous statement is false (this must be false) as you have defined statement 1 to be true.

you know what dont listen to what i wrote its pobabaly garbage,
noo wait, because if 1. (the following statement is true) is true it implies 2.( the previous statement it false) is true and 2. implies 1. (the following statement is true) is false, then it would be true to say, (the following statement is false) is true this implies 2. (the previous statement is false) is infact false, and since this is false then the previous statement is infact true. so if 1. is true the 2. is false so 3. is true.

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This is a so-called paradox (no such thing as a paradox). It's no different than if I said red is blue and asked if red is blue or red? The given facts conflict so any meaningful answer can't be had because the question doesn't mean anything. Everything I said is a lie except for the last sentence.

Hint # 2

Logic cannot answer everything. What are it's limitations?

thats like saying: this statement is false.

Final Hint:

When is a statement true?

Sorry is this has already been posted by someone else:

Whatever the first statement is, it isn't true. For if it were true then it affirms that it is false. Therefor, statement 3 is a conditional in which the premise is not true. Therefor it is a true statement.

It's a statement that can't be proven to be neither true nor false. This is Godel's incompleteness theorem, which states that in a consistant system, you can construct statements that can't be proved or refuted, thus resulting in a 'paradox'. It's just like the 'All what i'm saying is false' paradox.

meL
All assertions are false.

They refer to something
that does not exist.

Alkatran
Homework Helper
1. The following statement is true:
2. The previous statement is false.
3. If the first statement is true, then the second statement is false.
4. Is the third statement true or false?
'a' will be the proposition representing 1.
'b' for 2. etc...

Code:
1: a <-> b
2: b <-> ~a
3: c <-> (a > ~b)
-------------------
assume b
a from line 1
~a from line 2
therefore ~b
a from line 2
~a from line 1

c (you can prove anything from contradictions, therefore c is true)
~c (you can prove anything from contradictions, therefore ~c is true)

HAP
Look carefull at the third statement:

IF TRUE
"If the first statement is true, then the second statement is false."

IF FALSE
"If the first statement is true, then the second statement is NOT false."

Now you should be able to see that the third statement is not definied, when the first statement is not true. But the tricky part is that you can't determine whether or not the first statement is true:

if 1. is true => 2. must be true => 1. must be false => 2. must be false => 1. must be true => and then we are back at square one...

Since the first and second statement results in an infinitive loop, we have a paradox; their exits no such solution!

Logic requires that the originating premise be true. Now this opens up
a Pandora's box in itself-more later. A paradox is simply a
contradicting statement but this is not the whole picture. The original
statement invades our perception of logic completely. Everything you and I take for granted is based on our "knowledge" of true facts.

Therefore, when we argue with each other, we start with what we assume
is a known fact. We call them facts because together you and I take them to be true. The method by which we imply truths is called logic.

But lest we forget, it is all based on facts or truths. If we start with something that turns out not to be a fact, then the whole concept breaks down.

The opposite implication is that there may be hidden facts. In other words, what we all take to be for granted as being false, might actually be true. When NASA looks at problems, they categorize them into one of four categories:

a) Known knowns
b) Unknown knowns
c) Known unknowns and
d) unknown unknowns

All very logical, right? Well, where the system breaks down is when the problem doesn't fit our capability to reason-it doesn't fit in the box.

Our problem doesn't fit the box because it is illogical. This is where logic breaks down-when something is not logical. But be careful with categorizing your thinking because what may not be logical to us is not necessarily illogical in truth. When you say something is illogical, you are really saying it doesn't make sense to me.

Now since logic is devolved from the concept of truth, philosophers in the past have argued over whether it actually exists absolutely or not.

Or is truth just a concept that is man-made? Is your truth the same as my truth? Do we even know what truth is? Do you believe in truth?