Tuesday, December 27, 2011

Idle Minds And Twisted Logic

The Liar's Paradox And The GOD Paradox

Sentences, statements and expressions do not necessarily always evaluate to true or false.

We can say:

[A] 1 – 1


[B] One minus one.
[C] I think we should all go home.
[D] You look absolutely fabulous.
[E] In my opinion coffee is better than wine.
[F] We should go now.
[G] I am lying.
[H] I am telling the truth.
[I] This statement is a lie.
[J] This statement is false.

And all those would be valid statements. But there is no way to evaluate the statement on its own as true or false without other preceding or other following statements or arguments because there is either no conclusion inferred, no premise defined or it is matter of opinion. Where opinions are concerned the only possible evaluation would be if the person is telling the truth or telling a lie, whether the person is truly stating his/her opinion or trying to be agreeable or disagreeable.  Truth and lie are not necessarily the same as true and false.

[K] This statement is really true.

The above statements [I] to [K] can be called concluding statements, statements that infer a conclusion to confirm or deny a factual datum (or some factual data). Each of these on its own as a sentence is valid, but not as an argument (the supporting facts or logic for a conclusion) because there is no basis to evaluate it with some real factual or logic values. Unless we know what the ‘This statement’ refers to, there is no way to say whether the statement is true or false. Only totally insane or incompletely sane people can't understand this fact.  A standalone statement that makes a declaration without qualifying what its premise (the supporting fact or logic) is cannot in reality be truly evaluated as to its truth value. 

When a person state, ‘I am lying’ there needs to be further elaboration on what he/she is referring to. The only basis to evaluate if the person is lying is on some claimed facts or information that he or she is declaring or inferring. This means at least another previous qualifying statement that would then allow the declaration (conclusion) to be evaluated whether it is correctly inferred from the previous statement or statements. On its own the statements [G], [I] and [J] are not just self referring (self referencing or self referential) statements they are also self contradictory statements.  And that is the case with the Liar’s Paradox.

Now if the person was to state, ‘I am a liar’ then that would be an entirely different matter, since now there is an object to evaluate which in this case is the person making the statement or declaration. The reality is a person can be a liar whether habitual, blatant or pathological and still be telling the truth every now and then, as and when it is expedient for the person to do so.

The statements ‘I can never tell the truth’ or ‘I always tell lies’ or ‘Every word I speak is always a lie’ are obviously lies or untruth. If a person we know come up to us and he or she said nothing else but just ‘I am lying’ or ‘This statement I am making is a lie,’ the only conclusion we will make (if we are not insane or incompletely sane ourselves) is that this person is speaking utter nonsense, trying to be funny or trying to be smart by being a complete idiot. Now if a total stranger does that we will only conclude that that person belongs in an insane asylum. We are just not going to be trying to figure out whether this person is speaking the truth or is lying unless we too belong in an insane asylum. 

Only totally insane or incompletely sane people can’t understand these simple facts. 

As also I had mentioned in an earlier article in the statement of type [I] or [J] you can surmise or postulate a value of ‘This statement’ if you want to and you have nothing better to do with your life. You can say: if ‘This statement’ is false then the statement is true; and if: ‘This statement’ is true then the statement is false. But why stop there. You can as easily postulate that ‘This statement’ represents or stands for ‘a man without a head can walk around and live for a thousand years’ or ‘A horse is a heavier than an elephant’ or ‘Diamonds are made from eaten apples.’ And this you can continue to do occupying ever minute of the rest your life since you don’t seem to have anything better to do.

Similarly with statement [A] and [B] you can say ‘1 – 1’ is true because the result is ‘0’ or you can say ‘1 – 1’ is false because the result is twelve.

Some other examples that can be postulated by replacing ‘This statement’ portion of ‘This statement is false’ with some other values for ‘This statement’:

A boy is false.
A girl is false.
This horse is false.
This house is false.
This elephant is false.
Running is false.
The continent Africa is false.
Tom, Dick, Mary and Jane are false.
Any and every whatsoever is false.
Some is false.
Any is false.

Alternatively we can substitute the ‘is false’ value with ‘is true’ and it would still be the same utter nonsense.

Likewise too the statement [G] ‘I am lying’ or its alternative form ‘This is a lie’ can be easily proven for the utter nonsense that it is by substituting the ‘I am’ or ‘This is’ with some other value such as:

A horse is lying. (A horse is a lie).
The earth is lying. (The earth is a lie).
A boy is lying. (A boy is a lie).
Sound is lying (Sound is a lie).
The continent Africa is lying. (The continent Africa is a lie).
Any and every whatsoever is lying. (Any and every whatsoever is a lie)
Some is lying. (Some is a lie).
Any is lying. (Any is a lie).
One plus one is lying. (One plus one is a lie).

That is why the Liar’s Paradox is just plain and simply utter nonsense. The only people who can’t see that and insist that it is valid are either the incompletely sane (because they have been pretending humility while super feeding the pride component of their self identity) or the completely insane.

So here we have in language (in the examples [A] to [F] above) of what can be called valid or invalid without necessarily for it to be true or false. Another example of utter nonsense would be something like:

[L] If I see will you tomorrow then I shall come and visit you yesterday.

Logic and Evaluation

For any logical evaluation of a statement or expression to be possible it must have at least a premise and a conclusion. Some simple examples:

A horse is an animal. [premise - A horse]
Running is a form of exercise. [premise - running].
You can get the color orange by mixing the color red with yellow. [premises - mixing the color red and yellow].
Elephants because they are so heavy they are unable to jump. [premises - too heavy to jump].
A hungry shrew can eat a whole elephant. [premise- hungry enough to be able to eat a whole elephant].
Elephants can fly by flapping their ears. [premise - by flapping their ears].

All the above where the conclusion is not explicitly declared, the implicitly inferred conclusion is that these statements are true. So fully stated the first and last statement from the above examples would read:

A horse is an animal, it is true.
Elephants can fly by flapping their ears, it is true.

Rephrased another way:

It is true that a horse is an animal.
It is true that elephants can fly by flapping their ears.

So when we have a statement that goes:

This statement is true.

It follows that fully stated statement would read:

‘This statement is true, is true.’ Or ‘It is true that this statement is true.’

And likewise:

‘This statement is false’ fully stated would be ‘This statement is false, is true.’

So in other forms:

This statement is a lie, is true.
I am lying, it is true.

This is because the basis to making any declaration is in the intent which is to convey the truth of a matter. So even when a person says ‘I am lying’ the intent is to convey the truth to the extent that even if a person’s intent is to deceive his audience, his declaration has the intent to get the other party to believe that the declaration is true. This is our reality, the reality of our current existence. 

The only time this doesn’t apply is when we are ‘kidding’ or fooling around or trying to trick or shock someone. All of which is mostly done either in good fun or to mock someone, where expressing or stating truth is not the intention.

So immediately we can see that statements of type [G], [I] and [J] on their own without a pre-qualifying statement with a real premise are self contradictory statements. Now anyone who is truly sane will know that contradictions are invalid or something that cannot be accepted as truth. Anyone who contradict himself/herself just should not be believe (that what they say is true, correct or valid) let alone be trusted. 

Rephrasing these statements will make that abundantly clear. 

I am lying, it is true ====> I am lying and I am telling the truth.
This statement is a lie, is true ====> This statement which is a lie is actually true.

This statement is false, is true ====> This statement which is false is actually true.

Insisting On Evaluating The Liar’s Paradox.

The main logical evaluation on the truth of an argument or expression is in the conclusion. The premise is evaluated because it is the basis to infer or derive at the conclusion. For the conclusion to be valid or true the premise has also to be valid or true and the inference has to be logical. If there is more than one premise then all the premises must be evaluated individually and then collectively to verify that their relationships are valid or true. In situation of multiple premises, one or more erroneous premise may or may not invalidate the conclusion depending on whether the conclusion will still stand without the erroneous or invalid premise(s).  

A simple mathematic expression:

1 – 1 = 0

This can be evaluated as true of false because the premises are known and the conclusion is given. That is also what is called self cancellation principle meaning the value that is return is zero. When not dealing with numeric value, a self cancellation statement would involve adding a negative to the statement. This is the negation principle because adding a negative does not necessary makes the statement negative. It toggles or flips or inverse the state of the statement such that if the statement is positive it becomes negative and if the statement is negative it becomes positive. So is the Liar’s Paradox in its many forms. The self cancellation principle is basically when the statement is self contradictory thus canceling out its claim or voiding its validity as an argument. The most basic logic of the Liar’s Paradox is in what I called the embedded logic where the premise and conclusion are not separated making the premise also the conclusion. 

[a] This statement is a lie. (It is true).
[b] This statement is false. (It is true).
[c] This horse is a lie. (It is true).
[d] This cow is false. (It is true).

In multiple statements we will have one statement contradicting another or some other such combination. These statements when considered together are contradictory or we can say they are in contradiction. Now any sane person will know that when you contradict yourself you are invalid (or is incorrect or in error), that is, what you said should not be considered because you don’t make sense. This means you are talking nonsense.

[e] The following statement is true. The preceding statement is false.
[f] The following statement is true. The following statement is true. The first statement is false.
[g] The following statement is false. The preceding statement is true.

Now in statement [e] and [g] the circular reference (or what I called ‘the cyclic infinite’) is obvious. But statement [a] and [b] also has the same ‘cyclic infinite’ in each instance evaluation of the logic referring to the next in a circular reference. This will not be so if the declared or conclusion (argument total or final) value is not negative but positive or is not the opposite of or contradictory to the premise.

Every mathematician knows that when you have an algebraic equation that is in a circular reference or what I called the cyclic infinite the value of the formula changes with each succeeding evaluation. Now if we were to substitute a real premise into the statement [a] that says ‘Elephants live in trees’. Then we can evaluate the premise and say since the premise is false (elephants don’t live in trees) therefore the statement conclusion at ‘a lie’ is correct. So without a true premise there is no way to evaluate the statement whether its conclusion is correct or in error unless we put in our own. That would make that statement an invalid or illogical statement. So instead of seeing the invalidity of the statement, all those philosophers of old and our contemporary time try to evaluate the conclusion by postulating on the premise (putting in their own premise) that if it is false than the conclusion is true, etc. Of course that is really silly but they can’t see it and insisted that the statement is valid not understanding the principle of negation, that it changes false to true and true to false giving what I called the toggle or flip/flop principle.

x + 1 = x

In a true and false statement or statements the value at each subsequent evaluation is the opposite of the first instance evaluation. This is the toggle switch principle. In such self cancellation or negation situations the overview logical evaluation cannot be true or false but null just as 1 – 1 = 0 or a null value or invalid logic. Even as we can evaluate 1 – 1 = 0 as either true or false we must understand that the return value is zero or null (in cases where the operand is not numeric or quantifiable). To be able to understand such logic we must be able to differentiate the intent (conclusion) logic from the value or content (premise) logic. This we do by separating the premise from the conclusion. So then we can see that in the Liar’s Paradox the intent (conclusion) logic is to state that the statement is false or in error while the value (content) logic is also false (as is inferred since there is not predefinition of the premise/content value). It can’t get any simpler than this, unless you are the contentious type and want to challenge a nonsensical, meaningless  and harmless declaration - not something anyone sane and has a life would do. Once we separate the embedded premise from the conclusion we effectively break the cyclic infinite or circular reference. So the properly expanded statement ‘This statement is false’ by inferring a premise from the statement itself would be:

The statement that carry a self assigned value of false, is true to say that its value is false.


This statement with a concluded or inferred value of false, is true (meaning it does carry a final or overall value of false).

Let me illustrate intent (conclusion) logic from stored value or content (premise) logic in simple mathematical algebra.

For the statement ‘This statement is false’ let us assign a value 'x' to false.

x = ‘False’

Since the statement declare itself to be false therefore its declarative or content value is 'x'.

x = ‘This statement’

The evaluation of that statement premise would then be:

Is  x = x ?

Which would yield a value of yes, x is equal to x.

This would then evaluate (be concluded) that the statement logic inferring the statement final value of false is correct since it stated that x = x is true. So the conclusion logic of the statement inferring that its value is false is then correct or true (that is correctly evaluated).

In it most fundamental concept the Liar’s paradox can be simplified by substituting the premise ‘This statement’ with ‘A lie’ and therefore we get the statement redefined as:

‘A lie is a lie, is true’ or ‘False equal False is true.’ It will then be clear that the conclusion or intent of the statement ‘This statement is false’ is correct or true.

Our assessment would then be the statement that inferred that its premise value is false is correctly evaluated. ‘This statement is false (it is true)’ is correct or true.

All this mean is we can easily evaluate or conclude that the statement that says ‘This statement is false’ is true in intent and has a value (or content) of false without going in circles and becoming crazy by using the plain and simple method of delimiting the premise from the conclusion or by using value substitution ‘This statement’ = false.

Alternatively (if we wish to be contentious) we can presume that its actual content value is true and the statement's conclusion is erroneous or wrong which would then render ‘This statement is false (it is true)’ to be incorrect (in error or false or to be lying).

Now isn’t this just so simple?

The GOD Paradox Solved!

Before we start let us first understand that this is conjecture and not reality. The reality is the infinite value cannot be evaluated. GOD who is unlimited cannot be evaluated with limited concepts of the limited realm of humankind and Angels. Finite concepts cannot in reality accurately evaluate infinite concepts even as theoretically it can be done using theoretical correspondence concepts. The reality value infinity or the infinite value is a GOD value as it has no limit just as GOD has no limits. By inference we should understand that as a numerical value representation or type, infinity represents GOD as a type having no beginning and no ending. There is no other unlimited or infinite personage or object or value except GOD. There is and can only be one infinity value. That is the reason in the Scripture of Truth, JESUS declared ‘I and My Father are one.’ JESUS did not at any time declared ‘I, My Father and the Holy Spirit are a three in one Trinity’ contrary to the evil invented lies of the Christmas religion.

Understand this:
We exist in our physical universe. This physical universe (inclusive of every definitive reality within it: all the attributes of matter and energy including all the laws that define its structure of existence) can also be termed as the temporary realm of our existence. The reason the realm of our existence is temporary is because it was created to be temporary.
GOD does not have HIS existence within and limited by our physical universe or realm of existence. The very concept of the word existence or exist has not reality meaning when use to conceptualize GOD except when use as a referential concept type in our realm of existence. GOD does not 'exist' within a 'realm,' all realms that can possibly exist, exist only within or is 'contained' within GOD. But this does not mean that GOD is in all things or is contain in all things.
Everything (both the known realms - our universe and the Spiritual 'universe' and whatever other realms there may be, which is not to say that there are any additional realm) that exists 'exist' within GOD. The concept of the word 'exist' as well as 'realm of existence' is not a super set to GOD but a subset. From this perspective we can say that GOD is the super set of all super sets. GOD is the defining reality for all other realities whether temporary or permanent.
GOD is unlimited (from the perspective of our reality of the concept of unlimited, but is not limited by it). Space, time and mass are all concepts of the limited realm and do not apply to GOD. Even the very concept encapsulated in the words 'infinity' (which is a limited concept of time and quantum in our realm of existence) and unlimited (which has it reality concept defined by the meaning of limited) have no reality meaning when used to refer to GOD.
The concept of GOD 'not existing' is an invalid concept therefore exist is not a concept that can be used in any manner at all to reference GOD. GOD IS, in order that the concept of 'exist' can have a reality.
Please read the chapter 'GOD IS' of 'Bible 101' by this author for the discussion of these truths as were revealed in the records of the Holy Christian Scriptures.

For example even as we can say the set of all whole numbers is an infinite set we cannot in reality quantify it. Our physical universe is not infinite even though it is extremely mind bogglingly large so that it might have the appearance of being infinite.

For our solution we shall only focus on the two version of the GOD's paradox that I used in a previous discussion.

1. If GOD is all powerful then HE can create a rock so heavy that GOD HIMSELF can't lift. So in being able to create such a rock GOD can no longer be all powerful since HE can't lift the rock. And if GOD is unable to create such a rock then it also means that GOD is not all powerful since there is something HE is unable to do.

Firstly we must understand that as it is, the statement is in itself a logic contradiction. The finite realm cannot not have an immoveable object or irresistible force both of which are infinite values. Again we have the same 'cyclic infinite' in that statement. Again those who get caught in that paradox have no concept of finite and infinite. Again I will use mathematics algebra to solve the paradox.

First we will simplify the statement since the verb ‘create’ cannot be expressed as a logical operand. So we will instead use exist as create. So the statement about GOD creating a rock that can’t be lifted will become ‘Can a rock that GOD can’t lift exist.’ The evaluation criteria then will be ‘Can a rock that can’t be lifted exist’ and ‘Can GOD lift a rock that cannot be lifted’ whether both statements are true.

Assign the value of infinity (‘∞’) to GOD’s strength since GOD’s power is infinite.

GOD’s strength = ∞

For a rock to be so heavy it cannot be lifted its value (mass or weight) would have to be infinite. If it is not infinite then it can be lifted.

Weight of rock that cannot be lifted = ∞

The question whether GOD can lift the rock that cannot be lifted translates into an equation as:

Is ∞ = ∞?

I know some wrapped minds will say that ∞ is not equal to ∞ because we cannot know its value to have a basis to compare it. This again originated from minds that have no notion of what infinite is or what reality is, that there is only one possible infinite value in reality even as it cannot be measured in the finite realm. There is no basis to say that in reality two infinite values are different even if two different infinite values can exist in reality which cannot be. The very idea that would allow more than one infinite value to exist in reality would by itself render all those so called infinite values to become finite.

The equation would then evaluate to true, rendering both statements as valid. GOD can create a rock that cannot be lifted and GOD will still be able to lift the Rock as that is what the symbol ‘=’ means in an equation. The ROCK that GOD would create would be GOD (Psalm 18:31). Because the only ONE thing that in our reality is not finite is GOD. So anything that is infinite can only be the ONE GOD. Because the value of infinity is all encompassing, therefore there can only be ONE.

2. If God is all powerful, meaning He can do anything, then He can create a God more (or twice more) powerful than himself. If He can't then He cannot be all powerful and if He can then He cannot be all powerful because there can be another God (twice) more powerful.

For this again we assign the value ∞ to GOD’s power, since for GOD to be all powerful HIS power must be infinite. So we have:

GOD’s power = ∞

Then a GOD more powerful we will for simplicity assign the factor of 2 (it can be any value greater than 1) to the ‘more power’ value.

Power of more powerful GOD = 2 x ∞

So we now compare the first clause with the second, is ∞ = 2 x ∞?

And this will be true because 2 x ∞ is still equal to ∞. Fact is any number whether finite or even infinite multiplied with infinity would still resolve to infinity because that is what infinity is, which is having no limit or constraint.

So the GOD with more power whom GOD create would still be GOD, because that is in essence one of the definition of GOD - omnipotent. So in this case we have what twisted minds would consider a double paradox (or what in some terminology a ‘catch-22’) which is that anything GOD create that is bigger, stronger, heavier, wiser, better, more powerful, existing prior to or after, or in any manner invalidate the first CAUSE by being positively greater would still be the first CAUSE and that would be GOD. Of course if you can grasp the concept of the infinite you will understand that there is no paradox at all. Paradox resolved. No Paradox exists except in minds caught in the quagmire of the ‘cyclic infinite’ of being unable to grasp very simple concepts such as finite and infinite, contradiction or negation, and most of all having no understanding of reality (what is real from what is not real).

In both these God paradoxes the problem stems from not understanding what infinite means, thinking that a logical or real value can be assigned to something that does not exist in our finite realm and/or that computation can be carried out on an infinite (unlimited) value. Most logic paradoxes in language come from the assigning of the ‘cyclic infinite’ to a declarative statement or statements and from not being able to separate the declarative (conclusion) logic from the content (premise or value) logic.

I am sure many will not accept these solutions and that would not be strange. Many people today won’t accept that there is a GOD WHO created everything that exist either.

Utter Nonsense.

Now you have the wisdom to see it, all those paradoxes discussed above are not really paradoxes but utter nonsense because their basis is on some assumptions that are either not real or are self contradictory.

Let us take an imaginary fruit. This fruit is not real and it has no object value to our existential plane, our physical universe, which is the only reality we know. Since this fruit is imaginary and not real, it is has no real definitive value meaning it cannot really be defined as an object in reality. We next make a statement that this fruit is an apple. But our audience, the person or persons we are communicating with, dispute this fact and says that it is actually a lemon. Now who is right and who is wrong?

If you can see the ridiculousness of this scenario as an allegory I hope you can understand the same concept applies in the liar’s paradox. For this very reason that so many such brilliant minds of the times have been arguing the truth value of this so called paradox insisting that those various postulated statements are valid arguments, is why I say that most of human kinds are not completely sane. The reason these great and brilliants minds cannot see the ridiculousness of the liar’s paradox is because of a condition I called ‘super feeding the ego’. Termed in another way we can call it as of being an egomaniac. The Christian Bible termed this as vain glorying.

Real Mystery To Science.

Now if you want to occupy your idle mind with some really deep concepts, below I have listed some examples. You see, science despite making tremendous advances since two hundred years ago is still totally clueless why this Universe exist until this very day. They still have not the slightest notion why we have consciousness, or why a string of protein can define what and how an organism should be.

What is emptiness or empty space? When we empty a glass of water on our planet earth, the glass usually gets filled with air. What happen when we empty a glass of water in the vacuum of empty space? Is the glass now finally empty or is it now filled with emptiness?

Is empty space or a quantum vacuum nothing or is it something? How can it possibly exist if it is nothing or is filled with nothing? But the fact is space exist as a gap between celestial objects as well as sub-nanoscopic particles. How then can you explain empty space based on the fact that it exist between the earth and the moon, the planets and our sun, our milky way and the other galaxies even though science understands that it is not absolutely empty but just more so. The fact that gravity of the cosmic bodies exert their pull on each other tells us that empty space is indeed not empty by fill by forces that science have not found a way to fully measure. then again there is the so call dark matter or dark energy. This of course doesn’t solve the mystery of whether real emptiness (as being totally devoid of anything) exists.

What is time? Why is it always the present. This concept of time that allows our existence in reality cannot be measured? We say that space is three dimensional. Some scientists theorized that time is the fourth dimension from certain perspective. We know or anyway we should know that time exist only as, what we called, the present. The only concept of time that science can understand is that which can be measured and that is the displacement effect of time and lapse time expressed as a vector of space. Science is unable to measure absolute time or what I called ‘existential’ time – the only time that is really real, which is the only reality we know.

Gravity (as also is true of all the primary forces) is another concept that science have not fully understood. Again the only aspect of gravity (as well as all the other primary forces) that science understands is that which can be measured. All these measurable properties are actually displacement effect and are constrained by three dimension space. The only aspect of emptiness, time and the primary forces that science understands all relate to finite concepts of displacement effect. In its absolute sense as infinite (from our perspective) concepts: emptiness, time, energy, mass and gravity are not understood by science at all.

Energy is another mystery to science. From our finite perspective energy is indestructible or so our scientists tell us. Energy exists as a constituent of the four primary forces (according to science) and one of its expressions is in temperature.

Temperature as defined by science as the thermal energy in a substance. Temperature, as the so called thermal energy, is again understood by science only as displacement effect (a measurement) in the energy level of matter.

All the things that make the existence of our universe possible have properties that are indicative of being infinite and that is why our scientist can never fully explain them, why they exist.

Even as science theorized about a fourth, fifth and even to an nth dimension and parallel universe the only way for science to understand these is still from the concept of the finite three dimension space.

All of these are really real things that science understands mostly in theory. We and science (meaning the scientists who advanced these scientific theories) can sense all these things and know for a fact that they exist in as much as we know (through our severely limited mind consciousness) we exist, but we cannot in reality grasp the concept of their and our own existence (our mind consciousness) except as expressed as some sort of displacement which is just the effects of being propelled through three dimension space which science has quantified as being propelled through space-time which is not the reality. The reality is that time is an infinite constant that doesn’t change. An object a trillion light years from us exist in the same instance of time as we do, and that time is always the present. What separates us from the object is three-dimensional space not the reality of time.

Special Note
Please note that all discussion by this author are based on a general non expert assessment of information gathered from material published in the public domain (i,e, readily available to members of the public). All of this author's discussions are presented as material for any and all lay person with no special expertise. Anyone twelve years of age and older, who is not mentally incapacitated in some ways, would (or should anyway) be able to understand any and all the discussions of this author. You do not need to be an expert or a genius to understand the simple and straight forward truths discussed by this author.
All “proclaimed and acclaimed” super mega brilliant supremely intelligent geniuses leading experts, defining master authorities, super holier than GOD man, women, entities and beings of whatever godly glorious illustrative mega holy and reverent titles, please go somewhere else to announce and proclaim your supreme superiority and lowest humility over all other members of humankind.

Last updated: 2013 12 30
First Posted: 2011 12 27
© Quah 2011 - 2013. All rights reserved. 

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