Hi all, can you guys help me out in something?
Can you guys please tell me if there are any websites out there with uncommonly difficult logical paradoxes to solve (and yes please, don't find me easy ones)
Thank you.

I suppose that you are way beyond Zeno's Paradoxes? FYI an interesting interpretation (at least for me---I am not a math scholar) on a couple ot sites..
plus.maths.org/issue13/features/garbett/limit.html
mathpages.com

You might consider a google search because, if I am remembering correctly/I am not mistaken :rolleyes: , there is a link to a message board discussing Zeno.

I sure hope that I have not sent you on a wild goose chase.....what is life w/o a couple of paradoxes...here and there. ;)

Hope that you have a nice rest from you "studies"!

Sure I will have a good rest from my studies :)
16 hours 36 minutes 15 seconsd to freedom!
Opps let me clarify: I prefer philosophical paradoxes that hover around the syntac of logic and semantics.

If it's not a prob....would you be able to share what you find?

There is no such thing as a logical paradox.

is that logical or just paradoxical?

"There is no such thing as a logical paradox"??????

You better check your facts on that.
And please, don't ever jump to conclusion without reflecting on your thoughts regarding certain issues. Some things are not as obvious as they seem.

If it's not a prob....would you be able to share what you find?

Sure, if I have the time I will post the solutions here, oh, in english, for the sake of simplicity.

By the way, the picture displayed on my avatar isn't me! I know it looks silly, I will change it tomorrow.

um...I am not looking for the sollutions...just interested in the paradox itself. I would like to think and ponder so that I can come to my own clarification...if there is any. :eek:

And you don't need to worry about english...I follow you or at least understand where you are coming from. Keep saying what you say and how you say it!

There are loads of paradoxes on the internet anyway. Just use the google™ search engine to search. I'm trying to find what I deem as an "apocryphal and chimerical angel". Literally, I meant paradoxes which are deceptively perspicuous. I cannot find any witticism in most of the ubiquitous paradoxes found on the web since many of them are superficial and trivial. I prefer to transcend into the subcutaneous mundane of the "angels" as quoted ut supra, and get caught in an anfractuous labyrinth.

There is no such thing as a logical paradox.

By the way, if hadn't realized from the start when you typed this, that what you just typed above is really just another way of saying that logical paradoxes exist - think about it.

The law of excluded middle eliminates anything which could be considered a "paradox" in logic itself. Other sorts of "paradoxes" are really just faulty arguments with bad premises. A great example is the Russell paradox, which deals with a set containing itself as a member. All this "paradox" does is point out that the naive definition of a set as "a collection of elements" without restriction on those elements is a bad definition.

One way to phrase the Russell paradox is like this: Consider words in a dictionary. The word "heterological" refers to words that do not describe themselves. Is the word "heterological" heterological?

Logic says that this question is meaningless. Either answer is perfectly acceptable because both are equally consistent. (I.e. whether the word "heterological" is, in fact, heterological, or not, does not create any contradiction elsewhere.)

A more mathematical example is the undecidability of the continuum hypothesis. To explain this one would require a course in set theory that I am not prepared to give in this forum. You might try Googling for it, but I'm not sure you'll necessarily appreciate it unless you've had some higher maths.

To put it another way, is it a "paradox" that both Euclidean and non-Euclidean geometries exist? Not really. All the existence of a consistent, non-Euclidean geometry implies is that the parallel postulate is independent of the others, and no more. Nothing to see here, move along.

Most problems that have been classified as "paradoxes" are not really paradoxes by itself, that is to say, the premises and the conclusion do not support one another (as in what one would define as a real paradox). Many of these "unreal" paradoxes fall into the category of semantic paradoxes, where by the "paradox" arises due to the ambiguity in the definition of a certain epistemology and ontology. For many of these semantic paradoxes, the supposed "paradox" can be eliminated by circumscribing in detail, the definitions of the morphologies of certain words, as well as the semantics involved in the sentence. This can be done via the use of sentential logic or a certain meta-language, that deals with the foundations of the meaning of the words and semantics involved.

Other "paradoxes" which belong to the realm of physical paradoxes such as Zeno's paradoxes, are merely stratifications of certain fallacies in reasoning when certain topological and temporal properties are described or defined using descriptive logic. There really is no paradox (see the definition in brackets ut supra). That is, incoherence with reality.

Ergo, many of these supposed "paradoxes" are really not real paradoxes at all, since the main problems are caused by compiling the same fallacious statements on top of the rest of the problem, or are made to be "paradoxical" due tp the fact that some conditions and variables in the problem have been badly defined.

By the way, you brought out the problem of whether the word "heterological" is heterological or autological. You define "heterological", when used in reference to other words, as words which do not give their own meaning. Asking whether heterological is heterological in the first place cannot yield a proper answer unless you eliminate the equivocality that will result when you insinuate that heterological is heterological. By the way, you should bear in mind that using a negation in reference to another negation does not yield a different result. There are only2possibilies - A postulate with certain syntactic properties that of course, must exclude the property that it is the exclusion of itself or certain properties from a domain, and secondly, a negatory predicate that excludes the properties from the formal. This question cannot be answered unless these attributes have been defined. I hope I have provided a good hint in resolving the problem you brought out.

The next remark that I'm going to add is rather egotistical. By my subjective point of view, a paradox is merely a syntac that is self-resolving and self-transductive. In layman's term, it is a logical loop that resolves itself, but is logically inconsistent with the syntac of reality. Instead of saying that certain "paradoxical" problems such as those which are self-referential being meaningless, it would be stronger to say that many of them are self-resolving.

By the way, I have no clue to what you mean by the undecidability of the continuum hypothesis.

Anyway, I won't bother about resolving such paradoxes for the next few days - my exams were over a few hours ago and I really need a break before I break up.

By the way, I frustrated by the way where by just a little misunderstanding in a problem can lead to other ramifications that had, and will baffle logicians and philosophers alike.
Surprising indeed ...

Cool. I love paradoxes, but they are certainly not within the encirclement of my expertize. However, I am quite skilled at describing things using oxymorons :)

I sure agree with you guys regarding the importance of being consistent with the fundamentals of logic - that a postulate must either exist or not exist, given the specification that the properties in the postulate are not "negatory", and that at many times, paradoxes such as the one listed above regarding the problem of autology, are misunderstood and stratified due to the failure to distinguish between negatory and non-negatory postulates (from my understanding of your response, you are differentiating between the NOT from the NOT NOT, and the relationship between the NOT NOT and the original postulate. Sorry if I'm wrong, that is the easiest way I can describe it out, being a layman).

Interesting. I never realized that paradoxes could be described as "self-resolving". Why do you say that it is such? Ah! Let me guess! By self-resolving, do you mean that, for self-referential paradoxes such as "This sentence is false", being inconsistent and contradictory to realism, but consistent by itself and only itself, but being "wrong" when used in reality? Can we discuss this using our PM? It's interesting. Oh, wait, Avistar_sg, are you still around? Please respond if you are. Is that signature intended to be a joke or are you serious?

Oh, as for the Grelling-Nelson paradox that hovers over the issue of whether the word "heterological" is heterological, Avistar_sg, did you mean this, that:

Let A denote the word autological.
Let H denote the word heterological.

To the stronger,

Let A denote the arbituary and non-functional properties and functions in the functor autological, exclusive of A itself.
Let H denote the arbituary and non-functional properties and functions in the functor heterological, exclusive of H itself.

Arbituary and non-functional properties of A: {none}
Arbituary and non-functional properties of H: {none}

Where non-functional, I meant the intrinsic properties, and not those that serve as an agent to other sets.

Functions of the functor in A: {State that the functor and innate properties of set X being the same as the functor and innate properties of X itself}
Functions of the functor in H: {State that the functor and innate properties of set X NOT the same as the functor and innate properties of X itself}

Hence IFF Heterological is Heterological, then,
{Innate and functional properties of set H not the same as the functor and innate properties of H itself}

The problem right now is, Avistar_sg, are you saying that, due to Russell's paradox, which shows the ambiguity in defining whether a set belongs to itself, that we are stuck at a deadend - that is, unless the problem of whether a set belongs to itself, in the same way that a room and the gold in it should be distinct, is resolved/defined, we will never solve the problem right? Because if the set and its properties are separate, then the definitions laid out is inadequate: you need to define A and H as well, and the set and the properties within the set of A and H itself ad infinitum - that would be absurd right?

Hence, let's assume that because of this, we redefined the following:

Let A denote the arbituary and non-functional properties and functions in the functor autological.
Let H denote the arbituary and non-functional properties and functions in the functor heterological.

Arbituary and non-functional properties of A: {none}
Arbituary and non-functional properties of H: {none}


Functions of the functor in A: {State that the functor and innate properties of set X being the same as the functor and innate properties of set X itself}
Functions of the functor in H: {State that the functor and innate properties of set X NOT the same as the functor and innate properties of set X itself}

Hence IFF Heterological is Heterological, then,
{Innate and functional properties of set H not the same as the functor and innate properties of set H}
Inconsistency! Hence this must be wrong!
Hence IFF Heterological is autological, then,
{Innate and functional properties of set H the same as the functor and innate properties of set H}
Based on the definitions laid out, Heterological must be autological, and not heterological. And please note that it is such only BASED on the definitions that I had just laid out, which is the closest I can get to get out of proximity of the juxtaposition of equivocations posed by the semantic definition of the words Autological and Heterological.

Was that what you meant, that there are too much ambiguity in the question to solve it?

Amazing! Heterological is Autological and not Heterological after all! Problem solved.

I just realized that there is a lot MOORE to the liar's paradox than just simply rejection of a statement. Moore's paradox must be taken into account or else a simple paradox of "This statement is false" cannot be answered. Certain axiomatic systems must be introduced, and an absolute truth must be established, together with the elimination of the ambiguities in the "statements" - that is to say, they all must be defined logically in terms of it's intrinsic properties and it's properties as an agent.
Can I be your apprentice Avistar_sg? Please, come on you won't want to put down the plea of a 12 year old like me would you?

Sorry! I just realized I made a crucial fallacy in my solution. Allow me to correct my stance. Pardon me, I'm only 12. Please read the entire solution again since I altered a lot of things.

Note: When I say A belongs to B, it means, A has some properties which B has too.

Let A denote the word autological.
Let H denote the word heterological.

To the stronger,

Let A denote the arbituary and non-functional properties and functions in the functor autological, exclusive of A itself.
Let H denote the arbituary and non-functional properties and functions in the functor heterological, exclusive of H itself.

Arbituary and non-functional properties of A: {it has 11 letters etc}
Arbituary and non-functional properties of H: {it has 13 letters etc}

Where non-functional, I meant the intrinsic properties, and not those that serve as an agent to other sets.

Functions of the functor in A: {State that the functor and innate properties of set X belongs to the functor and innate properties of X itself}
Functions of the functor in H: {State that the functor and innate properties of set X NOT belongs to the functor and innate properties of X itself}

Hence IFF Heterological is Heterological, then,
{Innate and functional properties of set H NOT belongs to the functor and innate properties of H itself}

The problem right now is, Avistar_sg, are you saying that, due to Russell's paradox, which shows the ambiguity in defining whether a set belongs to itself, that we are stuck at a deadend - that is, unless the problem of whether a set belongs to itself, in the same way that a room and the gold in it should be distinct, is resolved/defined, we will never solve the problem right? Because if the set and its properties are separate, then the definitions laid out is inadequate: you need to define A and H as well, and the set and the properties within the set of A and H itself right?
Hence, let's assume that we need not do that hence, we redefined the following:

Let A denote the arbituary and non-functional properties and functions in the functor autological.
Let H denote the arbituary and non-functional properties and functions in the functor heterological.

Arbituary and non-functional properties of A: {it has 11 letters etc}
Arbituary and non-functional properties of H: {it has 13 letters etc}


Functions of the functor in A: {State that the functor and innate properties of set X belongs to the functor and innate properties of set X itself}
Functions of the functor in H: {State that the functor and innate properties of set X NOT belongs to the functor and innate properties of set X itself}

Hence IFF Heterological is Heterological, then,
{Innate and functional properties of set H NOT belongs to the functor and innate properties of set H}
Inconsistency! Hence this must be wrong!
Hence IFF Heterological is autological, then,
{Innate and functional properties of set H belongs to the functor and innate properties of set H}
Based on the definitions laid out, Heterological must be autological, and not heterological.
Ah! This was the stupid flaw I noticed and I didn't correct it:
If we only defined the properties and functors of the set itself and not itself, then EVERY word will be autological and not heterological! That would be absurd!

Now, let us defined the set and itself using the very first definitions.
Hence, this will eliminate the inconsistency.
Consider the word BIG.

Let B denote the word BIG.
Let B1 denote the set BIG itself.
Let B2 denote the properties and functions of the set BIG.

Innate properties of B1: {It has a property that cannot be disproved, that it is big, it has 3 letters too}
Functions of B1: {none}
Innate properties of B1: {none}
Functions of B1: {To state that another set has the property of being big}

Let C denote the word carcinogenic.
Let C1 denote the set carcinogenic itself.
Let C2 denote the properties and functions of the set carcinogenic.

Innate properties of C1: {it has many letters ... etc}
Functions of C1: {none}
Innate properties of C2: {none}
Functions of C2: {state that another set has the property of being purple}

Now we redefined autological and heterological again.
Let A denote the word autological.
Let A1 denote the set autological itself.
Let A2 denote the properties and functions of the set autological.

Innate properties of A1: {state that the set (A1) belongs to its properties and functions of the set (A2), it has 11 letters, etc}
Functions of A1: {none}
Innate properties of A2: {it has 11 letters, etc}
Functions of A2: {state that the set belongs to its properties and functions of the set}

Let H denote the word heterological.
Let H1 denote the set heterological itself.
Let H2 denote the properties and functions of the set heterological.

Innate properties of H1: {state that the set (H1) does not belong to its properties and functions of the set (H2), it has 13 letters, etc ... }
Functions of H1: {none}
Innate properties of H2: {it has 13 letters etc ...}
Functions of H2: {state that the set does not belong to its properties and functions of the set}

Hence, not we consider the case:
Is BIG autological or heterological.

If BIG is autological, then,

{functions and properties of B1 belongs to functions and properties of B2}
=> {Has the property of being big, it has 3 letters ...} belongs to {states that B1 has the property of being big}
Hence the statement BIG is autological is correct.

(My motto: The absence of evidence is not the evidence of absence, hence we must verify both ends of the story)

If BIG is heterological, then,

{functions and properties of B1 does not belong to functions and properties of B2}
=> {Has the property of being big, has 3 letters etc} does not belong to {states that B1 has the property of being big}
Hence the statement BIG is heterological is wrong.

Conclusion: BIG is autological and not heterological (law of verification).

Now consider the statement that,
carcinogenic is autological.

If carcinogenic is autological,
{functions and properties of C1 does belong to functions and properties of C2}, which is flawed
Hence carcinogenic is not autological.

If carcinogenic is heterological,
{functions and properties of C1 does not belong to functions and properties of C2}, which is correct.
Hence carcinogenic is heterological.

Conclusion: Carcinogenic is heterological and not autological.

Now consider the statement that,
Heterological is Heterological.

If Heterological is Autological, then,

{functions and properties of H1 belong to functions and properties of H2}
=> {state that the set (H1) does not belong to its properties and functions of the set (H2)} belongs to {state that the set (H1) does not belong to its properties and functions of the set(H2)}
Hence the statement Heterological is Autological is correct.

If Heterological is Heterological, then,

{functions and properties of H1 does not belong to functions and properties of H2}
=>{functions and properties of H1 belong to functions and properties of H2}
does not belongs to {state that the set (H1) does not belong to its properties and functions of the set(H2)}
Hence the statement that Heterological is Heterological is incorrect.

Conclusion: Heterological is Autological and not heterological.

Same conclusion, Heterological is still Autological and not heterological, BASED ON THESE DEFINITIONS THAT HAVE BEEN LAID OUT.

By the way, to use the so-called "accepted" argument (see below) that most logicians and philosophers use, is, in my own view, a too simple and ambiguous way to argue, as it fails to eliminate the ambiguities involved in the original problem.
That is, heterological is autological because it describes itself as being heterological. And precisely, because it describes itself as being heterological, it is heterological. Hence it is autological and heterological, and hence, the paradox. No! I do not accept this type of ambiguous inductive form of reasoning in my sphere; I believe that all semantic paradoxes can be reduced to the fundamentals of logic, hence eradicting all forms of ambiguity regarding the definitions of the words. The solution I showed above is one example, of what I said in my previous sentence. The dictionary, afterall, is meant to be ambiguous, and not specific - the language of reality is backed by the language of communication, which is in turn backed by the language of semantics, which is in turn backed by the language of logic, which is in turn backed by the language of meta-language, the axiomatized fundamentals of all language.

Ok let us consider the case of a self-referential paradox: the liar paradox.
This is the most fundamental form of the paradox:
"This statement is false" or "I am lying"
The amateurish way of solving this problem is this:
Let P be the statement that
"This statement is false"
Suppose P is true, then,
P is true
=> "This statement is false" is true.
Hence it is false.
And since it is true, it is true.
Suppose P is false, then,
P is false
=> "This statement is false" is false.
Hence it is true.
And since it is true, it must be false.
Conclusion: It is both true and false, and hence the paradox.
I do not accept such an answer.
A more formal way of answering the question is this:
Let P be the statement that
"This statement is false",
where the postulate laid inside is not a negation. Neither can it be proved or disproved, within the set itself.
Suppose P is true, then,
P is true
=> "This statement is false" is true.
Hence the non-negatory postulate in it that "This statement is false" is true, that it is false, with respect to itself. Hence it is true that it is false. But this does not show it is false in being false, with respect to itself.
Suppose P is false, then,
P is false
=> "This statement is false" is false.
Hence the non-negatory postulate in it that This statement is false" is false, that it is false, with respect to itself. Hence it is true that it is true. But this does not show it true in being false, with respect to itself.
However, one of my previous definitions states that the postulate laid inside is not a negation. Neither can it be proved or disproved, within the set itself.
Note: with respect to itself -> this is a very important statement.
Moore's paradox suggests that without a reference point of absolute truth, we cannot determine if the postulate in it is true or false.
Hence we cannot be 100% sure that it is true or false. Hence we cannot state that it is true or false with 100% confidence that it is true or false.
Conclusion: We cannot determine if the sentence is true or false.
Still I do not accept this answer.
The above 2 solutions are too ambiguous. There is no point answering the question if the properties and functions of the sets involved are not defined clearly, together with one or more properties that are always true, and cannot be disproved or proved in the set of reality itself.
Hence this is my solution:

Let P be the statement that,
"Statement A, This everything in this statement is false."
Where Statement A can mean almost anything - like God exists.

*note: I just realized that an object must either possess geometric or logical properties/functions, or both. This resolves the problem of the ambiguity of having to define the set, and itself as I did before. This time, the "itself" is the geometric set and the "set" is the logical set.

Let P1 be the set denoting the geometric properties and geometric functions.
Let P2 be the set denoting the logical properties and logical functions.

Geometric properties of P1, as described in terms of logic: {It contains X letters, has 7 Ts, 5 Is, and so on}
*note: it will be horrifically difficult to define it in terms of logic - one must define it in terms of geometry, by mathematics, which I shall not type it out here as it will take too long.
Geometric properties of P1, as described in terms of logic: {...}

Logical properties of P2: {contains a property that cannot be disproved or proved in the set of reality and it is always true, <in this example we use god exists> that God exists}
Logical functions of P2: {state that the logical properties of P2 <itself> is not true}

However, since the logical property in P2 is an axiom that is always true, and cannot proved or disproved, it must be always true.
The purpose of P2 is to merely STATE, and not prove, that the above is wrong. Furthermore, this is merely a function; it is not a STATE that is axiomatic and true.

Hence, the sentence,
"Statement A, everything in this statement is false."
is merely refering to the logical properties in itself (statement A) is false. This is not true, for we have assumed that statement A contains an axiom, that God exists, that is always true (we assume god exists for the sake of this question). The function merely tries to state that statement A, the logical property in itself is false. It cannot do anything to make it false. Hence this removes the problem where by it tries to make A true.
Similarly, "Everything thing in this statement is false" will yield the same result.
The functor is not the property.
Conclusion:
"Everything thing in this statement is false"
will yield no contradiction, and hence no questions that can be answered. It is hence not a paradox at all.

Problem resolved.

One way to phrase the Russell paradox is like this: Consider words in a dictionary. The word "heterological" refers to words that do not describe themselves. Is the word "heterological" heterological?

Logic says that this question is meaningless. Either answer is perfectly acceptable because both are equally consistent. (I.e. whether the word "heterological" is, in fact, heterological, or not, does not create any contradiction elsewhere.)
Well I guess based on my argument, heterological is autological and not heterological afterall.

Darn! I Spent So Much Time Typing Out The Solution For Newcomb's Paradox And The Forum Resetted By Itself And Deleted My Solution? Darn I Have To Retype Again!

Newcomb's paradox goes like this:



A highly superior being from another part of the galaxy presents you with two boxes, one open and one closed. In the open box there is a thousand-dollar bill. In the closed box there is either one million dollars or there is nothing. You are to choose between taking both boxes or taking the closed box only. But there's a catch.

The being claims that he is able to predict what any human being will decide to do. If he predicted you would take only the closed box, then he placed a million dollars in it. But if he predicted you would take both boxes, he left the closed box empty. Furthermore, he has run this experiment with 999 people before, and has been right every time.

What do you do?

On the one hand, the evidence is fairly obvious that if you choose to take only the closed box you will get one million dollars, whereas if you take both boxes you get only a measly thousand. You'd be stupid to take both boxes.

On the other hand, at the time you make your decision, the closed box already is empty or else contains a million dollars. Either way, if you take both boxes you get a thousand dollars more than if you take the closed box only.

As Nozick points out, there are two accepted principles of decision theory in conflict here. The expected-utility principle (based on the probability of each outcome) argues that you should take the closed box only. The dominance principle, however, says that if one strategy is always better, no matter what the circumstances, then you should pick it. And no matter what the closed box contains, you are $1000 richer if you take both boxes than if you take the closed one only. One can make the argument for taking both boxes even more vivid by changing the setup a bit. For instance, suppose that the closed box is open on the face opposing you, so that you can't see its contents but an experiment moderator can. The moderator is watching you decide between one box and both boxes, and the money is there in front of his eyes. Wouldn't he think you are a fool for not taking both boxes?

---------------

Ok so the summary is this:
1) I am given a choice or picking either both boxes or just the closed box.
2) If I keep both boxes, I would get only 1000 dollars.
3) If I keep only the closed box, I would get 1000000 dollars.
4) At the time when I am about to choose, the choice has already been made by the predictor. Either one million dollars or 0 dollars exist in the closed box.
5) On the other hand, at the time you make your decision, the closed box already is empty or else contains a million dollars. Either way, if you take both boxes you get a thousand dollars more than if you take the closed box only.

I am afraid that the flaw clearly lies in (5).

Firstly, we assume this, that,

For the ANOTHER bring (not the predictor),
1) He is omniscient, this means, he knows what goes on in every atom, hadron, quark etc in the universe, including the particles that made him up. He also knows their geometric properties at the present time.
2) He has a finite calculating capacity, but powerful enough to compute the information of every particle into the universe, with the exception of himself, to predict the future course/states of the universe.
3) He has no influence on our universe - He lies far away from the universe in another dimension that prevents his atoms from affecting those in the universe.

For the universe,
1) The universe has a teleological beginning.
2) The universe has no spatial boundaries.
3) The universe has a finite number of geometric objects with geometric properties.

If 1, 2 and 3 are false, then this happens:
<see below>

If 1 is true, 2 and 3 are false, then this happens:
The universe has existed forever, and will exist forever. Since it has existed forever, and it has an infinite amount of mass, and it has a spatial boundary - the universe will end up being crashed into a singularity and the night skies will be infinitely brighter. Due to the constraints of the cosmological anthropic principle, this clearly cannot happen.

If 2 is true, 1 and 3 are false, then this happens:
Universe is crashed into a singularity due to gravitation.

If 3 is true, 1 and 2 are false, then this happens:
The universe would have an infinite amount of mass, the being from above (the ANOTHER being) will not be able to predict the future, since he needs an infinite amount of computational capacity to predict the future.

If 1 and 2 are true, 3 is false.
Same as above, the being cannot predict the future.

If 2 and 3 are true, 1 is false.
This scenario is acceptable. No problem with it.

If 1 and 3 are true, 2 is false.
This scenario is acceptable, provided that the spatial boundaries are very far away from the current universe's location.

If 1, 2 and 3 are true.
This scenario is acceptable. No problem with it.

However, we assume the last condition is met, that 1, 2 and 3 are all true.

Ok now, the tricky part comes. We assume the following happens in order to eliminate the trick that comes, on whether an omniscient being can calculate what happens in the future of the universe if the particles on his body affects what goes on in the universe, and he includes the information of his atoms in the calculations. This ANOTHER being perform a calculation at a certain time frame, and predicts what happens in the future in the entire universe. Being highly intelligent, he simulates a scenario in his brain, of what will happen if he had suddenly appeared on the earth (he calculates what happens if all his atoms appear on earth at time X), to give a human being the choice as seen in the question. Doing this, he can accurately predict what the person chooses and hence, at time X, decide to appear and give a human being a choice, in a deterministic fashion (everything has been determined at the time he decides to appear on earth at time X). He will hence have 100% accuracy on deciding whether a person will take the closed box or both boxes, and hence place, or not place one million dollars in the closed box.

Since he has already determined, at time X, that the event B, where B is whether or not the Chooser will take the closed box only, or both boxes, the problem of which choice he chooses does not matter - he will always pick what this Predictor has predicted. In the subjectivity of the Predictor, since every event has been determined, the problem of which choice is better no longer matters - neither choice weighs more than the other, or less. Hence, HOLISTICALLY, speaking, we can conclude that since neither choice weighs more than the other, or less, the problem does not exist in the first place.

After some thinking (I will not type it out again - I'm too lazy to do that again), it would be theoretically possible if the being existed in our universe, that is, his atoms and the atoms of the universe exclusive of him, affect each other mutually, that he can still retain his ability to predict the future with 100% accuracy, by including the information of his atoms. Conclusion: It is logically possible that this "Predictor" can exist. I went through all this, just to show that it is possible for this to happen, and hence the event.

Anyway, we can conclude that, on the holistic level, that since neither choice weighs more than the other, or less, the problem does not exist in the first place. There is no paradox.

Hey! Can somebody at least respond? I'm the only one yammering here! In fact, I have been the only one yammering here since yesterday!

Nice, the Monty Hall problem - it's a good thing that I'm gifted with an uncanny ability to see through the deadiest knots, I was almost tricked into answer 1/2 instead of 1/3 for the answer! Check out this mathematical paradox at google - the result of the paradox will surprise you!

Goody! I contacted Avistar_sg via email yesterday, and had a discussion in a chat room - we had some pretty looong chat regarding the fundamentals of logic and on certain philosophical topics. Now I know why he decided not to come visit this forum any more - "personal" reasons partly due to his introverted nature, which I shall not state here since I respect his privacy and his choice. I sure learnt a lot from him, he's a great guy when it comes to topics involving mental imagery and calculations - he arrives to solutions almost instantly in some areas, which I took about 30 minutes to validate. My forte doesn't lie in those areas, but he claims he is "deficient" (perhaps comparatively speaking, relative to his other skills) in areas which I specialize in (languages, philosophy). Oh well, I guess we all got our unique combination of gifts and deficits right? No one's perfect. It's great that I finally found an interesting person to converse with. Being 6 years older than me, I'm sure he knows a lot more than me, and I certainly hope to learn more from him!