You've only explained that it has a reason to pick either a) or b) over c). You haven't explained that it has a reason to pick a) over b) or b) over a). That's the choice that leads to the paradox. — Michael

I understand what you mean. So you agree that I've demonstrated that the ass has to choose between the two stacks of grass. This wasn't part of the original paradox.
If you will allow an analogy to describe your objection to my ''solution''. It's like having a reason to go to the hospital but not having reason to choose between two routes. If I am right then...

Well, once the ass is logically compelled to make a choice it now has to analyze the options it has. Since both choices are equally acceptable it doesn't matter which is its choice - he may choose randomly. In other words the choice is no longer relevant to the problem. It chooses one and lives.

Ok. The way I see it decision making processes involve maximizing positive outcomes for the decision maker. Is this too simplistic a conception for the purpose of dealing with the paradox?

In the original paradox there was no reason to make a choice (random or otherwise).

I have shown you how, in fact, the ass must (has a reason) choose (random or otherwise).

The mechanism of rationality? What do you mean?

Yes, but there are two ways to avoid death, and no reason to pick one over the other — Michael

Hmmmm...

I already explained above that 2 stacks of grass is the same as NO stack of grass. Therefore the choice at that level is an illusion. There is NO choice.

The real choices are LIFE or DEATH. The choice is clear here - life. The next obstacle, as you've pointed out, is the juncture where we actually choose between the rwo stacks. In the original paradox it says that there's no reason to choose one over the other. Hence the paradox. However I've shown in my analysis that the ass having chosen life must be compelled (logically) to make a random choice between the two stacks. Therefore the ass has a reason to make a random (if you can call it that) selection.

The decision, then, is random. Whether or not a random decision can be considered an application of free will is then an issue. — Michael

What I'm saying is:

1. The real options are life or death. NOT the two stacks (as explained above).

2. The random element of actually choosing one particular path is actually guided by the realization that not making a choice is going to be harmful/fatal. So it's not really random

I thought the core issue was some kind of breakdown in rationality: the ass can find no reason to choose one stack over the other and thus will starve itself despite there being given TWO choices.

You all are right.

A: this statement is false

A has no truth value

So, we should be saying: "A is neither true nor false" instead of ''this statement is neither true nor false''

Your take on the matter is quite different and it may not be how others consider what the issue here is.

If I understood you correctly you mean to say the following 2 sentences are equivalent:

1. There's a book on the table
2. There's a book on the table is true

Then you criticize my argument by saying ''this statement'' in ''this statement is true'' is not a statement and assigning a truth value is meanigless. Have I understood correctly?

However take the following statement:

''This sentence has five words''.

Here we consider the entire statement in evaluating the truth-condition of it. We don't just take the ''this statement'' part.

Sorry if you find that wrong. I was replying to andrewk's as to where such a treatment of the paradox may lead us.

B: This statement is neither true nor false

Available options:
1. True
2. False
3. True and false
4. Neither true and false
The above four options are all that's available (as far as I know)

B can't 1 because then it would be false too

B can't be 2 because then it would be a contradiction (it says its neither true nor false and you're assigning a truth value ''false'' to it)

B can't be 3 because it is a contradiction

B can't be 4 because then B would be true (which is not possible as I've shown above)

So, what kind of statement is ''this statement is neither true nor false''? It's quite different from the Liar statement which is at least understandable as ''neither true nor false''.

Is it a useful definition though? Where does it get you that you couldn't get to otherwise? — andrewk

First note that
A: this statement is false
B: this statement is neither true nor false

For A the truth-value is indeterminate and we end up concluding B.

Now B can have the following truth values
1. True...this is not possible
2. False...this is not possible
3. True and false...this is not possible
4. Neither true nor false...this is not possible (refer to 1)

So now we have a very odd statement which is not any of the options available as shown above.

What then is this statement ''this statement is neither true nor false''?

If you can't distinguish between the two statements then you're probably dyslexic. — Benkei

Logic can't differentiate ''this statement is false'' from ''this statement is neither true nor false''. Therefore, they are equivalent — TheMadFool

Under this definition, questions, commands, expletives and meaningless sentences cannot be logically equivalent to anything because they are not equivalent to any well-formed sentence in FOPL — andrewk

If I can't distinguish the difference between A and B, then it can be inferred that A and B are the equivalent.

Logic can't differentiate ''this statement is false'' from ''this statement is neither true nor false''. Therefore, they are equivalent.

Consider the sentences "how old are you?" and "what is your name?". Both are neither true nor false but they are not logically equivalent. For two sentences to be logically equivalent it must be that iff one is true then the other is true and iff one is false then the other is false. It isn't a term that is applicable to sentences that are not truth-apt — Michael

I beg to differ. In logic we have no way of distinguishing ''what is yor name?'' from ''how old are you?'' These two are the same so far as logic is concerned. Likewise logic can't find a difference between ''this statement is false'' and ''this statement is neither true nor false''. Therefore they are logically equivalent.

Logical equivalence of two given statements means that the given statements must have the same truth value in all possible worlds.

I've shown you how ''This statement is false'' and ''This statement is neither true nor false'' have the same truth value as in
1. They cannot be true
2. They cannot be false
3. They cannot be both true and false

However both can be 4.Neither true nor false. Doesn't that establish logical equivalence?

''A: This statement is false'' is logically equivalent to ''B: This statement is neither true nor false''. Therefore, since B is true A must also be true.

No, what we're saying is that A. "this sentence is false" and B. "this sentence is neither true nor false" are not logically equivalent — Michael

Please read my previous post

Also...

''This statement is false'' is a claim about the truth value of itself. Analysis results in a truth value, if one may call it that, of neither true nor false.

That is to say: ''This statement is neither true nor false'' is a logically acceptable rephrased version of ''This statement is false''. Note, like A, B makes a claim only about truth value of given statement.

So you're saying that B: This statement is neither true nor false is

1. Not true
2. Not false
3. Not true and false
4. Not neither true nor false

It appears to me that the above 4 options are jointly exhaustive and mutually exclusive. I'm at a loss to find out what sort of truth value B has.

Below is a new look at the Liar's paradox.

The Liar statement A: This statement is false.

Options available for the truth value of A
1. True
2. False
3. True AND false
4. Neither true nor false

1 and 2 result in the true-false loop and 3 is a contradiction. The last option available is 4 which is neither true nor false.

Note A only concerns itself with the truth value of A. Nothing more nothig less. Therefore we can rephrase A as
B: This statement is neither true nor false.
I'm not making any illegitmate claims about A. It's only about the truth value of A. So, A is neither true nor false.

Let us now check the possible truth values of B.
It is:
1. True
2. False
3. True AND false
4. Neither true nor false

It cannot be 1 in a direct manner as it leads to a true-false loop. It can't be 2 because that leads to the original Liar statement. It cannot be 3 as its a contradiction. The last option is 4 (neither true nor false). Notice that this is what B states. So it must be that A (the Liar statement) is true since B is nothing more than a rephrased version of A.

X-) LOL. Thanks for your time guys. I'm wrong.

If B is TRUE, then it is not "neither true nor false". — Benkei

I think you're right. B cannot be true in a direct way. However...

It can be
1. True
2. False
3. Both true and false
4. Neither true nor false
B can be 2(false). So again, can I make a claim that I've opened a new option [2. False] for the Liar statement which was written off in the original paradox?

As others have been pointing out, the liar statement (A) is not equivalent to B. At the very least, you have to provide an argument for why the two statements are (supposedly) equivalent — aletheist

Let me try to explain it as clearly as possible.

The liar statement: A: This sentence is false

Please note that A is only concerned about the truth value of A, nothing less and nothig more.

Let us now assess what possible options of truth value are there for A:

1. True
2. False
3. Both true and false
4. Neither true nor false
The above 4 choices are jointly exhaustive and mutually exclusive.

Option 1 and 2 are impossible for the reason that a true-false loop results. Option 3 is impossible because its a contradiction. The only option available is 4 which is ''neither true nor false''.

Note again A is only about the truth value of A, nothing less nothing more.

Therefore it is acceptable to replace ''false'' in A with ''neither true nor false'' since the former equates with the latter as I've shown above.

Therefore A can be replaced with B: This statement is neither true nor false. This however is a TRUE statment about A. Therefore, the original Liar statement, A, must also be true by virtue of it being equivalent to B.

Please follow the line of reasoning...

The Liar statement: A: This statement is false

Available truth value options for the Liar statement are:

1. True
2. False
3. True and false
4. Neither true nor false

Option 1 and 2 are not possible because of the well-known true-false loop.
Option 3 is a contradiction so again, not possible
The only option available is 4, neither true nor false.

Therefore, This statement is false is saying exaclty what B: This statement is neither true nor false.

But B is a TRUE statement. Therefore the liar statement, which is equivalent to B, is also true.

Again, no. You're conflating statement A with a (different) statement about A. — Michael

No I'm not conflating the two statements. Please read below:

A: THIS (A) statement is false is
1. Not true
2. Not false
3. Not both true AND false

The only option left is that A is "neither true nor false.

So now we have the new statement:

THIS (A) statement is neither true nor false. This new statement is TRUE for A is neither true nor false. Thus even A (liar statement) is true

Please read my responses to other posters.

Directly, people's beliefs. People believe that their religion is true, and they act on their beliefs. Even if the beliefs are actually false, people still follow them so long as they believe them to be true — Chany

But how do you know religious beliefs are false? Can you tell me a method which I can use to show that god is a false belief ?

You're right. If I think of anything new I'll come back. Thanks

That's the extremely bare-bones version of it. In your example, you have not eliminated alternative hypotheses to God actually causing belief — Chany

Thanks for your informative response. However can you name some alternative hypotheses to God.

A: This statement is false is the original Liar statement.

Upon logical analysis we end up in a true-false never-ending loop. The end result being that we cannot assign a truth value to it i.e.

the Liar statement is neither true nor false.
Therefore the Liar statement can be rephrased as
B: This statement is neither true nor false.

But B is true - the Liar statement is neither true nor false. That is to say B is TRUE. Since B is just a different version of A (they're logically equivalent) it follows that A (the original Liar statement) is also TRUE.

A(the liar statement) =This statement is false

B=This statement is neither true nor false

As per how the paradox is known A cannot be true and cannot be false. In other words A can neither be true nor can A be false. But this is statement B. And statement B is true as shown above. Therefore A (the liar statement) must also be true

It comes across to me that you're making a distinction between the actual existence of a thing and belief in the existence of that thing. How do we distinguish between the two states with regard to something, say a stone or even god?

I am accounting for those religious observations. I'm saying that the hypothesis you are arguing for is unfounded and that the explanation for the religious behavior we observe can easily just be false belief in gods. — Chany

How do you know god-beliefs are false or true for that matter? This is the issue at hand. Your counter-objections to my argument is a circular one. You're already assuming god doesn't exist.

Setting aside the scientific method, which admittedly is flawed, as a philosopher, is the diversity of spiritual, emotional, mental, and physical experiences, as observed by you, best explained by an omnipresent, omniscient, omnipotent God — Rich

Well, what are the options available?

The only other option we have is that everything arose out of chance. How do we measure or verify that? The short answer is we can't.

That's just speculation, and I can do that too. For example, the way I see it, they're the effects of a celestial teapot.

It is crystal clear at this stage that you're unable to rule out any other competing theory, and that you're going to merely repeat yourself, make false analogies, and so on.

I suspect that this is another case of wishful thinking: you want to make this argument work, even though it doesn't. But your want is greater than your reason, so you keep trying to put your cube through the triangular slot — Sapientia

What I want to say is I'm simply following scientific methodology here. To verify the existence of a hypothetical entity we look for its effects - according to science. And I've shown you plenty of effects of god on people. Therefore god must exists.

You are ignoring observable effects in religion while calling on the same (observable effects) in science.

I'd rather be stoned — Wayfarer

I would throw a shiva lingam at youX-)

BY PICKING UP A STONE AND THROWING IT AT YOUR FACE — Wayfarer

Similarly I can take you to attend a temple worship

It is always such a joy seeing people live up to their titles — John

Ad hominem:D...a survival skill

Everything has uses. They exist and if they exist they can be used for learning. But this doesn't mean that we have to learn from everything. We pick and choose. — Rich

Exactly. So shouldn't logicians be cautious about condemning a useful way of thinking? Fallacies are part of the repertoire of our survival skills.