Thoughts on this? I got stuck -_-

A man goes past, riding on a horse, through a grass meadow. After he passes through the meadow, he sees a wall, and a dog sitting on a chair. The man approaches the dog, and the dog speaks to him. The dog tells the man answers to so many things, the dog is undoubtedly inerrant. A man notices a horse gallop by, and it goes behind the wall. The man does not notice anything about the horse apart from that there is a horse. The dog then tells the man "the horse is either red or black". The man thinks back to the principle of bivalence: Either P or not P is true. In addition, the man thinks back to the law of the excluded middle: It is necessary in every case to affirm or deny. Why should the man believe any option? Further, does the law of excluded middle still stand?

Preferably with mathematical workings.

Dude what'ya talking about? I am stuck.

At 3/16/2012 6:59:49 PM, Stephen_Hawkins wrote:
A man goes past, riding on a horse, through a grass meadow. After he passes through the meadow, he sees a wall, and a dog sitting on a chair. The man approaches the dog, and the dog speaks to him. The dog tells the man answers to so many things, the dog is undoubtedly inerrant. A man notices a horse gallop by, and it goes behind the wall. The man does not notice anything about the horse apart from that there is a horse. The dog then tells the man "the horse is either red or black". The man thinks back to the principle of bivalence: Either P or not P is true. In addition, the man thinks back to the law of the excluded middle: It is necessary in every case to affirm or deny. Why should the man believe any option? Further, does the law of excluded middle still stand?

Preferably with mathematical workings.

It is a complex questions who's answer has no use or value. In other words it's a way of expressing the blatantly obvious in the most complex and obscure manner possible.

At 3/16/2012 9:14:43 PM, sadolite wrote:

At 3/16/2012 6:59:49 PM, Stephen_Hawkins wrote:
A man goes past, riding on a horse, through a grass meadow. After he passes through the meadow, he sees a wall, and a dog sitting on a chair. The man approaches the dog, and the dog speaks to him. The dog tells the man answers to so many things, the dog is undoubtedly inerrant. A man notices a horse gallop by, and it goes behind the wall. The man does not notice anything about the horse apart from that there is a horse. The dog then tells the man "the horse is either red or black". The man thinks back to the principle of bivalence: Either P or not P is true. In addition, the man thinks back to the law of the excluded middle: It is necessary in every case to affirm or deny. Why should the man believe any option? Further, does the law of excluded middle still stand?

Preferably with mathematical workings.

It is a complex questions who's answer has no use or value. In other words it's a way of expressing the blatantly obvious in the most complex and obscure manner possible.

...thanks for that. The point was it is a question put forth. So far I've worked out with a mate that it (may) mean:

"So essentially the question is, as to whether there are any alternatives besides P or P's negation?"

At 3/16/2012 6:59:49 PM, Stephen_Hawkins wrote:
A man goes past, riding on a horse, through a grass meadow. After he passes through the meadow, he sees a wall, and a dog sitting on a chair. The man approaches the dog, and the dog speaks to him. The dog tells the man answers to so many things, the dog is undoubtedly inerrant. A man notices a horse gallop by, and it goes behind the wall. The man does not notice anything about the horse apart from that there is a horse. The dog then tells the man "the horse is either red or black". The man thinks back to the principle of bivalence: Either P or not P is true. In addition, the man thinks back to the law of the excluded middle: It is necessary in every case to affirm or deny. Why should the man believe any option? Further, does the law of excluded middle still stand?

Preferably with mathematical workings.

I thought this was supposed to be a riddle and my answer was going to be 'dogs don't talk' lol :/

To be honest, I have no idea... Grape is a philosophy major, if he's lurking, maybe he can answer this.

At 3/16/2012 9:17:57 PM, Stephen_Hawkins wrote:

At 3/16/2012 9:14:43 PM, sadolite wrote:

At 3/16/2012 6:59:49 PM, Stephen_Hawkins wrote:
A man goes past, riding on a horse, through a grass meadow. After he passes through the meadow, he sees a wall, and a dog sitting on a chair. The man approaches the dog, and the dog speaks to him. The dog tells the man answers to so many things, the dog is undoubtedly inerrant. A man notices a horse gallop by, and it goes behind the wall. The man does not notice anything about the horse apart from that there is a horse. The dog then tells the man "the horse is either red or black". The man thinks back to the principle of bivalence: Either P or not P is true. In addition, the man thinks back to the law of the excluded middle: It is necessary in every case to affirm or deny. Why should the man believe any option? Further, does the law of excluded middle still stand?

Preferably with mathematical workings.

It is a complex questions who's answer has no use or value. In other words it's a way of expressing the blatantly obvious in the most complex and obscure manner possible.

...thanks for that. The point was it is a question put forth. So far I've worked out with a mate that it (may) mean:

"So essentially the question is, as to whether there are any alternatives besides P or P's negation?"

The dog doesn't have to tell the truth, right? It could be any color, then.

At 3/17/2012 12:08:13 PM, SarcasticIndeed wrote:

At 3/16/2012 9:17:57 PM, Stephen_Hawkins wrote:

At 3/16/2012 9:14:43 PM, sadolite wrote:

At 3/16/2012 6:59:49 PM, Stephen_Hawkins wrote:
A man goes past, riding on a horse, through a grass meadow. After he passes through the meadow, he sees a wall, and a dog sitting on a chair. The man approaches the dog, and the dog speaks to him. The dog tells the man answers to so many things, the dog is undoubtedly inerrant. A man notices a horse gallop by, and it goes behind the wall. The man does not notice anything about the horse apart from that there is a horse. The dog then tells the man "the horse is either red or black". The man thinks back to the principle of bivalence: Either P or not P is true. In addition, the man thinks back to the law of the excluded middle: It is necessary in every case to affirm or deny. Why should the man believe any option? Further, does the law of excluded middle still stand?

Preferably with mathematical workings.

It is a complex questions who's answer has no use or value. In other words it's a way of expressing the blatantly obvious in the most complex and obscure manner possible.

...thanks for that. The point was it is a question put forth. So far I've worked out with a mate that it (may) mean:

"So essentially the question is, as to whether there are any alternatives besides P or P's negation?"

The dog doesn't have to tell the truth, right? It could be any color, then.

Well, it says the dog is undoubtedly inerrant. So assuming he's telling the truth, then you've got "p or q" and that's the only possible thing...

I think this is what you mean:

Ax - undoubtable inerrancy
Bx - Red
Cx - Black
a - Dog
b - Horse

If Aa then Bb and Cb
Aa -> (Bb & Cb)

If not Bb and Cb, then not Aa
~(Bb & Cb)
~(Aa), modus tollens

Is that the answer to your question?

I don't understand the question. For classical logic, P v ~P is a theorem. For some other forms of logic it is not.

At 3/17/2012 12:28:43 PM, nonentity wrote:
I think this is what you mean:

Ax - undoubtable inerrancy
Bx - Red
Cx - Black
a - Dog
b - Horse

If Aa then Bb and Cb
Aa -> (Bb & Cb)

If not Bb and Cb, then not Aa
~(Bb & Cb)
~(Aa), modus tollens

Is that the answer to your question?

The question is not whether it is "red and black" or not, but whether it is "red" or "not-red" AKA "black", and what the most reasonable stance would be.

At 3/19/2012 2:48:42 AM, Stephen_Hawkins wrote:

At 3/17/2012 12:28:43 PM, nonentity wrote:
I think this is what you mean:

Ax - undoubtable inerrancy
Bx - Red
Cx - Black
a - Dog
b - Horse

If Aa then Bb and Cb
Aa -> (Bb & Cb)

If not Bb and Cb, then not Aa
~(Bb & Cb)
~(Aa), modus tollens

Is that the answer to your question?

The question is not whether it is "red and black" or not, but whether it is "red" or "not-red" AKA "black", and what the most reasonable stance would be.

black is a default colour when thier is not enought light. not to be confused with not-ness. Which is even absense of that. And not knowable, and thus non-sense literally in that there is no-sense it which it is.

So not red doesn;t mean black,. we don't even have an idea of not-ness because it wouldn't even be an idea. The idea we tend to get when we talk about it is blackness. but what we really trying to say is that which is said in the next sentence. " ".
do you get what I mean?

Another reason is that (red and black) Synthesis to get dark red.

At 3/17/2012 8:59:49 PM, Grape wrote:
I don't understand the question. For classical logic, P v ~P is a theorem. For some other forms of logic it is not.

The Fool: Difference logics is nonsense. Its a fail caused by the move to an objective language being logic. I hope to over throw that in the next few years.

At 3/19/2012 5:13:43 AM, The_Fool_on_the_hill wrote:
Another reason is that (red and black) Synthesis to get dark red.

I am pretty sure this was the answer. I was a false dichotomy.

At 3/16/2012 6:59:49 PM, Stephen_Hawkins wrote:
A man goes past, riding on a horse, through a grass meadow. After he passes through the meadow, he sees a wall, and a dog sitting on a chair. The man approaches the dog, and the dog speaks to him. The dog tells the man answers to so many things, the dog is undoubtedly inerrant. A man notices a horse gallop by, and it goes behind the wall. The man does not notice anything about the horse apart from that there is a horse. The dog then tells the man "the horse is either red or black". The man thinks back to the principle of bivalence: Either P or not P is true. In addition, the man thinks back to the law of the excluded middle: It is necessary in every case to affirm or deny. Why should the man believe any option? Further, does the law of excluded middle still stand?

Preferably with mathematical workings.

This is simpler than you think.

Why should the man believe any option?

Because, the dog has not presented a statement of fact; instead, he has reduced the amount of available options there are that can satisfy fact.

In other words, let's say that the horse is h, red is r and black is b.

h = r ⊕ b. (Either h = r or h = b is true, but not both).

If we discard the assumption r = ¬b, and instead assume the relationship between r and b is r ⊥ b, then we can accept that you have two possible answers:

¬r ∴ b or ¬b ∴ r (not r, therefore b, or not b, therefore r).

This suggests there is information that was left out. In other words, we have definition for r, but not ¬r, and we don't have a definition for ¬b either, unless we refer to another value essentially independent of both ¬r and ¬b (which would be b and r, respectively). Moreover, the dog clearly saw the horse. Therefore, since, once again, red and black are essentially irrelevant to one another except in this circumstance, other distinctions must be made to draw a difference between r and b. Otherwise, the definition stands as it is.

Given this fact, you must then accept red or black as its own term. We'll call that t.

If we do that, you can accept that h = t. In this way, the statement is factual and the law of excluded middle does still apply (t V ¬t).

However.

If we were to leave it the way it was (¬r ∴ b or ¬b ∴ r), then the man cannot tell you what color the horse was; only what color it was not. Thus, bivalence would not apply, but the law of excluded middle does.

The Dog has no conception of RED Because they are RED-GREEN colour blind.

RED to them looks yellow so the answer is BLACK

http://www4.uwsp.edu...

At 3/19/2012 2:48:42 AM, Stephen_Hawkins wrote:

The question is not whether it is "red and black" or not, but whether it is "red" or "not-red" AKA "black", and what the most reasonable stance would be.

Why? You could take that stance of anything... Although the dog said the horse was either red or black, I could then respond "The horse is either purple or not purple" and no matter which colour I chose, I'd be right in every circumstance :/

At 3/19/2012 8:52:13 PM, nonentity wrote:

At 3/19/2012 2:48:42 AM, Stephen_Hawkins wrote:

The question is not whether it is "red and black" or not, but whether it is "red" or "not-red" AKA "black", and what the most reasonable stance would be.

Why? You could take that stance of anything... Although the dog said the horse was either red or black, I could then respond "The horse is either purple or not purple" and no matter which colour I chose, I'd be right in every circumstance :/

The question is NOT whether the claim "red and black" holds value, or is true or not because of the infallible dog. The question is whether we should claim the horse is red, or the horse is not-red AKA black. In the dichotomy between RED and NOT-RED, which is most reasonable?

At 3/19/2012 5:08:07 AM, The_Fool_on_the_hill wrote:

At 3/19/2012 2:48:42 AM, Stephen_Hawkins wrote:

At 3/17/2012 12:28:43 PM, nonentity wrote:
I think this is what you mean:

Ax - undoubtable inerrancy
Bx - Red
Cx - Black
a - Dog
b - Horse

If Aa then Bb and Cb
Aa -> (Bb & Cb)

If not Bb and Cb, then not Aa
~(Bb & Cb)
~(Aa), modus tollens

Is that the answer to your question?

The question is not whether it is "red and black" or not, but whether it is "red" or "not-red" AKA "black", and what the most reasonable stance would be.

black is a default colour when thier is not enought light. not to be confused with not-ness. Which is even absense of that. And not knowable, and thus non-sense literally in that there is no-sense it which it is.

Not an attempt to logically answer the question. You're basically saying that black is the lack of light (while saying it is not "nothing", where nothing is the absence of absence as well, which still makes no sense). You've basically ended up changing the question: "Thus non-sense literally in that there is no-sense it which it is." <-

At 3/19/2012 5:13:43 AM, The_Fool_on_the_hill wrote:
Another reason is that (red and black) Synthesis to get dark red.

Not an answer. You've just made the questio a trichotomy. That doesn't mean anything. In addition, the dog would say instead "either black, red, or dark red".

At 3/19/2012 5:10:27 AM, The_Fool_on_the_hill wrote:
So not red doesn;t mean black,. we don't even have an idea of not-ness because it wouldn't even be an idea. The idea we tend to get when we talk about it is blackness. but what we really trying to say is that which is said in the next sentence. " ".
do you get what I mean?

not-red means black, because the horse is either red or black. If it not red, then it is black.

I believe that the Fool and I are on the same train of thought...

However, you blended the colors, which I think is in err. I think the point of the question was to show that some propositions and some equations do not present answers themselves, but rather exclude answers. If the dog tells you that the horse was either red or black, then that's literally all you know -- that it was either red or black. Does that belie the nature of right and wrong? No, because "red or black" becomes a constant its own. That's how science works. Sometimes, we have no idea how principles will interact in given situations, leaving us the only option to exclude possible answers and satisfy ourselves with what we have until we have more information.

I would have interpreted the question differently, however, if the dog had said "purple or black."

Noooooooooooooo!!

THIS IS THE REAL ANSWER!

The Dog has no conception of RED Because they are RED-GREEN colour blind.

RED to them looks YELLOW therefor the answer is BLACK

http://www4.uwsp.edu......

At 3/20/2012 11:29:06 PM, The_Fool_on_the_hill wrote:
Noooooooooooooo!!

THIS IS THE REAL ANSWER!

The Dog has no conception of RED Because they are RED-GREEN colour blind.

RED to them looks YELLOW therefor the answer is BLACK

http://www4.uwsp.edu......

you have poop

Noooooooooooooo!!

THIS IS THE REAL ANSWER!

The Dog has no conception of RED Because they are RED-GREEN colour blind.

RED to them looks YELLOW therefore the answer is BLACK

The riddle is taking advantage to this logical principle:

That is if you have A it follow that A or (anything) except ~A (not-A)

But the riddle blows because that is an error in the classical logic account.. anyway.
Not that I think it is an error by Russal or Wittgenstein. But rather that of the Anti-positive back lash.. and the reinterpretation of logic. I don't think its reinterpretation remained faithful to the original understanding of logic. The move to logic as an object language is huge mistake. I think this was caused by a strong relativistic turn in ideology.