But consider this:
-What existed before the universe began? What’s beyond it? If it’s infinite and expanding, what’s it occupying?
-Why is Mathematics universal? (this relates to the numbers question, I think)
-Why can’t there be vacuum anywhere? Where does this manic obsession ‘stuff’ has with being somewhere?
-Entropy (which is intractably connected with our perception of time, another weird concept relevant to us because everything we know is temporary).
-How come there’s energy all over and inside everything? How did energy come to be? What IS it?

And finally, why is faith stronger than physical truth to some people and vice-versa – and where does faith come from, if not everyone believes in God (or more than one god)? Why would this or these deities allow people NOT to believe, if there’s a chance they exist and everyone is born with the ability for faith? Is it something physical in our brains? Or not physical? Am I going to hell, like all those people whose faiths are inaccurate, without it being their fault?

@michael (94): Don’t worry about it, we’re human after all.

I really mean that and I’m not trying to be condescending at all, but all you’ve done so far is explain why the paradox of the heap is a paradox and not logical. You haven’t explained why it is not a paradox and what the logical solution is.

Newsflash just in from LV news,

Mark is debating with Michael on the 10 Great Unsolved Problems List about whether or not the paradox of the heap is in fact a logical paradox. It appears that Mark believes that the paradox of the heap does exist as a logical paradox…

Need I say more?

As for your attempts to paint Wikipedia as inherently bad (it has strict referencing and anti-bias policies) LOOK AT THE REFERENCES.

http://plato.stanford.edu/entries/sorites-paradox/

If you don’t get it after that, well, I don’t know how else to explain it to you…

“…I believe that I can state without ambiguity that the paradox only applies to something that can be heaped (up)…”

It doesn’t matter… How do you not get that it doesn’t matter? I’m about to pull some of my own hair out in frustration…

“…Then you say “Seriously? Did you just seriously “out logic” me… with my own logic?” implying that my rejection of the premise proves you are correct…well, I guess it’s hard to lose an argument when you take both sides…”

You reject a premise that many others logically see as, well, logical and correct. If the premise of a problem can be logically justified as either true or false, voila, paradox. I’m not taking “both sides” you don’t grasp what I’m saying. I’m saying this is a paradox, you’re saying that it’s not logical – almost the definition of a paradox in the way you’re using it – YET YOU STILL MANAGE TO CALL ME “WRONG”?

“…Then you say “Seriously? Did you just seriously “out logic” me… with my own logic?” implying that my rejection of the premise proves you are correct…well, I guess it’s hard to lose an argument when you take both sides…”

“…You keep asking that, and I keep answering it, but you don’t seem to get it, so, once more: A heap is no longer a heap when it can no longer support itself to a level of greater than plus 1, or when the number of items within can be visually estimated. A non-heap becomes a heap when it can support itself to a level of greater than plus 1, or when the number of items within can no longer be visually estimated.
If you want an exact number, I would reply that it depends on the item beng heaped.
There is your logical solution, start admitting…”

A logical outcome requires objectivity so that it cannot be rejected by another with a differing opinion. That is not objective, by any stretch of the imagination. How do you not get that?

You might say “I’d call that pile of 1,000 apples a heap” but then I look at it and say “no, it’s not really a heap”. We then ask Bill and Fred to help us with our dilemma, Bill says yes it does look like a heap. Fred thinks that Bill is crazy and agrees with me. How can your subjective “solution” be called logical?

This is a common misconception. The big bang was not an explosion, but rather an expansion. Nothing went bang. Everything just expanded from a singularity. Read about it.

“You can’t fail to agree with the fact that 1,000,000 grains of sand are a heap, can you?”

Actually, yes I can, using a little thing I like to call the Heap Paradox. You may have read about it on Wikipedia.

The paradox states:
1 grain of sand is not a heap (premise 1)
Adding a grain of sand will not make it a heap (premise 2)

Repeated applications of Premise 2 (each time starting with one more grain), eventually forces one to accept the conclusion that 1 million grains of sand does not constitute a heap, that one could, in fact, pile grains to the scale of Mt. Everest, the moon, or the planet Earth, and still not have a heap.

See what I did there?

I did not say that all wikipedia entires are not to be trusted, but since it can be edited by anyone, I would not count it as a reliable source.
Here’s a link for you:

http://en.wikipedia.org/wiki/Criticism_of_Wikipedia
but because it is on wikipedia I would warn you not to accept the information as definitive.

Try this argument on for size:

A encyclopedia that contains inaccurate, biased or apocryphal information is not a resource one can trust.

Wikipedia contains many factual errors and errors of omission, edited by anonymous persons who cannot be held accountable for their work, or lack thereof.

Therefore, Wikipedia can not be trusted as a reliable source.

One more, this is a quote from the link referenced above, so accept it at your own risk: “Jimmy Wales, the de facto leader of Wikipedia, stresses that encyclopedias of any type are not usually appropriate as primary sources, and should not be relied upon as authoritative.”

However, since this is not a discussion of the value or validity of Wikipedia, let’s move on, shall we?

Your continued application of the informal definition of heap (your heap of apples statement from (86), your heap of water statement from (91)) only weakens your argument. I refer you to the portion of the article related to our discussion (I’ll quote it for you here, so you don’t have to scroll up):
The paradox of the heap is an example of this paradox which arises when one considers a heap of sand (or a haystack), from which grains are individually removed…
You certainly don’t mean to imply that you could spread a haystack over a million acres, and it would still be a haystack, do you? No, it is obvious that the primary definition of heap is what is being applied here, and not just because I say so. The paradox has also been presented as the bald man paradox (in a nutshell: A man with a headful of hair is not bald, removing one hair does not make him bald, etc.) This paradox does not take the hair on his
ass, legs or big toe into account. My argument all along has been utilizing the primary definition of heap, not informal, nor slang (e.g. “My car is a heap of junk”) I believe that I can state without ambiguity that the paradox only applies to something that can be heaped (up). Unless you can present me with an example (from a resource other than Wikipedia, thank you) whereby the paradox is expressed using items that cannot be heaped (such as water, or a gas), I will have to reject those arguments as a logical equivocation.

Bashing vs. non-bashing: While I freely admit the size of my ego (“If there’s anything on this ship more important than my ego, I want it caught and shot right now”
~ Zaphod Beeblebrox)– I never stated that there are not people who have greater intellect or education than I, only that YOU DO NOT KNOW WHO THESE PEOPLE ARE, because you do not know me, For you to compare me, an unknown quantity, to anyone else without first being exposed to the full brunt of my intellect and power of reason, is, on it’s face, insulting.
You also seem to be of the opinion that just because something hasn’t been done, it can never be done, in which case I would refer you to George Dantzig, a UC Berkely student who, in 1939, solved two previously unproven statistical theorems, which his “betters” had heretofore been unable to. The premise of the film “Good Will Hunting” is based on this event. It is possible, even reasonable, to conclude that someone without the depth of knowledge you seem to feel is necessary to engage in any discussion of logic, could still make statements or assumptions that would be of value.

So let’s get down to brass tacks:

You stated: So unless you can either tell me why you reject either premise, or when the amount of grains left doesn’t still constitute a heap (make me another premise), 1 grain of sand is a heap.

I rejected premise 2 on the grounds that to accept it would be contrary to the definition of the word heap (again, the primary definition).

Then you say “Seriously? Did you just seriously “out logic” me… with my own logic?” implying that my rejection of the premise proves you are correct…well, I guess it’s hard to lose an argument when you take both sides.

“Where is a heap a non-heap and a non-heap a heap. You tell me, and I’ll admit that this isn’t a paradox, that it has a logical solution and that you were right.”

You keep asking that, and I keep answering it, but you don’t seem to get it, so, once more: A heap is no longer a heap when it can no longer support itself to a level of greater than plus 1, or when the number of items within can be visually estimated. A non-heap becomes a heap when it can support itself to a level of greater than plus 1, or when the number of items within can no longer be visually estimated.
If you want an exact number, I would reply that it depends on the item beng heaped.
There is your logical solution, start admitting.

Now, to more important items: Zeppelin – best that has ever been, or best that will ever be?

So Zeppelin didn’t actually form in 1968 *gulp*

Look at the references dolt

Many, many laughs reading through the rest of that comment, and only at minimal cost to my patience.

“…Meanwhile, I’m still waiting for your refutation of my dismissal of Premise 2 on the grounds that something cannot be the opposite of it’s definition.

To reiterate: A heap CANNOT be one or zero items because a heap is defined as A GROUP of things. A single grain of sand CANNOT be a group. No grains of sand CANNOT be a group. They are mutually exclusive. Follow THAT with your logical thought pattern, you officious pseudo-intellectual…”

That’s why it’s a paradox… Seriously? Did you just seriously “out logic” me… with my own logic? Nice… that really is impressive.

You can’t fail to agree with the fact that 1,000,000 grains of sand are a heap, can you? Also that 999,999 are? And 999,998? So therefore, we *can* say that if n objects make a heap, so does n-1. It’s only one, the difference is negligible.

What’s that you say, one object isn’t a heap? I agree completely, but I’d be inclined to say that two aren’t either. Then you say, well, I don’t think that three really are, there still aren’t many there.

Where do those two meet? Where is a heap a non-heap and a non-heap a heap. You tell me, and I’ll admit that this isn’t a paradox, that it has a logical solution and that you were right.

The problem is that you cannot do that. Try all you will, there’s no purely logical way to make that decision. It’s always going to be an arbitrary decision.

“…As far as “bashing” is concerned, I draw your attention to this: “many of your betters have tried and failed”. As my wife would say, “If you don’t want none, don’t start none”…”

As crazy as this might sound, I wasn’t bashing you. You’re ego is just a bit too inflated for its own good methinks. Are you telling me that you actually think that it is unfair and insulting of me to assume that people who have higher educations in logic and linguistics aren’t any more qualified to solve this than you. I’m sorry your lordship, so sorry to snap you back to reality. There are people that *are* better than you out there, just as there are probably many more people that are better than me. I can deal with it, why can’t you?

“…Why don’t you just admit that you are unable to defend the paradox, or refute an logical assertion that the paradox is false, most likely because the only things that you know are what you’ve read in Wikipedia or some other dubious source…”

Yet again, Wikipedia *has* to be dubious? Before you ride in here brandishing your sense of shatteringly-logic thinking, maybe you should learn what a logical fallacy is.

“…“I’m right because I took all my information off Wikipedia, thereby not having to think for myself”…”

No… I’m right because I know what we’re arguing about. You can’t concede that the problem is in fact a paradox, and then call me a moron. It just doesn’t work that way… More laughs at this bit, you just can’t stop shooting off your mouth can you. How about proving to me that Wikipedia is a bad source on the subject, then come back and use “Wikipedia” as an argument. Because that’s how you’re “beating” (ROFLS!!!) me in this argument at the moment. “You got your information from Wikipedia, therefore you must be wrong.” Yet again… nice

“…You say, quote: “I could also refute some of your assumptions and consequent conclusions on heaps, but I don’t have the time or the energy”. What you mean is that you don’t possess the intellect or ability…

Just to start:

“…To say that heap is not spatial or geometric begs a question: Is there such a thing as a heap of water?…”

I’ll say this real, real slow for you.

THIS… IS… A… LINGUISTIC… FALLACY… AS… WELL… AS… LOGICAL… ONE…

Do you understand? I can say “I’ve got a heap of water in my dam at the moment,” that’s a correct way to use the word “heap” in natural language. Can I really not have a heap of water? Really?

“…Or that the Wikipedia page that would do it for you is still under construction…”

Thrice, in one comment? I literally did laugh out loud when I read the third one. Some people might take what you say on face value “Wikipedia is bad” but I’m not a moron. The information I got is reliable, just because you don’t like it, doesn’t mean that it is wrong or incorrect.

“…Pretty much done with you.”

Time to save what little face you have left on LV? Good idea.