Chickens and spatulas are also incapable of learning calculus. There is quite a long list of things incapable of learning calculus. A million retarded people tapping away at a million typewriters for an unlimited amount of time would eventually write Newtons Principia. That's a funny mental picture but I digress; it's something I do sometimes; yep, I'm a digressor, or is it digresser? Anyway, would a retarded person come closer to learning calculus than a dog? I suppose dogs have some language skills but I think even retarded humans have them beat on that front. Can a computer learn calculus or is being programmed different from learning? Would dogs have computers beat on this front? How about a robot dog like the one that belongs to Doctor Who. Or should that be: "Doctor Whom"? It is the objective case so I think it should be "Whom" but then "Doctor Who" isn't really his name it's just the name of the show; he's just the "the doctor" or rather "The Doctor". I think I use the semicolon too much. I have digressed. I don't see how equating retarded-human-calculus-learning-abilities and canine-calculus-learning-abilities achieves anything beyond the faint suggestion that retarded humans are more like dogs than they are like humans who can learn calculus. Was Rainman retarded? I bet he knew calculus or he could learn it or maybe it would just make him mad and he would start screaming about Wapner and K-mart and banging his head against the wall. That movie's old. I'm dating myself. However, I'm not putting out unless I buy myself dinner. I liked that song at the beginning of Rainman: "Iko Iko". The lyrics are wicked scary like some voodoo hex or something.

I'm not going to pretend I know what "Pr(P)>0" means, but I suppose you're speaking of a possible world example. The fact is, not everything is possible, and a retarded human will not produce brilliant thoughts simply based on the amount of time he/she thinks. It is a matter of ability, not time.

So, if I understand you correctly (which I'm not sure I do because you're not speaking plain English), I disagree.

"Pr(P)" just means the probability of P. ">" means above and "0" means zero. :p

So I was just talking about something that has a probability of happening that is more than zero. All such things will happen given infinite time. Is it possible for a toddler to type a sentence from your chosen work by accident? Yes. It is also more than logically possible, it has a non-zero probability. Is it likewise for all the following sentences? Yes. Is it also a nonzero probability that the toddler will type them in a row? Yes but extremely unlikely. However given infinite time all such unlikely events will happen.

I'm not going to pretend I know what "Pr(P)>0" means, but I suppose you're speaking of a possible world example. The fact is, not everything is possible, and a retarded human will not produce brilliant thoughts simply based on the amount of time he/she thinks. It is a matter of ability, not time.

So, if I understand you correctly (which I'm not sure I do because you're not speaking plain English), I disagree.

Brainman sees numbers and relations in shapes and colours and "nice feelings" . He learns languages in a few days by the way the words sound and feel. He also says most languages have a little sound for the word "little" - sound of words may have some relation to the meaning of the words and he recognizes them that way too.

But we're not talking about a toddler doing a stupid action which could cause uncanny results. We're talking about a toddler actually learning and understanding something substantial. But I'd like to steer away from toddler, and go back to very mentally retarded individual (as I am aware that some toddlers have been able to understand substantial material).

A million retarded people tapping away at a million typewriters for an unlimited amount of time would eventually write Newtons Principia.

I wonder if you think a million toddlers tapping away at a million typewriters would eventually write Newton's Principia, too.

The million very retarded people will not be able to learn a theoretical physics equation, for instance. No matter the amount of time given. An infinite amount of time does not mean that what is impossible becomes possible.

But I'm not sure how you would calculate which things are more than zero probability-wise. All things which are not contradictions, ie. all things which are logically possible, are higher than zero probability-wise?

The answer is "yes".

Wrong. You are confusing stupidity with ignorance. If people don't know something, then they are ignorant of that thing. But that is not stupidity. Look up both words, "ignorance" and "stupidity" in the dictionary. You are ignorant of the distinction between them, but that does not mean you are stupid (unless, of course, you cannot see the difference, or learn the difference between them). It makes no sense to say you are stupid of X. It isn't even English. But, of course, it makes sense to say that you are ignorant of X, and that is English. You cannot be "stupid of" something. But you can be "ignorant of" something.

Oh, I see. I misrepresented my position. I wasn't clear, my apologies. What I meant was that the toddlers wouldn't understand and come to sophisticated conclusions; not that, through random and childish action, they wouldn't eventually write Newton's Principia.

I should have phrased that differently, my bad.

Emil,
"Some people think that that something is logically possible logically implies that it has a nonzero chance of happening [◊P⇒Pr(P)>0] but that's not true."

Of course it is true.

Pr(p)=0 <=> ~<>P.
~(Pr(p)=0) <=> <>p.
therefore,
<>p => ~(Pr(p)=0).

But if we then accept that for all points, it is impossible that the arrow hits there we get a contradiction

Wait, why are we making this assumption? This is the only part I don't understand, leading to this premise:

4 is not an assumption. It is an inference. Read the argument again. It follows from 1, 3 by MP. I thought the inference signifier "thus" made that clear. Perhaps you skipped that word.

I never said premise 4 was an assumption. And it's odd you came to the conclusion I didn't know premise 4 followed from 1 and 3 by MP, since you explicitly wrote that. Huh, that's odd. I guess you think I can't read.

Wait, why are we making this assumption? This is the only part I don't understand, leading to this premise:

Read the first part of what I quoted above. You started as stating, "If we accept...", which I thought was synonymous with "If we assume...". I don't understand why you accept what you accept in the English version of the argument.

I don't think most people are stupid. I also don't think that most people think that most people are stupid.

---------- Post added 01-27-2010 at 07:13 AM ----------
Supposing that you really mean that you think most people are not stupid, then you're wrong. And if similarly you mean that most people think that most people are not stupid, then you are probably right, but they are wrong too.

Even stupid people can see that most people are stupid, but most importantly they should recognize their own stupidity. But then again studies/a study have shown that smart people tend to underrate themselves and stupid people overrate themselves. That is interesting.

What I said was that I don't think most people are stupid. Which is to say that I don't agree with the claim that most people are stupid.

And I'm correct.