please stop feeding the troll..... --guy
On Wed, 25 Apr 2007, Shachar Shemesh wrote: > Date: Wed, 25 Apr 2007 16:52:11 +0300 > From: Shachar Shemesh <[EMAIL PROTECTED]> > To: Uri Even-Chen <[EMAIL PROTECTED]> > Cc: linux-il <[EMAIL PROTECTED]> > Subject: Re: [off topic] Some new articles I wrote about science > > Uri Even-Chen wrote: > > On 4/25/07, Shachar Shemesh <[EMAIL PROTECTED]> wrote: > >> "Completeness" and "Consistency" relate to the relationship between the > >> provability of an expression (syntax) and it's core truthfulness > >> (semantics, or meaning). Since I was not talking about those, these > >> hardly seem relevant. > >> > >> A theory cannot be either, because a theory is something that needs > >> proof. In other words, using any moderately reasonable tools of proof, a > >> theory can be correct and provable, correct and unprovable or incorrect > >> (we usually do not let go of consistency because that leads to absurds). > >> You will notice, however, that the theory is neither complete NOR > >> consistent. These are measures not meant for theorems, but for logics. > > > > I agree. > > > >> Even for logics, the statement above is incorrect. Zero order logic is > >> both consistent AND complete. > > > > I'm not sure what zero order logic is.How do you say "this sentence > > is not true" in zero order logic? > Zeroorder logic (propositional logic) has no relations. "this sentence > is false" is represented as "!A", but as it has no relations, there is > nothing that claims anything else about A beyond being false, which > means it sees nothing special about you claiming that A is this sentence. > > In other words, the logic is not granular enough to contain the paradox. > > Good example.You assume this is true for all numbers. > No, I do not. I can prove it's true for all number under the conditions > specified. > > Take any > > positive number, > Take any positive whole number. Read the premise correctly. > > multiply it be 2, add one, devide by 4, and you get > > either 1 or 3. > Yes, you do. > > Although I agree with you that it's true for any > > number we can represent by a real computer, I don't *think* it's > > infinitely true. > See, the person doing assumptions is you. > > I don't think integer numbers exist to infinity. > It's your right, of course, but unless you have something substantial to > back this up with, then I'm afraid any further discussion is based on > differing opinions on how mathematics work, and are therefor meaningless. > > Out of curiosity, if natural numbers don't continue to infinity, there > must be a maximal natural number, right? Assuming we call it "m", what > is the result of "m+1"? > > We > > can define numbers so big, that 2n and 2n+1 is almost the same. > Almost, yes. > > In > > any representation, whether in bits or in turing machines, if we > > devide both numbers in 4 we will not necessarily get two different > > results. > See, not "any representation". The fact that you, or your computer, > cannot solve a given problem does not impossible to solve make it. In > mathematics, the numbers exist whether you can represent them in a > finite space or not. > > If you have an infinite number of natural numbers, it is obvious you > will need an unbounded number of bits to represent an unknown natural > number. That does not make that number not exist. > > As a side note, a Turing machine has a semi-infinite storage, and would > therefor have no problem to represent any natural number precisely. > > I can't define such a specific number, since you will be > > able to contradict me. > That's where you prove yourself wrong. If a specific number you name > turnsout not to be the largest natural number, we have proven nothing. > If, however, we are in agreement that ANY specific number you will name > will not be maximal, or, in other words, that it is impossible for you > to name the maximal number, then THERE IS NO MAXIMAL NUMBER. > > It's an unknown unknown. Look what I wrote > > about the largest known prime number. > > > > http://www.speedy.net/uri/blog/?p=25 > I'm currently at a client's that employs content filtering. Your site is > labeled as "propoganda" by fortinet. Being as it is that > mirror.hamakor.org.il is labeled as "freeware download site", I wouldn't > necessarily take their categorization too personally. Still, I cannot > check your logic. > > It's not a decision function.Decision functions return either 0 or > > 1.I'm referring to the question whether there is any decision > > function which can be proved not to be in O(the size of the input). > I'm not sure, but as, like I said above, we do not speak the same > language, it seems impossible to debatethis in a meaningful way. Since > your language also don't sit well with that of the rest of the > mathematicians in the world, and seems not to be self consistent, then > I'm not sure I will try hard enough. > > Shachar > > -- > Shachar Shemesh > Lingnu Open Source Consulting ltd. > Have you backed up today's work? http://www.lingnu.com/backup.html > > > ================================================================= > To unsubscribe, send mail to [EMAIL PROTECTED] with > the word "unsubscribe" in the message body, e.g., run the command > echo unsubscribe | mail [EMAIL PROTECTED] > -- guy "For world domination - press 1, or dial 0, and please hold, for the creator." -- nob o. dy ================================================================= To unsubscribe, send mail to [EMAIL PROTECTED] with the word "unsubscribe" in the message body, e.g., run the command echo unsubscribe | mail [EMAIL PROTECTED]