Laure

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About Laure

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    Laure Chipman

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  1. Thom, that's a lot of words, there. (So here are a lot of words back at ya!) I still don't see your point with the M statements. If I paraphrase them to be more exact, they all say "if H was true, I just added (or will add) a dollar". That statement is always true if we accept that the person will do what he says. So, the 2nd line in the truth table, "H was true but I didn't add a dollar", does not occur. So, I don't see a problem. Unless I'm still missing your point. I re-read what you wrote about the "paradox of entailment". I don't think that modern logicians would conclude "the U.S
  2. Thom, I still don't see what you're getting at with the "M" statements, but I think I understand your problem with statements such as HP4. Please see the thread I started, "Question on Conditionalizing", and visit the Wikipedia links mentioned there. I think you're a fan of "strict implication", which means that we look at the meaning of the P's and Q's and ask ourself if the P being true would in any way cause the Q to be true, and if not, we consider "P --> Q" to be false, even though the normal symbolic logic we learn in school says that it evaluates to true if P is false. I don't see
  3. A basic question, Roger. Do you agree that for all x, x+0=x? If not, how do you do the algebraic simplification step that gets us from: x + 0 = y + 1 to x = y + 1? If you agree that we can "drop the '+ 0'", how is that in any way different from "substituting 'x' in place of 'x + 0'"? Like my hero Spock says, "A difference that makes no difference is no difference." (He probably got it from some philosopher but I dunno... )
  4. Come on, Merlin, pay attention, fer chrissake! Laure (whom you were defending) was trying to show how ~MY PREMISES~ lead to a contradiction, and I was showing how they do not, that any attempt to use the distribute law gambit ended up with OTHER expressions that were undefined BY MY PREMISES. In other words, she AND YOU have failed to show a contradiction in my argument so far. "Fatally flawed" my pasty, white ass. You people are better than this, aren't you? REB I was trying to show the contradiction in your saying that 0*1=0 but 1*0 is "undefined". I think what I showed was that for your s
  5. Roger, of course you don't use "0" to "do" things, any more than you use "5" to "do" things. "0" and "5" are symbols; they are nouns. The operators (+,-,x,/) are the verbs; they are what "do" things. I say again, show me your equality principles and postulates.
  6. I showed you my equality principles and postulates. Show me yours, Roger. Let's nail down the specifics of your system, and then we will see whether it is logically inconsistent or just consistent and useless!
  7. Well,... yeah! The whole idea of mathematics is to abstract away the units, or the referents in reality, so that we can just manipulate the symbols. That's why we can say 2+2=4 and it doesn't matter 2 of what. We don't have to stop and think, "OK, if I take 2 apples and add 2 apples, I have 4 apples. But, what if I had 2 oranges and add 2 oranges?? Gee, what could the answer be?"
  8. Roger, "for all x, y, z, (x+y)+z = (x+z)+y" is a postulate in my math. "For all x, y, x+y = y+x" is another postulate. So, (1-1) + (1-1) = (1+(1-1)) -1 = ((1-1)+1)-1 = 0+1-1 = 1-1 = 0. Let's keep it real simple. Roger says x+0 is incalculable. Roger, would you agree that if you see "x+0" in an equation, that you can simply substitute "x", since the "+0" does nothing? Well, when we say that "x+0=x", we are saying precisely that "we can substitute 'x' for 'x+0'". That is what it MEANS. "x+0" is synonymous with "x". Another example, this idea that 0*1 is 0 but 1*0 is undefined. Let's go ba
  9. Interesting. The "strict implication" article goes to the heart of Thom's "Iffy" thread. I think what Thom is getting at is that "strict implication" is the way we intuitively interpret "if" in natural language. Taking an example from the article, "If Bill Gates went to medical school, then Elvis is still alive". A true statement, but intuitively false, since there's nothing about Bill Gates going to medical school that would cause Elvis to still be alive. Clicking around in Wikipedia, I found this article: Paradoxes of Material Implication. (It has a few "broken" formulas, unfortunately
  10. Thanks for the quick reply! So, given that the moon is a satellite, "if the moon is not a satellite, then the moon is a satellite" is just a funny little tautology and not a paradox.
  11. I have a question for the logic experts on the forum. (I'm not an expert, but I had a symbolic logic course in college and was the top student, and I had the benefit of a high school math curriculum that emphasized proofs. As a programmer, I use boolean logic just about every day.) In looking back at my high school math book, it describes Modus Ponens, Modus Tollens, and all that good stuff. It describes "Conditionalization": a conditional sentence follows from its consequent. So, if Q is true, P-->Q is true for any old P. 1) Is my interpretation correct, or does P have to be something
  12. Question: what is the square of 0? It is 0*0. And what is 0*0 ? It is 0. In fact 0^n, for n > 0 is 0. Proof: 0^1 = 0 so the thing is true for n = 1. Suppose 0^n = 0. Then 0^(n+1) = (0^n)*(0^1) = 0*0 = 0 The induction completes the proof. For all n >= 1 0^n = 0 Ba'al Chatzaf 0 does not have a square. 0*0 is undefined. 0^n is NOT 0*0 n times. It is 1 * n factors of zero. There is no number that corresponds to n factors of zero. 0*0 n times is just as undefined as 0*0 is. So 0^n = 1. No induction necessary here. REB *sigh* Roger, now you're saying that 0*0 is undefined, but 0^
  13. Thom, I'm sorry, but I think there's something I don't understand. I don't know the point you are trying to make about these "M" statements. You say, "MI1. Add dollar now if HP1." I interpret that as "if HP1 is true, then add a dollar". Is that correct? That is an imperative statement, not a material implication. If you want to phrase it as a material implication, you could say, "if HP1 was true then a dollar was just added", and you assume that your person with the money is "obedient", then the "M" statements are always true, because it's always the case that either a dollar was added o
  14. Oh, that's interesting... so 0^1 = 0^2 = 1 or in other words, 0 = 1 and 0 * 0 = 1 ? That is Objectivist mathematics? Bingo! Roger, you have just stated that 0 = 1. You can certainly come up with your own mathematical system where 0 = 1, but I thought you liked math to be useful in practical applications!
  15. Roger, the simplest way to explain why 0^0 should be thought of as undefined is to note that for nonzero n, 0^n = 0, and n^0 = 1. You'll accept that, right? So, what happens at zero? Is 0^0 = 0 or is 0^0 = 1? It depends which formula you use. Since it can't be both zero and one, it must be undefined. Also, you've got a contradiction in your post 106. First you say, Then you say, Here, you are taking (1 * (0^n)) / (1 * (0^n)) and you say 0^n is "nothing", i.e. 0. So, you are here assuming that 1 * 0 = 1, when above, you said that x * 0 = 0. *edit* Also, defining 0/0 as 1, as you want t