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You CAN prove a negative! (rantish)
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Mr Jack
Assistant Professor Usergroup: Members Joined: Apr 07, 2003 Total Topics: 1 Total Posts: 490 |
 #1
I'm getting heartily sick of people trotting out the same old wives tale that 'you can't prove a negative'. It's total and utter rubbish. Let's have some quick examples: 1. Mathematics, there does not exist any real number x s.t. xx = -1. [INDENT]Proof: x can be either positive, negative or zero. if x = 0, xx = 0. x cannot be zero. if x>0, xx > 0. x cannot be positive. if x<0, let y = -x, then x = (-1)y. Hence xx = (-1)y(-1)y = (-1)(-1)yy = yy. y > 0, hence yy > 0. x cannot be negative. Therefore there exists no real number x s.t. xx = -1.[/INDENT] Look! We just proved a negative! Oh, well that's just a mathematical example, you can't prove stuff in the real world like that. Can't I? 2. Water is not fatal to humans. [indent]Proof: A. I am human. B. I have, and indeed are, drinking water. C. I am alive. Therefore water is not fatal to humans.[/indent] Still not convinced, OK, let's try an existance proof. 3. Santa Claus does not exist [indent]Proof: If Santa Claus exists we would expect all children who live in houses with Chimney's to have presents delivered on Christmas morning. This does not happen, therfore there is no Santa Claus. [/indent] |
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great_brain
Professor Usergroup: Members Joined: Jul 08, 2003 Location: Atlanta Total Topics: 15 Total Posts: 555 |
#2
Unfortunately your assertion is horribly oversimplified and your proofs actually don't work. In all of your examples all you did was create a specific scenario with manufactured criteria to "prove" your assertion. You did not prove a negative in any of these cases - all you proved was that you could make a statement and then manipulate a series of parameters that would prove your statement Let's take a look: Water is not fatal to humans: It is if you are drowning, it is if there is toxic waste in it and you get cancer, it is if there is cyanide in it and you are poisoned. The only way to prove this is for there never to have been a single incident where water was involved in the death of a human - which you can't do. Santa Claus does not exist: This doesn't work either since you cannot know the holiday reality of every person on the planet or their chimney status. Also perhaps all the children have been naughty for hundreds of years and no one deserved any presents. However in this case the burden of proof is on the person who claims Santa Claus exists in the first place so this is not a valid assertion for proof - since to even attempt to prove the negative in this case you would have to have an established methodology to purport the existence of Santa for you to then disprove him. Mathematics, there does not exist any real number x s.t. xx = -1. This is just silly. letters in equations represent unknown variables and as such have no value in their own right except that which is assigned to them. Once you assign a value to the letter it then becomes a number and you can answer the question. However this does not prove a negative either. Alas, it is not an old wives tale. Please try again. |
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Mr Jack
Assistant Professor Usergroup: Members Joined: Apr 07, 2003 Total Topics: 1 Total Posts: 490 |
#3
Mathematics, there does not exist any real number x s.t. xx = -1. This is just silly. letters in equations represent unknown variables and as such have no value in their own right except that which is assigned to them. Once you assign a value to the letter it then becomes a number and you can answer the question. However this does not prove a negative either. *sigh*. Either you being facetious or you're not up on mathematical concepts. I have proved that for ANY real number x, xx is positive. Since this is true for any x, it is true for all x's. So there is NO number x s.t. xx = -1. That IS proving a negative. Water is not fatal to humans: It is if you are drowning, it is if there is toxic waste in it and you get cancer, it is if there is cyanide in it and you are poisoned. No. Water is not the fatal agent in any of your examples. The only way to prove this is for there never to have been a single incident where water was involved in the death of a human - which you can't do. Nonsense. I don't have to prove any such thing. If water is fatal to humans then if I drink water I will die. That's what fatal means. Since everyone drinks water, and no-one dies from it, we prove water is not fatal to humans. This doesn't work either since you cannot know the holiday reality of every person on the planet or their chimney status. I'll admit I should perhaps have defined Satan Claus better in my original post, but I didn't wish to get into pedantry. I don't need to know anything of the sort. Santa Claus delivers presents to all children on Christmas night. Christmas night is the night between December 24th and December 25th. He delivers the presents by coming down the chimney and depositing them for collection by the children when they awake. This does not happen. Therefore Santa Claus doesn't exist. Now, you can posit a 'Santa Claus' who turns up and gives Marshmallows to Muslims living in Caravans on October 8th every third year. And, sure, I haven't proved he doesn't exist but I have proved the Santa Claus I was talking about doesn't exist. Now, you can indeed come up with concepts I can't prove don't exist, but that doesn't mean you can't prove a negative only that there are some negatives you can't prove. |
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great_brain
Professor Usergroup: Members Joined: Jul 08, 2003 Location: Atlanta Total Topics: 15 Total Posts: 555 |
#4
Mr Jack wrote: *sigh*. Either you being facetious or you're not up on mathematical concepts. I have proved that for ANY real number x, xx is positive. Since this is true for any x, it is true for all x's. So there is NO number x s.t. xx = -1. That IS proving a negative. Again, you can't prove xx= -1 without assigning value to x (even if you are only saying positive, negaitve or zero) - all of these give x value and it ceases to be an unknown variable. Also the idea of "you can't prove a negative" typically doesn't refer to mathematics anyway No. Water is not the fatal agent in any of your examples. How do you figure water is not the fatal agent in drowning? I'll give you that the other two are argumentative due to the contaminants, but explain to me how water is not the fatal agent in drowning. Nonsense. I don't have to prove any such thing. If water is fatal to humans then if I drink water I will die. That's what fatal means. Since everyone drinks water, and no-one dies from it, we prove water is not fatal to humans. Again, this is massively oversimplified and you are manipulating the proof by limiting it to drinking water. However people die every day from drinking water in third world countries in addition to the cyanide and toxic waste examples. Theoretically you could make the statement "consuming appropriate amounts of purified drinking water is not fatal to humans" I don't need to know anything of the sort. Santa Claus delivers presents to all children on Christmas night. Christmas night is the night between December 24th and December 25th. He delivers the presents by coming down the chimney and depositing them for collection by the children when they awake. Prove it. Besides Santa Claus DOES exist as a fictional/mythological character, and you cannot disprove him with your current assertion in this context. Personally I am not trying to say that there is not a single situation where where a negative assertion and cannot be proved, but they are certainly the vast minority and require significant special circumstances and minute parameters to exist - which certainly doesn't create any kind of axiom. However, I also don't think you have sucessfully proved a negative in any of your examples so far. |
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Temulence
Aspirant Usergroup: Members Joined: Apr 02, 2003 Location: Sacramento Total Topics: 0 Total Posts: 20 |
#5
great_brain, No offense but your stance could be easily revearsed to say that you can't prove a positive either (leading to the absurd conclusion that you can't prove anything). You can't prove X*X=1 you also assume and limit values for X. I could prove that "there are no solutions to y=x^2 in the intervals (-oo,0) and (0, oo)", doesn't that count as proving a negative? |
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great_brain
Professor Usergroup: Members Joined: Jul 08, 2003 Location: Atlanta Total Topics: 15 Total Posts: 555 |
#6
Temulence wrote: great_brain, No offense but your stance could be easily revearsed to say that you can't prove a positive either (leading to the absurd conclusion that you can't prove anything). You can't prove X*X=1 you also assume and limit values for X. I could prove that "there are no solutions to y=x^2 in the intervals (-oo,0) and (0, oo)", doesn't that count as proving a negative? You could say that you can't prove or disprove anything that does not have defined values, which is what the whole "this statement is false" thread was all about. So in your examples X*X=1 and y=x^2 both of these require more information first, so to me neither represent valid examples for proof of any kind so neither would apply here. If you assign values to the variable in both cases then they can be easily proved or disproved based on those values. |
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darkcrow
Tenured Poster  Usergroup: Sponsors Joined: Feb 08, 2003 Location: San Diego Total Topics: 97 Total Posts: 4256 |
#7
I'm getting heartily sick of people trotting out the same old wives tale that 'you can't prove a negative'. It's total and utter rubbish. I agree----------There is no 100 ft. tall Pink Elephant hovering just above the Empire State building in New York City, N.Y at this minute. "To the success of our hopeless task." |
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Fire
Aspirant Usergroup: Members Joined: Aug 05, 2003 Location: in your eye Total Topics: 3 Total Posts: 27 |
#8
Mr Jack wrote: I'm getting heartily sick of people trotting out the same old wives tale that 'you can't prove a negative'. It's total and utter rubbish. I wasn't aware that a "negative" requires proof. "The Earth is not flat." This statement is a conclusion that presupposes other statements / arguments which are "positive" i.e. "The Earth has a circumference of XYZ north-south and circumference of ABC east-west." Now this statement is a report or measurement that also presupposes another statement: "In measuring the Earth's circumference twice along perpendicular axes whereby the starting point of each line-length is also it's terminal point." And on and on. Each statement is built up by prior statements all of which are embedded in web or network of other "positive" statements. "The Earth is not flat" is simply an inversion of "The Earth is round." Don't get hung up on semantics, Mr Jack: "negatives" or negations of a concept should be converted into a "positive" statement so that you can see what would count as proof and then how to proceed proving the statement. You cannot reason a man out of a position he did not reach through reason. |
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Temulence
Aspirant Usergroup: Members Joined: Apr 02, 2003 Location: Sacramento Total Topics: 0 Total Posts: 20 |
#9
You could say that you can't prove or disprove anything that does not have defined values, which is what the whole "this statement is false" thread was all about. Oh, ok, I am up to date (I think). Then why bother with the word "prove" in those situations? The word simply has no meaning or use in those contexts. I don't see a debate - I see a misapropriation of terms. |
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great_brain
Professor Usergroup: Members Joined: Jul 08, 2003 Location: Atlanta Total Topics: 15 Total Posts: 555 |
#10
Temulence wrote: Oh, ok, I am up to date (I think). Then why bother with the word "prove" in those situations? The word simply has no meaning or use in those contexts. I don't see a debate - I see a misapropriation of terms. I guess that's the point, unless I am misunderstanding you. Various folks have tried to use undefined assertions and then proved or disporved them to fit the debate - I'm saying you can't do that due to the undefined nature of it, and that is what Jack was doing to a certain degree. So in doing so, there really isn't a debate. In order to have the debate, I imagine we would need a mutually agreed upon premise to start from. But the initial question here was about "proving" negatives - so that is the contention. |
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