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Author Topic:   Question.... (Processes of Logic)
crashfrog
Member (Idle past 1721 days)
Posts: 19762
From: Silver Spring, MD
Joined: 03-20-2003


Message 16 of 210 (39159)
05-06-2003 10:52 PM
Reply to: Message 7 by mike the wiz
05-06-2003 6:09 PM


Re: Question...
are you suggesting evolution has a mind of its own , and why would it equip the mind with conclusions which are scarce or absent what purpose would that surve in evolution
Of course I'm not suggesting that. My use of the word "equip" should not be taken to imply a guiding intelligence. It's just that our language has yet to catch up to the idea of function without design, so sometime it's hard to talk about functions without the distant implicature of a designing force.
The reason that it's a survival advantage to make descisions based on limited information is because limited information is all the information you can have. If you waited for total information on ny subject you'd stand around doing nothing until something killed you.
Did you really need me to spell that out for you? Seems obvious to me.

This message is a reply to:
 Message 7 by mike the wiz, posted 05-06-2003 6:09 PM mike the wiz has not replied

crashfrog
Member (Idle past 1721 days)
Posts: 19762
From: Silver Spring, MD
Joined: 03-20-2003


Message 17 of 210 (39160)
05-06-2003 10:59 PM
Reply to: Message 14 by mike the wiz
05-06-2003 8:05 PM


Re: Question...
well thats the difference isn't it, you seek evidence and i dont.
And exactly what is the proof or evidence against heaven and hell, can you disprove these ?
Like the man just said, and like it's been repeated a hundred times, and like anyone who really cared about what logical reasoning can and can't do should know: you can't prove a negative!
We're not the ones saying a heaven and a hell exist. No one's ever been able to find them. There's no evidence that they exist. Therefore it's not our job to prove that they don't exist. Otherwise we'd have to prove the non-existence of every ridiculous thing anyone comes up with.
You're the one making the positive claim: Heaven and/or Hell exist. So prove it. That's your job because you made the claim.
And for the record, I never tried to impose my belief on you. If you want to believe in heaven and hell, fine. I personally don't because there's no evidence that they exist. If you can live with a belief in something for which no evidence exists, that's fine. I can't live like that.

This message is a reply to:
 Message 14 by mike the wiz, posted 05-06-2003 8:05 PM mike the wiz has not replied

Replies to this message:
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Dan Carroll
Inactive Member


Message 18 of 210 (39167)
05-06-2003 11:42 PM
Reply to: Message 9 by mike the wiz
05-06-2003 6:50 PM


Re: Question...
quote:
what about near death experiences?
As the brain starts blinking out, it begins seeing weird things? What's so mysterious about that? Hold your breath long enough, your vision will go funny.
Actually, the most fun theory I've heard of NDEs in a while is that it's the brain suddenly remembering the birth canal. Long tunnel, white light at the end, a strange sensation that your mother is there...
Mind you, there's nothing to back that one up either. It's just a fun little notion.
quote:
also , is not the life more than the body
Not as far as I've seen. I just posted my ideas on mind, body, and soul in the "SIN" thread, and I don't want to be that pretentious guy who posts the same thing in umptyzillion threads.
------------------
-----------
Dan Carroll

This message is a reply to:
 Message 9 by mike the wiz, posted 05-06-2003 6:50 PM mike the wiz has not replied

Replies to this message:
 Message 27 by compmage, posted 05-07-2003 3:52 AM Dan Carroll has not replied

Rrhain
Member (Idle past 261 days)
Posts: 6351
From: San Diego, CA, USA
Joined: 05-03-2003


Message 19 of 210 (39179)
05-07-2003 1:01 AM
Reply to: Message 17 by crashfrog
05-06-2003 10:59 PM


Re: Question...
Since when did it become impossible to prove a negative?
I've been doing it for quite some time. It's called "indirect proof." You start with an assumption, lead yourself to a contradiction, and thus you prove the negation of the assumption.
For example, let's prove there is no largest prime number.
Assume there is a largest prime number, p.
Thus, we can produce a list of all primes:
p1, p2, ... , pn-1, pn
where pn is the largest prime.
Now, construct q as follows:
q = p1 * p2 * ... * pn-1 * pn + 1
So the question then becomes, is q prime?
Well, we have a list of all the primes but we find that none of them divide q. Therefore, we are left with one of two possibilities:
1) A number between p and q is prime
2) q is prime
In both cases, there is a number that is prime that we haven't taken account of larger than what we thought was the largest prime.
Well, that's a contradiction.
Therefore, the assumption is not true: There is no largest prime.
Notice, the negative that was just proven isn't the "no" in "no largest prime." It was the negation of the assumption: There is a largest prime.
Proving a negative is quite simple to do. However, it requires well-defined objects behaving in well-defined ways. If you deviate from that, such as the methods of science which rely upon observation rather than definition, then things become more difficult.
But, this doesn't mean it cannot happen. Take, for example, the following biology experiment:
Take a single K-type E. coli bacterium. Grow it to a lawn and infect the lawn with T4 phage. The vast majority of the lawn will die though there will be a colony or two surviving. They have evolved to be immune to T4 phage and are now called K/4. But if we take one of these K/4 bacteria and let it reproduce to a lawn and then infect that lawn with T4 phage, we see plaques forming.
So the question is, which one mutated?
A little thought shows that it can not be the bacteria that mutated. If it were the bacteria that mutated, then they would be surrounded by K/4 bacteria that are immune to T4 phage. Thus, as soon as any of these K-type bacteria died, they'd be replaced with K/4 bacteria and we'd never see a plaque.
But since we do see a plaque, we necessarily conclude that it is not the bacteria that mutated but rather the phage.
Bingo! We just proved a negative. Once again, we had well-defined objects behaving in well-defined ways, but it does happen in the real world every now and again.
------------------
Rrhain
WWJD? JWRTFM!

This message is a reply to:
 Message 17 by crashfrog, posted 05-06-2003 10:59 PM crashfrog has not replied

Replies to this message:
 Message 20 by John, posted 05-07-2003 1:50 AM Rrhain has replied

John
Inactive Member


Message 20 of 210 (39183)
05-07-2003 1:50 AM
Reply to: Message 19 by Rrhain
05-07-2003 1:01 AM


Re: Question...
quote:
I've been doing it for quite some time. It's called "indirect proof."
But that isn't what he is talking about. In fact, what you've done isn't really proving a negative. It is a round about way of proving a positive, or of proving something about a positive-- that positive being the number you choose to test. Throughout the operation you have values, data, and other such things with which to work. What is meant by 'proving a negative' is different. Consider: Someone tells you that a giant lives in the mountains, but this person offers no proof but instead challenges you to disprove the existence of the giant. If the giant does exist then he will leave evidence and can be proven to exist. This is proving a positive. The giant could also be proven to be something other than a giant-- like a hoax or the result of the consumption of a peculiar fungus. This also is proving a positive. You have proven that something other than a giant can account for the alleged sighting of a giant. But you still haven't proven the non-existnce of the giant, but only that you have no evidence for the giant and do have evidence for other explanations. A believer in the giant could always say 'that was a hoax but the giant is real. Where is the proof that he isn't?' Here is the problem. If the giant does not exist there is no evidence, and there never will be. If the giant does not exist, he leaves no trace. There is no evidence to examine, and no information with which to construct a proof or a disproof. You can't prove, or disprove, a negative, because there isn't any evidence with which to work. So we are stuck with proving, or disproving, positives.
------------------
No webpage found at provided URL: www.hells-handmaiden.com

This message is a reply to:
 Message 19 by Rrhain, posted 05-07-2003 1:01 AM Rrhain has replied

Replies to this message:
 Message 21 by Mister Pamboli, posted 05-07-2003 2:26 AM John has not replied
 Message 23 by Rrhain, posted 05-07-2003 3:26 AM John has replied

Mister Pamboli
Member (Idle past 7831 days)
Posts: 634
From: Washington, USA
Joined: 12-10-2001


Message 21 of 210 (39189)
05-07-2003 2:26 AM
Reply to: Message 20 by John
05-07-2003 1:50 AM


Re: Question...
quote:
But that isn't what he is talking about. In fact, what you've done isn't really proving a negative.
I agree in a more restircted sense.
Firstly, it is reasonably clear, I think, that crashfrog has in mind (though not explicitly, so I may be wrong) not just a negative, but more especially a naegative existenial proposition. Although not explicit in the statement you can't prove a negative, it is clarified in crashfrog's examples.
Secondly, RhRain did quite elegantly prove a negative existential proposition. But Rh did so in a very special case indeed - a case where all possible observations can be canonically defined without actual definitions. I think Rh is aware of this special case, and correctly indicates this.
So is it true that one cannot prove a negative existential proposition? Well, if it were, it would lead us to a delightful paradox ... "There exist no provable negative existential propositions" is itself a negative existenial proposition which, if true would mean ...
Well, you see where that is going!
Cut the Gordian knot and get back to empiricism!
Rh does not prove a negative existential proposition in the second example. I guess you did not intend to, did you?

This message is a reply to:
 Message 20 by John, posted 05-07-2003 1:50 AM John has not replied

Replies to this message:
 Message 22 by crashfrog, posted 05-07-2003 3:01 AM Mister Pamboli has not replied
 Message 24 by Rrhain, posted 05-07-2003 3:39 AM Mister Pamboli has replied

crashfrog
Member (Idle past 1721 days)
Posts: 19762
From: Silver Spring, MD
Joined: 03-20-2003


Message 22 of 210 (39192)
05-07-2003 3:01 AM
Reply to: Message 21 by Mister Pamboli
05-07-2003 2:26 AM


Re: Question...
You're probably right, Mr. P. I should have qualified that statement a little farther.
But I think my point was clear, that if the onus was on us to prove that something non-obvious doesn't exist, then we'd have to do so for every ridiculous thing that could be imagined.

This message is a reply to:
 Message 21 by Mister Pamboli, posted 05-07-2003 2:26 AM Mister Pamboli has not replied

Rrhain
Member (Idle past 261 days)
Posts: 6351
From: San Diego, CA, USA
Joined: 05-03-2003


Message 23 of 210 (39195)
05-07-2003 3:26 AM
Reply to: Message 20 by John
05-07-2003 1:50 AM


Re: Question...
John responds to me:
quote:
quote:
I've been doing it for quite some time. It's called "indirect proof."
But that isn't what he is talking about. In fact, what you've done isn't really proving a negative. It is a round about way of proving a positive, or of proving something about a positive-- that positive being the number you choose to test.
No, it is, indeed, proving a negative. There is no largest prime. The result is not that the individual number before us isn't the largest prime (though that, too, would be proving a negative) but that there is no prime anywhere no matter how you try to construct one that is the largest.
The problem with "proving a negative" is not that it cannot be done but that the techniques available to do so require the ability to look at every single possibility.
That isn't always possible.
I can prove the negative that something doesn't exist in a particular room. Depending upon the specifics, it can be because the object in question is too large to fit in the room or that the object is definitively somewhere else or by doing an exhaustive search of all the objects in the room and determining that none of them are the object in question.
The problem with something like proving god doesn't exist is that the definition of "god" is not very specific and the arena which needs to be examined is too large for a brute force method such as an exhaustive search as well as being too vaguely defined to be amenable to abstract methods.
It isn't that you can't prove a negative. You can. It's that many things aren't amenable to the techniques involved. On the flip side, not all positives are amenable to proof, either.
quote:
Throughout the operation you have values, data, and other such things with which to work.
Didn't I say that? I'm sure I did. Yep...right here:
"However, it requires well-defined objects behaving in well-defined ways. If you deviate from that, such as the methods of science which rely upon observation rather than definition, then things become more difficult."
The fact that you have data to work with doesn't mean you aren't proving a negative. The fact that there is a positive means there is a negative, too. By the fact that an object is X, that means it is not Y.
quote:
What is meant by 'proving a negative' is different. Consider: Someone tells you that a giant lives in the mountains, but this person offers no proof but instead challenges you to disprove the existence of the giant.
No, it's still the same thing. It's just that the scenarios are dissimilar. Someone tells you that there is a largest prime but this person offers no proof but instead challenges you to disprove the existence of the largest prime.
Quite simple: Assume there is a largest prime, lead yourself to a contradiction, and thus logically conclude the negative: There is no largest prime.
The only difference between your situation and mine is that my scenario has well-defined objects behaving in well-defined ways. If you refuse to define what a "giant" is and how it behaves, not only does it become impossible to prove that there is no giant, but also it becomes impossible to prove that there is one.
Until we can get a concrete definition, one cannot prove anything.
Take, for example, the proof of the four-color theorem. For those who don't know, the four-color theorem states that any map drawn on a contiguous plane surface (that is...a plain sheet of paper) can be colored using only four colors such that no two areas that share an edge have the same color. You might be able to get away with fewer, but you don't need more than four.
Well, how do we prove that? For the longest time, we could handily show that for any map anybody had ever drawn, it could be colored using at most four colors. It's because we could come up with a concrete definition (this particular map), we could come up with an actual result (yes, it can be colored using no more than four colors). But, we couldn't come up with any progress on the larger question because we couldn't define what a "map" was in any concrete method.
Eventually, through a lot of work, a method was developed that could generate every possible map you could draw. It was noticed that some maps are equivalent. For example, suppose you have a map that consists of a circle within a circle such that the two don't touch. Well, that is the same as a map that consists of just a circle: The color of the inner circle can be anything because it is completely surrounded by a single color. Therefore, we can remove that inner circle completely and not affect the number of colors needed to color the rest of the map.
The technique allows us to get a much more concrete definition of "map." By using the greater comprehension, we can generate an exhaustive list of all possible maps. We can then go through every single one and determine if it can be colored using only four (this is where the computer came in which caused the controversy...did anybody bother to check if the computer did it right? Yes, they did.) If it turns out that the entire set of all possible maps can be colored using only four colors, then we have proven that there is no map that requires five.
By proving the positive, each map can be colored using four colors, we also prove a negative, each map requires no more than four colors to color.
quote:
If the giant does exist then he will leave evidence and can be proven to exist. This is proving a positive.
Indeed. But if the definition of "giant" requires a necessary result that does not appear, then the giant can be proven not to exist. This is proving a negative.
In fact, that's exactly what science does: Prove negatives. Nothing in science can ever be proven true. What is done all the time, however, is prove things not to be true.
Newtonian mechanics, for example, necessarily requires a linear universe. The universe, however, is relative and not linear, therefore we prove Newtonian mechanics to be not true. Oh, it's very close to being true for many instances, but there is always an error between what the theory claims and what we actually observe. It may require extremely sensitive equipment to actually measure that discrepancy, but that doesn't mean the discrepancy isn't there.
quote:
The giant could also be proven to be something other than a giant-- like a hoax or the result of the consumption of a peculiar fungus. This also is proving a positive.
Actually, it's also proving a negative: The evidence is not a giant. If a giant and only a giant results in X and what we have before us is Y, then we prove that it is not from a giant.
But again, it requires well-defined objects behaving in well-defined ways. When things become fuzzy, the ability to prove anything, positive or negative, becomes much more difficult.
quote:
You have proven that something other than a giant can account for the alleged sighting of a giant. But you still haven't proven the non-existnce of the giant, but only that you have no evidence for the giant and do have evidence for other explanations.
Only if the definition of "giant" is so vague as to be incapable of providing a definitive result.
What, precisely, is a "giant"? How does it behave? What actions can be ascribed to a giant? What actions must be excluded from the definition? Are there any that are unique to a giant?
Until these questions are answered, not only can we not prove the non-existence of the giant, we also can't prove the existence of the giant. We are left with an ill-formed premise behaving in an ill-formed way. No wonder we are at a loss to make any sort of acceptable statement.
quote:
A believer in the giant could always say 'that was a hoax but the giant is real.
That's where the logical part of burden of proof comes along. The claimant is the one that needs to show evidence.
And yes, that means those that say there is no giant. But, since this started with the person making the claim that there is a giant, it is his burden of proof to show that it is there. If my response is that there is no giant there, then it is my burden to justify my claim.
I can easily do that by defining what a "giant" is and then showing that the mountains do not contain any evidence that is necessarily required for there to be a giant.
If the other person then claims that my definition of "giant" is insufficient, then he needs to provide a better one. No proof in either direction can be provided unless a specific definition of "giant" is forth-coming.
quote:
Where is the proof that he isn't?' Here is the problem. If the giant does not exist there is no evidence, and there never will be.
Not a problem if the definition of "giant" allows there to be a scenaro that necessarily results in a certain situation. If that situation does not exist, then the absence of evidence is, indeed, evidence of absence.
The definition of ice requires the existence of a solid. If we can determine that there are no solids anywhere in the system, then we can necessarily conclude that there is no ice. The absence of solids is evidence of the absence of ice.
quote:
If the giant does not exist, he leaves no trace.
Then the definition of "giant" is so vague that not only can we not show it doesn't exist, we also can't show that it does.
If the giant leaves no trace, then there is also no evidence for the existence.
Of course, a difference that makes no difference is no difference. If the evidence that we have is perfectly consistent with both the presence and the absence of the giant, then we logically conclude that there is no giant since there is no difference between the two.
Note, this assumes that we have complete information. Again, the problem is not the act of proving the negative. The problem is the lack of definitive information. If the objects are not well-defined and we do not have a concrete definition of how they behave, then we become susceptible to overlooking something.
quote:
There is no evidence to examine, and no information with which to construct a proof or a disproof. You can't prove, or disprove, a negative, because there isn't any evidence with which to work. So we are stuck with proving, or disproving, positives.
You've just stated my point: With no information to go off of, you can't say anything either way. We aren't stuck with proving positives. We don't even have the ability to prove a positive.
Nothing in science is ever proven true.
Instead, science concerns itself with proving things false. The function of every experiment is to try and disprove the theory because a successful experiment doesn't prove the theory true, it merely shows it to be accurate. It may be, like Newtonian physics, that our instruments are sensitive enough to detect the error.
------------------
Rrhain
WWJD? JWRTFM!

This message is a reply to:
 Message 20 by John, posted 05-07-2003 1:50 AM John has replied

Replies to this message:
 Message 25 by crashfrog, posted 05-07-2003 3:43 AM Rrhain has not replied
 Message 28 by John, posted 05-08-2003 10:43 AM Rrhain has replied

Rrhain
Member (Idle past 261 days)
Posts: 6351
From: San Diego, CA, USA
Joined: 05-03-2003


Message 24 of 210 (39196)
05-07-2003 3:39 AM
Reply to: Message 21 by Mister Pamboli
05-07-2003 2:26 AM


Re: Question...
Mister Pamboli writes:
quote:
Rh does not prove a negative existential proposition in the second example. I guess you did not intend to, did you?
Correct...sorta.
In that case, I was showing a specific negative case. Given the scenario, we know that there was some sort of change. The bacteria could have mutated or the phage could have. We end up proving the positive by proving the negtive and leaving the positive behind.
In this case, we can list all the possible outcomes: The bacteria mutated or the phage mutated. And, in fact, the process of proving that the phage mutated is accomplished by proving that the bacteria couldn't be the one that mutated. We eliminated the impossible leaving behind the truth, to paraphrase Holmes.
My point is that we shouldn't rail against the idea of "proving a negative." It can be done and is commonly done in science.
What we should be railing against are the poorly defined objects that we are being asked to manipulate; the shifting definitions when the consequences prove to be disliked by the claimants; the equivocation of terms and ad hoc adjustments that revive statements that have no justification; the shifting of burden of proof.
The problem isn't proving a negative. It's the demand to prove a negative when there isn't even enough information to make a definitive statement in the first place.
[This message has been edited by Rrhain, 05-07-2003]

This message is a reply to:
 Message 21 by Mister Pamboli, posted 05-07-2003 2:26 AM Mister Pamboli has replied

Replies to this message:
 Message 26 by Mister Pamboli, posted 05-07-2003 3:49 AM Rrhain has not replied

crashfrog
Member (Idle past 1721 days)
Posts: 19762
From: Silver Spring, MD
Joined: 03-20-2003


Message 25 of 210 (39197)
05-07-2003 3:43 AM
Reply to: Message 23 by Rrhain
05-07-2003 3:26 AM


Re: Question...
Maybe what we're trying to say is that you can deduct a negative (which you have done), but you can't induct a negative. Ultimately, science is the process of induction (generalization from repeated observations), not one of deduction (derivation from postulates). Deductive science hasn't been considered a good way to arrive at truth since... Bacon, was it? Or Galileo? Certainly Aristotle was the prime proponent of deductive science, as I remember... Honestly my history of science is not coming back to me the way I wish it would. Time to hit the books...

This message is a reply to:
 Message 23 by Rrhain, posted 05-07-2003 3:26 AM Rrhain has not replied

Mister Pamboli
Member (Idle past 7831 days)
Posts: 634
From: Washington, USA
Joined: 12-10-2001


Message 26 of 210 (39198)
05-07-2003 3:49 AM
Reply to: Message 24 by Rrhain
05-07-2003 3:39 AM


Re: Question...
quote:
In that case, I was showing a specific negative case. ...
In this case, we can list all the possible outcomes: The bacteria mutated or the phage mutated.
Correct ... sorta.
In this example a negative existential proposition would be of the form There exist no bacteria in this sample which have mutated. etc. Given the finite nature of the set, you could probably observe all instances. The interesting cases of negative existential propositions are where the size of the set is unknown and not all ases are observable. Proving in a negative in such a case ... that's the narrower definition, I guess.

This message is a reply to:
 Message 24 by Rrhain, posted 05-07-2003 3:39 AM Rrhain has not replied

Replies to this message:
 Message 40 by DBlevins, posted 05-10-2003 3:15 PM Mister Pamboli has not replied

compmage
Member (Idle past 5407 days)
Posts: 601
From: South Africa
Joined: 08-04-2005


Message 27 of 210 (39200)
05-07-2003 3:52 AM
Reply to: Message 18 by Dan Carroll
05-06-2003 11:42 PM


Re: Question...
Dan Carroll writes:
Actually, the most fun theory I've heard of NDEs in a while is that it's the brain suddenly remembering the birth canal. Long tunnel, white light at the end, a strange sensation that your mother is there...
LOL. This sounds very much like the NDE experiance I had.
A warm, comfortable place.
A sensation of being pulled and called (by my mother).
And the feeling of not wanting to go.
Though at the time I associated the warm, comfortable place with bed and I really didn't want to get out of bed.
Creationists, does this prove the theory and adequately explain NDE's?
------------------
He hoped and prayed that there wasn't an afterlife. Then he realized there was a contradiction involved here and merely hoped that there wasn't an afterlife.
- Douglas Adams, The Hitch Hiker's Guide to the Galaxy

This message is a reply to:
 Message 18 by Dan Carroll, posted 05-06-2003 11:42 PM Dan Carroll has not replied

John
Inactive Member


Message 28 of 210 (39384)
05-08-2003 10:43 AM
Reply to: Message 23 by Rrhain
05-07-2003 3:26 AM


Re: Question...
quote:
No, it is, indeed, proving a negative. There is no largest prime.
Or... there IS a prime number larger than the assumed largest prime, which is exactly what you conclude:
In both cases, there is a number that is prime that we haven't taken account of larger than what we thought was the largest prime.
What you have proven is a positive statement, then flipped it, but I can see how this is largely semantic.
I don't have a problem with your examples, but they don't address the issue. What crash is refering to is the use of a logical fallacy called Appeal to Ignorance.
Appeal to Ignorance (Proving a Negative): an argument that asserts a claim is true because no one can prove it is wrong; this shifts the burden of proof to the audience or opponent rather than the claimant
No webpage found at provided URL: http://chuma.cas.usf.edu/~pinsky/logicguide.htm
quote:
The only difference between your situation and mine is that my scenario has well-defined objects behaving in well-defined ways.
Precisely why 'proving a negative' is fallacious. In the real world, objects are always ill-defined, or can be argued to be ill-defined, because we have incomplete knowledge of pretty much everything. Just look at the way creationists argue for a young earth or for God.
quote:
The fact that there is a positive means there is a negative, too.
Ummm... no it doesn't. I think you are confusing mathematics with logic or with existential propositions-- somewhat in line with statements made by Mr. P. Take, for example, two statements.
1) John exists.
2) Not-John exists. ( Not-John taken to mean the negative of John, rather than something like 'a person who is not John' )
Does the first imply the second? Nope. In fact the first and second are mutually exclusive.
But take only the second statement. It, in itself, makes no sense. The statement contradicts itself. John can exist, but Not-John cannot. The only real value-- the only value with existence or potential for existence-- is John . Not-John is just short-hand for the absence of the positive value. It is not a statement of the existence of the negative value. It doesn't work like numbers on a number line with zero in the middle, negatives on the left and positives on the right. Once you get to zero-- nothing, not existence-- that's it.
Well, I haven't really said all I'd like but I must leave for work.
Take care.
------------------
No webpage found at provided URL: www.hells-handmaiden.com

This message is a reply to:
 Message 23 by Rrhain, posted 05-07-2003 3:26 AM Rrhain has replied

Replies to this message:
 Message 29 by Rrhain, posted 05-08-2003 11:13 AM John has replied

Rrhain
Member (Idle past 261 days)
Posts: 6351
From: San Diego, CA, USA
Joined: 05-03-2003


Message 29 of 210 (39388)
05-08-2003 11:13 AM
Reply to: Message 28 by John
05-08-2003 10:43 AM


Re: Question...
John responds to me:
quote:
there IS a prime number larger than the assumed largest prime
Which is the negative of the assumption:
There is no prime number larger than the assumed largest prime.
quote:
Precisely why 'proving a negative' is fallacious. In the real world, objects are always ill-defined, or can be argued to be ill-defined, because we have incomplete knowledge of pretty much everything. Just look at the way creationists argue for a young earth or for God.
Incorrect. In the real world, objects are not always ill-defined.
Again, I gave a specific example of showing that an object is not in a room. We can show that the object is too big to fit in the room or that the object is located elsewhere or do an exhaustive search of all the objects in the room.
Or are you saying that, say, your car keys are ill-defined?
Indeed..."god" is an ill-defined object but that doesn't mean everything is ill-defined.
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The fact that there is a positive means there is a negative, too.
Ummm... no it doesn't.
Um... yes, it does.
If an object is X, that means it is not Y (assuming that there is no overlap of X and Y...that is, squares are rectangles so if an object is a square, then it is also a rectangle, but squares are not circles so if an object is a square, then it is not a circle. By showing the positive, X is a square, we necessarily show a negative, too, X is not a circle.)
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I think you are confusing mathematics with logic or with existential propositions--
No, I think that's what you're doing.
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somewhat in line with statements made by Mr. P. Take, for example, two statements.
1) John exists.
2) Not-John exists.
No, that is not the negative I had in mind. You're confusing the logic and the mathematics.
If John exists, then John does not not-exist. If I can show that X is a square, I automatically get X not being a circle as well.
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Rrhain
WWJD? JWRTFM!

This message is a reply to:
 Message 28 by John, posted 05-08-2003 10:43 AM John has replied

Replies to this message:
 Message 30 by John, posted 05-09-2003 10:48 AM Rrhain has replied

John
Inactive Member


Message 30 of 210 (39515)
05-09-2003 10:48 AM
Reply to: Message 29 by Rrhain
05-08-2003 11:13 AM


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Which is the negative of the assumption:
So, the negation of the statement...
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There is no prime number larger than the assumed largest prime.
... which would be "there is a prime number larger than the assumed largest prime" is somehow a demonstration of proving a negative? You've proven a positive statement and reworded it.
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Incorrect. In the real world, objects are not always ill-defined.
You apparently missed the second part of my sentence-- "because we have incomplete knowledge of pretty much everything." We have incomplete knowledge simply because we do not have absolute knowledge.
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Again, I gave a specific example of showing that an object is not in a room. We can show that the object is too big to fit in the room or that the object is located elsewhere or do an exhaustive search of all the objects in the room.
You are not making existential statements. 'X is not in the room' is not not equivalent to 'X is not.' Look at the structure of the arguments you make. They all depend upon examining what is present and detectable. You do not examine what is not detectable to prove that it is not there. You prove what is there. The rest is in limbo. You look at what exists, not what doesn't. Try proving that an object doesn't exist without refering to objects that do. You can't do it, because there is no information. The only things for which we have evidence are things that exist. Thus the only things we can prove are things that exist. We cannot prove or disprove things that don't exist.
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Or are you saying that, say, your car keys are ill-defined?
Usually.
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If an object is X, that means it is not Y
You are not making existential statements. An existential statement is of the form 'X exists' or 'X does not exist.' 'X is not Y' is not equivalent to 'X is not.' It doesn't even matter if X and Y are mutually exclusive, because we have have logic wrong. We may have math wrong. And it appears that there are sections of the universe where both are true.
Forbidden
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No, that is not the negative I had in mind.
It IS the relevant negative! This is what I have been trying to explain to you. You commented on crash's statement that one cannot prove a negative by stating that one can prove that 'X is not Y.' In context, 'God is not a Buick' ( but Jesus built my hotrod ). But the relevant formulation would be 'X is not.' This cannot be proven. A thing's existence can be proven with one case, but its non-existence cannot. The proof could be just around the next corner. You only need one apple to prove that apples exist. You need absolute knowledge to prove that they do not. To prove that purple-people-eaters do not exist you'd have to search not only here but across the entire universe from its beginning to its end and down to its very basic foundations. Even then, all you have is an absence of evidence, not evidence against. There may be other universes... and so on and so on. You can prove that an object is inconsistent with our understanding of the universe, but our understanding could be wrong. This is a relative statement, not an existential one. The orbital path of Mercury is inconsistent with Newtonian orbital mechanics. Does that mean that Mercury doesn't orbit as it does? Nope. It means Newton had a fly in the ointment. Einstein's ideas have replaced Newton's. The same thing could happen to any of our ideas. Logic, math, whatever-- it could all be very wrong. Can you prove that some as yet undiscovered theory for which, obviously, we have no evidence will not replace Einstein's theories? Nope. There is no evidence. That is a major snag when trying to prove a negative. Without absolute knowledge, we can't be sure and we are far from absolute knowledge if such a thing is possible at all.
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If John exists, then John does not not-exist.
So, if John exists then John exists? Brilliant.
You quite rightly point out that a thing implies the negation of its negation-- a trivial transformation. It does not imply the existence of anything that is not itself.
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No webpage found at provided URL: www.hells-handmaiden.com

This message is a reply to:
 Message 29 by Rrhain, posted 05-08-2003 11:13 AM Rrhain has replied

Replies to this message:
 Message 31 by Rrhain, posted 05-10-2003 12:02 AM John has replied

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