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Author Topic:   Question.... (Processes of Logic)
Rrhain
Member (Idle past 264 days)
Posts: 6351
From: San Diego, CA, USA
Joined: 05-03-2003


Message 136 of 210 (42303)
06-07-2003 2:00 AM
Reply to: Message 135 by crashfrog
06-07-2003 12:52 AM


crashfrog responds to me:
quote:
quote:
Think really, really had and make your hand have six fingers.
Fine, I have six fingers. Wasn't that hard, actually.
Two things:
1) By "six," do you mean six or do you mean "I'm just using the arbitrary convention of putting the Roman letters s, i, and x together to refer to the number of fingers...for anybody else, I would have said 'five'"?
2) If the former, cool! Can I come and get a picture? I gotta see this. Were you consulted for Bruce Almighty?
Oh, let's make it three:
3) Do it to my hand, next. I can't seem to get it to happen. Since you seem to be better at it, go ahead and do it to mine.
------------------
Rrhain
WWJD? JWRTFM!

This message is a reply to:
 Message 135 by crashfrog, posted 06-07-2003 12:52 AM crashfrog has replied

Replies to this message:
 Message 137 by crashfrog, posted 06-07-2003 12:04 PM Rrhain has replied

crashfrog
Member (Idle past 1723 days)
Posts: 19762
From: Silver Spring, MD
Joined: 03-20-2003


Message 137 of 210 (42319)
06-07-2003 12:04 PM
Reply to: Message 136 by Rrhain
06-07-2003 2:00 AM


By "six," do you mean six or do you mean "I'm just using the arbitrary convention of putting the Roman letters s, i, and x together to refer to the number of fingers...for anybody else, I would have said 'five'"?
I mean "six", as in 5 + 1 - as in, "one two three four five six."
If the former, cool! Can I come and get a picture? I gotta see this.
Tell ya what - prove to me your friends have a cat that detects parity, and I'll prove to you I have six fingers. Or don't you trust me?
Do it to my hand, next. I can't seem to get it to happen.
Only seems to work for my hand, sorry. I don't know why.

This message is a reply to:
 Message 136 by Rrhain, posted 06-07-2003 2:00 AM Rrhain has replied

Replies to this message:
 Message 139 by Rrhain, posted 06-08-2003 8:59 AM crashfrog has replied

Brad McFall
Member (Idle past 5289 days)
Posts: 3428
From: Ithaca,NY, USA
Joined: 12-20-2001


Message 138 of 210 (42324)
06-07-2003 12:58 PM
Reply to: Message 135 by crashfrog
06-07-2003 12:52 AM


when more was more or less
CRASH, you are aware that RHAIN may have "tricked" you to cash in on the frog's wart because he may have THOUGHT and then rejected MORE as an actual infinite number and then claimed that he could not use this sight to tell you. I must admit that the willingness to disagree and then continue to communicate baffles me here for for me when the goin' was raw i simply was and reach for something else.

This message is a reply to:
 Message 135 by crashfrog, posted 06-07-2003 12:52 AM crashfrog has not replied

Rrhain
Member (Idle past 264 days)
Posts: 6351
From: San Diego, CA, USA
Joined: 05-03-2003


Message 139 of 210 (42357)
06-08-2003 8:59 AM
Reply to: Message 137 by crashfrog
06-07-2003 12:04 PM


crashfrog responds to me:
quote:
quote:
By "six," do you mean six or do you mean "I'm just using the arbitrary convention of putting the Roman letters s, i, and x together to refer to the number of fingers...for anybody else, I would have said 'five'"?
I mean "six", as in 5 + 1 - as in, "one two three four five six."
OK...just wanted to make sure. You had been disingenuous before and I wanted to verify that you weren't being so now.
quote:
quote:
If the former, cool! Can I come and get a picture? I gotta see this.
Tell ya what - prove to me your friends have a cat that detects parity, and I'll prove to you I have six fingers. Or don't you trust me?
Oh, I trust you. That's why I asked if I could come and get a picture. And it uses the exact same method: Get off your ass and go to where the evidence is. I've invited you to come and see the cat...why are you hesitating at me coming to see your hand?
By the way, timing is everything: PBS is running (at least locally) the Nature miniseries: Inside the Animal Mind. The latest one had to deal with intelligence (the one coming up has to do with emotions).
Among the many examples were things such as the ability to create mental maps. For example, cabbies learn the streets of the city in which they drive. But, many animals learn that sort of thing, too. The big question is whether or not animals are capable of coming up with new routes if the way they always take is blocked.
Turns out some of them can. Experiments with rats show that when the rat has learned a maze and you alter the maze a bit to block the main route, the rats can adjust their routes and do so immediately without having to take a trial-and-error approach.
Hummingbirds are capable of remembering which flowers they have visited so they don't have to waste energy trying to get nectar from a flower that doesn't have any since it was visited yesterday. In experiments with artificial flowers that were filled with nectar only sufficient for a single visit, hummingbirds consistently avoided the ones that they had fed at the day before. And I should point out that hummingbirds have a brain about the size of a grain of rice.
There is a bird in the Grand Canyon area that buries nuts for the winter...some 30,000 of them, usually. And yet, it manages to find them in the winter...even when the ground is covered with snow and thus the geograhical picture of the land has changed...with a 90% accuracy.
They showed examples of animals coming up with novel approaches to problem solving. Primates who are presented with a banana out of reach can come up with new methods of devising a way to reach it...and will gather all the materials required before making the attempt. That is, they seem to know just how far the stick will let them reach and just how much the box will let them rise above the ground and noting that neither one is sufficient, will grab both of them before getting up on the box to poke at the banana with the stick.
There was an incident involving ice fishers and ravens: It seems the ice fishers would set up a few sites, cut a hole in the ice, put bait on a hook and set the line, then go off to do another one. But when they came back, they found that the catch was gone. The fishermen thought somebody was coming around poaching the catch until they caught the ravens at it. It seems the raven had noticed what the humans were doing and after the humans were gone, the raven would go to the line, pull it up a bit, step on it to hold it down, and then pull up a little bit more until they got to the fish on the end.
But is that just another example of trial-and-error? After all, with the chimps and bananas, they tend to need to know the various tools they are going to use fairly well beforehand. So, some scientists raised some ravens from hatchlings in order to make sure that they did not have any previous experience. They gave the ravens a choice: One line had food, the other a rock. The ravens consistently chose the food line, pulling up a bit, holding it down, pulling it up a bit more, etc. They even tried to trick the ravens by crossing the lines...and still the ravens chose the lines with food.
And then there is the work with pigeons and recognition, including the ability to think abstractly. Some pigeons were trained to peck at pictures of trees to get food. The pigeons were then shown pictures they hadn't seen or been trained on and still the pigeons were capable of distinguishing pictures of trees from those of non-trees...including other foliage: Pictures of ferns elicited no response. They were even capable of distinguishing Picasso from Monet...and were capable of coming up with a distinction of the Cubist style since pictures of Matisse, which as a style is very similar to Picasso's Cubism (and is often confused for Picasso, even by humans), elicited responses.
However, there are some differences between humans and pigeons in their pattern recognition. It seems that pigeons don't have the ability to come up with the concept of symmetry. That is, if you presented the pigeons with images of two lines, trying to get them to respond when the lines are of equal length while not when they are of unequal length, the pigeons can't seem to grasp this while humans pick up the rule quite quickly.
However, humans have a hard time dealing with a rule of amounts. That is, if the rule is to respond if there is a little amount of space taken up with color but not if there's a lot, pigeons pick this up quite rapidly while humans have a hard time...it seems that the human ability to seek deep pattern interferes with the simplicity of the presented rule. They are more attracted to the pattern of the boundary than the area which it contains.
And dolphins seem to understand syntax. Dolphins who were trained to respond to about 60 signals can follow the word order when those commands are strung together. For example, if you tell them "Right water, left basket fetch," they know to get the left basket and take it to the waterfall on the right. But if you then tell them "Left water, right basket fetch," they know to get the right basket and take it to the waterfall on the left.
And then there are the experiments regarding number. They show a chimpanzee that not only knows how to count but also how to add. The experimenter puts a number of candies in front of the chimp and then present her with a computer touch screen that gives a bunch of possible numbers, randomly scattered...including some boxes blank. Seems the chimp has figured out not only how to count, but the arbitrary nature of Arabic numerals...and also understands the concept of 0.
But wait, there's more. When given one basket in one part of the room with two objects in it and another basket in another part of the room with three different objects in it and is asked how many objects total, it knows that there are five, showing not only an ability to add but also the ability to abstract the properties of number so that it recognizes "five objects" and is not stuck on "two of this kind and three of that kind."
Then there is the work with grey parrots. Given an array of similar yet distinct objects such as blocks and bits of wool, some of which are painted green and others are painted yellow, the parrots are capable of telling you how many yellow wool balls there are compared to how many green blocks.
And let's not forget that even in humans, number seems to be connected to vision. That is, if you were to flash an image in front of a person and then ask them how many objects there were, he'll handily be able to tell you how many, provided there aren't too many. That is, you aren't mentally tabulating, "One, two, three, four" because there isn't enough time to do that. It's immediately absorbed and understood. For humans, the limit tends to be about 7 which seems to be about the limit for other animals (though other animals tend to have lower limits). It seems that small numbers are connected to vision and do not require conscious thought.
So please, crashfrog, do check your local listings to see when this wonderful program is being presented or purchase it from your local PBS store or check your local library to see if they have a copy to borrow, look at these animals, see directly what they can do, listen to the scientists that have carried out the experiments, and then tell me:
Is it really so odd to think that there might be a cat who understands the difference between odd and even?
Oh, but wait...I decided to do a little bit of searching on PubMed:
Pepperberg IM.
In search of king Solomon's ring: cognitive and communicative studies of Grey parrots (Psittacus erithacus).
Brain Behav Evol. 2002;59(1-2):54-67.
PMID: 12097860 [PubMed - indexed for MEDLINE]
From the Abstract [emphasis added]:
"During the past 24 years, I have used a modeling technique (M/R procedure) to train Grey parrots to use an allospecific code (English speech) referentially; I then use the code to test their cognitive abilities. The oldest bird, Alex, labels more than 50 different objects, 7 colors, 5 shapes, quantities to 6, 3 categories (color, shape, material) and uses 'no', 'come here', wanna go X' and 'want Y' (X and Y are appropriate location or item labels). He combines labels to identify, request, comment upon or refuse more than 100 items and to alter his environment. He processes queries to judge category, relative size, quantity, presence or absence of similarity/difference in attributes, and show label comprehension."
So we're left with at least a couple options, crash:
1) Number is an intrinsic property of objects.
2) Animals have invented mathematics, too.
I, as you most probably can predict, fall toward the first.
quote:
quote:
Do it to my hand, next. I can't seem to get it to happen.
Only seems to work for my hand, sorry. I don't know why.
Hmmm...perhaps you only have a virtual hand while my hand has independent existence.
------------------
Rrhain
WWJD? JWRTFM!

This message is a reply to:
 Message 137 by crashfrog, posted 06-07-2003 12:04 PM crashfrog has replied

Replies to this message:
 Message 140 by crashfrog, posted 06-08-2003 12:34 PM Rrhain has replied

crashfrog
Member (Idle past 1723 days)
Posts: 19762
From: Silver Spring, MD
Joined: 03-20-2003


Message 140 of 210 (42359)
06-08-2003 12:34 PM
Reply to: Message 139 by Rrhain
06-08-2003 8:59 AM


And it uses the exact same method: Get off your ass and go to where the evidence is. I've invited you to come and see the cat...why are you hesitating at me coming to see your hand?
No hesitation. Come on down. But bring the cat.
The latest one had to deal with intelligence (the one coming up has to do with emotions).
Those are fascinating examples, but what do they prove? That animals have precursors to human intelligence and can be trained in, or learn, some of the same mental models humans have? I'm not impressed because human intelligence is a social phenomenon anyway, so it's not surprising that something like it can bve found in social creatures.
So we're left with at least a couple options, crash:
1) Number is an intrinsic property of objects.
2) Animals have invented mathematics, too.
3) Animals can be trained to use the same mental models humans do, like numbers, or language.
Just as a map is a representation, a mental model, of the spacial relationship of objects, numbers are simply a mental representation of another kind of relationship. Or, do you think maps have an existence beyond our use of them? That maps are discovered, not invented?

This message is a reply to:
 Message 139 by Rrhain, posted 06-08-2003 8:59 AM Rrhain has replied

Replies to this message:
 Message 141 by Rrhain, posted 06-11-2003 5:04 AM crashfrog has replied

Rrhain
Member (Idle past 264 days)
Posts: 6351
From: San Diego, CA, USA
Joined: 05-03-2003


Message 141 of 210 (42539)
06-11-2003 5:04 AM
Reply to: Message 140 by crashfrog
06-08-2003 12:34 PM


crashfrog responds to me:
quote:
quote:
And it uses the exact same method: Get off your ass and go to where the evidence is. I've invited you to come and see the cat...why are you hesitating at me coming to see your hand?
No hesitation. Come on down. But bring the cat.
Not my cat to bring. I did mention that. If you want to see the cat, you gotta come here.
quote:
quote:
The latest one had to deal with intelligence (the one coming up has to do with emotions).
Those are fascinating examples, but what do they prove?
That there is evidence that what you are ascribing to a human endeavor appears to be something that exists outside of humans.
quote:
That animals have precursors to human intelligence and can be trained in, or learn, some of the same mental models humans have?
Um, no. If you look carefully, you will see that in some of these cases, the animals were specifically raised to ensure they did not have any human mental model and yet, they perform the same way.
So as I said in the end of my post, we have at least two possibilities:
1) Mathematics is not a mental construct
2) Animals have invented math, too
Can you think of another possibility?
quote:
I'm not impressed because human intelligence is a social phenomenon anyway, so it's not surprising that something like it can bve found in social creatures.
Hummingbirds aren't exactly social creatures.
But you're still avoiding the issue. You were saying that mathematics is a mental construct. You expressed shock and amazement that I would claim to know of a cat that seemingly understands the difference between odd and even, daring me to show any sort of evidence of such.
So I did.
Now, this is just me inferring, but it seemed to me that you were of the opinion that part of the reason that you claim mathematics is a mental construct is because animals don't do it. And yet, it is apparent that they do.
So I guess I'm wondering what your point was in displaying incredulousness at the idea of a cat who can tell the difference between odd and even. If animals engaging in mathematics doesn't change your opinion that math is a mental construct, then why all the bluster surrounding this cat?
quote:
quote:
So we're left with at least a couple options, crash:
1) Number is an intrinsic property of objects.
2) Animals have invented mathematics, too.
3) Animals can be trained to use the same mental models humans do, like numbers, or language.
No, many of the animals were specifically raised to ensure lack of human models. Remember the ravens.
quote:
Just as a map is a representation, a mental model, of the spacial relationship of objects, numbers are simply a mental representation of another kind of relationship.
Indeed. This is where you're being disingenuous and why I asked you if you really meant "six" as opposed to "I'm just calling it 'six.'"
You seem to be stuck on the symbology rather than the substance behind the symbol. The number of fingers on your hand is not dependent on if you call it "five" or "cinco" or "5."
quote:
Or, do you think maps have an existence beyond our use of them? That maps are discovered, not invented?
I think geography exists outside of your brain. I think the various animals who create the mental model are reacting to the reality of the geography. You make a map of something and that something is real.
Just because you can mentally picture the route you take in your head doesn't mean your body physically moving along that path is just a mental construction. Yes, the map in your head is an abstraction, but it becomes real when you actually take the path.
"1 + 1 = 2" is an abstraction that becomes real when you take one object and add another object to it.
------------------
Rrhain
WWJD? JWRTFM!

This message is a reply to:
 Message 140 by crashfrog, posted 06-08-2003 12:34 PM crashfrog has replied

Replies to this message:
 Message 142 by crashfrog, posted 06-11-2003 1:58 PM Rrhain has replied

crashfrog
Member (Idle past 1723 days)
Posts: 19762
From: Silver Spring, MD
Joined: 03-20-2003


Message 142 of 210 (42582)
06-11-2003 1:58 PM
Reply to: Message 141 by Rrhain
06-11-2003 5:04 AM


That there is evidence that what you are ascribing to a human endeavor appears to be something that exists outside of humans.
Actually (and my statements may not have accurately reflected this) but I didn't mean to decribe math as a unqiuely human endeavor, but rather an endeavor unique to symbolic, social intelligence. While humans consitute the most advanced example of that I don't believe we're the only ones.
If space aliens visit us, I assume they'll have some kind of math. If they're able to communicate with us at all it's likely we'll find they have the same numbers. But only because their minds are similar to ours, not because numbers have some kind of independant phsyical reality.
Um, no. If you look carefully, you will see that in some of these cases, the animals were specifically raised to ensure they did not have any human mental model and yet, they perform the same way.
I read the exact opposite. Your citations demonstrated animals trained by humans to absorb human-like mental models. I don't know how you think it could be otherwise - what techniques could humans use that would not result in human-like mental models?
Can you think of another possibility?
That animals can absorb human-like mental models because intelligence is a social phenomenon. I said that already.
Hummingbirds aren't exactly social creatures.
All creatures are social to some degree. Including hummingbirds.
Now, this is just me inferring, but it seemed to me that you were of the opinion that part of the reason that you claim mathematics is a mental construct is because animals don't do it. And yet, it is apparent that they do.
I can understand how you would have inferred that - that's not really my position. My position is that math is simply a mental construct because number is not a physical property of matter but rather a property of imaginary sets of objects, which exist only in our heads and which we communicate to each other via mathematics, language, and other ways of describing relationship. Most animals have some capability to communicate mental models, so it's not surprising to me that animals can be taught - or even learn themselves - other kinds of mental models, such as "number". Especially when humans are communicating to them.
That still doesn't prove that numbers have a unique, self-sufficient physical reality.
So I guess I'm wondering what your point was in displaying incredulousness at the idea of a cat who can tell the difference between odd and even.
Actually, my incredulity stemmed from the fact that your example was all too convenient. But even if it's true it doesn't speak against my position - the cat detects parity because it absorbed a mental model of parity through communication, not because parity is some inherent property of an object.
You seem to be stuck on the symbology rather than the substance behind the symbol. The number of fingers on your hand is not dependent on if you call it "five" or "cinco" or "5."
You don't seem to understand what we're arguing. And honestly, if you refuse to understand, why should I argue with you? I'm actually getting a little tired of this because you just repeat your assumptions over and over again and ignore any challenge to them. You're not a very good debater. I don't really see any reason to continue.

This message is a reply to:
 Message 141 by Rrhain, posted 06-11-2003 5:04 AM Rrhain has replied

Replies to this message:
 Message 143 by Rrhain, posted 06-12-2003 9:07 AM crashfrog has not replied

Rrhain
Member (Idle past 264 days)
Posts: 6351
From: San Diego, CA, USA
Joined: 05-03-2003


Message 143 of 210 (42663)
06-12-2003 9:07 AM
Reply to: Message 142 by crashfrog
06-11-2003 1:58 PM


crashfrog responds to me:
quote:
but I didn't mean to decribe math as a unqiuely human endeavor, but rather an endeavor unique to symbolic, social intelligence. While humans consitute the most advanced example of that I don't believe we're the only ones.
Please let us know what symbols a hummingbird uses in its mental map.
quote:
If space aliens visit us, I assume they'll have some kind of math. If they're able to communicate with us at all it's likely we'll find they have the same numbers. But only because their minds are similar to ours, not because numbers have some kind of independant phsyical reality.
But if the numbers are universal, how is that not indicative of a universal existence?
quote:
quote:
Um, no. If you look carefully, you will see that in some of these cases, the animals were specifically raised to ensure they did not have any human mental model and yet, they perform the same way.
I read the exact opposite. Your citations demonstrated animals trained by humans to absorb human-like mental models. I don't know how you think it could be otherwise - what techniques could humans use that would not result in human-like mental models?
You're forgetting about the ravens.
They were raised from hatchlings to make sure they never saw a human doing anything like pulling on a string, holding it down, and then pulling it up more. Did you not see that? Indeed, some of the animals need to be taught human methods such as the grey parrots counting bits of wool balls since the way we are getting them to tell us how many are there is through speech. Thus, we need to teach them the word.
But what human taught a hummingbird how to make a mental map? What human taught the nut-burying bird to make a mental map?
And what human taught the cat?
quote:
quote:
Can you think of another possibility?
That animals can absorb human-like mental models because intelligence is a social phenomenon. I said that already.
That would be the second case: Animals invented math, too.
quote:
quote:
Hummingbirds aren't exactly social creatures.
All creatures are social to some degree. Including hummingbirds.
That pretty much strips the phrase "social animal" of any meaning, then. Obviously, sexually-reproducing species need to find one another otherwise they will never reproduce. That doesn't make them "social creatures."
quote:
My position is that math is simply a mental construct because number is not a physical property of matter but rather a property of imaginary sets of objects, which exist only in our heads and which we communicate to each other via mathematics, language, and other ways of describing relationship. Most animals have some capability to communicate mental models, so it's not surprising to me that animals can be taught - or even learn themselves - other kinds of mental models, such as "number". Especially when humans are communicating to them.
But you're forgetting about the animals that were deliberately raised to have no human contact.
How did they get taught?
And what are they reacting to if not something that exists?
quote:
That still doesn't prove that numbers have a unique, self-sufficient physical reality.
I would say that it does. We start reducing the amount of mental cognition and still mathematics pops up. And when we finally completely remove all mental function and look at things that are purely physical, we still find mathematics all over the place.
And that's not surprising considering that physics is nothing more than applied mathematics.
quote:
quote:
So I guess I'm wondering what your point was in displaying incredulousness at the idea of a cat who can tell the difference between odd and even.
Actually, my incredulity stemmed from the fact that your example was all too convenient. But even if it's true it doesn't speak against my position - the cat detects parity because it absorbed a mental model of parity through communication, not because parity is some inherent property of an object.
Um, who taught the cat?
quote:
quote:
You seem to be stuck on the symbology rather than the substance behind the symbol. The number of fingers on your hand is not dependent on if you call it "five" or "cinco" or "5."
You don't seem to understand what we're arguing.
Strange...I've been saying the same thing to you for days now.
Why do you think I keep suggesting that you let it go?
quote:
And honestly, if you refuse to understand, why should I argue with you?
What do you think I've been saying to you for days?
I seem to recall saying that we were at an impasse. Did you not take it seriously?
quote:
I'm actually getting a little tired of this because you just repeat your assumptions over and over again and ignore any challenge to them. You're not a very good debater.
Strange...I was going to say the exact same thing to you. You don't respond to points, when asked direct questions you avoid them at all costs, you jump to psychoanalysis, ascribe ulterior motives, have no respect for the people you're debating with, etc., etc. You're not a very good debater at all.
quote:
I don't really see any reason to continue.
Then why not take the suggestion I made more than a week ago?
Let it go.
------------------
Rrhain
WWJD? JWRTFM!

This message is a reply to:
 Message 142 by crashfrog, posted 06-11-2003 1:58 PM crashfrog has not replied

contracycle
Inactive Member


Message 144 of 210 (42871)
06-13-2003 9:56 AM


If you'll forgive me for jumping in on what appears almost to be a private argument....
"number" is a human abstraction. Yes. But it is also a description of genuinely physical phenonmen.
And then we found we could manipulate the ABSTRACTION and get results that could be interpreted back usefully into the material world.
I don't actually find that too surprising given that number orignates from the material world.
Math IS.

Replies to this message:
 Message 145 by crashfrog, posted 06-15-2003 1:17 AM contracycle has replied

crashfrog
Member (Idle past 1723 days)
Posts: 19762
From: Silver Spring, MD
Joined: 03-20-2003


Message 145 of 210 (42953)
06-15-2003 1:17 AM
Reply to: Message 144 by contracycle
06-13-2003 9:56 AM


But it is also a description of genuinely physical phenonmen.
No, it's just a description of relationships that exist only in our heads. The objects themselves are physical, yes. But the set of objects your counting - the set itself - is something you make up.
Math IS.
Sure, but then Monopoly IS, too.

This message is a reply to:
 Message 144 by contracycle, posted 06-13-2003 9:56 AM contracycle has replied

Replies to this message:
 Message 146 by Autocatalysis, posted 06-16-2003 1:37 AM crashfrog has replied
 Message 149 by contracycle, posted 06-17-2003 8:03 AM crashfrog has replied

Autocatalysis
Inactive Member


Message 146 of 210 (43002)
06-16-2003 1:37 AM
Reply to: Message 145 by crashfrog
06-15-2003 1:17 AM


I agreeThe set is a construct beyond the empirical world.but worse still, principal mathematics was shocked when Kurt Gdel demonstrated there is no consistent way of determining mathematical truth. It's an axiom contradiction.

This message is a reply to:
 Message 145 by crashfrog, posted 06-15-2003 1:17 AM crashfrog has replied

Replies to this message:
 Message 147 by crashfrog, posted 06-16-2003 2:14 AM Autocatalysis has not replied
 Message 148 by Rrhain, posted 06-17-2003 7:07 AM Autocatalysis has replied

crashfrog
Member (Idle past 1723 days)
Posts: 19762
From: Silver Spring, MD
Joined: 03-20-2003


Message 147 of 210 (43003)
06-16-2003 2:14 AM
Reply to: Message 146 by Autocatalysis
06-16-2003 1:37 AM


Uh-oh, potentially irrelevant mention of Godel's theorem... Rrhain's gonna jump right down your throat. Doubtless he'll bring up Pressberger arithmetic without ever explaining its usefulness.

This message is a reply to:
 Message 146 by Autocatalysis, posted 06-16-2003 1:37 AM Autocatalysis has not replied

Rrhain
Member (Idle past 264 days)
Posts: 6351
From: San Diego, CA, USA
Joined: 05-03-2003


Message 148 of 210 (43105)
06-17-2003 7:07 AM
Reply to: Message 146 by Autocatalysis
06-16-2003 1:37 AM


Close, crash, but no cigar.
Autocatalysis writes:
quote:
but worse still, principal mathematics was shocked when Kurt Gdel demonstrated there is no consistent way of determining mathematical truth. It's an axiom contradiction.
No, that isn't what the Incompleteness Theorems state.
Instead, they state that any axiomatic number system sophisticated enough to model arithmetic will be either incomplete or inconsistent. Not everything is such a thing and thus, the Incompleteness Theorems do not apply.
Plus, the two concepts of incompleteness and inconsistency are the same thing...the difference is just in how you write things down.
------------------
Rrhain
WWJD? JWRTFM!

This message is a reply to:
 Message 146 by Autocatalysis, posted 06-16-2003 1:37 AM Autocatalysis has replied

Replies to this message:
 Message 151 by Autocatalysis, posted 06-17-2003 10:18 PM Rrhain has replied

contracycle
Inactive Member


Message 149 of 210 (43111)
06-17-2003 8:03 AM
Reply to: Message 145 by crashfrog
06-15-2003 1:17 AM


quote:
No, it's just a description of relationships that exist only in our heads. The objects themselves are physical, yes. But the set of objects your counting - the set itself - is something you make up.
Until we articulate them in bits and bytes, at which point they become realised physically. The notional non-materialism of "number" is mythological and has been since the development of cybernetics in the 40's, IMO.
The set you are counting does not exist only in your head. Or at least, it does in much the same way that the 270-degree field of vision you "experience" exists purely within your head. Your idea of your surroundings is "something you make up", and yet is none the less a reflection of the material realities (mostly) to which you are exposed.
quote:
Sure, but then Monopoly IS, too.
Yes. And when is the last time you heard a dispute about the ontological existence of Monopoly?

This message is a reply to:
 Message 145 by crashfrog, posted 06-15-2003 1:17 AM crashfrog has replied

Replies to this message:
 Message 150 by crashfrog, posted 06-17-2003 3:18 PM contracycle has not replied

crashfrog
Member (Idle past 1723 days)
Posts: 19762
From: Silver Spring, MD
Joined: 03-20-2003


Message 150 of 210 (43165)
06-17-2003 3:18 PM
Reply to: Message 149 by contracycle
06-17-2003 8:03 AM


Your idea of your surroundings is "something you make up", and yet is none the less a reflection of the material realities (mostly) to which you are exposed.
Right, but if you assume that the map is the same as the physical reality, then you confuse the model with the reality. You reify, in other words.
If this wasn't true, how could maps be wrong? We know that some maps are wrong, however, suggesting that maps are simply another kind of mental model. Based on reality, sure, but no more real than any other mental models.
And when is the last time you heard a dispute about the ontological existence of Monopoly?
I've never heard an argument for the ontological existence of mathematics that couldn't be applied to Monopoly, as well.
[This message has been edited by crashfrog, 06-17-2003]

This message is a reply to:
 Message 149 by contracycle, posted 06-17-2003 8:03 AM contracycle has not replied

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