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Can we know only what we are prepared to kno

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Can we know only what we are prepared to know?

If an individual has never learned to add and subtract that individual cannot learn how to divide and multiply.

Our American educational system, K-12, attempts to teach minimum fundamentals that prepare an individual to function within our high tech society. Our colleges and universities generally augment these fundamentals with some form of specialized knowledge that will make it possible for graduates to obtain good jobs.

Few graduates from our American educational system are prepared to comprehend the very complex type of problems our society encounters. In a democracy such as ours the citizens can choose the politicians to act as their representatives in government. In a democracy such as ours the citizen can veto any public policy that they do not comprehend even though it might be necessary for the survival of the American culture and perhaps even of the survival of the human species.

Under such circumstances is a democratic form of government adequate?

If not what form of government is adequate?

Is it possible for us to educate citizens to the higher level of sophistication that is required to manage a sophisticated high tech society such as ours?

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Can we know only what we are prepared to know?

If an individual has never learned to add and subtract that individual cannot learn how to divide and multiply.

Our American educational system, K-12, attempts to teach minimum fundamentals that prepare an individual to function within our high tech society. Our colleges and universities generally augment these fundamentals with some form of specialized knowledge that will make it possible for graduates to obtain good jobs.

Few graduates from our American educational system are prepared to comprehend the very complex type of problems our society encounters. In a democracy such as ours the citizens can choose the politicians to act as their representatives in government. In a democracy such as ours the citizen can veto any public policy that they do not comprehend even though it might be necessary for the survival of the American culture and perhaps even of the survival of the human species.

Under such circumstances is a democratic form of government adequate?

If not what form of government is adequate?

Is it possible for us to educate citizens to the higher level of sophistication that is required to manage a sophisticated high tech society such as ours?

You asked the right question. Just steer clear from the threads of ancient civilizations. They seem to think that people will question anything, even if they don't know to question. If one is born and taught that 1+1=3, and are never taught the truth, they'll never question it because they don't realize to. So yes, people only learn what they're are prepared to learn prior. :tu:

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I am convinced that we cannot "see" that which we are not prepared to "see"; metaphor ‘know is see’.

It is like walking in a forest such that we are unable to see very far because the trees restrict our view. We can use the analogy of walking in the forest, which to see beyond the surrounding trees we must have the means to climb a tall tree to see a bit further.

Perhaps we might extend the analogy to say that we must have some means to raise our self above the surrounding clutter before we can see a bit further. Only when we find a hill with tall trees and climb one of those trees can we see the mountain ahead, which we might climb and see a mountain range in the distance, which we might travel too so that we can see even further. But as long as we do not climb some trees we cannot see beyond the mundane appearances of our little world of trees that surround us.

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I am convinced that we cannot "see" that which we are not prepared to "see"; metaphor ‘know is see’.

It is like walking in a forest such that we are unable to see very far because the trees restrict our view. We can use the analogy of walking in the forest, which to see beyond the surrounding trees we must have the means to climb a tall tree to see a bit further.

Perhaps we might extend the analogy to say that we must have some means to raise our self above the surrounding clutter before we can see a bit further. Only when we find a hill with tall trees and climb one of those trees can we see the mountain ahead, which we might climb and see a mountain range in the distance, which we might travel too so that we can see even further. But as long as we do not climb some trees we cannot see beyond the mundane appearances of our little world of trees that surround us.

Exactly. :tu:

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you should read this article, Socrates felt the same way.

He realized the faults in Democracy. Don't get me wrong, I think Democracy is our

best path for progress, but that does not make it one without bumps.

The only way for it to work is for humanity to finally give up on its animalistic

striving for dominance for dominance sake. This behavior worked when we had

instincts to control our behavior and prevent us from committing atrocities against our own kind.

Now we have self-awareness and choice, and that makes us responsible for our behavior, and we

have to start admitting it. Its time to stop using our past as mere animals as excuses for acting

like that now. We are still animals, but we are animals with choice. We need to educate our populace,

and genuinely adhere to the principles we CLAIM

sorry hit wrong button :)

here's that article

http://allanstime.com/Government/socrates_democracy.htm

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you should read this article, Socrates felt the same way.

He realized the faults in Democracy. Don't get me wrong, I think Democracy is our

best path for progress, but that does not make it one without bumps.

The only way for it to work is for humanity to finally give up on its animalistic

striving for dominance for dominance sake. This behavior worked when we had

instincts to control our behavior and prevent us from committing atrocities against our own kind.

Now we have self-awareness and choice, and that makes us responsible for our behavior, and we

have to start admitting it. Its time to stop using our past as mere animals as excuses for acting

like that now. We are still animals, but we are animals with choice. We need to educate our populace,

and genuinely adhere to the principles we CLAIM

sorry hit wrong button :)

here's that article

http://allanstime.com/Government/socrates_democracy.htm

If there was an emote for applauding, I would. People need to take responsibility. :tu:

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I found a smiley face for clapping on my hard drive! right click and save for future use!

post-1304-1238585500.gif

I just had that already in my mind this morning.

Thanks to those who started this thread for giving me a place to vent!

and thank you. :D

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I found a smiley face for clapping on my hard drive! right click and save for future use!

post-1304-1238585500.gif

I just had that already in my mind this morning.

Thanks to those who started this thread for giving me a place to vent!

and thank you. :D

Thank you!

post-1304-1238585500.gif

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Too many green zones and forbidden cities. Egyptians had Chinese silk and Mongolians gave Israeli's authority when they invaded Europe. Did you hear about the 2 versions of 1 historical moment? What exactly was the 2nd Reich about?? Democracy's work so long as everyone does not freak out that is true but still too many green zones and forbidden cities.

The stars might fall from the sky when Andromeda gets here but, that will take another 3 to 4 billion years.

Any thoughts?

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I would have to say to the original question that of course people only know what they expect to question. There is of course that rare person that will question everything just for the sake of it, but people are going to think what they have been told most of their life, it's all perception..

On a seperate note, what exactly is a green zone?

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I would have to say to the original question that of course people only know what they expect to question. There is of course that rare person that will question everything just for the sake of it, but people are going to think what they have been told most of their life, it's all perception..

On a seperate note, what exactly is a green zone?

Saddam Hussein lived when he ruled Iraq lived in what today is called the "green zone". In many third world countries the leaders live separated from there population. A small state of the art city is built and that is where the leaders live completely separate lives.

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I am convinced that we cannot "see" that which we are not prepared to "see"; metaphor ‘know is see’.

I haven't had that experience in my life. Well-- actually it's impossible to tell whether I've had it or not because it's impossible to prove that I saw something I wasn't ready to see. If I wasn't ready to see it how would it look? Different from how it would look if I was ready to see it?

The reason I don't think it's been true for me is that I'm still capable of being totally surprised by things I didn't think were possible. Things that I learned were BEYOND DOUBT when I was a kid that held true for 40 years suddenly turn out to have exceptions that leave me slack jawed with amazement. I'm very thankful that this is the case because it makes growing older a lot more interesting.

There are many things in the world of science that I had no anticipation of ever learning. I wouldn't say that I wasn't prepared to see them but I'm positive that I never in my wildest dreams expected to see them- so that's not exactly "prepared" to see them either. There are also things that I thought were constants in my personal life that have changed (some for the better, some for the worse).

I refuse to believe that I was prepared to see things that have come as a total dumbfounding shock. If you say I must have been ready because I saw them then you're just playing around with a tautology.

I wonder if the older folks in this forum would be more apt to disagree with the statement that 'we only see what we're prepared to see'. I think I would have believed it when I was 25 but now that I'm 50 I've been surprised so many times I don't believe it any more.

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Siara

Our society has little regard for understanding because knowledge is sufficient for good production and consumption, besides understanding only creates independent thinking and that leads to problems. When we march passed knowing into understanding we better comprehend that we can see only what we are prepared to see.

Comprehension is a hierarchy, resembling a pyramid, with awareness at the base followed by consciousness, succeeded by knowing, with understanding at the pinnacle.

I have concocted a metaphor set that might relay my comprehension of the difference between knowing and understanding.

Awareness--faces in a crowd.

Consciousness—smile, a handshake, and curiosity.

Knowledge—long talks sharing desires and ambitions.

Understanding—a best friend bringing constant April.

I am a retired engineer and my experience in the natural sciences leads me to conclude that these natural sciences are far more concerned with knowing than with understanding.

Understanding is a long step beyond knowing and most often knowing provides the results that technology demands. Technology, I think, does not want understanding because understanding is inefficient and generally not required. The natural scientists, with their paradigms, are puzzle solvers. Puzzles require ingenuity but seldom understanding.

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If one is born and taught that 1+1=3, and are never taught the truth, they'll never question it because they don't realize to. So yes, people only learn what they're are prepared to learn prior. :tu:

I disagree with this statement. Half of the people will accept it unquestioningly like a bunch of complacent cattle chewing their cud, but the other half WILL question it because, for example, they'll realize that 1+1 can not equal the same thing as 1+1+1. There are a number of people around who are still capable of logic and common sense. Interestingly, this group is probably evenly divided between people with loads of formal education and people who have education in the trades (eg- auto mechanics, electricians, carpenters, etc.). The realization that 1+1 can't equal 3 if 1+1+1 equals three requires people to notice that SOMETHING ISN'T WORKING.

The problem with our modern education system is that we've just been through a long cultural period in which Faith was advanced as a alternative to Science. People in the general population don't apply the scientific method and notice errors in the system because it's now it's okay for logical errors to exist. Contradictions don't set off alarms. The problem isn't that people refuse to see. It's that they are too ready to accept the idea that things don't need to make sense.

Another problem is that people don't feel comfortable saying, "I don't know". They feel that this statement reflects some sort of intellectual immaturity.

The true scientific community is continuously evaluating itself with studies, peer reviews and so on.

I have concocted a metaphor set that might relay my comprehension of the difference between knowing and understanding.

Awareness--faces in a crowd.

Consciousness—smile, a handshake, and curiosity.

Knowledge—long talks sharing desires and ambitions.

Understanding—a best friend bringing constant April.

To me your premiss implies that people won't see the crowd at all until they're ready to see it. I disagree. If the people who don't notice the crowd are active in their environment they WILL COME TO NOTICE because eventually they'll bump into someone and that person will yell, "Hey, watch where you're going".

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I disagree with this statement. Half of the people will accept it unquestioningly like a bunch of complacent cattle chewing their cud, but the other half WILL question it because, for example, they'll realize that 1+1 can not equal the same thing as 1+1+1. There are a number of people around who are still capable of logic and common sense. Interestingly, this group is probably evenly divided between people with loads of formal education and people who have education in the trades (eg- auto mechanics, electricians, carpenters, etc.). The realization that 1+1 can't equal 3 if 1+1+1 equals three requires people to notice that SOMETHING ISN'T WORKING.

The problem with our modern education system is that we've just been through a long cultural period in which Faith was advanced as a alternative to Science. People in the general population don't apply the scientific method and notice errors in the system because it's now it's okay for logical errors to exist. Contradictions don't set off alarms. The problem isn't that people refuse to see. It's that they are too ready to accept the idea that things don't need to make sense.

Another problem is that people don't feel comfortable saying, "I don't know". They feel that this statement reflects some sort of intellectual immaturity.

The true scientific community is continuously evaluating itself with studies, peer reviews and so on.

To me your premiss implies that people won't see the crowd at all until they're ready to see it. I disagree. If the people who don't notice the crowd are active in their environment they WILL COME TO NOTICE because eventually they'll bump into someone and that person will yell, "Hey, watch where you're going".

You're misunderstanding what I said. If someone is raised away from all mankind and raised in the wild, they're not prepared to do for example math. Or to interact with people, or anything else for that matter. You added a variable by saying that a person that thinks 1+1=3 would be around others that knew 1+1=2. I said that they'd never encounter the truth. If someone is raised that way from birth, and then one day they come across something written that says 1+1=2, they'll think it is wrong automatically because they know no better. More to that, they won't even question the act of "correcting" it because from their viewpoint, they're right and what was written is wrong. Even in our current soceity, if everyone was taught completely wrong, they'd not question it. So my point is valid. If someone isn't prepared to know something, they'll never know it unless something changes it. This is why there are people in the world who are still uneducated and won't accept education because they "think" they don't need it. It's a sad truth, but it is the truth nonetheless.

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You're misunderstanding what I said. If someone is raised away from all mankind and raised in the wild, they're not prepared to do for example math. Or to interact with people, or anything else for that matter. You added a variable by saying that a person that thinks 1+1=3 would be around others that knew 1+1=2. I said that they'd never encounter the truth.

Wrong. They will encounter the truth in the course of their experience as logical beings in the rational, physical world. They will understand the difference between two and three because they'll notice that if they have 3 coconuts they can't hold each one in a different hand at the same time because they only have two hands and three does not equal two. They'll encounter the truth as soon as they begin interacting with the physical world because the truth exists outside our heads in the world around us.

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Wrong. They will encounter the truth in the course of their experience as logical beings in the rational, physical world. They will understand the difference between two and three because they'll notice that if they have 3 coconuts they can't hold each one in a different hand at the same time because they only have two hands and three does not equal two. They'll encounter the truth as soon as they begin interacting with the physical world because the truth exists outside our heads in the world around us.

You're still missing my point. If the word "two" didn't exist to everyone, and they equated "two" with "three", and all of mathematics ended up getting based around this concept. Then no one would question it. If the concept is not there, they'll never concieve it to ever be wrong. another example would be if someone doesn't realize that walking across the street was illegal(jaywalking), they'd never worry about it. Now yes, no one really cares about jaywalking these days, but technically it is illegal. Very few people even know this, and truly no police officer will issue a ticket for such, but they can issue one if they the police officer is a punk. I know many many people who don't know that jaywalking is illegal. If they are never told such, the concept is beyond them to question it. If the concept is beyond someone, if they are never taught it, they'll never know to ask. Truth doesn't exist outside our heads, but is a concept thought up by people. A person raised by animals would never understand 1+1=2 because they are raised by animals.

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It is a hypothesis of SGCS (Second Generation Cognitive Science) that the sensorimotor activity of collecting objects by a child constitute a conceptual metaphor at the neural level leading to a primary metaphor that ‘arithmetic is object collection’. The arithmetic teacher attempting to teach the child at a later time depends upon this already accumulated knowledge. Of course, all of this is known to the child without the symbolization or the conscious awareness of the child.

The pile of objects became ‘bigger’ when the child added more objects and became ‘smaller’ when objects were removed. The child easily recognizes while being taught arithmetic that 5 is bigger than 3 and 3 is littler than 7. The child knows many entailments, many ‘truths’, resulting from playing with objects. The teacher has little difficulty convincing the child that two collections A and B are increased when another collection C is added, or that if A is bigger than B then A+C is bigger than B+C.

At birth an infant has a minimal innate arithmetic ability. This ability to add and subtract small numbers is called subitizing. (I am speaking of a cardinal number—a number that specifies how many objects there are in a collection, don’t confuse this with numeral—a symbol). Many animals display this subitizing ability.

In addition to subitizing the child, while playing with objects, develops other cognitive capacities such as grouping, ordering, pairing, memory, exhaustion-detection, cardinal-number assignment, and independent order.

Subitizing ability is limited to quantities 1 to 4. As a child grows s/he learns to count beyond 4 objects. This capacity is dependent upon 1) Combinatorial-grouping—a cognitive mechanism that allows you to put together perceived or imagined groups to form larger groups. 2) Symbolizing capacity—capacity to associate physical symbols or words with numbers (quantities).

“Metaphorizing capacity: You need to be able to conceptualize cardinal numbers and arithmetic operations in terms of your experience of various kinds—experiences with groups of objects, with the part-whole structure of objects, with distances, with movement and location, and so on.”

“Conceptual-blending capacity. You need to be able to form correspondences across conceptual domains (e.g., combining subitizing with counting) and put together different conceptual metaphors to form complex metaphors.”

Primary metaphors function somewhat like atoms that can be joined into molecules and these into a compound neural network. On the back cover of “Where Mathematics Comes From” is written “In this acclaimed study of cognitive science of mathematical ideas, renowned linguist George Lakoff pairs with psychologist Rafael Nunez to offer a new understanding of how we conceive and understand mathematical concepts.”

“Abstract ideas, for the most part, arise via conceptual metaphor—a cognitive mechanism that derives abstract thinking from the way we function in the everyday physical world. Conceptual metaphor plays a central and defining role in the formation of mathematical ideas within the cognitive unconscious—from arithmetic and algebra to sets and logic to infinity in all of its forms. The brains mathematics is mathematics, the only mathematics we know or can know.”

We are acculturated to recognize that a useful life is a life with purpose. The complex metaphor ‘A Purposeful Life Is a Journey’ is constructed from primary metaphors: ‘purpose is destination’ and ‘action is motion’; and a cultural belief that ‘people should have a purpose’.

A Purposeful Life Is A Journey Metaphor

A purposeful life is a journey.

A person living a life is a traveler.

Life goals are destinations

A life plan is an itinerary.

This metaphor has strong influence on how we conduct our lives. This influence arises from the complex metaphor’s entailments: A journey, with its accompanying complications, requires planning, and the necessary means.

Primary metaphors ‘ground’ concepts to sensorimotor experience. Is this grounding lost in a complex metaphor? ‘Not by the hair of your chiney-chin-chin’. Complex metaphors are composed of primary metaphors and the whole is grounded by its parts. “The grounding of A Purposeful Life Is A Journey is given by individual groundings of each component primary metaphor.”

The ideas for this post come from “Philosophy in the Flesh”. The quotes are from “Where Mathematics Comes From” by Lakoff and Nunez

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It is a hypothesis of SGCS (Second Generation Cognitive Science) that the sensorimotor activity of collecting objects by a child constitute a conceptual metaphor at the neural level leading to a primary metaphor that ‘arithmetic is object collection’. The arithmetic teacher attempting to teach the child at a later time depends upon this already accumulated knowledge. Of course, all of this is known to the child without the symbolization or the conscious awareness of the child.

The pile of objects became ‘bigger’ when the child added more objects and became ‘smaller’ when objects were removed. The child easily recognizes while being taught arithmetic that 5 is bigger than 3 and 3 is littler than 7. The child knows many entailments, many ‘truths’, resulting from playing with objects. The teacher has little difficulty convincing the child that two collections A and B are increased when another collection C is added, or that if A is bigger than B then A+C is bigger than B+C.

At birth an infant has a minimal innate arithmetic ability. This ability to add and subtract small numbers is called subitizing. (I am speaking of a cardinal number—a number that specifies how many objects there are in a collection, don’t confuse this with numeral—a symbol). Many animals display this subitizing ability.

In addition to subitizing the child, while playing with objects, develops other cognitive capacities such as grouping, ordering, pairing, memory, exhaustion-detection, cardinal-number assignment, and independent order.

Subitizing ability is limited to quantities 1 to 4. As a child grows s/he learns to count beyond 4 objects. This capacity is dependent upon 1) Combinatorial-grouping—a cognitive mechanism that allows you to put together perceived or imagined groups to form larger groups. 2) Symbolizing capacity—capacity to associate physical symbols or words with numbers (quantities).

“Metaphorizing capacity: You need to be able to conceptualize cardinal numbers and arithmetic operations in terms of your experience of various kinds—experiences with groups of objects, with the part-whole structure of objects, with distances, with movement and location, and so on.”

“Conceptual-blending capacity. You need to be able to form correspondences across conceptual domains (e.g., combining subitizing with counting) and put together different conceptual metaphors to form complex metaphors.”

Primary metaphors function somewhat like atoms that can be joined into molecules and these into a compound neural network. On the back cover of “Where Mathematics Comes From” is written “In this acclaimed study of cognitive science of mathematical ideas, renowned linguist George Lakoff pairs with psychologist Rafael Nunez to offer a new understanding of how we conceive and understand mathematical concepts.”

“Abstract ideas, for the most part, arise via conceptual metaphor—a cognitive mechanism that derives abstract thinking from the way we function in the everyday physical world. Conceptual metaphor plays a central and defining role in the formation of mathematical ideas within the cognitive unconscious—from arithmetic and algebra to sets and logic to infinity in all of its forms. The brains mathematics is mathematics, the only mathematics we know or can know.”

We are acculturated to recognize that a useful life is a life with purpose. The complex metaphor ‘A Purposeful Life Is a Journey’ is constructed from primary metaphors: ‘purpose is destination’ and ‘action is motion’; and a cultural belief that ‘people should have a purpose’.

A Purposeful Life Is A Journey Metaphor

A purposeful life is a journey.

A person living a life is a traveler.

Life goals are destinations

A life plan is an itinerary.

This metaphor has strong influence on how we conduct our lives. This influence arises from the complex metaphor’s entailments: A journey, with its accompanying complications, requires planning, and the necessary means.

Primary metaphors ‘ground’ concepts to sensorimotor experience. Is this grounding lost in a complex metaphor? ‘Not by the hair of your chiney-chin-chin’. Complex metaphors are composed of primary metaphors and the whole is grounded by its parts. “The grounding of A Purposeful Life Is A Journey is given by individual groundings of each component primary metaphor.”

The ideas for this post come from “Philosophy in the Flesh”. The quotes are from “Where Mathematics Comes From” by Lakoff and Nunez

Thank you for stating it in a way that was more indepth than I would have. If the concept is not understood or taught, they won't advance further to question it. I'm not sure if others here would understand what you wrote, but good job anyway. :tu:

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Posted (edited)

You're still missing my point. If the word "two" didn't exist to everyone, and they equated "two" with "three", and all of mathematics ended up getting based around this concept. Then no one would question it.

I do not believe that we have to be taught to differentiate between the concepts of "two" and "three". I think it is innate. There are a few primitive cultures in the world that don't count, but they have physical symbols which they equate on a one-to-one basis with members of the group they're considering. Example: a hunter wants to catch a rabbit for each member of his family. He can't count but he wears a pouch around his neck containing 5 pebbles. The red pebble is associated with his mate. The large, dark pebble is associated with his oldest son. The tiny, white pebble is associated with the new baby, etc. After he's killed a few rabbits he takes the pebbles out of the pouch and spreads them out on the ground, then places a rabbit next to as many pebbles as possible. If any of his special pebbles don't have a rabbit, he keeps hunting. He does this until each pebble has a rabbit, then takes the kill home to his family. He knows that each family member will have a rabbit because every pebble in his pouch corresponds to a rabbit.

This is the absolute most primitive manifestation of counting in the world. Every human being has this or something more sophisticated. The feral children in central European countries that were adopted by dog packs still understand one-to-one correlation. It's hard wired.

There's quite a bit of evidence that many other mammalian species are hard wired to differentiate between one, two, three, and many as well. When a dog sees a single ball in a box and an experimenter puts other balls in the box, dogs in psychology experiments will spend more time examining the box if it sees one more ball put in the box from a distance and as it draws near it finds three balls in the box (with an extra ball added via a trap door). It knows that if there was one ball in the box to begin with and someone added another ball there shouldn't be three balls. The dog reacts the same way if it sees two balls put in the box and one is removed via a trap door. They realize there's a logic error.

I'm not missing your point. I disagree with you (I've read quite a bit about the subject too). There aren't any people for whom "two" and "three" aren't separate concepts- except very severely brain damaged people.

Edited by Siara

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Posted (edited)

The child knows many entailments, many ‘truths’, resulting from playing with objects. The teacher has little difficulty convincing the child that two collections A and B are increased when another collection C is added, or that if A is bigger than B then A+C is bigger than B+C.

At birth an infant has a minimal innate arithmetic ability. This ability to add and subtract small numbers is called subitizing. (I am speaking of a cardinal number—a number that specifies how many objects there are in a collection, don’t confuse this with numeral—a symbol). Many animals display this subitizing ability.

In other words, he doesn't need to learn it from other humans. All he has to do is manipulate elements in his environment. Any human who has been allowed to manipulate objects in his/her environment intuitively knows that two doesn't equal three.

This is what George Lakoff means by the "embodied mind". There is quite a bit of basic knowledge that doesn't come to us via other people and for which there's no such thing as "not being prepared to see it" ( referring to the OP). Lakoff was a student of Noam Chomsky's. He didn't go for the deconstruction of physical reality.

Meiliken wrote:

If the concept is not understood or taught, they won't advance further to question it. I'm not sure if others here would understand what you wrote, but good job anyway.

I don't see how you can draw the conclusion that the person needs to be TAUGHT when you've just read quite a bit of evidence that in fact the person DOESN'T need to be taught. The person understands intuitively, on his own, from manipulating his environment. Being taught is not our only source of understanding. Though "I'm not sure others here would understand" this :)

Edited by Siara

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I don't see how you can draw the conclusion that the person needs to be TAUGHT when you've just read quite a bit of evidence that in fact the person DOESN'T need to be taught. The person understands intuitively, on his own, from manipulating his environment. Being taught is not our only source of understanding. Though "I'm not sure others here would understand" this :)

A person will innately understand that if they add another object to their collection that they have more than they previously had, but the concept of "I had 2, now I have 3" is beyond their understanding unless they are taught it.

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A person will innately understand that if they add another object to their collection that they have more than they previously had, but the concept of "I had 2, now I have 3" is beyond their understanding unless they are taught it.

Then, according to your argument, how did the numbers two and three become constants in society? Somebody must have invented them, right? But what you are saying is it's impossible for someone to understand it unless they are taught it. All information on Earth today was created/thought of by humans.

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If one is born and taught that 1+1=3, and are never taught the truth, they'll never question it because they don't realize to.
If this was the case, our species would never discover anything new. Most individuals probably do not question what authority tells them, but quite a few must do.

This may interest some people. It's about the natural tendancy to believe what you are told.

http://books.google.co.uk/books?id=yq1xDpi...lt&resnum=1

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Then, according to your argument, how did the numbers two and three become constants in society? Somebody must have invented them, right? But what you are saying is it's impossible for someone to understand it unless they are taught it. All information on Earth today was created/thought of by humans.

Yes, by people who invented them to teach to others. A person who is raised by wolves will not magically know the concept of numbers until it is taught to them. It's not even an argument, it's been shown by people who were raised by animals.

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