Why INTP-types cannot really discuss anything with eachother

[Tannhauser]

A typical INTP has a religious faith in his own ability to reason in a vacuum – he has no respect for existing literature, or history, or tradition.

As long as the INTP has built a matrix of conceptual connection in his mind, supposedly using cold logic (he thinks), everything is seemingly solved. There is no reason to even read books or seek out the findings of other people.

Meanwhile, the reality is that all our knowledge is dependent on history, on tradition, on the works of our predecessors. If you think you have solved everything, it is probably because you have reasoned inside a tiny aquarium of knowledge.

 

[Andronas]

A typical INTP has a religious faith in his own ability to reason in a vacuum – he has no respect for existing literature, or history, or tradition.

As long as the INTP has built a matrix of conceptual connection in his mind, supposedly using cold logic (he thinks), everything is seemingly solved. There is no reason to even read books or seek out the findings of other people.

Meanwhile, the reality is that all our knowledge is dependent on history, on tradition, on the works of our predecessors. If you think you have solved everything, it is probably because you have reasoned inside a tiny aquarium of knowledge.

So basically limited/underdeveloped Ne.

 

[Teax]

the reality is that all our knowledge is dependent on history, on tradition, on the works of our predecessors

Not abstract knowledge (tools of thought):
2+2 is 4, regardless of existing literature, history or tradition.

 

[Analyzer]

This is why studying the classics and history is so important, yet neglected by modern education. Humans have been thinking for thousands of years. Learning Greek and Latin is beneficial for this very reason.

Not abstract knowledge (tools of thought):
2+2 is 4, regardless of existing literature, history or tradition.

Who came up with this theorem? Surely this is a mathematical axiom which is assumed in order to be of use. A priori knowledge can work independently of other(empirical) knowledge, but it still needs to be developed and put forth by someone.

 

[Teax]

Surely this is a mathematical axiom which is assumed in order to be of use. A priori knowledge can work independently of other(empirical) knowledge, but it still needs to be developed and put forth by someone.

Yes, even abstract knowledge like that cannot exist without some assumptions.

The assumptions for 2+2=4 are not imposed by culture, they exist as part of the human condition. Axiom is the word for such assumptions. Axioms do not have to be assumed, you assume them by default through interaction with what you perceive as reality.

Therefore axioms (and most of math) do not have to be developed and put forth by anyone to be useful. They're used by all kinds of illiterate creatures, and are merely discovered by culture to assign language-constructs to it so we can communicate to each other about it.

 

[Ex-User (11125)]

you have reasoned inside a tiny aquarium of knowledge.

i dont think its like that at all, i mean...i dont think a person who looks to build a personal "matrix of conceptual connection in his mind" and achieves fulfillment from that is feeling fulfilled because they think they have "reasoned" the problem

Spoiler

the following might be a good example of bubble of bullshit

imo people can generally be divided into two types:
the rational and the irrational

the rational is looking to deduce meaning thrpugh a series of retinal pictures, the observed is treated as an external and objectified problem, understanding is achieved through passive examination and accumulation of external references..."retinal" here is analogy for how the rational strives to be an un-involved spectator studying the observed from an external disposition

whereas the irrational understands through multi-sensory and synchronic imagination the irrational desires haptic contact and identification with the space, understanding comes through deliberate suppression of sharp focused "vision" and going for a more intimate contact with the subject. for the irrational, quality is in the peripheral which enfolds you within the space. sense of self is reinforced by fully engaging in, relating and mediating with the observed to project meaning...you lend your emotions and associations to the observed to incorporate your own existential experience to form a more strengthened coherence and significance of the world

Btw the titles i chose here "rational" and "irrational" were chosen this way to signify how each's approach is generally *percieved* and not meant to say that either is better than the other. I belong in the second category, you obviously belong in the first

 

[Terran]

It is illogical to not participate/acknowledge some social conventions and culture, as they are beneficial to society and general happiness. Even the 'Vulcans' practice a traditional culture and discuss history!

I Indulge in illogic for the greater, logical, good! I mean everyone does it to some extent, don't tell me no one here has had sex or ate junk food just because it was illogical. And I don't think most INTPs have "reasoned inside a tiny aquarium of knowledge". Being thoughtful and logical does not equate to being ignorant, in some cases rejective of unscientific ideas maybe, but rightly so!

There is a difference between being scientific and purely calculating, just because you know a religion or idea is wrong (or at least has no reason to be assumed right!) doesn't mean we are aggressively opposed to people who chose to belief them.

 

[Ex-User (9086)]

Even the 'Vulcans' practice a traditional culture and discuss history!

I Indulge in illogic for the greater, logical, good!

Lol, contextually the funniest thing I read today.

That's exactly the kind of response Tannhauser was looking for!

I think op has some wild expectations about what the outcome of a discussion should be. OP assumes discussions should lead to actionable and realistic conclusions most of the time and that the goal of a discussion isn't furthering the participants knowledge but staying relevant and compatible with existing real-life systems.

I'm inclined to presume OP detests some of the more abstract and subjective styles of deliberation.

 

[Sly-fy]

I don`t make it a habit of every fully making my mind up on any one thing, with few exceptions. I`m always open to new evidence and reasonings, although that`s not to say that I`m subjecting myself to be open to believing whatever crazy new idea I come across.

My views today are virtually a complete 180 of what they were just a few years ago, and they are subject to keep changing still. Sometimes I do a 360 after having done a 180. However, there are possibilities that I will entertain without having any intent on embracing them, if they for example contradict my morals and values which were highly influenced by the Judeo-Christian traditions of our society, which I consider to be objective truths (as they relate to my life anyway.)

So in other words while my mind is malleable my heart is less so, if you will.

 

[Tannhauser]

Therefore axioms (and most of math) do not have to be developed and put forth by anyone to be useful. They're used by all kinds of illiterate creatures, and are merely discovered by culture to assign language-constructs to it so we can communicate to each other about it.

That may hold for elementary arithmetic like 2+2. For the rest of math, that becomes a very dubious claim. Even just extending arithmetic to negative numbers (or the inclusion of the number 0), you have to start building a theoretical framework.

Actually, when I think of it, Gödel's incompleteness theorems suggest that even arithmetic cannot be a self-consistent axiomatic system. So that's that – we have to actively invent everything, even math.

 

[Sly-fy]

That may hold for elementary arithmetic like 2+2. For the rest of math, that becomes a very dubious claim. Even just extending arithmetic to negative numbers (or the inclusion of the number 0), you have to start building a theoretical framework.

Sorry if I`m misinterpreting what you`re suggesting, but do you mean that only simple adding and subtracting (and only if you, for whatever reason like you said discount negative numbers) and similar low complexity math is logical, while most of the rest of the math is subjective and illogical? And if so, would that imply that long division is not grounded in reality?

Like (a + b)2 = a2 + 2ab + b2; a2 + b2 = (a + b)2 − 2ab is true only for me, but not for you as well?

 

[Tannhauser]

I think op has some wild expectations about what the outcome of a discussion should be. OP assumes discussions should lead to actionable and realistic conclusions most of the time and that the goal of a discussion isn't furthering the participants knowledge but staying relevant and compatible with existing real-life systems.

I'm inclined to presume OP detests some of the more abstract and subjective styles of deliberation.

Not at all. In my opinion, the outcome of a discussion, in most cases, should indeed be the exchange of knowledge. But that exchange is either worthless or impossible unless the participants can provide bits of findings from a large collection of sources. Otherwise it is just two matrices of "logical" connections comparing each other, with the only outcome being a severe case of cognitive dissonance for both parties because each of them is exposed to knowledge slightly outside their own tiny aquarium.

I suspect that perceiving-types are more able to just say "hey, I read this thing from such and such author, where he said... etc etc" – without judgment and just for the sake of discussion.

 

[redbaron]

Don't see the need for MBTI, people in general have trouble discussing things.

Also, this is an internet forum and you're bound to find more disagreement and debate than in majority of real life situations because that's how internet forums work.

 

[Tannhauser]

Sorry if I`m misinterpreting what you`re suggesting, but do you mean that only simple adding and subtracting (and only if you, for whatever reason like you said discount negative numbers) and similar low complexity math is logical, while most of the rest of the math is subjective and illogical? And if so, would that imply that long division is not grounded in reality?

Like (a + b)2 = a2 + 2ab + b2; a2 + b2 = (a + b)2 − 2ab is true only for me, but not for you as well?

No, what I meant was that only isolated and elementary cases like 2+2=4 can be said to be easily put down as an axiom based on experience. Take for example 1/0 and suddenly there is nothing in experience that dictates the answer.

We all agree on the algebra of that equation (or at least if by (a + b)2 you mean (a + b)^2 ), but only because people before us built the system of those symbolic operations.

 

[Haim]

A typical INTP has a religious faith in his own ability to reason in a vacuum – he has no respect for existing literature, or history, or tradition.

As long as the INTP has built a matrix of conceptual connection in his mind, supposedly using cold logic (he thinks), everything is seemingly solved. There is no reason to even read books or seek out the findings of other people.

Meanwhile, the reality is that all our knowledge is dependent on history, on tradition, on the works of our predecessors. If you think you have solved everything, it is probably because you have reasoned inside a tiny aquarium of knowledge.

Because most INTPs can actually think, sorry I care only if you are correct, I care not that you are "expert" and that your professor once told you something that his professor once told him, he is passing on his teacher stupid ideas without thinking.Really we have universities full of professors for computer science that did not code in professional manner in their life, not to mention writing a real software, how can they know their ideas are any good?
Saying things which are different to the main accepted ideas does not make them false, also you assume beforehand that the INTP has no knowledge, you do not know that, they might have considered that and you do not understand why they rejected the source.
Also not every subject needs mass amount of knowledge to discuss, many times more knowledge just means you have more false ideas and assumptions not that you are more correct.

 

[Sly-fy]

No, what I meant was that only isolated and elementary cases like 2+2=4 can be said to be easily put down as an axiom based on experience. Take for example 1/0 and suddenly there is nothing in experience that dictates the answer.

We all agree on the algebra of that equation (or at least if by (a + b)2 you mean (a + b)^2 ), but only because people before us built the system of those symbolic operations.

Hmmm, I see! Thanks for explaining that to me.

 

[Teax]

I agree that culture is important to establish a common language for communication, but in respect to abstract knowledge, that's where its involvement ends.

For the rest of math, that becomes a very dubious claim. Even just extending arithmetic to negative numbers (or the inclusion of the number 0), you have to start building a theoretical framework.

No you don't. The understanding of the number zero and negative numbers is innate in all of us. Numbers don't exist in a vacuum, they always have a purpose, a direction. The sign is nothing more than a direction modifier. The minus sign is the opposite direction.

[BIMG]https://upload.wikimedia.org/wikipedia/commons/0/02/Caramels.jpg[/BIMG]

Alternatively, even a little kid can be shown to have instinctive understanding of the zero and negatives:

Spoiler

Integers: The understanding of integer numbers is innate in all of us, we all counted items since we were little, how many pieces of candy to you have?

Order: The understanding of that a next number always exists is innate in all of us. What would be better than having 2 pieces of candy? having 3 pieces! 3 is the "next" number from "2".

Zero: did you ever eat all your candy? When you eat candy, you traverse the integers in reverse order. You learn that zero is the "previous" number from one.

Negative numbers: The INTP kid would go one step further and ask himself how much candy you have if you ate one more. If traversal in the "up" direction is possible ad infinitum, then surely the opposite might be possible as-well. What would the previous number from zero look like?

It doesn't matter what we call the number, call it "-1", call it "E" or call it " 马", it's uniquely identifiable as the previous number from Zero, and that's all that matters.

You can prove that the innate understanding is in all (most?) of us by doing this little experiment: Ask a kid who can count, to jump 3 steps forward. Then ask her to jump one less step. Then one less. Then one less again. If you do it again, some children will jokingly jump one step backwards. proof enough?

Take for example 1/0 and suddenly there is nothing in experience that dictates the answer.

I must disagree, division a/b is the question "how often does b fit into a". Which is just another way of saying: keep adding b's and count how many you added until you reach a. The answer to 1/0: No matter how many, it won't be enough.

The one sided limit of a function is the mathematically formal way of coming up with the above solution. It is not an alternative way of figuring out the solution, it is the exact same approach, using symbolic notation instead of the English language.

All those old geezers of whom we learn about in our history lessons did back then is establish a notational system to be able to talk about this crap. None of it is invented, merely discovered and cataloged.

Actually, when I think of it, Gödel's incompleteness theorems suggest that even arithmetic cannot be a self-consistent axiomatic system. <=> So that's that – we have to actively invent everything, even math.

Non-sequitor at the "<=>" thingy. The incompleteness theorem does not interfere with the applicability of math, merely with what some mathematicians have perceived as the beauty of math. (All Gödel did was prove that there is no set of axioms that simultaneously "be used to prove/disprove every possible equation", and "provide exactly one solution for every possible equation". It's an interesting result, but nothing that pertains to our discussion. But many people misunderstand the implications of this so the internet is full of crap about this topic as you can imagine)

We all agree on the algebra of that equation (or at least if by (a + b)2 you mean (a + b)^2 ), but only because people before us built the system of those symbolic operations.

precisely, that's all they did, assign symbols. If an alien race started communicating with us about math, we could recognize this equation in their own notation, even if they never had anything like a "+" and "*" and instead used some sort of weird "ternary linear transformation operator". Because the underlying principle is the same and so their math will be mappable to our math. Therefore I completely disagree with this:

Otherwise it is just two matrices of "logical" connections comparing each other, with the only outcome being a severe case of cognitive dissonance for both parties because each of them is exposed to knowledge slightly outside their own tiny aquarium.

The two matrices of logical connections will exhibit major structural equivalence and the two INTPs have a chance to adjust their respective graphs to better understand the topic, or find premises that they disagree on.

I agree with you on one thing though: INTPs are usually too sure about their matrices of logical connections. The typical scenario is: they refuse to consider there being a flaw in their logic, instead they try to find premises the opposing party might have overlooked, and if those are all right, assume the opposing party lacks intelligence/logic to infer the answer from those premises.

 

[Sly-fy]

Wow Teax, you blew my mind!

 

[cheese]

I actually had a very similar discussion with Proxy last night, about why INTPs find it hard to get along or discuss things. First off, Ti is detached, so it's not the greatest tool to connect with, and secondly, the nature of Ti is to be suspicious of other people's reasoning abilities and trust only in your own working, so they tend to be doubtful of whether the other party has done their due diligence checking their assumptions and whatnot. This is also a problem with high N people, as each generates more and more potential holes/alternatives that 'maybe you haven't considered'. Can make conversation impossible.

The only solution to this is social experience. After a while you realise other people have brains too. I have a shorthand blanket disclaimer with some people that covers all the objections they might have. They trust from experience that we're thinking of the same counters, and I trust that they trust me enough to know if I haven't considered something in particular, all I need is a little push in the right direction (rather than a shove off a cliff). Much easier conversation without endless parentheses and justifying. (Though sometimes that's fun!)

 

[Absurdity]

Is this supposed to be a demonstration of Cunningham's Law?

Cunningham's Law states "the best way to get the right answer on the Internet is not to ask a question, it's to post the wrong answer."

 

[Tannhauser]

I agree that culture is important to establish a common language for communication, but in respect to abstract knowledge, that's where its involvement ends.



No you don't. The understanding of the number zero and negative numbers is innate in all of us. Numbers don't exist in a vacuum, they always have a purpose, a direction. The sign is nothing more than a direction modifier. The minus sign is the opposite direction.

[BIMG]https://upload.wikimedia.org/wikipedia/commons/0/02/Caramels.jpg[/BIMG]

Alternatively, even a little kid can be shown to have instinctive understanding of the zero and negatives:

Spoiler

Integers: The understanding of integer numbers is innate in all of us, we all counted items since we were little, how many pieces of candy to you have?

Order: The understanding of that a next number always exists is innate in all of us. What would be better than having 2 pieces of candy? having 3 pieces! 3 is the "next" number from "2".

Zero: did you ever eat all your candy? When you eat candy, you traverse the integers in reverse order. You learn that zero is the "previous" number from one.

Negative numbers: The INTP kid would go one step further and ask himself how much candy you have if you ate one more. If traversal in the "up" direction is possible ad infinitum, then surely the opposite might be possible as-well. What would the previous number from zero look like?

It doesn't matter what we call the number, call it "-1", call it "E" or call it " 马", it's uniquely identifiable as the previous number from Zero, and that's all that matters.

You can prove that the innate understanding is in all (most?) of us by doing this little experiment: Ask a kid who can count, to jump 3 steps forward. Then ask her to jump one less step. Then one less. Then one less again. If you do it again, some children will jokingly jump one step backwards. proof enough?

I must disagree, division a/b is the question "how often does b fit into a". Which is just another way of saying: keep adding b's and count how many you added until you reach a. The answer to 1/0: No matter how many, it won't be enough.

The one sided limit of a function is the mathematically formal way of coming up with the above solution. It is not an alternative way of figuring out the solution, it is the exact same approach, using symbolic notation instead of the English language.

All those old geezers of whom we learn about in our history lessons did back then is establish a notational system to be able to talk about this crap. None of it is invented, merely discovered and cataloged.



Non-sequitor at the "<=>" thingy. The incompleteness theorem does not interfere with the applicability of math, merely with what some mathematicians have perceived as the beauty of math. (All Gödel did was prove that there is no set of axioms that simultaneously "be used to prove/disprove every possible equation", and "provide exactly one solution for every possible equation". It's an interesting result, but nothing that pertains to our discussion. But many people misunderstand the implications of this so the internet is full of crap about this topic as you can imagine)
.

I think you put a lot of interesting stuff on the table with this, Teax. However, I am not sure about the implication of all the examples you gave. From what I see, the question is not whether there exists an intuition for every mathematical concept, but whether you could construct mathematics exactly as it is, by going the other way: from intuitions to axioms. What prevents you, for example from seeing a water drop being merged with another drop and then concluding that 1+1=1, and then building a mathematical system with that as an axiom? The truth is that you indeed can do that – the question is just whether that is a useful system.

Your 1/0 example seems to imply that 1/0=Inf. But why not count in negative units and get -Inf? What happens if you extend the set of numbers to complex numbers? It seems that we have defined 1/0 as "undefined" because there is no way to assign a value to it in a way that is consistent with the rest of mathematics. As you found yourself, there is a way to think of it as a magnitude – but this magnitude has no place in our system the way we have devised it.

 

[Analyzer]

Yes, even abstract knowledge like that cannot exist without some assumptions.

The assumptions for 2+2=4 are not imposed by culture, they exist as part of the human condition. Axiom is the word for such assumptions. Axioms do not have to be assumed, you assume them by default through interaction with what you perceive as reality.

You assume their existence in the physical world of space and time. 2+2=4 is the approximation we make using numbers, to represent a perfect reality of quantity that we assume by default when we interact with the world.

Therefore axioms (and most of math) do not have to be developed and put forth by anyone to be useful. They're used by all kinds of illiterate creatures, and are merely discovered by culture to assign language-constructs to it so we can communicate to each other about it.

Yes, they represent platonic forms which are discovered though reason, innate in the mind. When I see two sticks on the ground I am innately aware they consist of "2" things and if I put two more they become "4" things. But I wouldn't be able to understand this knowledge for creating and using formal systems like math, praxeology, unless culture systematized them.

 

[Hadoblado]

I can certainly relate a prior self to OP's explanation. An appreciation for what others can bring to the table sometimes needs to be learned. I avoided reading books by experts because I knew experts could be wrong, the hidden assumption being that I could not be. It was also a devotion to 'learning how to learn', which was something allowed to me because I had nothing better to do. I didn't need to be goal oriented and could therefore squander and afternoon figuring out how something worked on my own rather than looking at the instruction manual. Finally, there was a feeling of achievement I felt when I thought of something, later to find out that some great thinker got famous off of it. It's not a fair parallel, since even if I haven't read about something, I live in a world where exposure to that idea is prevalent.

The thing is, talking to people and being open to ideas is a way to learn itself. It's simply more efficient for two people to have separate experiences and then relay them to one another, than for both people to go it alone. Finding a way to engage with the things other people have learned can be a challenge, but as a learner, you're better off for it so long as it's not your sole source of learning. Being textbook smart is useful, but also kinda empty, as you're just a repository for the thoughts of others, rather than an independent thinker. If you have both, you get to do all your thinking with the material produced by both yourself and others, leading to a greater and more rounded thought output.

 

[redbaron]

I still don't know how this is somehow a barrier to, "INTP" discussion and not just people generally though.

 

[Hadoblado]

I guess it's a Ti vs. Te reference? Low Ne?

I agree it's more generally applicable, but I don't think it's universal. If some people defer to the experience of others while some people don't, representing this in theory and measuring it could be of benefit. It doesn't necessarily need to be an MBTI thing, but that's what the forums about so it's an obvious first step.

 

[redbaron]

Do people not interact with others in the real world or something? It's pretty much the norm for people to, "reason inside a tiny aquarium". It's not special to the 2.5% of the population that are INTP.

 

[Archer]

Not abstract knowledge (tools of thought):
2+2 is 4, regardless of existing literature, history or tradition.

2+2=1 if you use a modulus of 3.

 

[Ex-User (9086)]

Not at all. In my opinion, the outcome of a discussion, in most cases, should indeed be the exchange of knowledge.

The problem you defined applies to people in general. I don't see any need to specify groups.

And obviously its opposite where people stick to authority and sources too much without any understanding or input of their own, which is also commonly seen here and everywhere else.

 

[Teax]

2+2 is 4, regardless of existing literature, history or tradition.

2+2=1 if you use a modulus of 3

Yes, regardless of existing literature, history or tradition.

You assume their existence in the physical world of space and time. 2+2=4 is the approximation we make using numbers, to represent a perfect reality of quantity that we assume by default when we interact with the world.

It's even more basic than that, it's an "idealization". Even if you're not convinced about the existence of an objective/physical reality, math still exists between you and what you perceive as a subjective reality, as the idealization of what you perceive.

When I see two sticks on the ground I am innately aware they consist of "2" things and if I put two more they become "4" things. But I wouldn't be able to understand this knowledge for creating and using formal systems like math, praxeology, unless culture systematized them.

So you're saying you do understand the knowledge, yet you wouldn't be able to use the knowledge... until someone else also understands this knowledge? Where is the difference (in understanding) between someone else systematizing stick-counting for you, and you systematizing it yourself?

If you can't use it, I'm inclined to say, you haven't understood it in the first place.

Your 1/0 example seems to imply that 1/0=Inf. But why not count in negative units and get -Inf? It seems that we have defined 1/0 as "undefined" because there is no way to assign a value to it in a way that is consistent with the rest of mathematics.

Except, we never established that we have to assign one value to everything, so there is no consistency issue here. I don't like to refer to the solution of 1/0 as "undefined". It's intuitively well defined as "no matter how many, it won't be enough". In other words: there exists no such x that would solve the equation 1/0=x. Or simply, there is no solution/value.

The value is only undefined if we assume there has to be one. (which we are often foolishly brainwashed into believing by our culture).

Inf is not a magnitude. So 1/0=Inf is not true/false, instead it doesn't even make sense to write down unless you define exactly what Inf means in that context.

What happens if you extend the set of numbers to complex numbers?

The elusive i number, which is same thing as the minus sign, just a direction modifier. Except this time, you turn halfway-back.

So i * i * 1 = -1, because turning a "one" halfway-back two times, is turning a "one" back all the way.

What prevents you, for example from seeing a water drop being merged with another drop and then concluding that 1+1=1, and then building a mathematical system with that as an axiom? The truth is that you indeed can do that – the question is just whether that is a useful system.

Yes even that is a useful system. It models exactly the perceived behavior of liquids. Specifically it models the contiguous unit count during a merging process. You have to realize that, because formal math does not take away the burden of correct modeling. Even with all the work supposedly-smart people have put into meticulously formalizing math, you still have to figure out what pieces of reality correspond to what formalism. To do that you have to understand both (both are structurally the same so it's half as hard as it sounds).

So, what prevents us from using your new + sign (lets call it [+]) as a the default + sign for all math? Simply the fact that both axioms exist in your perceived reality. To model the mass of the 2 liquid drops, you'd use the normal + sign again, 1+1=2, while at the same time use 1[+]1=1 for drop count. Using [+] for everything would put you in denial about [+] not correctly modeling anything except drop count after merging.

From what I see, the question is not whether there exists an intuition for every mathematical concept, but whether you could construct mathematics exactly as it is, by going the other way: from intuitions to axioms.

Any one formalism that is based on the innate understanding of reality would be transferable to any other, since they're all based on the same innate understanding. Therefore structurally, math couldn't exist any other way it does now. Notation is just eye-candy.

 

[Analyzer]

So you're saying you do understand the knowledge, yet you wouldn't be able to use the knowledge... until someone else also understands this knowledge? Where is the difference (in understanding) between someone else systematizing stick-counting for you, and you systematizing it yourself?

Stick counting is simple, but when we get to things like geometry they are based off of theorems which are assumed. If I didn't study Pythagoras, I wouldn't understand the tautology proposed and it's relation to reality. Perhaps I could come up with something similar using my own reason but why reinvent the wheel? Even Einstein developed his theories based of Parmenides "Block time" and his development of axiomatic-deduction.

 

[Teax]

Perhaps I could come up with something similar using my own reason but why reinvent the wheel?

Yep I agreed that as a means of communication, culture is invaluable.

Even on a smaller scale, our feeble brains are unable to hold too much complexity. So developing any moderately complex project requires that you write stuff down, essentially communicating with yourself in the future.

What I was referring to is this:

the reality is that all our knowledge is dependent on history, on tradition, on the works of our predecessors

The premises in your studies might have been assumed for the purpose of whatever you were studying, but they are not just assumed because "Pythagoras said so". History has no influence on how technical stuff works today or how we think, instead history merely dictates the pace of discovery.

People who value history too much seem to think math is some sort of alternative framework of thinking, that only exists because important people decided it that way. Actually we're all walking through a dark room and those like Pythagoras were in front. If you want to name theorems based on who tripped over them and cried first, well.....

There's one piece of history that I respect because it played a major part in developing our thinking: When people decided not to burn people at the stake for thinking for themselves. I'm ranting.. have to stop...

 

[Haim]

Take for example 1/0 and suddenly there is nothing in experience that dictates the answer.

"/" is an operation the simply can not take zero as input, "1/0" value is not a number but a function, which mean you can not even compere it to numbers.
"1+1" is also a function, that produce the number 2,"1+1" is not 2!it is an operation that the output of his is 2, like sperm+woman=baby, "sperm+woman" is not an actual thing in this case but an operation /function that results in baby.
Lets break a pc, pc-GPU= a pc without a gpu, "-" is the operation of taking things in this case.
pc without a gpu -GPU= you cant even do it, the operation can not do it.
division is an operation that takes two inputs and return a new number, 1/0 is simple a case where it does not and can not return a number.

With that said, I have some doubts about math is universal, I mean there is no "2" in realty, it is just our way of interpreting realty, two what?particles?they themselves are not made of some constant number of things.Geometry?let me see a perfect line in realty.

 

[Tannhauser]

Yes even that is a useful system. It models exactly the perceived behavior of liquids. Specifically it models the contiguous unit count during a merging process. You have to realize that, because formal math does not take away the burden of correct modeling. Even with all the work supposedly-smart people have put into meticulously formalizing math, you still have to figure out what pieces of reality correspond to what formalism. To do that you have to understand both (both are structurally the same so it's half as hard as it sounds).

Well, exactly. But that seems to contradict your previous stance. If we choose our formalism on a case-by-case basis, then it becomes clear that what we think of mathematics, is just a particular choice of formalism amongst a huge collection of different possible ones. The one we are using now was built by people who wanted to crystallize certain notions into a consistent manipulation of symbols.

Any one formalism that is based on the innate understanding of reality would be transferable to any other, since they're all based on the same innate understanding. Therefore structurally, math couldn't exist any other way it does now. Notation is just eye-candy.

This is the problem with reasoning in a vacuum: we haven't seen a single justification of this claim. It seems to me that you have taken mathematics, as it exists in its current form, and said: "look at all these cases where math is intuitive", and used that as a basis for the reversed connection: that all things intuitive would lead to math as it is, and no other way. That's a pretty huge claim, which I see impossible to justify without a historical context.

 

[Teax]

Well, exactly. But that seems to contradict your previous stance. If we choose our formalism on a case-by-case basis then it becomes clear that what we think of mathematics, is just a particular choice of formalism amongst a huge collection of different possible ones. The one we are using now was built by people who wanted to crystallize certain notions into a consistent manipulation of symbols.

In principle yes. But knowing your stance, I suspect you imply by the words "crystallize certain notions" something else than I do. Because what I mean is they assigned a symbol to each mental concept they encountered.

I'm not sure where the contradiction is?

Also, just to be clear: We're already constructing abstract mind-concepts based on magnitudes on a case to case basis when we observe the subjective reality. Having to choose the corresponding formalism on a case to case basis is an... obvious.. consequence of that.

It seems to me that you have taken mathematics, as it exists in its current form, and said: "look at all these cases where math is intuitive", and used that as a basis for the reversed connection: that all things intuitive would lead to math as it is, and no other way. That's a pretty huge claim,

I'm not saying that all things intuitive would lead to math as it is right now on a symbolic level. I'm saying that on a structural level. Here's what I mean:

The number "2" takes 2 pen strokes to draw, and looks the way it looks because of history. But the meaning of 2 is the same for me or any alien humanoid creature who never heard about our history. Our subconscious ability to tell things apart (idealization) creates the innate understanding that there can be more than one thing. E.g. 2.

@Haim: Hereby it is irrelevant whether these things we see as "apart" really are apart in some sort of objective/physical reality or not. Because we're talking about idealization, not the actual reality.

Same goes for symbols like the "+" sign. But there is no reason why a plus sign requires exactly 2 inputs. I would love to have given it an arbitrary number of inputs, and build the rest of math around that. And if we do that, the resulting new_math would still be understandable by us in terms of idealized reality, we could still do all the calculations of... say.. grocery shopping, trajectory calculations with this new_math.

Math is a language, which, for each statement written in math, exists one corresponding mental concept. New_math is also a language which, has statements and corresponding mental concepts.

Take two statements, one from math, one from new_math, so that both correspond to the same mental concept. Are these two statements necessarily syntactically equivalent? No of course not.

Let's assume math has a relation/operator/action(whatever) applicable to the statement written in math. Since math is based on idealized reality, there must exists a corresponding idealized mental concept for that too. Since new_math is also based on the same idealized reality, new_math does not contain anything that would contradict the idealized reality. Therefore, either new_math already has a relation/operator/action that corresponds to this idealized mental concept, or if you prefer to think of math as not-yet-fully invented, one can be added without problems. So all theorems that can be written in math, can be written in new_math and mean the same thing. History is not involved here as far as I can see.

In layman's terms: Similar how the contextual meaning of English and Spanish can be translated in one another. Possible because the underlying structure of language can not be so different as to break out of the human condition.

which I see impossible to justify without a historical context.

Wait... now you tell me, how does a historical context help you justify any of this?

This is the problem with reasoning in a vacuum: we haven't seen a single justification of this claim.

(sorry I try to not write out a justification until I'm sure what/how far to justify, otherwise more of my posts would become as long as... well this one )

And yes I'm saying this precisely because I believe I see a valid reason why reasoning can exist in a vacuum. I could argue that it's never really a vacuum, because we are humans who are reasoning, and therefore our idealization of reality brings certain foundation with us that allows us to reason in a history-independent way. I would even argue that history and civilization is based on- because it started with- and could thus not exist without this foundation. Using English to reason this stance is no hypocrisy since English is a lackluster math that holds meaning, which is valid "in a vacuum".

 

[Haim]

I'm not saying that all things intuitive would lead to math as it is right now on a symbolic level. I'm saying that on a structural level. Here's what I mean:

The number "2" takes 2 pen strokes to draw, and looks the way it looks because of history. But the meaning of 2 is the same for me or any alien humanoid creature who never heard about our history. Our subconscious ability to tell things apart (idealization) creates the innate understanding that there can be more than one thing. E.g. 2.

@Haim: Hereby it is irrelevant whether these things we see as "apart" really are apart in some sort of objective/physical reality or not. Because we're talking about idealization, not the actual reality.

Same goes for symbols like the "+" sign. But there is no reason why a plus sign requires exactly 2 inputs. I would love to have given it an arbitrary number of inputs, and build the rest of math around that. And if we do that, the resulting new_math would still be understandable by us in terms of idealized reality, we could still do all the calculations of... say.. grocery shopping, trajectory calculations with this new_math.

Math is a language, which, for each statement written in math, exists one corresponding mental concept. New_math is also a language which, has statements and corresponding mental concepts.

That the thing, this is a language, a language links similar concepts, but when you have no concept this is where is breaks, an intelligent alien race might have no concept of numbers, they might interpret/separate reality in a different way, I am human so I can not think in other way but an alien race might, they might have entirely different organ than the brain, they might produce intelligence without a brain like organ at all but with group operations like germs do.

 

[Teax]

That the thing, this is a language, a language links similar concepts, but when you have no concept this is where is breaks, an intelligent alien race might have no concept of numbers, they might interpret/separate reality in a different way, I am human so I can not think in other way but an alien race might.

I said humanoid alien race, by which I mean humans living on another planet. They could be small, could have gray skin, big black eyes, kick-ass spaceships and their own star-gate, but if they have the ability to distinguish things like we do, their math will include ours for the reasons I stated in my previous post. Despite having no common history.

 

[JimJambones]

I agree with what was previously said, that most people find much to disagree with each other on, and is not really confined to type. With those that identify as "The Thinker", I think much of the disagreement is more due to philosophical differences than anything else. Since each INTP is likely to spend a considerable amount of time exploring and developing an epistemological foundation and a corresponding philosophy of life, they are not likely to budge on certain axioms in which everything else is built upon.

 

[Brontosaurie]

What if your name was Jam Jimbones

 

[Inquisitor]

I agree with what was previously said, that most people find much to disagree with each other on, and is not really confined to type. With those that identify as "The Thinker", I think much of the disagreement is more due to philosophical differences than anything else. Since each INTP is likely to spend a considerable amount of time exploring and developing an epistemological foundation and a corresponding philosophy of life, they are not likely to budge on certain axioms in which everything else is built upon.

+1

The premise of this thread is largely invalid as others have pointed out. I am surrounded with (probable) INTPs in my compsci program, and we find much to agree on. I suspect OP created this thread in reaction to an earlier post I made here, but I could be wrong. He and I have a long history of disagreement over the validity of the whole endeavor of typology, which he believes to be largely worthless...and yet, he's still on the INTPf posting about "INTP-types." Go figure. Walking contradiction.

 

[JimJambones]

+1

The premise of this thread is largely invalid as others have pointed out. I am surrounded with (probable) INTPs in my compsci program, and we find much to agree on. I suspect OP created this thread in reaction to an earlier post I made here, but I could be wrong. He and I have a long history of disagreement over the validity of the whole endeavor of typology, which he believes to be largely worthless...and yet, he's still on the INTPf posting about "INTP-types." Go figure. Walking contradiction.

Not necessarily. While I can't speak for the person you are referring too, I think one can identify with INTP for numerous reasons while remaining highly critical of any underlying theory that seeks to explain why an INTP is an INTP. That is what an INTP does by definition.

 

[JimJambones]

What if your name was Jam Jimbones

What if it was Jim BonesJam?

 

[Tannhauser]

Math is a language, which, for each statement written in math, exists one corresponding mental concept. New_math is also a language which, has statements and corresponding mental concepts.

Take two statements, one from math, one from new_math, so that both correspond to the same mental concept. Are these two statements necessarily syntactically equivalent? No of course not.

Let's assume math has a relation/operator/action(whatever) applicable to the statement written in math. Since math is based on idealized reality, there must exists a corresponding idealized mental concept for that too. Since new_math is also based on the same idealized reality, new_math does not contain anything that would contradict the idealized reality. Therefore, either new_math already has a relation/operator/action that corresponds to this idealized mental concept, or if you prefer to think of math as not-yet-fully invented, one can be added without problems. So all theorems that can be written in math, can be written in new_math and mean the same thing. History is not involved here as far as I can see.

But this seems to presuppose that there is only one idealized reality. What I think the historical perspective of math would show, is that all the mathematicians before us did not investigate the one and only idealized reality, but actively created idealized realities as they saw it fit – for their particular problem and their particular way of thinking.

Take probability theory for example. Originally, Fermat and Pascal invented probability theory by thinking of probability of an event as the number of outcomes corresponding to that event, over all possible outcomes. That is one way to think about it: the probability is the long-run stable ratio. However, in some cases that doesn't correspond to reality at all, because such a long-term ratio is not possible to observe. Another solution to that is the concept of Baysian probability, where you start with a prior belief of the likelihood of an event, and update it as more information is available to you. So here we have two different concepts for probability, which both serve a specific mental representation of reality.

In layman's terms: Similar how the contextual meaning of English and Spanish can be translated in one another. Possible because the underlying structure of language can not be so different as to break out of the human condition.

Even here, you have the problem that certain things can be said in one language and not in another. They do not necessarily map onto the same reality.

 

[Tannhauser]

+1

The premise of this thread is largely invalid as others have pointed out. I am surrounded with (probable) INTPs in my compsci program, and we find much to agree on. I suspect OP created this thread in reaction to an earlier post I made here, but I could be wrong. He and I have a long history of disagreement over the validity of the whole endeavor of typology, which he believes to be largely worthless...and yet, he's still on the INTPf posting about "INTP-types." Go figure. Walking contradiction.

You're clutching at straws, my friend. I have never claimed that typology is worthless. I have always maintained that it is a useful taxonomy. What I have claimed to be useless is all the Jungian-style woo-woo stuff.

 

[Brontosaurie]

What if it was Jim BonesJam?

It's real crazy just thinking about it like that

 

[Inquisitor]

Not necessarily. While I can't speak for the person you are referring too, I think one can identify with INTP for numerous reasons while remaining highly critical of any underlying theory that seeks to explain why an INTP is an INTP. That is what an INTP does by definition.

Well this is the official MBTI description:

Seek to develop logical explanations for everything that interests them. Theoretical and abstract, interested more in ideas than in social interaction. Quiet, contained, flexible, and adaptable. Have unusual ability to focus in depth to solve problems in their area of interest. Skeptical, sometimes critical, always analytical.

I've never come across any self-described INTP online who is simply wiling to accept this at face value without trying to investigate the theoretical foundation behind it. There is no other theoretical explanation besides that posited by Jung for this particular classification system, and all the traits on the MBTI basically come from Psychological Types, with a few minor differences. There are other personality classification systems, but I have not come across any other theories that adequately explain why people are divided up in this particular way. Have you?

You're clutching at straws, my friend. I have never claimed that typology is worthless. I have always maintained that it is a useful taxonomy. What I have claimed to be useless is all the Jungian-style woo-woo stuff.

If you do believe it's a useful and legitimate taxonomy (meaning it's not due to the Forer effect), then you must believe that there is a reason why people are divided up in this way, but apparently it has absolutely nothing to do with what Jung posited. Seems very strange to me but maybe you have a better theoretical explanation? I think something is better than nothing, especially given the strength of Jung's arguments, but maybe you feel differently, and that's fine, but very perplexing, especially if you haven't even read them.

 

[Tannhauser]

If you do believe it's a useful and legitimate taxonomy (meaning it's not due to the Forer effect), then you must believe that there is a reason why people are divided up in this way, but apparently it has absolutely nothing to do with what Jung posited. Seems very strange to me but maybe you have a better theoretical explanation? I think something is better than nothing, especially given the strength of Jung's arguments, but maybe you feel differently, and that's fine, but very perplexing, especially if you haven't even read them.

That's the thing – I don't have any theoretical explanation, and I don't think you need it. Very much like you can understand the difference between a pigeon and an owl without understanding evolution and biology.

There is also no need to read every word of someone's theories if you understand what those theories are based on. I know, for example, that astrology uses a method of inference that I find invalid. It will not make a difference for me to read more books about astrology.

 

[Teax]

I've never come across any self-described INTP online who is simply wiling to accept this at face value without trying to investigate the theoretical foundation behind it. There is no other theoretical explanation besides that posited by Jung for this particular classification system, and all the traits on the MBTI basically come from Psychological Types, with a few minor differences. There are other personality classification systems, but I have not come across any other theories that adequately explain why people are divided up in this particular way. Have you?

If we cannot (yet?) explain why things are the way they are, does it mean that we should ignore the way things are?

The apple falls because of Gravity. <-- that is not an explanation, it's a statement of redundancy, because we don't really know what exactly gravity is except that it makes things fall. How is MBTI different?

 

[Inquisitor]

That's the thing – I don't have any theoretical explanation, and I don't think you need it. Very much like you can understand the difference between a pigeon and an owl without understanding evolution and biology.

There is also no need to read every word of someone's theories if you understand what those theories are based on. I know, for example, that astrology uses a method of inference that I find invalid. It will not make a difference for me to read more books about astrology.

Hilarious.

A typical INTP has a religious faith in his own ability to reason in a vacuum – he has no respect for existing literature, or history, or tradition.

As long as the INTP has built a matrix of conceptual connection in his mind, supposedly using cold logic (he thinks), everything is seemingly solved. There is no reason to even read books or seek out the findings of other people.

Meanwhile, the reality is that all our knowledge is dependent on history, on tradition, on the works of our predecessors. If you think you have solved everything, it is probably because you have reasoned inside a tiny aquarium of knowledge.

You're basically doing the very thing you suggest others NOT do. I actually agree with the last paragraph above. Unless you read the theory, then there's no way for you to understand how and why this is in fact different from astrology.

If we cannot (yet?) explain why things are the way they are, does it mean that we should ignore the way things are?

The apple falls because of Gravity. <-- that is not an explanation, it's a statement of redundancy, because we don't really know what exactly gravity is except that it makes things fall. How is MBTI different?

Um. We know what causes gravity. Also MBTI is not a perfect reflection of reality by any stretch, only a probability. It would never have been conceived without Jung's descriptions of the types. The only reason we have words like "intuitive" and "thinking" and "feeling" are because he coined them out of his observations and extensive reading and analysis of the writings of others. Whether or not you agree that an "unconscious" or "function" exists, without these concepts, no categorization could have taken place. See what I'm getting at? The categorizations are by nature, at least somewhat theoretical, even if the MBTI has slapped on new descriptors. The whole thing is tied together. But this is getting into semantics, so I'll just leave it at that.

 

[Teax]

Also MBTI is not a perfect reflection of reality by any stretch, only a probability. It would never have been conceived without Jung's descriptions of the types. The only reason we have words like "intuitive" and "thinking" and "feeling" are because he coined them out of his observations and extensive reading and analysis of the writings of others. Whether or not you agree that an "unconscious" or "function" exists, without these concepts, no categorization could have taken place.

So if Jung based his theory on his observations, and Physicists base their theories on their observations..... Well yeah there is a huge quality gap between these kinds of theories. But simply for, whether MBTI taxonomy has any merit, all we need to know is: is the human psyche uniformly distributed, or are there density peaks in the right places.

Jung's guesses/theories about why the density peaks exist is separate topic that you can choose to believe in or not.

But this seems to presuppose that there is only one idealized reality. What I think the historical perspective of math would show, is that all the mathematicians before us did not investigate the one and only idealized reality, but actively created idealized realities as they saw it fit – for their particular problem and their particular way of thinking.

Take probability theory for example. Originally, Fermat and Pascal invented probability theory by thinking of probability of an event as the number of outcomes corresponding to that event, over all possible outcomes. That is one way to think about it: the probability is the long-run stable ratio. However, in some cases that doesn't correspond to reality at all, because such a long-term ratio is not possible to observe.

I'll ignore the red part, since if it's not observable, you cannot determine whether it corresponds to reality or not.

Another solution to that is the concept of Baysian probability, where you start with a prior belief of the likelihood of an event, and update it as more information is available to you. So here we have two different concepts for probability, which both serve a specific mental representation of reality.

Ok I can see what you mean by the term "different way-of-thinking", but it does not imply that the theories of those two historical figures are based on different idealized realities. If anything, the fact that both probabilities are magnitudes/numbers between 0 and 1, and you can use the probabilities interchangeably, is evidence of the opposite.

What probabilities essentially are, are ratios. Fermat's probability theory is worded differently than that of Bayse, and may have been worded in a different language, but does rely on the same intuitive framework of numbers+relations and uses this framework in the same way, as ratios.

Just reading this section: "update it as more information is available to you" - I translate, it means that Bayes adopts Fermat's definition of probability, as soon as it becomes applicable over time.

In other words Bayes' definition comes down to a hypothetical question: what would the probability (Fermat's definition) be if the experiment went the way you believe it would go. And later once the experiment stops being the uncertain future and becomes the observable past, your belief, and probability, adjust (accordingly to Fermat's definition).

What Bayes and Fermat did was not invent a new idealization of reality that they called "probabilities". Rather, they found words that would make creatures/humans who already have the ability to perceive an idealized reality aware of implications of this idealization. The inevitable implication of ratios. That's what I meant by "stumbling in a dark room", we are all relatively stupid, we can't easily see any but the most rudimentary implications of our own idealization. That's doesn't change the fact that those implications are still there.

Even here, you have the problem that certain things can be said in one language and not in another. They do not necessarily map onto the same reality.

If it's still relevant, maybe you can make an example of what you mean? Because the case I made about human idealization dictates one idealized reality.

How familliar are you with the concept of induction? (with it, it might be easier to explain my point of view, maybe)

 

[Tannhauser]

Hilarious.



You're basically doing the very thing you suggest others NOT do. I actually agree with the last paragraph above. Unless you read the theory, then there's no way for you to understand how and why this is in fact different from astrology.



Um. We know what causes gravity. Also MBTI is not a perfect reflection of reality by any stretch, only a probability. It would never have been conceived without Jung's descriptions of the types. The only reason we have words like "intuitive" and "thinking" and "feeling" are because he coined them out of his observations and extensive reading and analysis of the writings of others. Whether or not you agree that an "unconscious" or "function" exists, without these concepts, no categorization could have taken place. See what I'm getting at? The categorizations are by nature, at least somewhat theoretical, even if the MBTI has slapped on new descriptors. The whole thing is tied together. But this is getting into semantics, so I'll just leave it at that.

Whenever Inquistor disagrees with someone, all of his paragraphs tend to begin with some sort of annoying passive-aggressive term like "Lol" or "Hilarious" or "Umm". It's too annoying to reply to.