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A child can’t prove 1+1 = 2 because a child doesn’t know enough mathematics to prove it. Doesn’t even understand the basics of mathematical logic or set theory

A child can’t prove 1+1 = 2 because a child doesn’t know enough mathematics to prove it. Doesn’t even understand the basics of mathematical logic or set theory. You know so little about what it means to prove 1+1=2 that you think proving this is easy. Your grasp on the limits of your mathematical knowledge is greatly lacking. There are no right questions, only right answers. A point that does not pertain to what I said. I said nothing about “right” questions. There are dumb questions though. There are insightful questions. There are probing questions. There are nonsensical questions too. Like this question, “If vaccines are good for us then why do we have a bicameral legislative branch?” A person not trained in virology or microbiology is absolutely unqualified to discern the difference between good information and bad information on the topic of vaccines. Such a person can’t possibly do anything that can be reasonably ascribed to “having done the research”. A person who has “done the research” and concludes that vaccines are bad is a fool no matter how many thousands of words or thoughts they devoted to the topic.

giardini 3y ago
[flagged]
- synetic 3y ago
  The widely accepted axiomatic basis for the natural numbers is the first order Peano Axioms. Very few children are capable of understanding how to prove 1+1=2 in this axiomatic system. In this system an axiom says that each element has a successor. 1 is called the successor of 0. 2 is called the successor of 1. So on and so forth. Now we need to define a binary operation called +. Now show that the successor of 0 plus the successor of 0 is the successor of the successor of 0. How many children are capable of this level of abstract thinking? People without training in statistics don’t understand how to properly design trials. I’m a mathematician and I don’t understand this since it is not something I’ve studied. I need to rely on the expert knowledge of others to tell what is and is not a good study design. The large group of people that distrust certain vaccines rather than all of them are ignoramuses.
  - giardini 3y ago
    synetic says "The widely accepted axiomatic basis for the natural numbers is the first order Peano Axioms. Very few children are capable of understanding how to prove 1+1=2 in this axiomatic system." Presumably the "first order Peano Axioms" were noted sometime after Giuseppe Peano's birth in 1858. By your logic no one born before 1858 would be "capable of understanding how to prove 1+1=2", which is nonsense. You seriously underrate everyone except yourself.
vba616 3y ago
>A person not trained in virology or microbiology is absolutely unqualified to discern the difference between good information and bad information on the topic of vaccines. It seems hard to argue with that...but what exactly is the meaning of saying people are "absolutely unqualified" to do something which they in fact do constantly and which there is no obvious alternative in order for society to function? If we accept that non-experts are not qualified to determine what is good information, then doesn't it entirely undermine democratic control over society? For that matter, doesn't it entirely undermine the concept of management in industry or government? Individual autonomy and rights too? Again, I'm not saying you are wrong, or that I have a counterargument, just that the logical implications seem extremely radical, and I don't know of a plan for how society can function on such a basis.
- synetic 3y ago
  It seems hard to argue with that...but what exactly is the meaning of saying people are "absolutely unqualified" to do something which they in fact do constantly and which there is no obvious alternative in order for society to function? In my opinion the answer is this. Roughly speaking, in general: Overwhelming expert consensus opinion on a topic has a much higher chance of being correct than any contrary belief I have based off of “research” that I do. The overwhelming expert consensus might very well be wrong but it’s clear that they are way more likely to be right than I am.
  - vba616 3y ago
    "Overwhelming expert consensus" implies that you know who is an expert so I don't see how it helps an idealized clueless average citizen who arguendo cannot judge accurate information from mis- or dis- information. Also, you have heard of "100 Autoren Gegen Einstein"? Obviously people who bring that up in an actual conflict of ideas are almost certainly not Einstein, but how do we know, and if we think we know who is right and it is the majority, how do we refute the claim that polls don't determine truth?
machina_ex_deus 3y ago
You don't need set theory to prove that 1+1=2. You don't need mathematical logic. A child which answers that if he puts one thing and then another thing and then counts and gets two things have proved it just fine. Those later complications are just there when you try to put it in context of other things you know. Ancient Greeks did not do set theory or mathematical logic, yet their understanding of basic addition was completely fine. You inability to understand what is irrelevant complication, and your deferral to authority and expertise even when you are perfectly capable of understanding, is your own problem. Here are two quote you said: > "(There are no right questions, only right answers.) A point that does not pertain to what I said. I said nothing about “right” questions." > "Asking the right questions requires some perspicacity." You also say "The thoughts were completely wrong". There are also no wrong thoughts, only wrong conclusions. A person afraid to "think" wrongly as the narrative so strongly tries to program people, is infinitely dumber than a person who doesn't constrain his thinking. That's what they want to happen. Amazing there are NPCs like you who avoid "wrongthink". There are people who know a lot and understand nothing. Knowledge is spewing up complications from set theory. Understanding is being able to tell, by the context, that this is completely irrelevant. You appealed to authority to even tell me that the earth is flat. You didn't say that we can observe the curvature from measuring distances, from doing an experiment with ships masts disappearing into the horizon, or any other way even ancient people figured it out. It's true because "The knowledge that the Earth is spheroidal has been known for many hundreds of years. ". People "knew" the sun rotates around earth for thousand of years. And the truth won despite it being against the "authority". And nothing will change that understanding, even if some string theory will discover the 11th dimension or whatever, because that will be irrelevant in the same sense that set theory is irrelevant to 1+1=2. For these same reasons you don't need and shouldn't appeal to authority. Appeal to authority is only knowledge. Zero understanding. I said nothing about "doing the research". A person who deferred to authority and knowledge to answer a question is always inferior to a person who tried to understand and failed. A person appealing to authority is just trying to mirror someone's intelligence. A parrot who repeats a correct sentence is still dumber than a human saying a wrong sentence. A parrot who repeats "vaccines are good" because he heard that is always the greater fool than the anti vax who says vaccines are bad. A parrot who says 1+1=2 because set theory shows less understanding than a kid with an abacus. The parrot is saying irrelevant things while the child isn't.

giardini 3y ago

[flagged]

synetic 3y ago
The widely accepted axiomatic basis for the natural numbers is the first order Peano Axioms. Very few children are capable of understanding how to prove 1+1=2 in this axiomatic system. In this system an axiom says that each element has a successor. 1 is called the successor of 0. 2 is called the successor of 1. So on and so forth. Now we need to define a binary operation called +. Now show that the successor of 0 plus the successor of 0 is the successor of the successor of 0. How many children are capable of this level of abstract thinking? People without training in statistics don’t understand how to properly design trials. I’m a mathematician and I don’t understand this since it is not something I’ve studied. I need to rely on the expert knowledge of others to tell what is and is not a good study design. The large group of people that distrust certain vaccines rather than all of them are ignoramuses.
- giardini 3y ago
  synetic says "The widely accepted axiomatic basis for the natural numbers is the first order Peano Axioms. Very few children are capable of understanding how to prove 1+1=2 in this axiomatic system." Presumably the "first order Peano Axioms" were noted sometime after Giuseppe Peano's birth in 1858. By your logic no one born before 1858 would be "capable of understanding how to prove 1+1=2", which is nonsense. You seriously underrate everyone except yourself.

vba616 3y ago

>A person not trained in virology or microbiology is absolutely unqualified to discern the difference between good information and bad information on the topic of vaccines. It seems hard to argue with that...but what exactly is the meaning of saying people are "absolutely unqualified" to do something which they in fact do constantly and which there is no obvious alternative in order for society to function? If we accept that non-experts are not qualified to determine what is good information, then doesn't it entirely undermine democratic control over society? For that matter, doesn't it entirely undermine the concept of management in industry or government? Individual autonomy and rights too? Again, I'm not saying you are wrong, or that I have a counterargument, just that the logical implications seem extremely radical, and I don't know of a plan for how society can function on such a basis.

synetic 3y ago
It seems hard to argue with that...but what exactly is the meaning of saying people are "absolutely unqualified" to do something which they in fact do constantly and which there is no obvious alternative in order for society to function? In my opinion the answer is this. Roughly speaking, in general: Overwhelming expert consensus opinion on a topic has a much higher chance of being correct than any contrary belief I have based off of “research” that I do. The overwhelming expert consensus might very well be wrong but it’s clear that they are way more likely to be right than I am.
- vba616 3y ago
  "Overwhelming expert consensus" implies that you know who is an expert so I don't see how it helps an idealized clueless average citizen who arguendo cannot judge accurate information from mis- or dis- information. Also, you have heard of "100 Autoren Gegen Einstein"? Obviously people who bring that up in an actual conflict of ideas are almost certainly not Einstein, but how do we know, and if we think we know who is right and it is the majority, how do we refute the claim that polls don't determine truth?

machina_ex_deus 3y ago

You don't need set theory to prove that 1+1=2. You don't need mathematical logic. A child which answers that if he puts one thing and then another thing and then counts and gets two things have proved it just fine. Those later complications are just there when you try to put it in context of other things you know. Ancient Greeks did not do set theory or mathematical logic, yet their understanding of basic addition was completely fine. You inability to understand what is irrelevant complication, and your deferral to authority and expertise even when you are perfectly capable of understanding, is your own problem. Here are two quote you said: > "(There are no right questions, only right answers.) A point that does not pertain to what I said. I said nothing about “right” questions." > "Asking the right questions requires some perspicacity." You also say "The thoughts were completely wrong". There are also no wrong thoughts, only wrong conclusions. A person afraid to "think" wrongly as the narrative so strongly tries to program people, is infinitely dumber than a person who doesn't constrain his thinking. That's what they want to happen. Amazing there are NPCs like you who avoid "wrongthink". There are people who know a lot and understand nothing. Knowledge is spewing up complications from set theory. Understanding is being able to tell, by the context, that this is completely irrelevant. You appealed to authority to even tell me that the earth is flat. You didn't say that we can observe the curvature from measuring distances, from doing an experiment with ships masts disappearing into the horizon, or any other way even ancient people figured it out. It's true because "The knowledge that the Earth is spheroidal has been known for many hundreds of years. ". People "knew" the sun rotates around earth for thousand of years. And the truth won despite it being against the "authority". And nothing will change that understanding, even if some string theory will discover the 11th dimension or whatever, because that will be irrelevant in the same sense that set theory is irrelevant to 1+1=2. For these same reasons you don't need and shouldn't appeal to authority. Appeal to authority is only knowledge. Zero understanding. I said nothing about "doing the research". A person who deferred to authority and knowledge to answer a question is always inferior to a person who tried to understand and failed. A person appealing to authority is just trying to mirror someone's intelligence. A parrot who repeats a correct sentence is still dumber than a human saying a wrong sentence. A parrot who repeats "vaccines are good" because he heard that is always the greater fool than the anti vax who says vaccines are bad. A parrot who says 1+1=2 because set theory shows less understanding than a kid with an abacus. The parrot is saying irrelevant things while the child isn't.