Objective Truths / Absolute Knowledge / Conjectural Knowledge
Rami Rustom
Conjectural knowledge (K) is not absolute because it contains error
(∆EK) as compared to objective truth. So...
* K <> T
* K = T +- ∆EK
* ∆EK > 0
Some (or is it all?) mathematics is *knowledge* that are *objective
truths*. So that means that there is no error in these mathematics.
Lets calls these objective truths Tm. So...
* Km = Tm
* ∆EKm = 0
Some philosophies are *knowledge* that are *objective truths*. So that
means that there is no error in these *known* philosophies. Lets calls
these objective truths Tp. So...
* Kp = Tp
* ∆EKp = 0
Is there any other knowledge that is objective truth?
--Rami
Elliot Temple
On Jan 2, 2012, at 8:26 AM, Rami Rustom wrote:
> Objective truth (T) is absolute truth, i.e. there is not error.
>
> Conjectural knowledge (K) is not absolute because it contains error
May contain error. Or not. (In practice, it reliably does contain error.)
> (∆EK) as compared to objective truth. So...
> * K <> T
> * K = T +- ∆EK
> * ∆EK > 0
It would help to define your terms and symbols.
(Also non-standard symbols like triangles may not show up for all readers with other fonts and software. Please stick to standard characters.)
I figure delta means change and <> is supposed to mean not equal, and E is error. Those I could guess but maybe other people wouldn't.
But then we read stuff like "change in error multiplied by knowledge"? what's that?
Maybe EK is supposed to mean more like E subscript K, that is the error for K? it's hard to tell.
it'd be improved by an english explanation of what it's supposed to mean, how it works, what the conclusion is, etc
Also the basic assumption that our conjectural knowledge is never the objective truth is incorrect. There is nothing to prevent some of our guesses from being true (T). That can happen.
>
> Some (or is it all?) mathematics is *knowledge* that are *objective
> truths*.
No, all our ideas about math are conjectural and fallible.
> So that means that there is no error in these mathematics.
Definitely not.
Consider, as one of the issues, the argument from FoR that mathematicians use *physical processes* (e.g. they work out some math using paper and pen, not to mention their brains) and whether they have the mathematical conclusion right therefore depends on their understanding of physics (because if they misunderstand the physical properties of these tools, it invalidates their mathematical conclusions they reached using the tools).
-- Elliot Temple
http://elliottemple.com/
Rami Rustom
Conjectural knowledge (K) is not absolute because it may contain error
(EK) as compared to objective truth. So...
* T is objective truth
* K is conjectural knowledge
* K <> T <> means *not equal to*
* K = T +- EK K equals T plus or minus the error
* EK > 0 EK (maybe) greater than 0
Some mathematics and some philosophies are knowledge that are
*objective truths*, i.e. there is no error. Lets call this *absolute
knowledge*.
Are there any mathematics that are objective truths?
> No, all our ideas about math are conjectural and fallible.
that if a set of measured data points (on an X-Y graph) is
approximated with a polynomial equation, and if an extrapolation is
made to *guess* more data points, the further away the extrapolated
points get from the real points (on the X axis), the more wild the
error. Is this not an *absolute truth*?
Are there any philosophies that are objective truths? What about
Poppers conjecture/refutation philosophy?
--Rami
Elliot Temple
You conceive of error as an amount and positive or negative? That assumes that error can be in two directions from the truth. Actually it can be in many.
> * EK > 0 EK (maybe) greater than 0
I don't understand that maybe.
>
> Some mathematics and some philosophies are knowledge that are
> *objective truths*, i.e. there is no error. Lets call this *absolute
> knowledge*.
>
> Are there any mathematics that are objective truths?
There are, notionally, mathematical propositions which are objectively true. Also false ones. We only learn (about math or anything else) by fallible, conjectural processes and we can't tell, infallibly, which ideas are which (true, false).
>> No, all our ideas about math are conjectural and fallible.
>
> What about something like an idea in Numerical Methods which states
> that if a set of measured data points (on an X-Y graph) is
> approximated with a polynomial equation, and if an extrapolation is
> made to *guess* more data points, the further away the extrapolated
> points get from the real points (on the X axis), the more wild the
> error. Is this not an *absolute truth*?
No it's a fallible guess. Why would it be anything else?
> Are there any philosophies that are objective truths? What about
> Poppers conjecture/refutation philosophy?
While it could be the objective truth, I very much doubt it, and even if it was we couldn't (infallibly) know that it was.
Rami Rustom
> > Some mathematics and some philosophies are knowledge that are
> > *objective truths*, i.e. there is no error. Lets call this *absolute
> > knowledge*.
>
> > Are there any mathematics that are objective truths?
>
> There are, notionally, mathematical propositions which are objectively true. Also false ones. We only learn (about math or anything else) by fallible, conjectural processes and we can't tell, infallibly, which ideas are which (true, false).
sounds funny but in Linear Algebra we spent a day proving that 0 = 0
(but it wasn't in the real number space). It confused the crap out of
me. Is something like this an absolute knowledge?
> >> No, all our ideas about math are conjectural and fallible.
>
> > What about something like an idea in Numerical Methods which states
> > that if a set of measured data points (on an X-Y graph) is
> > approximated with a polynomial equation, and if an extrapolation is
> > made to *guess* more data points, the further away the extrapolated
> > points get from the real points (on the X axis), the more wild the
> > error. Is this not an *absolute truth*?
>
> No it's a fallible guess. Why would it be anything else?
>
> > Are there any philosophies that are objective truths? What about
> > Poppers conjecture/refutation philosophy?
>
> While it could be the objective truth, I very much doubt it, and even if it was we couldn't (infallibly) know that it was.
exists we can know any *absolute knowledge*, i.e. knowledge that is
objective truth and that we *know* it. And I want to know this because
this would be the stuff we would start with in an AI. This would be
what is in our HI.
So consider the mind (M) and its environment (E) (which happens to
include the brain tissue too). E contains all the objective truths T.
M must have a starting point of T. Something it knows to be absolutely
true, i.e. an absolute knowledge Ka that is equal to its associated
objective truth Ta.
* Ka = Ta
All other knowledge in M is conjectural knowledge (Kc), i.e. it is
fallible so it may contain error.
* Kc <> Tc
How else could M gain conjectural knowledge if it didn't start with
some absolute knowledge?
So what is Ta?
If it doesn't exist, then I don't think we can create an AI. But then
I also don't see how our HI are possible either.
--Rami
Elliot Temple
How do you know if 0 = 0?
Presumably you do some process of checking what is on the left, what is on the right, and comparing.
How do you do that process? Well, you use physical tools such as pen and paper, or a computer screen.
Did your process correctly check if the left and right are equal? How do you know that it did? In order to claim your process works, you must, among other things, make claims about the properties of your tools. Such claims are fallible.
For example, you have ideas about how paper retains pen marks over time. You believe what's written on the left won't change while you're looking at the right.
So, since your way of deciding it's true is contingent on getting various physics right, and your understanding of physics is fallible, then the whole thing is fallible.
This is explained in FoR. Maybe in BoI too, I forget offhand.
Another reason for fallibility is that your understanding of numbers could be mistaken. Also your understanding of how to read and interpret mathematical symbols. Also your understanding of equality. (Equality, by the way, is a more tricky concept than many people realize. Many computer programming languages have multiple equality operators that do different things. Javascript is an example of a language known for being complicated in this area.)
>>>> No, all our ideas about math are conjectural and fallible.
>>
>>> What about something like an idea in Numerical Methods which states
>>> that if a set of measured data points (on an X-Y graph) is
>>> approximated with a polynomial equation, and if an extrapolation is
>>> made to *guess* more data points, the further away the extrapolated
>>> points get from the real points (on the X axis), the more wild the
>>> error. Is this not an *absolute truth*?
>>
>> No it's a fallible guess. Why would it be anything else?
>>
>>> Are there any philosophies that are objective truths? What about
>>> Poppers conjecture/refutation philosophy?
>>
>> While it could be the objective truth, I very much doubt it, and even if it was we couldn't (infallibly) know that it was.
>
> Ok let me tackle this another way. I'm trying to figure out if there
> exists we can know any *absolute knowledge*, i.e. knowledge that is
> objective truth and that we *know* it.
No. That is impossible.
For many reasons, such as: all processes by which humans know are *physical processes*. Whether they work as we expect, or not, depends in some ways on our understanding of physics, which is fallible.
> And I want to know this because
> this would be the stuff we would start with in an AI. This would be
> what is in our HI.
That would be an infallibilist style approach to AI, where you start with the perfect truth and then build on it. Like Descartes wanted to do.
A fallibilist or Popperian style approach would be to acknowledge, accept and expect plenty of errors wherever one starts, and to consider the more important thing to be error correction abilities.0
It's kind of like Popper's criterion for judging political systems (see BoI or some Popper books, I forget which, maybe Open Society).
> So consider the mind (M) and its environment (E) (which happens to
> include the brain tissue too). E contains all the objective truths T.
The environment does not contain truths in the same way that human minds do. It only contains them in some unspecified, metaphorical way which may involve some misconceptions e.g. like the empiricist idea of reading from the book of nature.
>
> M must have a starting point of T.
No, we start with fallible guesses, and improve them to other fallible guesses.
> How else could M gain conjectural knowledge if it didn't start with
> some absolute knowledge?
By using a flawed, fallible way of conjecturing.
For example, one can start with his intuition, dreams, wild guesses, myths, religion, whatever.
-- Elliot Temple
http://curi.us/
Rami Rustom
What about the principle that...
* Knowledge is fallible because it could be objective truth or not.
Is that statement an objective truth? Or can we not use the term
*objective truth* in statements of knowledge?
--Rami
Elliot Temple
On Jan 2, 2012, at 1:04 PM, Rami Rustom wrote:
> Ok I have one more thing up my sleeve.
>
> What about the principle that...
> * Knowledge is fallible because it could be objective truth or not.
>
> Is that statement an objective truth? Or can we not use the term
> *objective truth* in statements of knowledge?
This is an old argument.
It's often stated more like, "You claim to be a fallibilist, but are you willing to question your principle of fallibility itself?"
The answer is: yes, fallibility is fallible.
This thread itself demonstrates the possibility of debating and discussing fallibility. And I certainly do not claim all my arguments on the topic must be absolutely true and couldn't have flaws. Nor do I think my understanding of the (somewhat completed) topic is beyond any doubt.
One more thing people say is like, "If fallibility isn't true (or isn't something you will assert is definitely true), then can we just ignore it as useless? What good is it?"
The unstated assumption is that only Justified, True Belief is Knowledge, and so "conjectural knowledge" or "fallible knowledge" is not knowledge (they would think we have misnamed them), and non-knowledge like that is worthless or useless or bad.
They see the goal as to acquire knowledge (JTB) and don't see the point of stuff that fails to do that. Considering JTB is impossible, they have themselves in something of a bind. Hence there are "skeptics" who have the same basic goals, but have recognized it's impossible, and thus have given up on knowledge entirely.
What they are doing is applying non-fallibilist standards for judging fallibility. But that doesn't make sense. You can't judge the concept of fallibility using criteria it rejects and refutes.
Fallibility itself, and fallible/conjectural knowledge generally, are not JTB, but that doesn't stop them from being useful, getting some things right, solving problems, and being improved.
-- Elliot Temple
http://fallibleideas.com/
Rami Rustom
things*? Can that be an objective truth?
--Rami
Rami Rustom
> On Jan 2, 2012, at 12:26 PM, Rami Rustom wrote:
> > On Jan 2, 1:48 pm, Elliot Temple <c...@curi.us> wrote:
> >> On Jan 2, 2012, at 11:06 AM, Rami Rustom wrote:
> >>> On Jan 2, 11:48 am, Elliot Temple <c...@curi.us> wrote:
> >>>> On Jan 2, 2012, at 8:26 AM, Rami Rustom wrote:
>
> >>>>> Conjectural knowledge (K) is not absolute because it contains error
>
> >>>> May contain error. Or not. (In practice, it reliably does contain error.)
>
> >>>>> * K = T +- ∆EK
> >>>>> * ∆EK > 0
>
> >>>> It would help to define your terms and symbols.
>
> >>>> (Also non-standard symbols like triangles may not show up for all readers with other fonts and software. Please stick to standard characters.)
>
> >>>> I figure delta means change and <> is supposed to mean not equal, and E is error. Those I could guess but maybe other people wouldn't.
>
> >>>> But then we read stuff like "change in error multiplied by knowledge"? what's that?
>
> >>>> Maybe EK is supposed to mean more like E subscript K, that is the error for K? it's hard to tell.
>
> >>>> it'd be improved by an english explanation of what it's supposed to mean, how it works, what the conclusion is, etc
>
> >>>>> Some (or is it all?) mathematics is *knowledge* that are *objective
> >>>>> truths*.
>
> >>>>> So that means that there is no error in these mathematics.
>
> >>>> Definitely not.
>
> >>> Ok starting over then...
>
> >>> Conjectural knowledge (K) is not absolute because it may contain error
> >>> (EK) as compared toobjectivetruth. So...
> >>> * T isobjectivetruth
> >>> * K is conjectural knowledge
> >>> * K <> T <> means *not equal to*
> >>> * K = T +- EK K equals T plus or minus the error
>
> >>> * EK > 0 EK (maybe) greater than 0
>
> >> I don't understand that maybe.
>
> > It just saying that error exists in K.
>
> >>> Some mathematics and some philosophies are knowledge that are
>
> >>> Are there any mathematics that areobjectivetruths?
>
> > Ok this might be a dumb question but what about 0 = 0? I know this
> > sounds funny but in Linear Algebra we spent a day proving that 0 = 0
> > (but it wasn't in the real number space). It confused the crap out of
> > me. Is something like this an absolute knowledge?
>
> How do you know if 0 = 0?
>
> Presumably you do some process of checking what is on the left, what is on the right, and comparing.
>
> How do you do that process? Well, you use physical tools such as pen and paper, or a computer screen.
Abstractions_ which helped me figure out what happened in this thread.
But I didn't write anything until I ran across a thread titled _The
"Influences" Model_ which lead me to jumping to BoI chapter 13 titled
_Choices_. I skimmed until I read the part about that math is
fallible; which is what you have said in this thread.
In your explanation above, you've discussed both the physical and the
meta-physical spaces but I only meant to refer to the meta-physical
space. So as an example:
There is the pure abstraction about 1 + 1 = 2, and I think its
accurate to call this meta-physical, and then there is the physical
idea of 1 hole + 1 hole = 2 holes. I conjecture that the meta-physical
one is objective truth. And that the physical one is not; and an
example of how the physical can be false is if the holes are next to
each other thus making only 1 big hole. Hence 1 + 1 = 2 in the
physical space is fallible while 1 + 1 = 2 in the meta-physical space
is infallible.
So the example given in BoI chapter 13 is about math in politics and
Deutsch says that it is fallible. And *math in politics* has 2
components which exist in the physical and the meta-physical spaces.
1> the pure math, i.e. the pure abstraction, i.e. a meta-physical
objective truth, i.e. infallible, which exists in the meta-physical
space, and
2> the reason [and way] in which to apply the pure math to politics,
which exists in the physical space.
I think that #1 is meta-physical objective truth while #2 is physical
knowledge and thus is fallible.
#1 is theoretical math and applied math, and I think both are
infallible.
#2 is philosophy and methodology, and both are fallible.
So the theoretical math is 2nd order meta-physical. And the applied
math (formulas) is 1st order meta-physical.
And the reason(s) in which to apply the math is the *philosophy*,
which is 2nd order. The way in which to apply the math is the
*methodology*, which is 1st order.
And as I stated in the thread titled _What is intelligence?_:
> I first employ philosophical logic before employing symbolic (math) logic. Philosophical logic provides the initial high-level aim while symbolic logic provides the zoom-in feature. Note that symbolic logic is less useful when viewing from far away, i.e. viewing a large portion of the knowledge network, and that philosophical logic is less useful when viewing from very close, i.e. viewing a small portion of the knowledge network. They must be wielded together like a sword and shield; the sword represents symbolic logic while the shield represents philosophical logic.
So my above paragraph involves the physical and the meta-physical
spaces.
The _What is intelligence?_ thread is here:
http://groups.google.com/group/beginning-of-infinity/browse_thread/thread/2e16e9954697ab08/9ba2d4452f06b6dc?lnk=gst&q=intelligence#9ba2d4452f06b6dc
---
On a related note, my original meta-idea that I should read BoI in
order by chapter was very wrong. Jumping around is way more useful for
me. And my new meta-idea makes more sense since it coincides with my
way of thinking as I described in the thread titled _Deutsch's way of
thinking IS methodical_:
http://groups.google.com/group/beginning-of-infinity/browse_thread/thread/7434deca542ea6d7/c76577400231cf10?lnk=gst&q=methodical#c76577400231cf10
The thread titled _Theory of Knowledge: How the mind learns_ is here:
http://groups.google.com/group/beginning-of-infinity/browse_thread/thread/eabf985d78f17f47/d7ea28f15e01e1b9?lnk=gst&q=how+the+mind+learns#d7ea28f15e01e1b9
All knowledge is connected!!!
Everything must reconcile!!!
--Rami
Rami Rustom
So I'm trying to reconcile my explanation of the physical and
meta-physical spaces with Poppers 3 worlds.
http://groups.google.com/group/beginning-of-infinity/browse_thread/thread/ecbbc63480485f7d/c5435e35659a672f?lnk=gst&q=art+objective+truth#c5435e35659a672f
And I'm not really sure how to. Can anyone help me?
I read this thread and didn't find the name Popper's work to go read.
And somebody said that he wrote about his 3 worlds many times.
Which of his works should I read to learn about his 3 worlds?
-- Rami
Elliot Temple
On Jan 2, 2012, at 3:13 PM, Rami Rustom wrote:
> Elliot wrote:
>> The answer is: yes, fallibility is fallible.
> What about the concept of *the necessity for error correction in all things*? Can that be an objective truth?
Those aren't opposites. We can have fallible knowledge of an idea that is, in fact, an objective truth.
Things can be objectively true, but our knowledge of which ones are is always fallible.
-- Elliot Temple
http://beginningofinfinity.com/
Elliot Temple
I disagree.
Your understanding of the abstract space exists physically, and was created by fallible physical processes.
You have no knowledge of infallibility or infallible knowledge, period.
You have no abstract access to any abstract space.
See also the math chapter in The Fabric of Reality by DD.