# The degree of certainty is indirectly proportional to the size of the reference frame.

Ktulu
Posts: 1806
Joined: 2010-12-21
Offline
The degree of certainty is indirectly proportional to the size of the reference frame.

I need this challenged so I'm going to put it down for critique.  Feel free to kick the idea around as much as you like, I have no emotional attachment.

Basically the back story is that I'm looking for an underlining currency of communication between any two individuals in an epistemic frame of reference.  The work and research is very fragmented at this point, and I'm not even sure if I have anything worth considering, but I find it extremely fascinating.  One of these days, when I have some real time to invest, I want to put it all together so it makes sense.

At this particular point in time I'm considering degrees of certainty and as I have been kicking the idea in my head over the past week or so, I seem to have arrived at this axiom.  The degree or certainty (relative to any proposition) is indirectly proportional to the size of the reference frame.

Let me present some extreme examples to illustrate.

If I present to you a reference frame, where a set of elements are sequentially incremented by a constant. In the format of 1, 2, 3, 4, 5, 6.  That frame of reference, represented by the stated relationship and not by the potential size of the set, is extremely small.  Therefor, a proposition that 2+3=5 has a very large degree of certainty, when the incremental constant is 1.

Conversely, if the frame of reference was the earth's atmosphere, and the relationships that govern the humidity, wind speed, cloud formation, etc, formed the frame of reference.  Because the frame of reference is so large, the degree of certainty of any proposition is small.  I can say that it will rain tomorrow, and attribute a percentage of certainty to that... so on.

The reason I believe this to be important in our little corner of the world, is because we seldom consider the frame of reference when arguing with theists.  We are asked to disprove god, and when showing said god to not be possible, they just keep increasing the size of the frame of reference (aka, moving the goal posts).  What that does, is lower the degree of certainty of any proposition.

In the end, the ultimate frame of reference is that which can never be simplified, namely, "outside our universe".  This makes the degree of certainty of ANY proposition so small as for it be impractical.

Let me know what you guys think, I'm hoping for some critique.

"Don't seek these laws to understand. Only the mad can comprehend..." -- George Cosbuc

luca
Posts: 397
Joined: 2011-02-21
Offline
first :(

I don't think it's the first time I see this argument. To be honest, even I thought of it, altough with a slightly different wording.

First: using numbers like 1, 2, 3, n may suggest that at some point you can have a finite, absolute, certainty. I would prefer to work in a logarithmic base. Maybe.

Second: if you are talking about propositions (and logic), then the prediction must work for the rule itself (unless you take it very axiomatically... wait, no, there's still a chance that it's a different cathegory).

Third: to better understand what the number would mean, do you think there could be a unit of measurement? (probably something about Planck, you know)

Anyway I will continue to think about it, but seeing as the problem is pretty common, I have a particular feeling about it... We'll see. Maybe I'm feeling also that it lacks something. I'm thinking about completeness, but I have to elaborate my thoughts. By trying to see what this thing could give in the extremes you could at least understand if it makes any sense or not* (like if the result has a meaning, confronting with determinism, things like that). Work work work. (Mmmmh, I think the tingling sensation I feel may found his fulfilment in Bayes.)

Expecially in the "reference frame" area: do you plan to artificially assign a weight or to extrapolate this number "naturally"?

Actually, four: do you have a "branch" in human knowledge where to put this... axiom with all the rest? Game theory? Statistics/probability? Mathematical logic? Maybe cathegory theory?

Quote:
I can say that it will rain tomorrow, and attribute a percentage of certainty to that... so on.

Are you sure this pertains to what you're trying to analyze? I am not sure if I get exactly what you're saying. It seems like classifying infinites with aleph, but then it seems another thing...

*holy crap, batman, an example: would this "degree of certainty" be relative? Because what would mean that this degree is absolute? (you get what I mean?)

FurryCatHerder
Posts: 1253
Joined: 2007-06-02
Offline
I think that your axiom has

I think that your axiom has merit, but your application to The God Problem is wrong.

Assume, for a moment, that some Deity exists with a given set of Special Powers.  I would assert that any set of possible Powers required for said Deity to be worthy of "worship" must include "created the entire Universe".  The reasoning is simple -- "everything" is much more "worthy" than "not a whole bunch".  Goddess of Grain (Ceres ...) is far less interesting than God Who Created The Entire Universe.

This would imply that The God Problem doesn't even become interesting until the God Who Created The Entire Universe is postulated, otherwise I suspect people would be off trying to locate that particular Deity rather than troubling themself with Cat God.  Not that cats are =bad=, just saying Universe Creating God is more "worthy" than a Deity who only created cats or trained them in their mysterious and evil ways.

"Obviously I'm convinced of the existence of G-d. I'm equally convinced that Atheists who've led good lives will be in Olam HaBa going "How the heck did I wind up in this place?!?" while Christians who've treated people like dirt will be in some other place asking the exact same question."

Ktulu
Posts: 1806
Joined: 2010-12-21
Offline
luca wrote:I don't think

luca wrote:

I don't think it's the first time I see this argument. To be honest, even I thought of it, altough with a slightly different wording.

First: using numbers like 1, 2, 3, n may suggest that at some point you can have a finite, absolute, certainty. I would prefer to work in a logarithmic base. Maybe.

Second: if you are talking about propositions (and logic), then the prediction must work for the rule itself (unless you take it very axiomatically... wait, no, there's still a chance that it's a different cathegory).

Third: to better understand what the number would mean, do you think there could be a unit of measurement? (probably something about Planck, you know)

Anyway I will continue to think about it, but seeing as the problem is pretty common, I have a particular feeling about it... We'll see. Maybe I'm feeling also that it lacks something. I'm thinking about completeness, but I have to elaborate my thoughts. By trying to see what this thing could give in the extremes you could at least understand if it makes any sense or not* (like if the result has a meaning, confronting with determinism, things like that). Work work work. (Mmmmh, I think the tingling sensation I feel may found his fulfilment in Bayes.)

Expecially in the "reference frame" area: do you plan to artificially assign a weight or to extrapolate this number "naturally"?

Actually, four: do you have a "branch" in human knowledge where to put this... axiom with all the rest? Game theory? Statistics/probability? Mathematical logic? Maybe cathegory theory?

Quote:
I can say that it will rain tomorrow, and attribute a percentage of certainty to that... so on.

Are you sure this pertains to what you're trying to analyze? I am not sure if I get exactly what you're saying. It seems like classifying infinites with aleph, but then it seems another thing...

*holy crap, batman, an example: would this "degree of certainty" be relative? Because what would mean that this degree is absolute? (you get what I mean?)

hehe, thank you for your response.   I have been over-thinking this axiom so it's starting to make less and less sense, just as repeating the same word makes it lose its meaning.  If you can remember where you have seen this before, PLEASE let me know because I would eat that piece of knowledge up.

I don't have this categorized, I just wanted to make sure I'm on the right path.  The resource I lack most is time, and this is wasting a lot of it, I want to make sure it's worth it and I'm not out to lunch.

For point number one.  I was careful not to use numbers, I was just attempting to set an example where the frame of reference is small.  Hence I used the word elements of set with this property... they incrementally increase by a constant.  This describes numbers, but it's not the infinite set of numbers I want to exemplify, it is the relationship that defines the reference.  x=x+y loop where y=1.  if you want to resolve z=a+b where a and b are elements of that set, you simply have to define the position in the set and you get values for a and b.  for example a=2( or the place where 2 is) and b is the next element.  You run the loop once and you get x=x+1 for the next position.  2+1=3 and 2 units + 3 units = 5 units.... I'm complicating the example to simplify it lol.

Point 2.  Yes you're right, I don't have this clear cut.  I was considering it as an axiom relative to certainty.  Take "Cogito ergo sum" as the one absolute certainty, the frame of reference is as small as it will ever get.  You, thinking.  You can not scale down any lower. From there on, the frame of reference increases in complexity for any other statement.  Hence the degree of certainty is still extremely high, but it gradually lowers.

Point 3.  As of right now, the epistemological classification would have to be under pragmatism.  I'm constantly adjusting my theory/axioms depending on how they fair in experimentation.  Again, the overall scope of an almost ABSOLUTE currency may be too broad to ever be accomplished, but I find it very good mental gymnastics to even attempt, at least I feel like I'm in original territory.  Again, if anyone can relate this line of thinking to any work PLEASE let me know because I would LOVE to read it.

The weather thing was a bad example on my part, I think I was on my second glass of wine at that point.  I was simply trying to point out the low degree of certainty.

More on this tonight, working now

"Don't seek these laws to understand. Only the mad can comprehend..." -- George Cosbuc

FurryCatHerder
Posts: 1253
Joined: 2007-06-02
Offline
Ktulu,I don't think you're

Ktulu,

I don't think you're wrong, or even heading off in the wrong direction.  Perhaps what's needed is to get away from something as discrete as "numbers" and as problematic (see my response) as "religion".

Here's an example --

Assume two potential definitions for "rape".  In the first definition of rape, there must be a physical act of violence which results in contact with "the genital region".  In the second definition of rape, there need only be an act of "coercion" which has the potential to result in an unspecified "sex act".

According to your axiom, the ability to communicate effectively is determined by how narrowly scoped the definition of "rape" happens to be, and I'd argue that this is precisely the case.  As "rape" has an ever wider frame of reference, communication breaks down on the subject of "what does 'coerce' mean?" and "what counts as 'sex'?"

From a practical application standpoint, creating a new term -- let's call it "date rape" -- which is closer to the second definition of rape would allow "rape of the first kind" to be discussed without the distractions caused by the overly large frame of reference created by "rape of the second kind".

I would argue that this approach is taken in some fields (criminal law, using the examples I gave above) where overly broad definitions might create sub-optimal results (failing to convict people guilty of crimes using an overly-broad frame of reference).

So, don't go giving up ...

"Obviously I'm convinced of the existence of G-d. I'm equally convinced that Atheists who've led good lives will be in Olam HaBa going "How the heck did I wind up in this place?!?" while Christians who've treated people like dirt will be in some other place asking the exact same question."

luca
Posts: 397
Joined: 2011-02-21
Offline
little ot

FurryCatHerder wrote:
Assume two potential definitions for "rape".  In the first definition of rape, there must be a physical act of violence which results in contact with "the genital region".  In the second definition of rape, there need only be an act of "coercion" which has the potential to result in an unspecified "sex act".

You're looking at a definition of rape which is for your aims: finding a crime. You should look from the part of the raper too. I think this is one the things that is causing confusion. In fact I'm surprise I don't see the word "abuse", or something like that.

Second, is: would the first definition need coercion, which is in the second definition? A "physical act of violence" is too unspecific (could be bdsm -- maybe gone "wrong" ), but if we're talking about rape then I suppose it's a violence the victim doesn't want on him/herself, which implies coercion. But then, what do I know.

FurryCatHerder wrote:
According to your axiom, the ability to communicate effectively is determined by how narrowly scoped the definition of "rape" happens to be, and I'd argue that this is precisely the case.  As "rape" has an ever wider frame of reference, communication breaks down on the subject of "what does 'coerce' mean?" and "what counts as 'sex'?"

I wouldn't say "what sex/coerce mean", but "where do they start", as there are even too many shades of gray.

FurryCatHerder wrote:
get away from something as discrete as "numbers" and as problematic (see my response) as "religion".

He doesn't want numbers, but "classes".

Religion is problematic for its unprovable and/or fact-free claims but obviously in building "data" for this theory one should begin from something much simpler.

luca
Posts: 397
Joined: 2011-02-21
Offline

Ktulu wrote:
hehe, thank you for your response.   I have been over-thinking this axiom so it's starting to make less and less sense, just as repeating the same word makes it lose its meaning.  If you can remember where you have seen this before, PLEASE let me know because I would eat that piece of knowledge up.

I don't have this categorized, I just wanted to make sure I'm on the right path.  The resource I lack most is time, and this is wasting a lot of it, I want to make sure it's worth it and I'm not out to lunch.

For point number one.  I was careful not to use numbers, I was just attempting to set an example where the frame of reference is small.  Hence I used the word elements of set with this property... they incrementally increase by a constant.  This describes numbers, but it's not the infinite set of numbers I want to exemplify, it is the relationship that defines the reference.  x=x+y loop where y=1.  if you want to resolve z=a+b where a and b are elements of that set, you simply have to define the position in the set and you get values for a and b.  for example a=2( or the place where 2 is) and b is the next element.  You run the loop once and you get x=x+1 for the next position.  2+1=3 and 2 units + 3 units = 5 units.... I'm complicating the example to simplify it lol.

Point 2.  Yes you're right, I don't have this clear cut.  I was considering it as an axiom relative to certainty.  Take "Cogito ergo sum" as the one absolute certainty, the frame of reference is as small as it will ever get.  You, thinking.  You can not scale down any lower. From there on, the frame of reference increases in complexity for any other statement.  Hence the degree of certainty is still extremely high, but it gradually lowers.

Point 3.  As of right now, the epistemological classification would have to be under pragmatism.  I'm constantly adjusting my theory/axioms depending on how they fair in experimentation.  Again, the overall scope of an almost ABSOLUTE currency may be too broad to ever be accomplished, but I find it very good mental gymnastics to even attempt, at least I feel like I'm in original territory.  Again, if anyone can relate this line of thinking to any work PLEASE let me know because I would LOVE to read it.

The weather thing was a bad example on my part, I think I was on my second glass of wine at that point.  I was simply trying to point out the low degree of certainty.

More on this tonight, working now

Overthinking it? They you just needs facts.

I think I have seen something like this maybe even here, but it didn't go on. As I said, the only thing I can think has something to do with this axiom (which I am not sure I would define it as an axiom as it needs other axioms to work) is Bayes and his work on certainty. But I am still not sure where do you want go with this thing, if with proposition, grammar, and logic, or something lower than that.

About point 1, why you want to discard numbers? It seems very akin to cardinality.

About point 3, pragmatism? mmmh, it can go as a tool, but at some point I think one could pretend more.

About point 2, "cogito ergo sum" as 'floor'? that's something on which to think about.

FurryCatHerder
Posts: 1253
Joined: 2007-06-02
Offline
luca wrote:But I am still

luca wrote:
But I am still not sure where do you want go with this thing, if with proposition, grammar, and logic, or something lower than that.

I think he's looking for a tool to use to argue with people who believe in G-d .

But seriously, I need cream for coffee, then I'll tackle your response to me, which I think is making some of Ktulu's points -- in re, how do we limit the frame of reference so we don't have the "shades of gray" issue you mentioned.  I hope this doesn't devolve into a meta-argument about the terms of an argument, though my sense is that what Ktulu has proposed is a way to get =that= argument out of the way before expending potentially wasted energy on the real argument.

I do think this is in the same circle as Rev. Bayes' (heh, had to point out Bayes was a minister, because I'm evil that way ...) work, so perhaps not completely original, but it does appear to be a new application.

"Obviously I'm convinced of the existence of G-d. I'm equally convinced that Atheists who've led good lives will be in Olam HaBa going "How the heck did I wind up in this place?!?" while Christians who've treated people like dirt will be in some other place asking the exact same question."

Philosophicus
Posts: 357
Joined: 2009-12-16
Offline
...

Ktulu wrote:

Point 2.  ...  I was considering it as an axiom relative to certainty.  Take "Cogito ergo sum" as the one absolute certainty, the frame of reference is as small as it will ever get.  You, thinking.  You can not scale down any lower. From there on, the frame of reference increases in complexity for any other statement.  Hence the degree of certainty is still extremely high, but it gradually lowers.

Are you on an Ockham's razor concept?

Ktulu
Posts: 1806
Joined: 2010-12-21
Offline
Philosophicus wrote:Are you

Philosophicus wrote:

Are you on an Ockham's razor concept?

Ockham's razor is a tool for economizing energy invested in reaching a conclusion.  It doesn't address the degree of certainty for one hypothesis versus the other.  It may very well be that the the hypothesis that makes the the most assumptions turns out to be the correct one.  What I'm considering is much more fundamental then that.

"Don't seek these laws to understand. Only the mad can comprehend..." -- George Cosbuc

Ktulu
Posts: 1806
Joined: 2010-12-21
Offline
FurryCatHerder wrote:I do

FurryCatHerder wrote:

I do think this is in the same circle as Rev. Bayes' (heh, had to point out Bayes was a minister, because I'm evil that way ...) work, so perhaps not completely original, but it does appear to be a new application.

Thank you for your responses Furry.  Don't think that I'm ignoring you, I'm just extremely busy and I'm actually considering your responses carefully.  I think you're right on the money with "getting my drift" as to where I'm going with this, to use three cliches in one sentence, hehe.  You're also correct that putting this against religion, at this particular point in time when it is so fragmented and incomplete, is jumping the gun.  It doesn't stand a chance.  Also perhaps I should stay away from numbers, I can see a lot of slippery slope arguments from considering that.

I'll respond in more detail when I have more time.

"Don't seek these laws to understand. Only the mad can comprehend..." -- George Cosbuc

FurryCatHerder
Posts: 1253
Joined: 2007-06-02
Offline
Ktulu,Not at all a problem

Ktulu,

Not at all a problem -- I'm engaged in the never-ending saga of wrestling with clients for payment, and the winter time joy that is new product development.  If I ever manage to pay Briant Sapient for membership, I'll have to send you a private message so you can see the joy that is my life outside the forum

"Obviously I'm convinced of the existence of G-d. I'm equally convinced that Atheists who've led good lives will be in Olam HaBa going "How the heck did I wind up in this place?!?" while Christians who've treated people like dirt will be in some other place asking the exact same question."

BobSpence
Posts: 5780
Joined: 2006-02-14
Offline
Not quite directly related,

Not quite directly related, but Quantum uncertainty decreases with increasing scale.

Even without that, uncertainty, if you mean unpredictability, still decreases with scale. For example, the average pressure on a surface exposed to an atmosphere becomes more constant as you go from a size where the number of gas molecules hitting it in a given time is small, to a scale where there are millions.

What makes something less predictable is not size, but complexity. This leads into non-linear systems theory, related to 'chaos' theory. What really makes things complex is causal loops, or 'feedback', especially if the effect is not a linear (simply proportional) function of the 'cause', easily leading to total unpredictability in various conditions. IOW infinite precision in knowledge of the initial conditions would be required to predict the results.

This gives the lie to the old idea that a 'deterministic' system, in the sense of one governed by strict cause and effect, means the course of events must be predictable, even without quantum uncertainty.

Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality

"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris

The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me

From the sublime to the ridiculous: Science -> Philosophy -> Theology

Philosophicus
Posts: 357
Joined: 2009-12-16
Offline
...

Ktulu wrote:

Philosophicus wrote:

Are you on an Ockham's razor concept?

Ockham's razor is a tool for economizing energy invested in reaching a conclusion.  It doesn't address the degree of certainty for one hypothesis versus the other.  It may very well be that the the hypothesis that makes the the most assumptions turns out to be the correct one.  What I'm considering is much more fundamental then that.

You said you would categorize the epistemology under pragmatism, but it sounds like foundationalism.

FurryCatHerder
Posts: 1253
Joined: 2007-06-02
Offline
BobSpence wrote:What makes

BobSpence wrote:
What makes something less predictable is not size, but complexity. This leads into non-linear systems theory, related to 'chaos' theory. What really makes things complex is causal loops, or 'feedback', especially if the effect is not a linear (simply proportional) function of the 'cause', easily leading to total unpredictability in various conditions. IOW infinite precision in knowledge of the initial conditions would be required to predict the results.

You've latched on to a =physical= size, rather than rhetorical / probability size.

There's a joke -- "2 + 2 = 5 for large values of 2."  If the "value" of a "number" is known within a specific range, say +/- 0.2, at some point, x + x != 2 * x, but rather either 2 * x + 1 or 2 * x - 1.

In the same sense, if the "level of agreement" for a premise in a argument is high (small "frame of reference&quot the probability of agreement for an argument containing those premises is likewise high.  But if the frame of reference is large -- you think the gods of all religions have brains, and I don't believe G-d has a brain at all -- the probability of agreement is low.

"Obviously I'm convinced of the existence of G-d. I'm equally convinced that Atheists who've led good lives will be in Olam HaBa going "How the heck did I wind up in this place?!?" while Christians who've treated people like dirt will be in some other place asking the exact same question."

luca
Posts: 397
Joined: 2011-02-21
Offline
BobSpence wrote:Not quite

BobSpence wrote:
Not quite directly related, but Quantum uncertainty decreases with increasing scale.

Even without that, uncertainty, if you mean unpredictability, still decreases with scale. For example, the average pressure on a surface exposed to an atmosphere becomes more constant as you go from a size where the number of gas molecules hitting it in a given time is small, to a scale where there are millions.

What makes something less predictable is not size, but complexity. This leads into non-linear systems theory, related to 'chaos' theory. What really makes things complex is causal loops, or 'feedback', especially if the effect is not a linear (simply proportional) function of the 'cause', easily leading to total unpredictability in various conditions. IOW infinite precision in knowledge of the initial conditions would be required to predict the results.

This gives the lie to the old idea that a 'deterministic' system, in the sense of one governed by strict cause and effect, means the course of events must be predictable, even without quantum uncertainty.

We'll ask the one who wants to debate to make a Nyquist plot to accompany his argument

furrycatherder wrote:
in re, how do we limit the frame of reference so we don't have the "shades of gray" issue you mentioned.  I hope this doesn't devolve into a meta-argument about the terms of an argument, though my sense is that what Ktulu has proposed is a way to get =that= argument out of the way before expending potentially wasted energy on the real argument.

Well I haven't still understood if he wants that, so I don't know exactly what to answer... But the "shades of gray" issue is because we're trying to make a generic definition. If it was per-individual it would be less uncertain.

furrycatherder wrote:
I do think this is in the same circle as Rev. Bayes' (heh, had to point out Bayes was a minister, because I'm evil that way ...) work, so perhaps not completely original, but it does appear to be a new application.

And Mosè, Noè and Abramo were polytheists. And what about Platone or Aristotele? Those filthy greeks...

luca
Posts: 397
Joined: 2011-02-21
Offline
:/

Holy crap, do all these threads have to die like this?

Ktulu
Posts: 1806
Joined: 2010-12-21
Offline
At this point it is still a

At this point it is still a preliminary form.  I don't  have a lot of basis for my argument.  I wanted to see how it sounded outside my head and I have accomplished that.  Thank you all for commenting.  It all helps, especially the criticism.

"Don't seek these laws to understand. Only the mad can comprehend..." -- George Cosbuc