Understanding Belief

[CV75]

Wow.

Heck if I know! Don't get too tied up in the words and by all means let's not make this into some kind of metaphysics! Sounds like you want to build worlds of subjective realities bumping into each other. That's far too complicated for me.

I don't worry about defining what people don't know.

I mean- give me a list of everything you don't know. It's a contradiction because you don't know what you don't know, and to write a list you would have to know what you don't know.

It's hard enough defining what we DO know!

I don't know how anything you don't know can be "subjective". The very term is speaking of what I personally know. If you are seeing something affecting me and I don't - that is YOUR perception not mine. Maybe I will discover it is affecting me sooner or later but for now I don't know, so it can't be "subjective" to me.

I guess. But don't make it too complicated - it is really intended to be very simple.

Here's an interesting essay by Feser who is an EV philosopher talking about the tyranny of scientism and the view that there is some kind of "objectivity" possible. Really good essay.

But among other things, it shows that I am not the only religious person drawn to this kind of thinking- it is catching on everywhere- finally since it has been around for 120 years or so.

http://www.thepublic...m/2010/03/1174/

It may be complicated and I wouldn’t have even contemplated it without the 2 or 3 threads that speak to the issue—one thing just leads to another and I thought somebody somewheres musta thunk it through… but I agree, if it’s starting to border on metaphysics it’s just as well to stick with religion.

For me, it’s not a matter of defining but just labeling—for example, if that which we don’t know can’t be labeled subjective, I’ll label it objective, non-subjective, intra-subjective; anything but “nothing” / “it doesn’t exist” because from experience we can all acknowledge that there are tons of things that we don’t know about that affect us.

I don’t really see why you get push-back on pragmatism, especially from religious folks, as it seems perfectly compatible (or at least compatible enough) with a religious point of view. The push-back seems to be from scientific folks as well, so it must be a personal problem... or a fear of anti-authority or something.

[Calm]

I will not attempt to argue with you. Either way, my point is still valid if what you are saying is true. My understanding is based completely on trust, as I imagine yours is as well. The fact that 1 sometimes equals 0.999... is just as weird if not more confusing than saying it always equals 0.999... When some of the best and brightest cannot agree on the most basic and fundamental of all numbers, the number 1, and what it is equal to, we have reason to question where we put our trust. What do we really know?

If by trust you mean quite a number of years of schooling in mathematics as well as teaching it, then yes, my understanding is based on trust of academic principles, etc.

I would feel more comfortable using the phrase "equivalent to" rather than "equal to". For me it carries the nuance that they are not identical but can at times n a practical sense be substituted for each other depending on how precise one needs to be.

Is it really any more weird then using the term "red" for a colour that at other times is called "pink"? Or accepting that Newton's laws work at a certain level of precision but not at levels that require the most precision.

And it is not a case of not agreeing on what it means, it is a question of how it is being used and what is appropriate and that is usually easily agreed upon. Just because something might have multiple definitions depending on context does not automatically imply disagreement. If you have an issue of trust because you have suddenly learned that at times mathematicians treat .9999.... as the equivalent of 1, then perhaps you might want to reconsider using anything that is built on mathematical principles such as the building you live in, the car you drive and the computer you are currently using. If on the other hand you are comfortable in using these, it seems to me you have a strong level of trust in math after all.

Edited November 29, 2012 by calmoriah

[pogi]

If by trust you mean quite a number of years of schooling in mathematics as well as teaching it, then yes, my understanding is based on trust of academic principles, etc.

I would feel more comfortable using the phrase "equivalent to" rather than "equal to". For me it carries the nuance that they are not identical but can at times n a practical sense be substituted for each other depending on how precise one needs to be.

Is it really any more weird then using the term "red" for a colour that at other times is called "pink"? Or accepting that Newton's laws work at a certain level of precision but not at levels that require the most precision.

And it is not a case of not agreeing on what it means, it is a question of how it is being used and what is appropriate and that is usually easily agreed upon. Just because something might have multiple definitions depending on context does not automatically imply disagreement. If you have an issue of trust because you have suddenly learned that at times mathematicians treat .9999.... as the equivalent of 1, then perhaps you might want to reconsider using anything that is built on mathematical principles such as the building you live in, the car you drive and the computer you are currently using. If on the other hand you are comfortable in using these, it seems to me you have a strong level of trust in math after all.

Do you disagree with the overall point I was making, or are you just being fastidious?

Yes, that is what I mean by trust. You were a pupil, now you are a teacher and think you know it all, but all you are really doing is teaching what has been taught to you. There are many mathematicians, that would disagree with you on 1 being equivalent to and not equal to 0.999... That is the only point I am making, they don't all agree.

[Calm]

There is one thing I absolutely know and that is I don't know it all.

CFR on the mathematicians disagreeing with me based on how I am stating it...that it depends on context.

[mfbukowski]

For me, it’s not a matter of defining but just labeling—for example, if that which we don’t know can’t be labeled subjective, I’ll label it objective, non-subjective, intra-subjective; anything but “nothing” / “it doesn’t exist” because from experience we can all acknowledge that there are tons of things that we don’t know about that affect us.

Well I think the problem is that such things are outside the theory- kind of like saying "How about them Yankees?" in the middle of a philosophical discussion. I mean there may be the proverbial butterfly in Africa that beats its wings and ends up creating a hurricane that destroys New York but we are talking about how we KNOW things and things we don't know don't enter into a theory about what we DO know.

We are not coming up with a comprehensive model of EVERYTHING, just everything we can know about so we are kind of bracketing those things we do not know about so we can talk about the things we DO know about. Everything we talk about automatically excludes all the things we are NOT talking about to make it possible to talk about some- THING.

It's like the question - do undiscovered species "exist"? I suppose in some sense they do in a kind of common sense way but they are irrelevant to our conversation about things we DO know about. Do unicorns "exist"? Of course they do in the set of "mythological creatures", they exist in literature and legend etc. We can draw a unicorn even though they do not "exist" anywhere else but in stories and pictures.

But what about some creature which will be "discovered" in 2016? There's literally nothing there to talk about now even though it might be swimming around somewhere right now. So even if it is a sea monster that eats Tokyo in 2016 it's not relevant to the epistemology of what we know about today and how we know about it. It is not in the set of known things that we can talk about in developing a theory about how we know what we know.

It's kind of like trying to talk about what's out there in the world which "causes" us to have experiences- we presume something is there but there is no way we can talk about it so it becomes irrelevant to any kind of discourse.

It may pop out and eat someone any minute but there's nothing to say about it now!

Edited November 29, 2012 by mfbukowski

[mfbukowski]

Is it really any more weird then using the term "red" for a colour that at other times is called "pink"? Or accepting that Newton's laws work at a certain level of precision but not at levels that require the most precision.

Exactly. I was shopping for a red tie today and I must have looked at 20 or 30 - all were red, but they were not the right color.

[pogi]

There is one thing I absolutely know and that is I don't know it all.

CFR on the mathematicians disagreeing with me based on how I am stating it...that it depends on context.

Which story are you going to stick with, that it "depends on the context", OR, that you are more "comfortable" stating that it is "equivalent to" rather than equal to?

Because, as you said, "for me (you agree then that other mathematicians disagree with you) it carries the nuance that they are not identical" But when you say, it depends on the context, it sounds like you are saying that there are contexts in which 1 does equal 0.999.... meaning they are identical.

Again, do you disagree with the overall point I was making, or are you just being fastidious?

[Calm]

Which story are you going to stick with, that it "depends on the context", OR, that you are more "comfortable" stating that it is "equivalent to" rather than equal to?

Because, as you said, "for me (you agree then that other mathematicians disagree with you) it carries the nuance that they are not identical" But when you say, it depends on the context, it sounds like you are saying that there are contexts in which 1 does equal 0.999.... meaning they are identical.

Again, do you disagree with the overall point I was making, or are you just being fastidious?

You have misread me. My "story" has always been the same. It depends on context, basically what mathematical language one is choosing to use at the moment. That I personally prefer to use "equivalent to" rather than "equal to" when speaking in general of the concept is merely me being precise in my own mind (because of the nuances I apply to both terms), not me insisting that it must be defined a certain way at all times.

As to your overall point...what exactly is it? That we can or cannot trust mathematics because in your view mathematicians disagree on the concept that 1=.9999....? If so, then I think you need to go back to square 1 or .99999..... if you prefer because I don't think you have demonstrated that mathematicians actually disagree on the given concept even if they choose to use a different concept in a different context.

If it is simply this: "My point is that things are not always as they seem, logically speaking" then you have a problem using the concept 1=.9999999 because that conclusion is based on pure logic so it is exactly as it seems, logically speaking.

Now if what you really mean is 'things are not always as they seem, intuitively speaking' then feel free to use the concept that in certain cases 1=.9999..... as a demonstration. However, honestly if I were you, I would use an example for a complex and nuanced concept from a field I had more familiarity with than just a few weeks or based on what I had heard on the radio. When it comes to math, knowing the theory behind it can prevent one from making huge errors of assumption and conclusion or simple misstatements such as mathematicians disagree, etc. I don't think I even dare make such assumptions and conclusions myself save for obvious observations about variations existing among the mathematics based on their given axioms, definitions, etc. What those variations might be and even more important...their significance I would prefer to leave to someone much better based in the fundamental theories.

BTW, I'd like to have my CFR answered that mathematicians actually disagree on the concept of context with me rather than are simply using appropriate context appropriately....as I have stated is appropriate.

Simply because one person says "red" in a certain context and another says "pink" in a different context does not mean there is disagreement. It is quite possible they are simply talking about the same things using different definitions that are equally appropriate given the context and thus are in total agreement at some fundamental level.

Edited November 29, 2012 by calmoriah

[Calm]

Exactly. I was shopping for a red tie today and I must have looked at 20 or 30 - all were red, but they were not the right color.

Red is one of the hardest colours to get right.

[CV75]

Well I think the problem is that such things are outside the theory

Ah so I was barking up the wrong (but related) tree.

Are there theories that address the things we don’t know but that affect us – I suppose those would have something to with faith and exploration; from the Gospel perspective, we are all about bringing things to light so that we can act instead of being acted upon.

[pogi]

That solely depends on the context where the number is being used. In other contexts .99999.... approaches 1, but never reaches it.

>Another problem I have is that I was always taught that .333... is

>just a decimal approximation of the exact value 1/3. Have all my

>teachers been mistaken?

If you stop after finitely many 3s, it's an approximation. If there

are infinitely many 3s, then it's exact.

http://mathforum.org...view/57174.html

We're all familiar with the fact that 0.999... is equal to 1. We're also probably familiar with an asymptote, a line that infinitely approaches a curve, but never reaches it.

We can see an example of an asymptote in the basic function f(x) = 1/x:

Both the x and y axes are asymptotes of the curve f(x).

So, let's take the X axis for our observation. f(x) has a negative slope, and one would expect it to intersect the X axis. However, as our curve gets closer and closer to zero, so does its slope, and we never see an intersection. These two lines will stretch out into infinity, always getting closer but never touching.

But wait a minute!

This is quite similar to another thought relating to infinity, and that is the fact that 0.999... = 1. It would appear that our left side is a non-terminating decimal, infinitely getting bigger but not approaching 1. This is not the case! We know that they are equal, as an infinitely small difference is no greater than a difference of 0.

Taking what we know from that equation, how is it that an asymptote can exist? If the two lines have an infinitely small distance between them, and the distance is infinitely becoming smaller, then the lines will join, will they not?

A: Yeah, they "join" at infinity. Have you studied limits?

http://forums.xkcd.c...=18926&p=545275

There were lots of interesting questions and comments through the course, but the most memorable for me was a debate on whether 0.999… = 1. At the beginning of the lecture all of the students unanimously agreed that the two numbers were not equal, and even after my best mathematical arguments I’m not sure I managed to convince anyone otherwise. This has also been true of every non-mathematician I’ve talked to since then! Almost everyone will say that 0.999… approaches 1 but never actually reaches it – it’s always slightly smaller than 1. To believe that the two numbers are equal requires a deep understanding of the nature of infinity, and even some mathematicians disagree on this. The concept is such a misunderstood one that a whole Wikipedia article is dedicated to it. Try reading the arguments and see if you can be convinced!

http://haggistheshee...21/openstudies/

Edited November 29, 2012 by pogi

[Calm]

Yes, and the wiki article agrees with me. It is equivalent in some contexts and not in others.

Quote:

The equality of 0.999... and 1 is closely related to the absence of nonzero infinitesimals in the real number system, the most commonly used system in mathematical analysis. Some alternative number systems, such as the hyperreals, do contain nonzero infinitesimals. In most such number systems, the standard interpretation of the expression 0.999... makes it equal to 1, but in some of these number systems, the symbol "0.999..." admits other interpretations that contain infinitely many 9s while falling infinitesimally short of 1.

Edited November 29, 2012 by calmoriah

[pogi]

Yes, and the wiki article agrees with me. It is equivalent in some contexts and not in others.

Quote:

The equality of 0.999... and 1 is closely related to the absence of nonzero infinitesimals in the real number system, the most commonly used system in mathematical analysis. Some alternative number systems, such as the hyperreals, do contain nonzero infinitesimals. In most such number systems, the standard interpretation of the expression 0.999... makes it equal to 1, but in some of these number systems, the symbol "0.999..." admits other interpretations that contain infinitely many 9s while falling infinitesimally short of 1.

Good, you just proved my point that there is disagreement among mathematicians. Who are you going to trust? Because that's really what it boils down to isn't it? Trust

Edited November 29, 2012 by pogi

[Azariah]

Ok, so I have heard a few positions and thoughts on the subject matter. I thank those who have participated.

Statement #1: God exists.

False.

Statement #2: I believe God exists.

True.

Statement #3: The LDS church is the one true church of God on the Earth.

False.

Statement #4: I believe that the LDS church is the one true church of God on the Earth.

True.

Would members of this board agree with the premises of these hypothetical statements? Do members also understand the core value of both statements? Statements #1 and #3 are false because they are unverifiable claims. Conversely, statements #2 and #4 are indeed factual statements solely based on the opinion of the person who claims and owns them.

Once more...

Statement #5: Joseph Smith saw God and Jesus Christ.

False.

Statement #6: Joseph Smith believes he saw God and Jesus Christ.

True.

Let me be clear again, I'm not trying to dissuade anyone out of faith. However, if there is not a rational, reasonable, or logical explanation for a worldview, leaving the "faith" construct out of the equation, then the worldview is inconsequential and goes onto the same shelves as mythology.

Again, I'm not saying that God does not exist. I'm stating that there seems to be a lacking of evidence to support the worldview that God does in fact exist. If the narratives found in scripture are simply narratives rather than actual historical writings then what greater value do they have than that of the story of Heracles or the Odyssey? Not an ounce.

With regard to Joseph Smith seeing God the Father and Jesus or Joseph Smith believing he saw them. A third option could be stated as: "I believe Joseph Smith saw God the Father and Jesus . . ."

[Calm]

Good, you just proved my point that there is disagreement among mathematicians.

No, you are again misreading my comments and you have misread the quote.

Simply because mathematicians don't use 1 or .9999.... in identical ways does not mean they are in disagreement, it may mean they are being sensitive to context. If a mathematician uses it as a equivalency in one case and as not an equivalency in another based on the number system being used, this does not mean he disagrees with himself anymore than someone who uses a knife in one context to cut meat and in another to pry open a can.

[mfbukowski]

Ah so I was barking up the wrong (but related) tree.

Are there theories that address the things we don’t know but that affect us – I suppose those would have something to with faith and exploration; from the Gospel perspective, we are all about bringing things to light so that we can act instead of being acted upon.

Exactly- "faith and exploration"- those would be considered "metaphysics" meaning effectively a "theory of everything". In my way of seeing the world, metaphysics does not include philosophy because metaphysical statements ultimately have no logic to them except as they make you feel good about you and your life- and in my book that would include religion, so I am not putting it down in any way. There is no way to verify metaphysical statements and whether or not they are "correct" in any way is irrelevant to their purpose. Plato's metaphysics says that there is no "reality" except ideal Forms; Aristotle believed that all was composed of Earth Air Fire and Water in different mixtures; Heraclitus said that the world was in constant flux and was like a river.

All these theories of "everything"- that we are all dreams in God's mind or etc etc cannot be verified and really cannot be shown to be true or false using reason and are therefore beyond the concerns of philosophy.

That doesn't make them less valuable - indeed they are beliefs which give our lives meaning and include the things which are most important in our lives but they are not considered in present day academic philosophy in the English speaking world. On the other hand, they ARE included in what is called "Continental" philosophy as taught in Europe and they are considered in Asia as well.

So for me philosophy is about speaking clearly about these subjects, metaphysics is mostly about what Wittgenstein would call the "unspeakable"- what we cannot speak clearly about. And I would guess I would include theology as kind of the meeting ground of philosophy and metaphysics.

So for me, if you are talking about anything metaphysical that kind of takes it out of the realm of logic and makes it a mixed bag and is an area which is subject to debate

Which is what we do here. But you couldn't write a paper about any of this stuff and submit it in any university philosophy department in the USA or Britain because it is not considered "philosophy" here.

I suppose that is kinda weird but that is the way it is.

That's why I think Wittgenstein was ultimately a mystic- he I think was a believer because his whole philosophy was about leaving room for such beliefs but he did not write much about religion because such things were beyond speaking about clearly. W thought the purpose of philosophy was to put itself out of business- like the perfect doctor would do in principle. Once all disease is eradicated there will be no need for doctors- once everyone speaks and therefore thinks clearly there will be no need for philosophers.

That puts religion in the realm of the mystical- which is fine with me, because it is definitely difficult to discuss the mixture of "faith and reason" which is what we supposedly do here.

I think that ultimately they don't mix very well though. In my personal life, when I am being mystical I am mystical and logic doesn't enter. When I am being logical I am logical.

When I am writing or discussing religion it is kind of a mish-mash which is uncomfortable but I think a necessary evil which I hope helps others figure stuff out. But in my own mind, these are two separate regions- like baseball and working on a car. Nothing to do with each other!

[mfbukowski]

With regard to Joseph Smith seeing God the Father and Jesus or Joseph Smith believing he saw them. A third option could be stated as: "I believe Joseph Smith saw God the Father and Jesus . . ."

And who's theory of truth are you using? What philosopher? Since you know so much about truth, I want to know where you got these silly ideas!

I love talking truth and falsity with fundamentalists like you.

Edited November 29, 2012 by mfbukowski

[Azariah]

And who's theory of truth are you using? What philosopher? Since you know so much about truth, I want to know where you got these silly ideas!

I love talking truth and falsity with fundamentalists like you.

Since when is saying "I believe" considered "silly ideas"?

[pogi]

This has also been true of every non-mathematician I’ve talked to since then! Almost everyone will say that 0.999… approaches 1 but never actually reaches it – it’s always slightly smaller than 1. To believe that the two numbers are equal requires a deep understanding of the nature of infinity, and even some mathematicians disagree on this. The concept is such a misunderstood one that a whole Wikipedia article is dedicated to it. Try reading the arguments and see if you can be convinced!

http://haggistheshee...21/openstudies/

Perhaps you are the one who is misreading my comment and quotes. See the part that says that "even some mathmaticians disagree on this." That has nothing to do with context.

[mfbukowski]

Since when is saying "I believe" considered "silly ideas"?

My mistake- I totally apologize !!

I took your quote of Valentinus with the quotes in red- post 164 to be YOUR comments (in red) on Valentinus's quote.

In other words I thought it was YOU who was saying it was "false" that God exists and was jumping down your throat for evidence of that assertion.

I expect it from Valetinus!

I totally apologize- I was wrong

Oh yeah - and welcome to the board!

I think I said something nasty on another thread too- sorry about that as well. I have to cool my jets a bit I guess!

Edited November 29, 2012 by mfbukowski

[Calm]

Perhaps you are the one who is misreading my comment and quotes. See the part that says that "even some mathmaticians disagree on this." That has nothing to do with context.

Unfortunately he does not explain what he means by this so I don't see how you can exclude that it is context that is creating the difference.

add-on: look, the only point I've been trying to make is that you are using a language that is meant for precision, etc. in a very imprecise way, a way it was not meant to be used for. Like the quote says you are dealing with the concept of infinity that needs much more than just a radio discussion to explore its depth and variety and impact.

It is like you have been given a fine precise music box and you decide to tune it with a hammer. You might get somewhere in the ballpark but it just doesn't come out sounding right. If your point on trust is self-evident or logical or commonsensical/intuitive or whatever you choose to call it, it should be easy enough to find another nonmathematical demonstration where you are more familiar with the elements so that your explanation doesn't come out sounding slightly off key.

When one is explaining something, it generally works better if one is familiar with the explanation rather than almost as ignorant of it as one's audience.

Edited November 29, 2012 by calmoriah

[Bill “Papa” Lee]

If we could define "belief" it would no longer be belief, it would then be "pure knowledge" and the judgements of God would pour down upon us like a hard rain.

[CV75]

Exactly- "faith and exploration"- those would be considered "metaphysics" meaning effectively a "theory of everything".

Great--thank you! I think I'm going to open up a thread to discuss how we can pragmatically meld baseball and car repair to improve the human condition!

[Calm]

I would be more likely to join in if it was soccer instead of baseball.

[mfbukowski]

I would be more likely to join in if it was soccer instead of baseball.

When I was little I had never heard of "soccer" and when I did hear about it I thought it was a terrible terrible game to play.

I had been taught to never hit girls and when I heard that someone was playing a game called "sock her" I thought that was absolutely awful!

I have always been good at rooting out ambiguity- even when it doesn't exist!