Thought this was interesting. I was debating near this topic a few weeks ago and find a big old article all freshly written about it. Keen.

http://www.sciencenews.org/view/generic/id/31392/title/Still_debating_with_Plato

I posit that logic itself is an abstract, but also lends structure to abstract models.

I posit that logic is a consequence of the reality of "abstract space" as part of existence.

I posit that mathematics is a consequence of logic.

I conclude that since logic is apparently a naturally occuring phenomenon (since we humans are natural creatures) mathematics is - from perspective of the entire timeline of this universe: an abstract inevitability.

So 'discovered' or 'invented' are neither really appopriate terms for explaining the existence of math.

take that plato.

I would say though that the symbols for it are obviously invented.

Oh hell now I'll argue against me and say that since the symbols are invented, so by extension their utilization is also invented. The meaning though, would seem inevitable.

Poor arguing agaist myself. I'm sure someone else can make me "take that" like I did plato, who conveniently isn't here to defend himself.

well I dont know really. but the various fields of math (logic) are evidently derived from a single most fundamental field of logic by means of definitions. if this field is invented then I guess there must be other alternate (most fundamental field of logic)s.

I dont know what this field is but I would guess that it would contain things like:
a thing cant be true and false at the same time.
2 things equal to a 3rd are equal to each other.
etc...

what is posit?

http://dictionary.reference.com/search?q=posit

well I dont know really. but the various fields of math (logic) are evidently derived from a single most fundamental field of logic by means of definitions. if this field is invented then I guess there must be other alternate (most fundamental field of logic)s.

Agreed but wouldn't that field be simply "logic"?


I dont know what this field is but I would guess that it would contain things like:
a thing cant be true and false at the same time.

But lots of things are true and false at the same time, whereas the truth is a matter of perspective. Of course the typical application of logic wouldn't allow for this.


2 things equal to a 3rd are equal to each other.
etc...

These things apply to idealized mental objects, as in physical reality no two things are exactly equivalent, as if nothing else they occupy separate regions of space-time and/or their molecular composion/charge can't be precisely identical. *shrug*

IF 2 things equal to a 3rd THEN they are equal to each other. numbers are exactly equal to each other.

fuzzy logic does not say that something can be true and false at the same time. it is the probable probability that it is true. (Bayesian probability)

IF 2 things equal to a 3rd THEN they are equal to each other. numbers are exactly equal to each other.

I'm quite familiar with the typical applications of logic, commutative stuff and blah blah. I mentioned perspective as the basis for departure from this typical application. Things to be judged as equal or different aren't always necessarily static or exactly what they seem. For the commutative law to apply always, what it is applied to must remain static. Further, two things that are evaluated as equal in individual comparisons to a third could all be wrong if for instance, etc.

http://www.lhup.edu/~dsimanek/3d/herring.gif

How many illusions exist that can't be determined to be illusion?


fuzzy logic does not say that something can be true and false at the same time. it is the probable probability that it is true. (Bayesian probability)

Not fuzzy logic, perspective.

I'm annoying and not annoying, loved and not loved, etc. etc. A point in four dimensions appears to be in two places at the same time from a perspective in the third or something as well.

Again, "These things apply to idealized mental objects, as in physical reality no two things are exactly equivalent, as if nothing else they occupy separate regions of space-time and/or their molecular composion/charge can't be precisely identical. *shrug*" Idealized mental objects reasonably approximate reality for practical purposes, but don't necessarily reveal a damned thing about it.

just because something LOOKS different from different perspectives doesnt mean it actually is different.

if objects change over time then the comparison would have to made at one particular time to be meaningful.

a tree is a tree as long as it falls within certain bounds. all trees dont have to be identical. all trees can be different but still be 100% trees. a tree would be DEFINED as any object for which a certain set of (possible probabilistic) truth statemets is true. now you want to say that we cant know anything about a tree because they are all different. if we couldnt know anything about it then we couldnt define it in the first place.

A point in four dimensions appears to be in two places at the same time from a perspective in the third or something as well? I have no idea why it would appear to be in 2 places at the same time.

Am I right in saying quantum physicists purport atoms arise simultaneously with the observer's interaction. Schrödinger's cat being one of the main tennets. Perhaps a little leftfield of the original question but still valid concepts to regard.

just because something LOOKS different from different perspectives doesnt mean it actually is different.

Uhm. Thank you for the clarification. Believe me, I know what you mean. I don't think you understand or give credence to what I mean, which is really illuminated by the rhetorical question, how do you know what it actually IS? I realize it's an easy question to shrug off, but I think it important to understanding what really is, and the nature of our interaction with it.


if objects change over time then the comparison would have to made at one particular time to be meaningful.

Hey I said that already. Consider not a specific case but the implication of the static nature of logic, and how nothing in reality seems to be static. Again that's not to say logic is useless or wrong, but merely that it's only applicable to idealized mental objects like numbers and symbols and stuff.


a tree is a tree as long as it falls within certain bounds. all trees dont have to be identical. all trees can be different but still be 100% trees.

Those bounds are exceedly difficult to exactly define if you've ever done one of those fun thought experiements that pushes the limits of whatever definition you can come up with. There was a thread here a few years from prince james I think about the definition of a car. It was interesting.


A point in four dimensions appears to be in two places at the same time from a perspective in the third or something as well? I have no idea why it would appear to be in 2 places at the same time.

Let's try using our idealized imaginations! Yeah!

Let's say the surface of a piece of paper represents three dimensions. Pick it up and touch two ends of it together. Poke a hole in it with a pencil or something. The point at which the pencil entered both sides of the sheet is now at two different places on the plane of the paper, but in the same place considering where the pencil jabbed through it. Now you have an idea as to how to imagine it.

Am I right in saying quantum physicists purport atoms arise simultaneously with the observer's interaction.

No I don't think so. You're in the ballpark at the wrong base I think.


Schrödinger's cat being one of the main tennets. Perhaps a little leftfield of the original question but still valid concepts to regard.

shrodinger's cat plays out the quantum mechanical view of things as a probability function that collapses to a conclusion when an observation is made. by the math of quantum physics the cat is both dead and alive until the state is collapsed by someone checking on the cat.

a little too leftfield for me.

I have to sit this one out.

I concede that some things are by their very nature 'unknowable'.

"The point at which the pencil entered both sides of the sheet is now at two different places on the plane of the paper, but in the same place considering where the pencil jabbed through it. Now you have an idea as to how to imagine it."?

2 places? the only thing i can think of is that maybe you are somehow referring to the 2 sides of the paper.

Those bounds are exceedly difficult to exactly define if you've ever done one of those fun thought experiements that pushes the limits of whatever definition you can come up with. There was a thread here a few years from prince james I think about the definition of a car.

you're absolutely right. there is a grey area around the edge that is very hard (I dont say impossible) to categorize. but so what? you dont need to know the EXACT bounds to KNOW for certain that a sedan is definitely a car.

I suppose that technically an object would be defined by 'why' it exists at all. unfortunately it is very hard (perhaps even impossible) to know why things happen. we may never know why fish left the water or why mammals became warm blooded. fortunately we dont seem to need to know this. we simply recognize that rather than a continuous spectrum from reptile to mammal we see instead that animals in the real world TEND to be concentrated at the ends of this spectrum. we dont really try to explain why. we just accept it as a fact.

the most questionable part of knowing beyond a doubt is knowing how improbable something has to be to be considered unreasonable. its a very big universe. no matter how improbable something is its virtually certain to happen sometime.

Good work wes.

now wait a minute. why is it hard to define the boundaries of what is considered a car? if you want to move on land you use a car. if you want to move on water you use a boat. we can imagine a continuous spectrum from land to water. but you dont see a continuous spectrum from car to boat. at some point a car simply no longer works and one has to use something else.

on the other hand, fish did gradually evolve into amphibians. it would be hard to say exactly where it stopped being a fish and became an amphibian. there is a grey area there.

He doesn't talk to people like us, gp. :(

Not fuzzy logic, perspective.

I'm annoying and not annoying, loved and not loved, etc. etc. A point in four dimensions appears to be in two places at the same time from a perspective in the third or something as well.

Logic and Subjectivity
Subjective truths have objective truths behind them.

Example 1:
When Bob says "Rap is annoying" and Alice says "Rap is not annoying", they are both stating subjective truths, which are apparently contradictory.

But, their statement can be stated as objective truths, which do not contradict:
"Rap is annoying to Bob."
"Rap is not annoying to Alice."

subjective truths are opinions
truth then is a misnomer

one is entitled to their truths as long as it does not harm anyone

a degradation of the term, ja?

subjective truths are opinions
truth then is a misnomer

one is entitled to their truths as long as it does not harm anyone

a degradation of the term, ja?

degradation of the term eh?

does what you hold to be true matter so much to you that you absolutely insist it's true outside yourself?

if so, then yes it's a degradation.

if not, then it's an acknowledgment of a limitation of the term.

Logic and Subjectivity
Subjective truths have objective truths behind them.

Example 1:
When Bob says "Rap is annoying" and Alice says "Rap is not annoying", they are both stating subjective truths, which are apparently contradictory.

But, their statement can be stated as objective truths, which do not contradict:
"Rap is annoying to Bob."
"Rap is not annoying to Alice."

What if bob thinks rap is annoying to alice? What if she says it isn't, he thinks she's wrong?

I'm trying to come at it from the subjective. I'm not objectively talking about the subjective. I'm subjectively talking about it. As such if I insist that what I think it real is so outside of myself, in my mind - it's true for you too - regardless of your acknowledgment thereof.

While you're correct that each can be restated - it wasn't by bob or alice themselves. To each of them, if they do not consider the possibility of other perspectives at the time of thought, rap is annoying... period.

Thus, while by your analysis (which I agree with when attempting to be objective about it) is correct when imagining an objective scenario, if I presume x to be true beyond doubt - it should be true for you too (in my world). Even if you object it doesn't necessarily change my mind about it so to me it is still true, objectively - that rap is annoying because I simply do not acknowledge your perspective on the matter. God is real, the moon is made of swiss cheese, etc.

We have to imagine our objective anlaysis though, rendering it subjective, etc. etc.

That an experiment is repeatable or that everyone agrees x is true is simply consensus, proving nothing, dependent on your criteria for Truth of course - mine is unquestionable, and from this simple thought experiment I find there is no such thing.

To me, this necessitates faith to breach the gap.

And with this faith, we can say what exists beyond ourselves and even justify the hypothesis of self in the first place. From there it's a matter of practicality to accept consensus on things or from experts or other authorities. From there one can accept one's own authority. But I think in a rigorous analysis of the subject it's important to note the role of faith in the process. Faith doesn't always lead to religion damnit. Lol

It's generally far more practical to restate as you've done. I'm just more interested in what it means to in terms of alice or bob, as ultimately - I have only what it means in terms of me. To be a proper representation, I think you have to go from the inside out and you can't keep speaking for bob and alice damnit. Lol.

I guess inclusion in a category isnt all or nothing. at first the fish was a poor amphibian and it gradually became a better and better one. even now amphibians could probably be greatly improved via genetic engineering. If it were perfect though then i dont see how it could belong to more than one class.

sometimes I learn something here. Thats what keeps me coming back.

Faith doesn't always lead to religion damnit. Lol




sure it does
its a common context
your revolutionary zeal is doomed to fail
linguistically speaking that is

sure it does
its a common context
your revolutionary zeal is doomed to fail
linguistically speaking that is

and you believe that eh? how?

it's only a common contex because it was hijacked, though I don't think exactly purposefully - as I doubt those doing the hijacking necessarily realize what they were doing.

oh and most of those faithful non-religious folks wouldn't admit to faith even in the context I've framed for the same reason the people who hijacked it didn't realize it.

and maybe I've framed it all wrong anyway.

I suppose it depends on what you believe, and how intensely you believe it.

i attempted to reply to post #21 twice
i remain baffled and astonished
what i glean from the general tenor.....

you are gay. you just dont know it yet aka megalomania rules

on this "faith" thingy

*In traditional logic, an axiom or postulate is a proposition that is not proved or demonstrated but considered to be self-evident. Therefore, its truth is taken for granted, and serves as a starting point for deducing and inferring other (theory dependent) truths.

*Unlike theorems, axioms (unless redundant) cannot be derived by principles of deduction, nor are they demonstrable by mathematical proofs, simply because they are starting points; there is nothing else they logically follow from (otherwise they would be classified as theorems)

*In the modern understanding, a set of axioms is any collection of formally stated assertions from which other formally stated assertions follow by the application of certain well-defined rules. In this view, logic becomes just another formal system. A set of axioms should be consistent; it should be impossible to derive a contradiction from the axiom. A set of axioms should also be non-redundant; an assertion that can be deduced from other axioms need not be regarded as an axiom.

*Outside logic and mathematics, the term "axiom" is used loosely for any established principle of some field.

eg:
*A finite whole is greater than any of its parts
*It is impossible for the something to be and not be at the same time in the same manner.

thats wiki shit

now
why would i have faith in shit that is at best, tentative and provisional
axioms are shit we make up thus amenable to modification.

http://img151.imageshack.us/img151/3923/aa1nf5.jpg

http://img388.imageshack.us/img388/2860/aa2rp3.jpg

http://img146.imageshack.us/img146/5555/aa3gc0.jpg (http://books.google.com/books?id=ldh_LqMhsccC&pg=PA233&lpg=PA233&dq=axiom+tentative+provisional&source=web&ots=8W6A3XZCbm&sig=bRe8QMYdfOzBVtf0GfTt9ATpAxg&hl=en#PPA233,M1)

/eek

check out the fucking tear!

So 'discovered' or 'invented' are neither really appopriate terms for explaining the existence of math.

take that plato.All the mathematicians I have spoken with say "discovered".

now
why would i have faith in shit that is at best, tentative and provisional
axioms are shit we make up thus amenable to modification.

perhaps because "you are gay. you just dont know it yet aka megalomania rules"?

otherwise, I'd say because you have a mind and the 'beliefs' that comprise the significant structual elements of ego are taken as given. because you presume anything, even if temporary. I'd contend that sure maybe it was temporary, but for the time you indulged it - you accepted the idea with no proof. more fundamentally though, I'd say because you probably presume you exist. perhaps you don't.

I do. Sure I have evidence and I could argue it's tentative, blah blah blah - but I can't utter the simplest word without invalidating evidence that might contradict the argument that I don't exist.

Probably as close to a "Proof" as we can get I suppose, but still it's a tautology that logic simply can't allow - yet we know it to be true. There's little tentativeness about self, generally speaking and even that which is, is bogus as an argument because making the argument makes it impossible to say you're not you and be taken any kind of seriously.


So as far as I can see it, there's faith involved in any form of knowing - as it presumes for instance, that the whole of reality is consistent from one moment to the next, or that there are moments, etc. I make those same presumptions of course, but think that they are fundmentally equivalent to matters of faith.

All the mathematicians I have spoken with say "discovered".

Same here, but what do YOU think?

Do you think there's a even a smidge of validity in my reframing of the issue?

When a sculptor works on a large block of stone, resulting in Pegasus or a human figure, did he create something or merely discover what was already in that block of stone?

Whenever I hear talk about discovery rather than invention of some law of mathematics or science, I think of the scuptor merely chipping away all the stone that was not Pegasus or the Thinker.

more fundamentally though, I'd say because you probably presume you exist. perhaps you don't.


employing industry jargon....you violate a foundational axiom by invoking an inconsistent and contradictory proposition

a disavowal of self is actually an affirmation of self

So as far as I can see it, there's faith involved in any form of knowing - as it presumes for instance, that the whole of reality is consistent from one moment to the next, or that there are moments, etc. I make those same presumptions of course, but think that they are fundmentally equivalent to matters of faith.


i say probability equation
an estimation of trends
the likelihood

never faith nor belief simply cos those terms come with baggage
dirty underwear if you will

employing industry jargon....you violate a foundational axiom by invoking an inconsistent and contradictory proposition

a disavowal of self is actually an affirmation of self

No - I said: "but I can't utter the simplest word without invalidating evidence that might contradict the argument that I don't exist" which you basically also said above eh?

I didn't violate it, I used it as a lock against your next post.

i say probability equation
an estimation of trends
the likelihood

You can have none of these things without some basis from which to calculate or estimate them.


never faith nor belief simply cos those terms come with baggage
dirty underwear if you will

As you noted yourself, the notion of self can't really be violated - so you're sort of forced to take it for granted. If you don't, you can't say it to reject it. This is a primary example of taking something on faith. (This case in particular I think of as "a leap of faith of zero distance", if you can see what I mean.)

I believe that would be described by most as 'self-evident' and I'd be laughed at for calling it faith, because the word has as you describe it - so much baggage and is largely a religious term. Some might call it "an axiom" or "assumption" or "what the fuck are you talking about you fucktard?".

I tend to agree for the most part.

But I can't get past the functional mental equivalency of what's called "faith" and what are assumptions or axioms. They're things we take for granted, if only for a time.

Maybe you don't like the word, but if you can get past your bias temporarily, you might see some stuff about minds you didn't see before. Maybe instead you'll just call me gay again. *shrug*

pardon

/kowtow

Maybe instead you'll just call me gay again. *shrug*


i did not
it was a play on your "rap is annoying" per se
a forcible imposition of a mindset


You can have none of these things without some basis from which to calculate or estimate them.

ja
a self

wes
faith works
just a trifle unorthodox
thats all

You can have none of these things without some basis from which to calculate or estimate them.


another 'what is the basis of reason question'. Reason IS the basis. an unreasonable system would be self-contradictory.



As you noted yourself, the notion of self can't really be violated - so you're sort of forced to take it for granted.


what exactly is the alternative? What would be your basis for asserting it?



But I can't get past the functional mental equivalency of what's called "faith" and what are assumptions or axioms. They're things we take for granted, if only for a time.


axioms are definitions not assumptions.

chicken/egg

there is a bootstrapping issue but it boils down to 'how do you retrieve a message from a lot of noise'? its all done with error correction.

another 'what is the basis of reason question'. Reason IS the basis. an unreasonable system would be self-contradictory.

It was not a question.


what exactly is the alternative? What would be your basis for asserting it?

Not that I was going this direction, but... madness? There are plenty of insane people (by my standard at least) who need no basis for their reasoning. Emotion or simply "function" can suffice. Apes don't have to explain themselves.



axioms are definitions not assumptions.

They are functional mental equivalents to me. There is no compelling reason to believe A=A if you don't give a shit about reason or logic. A=mygatinyourass in many equations. Certainly there are differences in the way they are defined in books and such, but what affect do the words impart on mind? To me, it's "accepting something as given" - basically.

i did not
it was a play on your "rap is annoying" per se
a forcible imposition of a mindset

my bad.


ja
a self

ja.


wes
faith works
just a trifle unorthodox
thats all

The point is: Faith - or whatever you have to call it - is common to all creatures of the abstract. It's a necessity. Everything that is alive in the mental world is steeped in it. It's not even about humanity or altruism or shit. It's about the relationship of the abstract world to the physical, a least to me. It's inescapable.

Further, I think maybe it's this that allows the cohesion of ego from potentially disparate modes of existing. People who lose it die, often from killing their own selves. People who are powerfully faithful in their context are unstoppable forces of will.

Come on man it's fucking fascinating goddamnit.

what is the reason for reason?
what is the purpose of our purpose?

anybody besides me see anything wrong with these questions?

I don't see how they apply here.