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"How Modal Logic Proved Gödel was Right, and God Exists"

r4ch3l

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Coolydudey

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There are more unstated axioms - propositions about reality. Not to mention that the axioms themselves are completely nutty. Still quite amusing though and I admire Godel for his accomplishments.

For example, take axiom 5: Let the property be "There is a child molester necessarily existing in America". By axiom 5, the property of necessarily existing is positive, so the above is positive.

Axiom 2 is similarly flawed - for example, take the property to be"there are good people in america"; this is clearly positive (think about there being no good people in america), yet it implies that there are bad people in america, which is clearly negative. I don't see the point of 4 as the proof isn't presented, but it looks dubious too.

What about Axiom 1 - must all properties be positive or negative?
 

Cognisant

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Wait-wait-wait isn't this essentially saying that god exists because a god that does not exist doesn't fit the definition of god?

Obtuse circular reasoning at its best :D


Yeah I go to church, it amuses me greatly.
 

Coolydudey

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Wait-wait-wait isn't this essentially saying that god exists because a god that does not exist doesn't fit the definition of god?

Obtuse circular reasoning at its best :D


Yeah I go to church, it amuses me greatly.

I don't think so (edit - I have no idea). We need to see the proof to be certain, but the thing will be unnecessarily long and contrived given such weak axioms, so nobody will bother to look at it.
 

r4ch3l

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Wait-wait-wait isn't this essentially saying that god exists because a god that does not exist doesn't fit the definition of god?

Obtuse circular reasoning at its best :D


Yeah I go to church, it amuses me greatly.


Yer supposed to be a systems thinker. :(

"Thus it is possible that it will rain today if and only if it is not necessary that it will not rain today; and it is necessary that it will rain today if and only if it is not possible that it will not rain today."

My take on it is:
0 if and only if -0 (1);
1 if and only if -1(0).

Incompleteness is God, and everything is so boring.
The only holy thing is linear time.
 

Glaerhaidh

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This only shows what happens when logic is not grounded in reality whatsoever. It's using its own made up facts to back itself up--its just a little hidden at first glance.
There is no such thing as being grounded in reality. Being grounded in reality is believing in a set of sensual information, believing that you receive this information and interpret it correctly.

Incompletness Theorems

In any scientific enviroment you rely on propositions and axioms that rely on incomplete arithmetic proofs and cannot verify its own correctness.

Modal Logic

Proof of God


Good intro:
[JUSTIF]The 1st ontological argument for the existence of God was written by St. Anselm (1033-1109). The argument considers a maximally concievable being. This being must exist, because if it did not have the property of existence, then we could concieve of a greater being that apart from the other properties also has the property of existence. The main critique of this argument is that we do not know whether the concept maximal concievable being in fact designates anything or if it is inconsistent,like a round square. The question is if the argument is sound.

As Bertrand Russell has pointed out the denition of maximal allows us to define properties, like having boots, which the maximal being then also must have. Kant, on the other hand argued against the ontological argument on the basis that existence is not an analytic property. This means that existence cannot be contained in the denition of a concept, because it is generally synthetic.
All that we can say is that if God exists, then he necessarily exists.

St. Anselm's proof was processed by Descartes and Leibniz. Leibniz identified the critical point of the argument as establishing the possible existence of God. Leibniz gave an argument for that the properties of God, the perfections, are compatible. This implies that it is possible to have all perfections at once and therefore the existence of a maximal being with all these properties is possible.

Godel continued this argument by defining the properties that must hold for these perfections and giving axioms from which the existence of God can be derived. The acceptance of the correctness of the ontological argument by Godel's work boils down to the intuitive correctness of the axioms and denitions and the belief in the soundness of the deductive system.The formal argument of Godel is based on Leibniz proof, which in turn is based on Descartes proof.
These proofs have two parts; a proof that if God's existence is possible, then it is necessary and a proof that God's existence is in fact possible. The deductive system used in the formal proof is a system for modal logic extended with secondorder quantication (or possibly third-order quantication), because the axioms and denitions required for the concept of positive properties or perfections involve quantification over properties.

Godel treated positive properties as not just atomic properties, like Leibniz, but also consisting of collections of these properties, which by Leibniz argument are compatible or possible. (Fitting, p.139) Godel fomulated an axiom stating that the conjunction of any set of positive properties is positive. The property of God-likeness, which defines what a God is, must therefore be an infinite conjunction of all the positive properties. This axiom of the positiveness of conjunctions can be given a third order formulation which is the reason for the claim that third-order quantification may be required. (Fitting, 2002, p. 148).
However, this axiom is only used in the proof to establish that the property of God-likeness is itself positive that led Scott to simply assume the positiveness of God-likeness as an axiom instead.

Nevertheless, both axioms have the unfortunate property of being equivalent to the possibility of God's existence, given the other axioms of Godel. The possibility God's existence in turn is equivalent to God's necessary existence as well as God's existence itself. Thus, we have an axiom which seems to be equivalent to the conclusion.

If one assumes extensionality, that two objects with the same properties are identical, then the definitions of Godel's proof give monotheism. Namely, two Gods would both be God-like and by the denition of god-like, they would have the same positive properties and be identical.

It may be so that for all formulas the formula implies its boxed version.
That is all that is is necessarily and modality collapses. Fitting provides two solutions to the problem by modifying the axioms.[/JUSTIF]

Good PDF with above intro and with some information as to the sources and natural deduction proof and modal logic explanations.


Interesting repository for Godels God proof and resource of logical tests.

Godel provides a God being that has every God-like property. God-like property would be any perfectly good property that exists. Any being that has some God-like properties comes from this God being.

God could be viewed as a single entity, in Uni/Multiverse, that is good and only good.

Resource of discussion
 
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Glaerhaidh

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I posted something but It needs to be approved? Wait what is wrong :( . Well hell, good luck guys I can wait.

Edit: Yes I understand how it works now, sorry for this double post.
 
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Cognisant

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But just because it's possible for rain to occur dosen't mean it will/must occur, dress it up in double negatives all you like two wrongs don't make a right.

Saying god must exist because god cannot not exist is either sophistic circular logic or just plain stupid.

Don't argue logic with a robot luv :p
 

r4ch3l

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what does god mean to you?

it's a very loaded word and very hard to talk about in a neutral way. :(
speaking as a very-damaged-by-someone-else's-god person.

for me god means Ultimate Abstraction, Root Cause, nothing more. I don't worship the fucker, quite the opposite.
 

r4ch3l

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This only shows what happens when logic is not grounded in reality whatsoever. It's using its own made up facts to back itself up--its just a little hidden at first glance.

wats reality.
 

Cognisant

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for me god means Ultimate Abstraction, Root Cause, nothing more. I don't worship the fucker, quite the opposite.
If you're looking for the great unified answer for everything, this isn't it.
 

r4ch3l

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Going through this line-by-line, very insecure b/c i'm dumb:


1. Any “property”, or the negation of that property, is “positive”; but it is impossible that both the property and negation are positive. [0 or 1]
2. If one positive property implies that some property necessarily exists, then the implied property is positive. [0 is 0; 1 is 1]
3. The property of being God-like is positive. [1 is distinct from 0]
4. Positive properties are necessarily positive. [1 is not 0; 1 is moving away from 0]
5. The property of necessarily existing is positive. [1 is moving away from 0 toward 1-ness]


it's pretty boring and obvious, y'all. no worship required. all it says is time is the product of god. and that god is necessary.

you being here/experiencing is necessary.

no worship required. carry on.
 

r4ch3l

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what does "answer" mean?

i. don't. care.
i'm interested in computers and complexity, and interested in how applied things came to be.
 

Brontosaurie

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well i guess it's something like: "math is about you know like everything, and like god like is too, and like therefore like math like proves like god, like how could you like believe math then, without believing in god?"

i won't be reading the article because that would surely speed up my neural decay
 

r4ch3l

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i don't see it as a proof for god.
i think i see it as a proof for the necessity of time?

edit: i hate words.
 

Architect

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Computers are finite state machines so could not prove those axioms. For example, take the first axiom

Any “property”, or the negation of that property, is “positive”; but it is impossible that both the property and negation are positive.

Take a variable X as an integer. Write a computer program to check whether "x == -x" up through enumerable infinity (aleph-null). Oops, here's the problem, integers are normally 32 or 64 bit, you quickly run off the end of what you can represent. Some libraries give you larger like 128 bit, but those are normally in floats not ints.

So, no proof. You can't prove this for all numbers. Even if you could represent arbitrarily large integers you'd be there forever (Aleph-null remember?) computing whether it was true or not.

Basically the people who did this are idiots mixing apples and oranges and so getting fruit salad. If you want to believe in god why are you trying to prove it?
 

r4ch3l

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well i guess it's something like: "math is about you know like everything, and like god like is too, and like therefore like math like proves like god, like how could you like believe math then, without believing in god?"

something like that.
incompleteness essentially says that math is not and cannot be a closed system.
which to me says that it is always computing and consciousness cannot keep up.

but we want to so badly.
the strive for P=NP is divinity. nature is a capitalist +blah blah blah.
 

r4ch3l

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So, no proof.

posted for discussion. i don't think you can prove god. i don't think you can disprove god either. patterns i can't quite express are frustrating me and i get really sad over "god" being such a loaded term. i wish we had a language where there were variations on the word...i wonder how limited i am by the english language?
 

Architect

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What's odd is that it was Goedels Incompleteness Theorem which proved that for even as simple a system as arithmetic you had to base it on a set of unprovable axioms. Thus, in some sense, nothing is "ultimately" provable. To me that implies gods don't exist, since they are a source of perfect truth (proof). So this whole thing is fishy, but I don't have the interest to look into it.
 

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This sounds suspiciously familiar to a Gödel incompleteness theorem based argument against anthropic mechanism which is false because it assumes we think with strict logic.

To make this easier for everyone to understand consider flipping a coin, the more flips observed the more the occurrence of heads or tails would tend towards 50% however even if near infinite flips were observed mere observation would never conclusively prove the even probability distribution, it can always be flipped again.

Which makes it seem miraculous that we know it, but it isn't because we don't, instead based either upon the observation that the coin only has to faces it can sit stable on or that in a series of flips the results will tend towards an even probability distribution over time, we are able to assume that there's an even chance of a coin flip being either heads or tails.

The fact is we're not mathematical processors, we're probability distribution based recognition engines, that's why we excel at fuzzy logic and comparatively suck at mathematical computation.

We don't actually know for sure that a coin flip is an exact 1/2 probability, indeed it probably isn't, factors that are so far beyond our predictive scope as to be effectively negligible almost certainly prevent the coin flip from being exactly 100% fair, but since nobody can predict these factors they don't matter, not unless you're a mathematician or a theoretical physicist.
 

Absurdity

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I posted something but It needs to be approved? Wait what is wrong :( . Well hell, good luck guys I can wait.

Your comments got caught in the spam filter, possibly because you posted so many links in your initial post. They're there now though. Sorry for the delay.
 

Milo

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There is no such thing as being grounded in reality. Being grounded in reality is believing in a set of sensual information, believing that you receive this information and interpret it correctly.

What else do you have to go off of?
By this logic, you think that words by themselves are good enough to prove anything--this is the inherent flaw in reasoning, that reasoning itself proves its own limitations. And with that fact, there is actually no reason to discuss what is truth and what is not.

Incompletness Theorems

In any scientific enviroment you rely on propositions and axioms that rely on incomplete arithmetic proofs and cannot verify its own correctness.

This is what all the people inside of Plato's cave would say. They are projecting the world around them with their imagination, and saying that is what reality is--not acknowledging that fact that they are projecting.


More cave speak

Godel provides a God being that has every God-like property. God-like property would be any perfectly good property that exists. Any being that has some God-like properties comes from this God being.

God could be viewed as a single entity, in Uni/Multiverse, that is good and only good.

Resource of discussion

What if I told you that good and evil are projections of your imagination, false dichotomies presiding from your perceptions of what you think is fair? There is only existence.

wats reality.

Your existential cage decorated by your projections.
 

Glaerhaidh

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The funny thing is you are in your own cave and you wave a flag that shows how I am false but because of the distance and darkness it seems to me that you surrender with this flag.
:confused:

Words themselves are biased and have to be good enough for us, for now.

You just used words, calling something an inherent flaw in reasoning, you assume that I project my reality, you should rather assume that we agree on a similar view on reality when we begin to discuss. With this basic belief we can then have a valuable discussion about what is true in our beliefs and what is not.

Lets assume you listed a large amount of evidence, in my post I have shown how this evidence relies on our basic belief and willingness to cooperate with similar assumptions.

Are you rejecting your basic beliefs because what you sense and feel and how you interpret it is not universal and axiomatic?

Are you rejecting belief by the notion that you couldn't be rational if you believe in some basic assumptions?

Hey, lets be rational here. :p
 

Reluctantly

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What if I told you that good and evil are projections of your imagination, false dichotomies presiding from your perceptions of what you think is fair? There is only existence.

If you're so smart, then what exacty is existence, if it's not our perceptions of it?
 

Milo

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So, now that I've actually gone and read the entire thread, I read that you're actually interested in "computers and complexity, and interested in how applied things came to be."

I'd say it would have started with much more inductive logic--trial and error. Mixing elements, seeing what they do, documenting it, then doing this for all combinations until they got the desired results. Of course this was also probably the beginning of bureaucracy.

Same thing with math, I'd say. Just working out long versions of equations, getting answers, then trying to find formulas that act as shortcuts to get a persistent answer--although this is probably where deductive proofs came to be--having to show the limitations of the shortcut, or that there are none.

When combining math with the mixing of elements, this slows things down quite a bit, because you are no longer just looking at the broad view of results, but you are looking deeper and deeper into the same reactions with different amounts of the elements, usually for the purpose of making things maximally efficient--making things seem much more complex and hard to understand for those who are introduced to this sort of stuff when presented in this way from the beginning.

And then to get everything neat and tidy, words had to be assigned to each element and mixture for them to remember everything easier and allow them to use logic instead of experimentation.

Now, we can all be full-fledged alchemists.
 

Glaerhaidh

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I'd say it would have started with much more inductive logic--trial and error. Mixing elements, seeing what they do, documenting it, then doing this for all combinations until they got the desired results. Of course this was also probably the beginning of bureaucracy.

Of course that's what we do. It usually works quite well, we even managed to build satelites playing this game.

You believe here that you will find all combinations, otherwise there will be some undiscovered outcomes. You generally find all combinations you are able to conceive.

Same thing with math, I'd say. Just working out long versions of equations, getting answers, then trying to find formulas that act as shortcuts to get a persistent answer--although this is probably where deductive proofs came to be--having to show the limitations of the shortcut, or that there are none.
Besides all that, what have you proven for yourself other than reading and being taught? Obviously you believe all this as we usually do, however I was very disconcerted when my physics teacher by the time refused to prove something as basic as heliocentrism, not that it isn't right, rather that even people who teach you are abstract.

When combining math with the mixing of elements, this slows things down quite a bit, because you are no longer just looking at the broad view of results, but you are looking deeper and deeper into the same reactions with different amounts of the elements, usually for the purpose of making things maximally efficient--making things seem much more complex and hard to understand for those who are introduced to this sort of stuff when presented in this way from the beginning.
So we tunnel our proofs to the evidential and then with this equations we can proof different not directly evidential things relying on evidence.

Why then every equation is simplified this way, there is a margin of error in every evidence that is not included in equations.
And then to get everything neat and tidy, words had to be assigned to each element and mixture for them to remember everything easier and allow them to use logic instead of experimentation.
Words came after sensual observations, they were used well by the individual that created them. Usually you have to redefine words any time you disagree with someone so that you can think similarly and come to the same conclusions.
This would mean that other conclusions were not worth deducing, which isn't right on its own.
Now, we can all be full-fledged alchemists.
Visita Interiora Terrae...

edit:Who messes this timeline, is it you god? Don't mess with me now!
 
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Milo

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The funny thing is you are in your own cave and you wave a flag that shows how I am false but because of the distance and darkness it seems to me that you surrender with this flag.
:confused:

The difference is realizing you are projecting, once you do that, you can project anything you like all the time, but know it is a lie--much like a mad hatter's point of view

Words themselves are biased and have to be good enough for us, for now.

This depends on how specific you use your words, but for the most part, biases usually make their ways in there--but that is why we use logic such as this, though we usually don't want to go the way of just assuming something then trying to prove it. That is more tending towards bias. Usually you want to use facts that you've proven with experimentation to back up other logical implications to make a hypothesis, not make a hypothesis, then try to find logical implications that back it up.

You just used words, calling something an inherent flaw in reasoning, you assume that I project my reality, you should rather assume that we agree on a similar view on reality when we begin to discuss. With this basic belief we can then have a valuable discussion about what is true in our beliefs and what is not.

The inherent flaw in reasoning is that it may or may not apply to reality no matter how reasonable it may seem. I can assure you that we do not have a similar view on reality--because I do not have a view on reality, I live second by second spontaneously without a thought referring to the future or the past, just the here and now.

Lets assume you listed a large amount of evidence, in my post I have shown how this evidence relies on our basic belief and willingness to cooperate with similar assumptions.

I am very unassuming and all of my evidence is either primary or psychological--of which we may or may not share similar views on, so assumption is not something I tend to do unless necessary.

Are you rejecting your basic beliefs because what you sense and feel and how you interpret it is not universal and axiomatic?

We'll I don't really have any basic beliefs floating around in my mind at any given moment, so I'm not rejecting them. But I would say that each person's experiences are not universal and definitely mostly not axiomatic, except the things that conscious beings automatically must share by the definition of a conscious being.

Are you rejecting belief by the notion that you couldn't be rational if you believe in some basic assumptions?

I think I've thought though and eliminated unnecessary assumptions throughout my life enough to where thoughts of them don't even occur.

Hey, lets be rational here. :p

Let's ;)
 

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If you're so smart, then what exacty is existence, if it's not our perceptions of it?

We'll, you're limited by your perceptions of it, and without any perceptions of it--just taking it as it is, then you are in the real world--a world consisting of only the most basic animal drives.

The difference is recognizing that you are projecting, then you are free from truth being your only way to see the world. You're free to project anything you want.
 

Glaerhaidh

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It's like running a new A.I algorithm if it uses only logic it would have to write its own Principia Mathematica. It would have to calculate more and more slowly or just make jumps in cognition and possibly err later.

It will be a long time, or it may never happen, that you will have a deterministic evidence for anything.

What is not in this evidence relies on belief, as long as we are not in our one of many deterministic causalities we can allow ourselves a degree of abstract and irrational, something resembilng human emotion so much after all.

Or we may move one dimension up, there is place for selecting your own causalities there :)

But is the universe infinite?
 

Milo

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It's like running a new A.I algorithm if it uses only logic it would have to write its own Principia Mathematica. It would have to calculate more and more slowly or just make jumps in cognition and possibly err later.

It will be a long time, or it may never happen, that you will have a deterministic evidence for anything.

What is not in this evidence relies on belief, as long as we are not in our one of many deterministic causalities we can allow ourselves a degree of abstract and irrational, something resembilng human emotion so much after all.

Or we may move one dimension up, there is place for selecting your own causalities there :)

But is the universe infinite?

Mind over matter, man. The universe doesn't have to be infinite because your mind is. I live in the abstract and irrational world. It's quite the place to be.
 

Glaerhaidh

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Mind over matter, man. The universe doesn't have to be infinite because your mind is. I live in the abstract and irrational world. It's quite the place to be.
Quite optimistic. I would feel good knowing that my mind is infinite, let's leave it at that.
 

Duxwing

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Godel seems to assume that an objective, definite set of "positive" properties exists.

-Duxwing
 

Reluctantly

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We'll, you're limited by your perceptions of it, and without any perceptions of it--just taking it as it is, then you are in the real world--a world consisting of only the most basic animal drives.

A world of basic animal drives is still a projection; it's your perception. If we act on instinct, we might as well be considered dead because we have no ability to interpret and develop a form of awareness from it; we are unconsciously functioning. And then what you consider a limitation I could argue is an enhancement.
 

Milo

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A world of basic animal drives is still a projection; it's your perception. If we act on instinct, we might as well be considered dead because we have no ability to interpret and develop a form of awareness from it; we are unconsciously functioning. And then what you consider a limitation I could argue is an enhancement.

Ummm...yeah. Did you not read the second paragraph?
 

Reluctantly

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Ummm...yeah. Did you not read the second paragraph?

I did, but it contradicts what you said earlier - that good and evil are false dichotomies; there's also a contradiction when you refer to a 'real world' without projections.

The reasons being, one could argue there is no 'real' world aside from projections.
 

Milo

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I did, but it contradicts what you said earlier - that good and evil are false dichotomies; there's also a contradiction when you refer to a 'real world' without projections.

The reasons being, one could argue there is no 'real' world aside from projections.

I think you're confusing yourself. I see no contradictions whatsoever. You may be assuming something I am unaware of.

As for your second sentence, I think you need to read this:
http://en.wikipedia.org/wiki/Psychological_projection because it seems your definition of projecting is not what I am talking about.
 

~~~

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Yer supposed to be a systems thinker. :(

"Thus it is possible that it will rain today if and only if it is not necessary that it will not rain today; and it is necessary that it will rain today if and only if it is not possible that it will not rain today."

My take on it is:
0 if and only if -0 (1);
1 if and only if -1(0).

Incompleteness is God, and everything is so boring.
The only holy thing is linear time.

I'm pretty rusty on this but does the reverse work (i.e. not rain)?
 
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