God &The 4-sided Triangle

[LardLord]

One of the problems that exercised theologians during the middle ages was the question of whether God could envision or, indeed, make a four sided triangle or a three sided square or some such monstrosity. At first sight the problem seems trivial or foolish, but it really is an instance of a more fundamental problem: Is God bound and limited by the laws of reason and logic or can She overcome them or alter them as She chooses. On one hand God is omnipotent; She may do anything She pleases, logic and reason notwithstanding. On the other hand it seems inconceivable that anyone, even God Herself, can maintain that 1=2.

At first sight it would seem that there is no theological problem here. It is a well founded principle of theology that revelation is superior to reason; that God may work miracles if She so chooses; that the universe is an artifact of Hers that She may alter without regard as to its internal logic or laws. The trouble is that logic and reason, truth and beauty, are not in the universe per se. That is, there is not thing that is truth, no object that is reason. They are absolutes, ideals, outside the universe, affecting and shaping the character of the universe but unaffected by it. In fact, their existential character is much like that of God Herself, and it widely held that these ideals are aspects of God. That is the crux of the problem; for if God is Truth and Truth is God, then how could God conceive of that which is not truth. On the other hand, it is held that God is omnipotent and therefore may do as She chooses, including thinking untruths. So you see, the four sided triangle is an aspect of a fundamental theological problem.

Now it seems to me that the answer must be in the affirmative; that God can make four sided triangles if She so chooses. My answer is based on the observation that it is in fact possible to conceive of four sided triangles and defend their existence. I suspect that She has chosen not to do so, but I argue that it is within Her powers, Let us consider for a moment a conversation between those redoubtable and hoary combatents, Sage and Simp:

Sage: Greetings Simplicitus. See thou the line figure I have inscribed in the sand. I have been musing on it for an hour or more.
Simp: I see it, oh Sage. But to tell the truth, I know not what to make of it, for it seemeth to me to a shaky and irregular circle. What is it supposed to be?
Sage: Alas, my infirmities grow, and my hand is palsied with age, so the drawing it somewhat irregular. It is a representation of a geometrical figure. As you know, matter and man are corruptible whereas the content of geometry is incorruptible. So it is that this figure fails of good form whereas that which it represents is clear and true.
Simp: So I understand, oh Sage. But I remain puzzled; what form is it that your line represents?
Sage: Why, it is a four sided triangle.
Simp: I am not sure I heard you rightly, oh Sage. You speak of a four sided triangle whereas it is well known that triangles possess three and only three sides. I have hear it argued that God may conceive of such a thing even though it is not possible; but such a thing is surely beyond man.
Sage: So have I understood. You may appreciate my amazement at realizing that such a construction was possible and that its conception was with the powers of a man's mind.
Simp: But sire, I find this incomprehensible. I cannot conceive of such a thing. Nor, if it were possible, do I see it implemented in this line, which I see only as a rather shapeless form.
Sage: Well then, let me make things clear. Let me poke three holes in the sand to represent the three vertices. You see.
Simp: Why yes, I see. There are now three points in the sand that are the vertices of three angles.
Sage: Well then. Joining each pair of vertices is a line that we shall call the side of a triangle. Now we count these sides and we see that there are four of them.
Simp: But sire, surely you jest. They are readily counted and there are but three of them. Let me make it clear. You agree that I am holding up three fingers.
Sage: With those reservations well known to philosophers everywhere concerning sensory perception, yes, I agree.
Simp: Well then, sire, I place one of each of these fingers one to a line, thusly. Now would you not say that for each finger there is a line and vice versa?
Sage: Why, yes, I would say that.
Simp: Why then, as there are three fingers, and there is one line for each finger, there must be three lines.
Sage: Why no, Simplicitus, I sorrow to see your error. Thou has three fingers pointing at four lines.
Simp: But sire, did thou not say that there were as many fingers as there were lines?
Sage: Why yes, I agreed to that.
Simp: Well then, it would seem that thou art maintaining that three is the same as four.
Sage: Oh no, I would never maintain that. The difference between three and four is clear and self evident - no one would dispute that.

I think we can leave them here. It is clear that their dispute can go on indefinitely. Sage is going to say, in one way or another, that three and four are the same. Simp is going to catch him at his trick and point out that Sage is, in effect, saying that three and four are the same. Sage is going to deny that he is saying any such thing. Simp is going to go back and ask what he did say if it wasn't sayiing that three and four are the same. Sage is going to assert the same thing in a different form. Round the mulberry bush they go again. Simp can never establish that Sage is being inconsistent because Sage always changes his position to avoid the immediate inconsistency while retaining the basic inconsistency by returning to it whenever he gets the chance.

[LardLord]

Sage's rather heavy handed little game with Simplicitus is based on a principle well known to mathematicians; it is perfectly possible to be consistent within a formally inconsistent system provided you never carry inconsistent lines of reasoning to the point of inconsistency. This is done in the foundations of Mathematics wherein traditional Mathematics, which is consistent and not totally rigorous, is based on Set Theory, which is rigorous and inconsistent.

Now it is presumed, at least by Mathematicians, that Mathematicians know what they are doing when they are skirting the edge of inconsistency. However we have many instances of people who engage in inconsistent conceptual frames of thinking and don't know that they are doing so. Such people are called psychotics, or, sometimes, politicians.

Now surely god, if she chose to, could engage in such modes of thought if She wished. However She would have great advantages for She could shape the universe to Her will. Not only could She create a formally inconsistent universe, but She could also rig things so that the thinking beings in Her universe could not detect it.

For all we know that's exactly what She did. Maybe triangles "really" do have four side and we have been tricked into incorrectly perceiving them as having three sides. Certainly we would have no way of ever knowing. I kind of like to think that She did. To me it seems like the sort of trick that a God that could create a universe having theologians and politicians would pull.

[Benovere]

One thing I see wrong off the bat is that during the middle ages (assuming you are talking about the European middle ages) is that they worshiped under the Holy Roman Catholic church. God was a he to them. Im pretty sure they weren't worrying about some stupid triangular square or four-sided triangle when they were busy extorting money from the poor and stupid. (Dark age of the Middle Ages on through till some time)

[LardLord]

At 11/22/06 01:31 AM, Benovere wrote: One thing I see wrong off the bat is that during the middle ages (assuming you are talking about the European middle ages) is that they worshiped under the Holy Roman Catholic church. God was a he to them.

You're wrong.

[LazyDrunk]

Nice fucking post/topic.

Kudos.

[LardLord]

At 11/22/06 01:46 AM, LazyDrunk wrote: Nice fucking post/topic.

Kudos.

Agreed. My topics are the shit.

[JakeHero]

God isn't a "she." If God were she would of wiped humanity out due to her innate temperment.

[KingCharles]

At 11/22/06 07:54 PM, BanditByte wrote: God isn't a "she." If God were she would of wiped humanity out due to her innate temperment.

Damn Straight.

[therealsylvos]

At 11/22/06 01:43 AM, LardLord wrote: You're wrong.

perhaps you ought to read the bible, where god is clearly refffered to as he. however god is netiher but is merely reffered as he. of course the whole topic is infantile. the whole question is in fact infantile. triangle is a term for something that has 3 sides. thats all. its merely a term.

[TheMason]

God: "Proof denies faith and without faith I am nothing!"
Man: "But you have given us proof, therefore you do not exist. QED."
"Oh, my," says God, and disappears in a puff of logic.
-Douglas Adams

[TheMason]

At 11/22/06 08:40 PM, therealsylvos wrote:

At 11/22/06 01:43 AM, LardLord wrote: You're wrong.

perhaps you ought to read the bible, where god is clearly refffered to as he. however god is netiher but is merely reffered as he. of course the whole topic is infantile. the whole question is in fact infantile. triangle is a term for something that has 3 sides. thats all. its merely a term.

There are more errors and inconsistencies in the modern bible than there are words in the New Testament. The fact is we do not know what the original Bible said, so how can we be sure that God is a He, She or sexless? Furthermore, wouldn't a "He" or "She" God imply that there was another Diety that would embody the opposite sexual tendencies?

Furthermore, what the author of this topic is doing is restating the logical paradox "Can God create a boulder so large S/He cannot lift it?" in a mathematical context.

[MortifiedPenguins]

At 11/22/06 09:41 PM, TheMason wrote: God: "Proof denies faith and without faith I am nothing!"
Man: "But you have given us proof, therefore you do not exist. QED."
"Oh, my," says God, and disappears in a puff of logic.
-Douglas Adams

When you quote somehting, its usually nice to have the full quote.

I've read the HGTTG.

Your missing the Babel fish part.

[TheMason]

At 11/22/06 09:49 PM, Grammer wrote:

At 11/22/06 09:41 PM, TheMason wrote: God: "Proof denies faith and without faith I am nothing!"
Man: "But you have given us proof, therefore you do not exist. QED."
"Oh, my," says God, and disappears in a puff of logic.
-Douglas Adams

That logic is so retarded it's not even funny. I look down on my friend for reading that piece of shit for a book. When did God ever say that without faith he is nothing?

So then what you are telling me is you are violating your religion and being Judgemental? Listen up folks, grab your Hitchiker's Guide to the Galaxy books and DVDs! Grammer is gonna have an ole' fashioned book burning!

Seriously, have you ever read it?

[TheMason]

At 11/22/06 10:23 PM, MortifiedPenguins wrote:

At 11/22/06 09:41 PM, TheMason wrote: God: "Proof denies faith and without faith I am nothing!"
Man: "But you have given us proof, therefore you do not exist. QED."
"Oh, my," says God, and disappears in a puff of logic.
-Douglas Adams

When you quote somehting, its usually nice to have the full quote.

I've read the HGTTG.

Your missing the Babel fish part.

True, but I had a hard time finding it in total; and I didn't have my copy handy... Sorry!

[Proteas]

At 11/22/06 02:15 AM, LardLord wrote: Agreed. My topics are the shit.

That they are.

And God is a spirit, gender does not apply to something that lacks a physical earthly body.

[Draconias]

The question isn't at all a challenge, and I don't quite understand why you spend so much space trying to explain the problem.

Geometry is an instance of artificially defined systems created by humans. You can never have a four-sided triangle because humans have defined that you cannot. The word "triangle" in this instance is merely a descriptor for a particular class of polygons, and thus does not have any adjustable properties.

Omnipotence is effectively limited to control of "literal" things, which have specific sets of adjustable properties, like a rock or a specific triangle. This paradox is easily solved by realizing that artificial definitions are not equivalent to literal things.

Detour:
This problem is similar to the one that goes: "Can God create a boulder so heavy he can't lift it?" In this situation, "lift" is an artificial human term that only has meaning with reference to the Earth and with objects far lighter than our planet. For example, a heavy enough boulder, when lifted, would cause the Earth the move the distance. Does that still count as lifting? What about if the "boulder" is Jupiter, a ball of gas which can not be gripped, and which has no point of reference to "lift" it from? The flaw lies with the human definitions, not the logic of the situation.

[AdamRice]

At 11/22/06 11:57 PM, Draconias wrote:

Omnipotence is effectively limited to control of "literal" things, which have specific sets of adjustable properties, like a rock or a specific triangle. This paradox is easily solved by realizing that artificial definitions are not equivalent to literal things.

Detour:
This problem is similar to the one that goes: "Can God create a boulder so heavy he can't lift it?" In this situation, "lift" is an artificial human term that only has meaning with reference to the Earth and with objects far lighter than our planet. For example, a heavy enough boulder, when lifted, would cause the Earth the move the distance. Does that still count as lifting? What about if the "boulder" is Jupiter, a ball of gas which can not be gripped, and which has no point of reference to "lift" it from? The flaw lies with the human definitions, not the logic of the situation.

But if god created the universe then he would have to understand human forms of logic since he created them and had to implement them into the human race. You also make false claims about jupiter, which does infact have a central point and a boundary.

[poxpower]

At 11/22/06 11:57 PM, Draconias wrote:

Omnipotence is effectively limited to control of "literal" things, which have specific sets of adjustable properties, like a rock or a specific triangle. This paradox is easily solved by realizing that artificial definitions are not equivalent to literal things.

Can go be absolutely wrong and absolutely right at the same time?

No.
Because, they are two completely opposite concepts.

Period. Use whatever example you want, the base of it is that: one is the opposite of the other, both cannot, BY DEFINITION, a definition TO WHICH GOD WOULD AGREE, happen at the same time. But omnipotence says it can.

proof: can got create two completely opposing concepts? omnipotence says yes
then: can he use them together at the same time without having them oppose? omnipotence says "paradox"

In conclusion: omnipotence is simply a logical paradox no more complicated than the ole "barber cuts the beard of everyone but people who cut their own, does he shave his?". If you use omnipotence to justify things about God, you're an EEEEDIOT.
There is no answer to those questions, THAT'S THE POINT OF THE QUESTION. If you answer "yes" or "no", it doesn't ANSWER anything, you just said a word with your mouth.

blablabla

anyways, topic starter: when you write, make sure there's a CONCLUSION to your text, that TELLS US WHAT THE HELL YOUR POINT WAS IN THE FIRST PLACE X_x

[CyanClock]

Your logic is pretty flawed. What reason would God have to trick mankind? Trickery seems to dance along the border that defines sin, and, as God is without sin, He would not even approach such a deed.

Also, your use of the pronoun "She" is biblically incorrect. If I recall correctly, the Bible uses the Hebrew word "Hu", which literally translates to "He".

[MortalWound]

It is quiet simple to make a four sided triangle or a three sided rectangle/square. All you have to do is go back in time, find the person who gave the terms to the shape, tell him to name all triangles squares and all squares triangles and thus, you'll have a 4 sided triangle. So it is possible for the argument of a 4 sided triangle to exist can be true.

I'm sorry if this is just dumb to you, It's a little past my bed time when I wrote this.

[TheMason]

At 11/23/06 02:37 AM, CyanClock wrote: Also, your use of the pronoun "She" is biblically incorrect. If I recall correctly, the Bible uses the Hebrew word "Hu", which literally translates to "He".

There are many problems involved with translating the Bible, and the Old and New Testament that we have is very much flawed. In fact there are more errors/inconsistencies than there are words in the New Testament.

But what are the ramifications of a gendered God? If God has a gender does that not imply that He would have a consort of the opposite sex? If God has a consort, what then does this mean for our concept of monotheism?

Linguistically then if God does not have a gender shouldn't we use the pronoun 'It' to describe God? Our maybe we shouldn't use a pronoun at all?

[CyanClock]

At 11/23/06 10:56 AM, TheMason wrote:

At 11/23/06 02:37 AM, CyanClock wrote: Also, your use of the pronoun "She" is biblically incorrect. If I recall correctly, the Bible uses the Hebrew word "Hu", which literally translates to "He".

There are many problems involved with translating the Bible, and the Old and New Testament that we have is very much flawed. In fact there are more errors/inconsistencies than there are words in the New Testament.

That isn't particularly true. I am aware of all of the issues (lack of spaces or capitals, no vowels, etc.), but it was also copied incredibly meticulously. A more accurate statement would be that there could be more errors than words in the new testament.

But what are the ramifications of a gendered God? If God has a gender does that not imply that He would have a consort of the opposite sex? If God has a consort, what then does this mean for our concept of monotheism?

But God is portrayed as genderless in the scriptures. The fact that a masculine pronoun is used in the original text should be enough to put the issue to rest.

Linguistically then if God does not have a gender shouldn't we use the pronoun 'It' to describe God? Our maybe we shouldn't use a pronoun at all?

Well, "It" really detracts from the person of God. Some groups just use "God", but it isn't mainstream.

[Durin413]

Keep in mind that god created MAN is his own image i.e. with a penis. Then he made woman for man to enjoy. Since therefore god has a penis, then god is male.

[Draconias]

At 11/23/06 12:27 AM, fasdit wrote: But if god created the universe then he would have to understand human forms of logic since he created them and had to implement them into the human race. You also make false claims about jupiter, which does infact have a central point and a boundary.

Human logic is not the issue here; human labels are. Omnipotence can not act on the abstract concept embodied by a label without changing the label itself. That's the entire "paradox" here, and it isn't that confusing. Omnipotence applies to physical, real things, not imaginary, totally abstract things.

I never said Jupiter doesn't have a central point or boundary, and I don't know where you got that from. It has no distinct surface to apply force on (gas molecules would simply shift, not the planet) and there is no nearby point of reference (like the surface of the Earth) from which to "lift" it.

At 11/23/06 01:15 AM, poxpower wrote: Period. Use whatever example you want, the base of it is that: one is the opposite of the other, both cannot, BY DEFINITION, a definition TO WHICH GOD WOULD AGREE, happen at the same time. But omnipotence says it can.

There is no such thing as true opposites in the real world. They only exist in the human imagination, an area where omnipotence does not apply.

Look at examples of "opposites" in the real world: protons and electrons. They seem totally incompatible, right? But in radioactive beta decay, a neutron changes into a proton and emits an electron. Neutrons are the combination of both protons and electrons, supposed "opposites."

Look at another example of "opposites," matter and energy. They have completely different properties; one consists of particles and the other of waves. But wave-particle duality shows that light (energy) is both a wave (electromagnetic radiation) and a particle (photon), while particles like electrons (lepton particles) are also waves and have associated wavelengths.

Opposites don't actually exist, not how humans imagine they do.

proof: can got create two completely opposing concepts? omnipotence says yes
then: can he use them together at the same time without having them oppose? omnipotence says "paradox"

God creates the opposing concepts of "Good" and "Evil." God creates Man, who is both compassionate (Good) and cruel (Evil). Opposites can always be combined when considering multi-faceted or dynamic targets.

It isn't that hard to understand.

[Draconias]

At 11/23/06 12:08 PM, Durin413 wrote: Keep in mind that god created MAN is his own image i.e. with a penis. Then he made woman for man to enjoy. Since therefore god has a penis, then god is male.

Who ever said it was literally in his image? If he is a non-physical entity then the only "image" which could be copied is conciousness and intellect. Also, it could be easily justified that it was "tacked on" when Eve was added.

[JakeHero]

I believe the part of how God created man in his own image isn't intended to be literal not physical. I deem that humanity's creativeness is what similarity we share with God. Thus that exerpt from the Bible is another metaphor.

[poxpower]

At 11/23/06 01:10 PM, Draconias wrote:
There is no such thing as true opposites in the real world. They only exist in the human imagination, an area where omnipotence does not apply

omnipotence, BY DEFINITION, applies to all areas of everything.
As soon as you invent a new of area, omnipotence AUTOMATICALY applies to it. That's the concept.

Opposites don't actually exist, not how humans imagine they do.

It doesn't matter.
And yes, opposites do exist. Yes is the opposite of no.
And I can even create new concepts that oppose each other, it is perfectly within my capacities.

For instance, I create fig 1, and this is the definition of figure 1 = it has 3 sides. If it has any number of sides that isn't 3, it ceases to be fig1

By definition, fig1 can not have 4,5,2 sides. Who cares about the real world??? Its just definitions. If an omnipotent being creates a fig 1 with 4 sides, then its no longer a fig1. It can never be a fig1 at the same time as having a different number of sides than 3.

Hence, the paradox.
It has nothing to do with any real-life examples that you give me from the bibles or from electrons or whatever :o

The paradox simply exists.

[TheMason]

At 11/23/06 12:02 PM, CyanClock wrote:

That isn't particularly true. I am aware of all of the issues (lack of spaces or capitals, no vowels, etc.), but it was also copied incredibly meticulously. A more accurate statement would be that there could be more errors than words in the new testament.

Obviously you are not as informed as you think you are my friend. It goes further than that. There is an estimated 300,000 to 400,000 inconsistencies between manuscripts. Furthermore, there are many problems in comparing Latin to Greek texts of the same age. Some of these are minor, others are much more severe such as the last 12 verses of Luke appear to have been added rather late in their history. Also perblepsis occassioned by homoeoteleuton was common amongst scribes.

Remember this was not only before the printing press and spell check but dictionaries...

Furthermore, it was not copied "incredibly meticulously". This betrays an ignorance of early Christian history. The original scribes were volunteers, Christians who happened to be literate and not professional scribes. Mistakes were very common. It was not until after the reign of Constantine that transcription became "meticulous".

But what are the ramifications of a gendered God? If God has a gender does that not imply that He would have a consort of the opposite sex? If God has a consort, what then does this mean for our concept of monotheism?

But God is portrayed as genderless in the scriptures. The fact that a masculine pronoun is used in the original text should be enough to put the issue to rest.

If S/He is genderless does the pronoun issue really matter then? That was my point.

[TheMason]

At 11/22/06 09:49 PM, Grammer wrote: That logic is so retarded it's not even funny. I look down on my friend for reading that piece of shit for a book. When did God ever say that without faith he is nothing?
I'm not judging a person, now am I?

This is the kind of retarded logic I expected to hear from someone who read that piece of shit.

Seriously, have you ever read it?

No.

That quote from the book is retarded. In no way does it actually prove God wrong, but to the misinformed naive fool it will convince him he somehow has one-up on Christianity. It really speaks about someone's intelligence when they use that little passage from that book and try to pass it off as an intelligent argument.

Not only are these comments full of you being very judgemental you show that you are also very arrogant in that you are calling people stupid because they happen to like a book you do not like; that you have never read. You sir have not proven fans of Douglas Adams to be stupid, you have only proven yourself to be an ignorant fool.

What is left for us to see now is whether or not you heed Mark Twain's advice and keep your mouth shut so we only think you a fool, or if you open it and prove it!-)

I used that quote to be very tongue in cheek, and to inject a little bit of humor into the post. Your ignorant commentary on the subject has just provided me with a little bit of unexpected
amusement.

[Draconias]

At 11/23/06 06:55 PM, poxpower wrote: omnipotence, BY DEFINITION, applies to all areas of everything.

Regardless of whether or not you have the power to do anything, imaginary things are outside of your power. They can not be acted upon in any way, and only a fool would demand action on them. Omnipotence can not change what something is when that state is the entirety of its existance-- it would become something else. That's all there is to it.

And yes, opposites do exist. Yes is the opposite of no.

Uncombineable opposites. Yes is the opposite of no, but you hear people respond with mixed feelings all the time-- both yes and no. Maybe also exists. Yes and no are part of a spectrum, not true opposites.

For instance, I create fig 1, and this is the definition of figure 1 = it has 3 sides. If it has any number of sides that isn't 3, it ceases to be fig1
Hence, the paradox.

There is no paradox here. Fig1 is fig1-- and that's all there is to it. There is nothing to change, nothing to act upon, so omnipotence is irrelevant. Omnipotence allows you to do anything which is possible (because, by definition, if you did it then it was possible), but altering static, abstract definitions or labels is not possible by the nature of the concepts.

The "paradox" here is spawned from the assumption that "omnipotence" means that you should be able to do anything, but there is no "anything" which can be done to abstract things.