Did Absolute Truth Need To be Created?
Posted 04 January 2012 - 09:30 PM
I had a question that I hope the Rav can help me with.
It all started when I casually told a friend that 1+1=2 is an absolute truth and was true before brias haolam. Suddenly everyone was staring at me like I had two heads. They began to joke around about whether they can drink my wine. They were absolutely convinced that it was complete kfirah.
Let me be clear that I understand that the whole concept of units and groups were only possible after brias haolam, but I think that that’s just beating around the bush. There was nothing to count, but that doesn’t mean that 1+1 equaled something other than two.
To put this dilemma in other words, now that Hashem created our finite world with units and groups, was He “forced” into the “rule” of 1+1=2? In my perspective, this isn’t a rule, it’s a definition. Two is defined as the sum total of two singles, or 1+1. Is that considered a limitation of Hashem’s powers to say that he couldn’t create a “2” that wasn’t the sum total of two singles? Or that He couldn’t create two singles that don’t total two? To me that sounds ridiculous, like asking why Hashem can’t create a stone that He can’t lift.
Even if my assumption isn’t kfirah, where do we draw the line? Are we to say that all the vast chochma of mathematics and logic have nothing to do with brias haolam? That would seem to be definite kfirah. So what do we take as absolute truth, and what do we say is a part of the briah as we know it, but doesn’t represent absolute truth? We can quickly weed out anything to do with shapes and size, as space is definitely a briah yesh meayin. But that would still leave us a great portion of conventional chochma in the grey.
It would be greatly appreciated if the Rav can untangle this issue for me. Any sources that deal with this idea will also be very helpful.
(This email was sent from a friend’s house, and I may not get the Rav’s response right away.)
Posted 04 January 2012 - 09:34 PM
I will explain the idea:
1+1=2 is not a rule that needs to be created. If I have one thing and then and another, there are several ways I can express the quantity of things that I now have: I can say “two” or I can say “shtayim” or I can say “deux” or I can say “1 plus 1”. It’s just 2 ways of saying the same thing. You should ask your friends if “two = shtayim” also did not exist before the briah. Or whether it was possible before the briah to have a sakanah that is not dangerous. Sakanah = danger, and 1 +1 =2. Or even better: 2 =2. Did that need to be a briah also? Of course not. These are not rules of nature that need nature. They are merely different language for expressing the same idea.
Regarding your question about where we draw the line, the answer to that is, we draw the line at definitions (as you correctly put it) as opposed to rules.
In the Chazon Ish’s example, the hypotenuse of a right triangle is greater than any of its other sides. That did not need Brias HaOlam.
But E=MC^2 would need to be created. The difference is, E=MC^2 is not a definition; it is a rule. It is not true that “Energy” is the same thing as “MC^2”. It is a rule of nature that says matter can only travel a certain speed before it becomes energy. That did not have to be true had nature been different. So it needed Hashem to say it should be true.
Arithmetic on the other hand, is indeed definitions and not rules. No matter how complex the equation, if it is not a law of nature but a definition, i.e. if it could not have been any other way if nature was different, then it is not nature that makes it that way and therefore it does not need to be created.
By the way – the fact that 1+1=2 is clear from the Torah. I believe it was the Bnei Yisaschar that said this – it says vayehi erev etc. Yom echad, and then after one day was added it says Yom Sheni. Therefore we see that 1 day + 1 day = 2 days.
See also this forum.
Posted 25 January 2012 - 01:51 PM
For example, that Avraham not be burned by fire could have been accomplished either by temporarily changing his nature (eg. making him fireproof) or by changing the nature of fire (eg. that it not have the effect of burning, in which case it might not be fire altogether). On the other hand some Nissim involve one object having two natures at the same time, not just an illusion or a temporary change. The paradigm for this is of course Ein Makom HaAron Min HaMida. In this Nes, the Aron retained its measurements as did the Kodesh Kodashim. If either had changed they would have no longer been halachically acceptable. Yet it would seem to be not a rule of physics but a basic issue of definition that a larger object take up more space that a smaller one, and that such a Nes is as meaningless as saying that Hashem can make 10 less than 5.
(Other examples from the Makos include the Nile being blood for the Mitzrim and water for the Jews, such that it was both at the same time, not that it changed into blood when it entered the mouth of a Mitzri. Similarly the Barad contained both real fire and real ice, one with the nature to melt ice and the other to extinguish fire yet they coexisted. (I heard both of these examples from R.Moshe Shapiro Shlita)).
It seems that this class of Nissim requires something to both have a property and not to have it at the same time. This would seem to be closer to your category of definitions than rules. I can imagine a universe where e is not equivalent to mc^2 but not one in which a larger object can be smaller than a smaller one.
Do you have any ideas on how to handle the issues raised by these Nissim?
Posted 29 January 2012 - 04:05 PM
1+1+1 = 3.
The reason that 1 + 1 + 1 = 3 is not due to any rule of nature. It is simply an expedience of language. Consider the following:
1 1 1
I can describe the above in different ways. I can say it is three ones, or I can say it is one and one and one.
Saying it is "one and one and one" and saying it is "three ones" means the same thing. If I want to express that last sentence in short, I can write it as follows:
1 + 1 + 1 = 3
On one side of the equals sign I have "one and one and one" and on the other side I have "three ones". Because three means three ones.
On either side of the equal sign are different words (or symbols) that express the same idea. This is the same as saying
"Danger = Sakanah", or
"Two = 2" or
"Two = שתים."
1 + 1 + 1 = 3 says no more than that.
Such equations do not need to be created, because they are not the result of nature being the way it is, or even the result of nature being - period. They are the result of human expression and language.
However, an equation, or a rule, that is true not because of semantics but because nature makes it that way, needed to be created, since if not for nature, the rule would be different.
Now let's take your examples. But first, I'd like to add two more of my own. One, the miracle of Yehoshua stopping the sun for the Jews but for the rest of the world it still moved. Meaning, the sun was in two different places at the same time - one in relation to the Jews and the other in relation to the rest of the world.
Two: The miracle that the words on the luchos were engraved all the way though, but were readable and not backwards on either side.
(I remember when I first heard about this when i was in 5th grade, from my Rebbi. I had a very hard time digesting it and argued with the Rebbi about "How could that be?" He said "Well thats why they call it a miracle." I remember being very frustrated and asking him "OK, so if someone would have stuck their finger in one of the letters, where would it come out? "They didn't stick their fingers in the Luchos," he said. I am sure that is true, But I was never so frustrated about something I heard in Yeshiva until 5 years later when my 10th grade Rebbi taught us about מיגו זכות הטענה.)
Anyway, this miracle, and all the miracles you mentioned, do seem to cause something that possesses contradictory attributes at the same time. However, they are not definitions. They are still rules of nature.
All of these miracles have the same thing in common: They violate the boundaries created by space. The fact that if something is located in a certain place something else cannot occupy that same space, is not a definition created by expressions of language. It is a limitation created by the nature of space. Yes, the Aron had to be a certain size in order to be Kosher, but it doesn't say that once it is a certain size, it must displace other matter from the space it occupies. It is impossible for us to visualize any of the set of miracles we collected above because because we cannot conceive of anything outside of space. But if you notice, all of the above miracles are violations of the limitations of space, limitations that were created with the world.
If we could imagine a world without space, we would be able to understand these miracles. But we can't. So these miracles will never be conceptualized by us. But still, they are miracles of nature, not violations of definitions.
Something cannot be smaller and bigger at the same time. But the Aron miracle was not that it was bigger and smaller at once, but rather it had the properties of something big and small at once, which is impossible due to the rules of how space is taken up. Those rules were violated, and yes, it is a totally different level of miracle than let's say Krias Yam Suf, which broke the pattern of behavior that Hashem chooses to use when He makes things happen in the world. Having something act above time and space is much more than that - it is ignoring the fabric of creation altogether.
Time (and space, which is the same thing in this sense) is the "boundary" within which everything was created. That is why the ancient Nations worshiped the stars. The stars "control" time, and time is the building block of all creation. Everything is subject to time. WIthout it, nothing would be here. Same with space.
When we want to describe something that transcends nature we say למעלה מן המקום or למעלה מן הזמן, because whereas the fact that bread doesn't fall from the sky is a law of nature, time and space are the building blocks of nature.
But they are still nature. They are still creations.
So, yes, those miracles we mentioned are in a different category that the Mon or the Be'Er, for example, but they are still not a violation of definitions. They are still a violation of nature.
(See also Toras HaOleh of the Rama 1:25, and Magen Avos (Tashbetz) on Avos 5:5)
Posted 31 January 2012 - 11:05 PM
R.Saadia (ED 2:13) says that we don't say that it is a deficency in Hashem that He cannot make the world fit through a ring (ie. a small opening) without making one bigger or the other one smaller. Presumambly he maintains that of course Hashem could make one smaller or the other bigger, but that each should maintain its actual size and yet one pass through the other is impossible even for Hashem. This seems to me a very good analogy to our case of Ein Makom HaAron Min HaMida.
Similarly the Ikarim (3:25) gives the example of a thing being in two places at once as something we need not believe Hashem can do.
These two examples are only violations of space and yet still impossible.
Finally, the Rambam (MN 3:15) gives 11 examples of things which might be impossible for Hashem to do. He only admits to 10 of them and says we argue with the philosophers and we believe that Yesh MeAyin is not impossible for Hashem. But the first one he lists, which he says everyone agrees to, is that one thing cannot have two contradictory or opposite properties at the same time. What properties does the Rambam mean? He doesn't say but presumably location is one of them (as are time, position, size, quantity etc). Yet if location is a property then one thing being in two places at the same time, or something smaller fitting in something larger would be impossible according to that definition even though Hashem creates space, time, all things and their properties. Saying something is hot is equivalent to saying it is not cold and vice versa. So to saying something is here is equivalent to saying it is not anywhere else. Both are examples of contradictory properties.
So two questions: (ii) can our chiluk between a definition and a rule be made to work with these examples; and (ii) why did the Rambam need to accept that Hashem cannot give a thing two opposite properties, and how then did he understand those nissim?
Posted 01 February 2012 - 07:41 PM
Your questions are: If Hashem can make the Aron אינו מן המדה why can't He make the world fit through a ring, or make one thing be in two places at the same time?
Those are valid questions on Rav Sadiah Gaon and the Ikarim, but they were equally valid before we started this conversation. The Gemora seems to say that Hashem can do what they say He cannot.
Before I answer, I first want to try to not use the phrase "Hashem cannot" or "is impossible for Hashem," if only because they may confuse people. Those phrases are are not meant the way they sound. The following are givens:
1) Hashem can do anything. Hashem is הכל יכול.
2) 1+1 cannot be made into 3
Those two statements are unmovable. They are not a matter of debate.
Therefore, if you find in a Sefer that Hashem cannot do something, it is always going to be for one reason and one reason only: The question is an illusion. In other words, if I ask you "Can Hashem Sgyebt kkeiun ywa Mdemm?" the answer will be "no". Not because Hashem cannot do it, but because there is nothing here for Hashem to do! "Sgyebt kkeiun ywa Mdemm" is meaningless gibberish. When I say it is not an imperfection in Hashem that He cannot Sgyebt kkeiun ywa Mdemm, it does not mean that Hashem has an inability but this inability is not an imperfection. I mean that Hashem has no inabilities and the thing you are asking whether Hashem can do, is not a thing at all but gibberish.
Now sometimes the gibberish component in such a question may not sound like such obvious gibberish, but it is gibberish nonetheless. An example of such gibberish is 1+1=3. It is not that it is "impossible" to get 3 as a result of adding 1 and 1, but rather it is the same as saying "Two that is also three". It is gibberish.
And so, when Rav Sadiah Gaon or the Ikarim or anyone else gives you an example of something Hashem "cannot do", it is invariably
a fancy way of talking gibberish. It is not that they identified something Hashem cannot do. They merely identified a fancy way of saying "Sgyebt kkeiun ywa Mdemm."
Those are the givens. Now to your questions.
Rav Sadiah Gaon is merely giving an example of how one can say nothing in fancy words. "A smaller thing that is larger than a larger thing" is meaningless gibberish. Asking Hashem to make the world fit through a ring where (a) the world is bigger, ( b.) the ring is smaller, (c.) but the ring will be larger than the world -- is like asking Hashem to jkhjhgn YFGU ^%R%$E. It is meaningless.
Of course Hashem could make the world fit into a ring. But then, by definition, the ring is bigger than the world. A physical something that can physically fit into a physical something else is by definition smaller. If a miracle would happen the the world would fit into a ring, then you cannot refer to the ring as "smaller" than the world.
As opposed to the Aron. The reason the Aron was able to be אינו מן המדה is because Torah is למעלה מן המקום (see the two references I cited at the end of my last post. There are many more that say this as well.) Now this is true despite the fact that the Aron felt like a solid mass and it had measurements. The idea of something being above time and space is not merely a miracle like Krias Yam Suf which broke the laws of nature. Time and space are not laws of nature - they are the clay out of which nature is made. The Aron, being Torah, was not bound to time or space. We cannot imagine what such a thing means for we never experienced anything outside of time or space, but we know that time and space were creations. They are not intrinsic reality. Torah is not bound to time or space.
The Aron being אינו מן המדה was not because Hashem took a this-worldly thing and made it not take up space. Rather, the Aron was not a this-worldly thing to begin with. Without time and space the Aron would still exist.
As opposed to physical things like rings and the earth. Without time and space they would not exist.
Can Hashem make the earth and a ring not bound to the confines of space? Of course He can, but then a physical ring that is not bound to time and space is not a physical ring, and a physical planet that is not bound to space is not a physical planet.
Can Hashem allow the ring to still be physical yet not bound to space? But physical things are by definition subject to space. So that is like asking "Can Hashem make something bound to space and not bound to space?" or Can Hashem jyhbfuytfytftfuytfn8yu8tfbnuytfigmgynigyyugm8uygnmyug ?
The answer is "no."
An Aron that is אינו מן המדה is not a problem. An Aron that is physical, bound to time and space, in a room that is physical and bound to time and space and at the same time אינו מן המדה would be gibberish. If it's bound to time and space you are saying it is מן המדה, but in English. Saying it is also אינו מן המדה makes no sense. The Aron, the Meforshim say, was אינו מן המדה because it was למעלה מן המקום.
You can have something that is אינו מן המדה but to say for example that something is אינו מן המדה and also מן המדה makes no sense. it's not that it cannot happen. Rather, there is nothing to happen.
A ring and a planet that are at the same time physically larger and physically smaller than each other is equally gibberish.
And that is what the Rambam means by "opposite properties." He means for example, you cannot be "existent" and "non-existent" at the same time. it's gibberish. You cannot be both alive and not alive. You cannot be both blue and not blue. It's not that these things are impossible. They are not things. The words convey no meaning.
This is not at all contradiction to those Nissim we mentioned. The Rambam has no problem for example with something being heavy yet intangible at the same time - the laws of nature preclude such a thing, but that's what miracles are for - to make things happen that are against the laws of nature. But the Rambam would have a problem with something being tangible and intangible at the same time - that's gibberish. The Rambam would have a problem with something having weight and no weight at the same time - that's gibberish too.
That's all the Rambam means.
(to be continued)
Posted 03 February 2012 - 12:13 AM
how is this not giberish? to say that the aron was physical (it had measurements, it was carried by the tribes) yet it was למעלה מן המקום?
Posted 03 February 2012 - 11:55 AM
Defining "Gibberish" (i.e. Two contradictory properties")
If you want to know if something falls under the category of the Rambam's "contradictory properties" you need to identify why the two properties cannot coexist. The reason for the incompatibility will determine whether a miracle can make them compatible.
Consider the following two statements:
1) XYZ is true
2) XYZ is not true.
The reason these two statements cannot both be true is because the information that statement #1 conveys is, in and of itself, a contradiction to what statement #2 says. These two statements cannot be true without altering the meaning of one of the two statements.
Even a miracle cannot make both statements above true. And the fact that they both cannot be true does not need to be created. This is what we mean by "gibberish." To say "XYZ is true and also not true" is gibberish. It does not say anything.
Now take this example:
1) XYZ is true
2) If XYZ is true then ABC is true
3) ABC is false
In this case, the information in statement #1 does not contradict the statement in statement #3. Yet they both cannot be true because of statement #2. The reason for the incompatibility of #1 and #3 is not because they contradict each other in and of themselves, but because of the requirements of Statement #2.
In such a case, the fact that #1 and #3 cannot both be true can in fact be overridden by a miracle. Their incompatibility must be a creation. Stating both of them together is not "gibberish" because it contains a valid coherent idea - XYZ is true and ABC is false. That is a self-contained logical statement. But even though it is a coherent idea, it is impossible. Because #2 tells us it cannot be true.
In the first example, saying #1 and #2 are true is self-contradictory. It is not merely impossible, it does not convey any coherent thought.
In the second example,saying XYZ and ABC are both true is not self-contradictory. It is a coherent thought. But it is impossible, because it violates the rule of Statement #2.
When the Rambam says something cannot have contradictory properties, he means two contradictory properties as in the first example above. He means two properties that intrinsically contradict each other. So that if you put both of them into one sentence the sentence becomes meaningless. Examples:
1) My house is blue and also it is not blue.
2) Mr. Mxyzptlk exists and also he does not exist.
3) I can lift 200 pounds and I cannot lift anything above 100 pounds.
4) Hashem is all-powerful but He can create a rock that is too heavy for Him to lift.
5) Climbing this ladder is dangerous but not a Sakanah.
6) 1 + 1 = 3
None of these statements convey any coherent ideas. They are self-contradictions. They are meaningless combinations of words. In this category is Rav Sadiah Gaon's example and the Rambam's example.
In the other category, we would have the following:
If you throw a rock up, the rock will stay in the air.
This is like the second case above. We can break this impossibility down into these 3 parts:
1) The ball is in the air
2) If a ball is in the air it gets pulled down by gravity
3) The ball does not get pulled down by gravity.
A miracle can make statement #1 and statement #3 true because those two statements by themselves are not gibberish.The statement If you throw a rock up, the rock will stay in the air is coherent, but it is false, because of the fact that gravity will pull the rock down. Hashem can make a miracle here and keep the rock in the air.
The following would not be able to be done even by a miracle:
If you throw a rock up, it will stay in the air and not stay in the air.
This statement issimilar to the first example above. It says:
1) The rock is in the air
2) The rock is not in the air.
That is a self-contradictory statement That cannot be accomplished even with a miracle. Not because of a lack of ability in the miracle, but because there is nothing to accomplish.
(to be continued)
Posted 03 February 2012 - 03:59 PM
Posted 05 February 2012 - 08:35 AM
למעלה מן המקום means it can break the rules that time and space create. But that does not mean it cannot mimic some of the characteristics of space-bound things if that's what Hashem wants it to do. The Aron was solid not because space forced it to be, but because Hashem decided it should be. As opposed to space-bound things, where it is solid by default due to the restrictions of space.
rabbi, you write "Now this is true despite the fact that the Aron felt like a solid mass and it had measurements"
how is this not giberish? to say that the aron was physical (it had measurements, it was carried by the tribes) yet it was למעלה מן המקום?
Posted 28 June 2012 - 03:28 AM
I understand that if there is such a thing as 1, which there would have to be if there was a creation at all as whatever was created there would need to be at least 1 of it, then there would need to be the concept of 2. That is because the whole idea of the unit is that conceptually it can be replicated. By this I mean that even if only 1 of something was ever created, there could, technically, have been a second created as well. Therefore we could conceptualise two of them and therefore 1+1=2.
However, before creation itself, hard as it might be to imagine, surely even the concept of 1 did not exist. I know that with regard to “Hashem is 1” 1 did exist, but that is really not the same thing as that is not 1 as in a unit; a unit is a bounded thing. Hashem is unbounded and therefore not a unit in the sense of 1+1=2.
Therefore why would it be correct to say, as the questioner did, that “1+1=2 ... was true before brias haolam” surely it was not true as the entire concept of 1 did not exist. It is like saying that a day was 24 hours before brias haolm. It is true that necessarily if the concept of time was created we could take a unit of time, callit a “day” and then subdivide that into 24 periods and call them “hours”, but that does not mean that this was true before time itself existed. If time does not exist, neither does a day or an hour nor saying a day = 24 hours would be totally meaningless and therefore not true.
Posted 28 June 2012 - 07:49 AM
You're saying that because there was no independent unit of anything in existence before the creation (and you are correct that Hashem is not "one" in that sense), the statement 1+1=2 would not refer to anything.
Yes, that's true, but it does not impact on what I said.
The question on the table is, could 1+1 not have been equal to two if the creation had been different? The answer to that is "no."
Yet E could have not been equal to MC^2, what goes up did not have to come down, and people could have had three eyes instead of two. Hashem had to create not only Energy but this specific rule as well; Hashem had to create not only people but this specific characteristic as well.
But when Hashem created "one" he did not have to additionally create a rule that two ones equals one two.
1+1=2 is a different type of statement than the rest, one that is not affected by creation. All we are saying is that 1+1 could never have equaled anything except two, regardless of whether there was a creation or what the creation was like.
It's like asking whether we needed a creation for danger to be a סכנה. Obviously without a creation the statement would not mean anything, but that's only a technicality. The equality between "danger" and "סכנה" did not need creation. The words and the concepts did but not the equality.
1+1=2 does not say anything more than the statement that "danger is dangerous". These are statements that could never be otherwise, no matter how the world is set up.
The disconnect here is that you are referring to a different part of the equation than I am.
The equation says: 1+1=2.
You are saying that the part of the equation that says "1" became meaningful only after creation.
I am saying that the part of the statement that says "=" was not affected by creation in the slightest.
Both of those last two sentences are correct.
Posted 29 June 2012 - 09:11 AM
Just to clarify, I was not trying to disagree with you in any of those points. I was merely pointing out that the original questioner made a statement to his friend that "1+1=2 is an absolute truth and was true before brias haolam". This statement is not only untrue, but potentially misleading as it implies that certain concepts existed before Hashem created them. A more correct statement could be '1+1=2 is an absolute truth and could not have been created otherwise' i.e. without commenting on the state of affairs before creation.
Posted 29 June 2012 - 09:52 AM
And there's also a semantic disconnect here I think. Even though 1+1=2 was not "true" before creation, it was also not false. Before creation, saying 1+1=2 is like saying "oiwqjencv sngn dt" . It just didn't mean anything. But it's not that 1+1 equaled anything else other than two. The statement was neither true nor false, any more than "oiwqjencv sngn dt" is true or false.
Nobody, then, is really disagreeing.
Posted 29 June 2012 - 10:36 AM
"Nobody, then, is really disagreeing"
Just the way it should be
תלמוד ירושלמי מסכת סנהדרין דף כא/א
א"ר ינאי אילו ניתנה התורה חתוכה לא היתה לרגל עמידה
.ועי' בפני משה שם
תלמוד ירושלמי מסכת סנהדרין דף כא/ב
וידבר ה' אל משה אמר לפניו רבונו של עולם הודיעני היאך היא ההלכה אמר לו אחרי רבים להטות רבו המזכין זכו רבו המחייבין חייבו כדי שתהא התורה נדרשת מ"ט פנים טמא ומ"ט פנים טהור
.ועי' בפני משה שם