Can you ever be certain that you are reasoning correctly?

Discussion of the nature of Ultimate Reality and the path to Enlightenment.
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Fujaro
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Re: Can you ever be certain that you are reasoning correctly?

Post by Fujaro »

prince wrote:You are affirming A=A, whether you (or your ego) likes it or not.

A cannot be anything but A. It's that simple, whether you view it as the letter A, or anything broader.

Something is what it is, and nothing is what it is.

You can only understand this if your consciousness resonates truth only, ie .no anthropomorphic lens.
You as a fully certified logician of the Fullfledged Windbag Philosopher's Circle do acknowledge that A=A is not enough to prove that 1+2 = 2+1?
Then how are you gonna prove that?
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Re: Can you ever be certain that you are reasoning correctly?

Post by Fujaro »

Kevin,

I'd like to know with which of the folowing staements do you agree?

1) A=A cannot be verified empirically
2) A=A cannot be proven logically
3) From A=A alone non-trivial sentences cannot be build
4) The reason for adopting A=A is it's congruence with macro-level appearences
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Re: Can you ever be certain that you are reasoning correctly?

Post by Fujaro »

And Kevin, to that please add this one:

5) A=A can have no complete mapping to reality for it is impossible to know if all properties are known about a thing existing in reality
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Trevor Salyzyn
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Re: Can you ever be certain that you are reasoning correctly?

Post by Trevor Salyzyn »

Fujaro wrote:True wisdom is knowing how to gain knowledge, the path itself if you will, not a vegatative state in trivials like A=A.
Wait, so wisdom is having some knowledge that gets more knowledge? Is there nothing more to wisdom than a certain type of knowledge?
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Re: Can you ever be certain that you are reasoning correctly?

Post by Kevin Solway »

Fujaro wrote:
Kevin Solway wrote:The only way we could suggest that it might persist in time is if we had solid empirical evidence, and with empirical evidence we are always in the realm of mere speculation.
A=A itself also cannot be proven.

It doesn't matter that A=A cannot be proven, because it is self-evident.
The only reason to accept it is the congruence with reality as you perceive it.
Absolutely not.

We don't "accept" logic (A=A) because the only way we could possibly "accept" it is if we already had logic in the first place. Logic is automatically built-in to the conscious mind. It is not something that can be accepted or rejected.
So in that you are also using empirical evidence.
In normal science, empirical evidence is something that can be duplicated and tested over time. This is in sharp contrast to pure logic which can be carried out by an individual in the moment, and doesn't require further testing and verification.

"Empirical evidence" only exists because logic is already in operation.
You can't construct existence from logical thought alone.

Nobody is trying to construct existence from logical thought that I know of.
In your snapshot view there is no interaction between objects, because everything is frozen in time.
"The present" is a snapshot, yet the present is caused by the past. So while there is no interaction between the present and the past (since the past has already gone) the present is caused by the past.
You cannot possibly conclude anything about causation between different snapshots without inductive reasoning
I can conclude that a thing was caused by that with is not itself entirely with deductive reasoning.
This strict kind of philosopher is not participating in knowledge gaining but is like a donkey refusing to walk on because on logic alone it can't be deduced that the road will lead anywhere.
The practitioner of pure logic can tell us that the road will definitely lead somewhere - even if it is round in a circle - and he can tell us that through pure deduction.
Kevin Solway wrote:There is a time-aspect in the existence of physical things, such as electrons.
You have only instantanious existence within the snapshot when you say that in every snapshot there is another electron.
We can have an observation of an electron (a "snapshot") and we can still ask "What caused the electron?" and "What will become of the electron?" Hence we have a snapshot, and we also have time.
Kevin Solway wrote:For example, the first electron definitely has effects. There are consequences to its existence. It's just that we don't know that the second electron is one of them.
The word 'effect' you use is based on experience of existence through time, or in other words on the inductive comparison (pattern recognition) of snaphots in a row. You are not allowed to use it in your strict snapshot view.
No. I know that a thing has causes (and effects) through deductive reason alone. It's not something I have learned from empirical experience (which is always uncertain).
. . . it is conceivable in logical sense that between the first and the second statement a new I is inserted with the collective memory of the old I. You cannot be any more certain about this conclusion than about the existence of an electron through time.
A thing only "exists" when observed. Things naturally have no boundary separating them from the rest of Nature. The human mind provides that boundary. That is, the human mind draws a boundary and says "electron", where no boundary previously existed. Similarly with the "I".
A=A has no bearing on existence itself, it's a purely logical concept, placed not only out of time, but also out of reality.
A=A is not a logical concept, but is logic itself. So its value is the value of logic itself.
I'd like to know with which of the folowing staements do you agree?

1) A=A cannot be verified empirically
True, since all empirical evidence requires logic.
2) A=A cannot be proven logically
True, since A=A is itself logic.
3) From A=A alone non-trivial sentences cannot be built
This depends on what you mean by "trivial".
Pure, deductive logic, independent of all empirical evidence, can deliver incredibly profound, valuable, and significant knowledge that can be very hard-won. If all this can be called "trivial" then logic alone can deliver no more than this.
4) The reason for adopting A=A is it's congruence with macro-level appearences
A=A comes built-in with any appearance at all. If you can identify anything at all, then logic is already taking place.
5) A=A can have no complete mapping to reality for it is impossible to know if all properties are known about a thing existing in reality
This statement doesn't really mean anything, since it draws a false distinction between "reality" and logic.
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Re: Can you ever be certain that you are reasoning correctly?

Post by brokenhead »

DQ wrote:Double-talk?
Yes. Double talk. By that I mean I have so far used only logic in trying to show the limits of logical thinking. I shall recap, and this time I'll try to use your terminology a little more.

Let A be the set of all possible logically true statements. A must be a subset of Reality. You prefer the term Totality, and this seems to be one of your objections. This is an example of your double-talk. Whether we call it Reality or Totality doesn't matter and you should not be raising it as an issue. Therefore, I will let you have it your way.

1. Let A be the subset of the Totality that includes all possible logically true statements and nothing else. Totality is an infinite set, and set A may also be infinite.
2. Let B be the subset of the Totality that includes every member of the Totality not in set A. We call B the complement (in the set Totality) of set A. B may itself be infinite. We agreed that it doesn't matter. Given its definition, it seems as though it must be - it is the set of everything that is not a logical truth.
3. The intersection of A and B is the empty set; it contains no members by definition.
4. The union of set A and B is the set Totality, by definition, which is infinite.
5. The Totality is unique. A is unique. B is unique.


Are we agreed so far? If not, please tell me why not, specifically.
And so is Reality the totality, in your view, or not?
Yes. That should have been obvious from my previous posts. I hope it is now.
If a logical truth necessarily applies to all things in existence, then it will apply to every member of both subsets.
You have not shown it to be possible that a logical truth can necessarily apply to all things in existence. Instead, you introduced the term "things," and I objected , calling this another example of double-talk. I simply refered to the members of each of our defined sets as "members." I will agree to the term "things" if you are saying that 1.) Every possible logically true statement is a "thing," and 2.) Whatever is not a logically true statement is also a "thing." That is, a golf ball is a thing, sorrow is a thing, indecision is a thing, the wind is a thing, etc. There can be no concept, named or unnamed, or anything preconceptual or unconceived, that is not a thing. Therefore, the term "Thing" can convey no information whatsover, because there is and can be nothing that is not a thing. In this sense, a thing is merely a member of the infinite set we are calling the Totality.
Even if only one person in the entire Universe thinks of a logical truth which necessarily applies to all things, then that one truth from the location inside that person's head will instantly embrace everything there is.
Again, you have not shown this to be possible.
The kind of philosophic logic that I am interested is very different, as it involves using concepts and definitions which do necessarily apply to all aspects of reality. A=A is such an example. Other examples involve the concept of the "totality" (defined as utterly everything), and "thing" (defined as a portion of the totality).
But so far neither Fujaro nor I have used anything besides logical reasoning.
You're not seeing the simplicity of this kind of thinking and thus you're not seeing its heart - mainly because of an attachment to a God whose survival depends on things remaining unnecessarily complicated.
Again, have I mentioned God once in this line of questioning? You are using what you erroneously believe to be my concept of God to defend yourself, which is interesting, don't you think? Why don't we leave Him out of it, since if your position is sound - which it isn't - you have no need of Him.

Look at the paragraph in blue above and answer the question, please. In what manner can members of set A be mapped to members of set B?
Last edited by brokenhead on Sun Jul 20, 2008 4:43 am, edited 3 times in total.
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Re: Can you ever be certain that you are reasoning correctly?

Post by brokenhead »

I should point out that Fujaro and I are asking exactly the same thing.

Also, I know we agreed that it is moot whther set B is infinite or not. I said it is infinite without requiring proof, to which you objected. This was my reasoning: Totality (T) is infinite. The set A of all logically true statements may be infinite. The union of everything in T which is also in A (that is, A itself) with everything in T that is not in A (set B) is just the set T, which is infinite. We have said A might be infinite. If it is not, then B must be, by definition, since T is.

This is not a logical proof that set B is infinite, but the reasoning strongly suggests it is when you consider how we have defined set A. At least one of them has to be infinite, and we cannot logically prove that set A, the set of all logically true statements, is infinite.

So even if it is moot whether set B is infinite, you can see that it really has to be, can't you?


*edited to include this from Kevin since it is salient:
Kevin Solway wrote:1 + 1 = 2 is a truth about Nature, and so is 1 + 1 + 1, etc. Hence pure logic can deliver countless truths about nature.
1+1=2 would be an element of set A. It is not a truth about Nature, Kevin. It is not "about" anything. It is purely a logically true statement, nothing else. It is an element of set A, which is a subset of T. Thus, it is a part of Nature, or the Totality, if we agree that Nature is an alias for the set T.
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Trevor Salyzyn
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Re: Can you ever be certain that you are reasoning correctly?

Post by Trevor Salyzyn »

brokenhead...
brokenhead wrote: 1. Let A be the subset of the Totality that includes all possible logically true statements and nothing else. Totality is an infinite set, and set A may also be infinite.
2. Let B be the subset of the Totality that includes every member of the Totality not in set A. We call B the complement (in the set Totality) of set A. B may itself be infinite. We agreed that it doesn't matter. Given its definition, it seems as though it must be - it is the set of everything that is not a logical truth.
David Quinn wrote: You honestly can't see how each member is necessarily a portion of the totality?

Even the two subsets, by their very nature, are portions of the totality, let alone the members they each contain within.
How carefully can you read? I suggest reading as carefully as you can.
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Re: Can you ever be certain that you are reasoning correctly?

Post by brokenhead »

Fujaro wrote:You as a fully certified logician of the Fullfledged Windbag Philosopher's Circle do acknowledge that A=A is not enough to prove that 1+2 = 2+1?
Then how are you gonna prove that?
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Re: Can you ever be certain that you are reasoning correctly?

Post by brokenhead »

Trevor Salyzyn wrote:brokenhead...
brokenhead wrote: 1. Let A be the subset of the Totality that includes all possible logically true statements and nothing else. Totality is an infinite set, and set A may also be infinite.
2. Let B be the subset of the Totality that includes every member of the Totality not in set A. We call B the complement (in the set Totality) of set A. B may itself be infinite. We agreed that it doesn't matter. Given its definition, it seems as though it must be - it is the set of everything that is not a logical truth.
David Quinn wrote: You honestly can't see how each member is necessarily a portion of the totality?

Even the two subsets, by their very nature, are portions of the totality, let alone the members they each contain within.
How carefully can you read? I suggest reading as carefully as you can.
Trevor! I suggest you do the same.

You must not be getting my question, because this post isn't answering it. I know the two subsets are portions of the Totality because I have defined them to be so and because they could not be otherwise.

Now, Trevor, read carefully, and think while you do so.

In what manner can elements of set A be mapped to elements of set B?
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Re: Can you ever be certain that you are reasoning correctly?

Post by brokenhead »

Hint: I am not claiming they can't be so mapped.
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Re: Can you ever be certain that you are reasoning correctly?

Post by Trevor Salyzyn »

brokenhead wrote:Hint: I am not claiming they can't be so mapped.
Actually, you are. This sort of confused thinking is exactly what I was trying to point out, but you seemed incapable of slowing down enough to read.

Maybe with a few of your own quotes, you might be able to see why your confused thinking in action:

"3. The intersection of A and B is the empty set; it contains no members by definition."
leading up to a question that you answered by your own statement:
"In what manner can elements of set A be mapped to elements of set B?"
leading to the opposite answer of what you claimed earlier, in step 3:
"I am not claiming they can't be so mapped."

If you are concluding something that is the opposite of what you are claiming in step 3 of your proof (false by contradiction), which follows from premises 1 and 2, there is a problem in premises 1 and 2. One or more of these premises makes a false assumption.
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Re: Can you ever be certain that you are reasoning correctly?

Post by brokenhead »

Trevor wrote:Actually, you are. This sort of confused thinking is exactly what I was trying to point out, but you seemed incapable of slowing down enough to read.
No I am not claiming that. You have not shown that my thinking is confused, because so far, at least, it cannot be. So far, all I have done is made some definitions. I haven't asserted anything. The confused thinking is in your own head, Trev.
"3. The intersection of A and B is the empty set; it contains no members by definition."
leading up to a question that you answered by your own statement:
"In what manner can elements of set A be mapped to elements of set B?"
leading to the opposite answer of what you claimed earlier, in step 3:
"I am not claiming they can't be so mapped."
This part of your post is where the confused thinking is. You begin by restating point 3. Remember that what I am trying to do is to indicate the limitations of logical thinking by strictly using logical thinking. David claims it is possible to make a logically true statement that applies to "utterly everything." So that is simply what I am doing. Either a "thing" is a logically true statement or it is not. That is all that point 3. states, nothing more, nothing less.

My thinking is not confused, but it apparently is confusing you, so I will recap what we have so far:

1.) A is the possibly infinite subset of Totality T that consists of all possible logically true statements.
2.) B is the complement of A in T. B is thus a subset of T, by definition. It consists of every "thing" (as defined by David) that is not a logically true statement. B may be infinite; I say it is, but David and I agree that the point is moot.
3. The intersection of A and B is the empty set; it contains no members by definition.
4. The union of set A and B is the set Totality T, by definition, which is infinite.
5. The Totality T is unique. A is unique. B is unique.

Are we agreed so far?
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Re: Can you ever be certain that you are reasoning correctly?

Post by Fujaro »

Trevor Salyzyn wrote:
Fujaro wrote:True wisdom is knowing how to gain knowledge, the path itself if you will, not a vegatative state in trivials like A=A.
Wait, so wisdom is having some knowledge that gets more knowledge? Is there nothing more to wisdom than a certain type of knowledge?
Some bloke started to name it science for some reason. Well, it's a name. And yes, there are certainly more types of knowledge than the natural sciences if that's what you mean.

Has the A=A grown any lately?
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Re: Can you ever be certain that you are reasoning correctly?

Post by Trevor Salyzyn »

brokenhead,
You have not shown that my thinking is confused, because so far, at least, it cannot be. So far, all I have done is made some definitions. I haven't asserted anything.
And yet, it is. Primarily because you have not simply made definitions, but have also have made assumptions within your definitions. Your definitions, thus, are composites of definition and premise. They need to be simplified further. You should have been able to see this from the fact that you drew a conclusion (#3) from two definitions (#1 and #2), something which is not possible to do. Conclusions are drawn from premises, so within your definitions, you must have invented some assumptions.

Since later, you denied your conclusion, either one of your hidden assumptions was wrong, or you do not know the consequences of your own deductions.
2.) B is the complement of A in T. B is thus a subset of T, by definition. It consists of every "thing" (as defined by David) that is not a logically true statement. B may be infinite; I say it is, but David and I agree that the point is moot.
Otherwise, there is another problem that emerges. I was trying to recall exactly what it was that is suspicious about this, but it is your misapplication of set theory. Sets are designed to contain particulars, as defined by the type of set it is. A set of numbers contains numbers; a set of sets contains sets. Here, you contrast a set of all true statements with a set of things. This is actually very misleading of you. Does this set of things contain statements; does it contain sets; does it contain itself; does it merely contain things?

If you create a set of "everything that isn't a logically true statement", it is actually quite important that this set is consistent with its complement. That is to say, it should be "every statement that is not a logically true statement." But, that might interfere with your desire to make your two sets contain the entire Totality, so it's clear you'll continue to want to overlook this. You need the Totality to have form, so you will disregard all evidence to the contrary.
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Trevor Salyzyn
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Re: Can you ever be certain that you are reasoning correctly?

Post by Trevor Salyzyn »

Fujaro wrote:Some bloke started to name it science for some reason. Well, it's a name. And yes, there are certainly more types of knowledge than the natural sciences if that's what you mean.
Since I usually see wisdom considered a separate thing from knowledge -- and in some traditions, in direct opposition to knowledge -- I was assessing if you really meant what you said. It's clear now that you did. Your idea of wisdom is directly tied to how much a person knows and is capable of knowing, so is actually what I would call "intelligence".
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Re: Can you ever be certain that you are reasoning correctly?

Post by Fujaro »

Trevor Salyzyn wrote:
Fujaro wrote:Some bloke started to name it science for some reason. Well, it's a name. And yes, there are certainly more types of knowledge than the natural sciences if that's what you mean.
Since I usually see wisdom considered a separate thing from knowledge -- and in some traditions, in direct opposition to knowledge -- I was assessing if you really meant what you said. It's clear now that you did. Your idea of wisdom is dilirectly tied to how much a person knows and is capable of knowing, so is actually what I would call "intelligence".
Don't jump to conclusions Trevor, especially in places where the ceiling is low. I was talking of the wisdom of a culture not of personal wisdom.
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Re: Can you ever be certain that you are reasoning correctly?

Post by brokenhead »

Trevor, you are proving my point. I can subdivide Totality any way I want. And so can you. A "thing" is either a logically true statement or it is not.

I frankly do not understand your objections. I have not made a propostion yet.
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Re: Can you ever be certain that you are reasoning correctly?

Post by Trevor Salyzyn »

Fujaro wrote:Don't jump to conclusions Trevor, especially in places where the ceiling is low. I was talking of the wisdom of a culture not of personal wisdom.
But earlier you said wisdom is knowing how to gain knowledge, and contrasted it with a vegetative state. If you honestly meant that in relation to culture, and not in relation to a single person, that would surprise me. Either way, whether cultural or personal, I still call what you described as wisdom "intelligence". Cultural intelligence.
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Re: Can you ever be certain that you are reasoning correctly?

Post by brokenhead »

Trevor wrote:This is actually very misleading of you. Does this set of things contain statements; does it contain sets; does it contain itself; does it merely contain things?
I have used logical thinking and nothing else. There is nothing "misleading" whatsoever in my posts. Thus logical thinking has confused you.

Explicitly, set B contains everything that is not a logically true statement.
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Re: Can you ever be certain that you are reasoning correctly?

Post by Trevor Salyzyn »

brokenhead:
You have included premises within your definitions, making your separations into points 1-5 arbitrary. (point 1, for instance, includes both the definition and the claim that the Totality is an infinite set.) Further, you have been hypocritical about whether or not one of your points (#3) is true or false. You have given both answers, and for some reason have claimed that this contradiction proves your point, when all it does it prove you have made a mistake.

Further, you made set A a set of statements, and only now change it to a set of things, so as to justify calling B its complement earlier. You are constantly correcting yourself to try to invent consistency. Every time I point out a mistake you made, you weasel around, looking for wiggle room. This isn't going to deceive me. You are bullshitting.

I don't know how much more clear I can make myself.
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Re: Can you ever be certain that you are reasoning correctly?

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You have included premises within your definitions, making your separations into points 1-5 arbitrary. (point 1, for instance, includes both the definition and the claim that the Totality is an infinite set.)
I see you are confused.

So let's slow down.

Why can I not claim the Totality is an infinite set? David Quinn has said many times that the Totality is infinite.
Further, you made set A a set of statements, and only now change it to a set of things, so as to justify calling B its complement earlier. You are constantly correcting yourself to try to invent consistency. Every time I point out a mistake you made, you weasel around, looking for wiggle room. This isn't going to deceive me. You are bullshitting.
You're making excuses, Trevor. You are not up to handling this argument, I understand that. I had been interacting with David, you will recall. I am not trying to "bullshit" or "deceive" you or anyone else. As I have mentioned, although this is a public forum, I was not specifically talking to you.

I don't know how much more clear I can make myself.
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Re: Can you ever be certain that you are reasoning correctly?

Post by Fujaro »

Trevor Salyzyn wrote:
Fujaro wrote:Don't jump to conclusions Trevor, especially in places where the ceiling is low. I was talking of the wisdom of a culture not of personal wisdom.
But earlier you said wisdom is knowing how to gain knowledge, and contrasted it with a vegetative state.
That is what I meant.
Trevor Salyzyn wrote:Either way, whether cultural or personal, I still call what you described as wisdom "intelligence". Cultural intelligence.
How you name it is your choice, but I will keep to 'Trevor' in your case.
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Re: Can you ever be certain that you are reasoning correctly?

Post by Trevor Salyzyn »

brokenhead wrote:Why can I not claim the Totality is an infinite set? David Quinn has said many times that the Totality is infinite.
You could start by ordering your claims, perhaps restricting yourself to one claim per line.

eg.
1. The Totality is defined as "the set of all things".
2. The universe is the Totality.
3. Set A is the set of all things that happen to be logically true sentences.
4. Set B is the absolute complement of set A.

There, I said everything you said in your 5 steps, minus the errors. Except, now it becomes increasingly clear that when someone says "the Totality", they do not specifically mean "the set of all things". Also, calling it an infinite set is different than calling it infinite. Certainly you can see that distinction.
You are not up to handling this argument, I understand that.
Don't make me laugh. It's not that good of an argument. You are playing with deductive logic, but you don't seem to have much, if any, training in it.
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Re: Can you ever be certain that you are reasoning correctly?

Post by brokenhead »

Also, calling it an infinite set is different than calling it infinite. Certainly you can see that distinction.
That is precicesly is the point I'm trying to make, you goof.

Oh, and your syntax is sloppy. "Different" from, not than.
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