Whats an example of an atheist trying to impose their views? — DingoJones

In order to impose your views onto others, you need to grab control over the government in one way or another, and get them to do it for you.

For example, look at the rules and procedure for divorce in the West. Do they apply the Jewish, Christian, Islamic, or any other religion's rules-cum-formalisms? No. Absolutely not.

So, what they apply, is a non-religious system. Hence, for all practical purposes, it is an atheist/secular system.

Furthermore, if you confess to being of religion X, will the secular state respect that? Will the secular state let you use the procedures and rules of religion X? No, they will force their atheist system down your throat.

For myself, I can happily accept any of the three Abrahamic religious systems of divorce (Judaism, Christianity, Islam), because they are in my opinion fair in one way or another. Over the centuries, they have turned out to be sustainable practices. Furthermore, if I sign a marriage contract with someone, specifying that one particular choice of these three systems is applicable, why does the State's godless vermin stick their noses into none of their business, and declare their godless rules to be applicable instead?

That is just one example, one of the many actually, of an instance in which the atheist/secular state forcibly overrules people's religion, because they somehow mistakenly believe that their atheist/secular bullshit would be superior to the religious take on the matter.

That belief of superiority is utterly baseless, though, because there is absolutely nobody who believes that the atheist/secular divorce-rape procedures are even fair. Now that pretty much nobody wants to get married anymore, how can they still claim that the atheist/secular marriage contract would be somehow "better"?

So, the atheists have managed to wholesale destroy the nuclear families in the West, and hence, the entire social structure, but hey, their views on the matter would still be better!

…I feel sorry for Atheists. — 3017amen

I believe that every misbehaviour is its own punishment. If someone does something that will not keep flying, then let it just crash in a natural way. That is why I do not give a flying fart about atheism. Let them just do whatever they want, because in the end, who cares? Unless, of course, if they try to impose their views onto me. That is when I get pissed off.

Still, in an idealized world the "isProvable" predicate can really be implemented — alcontali

Meaning that ideally every true statement has a corresponding proof and every false statement has no corresponding proof (or perhaps a corresponding disproof)? — Andrew M

Not every true statement but every theorem will have a corresponding proof. A theorem is defined as a sentence that has a corresponding proof. A true statement is a statement that just happens to be logically true. So, false statements will have no corresponding proof, but the lemma guarantees that there will also be true statements that have no corresponding proof. Such lemma-witness statement will be true, but there is no way that you can prove it.

And is that the diagonal? (i.e., false/not provable, true/provable) — Andrew M

OK, how does this part work? — Andrew M

In general the diagonal is:

== GENERAL CASE ==

$\begin{bmatrix} sentence/hasPropertyX & false & true \\ false & \color{blue}{\boldsymbol{(false,false)}} & (false,true) \\ true & (true,false) & \color{blue}{\boldsymbol{(true,true)}} \end{bmatrix}$

The diagonal lemma's "diagonal" is depicted in blue in the table.

The diagonal lemma says that it is always possible for any arbitrary property about numbers to hit the diagonal. This means that you can always find a true sentence that has the property but also a false sentence that does not have the property.

In logic language, if S is a sentence and P is a property about numbers and %S is the numerical encoding of S then the canonical logic form for that is: S $\leftrightarrow$ P(%S).

This lemma is provable for all number predicates; not just provability (which is itself also just a number predicate). Gödel's incompleteness theorem is just an application of this diagonal lemma. It just just one particular example of the diagonal lemma:

== SPECIAL EXAMPLE CASE ==

$\begin{bmatrix} sentence/\boldsymbol{\color{green}{isNotProvable}} & false & true \\ false & \boldsymbol{(false,false)} & (false,true) \\ true & (true,false) & \color{blue}{\boldsymbol{(true,true)}} \end{bmatrix}$

The general diagonal lemma itself is not considered to be "amazing". It is this one special application of the lemma in the table above, simply by picking propertyX=isNotProvable, that has shaken heaven and earth in 1931.

In my experience, you can develop a good intuition for these theorems by playing the diagonal game a few times more often.

Pick whatever property. Then, generate arbitrary false sentences until you find one that does not have the property. Next, generate true sentences until you find one that does have the property. You win the game as soon as you hit the two boxes of the diagonal.

I think either something about the form of the sentence (e.g., HasAnEvenNumberOfLetters) — Andrew M

HasAnEvenNumberOfLetters is also just a property of the number associated with the sentence. Instead of converting to decimal, convert to hexadecimal (or just convert back). Example:

utf8( hello ) = 0x68 0x65 0x6c 0x6c 0x6f

Each group of 2 hexadecimal digits represents a byte. So, for "hello" we have 5 bytes, and therefore an odd number of letters. This simple procedure works for digits in the base plane of utf8. For Greek, Chinese, Japanese, Russian characters (and other non-Latin character sets), it represents one letter as two, three, or four bytes. But then again, you know from the first byte (special value), how many other bytes are attached. So, you can then count the letters by counting the groups of bytes.

Since the restriction of the Unicode code-space to 21-bit values in 2003, UTF-8 is defined to encode code points in one to four bytes, depending on the number of significant bits in the numerical value of the code point. The following table shows the structure of the encoding. The x characters are replaced by the bits of the code point. If the number of significant bits is no more than seven, the first line applies; if no more than 11 bits, the second line applies, and so on.

byte number one (represented in binary) indicates the size of the group of bytes:
0xxxxxxx --> 1 byte, 110xxxxx --> 2 bytes, 1110xxxx --> 3 bytes, 11110xxx --> 4 bytes.

So, counting letters in utf8 is just another numbers game.

IsProvable doesn't seem to meet that criteria since it depends on the meaning of the sentence. — Andrew M

It is also just another numbers game. Say that "12>3" is a simple theorem in arithmetic. Then, the following sequence of sentences is one possible proof:
1) 12>3
2) 12-3>3-3
3) 9>0
In 3) we hit axiom 15 in the equivalent axiomatization: i.e. zero is the minimum element.

So, now we convert the theorem to a number:

utf8("12>3")=49506251
utf8("12>3 ; 12-3>3-3 ; 9>0")=495062513259324950455162514551325932576248

So, now we can say that theorem 49506251 is provable because it is associated to another number. 495062513259324950455162514551325932576248, which is its proof. Therefore, the predicate isProvable(49506251) results in true.

What we need to do, to effectively implement a complete solution, is to store and/or compute the set of all possible 2-tuples :

{ (49506251, 49506...32576248), (theorem2, proof2), (theorem3, proof3), (theorem4, proof4), ... }

From there on, the "isProvable" predicate should work fine simply by attempting a look up in this set of tuples and return true, if it can find a proof for the theorem. It is obvious that this is a thought exercise. Gödel did not go on to execute this plan as to effectively implement "isProvable". He would have needed a computer for that in 1931, which did not even exist by them. Furthermore, even then, it is practically not attainable. Still, in an idealized world the "isProvable" predicate can really be implemented. From there on, it will still not be able to avoid hitting the diagonal lemma: there exists a true sentence which "isNotProvable".

But "the face is green" is not a predicate. It's fine as a sentence however (with a Godel number). — Andrew M

Yes, again, bad example. There is no easy way to attach a truth value to "the face" (a digital image), even if "green" is a calculable predicate about a digital image. In fact, the sentence really has to be sentence in one way or another ...

So would this show that some true sentences are not provable, or just that those "true" sentences are problematic in some way, similar to the liar sentence or the above "heavy" sentences? — Andrew M

Well, the term "heavy" was probably a bad choice. I couldn't think of a some good predicate, because the literature pretty much never mentions one. It needs to be something calculable true or false about a sentence. The literature typically says something like: "The sentence S has property K". Any idea of what could be a good example for K?

So would this show that some true sentences are not provable, or just that those "true" sentences are problematic in some way, similar to the liar sentence or the above "heavy" sentences? — Andrew M

Well, since "heavy" is just an arbitrary choice, I wouldn't worry about that. As long as you can calculate the property from a number, it should be ok. For example: "the face is green" should probably work better, because a face can be represented as a number, and figuring out that is green, is just a calculation on its bits and bytes. So, the diagonal lemma says that it should always be possible to construct a face that is green, but also one that is not green.

Again, maybe my memory is playing tricks on me. So I ask you, instead of accusing you: did you reword the opening post? — god must be atheist

No. I stopped drafting it after probably half an hour or so, and then left it like that.

The theist has to decide first how many gods there are, and the set must include one specific number, for instance, 4565 in case of Greco-Roman worship. — god must be atheist

So, this whole exercise just depends on what theists say and not on what objectively the possibilities would be? So, if I get it right, you have no way of determining the number of gods, except by listening to theists. Hence, these probabilities are not fixed, because different theists could report different numbers. Again, Cox' theorem does not allow for that:

Consistency – If the plausibility of a proposition can be derived in many ways, all the results must be equal.

I addressed this already. Assuming {0,1,2,3,4,5} gods, has the counter assumption of not having {0,1,2,3,4,5} gods.

Go from here. — god must be atheist

What is the difference between "having 0 gods" and "not having {1,2,3,4,5} gods"? Isn't that the same possibility?

t is plausible that they have equal probability to be true while they are mutually exclusive
Consistency: If there are more gods, or the possibility of more than one god, then the probabilities get divided into more subsets. That is, (There are no 5 gods), (there are no 5938 gods), their opposite (non-existence of gods) grew to be an equal number of subsets (Five gods don't exist,) (5938 gods don't exist). — god must be atheist

I am not sure that it can work like that. For the number of gods, you assume a set that looks like this: {0,1}. You do not assume, for example, {0,1,2,3,4,5}. Therefore, you implicitly use information that you do not mention, something like, "There is only one God".

You clearly know more about the problem than you disclose.

In that implicitly-assumed information, you undoubtedly already assume the existence of God. How else do you know it it is just one?

Therefore, you use the assumption that God exists to argue that he possibly does not exist.

If you do not want to use that particular information, then you can perfectly assume any arbitrary set of possibilities {0,1,2,..., k}, with k any natural number. In that case, you cannot assign equal probabilities 1/k to each possibility, because every possible value of k is equally probable. You will simply not succeed in fixing k. Therefore, in my opinion, your proposal does not satisfy Cox' consistency requirement.

I'm guessing here so consider it carefully...I think zero as a number was born in subtraction problems where the minuend and the subtrahend are equal. — TheMadFool

Yes, I think that accountants have procedures in which the sum in one column must be equal to the sum in the other column.

If these numbers are, for example, not supplied in order, you can still verify this equality by substracting the numbers in the second column instead of adding them. The final result must then be zero.

Still, they did not document much back then, and with many of these scant, historical documents now gone, they have left us guessing. Even of Algorithmi's original book, "The Art of Hindu Reckoning", there is no extant copy left. We only have access to a translation.

Please only attend to the OP propositions and their continuations directly. — PoeticUniverse

Either you reason within a system, or else you reason about a system, because in all other cases, you are just system-less bullshitting.

So, you spout 175 different baseless system-less claims, of which I pick just one.

You refer to probability theory, which is a real system, and which obviously does not belong somewhere in the middle of system-less bullshit. Hence, I ask, what the hell is that serious principle doing in that complete mess of 175 nonsensical declarations?

What you cannot do, is to arbitrarily appropriate the credibility of real systems in order to make your own system-less bullshit sound better.

God is a basic belief in a system of beliefs. There are several such mainstream belief systems that incorporate that basic belief. It is a system-wide premise amongst several other system-wide beliefs. You cannot just lift that one premise out of its particular system and start spouting system-less nonsense about it.

Furthermore, it is a basic belief, meaning that it is part of the construction logic of such system. It is necessarily unexplained, because otherwise it would not be part of the construction logic. Why don't you question why there is an unexplained, basic belief in arithmetic concerning the existence of a successor function? Why don't you call that "equiprobable" with something else? If you want to reject axioms in a system, why don't you pick something like arithmetic? It is full of axioms.

I have never heard anybody say that an axiom would be "equiprobable" with some other axiom ...

Actulally, he can.

There are two subsets: "God exists" and "God does not exist". Together they form the superset, "Making statements at god's actual existence". — god must be atheist

Well, no, the bureaucracy will throw up another hurdle there.

According to the paperwork factory, his setup must either satisfy Kolmogorov's axioms or Cox' theorem. So, he has to produce all kinds of paperwork that extensively demonstrates that everything is properly stamped, signed, and certified. Otherwise, the official clerk, who works from nine to five, with a thirty-minute break at lunch, will declare the proposal to be irreceivable.

Mathematics is just some kind of extensive bureaucracy of excruciatingly annoying formalisms, not particularly much different from other such obnoxious bureaucracies:

The Dispute Tribunal should also have power to make interim orders, including orders for the suspension of action in any case where there is a good prima facie case and the award of compensation or damages would be inadequate and power to summarily dismiss matters that are clearly irreceivable or are frivolous or vexatious.

Personally I think zero began simply as a symbol for nothing and the rules of mathematical operations were a later development. I have no idea what the actual problems were in which zero was used as a number and not just a symbol for nothing. — TheMadFool

In my impression, the systematic use of the digit zero became a necessity with the introduction of the decimal (positional) system. For example, the number 504 has a zero in the middle, because of the mere bureaucratic-administrative formalisms imposed by the decimal place system. It only has a syntactic meaning.

Still, that system makes arithmetic easier. The procedures for addition, substraction, multiplication, and division are incredibly straightforward in comparison to the ancient, Roman numerals.

But then again, when this system was new, people could already calculate with Roman numerals, and were undoubtedly good at it. So, the new system did not solve a problem. On the contrary, it created one! Now they had to learn to do something in a different way, while they already knew how to do it in the old way and get perfect results.

Although Al-Khwarzimi also wrote a book about Hindu arithmetic in 825, his Arabic original was lost, and only a 12th-century translation is extant.[1] Kushyar ibn Labban did not mention the Indian sources for Hindu Reckoning, and there is no earlier Indian book extant which covers the same topics as discussed in this book.

As you can see, pretty much nobody wanted to read that book. That is undoubtedly why all copies were lost.

Leonardo Fibonacci brought this system to Europe, his book Liber Abaci introduced Arabic numerals, the use of zero, and the decimal place system to the Latin world. The numeral system came to be called "Arabic" by the Europeans, it was used in European mathematics from the 12th century, and entered common use from the 15th century to replace Roman numerals.[13][14]

So, after introducing it, it took another 300 years for people to switch to it.

You see, if you already know how to do arithmetic with roman numerals, then you will most likely think that the new system is just bullshit.

All the existing registers are done in roman numerals. All the accounting books are done in them. Why would anybody waste their time on such unfamiliar system that is not particularly compatible with the miracles and the horrors of the past?

So, I think that they fundamentally rejected the new system.

Still, it ultimately broke through anyway, because some people must have found niche applications in which it was incredibly useful. So, niche after niche started converting. Familiarity grew. After a while, the new system was so widespread that the original objections no longer made sense. The last standing irredenti ("We will never surrender!") eventually caved in, and grudgingly adopted it too.

I think that they still couldn't care about number zero in calculations (What for anyway?) after converting to the decimal place system. Does accounting really need it? Does astronomy really need it? (astronomy: navigation by ship on the high seas to move the expensive spices around!) Does anything else really need it? It was just people who philosophized and played with numbers for the sheer sake of doing that, who used zero as a number. In a sense, mathematics is just a game, and the number zero will then eventually emerge out of that game. Intrinsically, however, it does not have a use in itself, outside that game. Of course, when science and engineering started committing to all of that, things became a bit different. From there on, there were real-life implications too. However, it is not mathematics itself that does that. It is the downstream users in empirical, real-world subjects that cause that transformation.

7. If I am too stupid to understand this, please tell me now, outright, so I shall cease and desist, and not bother you with questions. — god must be atheist

I am convinced that a 12-year old can understand it. Seriously, I mean this.

You haven't told us how to determine the number of a sentence. And once you give us the rule to determine the number of a sentence (I imagine it's ordinal numbers, not cardinals), then... — god must be atheist

This first step is the hardest part and it amounts to learning how to use one text box in a particular web page.

I know from experience that 12-year olds can use otherwise very complicated pages in mobile games. This page is much, much easier to learn how to use than what they already know how to use. Furthermore, learning how to use this page is the hardest part in the Gödel game.

Every minute that I spend on this issue, I get more convinced that it can be explained to a 12-year old.

First, you must be able to reach this page: https://onlineutf8tools.com/convert-utf8-to-decimal.

Just copy this link to your browser bar, or click on the link, or whatever. You will need to go there.

The reason is that we are operating in number theory. So, everything you will say in the game has to be a natural number. This is non-negotiable. Still, you can trivially convert every sentence (or sequence of sentences) into just one number.

You first must configure the page correctly. Somewhere in the middle of the page, you will find the heading:

Utf8 to decimal converter examples Click to use

Below that heading you will find three boxes:

Aliens, UTF8 Lottery Balls, and Big Decimal Number

Click in the box "Big Decimal Number".

Now you will see that the page has moved you up again. You can see two boxes at the top of the page: one box on the left, titled utf8, and another box on the right, titled decimal.

Now you can type any sentence in the utf8 box and it will automatically convert everything that you have typed into one big decimal number in the decimal box.

Example:

I am hungry and I want to eat fish
becomes:

733297109321041171101031141213297110100327332119971101163211611132101971163210210511510446

Again, you really need this step, because if you do not convert your sentences into numbers, you cannot use number theory to say anything about your sentences.

Try to do it for the following example sentences:

CIA Whistleblower 'Professionally Tied' To 2020 Candidate

Which should yield:

677365328710410511511610810198108111119101114323980114111102101115115105111110971081081213284105101100393284111325048504832679711010010510097116101

Try also:

The Surge In "Surprise" Medical Bills Bankrupting Americans Can Be Blamed On Private Equity

Which should yield:

84104101328311711410310132731103234831171141121141051151013432771011001059997108326610510810811532669711010711411711211610511010332651091011141059997110115326797110326610132661089710910110032791103280114105118971161013269113117105116121

Copy/paste a few other arbitrary examples by yourself and convert each sentence into a corresponding big decimal number. Once you can do that, the remainder of the game will be much easier to play.

Let me know if it works for you!

-- Note --

Funny, but true, the entire internet happens to be encoded in a Gödel numbering scheme. Every single page is like that! It is not that they consciously "wanted" to do that. It just turned out to be like that.

You actually did not describe the lemma ... What is the meaningfulness of talking about two somethings none of us understands, and none of us has any comprehension or concept of? — god must be atheist

Let me try again.

It is just a game and you must hit the diagonal.

$\begin{bmatrix}(false,false) & (true,false) \\ (false,true) & (true,true) \end{bmatrix}$

The first example predicate, "isEven", will return true if a number is even and false if it is odd.

In this game, you can use whatever logic sentence you want, but if it is true, its number must be even. If it is false, then its number must be odd. You must stay on the diagonal!

The diagonal lemma does not tell you how to do that. It only says that it should be possible to find at least one sentence that will successfully hit the diagonal.

So, let's start up a simple search strategy. We generate arbitrary true sentences and convert them to numbers (using their standard utf8 encoding):

1. utf8( 1=1 ) = 496149
2. utf8( 1=1 or 99=99 ) = 49614932111114325757615757
3. utf8( 1=1 or 99=99 or 0=0 ) = 496149321111143257576157573211111432486148 $\Leftarrow$ BINGO!

Example 3 is true and even. So, it is a solution, i.e. a witness to the lemma. Just for the sake of the argument, let's now try to find an arbitrary false sentence that is odd:

4. utf8( 0=1 ) = 486149 $\Leftarrow$ BINGO!

Example 4 is false and odd. So, it is also a solution, i.e. a witness to the lemma.

Let's take another example predicate, "isPrime", which will return true if the number is a prime number, and false if it is not.

Well, again, the lemma does not tell you how to conduct your search strategy. It only says that you can always hit the diagonal. It is always possible. Hence, you should always be able to win that game if you try long enough. There is even an obnoxious proof that guarantees it (and that everybody seems to be complaining about).

By the way, you can use the utf8 to decimal test page to convert directly from logic sentence to natural number. Just use the "BigDecimal" box. It works really well.

So, what is the link with Gödel's incompleteness theorem? The "isProvable" predicate works exactly in the same way as the "isEven" or "isPrime" predicates.

So, you can also play this game with the "isProvable" predicate, but the really interesting game is with the "isNotProvable" predicate, because as soon as you win the game by finding a true sentence, you will have a true sentence that also "isNotProvable", and that is considered to be an astonishing result in metalogic and metamathematics.

So we don't know what the problem is, and we don't know its solution. — god must be atheist

Well, I am just using a trick of collaborative learning here. I try to force myself to give an understandable explanation about a difficult subject to people who do not understand it, because that also improves my own understanding. So, I was rather hoping to hear really "hard" questions that would somehow compel me to solve them.

Of course, all of that requires people who are interested in learning and who will not merely be complaining that they do not understand things.

So, no, you cannot just say, "you do not understand it". That is not how you test someone's understanding. If you really believe that, then you simply do not understand the term "understanding" itself. You simply need to ask a (difficult) question (and then another one, and so on) and then discover that I cannot find the answer, while I should, if I really understood the problem. It is only the inability to solve problems that reveals a lack of understanding.

we only know that there is some false proposition that has the same truth value as a predicate function that always returns false, which... duh. — Pfhorrest

Well, p $\leftrightarrow$ q also means not p $\leftrightarrow$ not q, which is indeed a bit "duh", but formally still correct.

I don’t see how any conclusions can be drawn from that to more general statements about predicate functions that sometimes return true or sentences that are true. — Pfhorrest

My argument just shows an example of an extreme case, really. It is just a case in which you would intuitively not expect the lemma to work, but it still does.

If you want to cover all possible cases, you can always fall back on the full proof. The problem with that full proof is that it is exclusively syntactic symbol manipulation. In the video of the workshop, they pointed out many complaints from people who simply disliked the theorem and its proof for that reason. So, I wanted to show an example where it (unexpectedly) works.

If you provide another example of a class of computable predicates (that return sometimes true and sometimes false) it should also be possible to locate a sentence that will satisfy the lemma.

We could trivially invert the truth values and say that any true sentence has any predicate that always returns true — Pfhorrest

Well, in that case, you would reasonably expect that every sentence would have the property, which is surprisingly, also not the case. There will still exist a sentence that does not have the property.

which just says that in a system in which nothing is provable, any true sentence is not provable, which is again trivial. — Pfhorrest

Gödel's system will first have loaded all the axioms of logic and all the ones of a (sufficiently strong) theory of arithmetic, and the system understands the full language of first-order logic. Gödel spends dozens of pages doing exactly that in his original paper. The problem is that lots of readers will give up because they consider it to be unreadable (which it actually isn't). Therefore, "nothing is provable" will not occur. You will, for example, be able to prove that "1+1=2".

Just curious, is there a constructive argument for the lemma, such that it also holds for intuitionistic logic where proof by contradiction is not allowed? — aletheist

Yes, the standard proof does not exploit any contradictions. Its proof strategy is exclusively based on judicious symbol manipulation.

Unfortunately, the standard proof use the original Gödel encoding, which means that it must use two successive encodings/decodings, which is not needed when using a modern numbering scheme. But then again, I guess that tradition has its weight.

What I did was just showing that even in the most extreme case the lemma still holds. In a complete proof it would be a case of formally covering all possibilities. Still, such complete proof would probably no longer be suitable as a clarifying explanation either.

At the Workshop on Proof Theory, Modal Logic and Reflection Principles (October 18, 2017), Moscow, Steklov Mathematical Institute, the speaker was so fed up with the standard proof ("I can never remember it!") that he proceeded by show casing diagonal-free proofs. During the public Q&A, quite a few members of the audience were not convinced about the idea of dropping the diagonal lemma. I actually share that opinion. I think that it is much better to build a better narrative around its proof.

The positions are not necessarily equiprobable. — PoeticUniverse

You cannot use probability theory for this problem. It just does not work like that. The following would be a probabilistic argument:

Imagine we have a set of universes. Some universes have a God. Other universes have no God. If we randomly pick a universe from that set, will it have a God or not?

What you are doing, however, is not probability theory at all.

Probability theory only works within the strict confines of set theory. It only concerns the cardinality of sets and subsets. Furthermore, you must demonstrate that the setup of your problem satisfies the Kolmogorov axioms or Cox' theorem.

Otherwise, what you are doing, has simply nothing to do with probability.

Furthermore, if you consider a statement P and its very opposite ~P to be equiprobable, it is just a way of saying that you do not understand the problem. It does not mean that they really are equiprobable. Of course not. It just means that you know absolutely nothing about the problem.

Well said !
Alas some members rely on pedantry as an excuse for ignorance of the literature. — fresco

:lol:

You know, using reason to figure out what's true. — Bartricks

You cannot do that with reason. You can only use reason to verify -- and not to discover -- what is provable.

We are now long past the idea that "true" and "provable" are even related to each other.

Seriously, that misconception was abandoned after Gödel's famous lecture at the Second Conference on the Epistemology of the Exact Sciences on 5–7 September 1930 in Königsberg.

You are almost 100 years behind now.

My question is how can it be that the Chinese knew about negative numbers, defined as numbers less than zero, and didn't know about zero itself? — TheMadFool

Let me offer a completely unjustified speculation on that.

As soon as people started farming, they ended up with periodical harvests and a problem of warehousing stocks of agricultural produce. You also had to protect the fields, the harvests, and the stocks. So, specialization kicked in, with some people getting paid to beat the hell out of the occasional scavenging tribes, which would otherwise confiscate the inventory of produce.

You do have an "add 15 bags" transaction in such inventory, while you also have a "substract 10 bags" one. So, "add 15" could be abbreviated as "A15", while "substract 10" as "S10".

You really don't need to represent them as "+15" and "-10", because that would defeat the object of explaining what happened:

Between the 4th millennium BC and the 3rd millennium BC, the ruling leaders and priests in ancient Iran had people oversee financial matters. In Godin Tepe (گدین تپه) and Tepe Yahya (تپه يحيی), cylindrical tokens that were used for bookkeeping on clay scripts were found in buildings that had large rooms for storage of crops. In Godin Tepe's findings, the scripts only contained tables with figures, while in Tepe Yahya's findings, the scripts also contained graphical representations.[4] The invention of a form of bookkeeping using clay tokens represented a huge cognitive leap for mankind.[5]

These people quickly discovered that "A15" + "S10" = "A5".

So, several transactions in both directions can be represented by one aggregate transaction that will have one particular direction. In this context, there is absolutely nothing special about "S10" (or "-10") because it naturally emerges out of the fray.

However, these people were not interested whatsoever in adding a transaction with no items added or removed. Hence, "A0" or "S0" did not occur in their books. Since it reflects that nothing happened, why would they record a non-event? Hence, there is no need for representing transactions with a zero magnitude. There is also no need to aggregate them.

Of course, you could still occasionally end up with a zero balance, but again, you can just report the natural-language term "nothing" in that case. This "nothing" does not need to participate in aggregating calculations. Just do not enter "nothing" in such calculations, and the totals will still be correct. Adding zero to a number does not change that number. So, "not adding" zero does not change it either.

You do not need zero for adding or substracting numbers because you can just cross out the zero and the sum will still be correct. Hence, for the financial management of their inventories they were not interested in expressions like "5+0=5". It was irrelevant.

Well, that is my speculative take on why they could not be bothered to calculate with the number zero, back then.

It is not that the language expression "nothing" did not exist. I am quite sure that it did. It is also not that they did not know that adding nothing to three will yield three as a result. It is just that formalizing all of that was not needed for the basic accounting of warehouses full of wheat or rice.

Arguing against logic using logic will inevitably lead to the equivalent of saying "this sentence is a lie." — Artemis

Well, it is a little bit more elaborate than that.

First, you have that strange conclusion that occurs when you represent sentences as numbers. For every predicate that is calculable about numbers, there exists a sentence that says that it satisfies that predicate.

So, if "green" is calculable, then there will be a sentence provable in such system that says:

I am green.

The corollary is true as well. There will be a sentence provable in such system that says:

I am not green.

That is the notorious Gödel-Carnap diagonal lemma.

Its proof is purely syntactic. Up till now, nobody has been able to produce an intuitive interpretation for this. It is just four or five entirely correct steps in a strange reasoning, and voila, there it is. In the field of metamathematics, you really need good resistance against syntactically correct propositions that otherwise sound nonsensical.

Still, as a side note, propositional logic is just a system of 14 arbitrary beliefs that correspond with absolutely nothing at all in the real, physical world. It is an abstract, Platonic world in itself. Therefore, we should not be surprised that syntactic conclusions in that world mean nothing to us or correspond to nothing we can identify with. In fact, that should rather be expected.

So, from there on, Gödel famously went on to show that provability is just a relation between numbers (=theorems/conclusions) and other numbers (=a set of sentences that proves such theorem), and that therefore, the following sentence is necessarily provable in such system:

I am not provable.

That sentence is also logically true. So, Gödel's first incompleteness theorem created a first consternation about the limitations of logic. Next, Tarski used the same system to show that another sentence would be provable in such system:

I am not true.

However, the problem can still be fixed by disallowed the definition of a "true" predicate in arithmetic. Hence, Tarski's famous undefinability theorem: truth cannot be defined in a system of arithmetic. That is forbidden.

So, yes, the liar sentence plays an important role in Tarski's undefinability theorem. Still, it is not insurmountable. Just ban the practice that allows it to emerge in your system.

This is true only if we decide to leave out objective reality in our logic. If you base logic on what really is/occurs around you, than it is 'speculative' only to the extent you don't trust your senses and their interpretation. — lepriçok

I cannot disagree more. Seriously, it simply does not work like that.

A system such as logic is not the real world, and does not even try to correspond to the real world. It is an abstract, Platonic world constructed from -- and dealing with -- language expressions. Any claim that says that such abstract, Platonic world corresponds with the real, physical world is wrong. It simply doesn't.

The same holds true for arithmetic. Standard arithmetic gets constructed from 9 speculative beliefs. Anybody who says that this corresponds to the real, physical world, is basically saying that the construction logic of the real, physical world would consist of 9 rules. That is simply nonsense. We do not know the construction logic of the real, physical world.

You can use language expressions to build -- and reason within -- completely imaginary worlds that have nothing to do with the real, physical world. You can use it to construct stories in science fiction. You can describe imaginary events that never took place, in a world that does not even exist, and so on.

If you seek to establish and somehow guarantee correspondence with the real, physical world, you will need to use the principles of an empirical knowledge-justification system such as science.

Therefore, without a knowledge-justification guarantee from an empirical domain of knowledge (such as science), you are not even allowed to assume correspondence between language expressions and the real, physical world.

These are not axioms, rather basic truths of life that everyone agrees with. This solves your problem. Reason and logic must be grounded in this reality to avoid the speculative catastrophe — lepriçok

Logic has nothing to do with the real, physical world. It is an axiomatic system based on 14 speculative beliefs. You can perfectly use it to reason about imaginary worlds. In fact, out of the box, that is even all you can do. You usually add more premises, i.e. more speculative beliefs than the original 14 ones, and then draw conclusions inside this completely speculative system. Your conclusions/theorems will then be provable from the speculative beliefs in the system.

If you want to establish some kind of correspondence with the real, physical world, you will have to use an empirical knowledge-justification method such as science. Logic is purely axiomatic and does not offer such guarantees whatsoever.

You are badly confusing logic with science.

Science will demand that you experimentally test your conclusions. It will therefore demand that your conclusions are testable (falsifiable). In science, you cannot stop after declaring a few logical inferences and calculations, and then be done with it. That is not simply not allowed. In science, you must also satisfy the numerous requirements of the regulatory framework of falsification. You see, science talks about the real, physical world. Logic does not do that. Logic just talks about arbitrary premises, using some other arbitrary premises (its axioms).

We have to take it on blind trust. — lepriçok

On what other basis do you accept the 14 axioms of propositional logic, other than blind trust?
On what other basis do you accept the 9 axioms of standard arithmetic, other than blind trust?

You do not want to blindly trust, only because you are ignorant of the fact that you are doing that already. It is ignorance and arrogance.

You're trying to logic your way out of logic. It's not going to work. — Artemis

Well no. It is possible to talk about logic as an abstract system. You can certainly look at what happens when you change the axioms of logic. That is in fact what the Hilbert calculi do.

Of course, at that point you will end up with the same problem as in Gödel's work, i.e. the fact that you must carefully distinguish between the rules of the system being studied versus the rules of the system with which you study it (the meta-system); which is incredibly tricky:

Metamathematics is the study of mathematics itself using mathematical methods. This study produces metatheories, which are mathematical theories about other mathematical theories. Emphasis on metamathematics (and perhaps the creation of the term itself) owes itself to David Hilbert's attempt to secure the foundations of mathematics in the early part of the 20th century. Metamathematics provides "a rigorous mathematical technique for investigating a great variety of foundation problems for mathematics and logic" (Kleene 1952, p. 59). An important feature of metamathematics is its emphasis on differentiating between reasoning from inside a system and from outside a system.

So, it can be done, and it has been done extensively, but it is indeed full of gotchas.

My thoughts exactly. And I was already thinking about mathematics and abstract concepts. Nobody knows why they are so effective in cosmology and science, yet we just assume...………what? — 3017amen

Plato already complained about that. So, he wrote that allegory of the cave. There may be a good reason why we only see Platonic-cave shadows. It may even be necessary to maintain our sanity:

If, however, we were to miraculously escape our bondage, we would find a world that we could not understand—the sun is incomprehensible for someone who has never seen it. In other words, we would encounter another "realm", a place incomprehensible because, theoretically, it is the source of a higher reality than the one we have always known; it is the realm of pure Form, pure fact.

Mathematics has highly-Platonic ontological elements but the link with our reality is not particularly understood. That is one reason why we avoid using it directly in reference to the real, physical world. Dealing with that, is the job of downstream users of mathematics, such as science (undoubtedly the flagship user of mathematics). Of course, these downstream users will ultimately not be able to avoid the problem either.

Indeed! I too, don't understand that rationale. I mean, there is plenty in the world that is unexplainable...including our own conscious existence. — 3017amen

Agreed, and the worst is that they think that they are going to use logic for that, which is a system of which we cannot possibly explain the reason for its basic rules. The axioms of logic just appear out of the fricking blue.

The same problem occurs in standard arithmetic, where we simply assume the 9 unexplained, speculative, unjustifiable and highly arbitrary axiomatic rules of Dedekind-Peano. They just happen to land out of nowhere!

We assume so many things, and we simply cannot explain why we do that. Seriously, these people adopt that rationale only because they don't know what they are talking about. It is sheer ignorance!

I think that it is a rather strict system, which allows very little for freedom — lepriçok

That is obviously debatable. Still, whatever the level of restrictions exists, it cannot be increased. You do not have that guarantee when politicians are allowed to invent new laws.

For instance, what does Islam say about religious freedom, and by its norms, am I allowed to choose my creed, or not to believe in God at all. If Islam doesn't allow this, it has little relevance in libertarianism. — lepriçok

It is not possible to know what an individual believes. Therefore, there are no rules about what you have to believe. Who is going to enforce that anyway? There may be rules about what you can publicly declare, but those exist in every society.

Another problem is that there could be distinguished God as the source of moral law and human reason as the source moral law. The first is very speculative, therefore easily refuted using strict logic and empirical facts, while human reason is the only trustworthy place of insights into the human nature and the needs of society, for it to prosper. — lepriçok

You see, propositional logic is a rule-based system that rests on exactly 14 axioms, i.e. otherwise unexplained, "speculative", and not further justified beliefs.

So, the average atheists -- just like you just did -- invariably ends up claiming that he will use a system based on 14 "speculative" beliefs, i.e. logic, to justify why you should not use systems based on "speculative" beliefs.

Every time you use a number, you drag 9 "speculative" beliefs into the fray, i.e. the Dedekind-Peano axioms. Hence, by using any form of logic, along with any form of numbering, no matter how basic, you base your conclusions on 14+9 = 23 such "speculative" beliefs.

If you oppose logic to "speculative" belief, it only demonstrates that you do not understand the axiomatic nature of the system of logic. Furthermore, there are no systems, i.e. theories, that do not ultimately rest on "speculative" beliefs. That is simply impossible.

We have written laws — lepriçok

Well, it is exactly by inventing new laws that the State manages to encroach on people's freedom.

The core concern of libertarianism, i.e. the loss of freedom, is caused exactly by continuously imposing new, politically-invented laws, the primary goal of which is to create winners and losers, inevitably leading to the emergence of an oligarchy which concentrates wealth and resources. If you control the law, then you control all the money, if only, because in that case, it is you who prints the money.

Organizing a voting circus to elect law makers who will in turn invent better laws is obviously not the solution either. If the voting circus were able to address the problem, then libertarianism would not even exist as a concern today.

A central belief in Islam is that politicians, elected or not, have no authority to invent new laws because God has invented all the laws already. This makes such continuous freedom-encroachment process impossible.

Therefore, Islam, which is a complete and documented system, has a credible solution for the aforementioned problem, while libertarianism may not have one. Again, I consider libertarianism to be a legitimate concern but certainly not a legitimate system.

Everyone, guided by the main libertarian framework, can document their moral principles themselves. — lepriçok

Why doesn't one person accept the job of documenting it on behalf of everyone else? I am very wary and also suspicious of the refusal to commit to an immutable set of documentation. That practice allows people to claim a thing and tomorrow the very opposite of that thing. So, no, I am very opposed to that.

We have totalitarianism, communism, fascism, statism, eugenics, social Darwinism, elitism that have all sorts of ethics rules that serve only the needs of narrow groups and do nothing good to humanity. — lepriçok

What these false ideologies all have in common, is that they are not documented in a firmly established system of rules, i.e. a sound theory. That is why these things are mere bullshit.

I agree with quite a few of the concerns in libertarianism. I also totally distrust the State. However, I will only adopt, in practical terms, systematic and functioning alternatives to the State. That is why I am fully committed to bitcoin. I do not trust the State's money. I do not want to hold my savings in it.

So, it is not that I am against libertarian ideas. However, abstract concepts have to be systematic for me to adopt them. Otherwise, they will create the same problem as the false ideologies (such as communism, fascism, ...) that you have mentioned. If you do not systematize and guarantee consistency then you are bound to do just the same as them. Then, it is just going to be yet another evil.

For instance, would you acknowledge that there are prescriptions of reason? Would you acknowledge that this argument form is valid:

1. P
2. Q
3. Therefore P and Q

And that the validity of this argument consists of no more or less than a prescription of reason to believe 3 if 1 and 2 are true? — Bartricks

It requires a system of 14 axioms, i.e. 14 unexplained beliefs, to make propositional logic possible in the first place. Without such system of unexplained beliefs, there simply is no logic. Any attempt at further justifying these 14 unexplained beliefs must be deemed ridiculous, pointless, and utmost ineffective. The construction logic of logic itself, i.e. the metalogic, simply materializes out of the blue. Since atheists reject the very principle of unexplained belief, they also reject logic. Hence, atheists are not logical.

There is nothing more stupid than attacking a system merely because it ultimately rests on unexplained beliefs, given the fact that all systems are like that, including logic itself.

I think you might be in Thailand. — Wayfarer

Well, next-door to Thailand, in Cambodia. I have never had a look at how the Thai do things, actually. I only have some kind of vague familiarity with the Cambodian take on religion. The thing is, the ordinary believer does not seem to know more than me. I know because I have asked so many people if there was more to what they are doing, and there isn't.

apanese Pure Land services are very like church services, complete with hymns, which imitate the Christian style, and sermons ('dharma talks') along with sutra recitation (which is regulated to the minutest details in intonation and pronunciation.) — Wayfarer

That is really not how the Khmer do it. These "services" must be a Japanese thing. There are no "services" here in Cambodia. There is only the morning-prayer round of the mendicant monks. If there were "services", I would have run into one a long time ago already. There really aren't any.

Elders > monks > laymen & laywomen? — praxis

They have temples, i.e. a particular type of buildings. So, there are obviously people who take care of practicalities surrounding these temples. I am not privy to the nitty-gritty details of the facilities management involved in each one of these buildings, but all of that looks very, very practical.

A monk is mostly a young man who spends a few years in that temple; after which he comes back to civilian life. He may do it again several decades later, when he is quite old already and he feels like investing again some time in monastic life.

With the Buddha being the ultimate authority, of course. — praxis

For the ordinary Buddhist believer, the Buddha does not even seem to play a particularly large role in the religion. That would require these believers to understand what exactly the monks recite during the morning prayer, which they generally don't. I know because I speak the local language. So, I know that what they are reciting is absolutely not in that local language.

Even most monks are incapable to tell you what exactly they are reciting in Pali language.

To tell you something funny, I can also recite their main prayer, but I do not really understand what it means. When I ask other people who recite it, they do not know either what it means. Transliterated, it goes like this:

Nek mo ta sa
Nek mo ta sa phekevek tau ara hak tau
sama sampot tau sa

I do not know what it means, but I can recite it from memory, simply because I have heard it so often.

I am afraid that this is what they all do. Seriously.

It is most likely an excerpt from the Tipitaka, but I am not even sure about about that. There are more prayers similar to this one, but they are recited less often. So, I may recognize them, but I cannot recite them by myself.

I am not deeply invested in that stuff. I just wanted to know what it was. So, I ended up participating in their things, once in a blue moon, just for the hell of it, but that is all there is to it.

By the way, I have never heard a Buddhist mention the word "Buddha". Ever. It rather seems to be some kind of misguided western idea that Buddhism revolves around a "Buddha". Seriously, it doesn't.

Buddhism is all about reciting prayers in an ancient language that you do not understand yourself. That is main pillar in Buddhism.

The second pillar of Buddhism is to show respect for traditional morality, rules, and social conventions.

God does not exist. Religion is nonsense. We all know it. Get over it. — Swan

God is a system-wide premise in a religious system, i.e. a religious theory. Atheists do not seem to grok the concept of "system" or do not even understand what could be legitimate criticism of a system.

Criticizing the fact that every possible system ultimately rests on an unexplained construction logic is nonsensical and even absurd. Atheists criticize a premise simply for the mere fact of being a premise. What kind of nonsense is that?

You need to look at systemic properties such as consistency, completeness, and so on. A legitimate remark about a system could be, for example, that it is non-ergodic, or compact, or isomorphic with another system, and so on.

Atheists do not seem to be capable to reason at that level either within a system or about a system.

That is why atheist remarks are invariably dumb, unwarranted, anti-intellectual, and ultimately even an attack on reason itself. Reason is simply not possible without axiomatizing basic beliefs. Get over it!

It is akin to saying that those who do not believe in the tooth fairy have the aim of disproving the existence of a tooth fairy... rejection of a belief does not infer or confer the responsibility, goal or even desire to disprove said belief. — Soap Needswater

The rejection of unexplained system-wide premises degenerates in the complete inability of building systems or deriving conclusions in such system.

For example, if you do not accept the unexplained axiomatic premises of a theory of arithmetic, such as Dedekind-Peano, Robinson, Presburger, Skolem, and so on, you cannot calculate anything. Furthermore, these rules do not correspond to anything in the real, physical world. They are completely abstract and Platonic.

So, an atheist would say, "I do not believe in the existence of a successor function". Fine, but how do you generate natural numbers in that case? Atheists are completely correct to point out that there is no evidence for the existence of such successor function. That is ompletely true. However, without that kind of unexplained beliefs you will end up without theory and without any ability to reason in it.

Every criticism that atheists may have on religious systems perfectly apply to any other theoretical system. Since every axiomatic system ultimately rests on unexplained beliefs, and since science extensively uses them to maintain consistency in its own theories, the rejection of the notion of axiomatization also constitutes an implicit rejection of science.

The idea that someone refuses to accept any kind of premises to start reasoning for, constitutes in effect a complete rejection of the concept of reason itself. Atheists mistakenly believe that their views are reasonable, while they are absolutely not.

Even among scholars of philosophy and religion there is no consensus as far as Buddhism's position is concerned. — Daniel C

The Southeast Asian country in which I live, is largely Buddhist. My wife is Buddhist. My in-laws are Buddhist. In my opinion, Buddhism is first and foremost a religion. I seriously wonder why people in the West think it is a philosophy? My wife is not philosophical at all. She wouldn't want to follow a "philosophy".

Of course, Buddhism doesn’t speak of a divinity in the strict sense, but it deals with some sort of universal power and that amounts to the same. — Congau

Agreed. When the monks come over the noodle soup restaurant in the morning, where I would be having my noodle soup, any Buddhist will give the monk twenty cents or so, and then they will pray together for twenty seconds or so, in ancient Pali language. (Almost) nobody understands what they are praying about and whom they are praying to.

Religion, and this absolutely includes Buddhism, has a hierarchical authority structure and is primarily concerned with meaning and social cohesion. — praxis

There is no hierarchical authority in Buddhism that I know of. If there were, I would be able to see such authority here in this largely Buddhist country. There are certainly monks but there is no organization beyond the practical management of a single temple. These temples do not report to a higher authority. They were built by collecting donations. Some local elders manage the premises.

There are indeed different monastic fraternities, but these loose associations have no governing authority. They do not own the temples. They do not appoint their administrators, and so on.

By the way, Buddhists do not go to the temple like Christians go to church. That is a complete misconception. These temple buildings primarily house the monks. Furthermore, monks are not monks for life. They do that for a few years only; after which they return to civilian life. Occasionally, there are festivals and other festivities at the temple (not inside but in front of). I have been to a few in the past.

Every day the monks visits the population in the morning and pray with people in front of their houses or shops. It is this morning-prayer round of mendicant monks that is the central pillar of Buddhism. The other pillar is the notion of traditional morality and law.

By the way, the vast majority of Buddhists have no clue whatsoever what is written in the ancient Buddhist scriptures (Tipitaka). I have never seen a local translation either. Ordinary believers simply do not read them (and are not encouraged to read them by anybody). Only the older monks do, and always in original language (Pali or Sanskrit).

There's no necessity to fall back on anything, because libertarians use common sense morality, not based on any metaphysical doctrine. — lepriçok

The term "common-sense morality" creates the impression of referring to something rather undocumented. If it is not worth documenting, why use it in the first place? If it is worth documenting, then why hasn't it been done already?

A collection of basic rules will collectively form a system, i.e. a theory. How can you possibly know if a particular conclusion is a theorem in that system if you fail to document the basic rules of such system?

Can God be immoral, if he does, why doesn't he choose to be immoral. — lepriçok

Well, how was Russell's paradox eventually addressed? Does the set of all sets that do not contain themselves, contain itself? The 1905 Russell's paradox has a long history, but I have rarely run into anybody who actually feels like learning from it. That represents 100+ years of progress in dealing with paradoxes thrown out of the window ...

I think that libertarian ethics are optimal for modern times, because other systems just add other unnecessary objects of transgression and forbidden types of action that are too restrictive to have a comfortable, yet pacifist life. — lepriçok

So, according to you a functioning system of rules is not needed because that would be "too restrictive"? What about systems of arithmetic, such as Dedekind-Peano, Robinson, Presburger, or Skolem's systems? Are their rules also "too restrictive"? These systems may be considered relatively "hard" but that is a feature, and not a bug.

Reasoning outside the confines of a system that imposes strict rules may look remotely attractive, because that is indeed "easier", but that is also rarely how progress is made.

I personally believe that it makes more sense to simply bite the bullet, learn the system -- even if doing so is hard -- and then produce much more meaningful results. It is exactly because logical reasoning within complex systems is hard that mathematics is a respected field. If you want respect for your work, you will have to do what it takes, even if it is hard to do that. The same holds true for morality. If the only reason why you think that it does not need to be a complete (and even complex) system, is that you are looking for an easy way out, then I must reject that approach as worthless.

Systems tend to be indeed difficult to learn, but I learn them anyway. I have always handsomely benefited from that view.

How this distinction is related to the question of religion, and is it necessary for libertarians to be atheists. — lepriçok

It really depends on whether there exists a list of forbidden behaviours. For example:

Some right-libertarians consider the non-aggression principle to be a core part of their beliefs.

That sounds very much like defining a forbidden behaviour. A moral system that has just one rule is pretty much surely incomplete. In such trivial system, it will not be possible to determine for any possible behaviour if it is moral or immoral. Therefore, you can expect the users of such trivial moral system to fall back on a real moral system that will be lurking somewhere in the back and that will be the true source providing answers in morality.

For example, you will find that atheists in the West tend to implicitly fall back on rules provided by Christianity. So, what they believe in, is not really "no rules" or "atheism" but some badly-defined, crippled system of implicitly-assumed but not well-understood Christianity. The real stuff tends to be more consistent. Still, I personally admire the incredible consistency of Islamic law which in my opinion defeats the much, much weaker consistency of Christianity.

Are we slaves to God as well? — lepriçok

Only if you choose to be.

Still, choosing not to be, has consequences.

Someone will make the rules, and if it is not God, then it will most likely be a mafia cartel of banksters that controls the local legislature by hacking and subverting the voting circus. In that case, you will inevitably become the slave of that bankstering mafia. At that point, being a slave to God does not look so bad anymore. On the contrary, God won't suck you dry by requiring you to hand over evermore taxes to be used by the indebted State for evergrowing interest payments to the bankstering cartel.

Is it good or we should rebel? — lepriçok

If you rebel against God by rejecting his law, then the alternative will invariably be even worse. Still, you are perfectly allowed to do that. You can happily enjoy the misery of your own choice, why not?

I personally like quite a few principles of libertarianism. I have a profound distrust for State power and the State in general. I am an avid user of bitcoin. Furthermore, I only use free (and open-source) software. I am a tor user, and I am deeply invested in cryptography. However, I still recognize that libertarianism is not a complete moral system. It is not the complete answer.

This tension between what the individual wants, and what they must do for something like a workplace is taken as a given of living in a society. — schopenhauer1

Nay saying surprisingly often works.

Nassim Taleb has written quite an interesting article on the matter: The most intolerant wins. Society automatically re-normalizes around the choices made by its most intolerant members.

On the long run, agreeable people do not achieve much, because they will just start doing what is expected from them without having particularly much of a say in what the expectations should be. If you just seek to fit in, it is other people who will define the culture in which you will be made to fit in.

If you don't know what to do, then by all means, go with the flow. If you see the light, however, do your own thing and ignore everybody else, because they have no clue anyway.

Seems to be way off topic. Can you lead us back? — Banno

Let me try.

Concerning "omnipotence", there will necessarily exist a provable language expression:

I am omnipotent.

On the condition that omnipotence is a computable predicate which maps natural numbers onto yes/no in a theory of arithmetic that is strong enough to represent such predicates.

Weird, isn't it?

Of course, the Achilles heel of the problem is the whole idea of "computable predicate". If it is possible to readily determine if something is omnipotent or not, then it is computable.

The next problem would be to formally establish the conditions under which there will only be exactly one such provable language expression.

And, to be sure, the sentences in English are different animals from their counterparts in math-logic. The math-logic being rigorous, the English not. — tim wood

Yes, in a sense that the symbolic language of first-order logic is obviously less prone to ambiguity. No, in a sense that some of the most famous proofs in math were written in natural language.

For example, John Nash's (published 1950) Nobel-prize (1994) winning theorem and proof is entirely in natural language:

----
Equilibrium points in n-person games

One may define a concept of an n-person game in which each player has a finite set of pure strategies and in which a definite set of payments to the n players corresponds to each n-tuple of pure strategies, one strategy being taken for each player.

Any n-tuple of strategies, one for each player, may be regarded as a point in the product space obtained by multiplying the n strategy spaces of the players. One such n-tuple counters another if the strategy of each player in the countering n-tuple yields the highest obtainable expectation for its player against the n − 1 strategies of the other players in the countered n-tuple. A self-countering n-tuple is called an equilibrium point.

The correspondence of each n-tuple with its set of countering n-tuples gives a one-to-many mapping of the product space into itself. From the definition of countering we see that the set of countering points of a point is convex. By using the continuity of the pay-off functions we see that the graph of the mapping is closed.

Since the graph is closed and since the image of each point under the mapping is convex, we infer from Kakutani’s theorem that the mapping has a fixed point (i.e., point contained in its image). Hence there is an equilibrium point.
----

Even though the text above is in natural-language English, it has always been considered an entirely legitimate proof.

This a description of how power plays out, right? — frank

Yes. In my impression, there is a price tag to telling lies. It is not cheap.