Yes, the number 2 is also a problem. Either we allow the number 1 to be a prime number again, or we also take the number 2 out of the prime number set and say: “Within the whole positive number set, the number 2 can only be divided by itself and by 1, because there is only one positiv number which is smaller than 2”. So then the new definition would be: “A prime number is that integer positive number which is greater than 2 and divisible only by itself and 1”. In this case, the prime numbers would begin with the number 3.
This would lead to other problems. So we should leave it at the first definition, so that 1 and 2 are prime numbers: “A prime number is that integer positive number which is divisible by itself and 1”.
Mathematicians are the ones among scientists who are the least corrupt (well, some people say that mathematics is not a science at all), but scientists want money, and that is why they have been bought more and more.
The worship of the number 1 can culturally work like a taboo. Ancient Greeks believed that everything is uniform, abyssal, delimited (everything also in the aesthetic sense). The number 1 means “unit”.
Since the conquests of Alexander the Great, the special role of the 1 declined in Ancient Greece.
Yes, it is also the case that children first learn the word “one” and then the number “1”. But in the beginning, they can’t separate the two. For children, “one” and “1” initially mean the same. It is only later that they come to understand the difference. And that’s probably how it was with the Ancient Greeks too - on a higher level of course - in their early times.
You could understand the meaning of the word “one” before you could understand the meaning of the number “1”.
Young children know very early what words are, but they separate the numbers - as numbers (and no longer as words) - from the words a bit later, when they begin to count with their fingers (counting, firstly accompanied by speaking, later no longer). When they have learned to count, they are fit for arithmetic and therefore for mathematics lessons - not before.
When a culture begins, it’s not much different, but the level is higher (after all, it’s mostly adults). The question is, whether and which words are holy or not, and later eventually, whether and which numbers are holy or not. It depends on the conditions of the early culture (which people and which environment?).
The best known of the Ancient Greek mathematicians who have come down to us and who were still mystical/religious about it, is Pythagoras. The time I have just spoken about is even far before Pythagoras.
Okay - I think i can see where you are going with this -
I see these things a little differently. I know that people think in different ways - I am referred to an an “analytical reductionist”.
An analytical reductionist is someone who reduces issues down to their basic concepts. We discern the “conceptual” or the “divine” - the abstract concept involved - the angels, demons, devils, and gods. And we tend to be able to easily understand the simple logic of what we each say as being exactly true or false or just too vague to be certain about. We tend to all agree very much on anything we have much education about. We learn from each other very quickly. And when I read about what people like Plato, Aristotle, and even Jesus have said - it all seems almost too obvious to mention.
Similar things happen with other kinds of minds - they see the “sense” all of the others of “like minds” are trying to explain. They see it instantly - whether it actually makes any real sense or not. That is why observers are chosen by their mind-type. - so they can relay what the intention really was to those concerned with whatever they said (dogs can’t see color) - much like a language interpreter but more like a thought interpreter.
So when you ask of the difference between the number 1 and word or concept of one - I have to scratch around to try to discern any difference. To me it turns out to be merely superficial semantics. And now that you have raised this issue of social beginnings I have to believe that with Plato, Hebrews, and the like - it was the same.
I doubt that their society started as one kind of mind that grew through time to become another kind. It seems much more likely to me that in the mix of minds they had when they started, a type of Darwinian interaction caused dominance of a variety of types of cultural norms and ideas. And through time, different aspects of those norms got more or less attention by others who could identify with them. Often they form identifiable groups.
And those groups, like the soap bubbles foaming up from the stream of life’s splashing issues, interact and role around each other rising, growing, and at times bursting while they form the world of mankind.
And in this vein of number vs concept and original prime vs new age - to us analytical reductionists - it is all just - “a rose by any other name” ( - but get your bloody words straight).
Everyone must reduce analytically in his life, but everyone must also observe in his life. This is also how science came into being. According to the theory/practice duality, the purely theoretical (related to philosophy) and the experiment have come into being. If science would not be corrupt through and through in the meantime - like e.g. also politics - then it would still appreciate this duality.
So, as I already indicated above, I am also an analytical reductionist and an observer. What I have written about language development in children is based more on observation than on analytic reduction, but from this one can not conclude that I prefer observation to analysis or even analytic reduction.
Do you have children?
If you observe young children intensively while they are learning the language (including the numbers, which are not separated from the words in the beginning), you will quickly realize that this development and acquisition is anything but superficial (I even believe that this learning is the greatest ever in a human life). Children have the same great “aha” experience when they can separate the numbers from the words. It corresponds to the difference of word and concept, of more concreteness and more abstractness, of more practice and more theory.
I did not say that they “become another kind”, I said that they give themselves a culture, that is something that has to do with them and their environment, and that from now on they will shape more differently than before.
A child does not “become another kind” by suddenly being able to separate numbers from words, but this child can suddenly do more, has learned, comes closer to the environment, wants to shape (with) it too.
Yes, and that does not contradict what I said.
What do you think about the following statement of Niklas Luhmann: “Evolution is the transformation of improbability of origin into probability of preservation”?
You seem the type to have written papers or books, have you?
I’ll have to ask around on that (I assume you don’t mean my wife and her entourage).
Now I am suspecting you have been referring to a different distinction between 1 and “one” than what I was thinking. Perhaps if you could describe more exactly that distinction.
There seems to be a great deal of confusion in the population concerning the separation of “Map vs Terrain”. I certainly agree that is a very important distinction to acquire - although I am not sure that everyone began with any confusion about that - communication confusions have been seeded, nurtured, allowed to blossom.
We could have a philosophical discussion about that.
A well stated focus of one aspect of evolution.
Luhmman struck me as one of those myopic global elitists - in his case way over focused and saturated with the extreme details of communication within a society without ever giving regard to the rest of what a society is (of course the big tech Internet world fawns over him). It is like someone describing a human in extreme detail as a complex nervous system - never giving credit to the heart, meat, digestion, and bone (never mind the actual impetus of the life it is). To me he just seemed like another myopic globalist too consumed with glee about one way to get there without regard as to why or whether anyone should - far too much “how”, not whole in “what”, and not nearly enough “why” - intensively focused on shoveling more bodies into the firebox to get the train to the top of the mountain giving no mind to the cliff just on the other side (I keep feeling like these are spoiled children in need of growing up - but perhaps another topic).
Stepchildren or all other children - it doesn’t matter, it’s „only“ a matter of observing them intensively and drawing the right conclusions from the observation. I have always observed a lot and intensively, also and especially children, most of all and most intensively my own children.
Who said that „everyone began with any confusion about that“?
Yes, with pleasure
Maybe we should discuss that in another thread. Luhmann was first a lawyer, then a sociologist (with a strong urge towards theory/philosophy). I mentioned him in the context of evolution/history, not in the context of child development, although one can also make connections between these two, but that was not my intention.
Now perhaps we should get back to the topic of this thread, although I would actually prefer to continue talking about the topic we are talking about now.
There are no true and false definitions, only more and less useful definitions in relation to a goal. Definitions are tools invented by people for certain prupose. And if the existing definition proves to be less useful than another one, it’s only logical to change it.
They obviously changed it, so the only question is why and whether they are justified in doing so.
I can’t answer that question because like obsrvr524 I do not understand the purpose of prime numbers.
If you define a horse as a being that usually lives on the moon (because you may have seen such a being on the moon), then that definition is false (a false definition!), until people agree that it needs to be changed.
The reasons, which Wikipedia is giving here, are based exclusively on meanwhile created facts in the area of applied mathematics, but have nothing to do with the matter itself (prime numbers). If I change something in an area, then this may be “unfavorable” for this area (e.g. for money reasons, because money is needed for the research), but changes nothing at the problem in itself, and this problem in itself is a purely mathematical one, thus without consideration on whether another mathematical area gets problems through it.
Just ask yourself why a number according to the definition (!) should be a prime number or not a prime number. The old definition for the prime numbers had existed for more than 2000 years.
You can define the word “horse” to mean anything you want. For example, you can define it to mean the same thing that the word “shoe” normally means. Of course, such a choice, like every other choice, might turn out to be a bad choice in the sense that it might lead to less preferrable consequences (for example, people might have more difficulty understanding what you’re trying to say and you might end up equivocating because your brain has yet to forget the old meaning and get accustomed to the new one.) But it cannot be true or false in the way that beliefs can. This is because it’s not a belief but an act of attaching a concept to a word. You took some word and said “Okay, this is the concept that will be attached to this word from now on.” Everyone is free to do that but noone is free from the consequences. It’s an act, and like all other acts, it is neither true nor false but rather either good or bad.
And a concept can easily become superfluous, no longer necessary, perhaps because a different, more suitable, one has been discovered. When such a thing happens, one is presented with a choice to preserve the old word-concept association and come up with a new word for the new concept or ditch the old concept, erase the old word-concept association and associate the new concept with the old word. The advantage of the latter approach is that it keeps one’s language simple (low word count, low concept count, familiar words) and that it requires less effort. The disadvantage is the increased possibility of being misunderstood and the increased possibility of making logical errors such as equivocation.
I’ve also noticed a tendency to use the word “definition” to refer to explanations of what a portion of reality represented by some word consists of rather than what the word means. That leads to all sorts of problems in communication.
I’d have to know what the purpose of prime numbers is, though. Why is it bad to define the word “prime number” as “a number greater than 1 that is not a product of two smaller natural numbers”?
If there were always only any, “free-floating” definitions, then it would be as if there were also only any, “free-floating” meanings. If neither concepts needed a definition nor words a meaning, then we could not create any theories, do any philosophy, not even talk to each other, because we would then be exposed to something like the “Babylonian confusion of languages”. Everybody thinks and says what everybody wants - well and good, but this must also have limits, because one must at least still know the meanings.
Why is it not okay to define a prime number as it was defined earlier: “a prime number is divisible only by itself and 1”, thus without the new addition of “greater than 1”?
I believe that there are extra-mathematical reasons behind it and the “mathematical reasons” are only pretended reasons (sham reasons). There are interests!
