According to some web links, the initial 13 rules(?) of basketball are infact axioms. eg:
and

While there might be other basketball specific axioms, I’d like toi focus on one – that if the activity is basketball, then scores are made by making the ball go Through the hole in the top of a “basket”.

The focus here is 2 fold:
The game specifity of the axiom.
The illustration of transmissions between rules and axioms.

Rules and axioms, as the example with basketball’s history shows, may seem similar to the extent of being the same.

I think that while there are indeed similarities – some distinctions are ramarkable. And if a discussion is not about certain rules/axoms – but rather whether these element are rules, axioms, or something else – then perhaps the issue of the transmitting beats between axioms and rules are indeed relevant.

The postulation am proposing is that an axiom is ontological to the element being axiomatized – or the axiom itself.
i.e. an axiom of 2 is that it represents all values of couples. A couple can not be 3 because then it is Not a couple. This is not a rule, but a plausible fact. that fact might have evolved and became specific to our universe – e.g. L. Smolin. I think its a fair point, hence the importance of attempting to disprove the axiom. I am unable, but maybe someone can.
In that ontological way, scoring by making a ball go through a “basket” is a basketball specific axiom. It doesn’t provide a rule but a description of what makes basketball a game of basketball rather than football or tennis.
The fact that most times a ball goes through the “basket”, everyone involved counts it as 2 points is a rule. It can change, we can count as 2.5 or 5 – and the game will still be basketball. Maybe a slightly different version, but of basketball. If we said that points are awarded by crossing a goal line, then we might struggle to still call it basketball.
Right?

Now, if correct, then perhaps the text illustrates the idea of Logical and illogical axioms. The logical ones are considered not specific to one system, the illogical ones are system specific.
Hence the axiom of 2 is a logical one, where as the axiom of scoring in a basketball game is illogical.

Here, I’d like to argue there is a crossing of frequencies, of transmissions between being an axiom and a rule. From the perspective of description opf How to play basketball as a game, ie outside of that game, one checks for definitions, distinctions of that activity. The scoring via “making a basket”, is definitely one of them. The fact this particular element can operate both as an axiom and a rule, is not very important indeed.
Yes?
Say the question is How to play basketball. I might say that one of the goals in the game is to get the ball go through a “basket”. I can also say that this getting through the basket is done by hands. However these 2 elements, from the view of basketball practice and evolution, are not the same. One defines where the game comes from in terms of being itself. The other, defines a rule, a boundary that is relatively temporal and does not define the game as a whole. e.g. to begin with the use of hands was very strict. Nowadays, if the ball happens to come off my arms and into a “basket” – its cool.

While this might seem very trivial, indeed basketball is, I think its a rather less culturally weighted way to consider Rules, Axioms and Religions.
Here, like basketball, my position is currently that religions to be who and what they are, have to hold illogical axioms. e.g. Jesus is the son of god. There is a god. There are gods. There is a god and it is always, everywhere, all knowing, omnipotent and can never have kids. That god sends prophets and Mohammed was the last ever. That it sends prophets and Mohamed wasn’t last ever. (Baha’i..) That there are universal levels and Buddha got in the top one. etc..

The am calling axioms because, as in the basketball example, a christian might fancy the pope as gods rep, and another might consider the pope a religious head honcho rather than a rep. Yet each person’s communities, after years of fighting, of killing and dying, kind of came to agree that they are both christians – but with different rules.

If indeed these axioms in religions are of the illogical kind, then perhaps it might be interesting to compare it to basketball in a different way.
Say the game of basketball was perceived as playable, but deficient, so long as it is not being played in each and every community on earth, or the universe?
ie what if the practice of getting a ball through a “basket” to score –
was seen as having a universal need, in order for it to become true?

In that way, I think perhaps games such as basketball might differ from religions. When we come to the universality requirements, of having a god, of having levels, etc. – that is when the transmissions of games and religions become more distinctive?

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