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> axioms are by definition arbitrary. That is very reductive view of what constitutes most axioms. Merriam-Websters has:[1] >2: an established rule or princ

> axioms are by definition arbitrary. That is very reductive view of what constitutes most axioms. Merriam-Websters has:[1] >2: an established rule or principle or a self-evident truth Etymonline has:[2] >"statement of self-evident truth," late 15c., from French axiome, from Latin axioma, from Greek axioma "authority," literally "that which is thought worthy or fit,"... So, no, not arbitrary at all. Which particular axioms do you find arbitrary? Is game theory arbitrary? [1] https://www.merriam-webster.com/dictionary/axiom https://www.merriam-webster.com/dictionary/axiom [2] https://www.etymonline.com/word/axiom https://www.etymonline.com/word/axiom

diogenes4 3y ago
> So, no, not arbitrary at all. Nothing you say conflicts with being arbitrary. Axioms are arbitrarily self-evident—they are "arbitrary" because they are the result of some person's judgement, not somehow produced with some other processes, and they are self-evident because they provide the basis for reasoning and cannot be contradicted within reasoning parameterized by the axioms.
lossolo 3y ago
What OP likely intended is that our Western axioms, such as considering human life as the most important value, may be arbitrary because there are other cultures where it holds a lower position in the hierarchy of values. In Western cultures, the belief in the intrinsic value and sanctity of human life is often considered a foundational and self-evident moral principle. It underlies many ethical and legal frameworks, including principles related to human rights, the value of individual lives, and the importance of protecting life. An axiom, in this context, is a fundamental and self-evident belief or principle that serves as a basis for other beliefs and actions within a particular culture or belief system.
jumpman500 3y ago
Yea a lot of game theory is built on the arbitrary axioms like that people will follow a given strategy with given information, or that there’s common knowledge. In reality people don’t necessarily follow the axioms of the theory.
osti 3y ago
Even in math, axioms are kinda arbitrary. They are mostly defined because they can be used to prove stuff that are perhaps useful, in this sense, they aren't arbitrary. But there are infinite sets of axioms out there for the same branch of math, which makes them rather arbitrary. https://math.stackexchange.com/questions/327201/are-there-infinite-sets-of-axioms https://math.stackexchange.com/questions/327201/are-there-in...
- effed3 3y ago
  chosen, yes, but -not- arbitrary. Axiom are chosen very carefully at the foundation based on all the upper knoweledge, based on these axioms -all- above must be proved (under Goedel blessing), not -some- stuff. Change axiom and you end with -another- math.
afwef 3y ago
By axiom OP meant "assumed truth on which we base all of our other deductions" not "a self-evident truth"

diogenes4 3y ago

> So, no, not arbitrary at all. Nothing you say conflicts with being arbitrary. Axioms are arbitrarily self-evident—they are "arbitrary" because they are the result of some person's judgement, not somehow produced with some other processes, and they are self-evident because they provide the basis for reasoning and cannot be contradicted within reasoning parameterized by the axioms.

lossolo 3y ago

What OP likely intended is that our Western axioms, such as considering human life as the most important value, may be arbitrary because there are other cultures where it holds a lower position in the hierarchy of values. In Western cultures, the belief in the intrinsic value and sanctity of human life is often considered a foundational and self-evident moral principle. It underlies many ethical and legal frameworks, including principles related to human rights, the value of individual lives, and the importance of protecting life. An axiom, in this context, is a fundamental and self-evident belief or principle that serves as a basis for other beliefs and actions within a particular culture or belief system.

jumpman500 3y ago

Yea a lot of game theory is built on the arbitrary axioms like that people will follow a given strategy with given information, or that there’s common knowledge. In reality people don’t necessarily follow the axioms of the theory.

osti 3y ago

Even in math, axioms are kinda arbitrary. They are mostly defined because they can be used to prove stuff that are perhaps useful, in this sense, they aren't arbitrary. But there are infinite sets of axioms out there for the same branch of math, which makes them rather arbitrary. https://math.stackexchange.com/questions/327201/are-there-infinite-sets-of-axioms https://math.stackexchange.com/questions/327201/are-there-in...

effed3 3y ago
chosen, yes, but -not- arbitrary. Axiom are chosen very carefully at the foundation based on all the upper knoweledge, based on these axioms -all- above must be proved (under Goedel blessing), not -some- stuff. Change axiom and you end with -another- math.

afwef 3y ago

By axiom OP meant "assumed truth on which we base all of our other deductions" not "a self-evident truth"