I bet you people can't even agree on what "axiom" means.
>>23315741That which is axiomatic
self evident propositions like lines are straight, triangles have three sides
A fancier platitude
An intellectual "Here be dragons".
The event horizon of discourse.
Necessary arbitrariness.
>>23315741Who cares? Not literature, you pseud.
>>23315741Cow farts - no one hears. Why?
>>23315762They're not self-evident, but rather imposed.
>>23316096imposed by whom?
>>23316144Whoever defined it.
>>23316144>>23316149Also by those who believe in it. Belief is imposal after all.
>>23316096Impositions are voluntary so that doesn't follow. There's a difference btn saying god is the truth and saying that lines are straight. The former is vague, the latter self evident from language use.
>>23316179>lines are straightThat's a definition for what a "line" is. It's something "straight". It isn't self-evident until it is defined as so and "accepted", as in imposed. The same applies to "triangle", it's defined as something with "3" "sides".
>>23316184Not necessarily, lines in non-euclidean geometry are not always straight so you need to make this distinction when jumping btn the two. Also 'something' straight may mean a flat plane as opposed to a wobbly one, its not self evident or obvious to anyone.
>>23316196That's besides my point, I just used the examples you provided. I guess there's misconception going on here with the term "axiom". You meant it as a mathematical term, right? I meant it as in postulate or assumption, t general idea of a arbitrary bedrock on which arguments are built upon.
>>23316210And your point doesn't refute mine. Axioms are self evident atomic propositions like x=x, which is not a definition, that is also not an imposition, it is something you presuppose in your thinking and language use, no one imposed it on you, you could say reality did, but that wouldn't be the same thing.
>>23316219>no one imposed it on youI agree, I'm saying (You) impose it. Isn't presupposing precisely imposing? Axioms aren't found, they're just decided as so.
>>23316230But that's just it, reality imposes it on you, you discover this, just like you discover that lime is bitter and sugar is sweet.
>>23316230Presupposing to me means, you rely on it unconsciously, not that you have any say in it.
>>23316231>>23316241Would you consider the law of non-contradiction to be an axiom? I think it's something decidedly imposed, even if it usually is unconscious in the sense that it's inferred from how logic is commonly applied. Your point about tastes being discovered axioms does make sense.
>>23316231Also, what do you think about this:>cilantro tastes soapy>cilantro does not taste soapyThere's no objective way to taste it due to genetics, so you can't generalize an universal axiom for it.
>>23316254>>23316310I think axioms mostly apply to deduction, when you try applying them inductively or subjectively they will break down because that depends on time.
in regards to mathematics (the only subject that matters) an axiom is the unproven starting point to our systemsit is not self evident, thats something idiots say to try to get out of explaining themselves (most people dont even know what their saying)to say "self evident" you mean "definitional" ie: to be a line, is to be straightso lines are straightthis isnt a working system as it works on circular logic, its only rigorous if you openly admit the straightness of the line remains unproven, because ofcouse, it isyou can never prove the line to be straight, as to show straightness, you need something straight to compare to
>>23315741Uhhh 1. A proposition that commends itself to general acceptance; a well-established or universally-conceded principle; a maxim, rule, law.2. Logic. A proposition (whether true or false).3. Logic and Math. `A self-evident proposition, requiring no formal demonstration to prove its truth, but received and assented to as soon as mentioned' (Hutton).
I’m sorry if my ten dollar word offended you hemmingway No (you) granted
Axioms for a system S are sentence-forms instances of which are taken to be valid without justification in proving theorems of S.
>>23315741Fundamentally, an axiom is something we take as true in order to stop an infinite regress.Practically, these consist of principles and ideas that are impossible to refute and generally impossible to prove, but have very strong evidence for their existence.
>>23316802lmao there is nothing straighter than a line retard, there is nothing to compare against.
>>23316219Axioms don't have to be self evident. I can axiomatize an algebraic structure with 1 as its only element and it will be well defined in mathematical terms. I can also axiomatize the game of chess. How our axioms relate to the real world is a difficult question, there seems to be something specianl about e.g. the natural numbers but from the axioms themselves can't explain that.
>>23319371Algebra does not have axioms, it relies on arithmetic and set theory for that, algebra has definitions and theorems, corollaries, lemmas, propositions, etc.
>>23319563Are you sure? My professor called them axioms, but my degree is in CS and not mathematics. Wikipedia seems to agree with me (not the best source but usually correct about basic mathematics)
>>23320046The one you axiomatize would apply to arithmetic not algebra, if you assumed one as the only element, it would violate the peano axioms of arithmetic which requires that one has a successor for the natural numbers to follow. You would not be doing algebra with only one element.
>>23320085I think that's only true in elementary algebra, I was talking about abstract algebra which deals with many different algebraic structures. A vector space for instance is an algebraic structure that you can analyse and it's based on different axioms than the natural numbers.My structure is a Abelsh group with 1 + 1 = 1. It's boring but afaik correct.
>>23320172I don't know, addition requires peano's axioms even if the result isn't 2 or three, the successor function or operator is a peano axiom, any operation that involves more than one number requires these axioms.
