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> Axiom is a fancy word, but popping a few layers off the etymology stack we arrive neatly at the ancient Greek word ἀξίωμα, or "that which is thought fit or wo

> Axiom is a fancy word, but popping a few layers off the etymology stack we arrive neatly at the ancient Greek word ἀξίωμα, or "that which is thought fit or worthy". Pet peeve time. It would be so great if people used the word "axiom" to mean exclusively "I need to blindly assume this is true, otherwise I do not see how can I make any progress". This article contains, I think, author's advices. The dictionaries (and people) usually conflate "a proposition which cannot actually be proved or disproved" with "a self-evident principle"/"an established principle", which looks like a very huge confusion to me. It's like mistaking math and physics. It's like claiming Euclid's fifth axiom is self-evident, when others have already shown this was just an implicitly made decision (hence non-euclidean geometries), which cut off some very interesting, but difficult, mental models. (Quotes are from https://en.wiktionary.org/wiki/axiom https://en.wiktionary.org/wiki/axiom) I wouldn't protest, but I see educated people repeating this confusion over and over like a broken record. Or is there a more precise term in English for those things?

nevinera 6y ago
English is rife with metaphorical or imprecise uses of words with precise meanings, so the rigorous definition of 'axiom' doesn't become relevant in a (non-math-focused) essay very often. But I agree that this list of opinions stretches the term enough that it's a distraction - these are just well-framed observations about the nature of engineering.
- kubanczyk 6y ago
  In my head there is a clear distinction between the axiomatic mode of thinking and the non-axiomatic one. It's fundamental to any mental activity. I cringe anytime I hear "but how can you even prove <non-axiomatic theory>?" or "but why is <an actual axiom> true?". It would be a shame not to have a very precise term for that, so I stick to "axiom" anyway.
  - nevinera 6y ago
    Oh I agree, I've just found it counterproductive to hold others to my personal standards for precision in communication :-)
jmcqk6 6y ago
The problem is that language is not precise, pretty much by evolved design. I totally get the desire for a language with maximum precision and lack of ambiguity, but no one has ever been able to do that successfully. I think it's reasonable to wonder if its even possible. One thing that feeds into it, and is due to the poor way we teach language, is that people think that dictionaries prescribe how we should use language. But that's not what dictionaries are. Dictionaries are descriptive, recording how people are using language. This is a very important distinction. Instead of trying to remove the possibility of ambiguity from language, we should instead focus on gaining the skills to reduce ambiguity through discourse, which we are extremely bad at.
- not_knuth 6y ago
  Totally agree. As programmer's I think we are specifically enclined to attempts of formalizing natural language into something precise and reducing it to syntax and semantics. Yet like you say, natural language is imprecise. And the more I think about how much of a bodge the way we communicate is, the more impressed I am we can have conversations at all. All those layers of indirection, wtf? But of course for almost every layer of indirection there is a safety net, that assures the meaning of what is said is passed on: If I mumble, my body language will help you figure out what I'm trying to say. If write gbbrsh sntce, context make you understand. And if you can't hear me, you can probably make out what I'm saying by lip reading.
petters 6y ago
It's always nice when you want to make a comment and it's already the top one. Happens a lot on HN. Indeed, some of these are possible to falsify with experiments. For example: > 14. A good type system is worth its weight plus some. See e.g. what Dan Luu has written on this subject.
chrisweekly 6y ago
IMHO, given the author labelled them "my ... axioms", it's natural to infer that they are principles which the author personally considers foundational. It's a context that's orthogonal to scientific terminology (as in Euclid's 5th). And in natural language, context is everything.

nevinera 6y ago

English is rife with metaphorical or imprecise uses of words with precise meanings, so the rigorous definition of 'axiom' doesn't become relevant in a (non-math-focused) essay very often. But I agree that this list of opinions stretches the term enough that it's a distraction - these are just well-framed observations about the nature of engineering.

kubanczyk 6y ago
In my head there is a clear distinction between the axiomatic mode of thinking and the non-axiomatic one. It's fundamental to any mental activity. I cringe anytime I hear "but how can you even prove <non-axiomatic theory>?" or "but why is <an actual axiom> true?". It would be a shame not to have a very precise term for that, so I stick to "axiom" anyway.
- nevinera 6y ago
  Oh I agree, I've just found it counterproductive to hold others to my personal standards for precision in communication :-)

jmcqk6 6y ago

The problem is that language is not precise, pretty much by evolved design. I totally get the desire for a language with maximum precision and lack of ambiguity, but no one has ever been able to do that successfully. I think it's reasonable to wonder if its even possible. One thing that feeds into it, and is due to the poor way we teach language, is that people think that dictionaries prescribe how we should use language. But that's not what dictionaries are. Dictionaries are descriptive, recording how people are using language. This is a very important distinction. Instead of trying to remove the possibility of ambiguity from language, we should instead focus on gaining the skills to reduce ambiguity through discourse, which we are extremely bad at.

not_knuth 6y ago
Totally agree. As programmer's I think we are specifically enclined to attempts of formalizing natural language into something precise and reducing it to syntax and semantics. Yet like you say, natural language is imprecise. And the more I think about how much of a bodge the way we communicate is, the more impressed I am we can have conversations at all. All those layers of indirection, wtf? But of course for almost every layer of indirection there is a safety net, that assures the meaning of what is said is passed on: If I mumble, my body language will help you figure out what I'm trying to say. If write gbbrsh sntce, context make you understand. And if you can't hear me, you can probably make out what I'm saying by lip reading.

petters 6y ago

It's always nice when you want to make a comment and it's already the top one. Happens a lot on HN. Indeed, some of these are possible to falsify with experiments. For example: > 14. A good type system is worth its weight plus some. See e.g. what Dan Luu has written on this subject.

chrisweekly 6y ago

IMHO, given the author labelled them "my ... axioms", it's natural to infer that they are principles which the author personally considers foundational. It's a context that's orthogonal to scientific terminology (as in Euclid's 5th). And in natural language, context is everything.