Well, that’s not entirely true. If someone demanded a justification and your response was “It’s obvious” then you’ve done something wrong. But in absence of such a demand, it’s a perfectly fine justification. You have to start from somewhere.
It doesn’t matter if they felt obvious or non-obvious. Obviousness is not justification, it is an opinion about its accessibility. To be fair to you, I am mostly annoyed by that word alone. I could be way off the mark here in terms of common opinion.
Indeed. When I was a student, I often found myself telling my classmates in math classes, “Just because it is obvious does not mean it is true.” It was amazing how many “obvious” conclusions we were able to disprove.
Justification usually requires more than “It’s obvious!” That is the whole point of justification.
Well, that’s not entirely true. If someone demanded a justification and your response was “It’s obvious” then you’ve done something wrong. But in absence of such a demand, it’s a perfectly fine justification. You have to start from somewhere.
Somewhere is not “It’s obvious!” 2 + 2 = 4 is not obvious. It is a definition. (Edit) Yeah, uh, theorem.
But I see and agree with your point. I am merely arguing semantics now, which is not particularly useful.
I do stand by my original claim, however, that justification usually requires more than “It’s obvious!”
Strictly speaking, it is a theorem (obvious one). 4=3+1 is a definition.
I thought “4 comes after 3” was a definition and “3+1 = 4″ was a theorem.
Which instances of “obvious” in the text felt non-obvious to you?
It doesn’t matter if they felt obvious or non-obvious. Obviousness is not justification, it is an opinion about its accessibility. To be fair to you, I am mostly annoyed by that word alone. I could be way off the mark here in terms of common opinion.
You’re not the only one annoyed by that word.
As my first real analysis professor was fond of saying, “If it’s obvious, prove it!”
Indeed. When I was a student, I often found myself telling my classmates in math classes, “Just because it is obvious does not mean it is true.” It was amazing how many “obvious” conclusions we were able to disprove.