On 08/02/2014 09:00 AM, Chris Cain wrote:
On Saturday, 2 August 2014 at 06:36:00 UTC, Timon Gehr wrote:
http://en.wikipedia.org/wiki/Falsifiability
^^ See?
"A statement is called falsifiable if it is possible to conceive an
observation or an argument which proves the statement in question to
be false."
If we have proven the statement true, we won't readily deem it
possible to conceive an observation or argument which proves the
statement in question to be false.
It's an important part of science that there is the possibility
of proving it false.
Not exactly. The article is stating that it should be conceivable that
there might be an argument or an observation proving it false. But
that often holds simply because we cannot prove properties of reality
to hold. It is conceivable that gravity will not exist tomorrow and
this would falsify many theories of physics. I don't really believe
that this will happen, but it is conceivable.
That *doesn't* imply it *is* false, though.
Likewise for verifiability (they're really just synonyms, which should
really show you that there actually existing both a proof for truth and
falseness doesn't make sense)
http://www.synonym.com/synonyms/falsifiable/ -> verifiable is a synonym.
...
Thanks! My hypothesis that verifiable/falsifiable are just idioms not
extending to verify/falsify is not shattered by this though.
Perhaps I just don't understand what you're getting at. It seems
throughout that you are thinking "statements of fact" has a meaning that
it's inherently true and is proven or must be proven.
...
No, this you made clear already. (However, the post with the explosions
was still warranted from my viewpoint, because the terminology was
accidentally changed by you and I didn't notice and just implicitly
assumed the two expressions were intended to be synonyms.)
It seems to me that you've suggested:
If falsifiable -> can be proven to be false -> must be proven false ->
is false
and
If verifiable -> can be proven to be true -> must be proven true -> is true
(falsifiable == verifiable)
(can be proven to be false == can be proven to be true)
(false == true) is trivially false.
...
No, I have suggested that _maybe_
verify != falsify
but that idiomatic usage of
verifiable == falsifiable.
...
If you disagree with my conclusion, I don't
think there's any more that we can communicate to each other about it. I
totally understand why you think asserts meant that you wanted the
compiler to check before (because that was my understanding originally),
but this way makes much more sense and simplifies my mental model of the
world. I no longer have to keep two (not-so) subtly different
definitions in my head of what programming-assert means and
English-assert means. Now they mean the same thing, which I'm pretty
happy about overall.
...
Indeed, I still disagree with this conclusion, so let's put this aside
for now, unless you see another point to discuss. Thanks for having been
a reasonable discussion partner.
It is not so clear where to draw the boundaries. In some languages you
may need to prove the assertion true in order for it to pass the type
checker.
That would be a cool construct as well, don't get me wrong. But
considering the vast majority of programs could not reasonably have such
proofs, I think the two concepts are orthogonal. I'd rename that to a
"prove" statement and not an "assert" because assert has nothing to do
with checking and conflating the two has caused confusion.
Well, this was just noting an existing reality that many people with a
CS background might have been exposed to.
