
Conjectures vs. Hypotheses - wslh
http://mathforum.org/library/drmath/view/52249.html
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_delirium
This might be idiosyncratic, but I tend to use 'hypothesis' for conjectures
whose truth is an empirical question, and 'conjecture' for those where that
isn't the case. So I'd 'hypothesize' that rigorous testing would show the
FreeBSD kernel to have good SMP scalability properties up to 32 cores but
perhaps not above that, while I'd 'conjecture' that a particular problem can't
be solved in better than O(n log n) in the general case. The first hypothesis
is one you could confirm or refute empirically, while the second conjecture is
one you could prove or disprove analytically.

In some parts of science 'conjecture' can also be used to give the connotation
of a weaker, less grounded 'hypothesis'. This seems to be particularly used in
astrophysics, where 'conjecture' sometimes means 'very speculative
hypothesis'.

I don't find the distinction _that_ important, though; it's pretty rare that
flipping these two terms causes a real misunderstanding.

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mildtrepidation
I'd say using them interchangeably or incorrectly contributes to people's
misunderstanding of the word hypothesis, which fuels more than a few baseless
arguments against scientific theory in general.

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_delirium
Even correct use of 'hypothesis' doesn't require any particular level of
evidence, though. It's somewhat discipline-specific, but a hypothesis _could_
be a complete guess with no real backing. It's just whatever the experiment is
setting out to confirm or refute. Especially true in fields where it's cheap
to run experiments, in which case the bar for a 'hypothesis' is nearly zero,
amounting to just anything testable that you find interesting to design a test
for.

Perhaps you're thinking of the debate with creationists and similar people
over the term 'theory'?

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atmosx
Marcus du Sautoy has a different approach on the issue, which goes along the
lines:

Conjecture: some evidence there

Hypothesis: strong evidence or very strong evidence, such that sciences would
have accepted the hypothesis as a theorem. The Riemann Hypothesis mentioned,
is the prominent example: Everyone beliefs it's true for more than 100 years,
none has provided a full-featured proof BUT even huge clusters failed to find
a stretch of evidence that might NOT be correct.

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pash
I agree with that distinction. Another notable class of mathematical
"hypotheses" are those, like the continuum hypothesis [0], whose truth is
formally undecideable but that many mathematicians nevertheless believe to be
true in some sense. If this class of statements has any analogue in the
empirical sciences, I guess it must be "unscientific" (untestable) hypotheses,
about which philosophers (or theoretical physicists) might still find
interesting things to say.

Mathematicians also use the word "hypothesis" to refer to a whole implication
in the phrase "inductive hypothesis". But it most often simply means the left
side of an implication: the phrase "A is true by hypothesis" means that A was
assumed to be true—that is, it was the starting point of a proof.

0\.
[https://en.wikipedia.org/wiki/Continuum_hypothesis](https://en.wikipedia.org/wiki/Continuum_hypothesis)

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nraynaud
there is a bit of irony that mathematicians are not really rigorous in the
naming of things :)

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tootie
Wasn't Taniyawa-Shimura proven true?

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thenerdfiles
A conjecture has a propositional attitude while a hypothesis does not. A
conjecture may depend on a system, but it may be true outside of the scope of
that system — think "true but unproved". (Not ___unprovable_ __like a Gödel
sentence!) Once its proof is discovered (made), it becomes a valid hypothesis
of the system by its proof which augments that system 's domain of truth.

A conjecture is _someone 's conjecture_ while a hypothesis is derived from a
system itself ("my system has a valid hypothesis"). We don't "derive
conjectures" from brains, they're made by persons.

When someone says "my hypothesis is", there is an implicit system they are
strictly speaking from (channeling the system? Either way, they're not saying
_what the believe_ but rather placing confidence in their understanding of the
system strictly spoken from) — they're saying that this is provable within the
system we know, but personally they do not have the proof on hand and it may
require a little work. ("I don't know _all_ the rules off hand!")

A conjecture has an implicit system, but the speaker has a purpose to say that
the system _as we know it_ may have a derived rule we have not discovered.
There is "intuition" with conjecture, and "mention" with hypothesis".

