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[MarkE]

sarkeizen, YOU stated: " a) A theorem is different than a theory.  A theorem is a mathematical proof."
if you cannot understand that 'a statement', which is ALL a theorem is, is NOT proof by itself, then you may be a very dull knife indeed, likely the dullest in the drawer (at least the drawer that I am in).

A theorem is more than a mere statement.  It is a statement that has been proven.   

If we want to get really stick up the chair pedantic it is incorrect to call a theorem a mathematical proof.  It is not the proof proper.  It is the result of a mathematical proof. 

ETA: Coffee is for proof closers.  Whatever Sarkeizen may or may not be, he/she is definitely not a dull knife.

[sarkeizen]

Somehow over the course of my life I adopted the idea that words are defined by their use.  The way people use the term "theorem" is interesting.  While I agree the most common usage is referencing a statement.  However people - even mathematicians - do use it to reference the proof itself.  To wit people often say "X theorem proved that..." clearly the statement (even a proved one) is not the thing doing the proving.

Semantics aside if memoryman had actually took a few seconds to think about the context of my statement the objection seems even less relevant.  Lumen implies that a theorem and a theory are the same in the sense that a single observation disproves it.  While I might quibble on that statement itself as it implies that observations are never in error.  It's especially wrongheaded when you compare it with something like a proof.  If you were to observe something which runs counter to a proof it's far more likely that either your observation or interpretation is incorrect and switching from "theorem" meaning "proof" to "mathematically proved statement" doesn't alter that.

[profitis]

Sarkeizen:'Are you saying that Philip's machine can't sort?'

It reacts,the result is a sort.react-sort in that sequence and only ever in that sequence.in the same way that throwing ammonium nitrate crystals into water causes it to cool,react(ionization/hydration)-cool(temperature drop below ambient). Please note that while these local (earthly) demons are react in such a way as to result in local entropy reduction the sun's entropy increases much more.nothing wrong with the 2lot,except kelvin statement.like holding a bucket under a waterfall and spontaneously catching some h2o.no big deal

[sarkeizen]

a simple "yes" or "no" may suffice for you; you did not say that it 'may refer to' but 'is'.

Because it is not necessary in English use.   To wit: A dog is a quadruped.  "dog" can refer to a worthless or contemptible person (m-w) without making any comment on their method of locomotion.  Now perhaps, in the linguistic police-state where you grew up they beat you with sticks unless you say "may refer to" in these cases but I assure you, the rest of the world is a (slightly) kinder place.

Also YOUR argument appeared to be "'a statement is ALL a theorem is" which only requires a single reasonable example of an alternate use to falsify.  Since you appear to implicitly agree that if I had said "may refer to" would have made my sentence correct.  You agree that your original argument was wrong.   Feel free to squirm on this a bit if it makes you feel better.

Aside: You assumed that I relied on Wikipedia

It seems likely.

I can give you other sources.

Sources for what?  So far you appear to veer toward and away from a few different arguments:

i) "'a statement is ALL a theorem is" - which you appear to agree is wrong.
ii) The word "theorem" can be used in other senses if and only if preceded by "can refer to" - this again seems to be an argument relying on arbitrarily applying a linguistic rule.
iii) You consulted more than one source to come to your conclusion in i) - This seems to be a disconnect between your premise and what would support it.  You could show me a hundred examples of a word being used or defined in a way but that doesn't say anything about what you relied on to make your decision.
iv) I am wrong in some other vague way which you have yet defined.

Do YOU get to make up definitions?

Sure, as long as I am clear about my use.  Everyone does, it's part of how language evolves.  However to answer the larger question: Did I make up a definition here?  Obviously not.  How I used "theorem" is common enough to be acceptable and does not appear to require any special language in use.

Now there are literally over a thousand posts from me.  It's likely I made an error in there somewhere.  Why not go through those and find one so you can feel better about all this.

[sarkeizen]

Are you saying that Philip's machine can't sort?

It reacts,the result is a sort.

Is the sorting instantaneous?