Rice's Theorem Wikipedia article wrong definition https://en.wikipedia.org/wiki/Rice%27s_theorem
Linked above is the wiki article in question.
The section name "Proof by reduction to the halting problem" is not correct, right? It should be "reducing the halting problem to our problem", not the other way around, right? Otherwise it doesn't make sense (reducing to the halting problem doesn't make sense, it should be the other way around).
 A: This is a community wiki post for the record.
When we say that we "reduce a problem $A$ to a problem $B$", we mean that we have a way of converting instances of $A$ to instances of $B$ so that if we could solve $B$ then we would also be able to solve $A$. There are several kinds of reductions, including many-one reductions and Turing reductions, but they all act in this way.
In the case of Rice's theorem, one proof goes like this: given a nontrivial property $P$ of functions, the proof shows that if we were able to decide which programs compute functions in $P$, then we would be able to solve the Halting problem. So the proof constructs a reduction of the Halting problem to the problem of telling whether a particular program computes a function in $P$. 
The way that the Wikipedia article is presently worded is confusing in several ways (link to current version). But it does seem to phrase things backwards: the proof reduces the Halting problem to another problem, rather than reducing another problem to the Halting problem.
Actually, there are nontrivial properties of a function that are not reducible to the Halting problem. For example, let $I$ be the set of programs that compute a function with an infinite range. Then $I$ is not computable, by Rice's theorem. But $I$ is also not computable even with an oracle for the Halting problem, because the Turing degree of $I$ is known to be the Turing jump of the Halting problem, which cannot be computable from the Halting problem.  So it is not possible, in general, to reduce the kind of problem that comes up in Rice's theorem 
to the Halting problem.
