The steps in an algorithm are also specific and guarantee that you will get the same result every time you follow those steps provided you're operating on the same data. The result you're pursuing is unambiguous: if you're using Djikstra you're trying to get the shortest distance between a source node and every other node in a graph, for instance.
Compare this with consciousness in general: if it is an algorithm, what goal is it being used to achieve? What would the steps even be?
Regarding the point on finitude, "discrete" might have been a more appropriate word. What I'm trying to get at is that people in this thread are playing so fast and loose with the word "algorithm" that the use of the word becomes incoherent '.