rewebster said:
I think a lot of slippery slopes aren't seen until another way to get up the hill is found--for example, the Terra-centric view of things to the heliocentric.
I don't think that would be a good slippery slope example, at all.
The heliocentric Copernican model was supposed to be a
radical departure (not a small step) right off the bat to get away from a geocentric model was becoming so overly complex in order to force the model and real world observations to synch up that people were beginning to suspect its validity. The problem is that a Copernican model using circular orbits required just as many epicycles and deferents to make it synch with real world observations as the geocentric model did.
The most likely fallacy to be pointed out about the Copernican model at that time was that it wasn't any improvement over the geocentric theory, so how do you choose between them?
At that time, I don't think there's anyone that would have suggested that a heliocentric model would inevitably lead to a model that used elliptical orbits (if they had, it might have defused some horrible arguments between the two circular orbit models). Proposing elliptical orbits was a rather radical proposition in itself. Perhaps one could say a circular heliocentric model at least made a better model possible, since surely people had thought of elliptical orbits before, but just applied them to the wrong model, but I don't see any kind of inevitability, even in retrospect, other than correct models eventually displace incorrect models when better technology to make observations is developed.
Des Cartes' development of Cartesian coordinates and analytic geometry pushing math down the slippery slope to development of calculus would be a better example. Not only is it a natural extension, but the fact that two different people developed calculus independently nearly simultaneously following DesCartes' work is a pretty strong suggestion of the inevitability.