Ha, hadn’t thought of that but good point.
I think the point (not that I’ve read through the linked commentary thread) is just that what it means for something to be logically necessary is subject to empirical revision—once, it might have been thought that ‘if the train travels at x mph, and I move through it at y mph, then my speed relative to the ground is x + y mph’ is true in an a priori sense, i.e. it could not be different; but then, it was found out that in fact, it may be different. Thus, the point is presumably that one may be mistaken even about such apparently a priori deductions.
However, the example is a bad one: there’s not really any a priori necessity that velocities add. Nevertheless, similar arguments have been proposed, for instance, by Hilary Putnam, who claimed that since the logic of quantum mechanics differs from that of classical mechanics, ultimately, logic may be thought of as being itself empirical, and thus, subject to revision, at least in principle. I don’t think that this is a widely accepted notion, though: most would probably appeal to something like Carnap’s principle of tolerance, which effectively says that there is no ‘true’ logic, but that different logics simply say different things about different things—meaning that if with one logic you derive something that seems to contradict some other logic’s derivation, then you are in fact just not talking about the same kind of thing, i.e. you have somewhere confused your interpretation.
The implicit assumption is that if we have two velocities, v1 = speed of A with respect to B, and v2 = speed of B wrt C, then we can calculate v3 = speed of A wrt C as v1 + v2.
That is, the assumption is that we can add speeds reletive to different references as though they were apples, and the results are as accurate as the inputs.
Newton used this assumption, but I believe he stated it explicitly (just as he explicitly stated his assumption that mass is independent of speed, when calculating momentum). Two strikes against him, but I’m pretty sure they were called out, in Principia.
The assumption turns out to be false, thanks to relativity. From a philosophical standpoint, it doesn’t matter that the discrepancy is too small to measure, or is smaller than other coincident effects (.e.g, reaction to the acceleration of starting to walk – though that’s not really a valid objection.)
The question really ends up being whether Newton articulated the assumption or not. That’s a factual question. Anyone have a well-worn, dog-eared copy of Principia handy?
Irrelevant. The problem states “the train is moving at 20 mph.” It doesn’t matter how that’s accomplished, such as a speed governor that compensates for any forces that slow it down.
If the question had been about jumping from a projectile that had previously been moving at some speed, then the point would be relevant.
We now know that if you are on a normal sized train travelling from Chicago to New york it doesn’t make a difference how fast your are trotting up or down the train, it’s not getting you any faster to your destination:)
Right, like an airplane on a treadmill…
- sneaks up on TriPolar, injects an unknown substance into the base of his neck, hauls the limp body out of the room *