Anscombeの哲学三課

(discussing whether a small margin of error for measuring the motion of the ball is possible)
For very small quantities, classical mechanics cannot be used. The author states that the "truth of the system" must be acknowledged in order for mechanics to be used in calculating the results, and that mechanics has not proven to be reliable enough in the domain of small objects for this to occur.
On the other hand, each individual stage of the ball's path (e.g. from one impact to the next) is determined. The author now digresses to precisely define what it means to be "determined". The result is determined if it is derived from an antecedent set of possibilities, of which all but one are disallowed. An example of this is a position on a chess board. There may be five pieces on a side which could be moved on a given turn (the set of possibilities). However, if the king is in check, it may be that only a single move is possible. Thus, the next move is determined by logical antecedence. It may be that an effect is determined by temporal antecedence as well.
The author mentions that Aristotle derived past and present from the fact that something which had already happened was determined.
Returning to the steel ball example, the author indicates that the range of possibilities for its motion in one stage is analogous to the range for a ball which can move to either the left or right of a pin with equal probability. In order for the outcome to be determined, something must narrow the range of possibilities to one.
Without clarifying whether the path of the ball is in fact determined, Anscombe digresses to discuss a hypothetical physicist who desires causality within his experiments, i.e. that only one outcome is possible within his controlled experimental domain. He compares such a physicist with Einstein and Schrodinger. Schrodinger stated that, "the exact physical situation at point P at a given moment t is unambiguously determined by the exact physical situation within a certain surrounding of P at any previous time, say t-tau". Einstein made similar comments about the state of the center of a sphere of radius 186,000 miles (i.e. that you could predict what would happen there in the next second if you understood the sphere). Anscombe's physicist does not express such generalities, and wishes to predict outcomes only in the isolated experiment.
The next discourse discusses misinterpretations of Newtonian physics.