Einstein’s theory of relativity led to an entirely different understanding of Galileo’s law. Thus, when we examine the history of the law of falling bodies that Friedman alludes to and then ignores we find that all of the major advances in the physical sciences that have come about since the time of Galileo were accomplished as a result of 1) Galileo rejecting the “In so far as a theory can be said to have “assumptions” at all, and in so far as their “realism” can be judged independently of the validity of predictions, the relation between the significance of a theory and the “realism” of its “assumptions” is almost the opposite of that suggested by the view under criticism.
Truly important and significant hypotheses will be found to have “assumptions” that are wildly inaccurate descriptive representations of reality, and, in general, the more significant the theory, the more unrealistic the assumptions (in this sense). 14)” The Irrelevance of Logic in Friedman’s Methodology The degree to which Friedman’s arguments are totally oblivious to the central role played by assumptions in scientific inquiry is indicated by his delineation of this role as he sees it: sophisticated those explanations based on false assumptions may seem to be.
All that matters is the accuracy of a theory’s predictions, not whether or not its assumptions are true. The only thing that matters is the accuracy of the predictions obtained if we they are falling in a vacuum.
He attempts to demonstrate this by examining “the law of falling bodies” where he tells us that it “is an accepted hypothesis that the acceleration of a body dropped in a vacuum is a constant—g, or approximately 32 feet per second per second on the earth . It is the role of the scientist to “to specify the circumstances under which the formula works or, more precisely, the general magnitude of the error in its predictions under various circumstances.” Even though a more general theory exists that can give more accurate predictions “it does not always pay to use the more general theory because the extra accuracy it yields may not justify the extra cost.” [Friedman (pp.
“Consider the problem of predicting the shots made by an expert billiard player. complicated mathematical formulas” may be an interesting analogy, but it tells us nothing about billiard players.
It seems not at all unreasonable that excellent predictions would be yielded by the hypothesis that the billiard player made his shots as if he knew the complicated mathematical formulas that would give the optimum directions of travel, could estimate accurately by eye the angles, etc., describing the location of the balls, could make lightning calculations from the formulas, and could then make the balls travel in the direction indicated by the formulas. It was obvious to me at the time that Friedman’s argument to the contrary is circular: How do we know expert players play this way?
This understanding differed from Galileo’s in that Galileo had that there is an inverse-square relationship between the force of gravity and the distance between the centers of gravity of the earth and a falling body.
These two assumptions, taken together, imply that the rate of acceleration must increase as a falling body and earth approach each other. 398, 83)] Thus to make Galileo’s law of falling bodies that the rate of acceleration increases as the falling body and earth approach each other in accordance with Newton’s theory of gravity and second law of motion.
It is the form of a logical argument that makes it valid, irrespective of the truth of its premises.
The argument a) all men with blue eyes are infallible, b) I have blue eyes, therefore, c) I am infallible is meaning, in spite of its logical validity and my blue eyes, because it is based on the demonstrably false premise that all men with blue eyes are infallible.