SIMP. Your discussion is really admirable; yet I do not find it easy to believe that a bird-shot falls as swiftly as a cannon ball.
SALV. Why not say a grain of sand as rapidly as a grindstone? But, Simplicio, I trust you will not follow the example of many others who divert the discussion from its main intent and fasten upon some statement of mine which lacks a hairsbreadth of the truth and, under this hair, hide the fault of another which is as big as a ship's cable. Aristotle says that "an iron ball of one hundred pounds falling from a height of one hundred cubits reaches the ground before a one-pound ball has fallen a single cubit." I say that they arrive at the same time. You find, on making the experiment, that the larger outstrips the smaller by two finger-breadths, that is, when the larger has reached the ground, the other is short of it by two finger-breadths; now you would not hide behind these two fingers the ninety-nine cubits of Aristotle, nor would you mention my small error and at the same time pass over in silence his very large one. Aristotle declares that bodies of different weights, in the same medium, travel (in so far as their motion depends upon gravity) with speeds which are proportional to their weights; this he illustrates by use of bodies in which it is possible to perceive the
pure and unadulterated effect of gravity,
eliminating other considerations, for example, figure as being of small importance [minimi momenti], influences which are greatly dependent upon the medium which modifies the single effect of gravity alone. Thus we observe that gold, the densest of all substances, when beaten out into a very thin leaf, goes floating through the air; the same thing happens with stone when ground into a very fine powder. But if you wish to maintain the general proposition you will have to show that the same ratio of speeds is preserved in the case of all
heavy bodies, and that a stone of twenty pounds moves ten times as rapidly as one of two; but I claim that this is false and that, if they fall from a height of fifty or a hundred cubits, they will reach the earth at the same moment.
在我看来,伽利略的成功之处,就在于他意识到,亚氏的论断中包括了太多因素的作用,因此很难得到一个一般规律(由轻物得到的规律不能应用于重物,反之亦然)。因此,他特意地只讨论重物下落,使得其它因素可以忽略,从而能够找到自由落体的一般规律。这正是科学还原法的一次伟大胜利。
是的,如果仅仅只看前面他对于思想实验的表述,很难说是严格的。但是,“严格”地说,伽利略并没有给出一个数学形式的“定理”或“定律”,而是以对话的形式阐述他的思想和他观察、总结出来的自然规律。因此,“不严格”地说,寻找伽利略的逻辑漏洞的过程,很有可能成为一个对伽利略思想随意打扮的过程。