G. E. M. Anscombe writes in An Introduction to Wittgenstein's Tractatus (page 15-16):
Again, the following fallacious piece of reasoning is found in Aristotle: 'All chains of means to ends must terminate in a final end. This final end will be the supreme good.' The first statement is reasonable; the second assumes that the first has shewn that there is some one end, the same for all chains of means to ends, in which they all terminate: the fallacy is immediately avoided by writing:
For all x, if x is a chain of means to ends, there is a y such that y is a final end and x terminates in y,
is a final end and x terminates in y,
which is quite different from:
There is a y such that y is a final end, and for all x, if x is a chain of means to ends, x terminates in y.
- Is there a reference to Aristotle justifying Anscombe's claim?
- Could someone symbolize further the two statements (which I put in italics) showing they are not the same? Part of my problem with symbolizing this is I do not know what the domains of "x" and "y" are. Specifying the domains would be important for the answer.