Last Update: Sunday, 27 March 2022 |
Although this premise is Knuth's explication of 'algorithm', the rest of this argument is mine, not his. |
Note: We can also say that A is an algorithm for computing a function f means that A is an algorithm as characterized above and that, for any input i, A's output for i = f's output for i; that is, for any i, A(i) = f(i).
And so on.
So, if you ever come across an argument that you think is sound, but whose conclusion you don't believe, then either:
To determine whether it is valid, you must suppose "for the sake of the argument" that all the premises are true, and then consider whether the conclusions logically follow from them.
(Or: Can you imagine some way the world might be so that the premises are true but the conclusion is false?)
Note that, in this argument, there are two conclusions: conclusion 5 and conclusion 6.
Or you might think that there's something wrong with the argument but agree with the conclusion anyway;
Or you might not agree with the conclusion(s);
As before, this doesn't have to be a beautifully written essay with an abstract. You should just plunge in and evaluate the argument.
But you do need to give full citations to any sources that you cite.
Spend no more than 15 minutes per paper (because you've only got about 45 minutes at most).
Perhaps one member of the group can be a timekeeper.
So, in disagreeing with premise 1, an author must