Imparcticle said:
They apply to all that has been tested.
All rules apply to all that has been tested? "All cats are brown" applies to cats. There are rules that apply only to rational numbers, right triangles, chess, nonrelativistic particles, American citizens, etc.
It seems like you think quite quickly, and sometimes too quickly for your own good :) There is something to be said for circumspection, besides that it's a funny word.
Imparcticle said:
By definition infnite is all that there is.
Are you talking about the Universe or a rule that applies to an infinite number of cases?
Imparcticle said:
Is this what you refer to : "All cats are brown except those that are not brown"? I believe this statement is false, because it says "All cats are brown" and goes on to say this excludes those that are not brown. If all cats are brown, then some cannot be another color, correct?
The first statement is redundant, not false. Read it carefully ;)
"All cats are brown" could be changed to "Some cats are brown.", and there are other equivalent ways of saying this same thing.
You could also say "All cats are brown or black or orange or..." and keep adding colors as you observe them. I'm sure you know that this is, more or less, how most physical sciences progress. I find this case interesting because if the list is never considered to be "finished", then it comes close to always having an exception. But some things would have to be clarified before you could say *how close* it comes.
Of course, if you instead throw out "Some cats are brown or black" and replace it with "Some cats are brown or black or red", that is, if you consider the "new and improved" rule as separate from the old rule, then the continuity is lost, and, though there is an exception to every old rule, there is no exception to the new rule.
(Should I have said "there is no *known* exception to the new rule"? This is one thing that needs to be clarified)
Yes, "All cats are brown" and "Some cats are not brown" cannot both be true.
However, "Some cats are brown" and "Some cats are not brown" can both be true.
Happy thoughts
Rachel