erikp writes:
It is absolutely possible to phrase theories that can only be falsified by a finite number of facts. For example, "it will rain tomorrow". This theory can only be falsified by one fact.
"It will rain tomorrow and next week on Monday." This theory can only be falsified by two facts.
"It has rained yesterday and the day before and also the day before that" can only be falsified by three (already known/knowable) facts.
Therefore, theories that can only be falsified by a finite number of facts, do exist. This kind of theories is the only kind that can be proven. This kind of theories can also be completely true.
I haven't read the thread any further than this, so sorry if I'm running behind. But I'd like to address this line of reasoning because you're running exactly into the problem of the "necessarilly limited scope" as I expressed it.
When you state the "theory"
"It will rain tomorrow and next week on Monday.", it might afterwards turn out to be "true" for
you (your
location). But what will
also likely happen afterwards is that somebody will say "This is
false, because I was in New York and it
didn't rain!" So you'll be forced to add a qualifyer like "It will rain
in Berlin tomorrow and next week on Monday." to "save" your theory by limiting the scope.
The point is that there is absolutely no way to know for sure whether such additional qualifyer will be necessary at some point or not, and what kind of qualifyer it will be. Maybe one or more additional qualifyers will be necessary, maybe not. But it
does indicate that (scientific) theories that can be falsified by a limited number of facts, are an illusion. You will never be sure that you've covered all the facts because you'll never be sure your initial "scope" was broad enough.
For this reason it makes no sense to hypothesise (scientific,useful) theories that can be falsified by only a limited number of observations.