One frequently, as standard procedure, argues from appropriate premises that "if A then B". If the argument is (logically, as agreed) valid, it establishes "If A then B" logically. This is then knowledge, in most people's view - most people accept the conclusions of valid reasoning, logical truths, as information of a useful kind, as knowledge of the situation.
Note that not even A, let alone B, need be specified in advance - A could be a complicated end product of a very long chain of reasoning from whatever the premises of the whole situation were, and B of course is established by validity of the argument from A.
Example: after a long chain of reasoning the philosopher of natural science concludes that if basement centipedes grow to be the size of wolfhounds then they seriously endanger children. Suppose careful inspection of his reasoning finds it impeccable: given his premises, his conclusion does follow - a logical truth.
And we see that is a bit of knowledge - we do know that if A then B, here. It can even be useful knowledge, as similar conclusions of valid reasoning have been in the past - say: leading to the realization that there was an absence to explain (large predatory centipedes endangering large mammals) and focusing attention on matters that would in fact explain the absence (one or more of his premises is not met in the physical world).
I don't think you quite understood the OP. It seems we're not talking at all about the same thing here.
If I understand what you say, you are talking about a situation where B has been observed to be true whenever A has been observed to be true, which leads you to conclude that the implication A ⇒ B is true. This is your standard empirical method. And if you ever came to observe even one case of B being false while A would be true, you would then discard the implication A ⇒ B as being false, again standard procedure, in fact not only of scientists but of every reasonable person on earth.
Obviously, in this context, establishing the truth of the premise A is absolutely necessary. In science, this will be done presumably by careful observation and, if necessary to that end, by carrying out an experiment or using an experimental setup.
That's all interesting but I already had a fairly good idea of how the scientific method works and that's just all fine with me. So your point is all well and good but apparently entirely beside the point. I'm talking about logical truths, not about the scientific method. And in this case, I fail to see where I would need to use any premise.
Unless you can demonstrate that we tell logical truths using the same modus operandi as you sort of described in your post.
Now, I'd be very interested to see that because if I'm doing anything like this, I would be doing it while being totally unaware I'm doing it, even as I'm trying to find out how I'm doing it. It would truly come as a major revelation to me, somewhat like the sea opening up for Moïse to cross.
It would be a revelation for me but I think it would be a revelation for all those people who do understand what a logical truth is, including quite a few bright minds in the long history of philosophy. They'll be watching this space very carefully I'm sure from wherever in Heaven they must be brooding now.
EB
