Greg Browne writes:
The big question is:
How can we know the truth of universal generalizations (All S is P) about kinds (such as "All triangles have angles that had add up to 180 degrees" and "All water is H20") with certainty?
To know them with certainty, or even with probability, requires that they be necessary.
Some, such as Hume, deny that any factual truths are necessary, but they are wrong.
Some who admit that they factual truths can be necessary will still say that we need innate ideas or other a priori aides to know them, that experience is not enough, but they are wrong, too.
So how can we know necessary factual truths empirically (through experience)?
I saw that it is my discovering and analyzing patterns. For example, we encounter several things with triangular surfaces and realize that there is a pattern here, the pattern of being a triangle, or we encounter several cases of water and realize that there is a pattern here, the patter of being water.
Now of course the process is different in these 2 cases. In the case of triangles, we can do it in our armchair (more geometrico). In the case of water, it is much more complex and difficult--and so many don't even think it is possible. Indeed, while we can deduce from the basic concept of a triangle many truths, such as having angles add up to 180 degrees, in the case of water we cannot easily, if it all, deduce the superficial qualities from any one of those superficial qualities: rather, the quality that we can deduce the superficial qualities from--namely, the atomic structure--required a lot of effort and time to discover. Nonetheless, once we have this fundamental quality, we can deduce the other qualities from them.
So in both cases we deduce from concepts, though in the case of water the concepts require a lot more work to discover.
So forming the concept, by discovering the pattern, is key.
And it Aristotle would agree, and call the process by which we discover it "induction". It sounds like Harriman is going to say the same thing.
Note: I do believe that this process can take place by analyzing just one example. For example, if you know that a key does not fit in a lock, then you know that all keys of that shape and size will not fit in that lock--indeed, that they will not fit in any lock of that size and shape. As to the example you gave of Galileo (I am going only by what you said, since I am that familiar with methodology), you said that he tried many tests of hypothesis--but you also added that he tried them in many variations--many different substances and/or many different sizes of ball, etc.
In general, I give the "Continental Rationalists" such as Descartes more credit than do most Randians (or most Aristotelians).
Note: though I think that this demonstrative method works in a much wider range of fields than most do, I admit that sometimes we can only have probabilistic knowledge. For example, we may say that a correlation is so strong that there is probably a necessary causal connection even though we do not yet know what the causal connection is (e.g. aspirin use and pain relief for a century, until recent decades.)
Also, I got the Harriman book today, but I have just started reading it, and these thoughts are from before I got it.