| | Joe,
You did a great job at articulating the 'scientific method' (as informed by Popper's hypothetico-deductive method of falsificationism). A relevant debate, however, would be whether the scientific method is truly scientific in the first place -- whether hypothetico-deductivism is a "proper" method for science, or for acruing personal knowledge in general. Harriman, in The Logical Leap, decries the hypothetico-deductive enterprise, arguing that something more than that is needed to ground a growing knowledge base.
You outlined a few of the things that one can do when presented with a subset of numbers (4, 6, 8, 12, and 14) and given the chance to ask yes/no questions about the larger set of which it is a part. The point of that is well taken but I'd argue that that was only a few of the things that one can do -- leaving certain other, relevant things off of the table. For instance, if you presented me with those 5 numbers, I could either ask about the outcomes only (Does the superset contain the number 16? Does it contain 3? etc.) or I could take a step back and ask more basic yes/no questions about the very process of number generation for this set.
For instance, I could ask about a possible algorithm used in order to generate the numbers of the set. For example, let's say I asked these 2 questions:
1) Is an equation for generating or filtering the numbers: [all x such that x(n) = x(n-1) + 2]? 2) Is that the only equation?
Now, if I'm lucky -- or if I continue asking until I do get lucky -- then I did not arrive at a hypothesis that has the possibility of being falsified. Instead, I arrived at a full or real knowledge of the set (including numbers never seen or even imagined, let alone experimented on to determine whether they are "in" or "out"). Admittedly, it's a little harder uncovering the nature of something. It is easier to ask about an outcome or result. I'm not saying this method is easier than hypothetico-deductivism, just better. By bypassing the outcomes (e.g., 16, 3, etc.) and going straight to the source of the numbers -- the very "nature" of the set -- I "pass" the test in just 2 questions (if I'm really lucky). Also, by asking both questions, I preclude the possibility of being wrong.
This seems to me to be better than asking endless questions about endless possibilities. Using Popper's method, you never "pass" the test, because you never exhaust all that there is to be imagined.
Ed
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