If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
Notes for future OT posters:
1. Please add the 'open_thread' tag.
2. Check if there is an active Open Thread before posting a new one.
3. Open Threads should be posted in Discussion, and not Main.
4. Open Threads should start on Monday, and end on Sunday.
I have a question about the nature of generalization and abstraction. Human reasoning is commonly split up into two categories: deductive and inductive reasoning. Are all instances of generalization examples of inductive reasoning? If so, does this mean that if you have a deep enough understanding of inductive reasoning, you broadly create "better" abstractions?
For example, generalizing the integers to the rationals satisfies a couple of things: the theoretical need to remove previous restrictions on the operations of subtraction and division, and AFAIK the practical need of representing measurable quantities. This generalization doesn't seem to fit into the examples given here http://en.wikipedia.org/wiki/Inductive_reasoning at first glance, and I was hoping someone could give me some nuggets of insight about this. Or, can someone point out what the evidence is that leads to this inductive conclusion/generalization?
A couple of starting points to improve your investigation.
First, rigorous inductive reasoning, i.e. bayesian probability, includes as a special case deductive reasoning, at least in the case where deductive reasoning is conflated with "classical logic". AFAIK there have been only sparse and timid research into widening probability to fit other kinds of logic.
Second, the example you use to illustrate generalization is a case of what in logic is known as elementary embedding, and it's a pure application of deductive reasoning. Although the process ... (read more)