A previous post discusses the relation between Analogy and Logic. Sowa and Majumdar have some insightful things to say about this. I discuss how analogy might be used for semantic role labeling in The Latent Relation Mapping Engine. Lakoff and Núñez talk about metaphor and logic in Where Mathematics Comes From. However, I believe this is only scratching the surface of your question; there’s a lot of research that remains to be done.

Embodiment and Metaphor

Embodiment and Metaphor

“If all the assertions which mathematics puts forward can be derived from one another by formal logic, mathematics cannot amount to anything more than an immense tautology. Logical inference can teach us nothing essentially new, and if everything is to proceed from the principle of identity, everything must be reducible to it. But can we really allow that these theorems which fill so many books serve no other purpose than to say in a roundabout fashion ‘A=A’?” – Pointcare

Here’s what I mean. Consider the following classical example of deductive reasoning:

Premise 1: All men are mortal.
Premise 2: Socrates is a man.
Conclusion: Socrates is mortal.

Slightly more formally:

Premise 1: For all x, if Human(x), then Mortal(x).
Premise 2: Human(Socrates).
Conclusion: Mortal(Socrates).

If the premises here are true, then the conclusion is certainly true. But how do we know that all men are mortal? Where did this knowledge come from? Premise 1 is a much stronger statement than the conclusion. Doesn’t that mean that Premise 1 is more dubious than the conclusion? Perhaps there are other premises from which we can derive Premise 1, but then where do these other premises come from? Ultimately, our foundational premises must come from some sort of non-deductive reasoning (induction, abduction, analogy, or something else), or maybe non-reasoning. This argument shows that the truth-preserving guarantee that we have for deductive reasoning (if the premises are true, then the conclusions are true) is of quite limited value.

Here’s another way of saying the same thing. Science is full of mathematical models, and we know that these models are mathematically true, but are they accurate descriptions of the real world? A typical scientific model has the general form, “If you have situation X and you intervene by doing Y, then the result will be situation Z.” This may be deductively correct, in the sense that X and Y necessarily imply Z, but it’s no use to us in the real world unless we know that X and Y are really true. That is, deductive reasoning has no practical value unless we assume that the premises are true, but we have no way of knowing for sure whether the premises are true.

See Incremental Doubt.

This is called abductive reasoning, which is often concisely defined as “inference to the best explanation.”

Lakoff and Gentner

I liked the idea of looking at the different logics from the evolutionary perspective, I think it is pretty analogous to the evolution of language,
maybe you can draw similar trees ilustrating them evolving.