Why do mechanisms and logic have to be "the same thing" before we can accept that mechanisms can do logic? "Wings" and "flight" are not the same thing but planes and birds can still fly.
There is no question that we build machines to help us with certain tasks; the issue is whether we are relying on anything more than causality among physical things when we do that. Flight is quite well understood in terms of cause and effect. Why would we ever think that a machine, which we built to do what we want through the application of deterministic principles, was ever implementing or "doing" anything more than causality required of it?
When I say logic has inevitability I mean that if you are doing logic correctly (which is to say if you are doing logic at all) then your actions are predictable and inevitable. Like a forced move in chess. Obviously a machine could work in this way.
Strangely, I think the inevitability of logic is what makes it most like free will... the fact that we are able to understand correct logic seems very unlike a forced move. (more on "freedom" below)
So one thing can only be a source of another thing if it is the same kind of thing, is this your contention? And the same similarity must exist if one thing is to be reduced to another thing. But this just rules out all emergent or supervenient properties.
In this sense logic would be a weakly emergent phenomenon of certain configurations of the physical world.
Logic deals only with propositions... a set of premises, and any conclusions drawn from them, are propositions. I have a very hard time imagining what a material proposition might look like. Further, when we consider that logical inference is a capacity or power that we humans possess, which deals with propositions... well, you can see how difficult I find it to think of this as a materially emergent anything.
I would like to delve more into emergence. I do think "emergent property" is a misnomer (i realize you didnt use that phrase, but others do). I will need to re-read what you said in the other thread.
This doesn't follow. Logic is usually better than illogic for creatures like humans as it better aids our survival. Or helps us satisfy desires that originally evolved to aid our survival.
Why is it better? If you say "because it is true", then you are merely presuming its truth... we could deduce that logic is more like a giraffe's neck, or camoflage..., and wonder whether it has any actual truth value. If logic is an evolutionary product, we could just as easily evolve away from it... irrational fanaticism might be the way it will go. I personally think that logic is a better thing than a mere survival aid.
It also does not seem to me that logicians are any better at passing on their genes. Intuition and emotion are much more useful from a survival standpoint (my spouse, for example, does not appreciate when I start applying logic in our relationship

). This last paragraph offered more for humour than anything else...
I don't understand your point here. In as far as the human is doing logic he is also merely doing what he is "designed" to do by his training. Note, if he is doing correct logic then he is not exercising "free will" either (he is not free to infer that 1 + 1 = 3 while still being correct). Of course there may be rather more than just "logic" involved in programming a computer. But you are not arguing that human creativity or emotions make us different from machines so you can't really use that argument.
You mention "training". Logic is not like a technical skill, such as being an electrician, nor is it a matter of collecting facts, like some might view history (not me! no historian onslaught please). Logic is something you see for yourself, even though you may need guidance in order to gain a deep vision of it. A logician sees for himself. My background is originally in mathematics and physics. What astonished me about math was that I could see the truth of propositions which go infinitely beyond the possibilities of materiality.
You bring up free will. The odd thing is not that we are constrained somehow to be logical - as though logic was a straightjacket - but that we are free to be logical... by this I mean the freedom of the human mind to see and assent to the truth. This corresponds to the freedom of the will to assent to the good. Now lets never speak of this again (on this thread anyways... we dont want to invite the wrath of hammegk).
Out of time again... the evolutionary demands of child rearing call...