Logic is a curse when applied to anything but logical subjects. Arithmatic is logical and thus requires logical thinking.Although, even in something like physics the 'impossible' becomes possible all the time. There are some people that believe space is comprised of 11 dimensions. How possible is that to the logic of yesterday. But that is a digression from my answer. My simple answer to you is that not everything in life or in the mind is logical and therefore logic is not always required.
Interesting idea - if I'm not misunderstanding you, are you saying that logic is usually one step behind (the latest development in) physics, and that it can't be used for it? If so, I'd argue that once the new rules of physics are discovered, then logic will be applicable to them.
As to what you said about logic not always being required, I'd argue that it is always
applicable provided you have sufficient knowledge about whatever you're applying it to - since by definition, something which not logical (I use illogical from an 'absolute' perspective, *not* as if you ask someone with an IQ of 1 whether orbital dynamics are logical - but as if you ask someone with perfect logical skills and perfect knowledge about physics) is illogical, and hence is *probably* wrong (provided that the basis for your logic is sound - if it isn't, then the 'if you put crap in, you get crap out' thing probably applies). But I may have tied myself in knots here, so I'll shut up now.
And RE: the posts about we can't know anything for sure: I agree, we can't. The possibility always exists that everything we think is just an illusion, and that the entire world is just a fragment of our imagination. But at the end of the day, so what? I think a few assumptions are useful in this thing: namely, we exist, and the world is as it appears to our eyes. Additionally (and this is where I think science comes in), we can make measurements of things in the world and the universe. If we can provide 'reasonable' evidence that your measurements are accurate (such as repeating the measurements, or checking them with other related measurements), then you can use what I guess is a 'projection' of logic called 'mathematics', and use that to make a model which will predict your measurements from a given set of premises. If your model continues to agree with future measurements, then that's more evidence for the model being correct. However if ever it doesn't agree with your observations, then you probably need a new model. In this way, I think logic can be applied to physics - but with the understanding that you may find things which appear illogical, but that they're not really illogical - you just don't understand yet why their logical.
And I think I went completely off track with that last paragraph, but my last sentence pretty much sums up at least some of my opinions on this topic. (I probably should have actually shut up when I said I would earlier
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