Is Logic Really Based on Mathematics? A Question for Scientists

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Alexx.
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Lately I've been through a matter that seemed quite ridiculous at the beginning.
I believe I'm aware of what both Logic and Mathematics are. But I've come across people defending that Logic is not based on Mathematics, and as well that all Sciences need to be based on Mathematics or either they are not Science.
Science is the language of nature, so I'm sure everything is either directly or indirectly based on Mathematics. But I'm lost as to how to explain people that Logic IS indeed based on it, more than indirectly; A Mathematical reasoning is not only using numbers to think, and to live, is it?
I might however be also wrong, but until now I do keep my arguments.
So, if somebody thinks so as well, I ask to aid me on said matter. Explaining how everything, and more specifically Logic is based on Mathematics, that is.
Beforehand, thanks everyone in the Physics Forums.
 

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Frankly I can't make heads or tails out of this.

You state: "But I've come across people defending that Logic is not based on Mathematics, and as well that all Sciences need to be based on Mathematics or either they are not Science."

Well, I'm one of those people and I am a mathematician!

You can set up a form of "logic" that is based on mathematics, or you can set up a different basis for logic and then base mathematics on that- it's all a matter of "style".

Science doesn't have to be "based" on mathematics- although, certainly, mathematics makes it easier to write clear, precise, statements.
 
Of course logic is not based on mathematics. You have it backwards. Mathematics is based on logic.