One has to provide evidence for the propositions advanced in a deductive argument, or alternatively show that they are plausible in light of (a) their consequences and (b) what consilience can be created.
Scientific research works by using all three sorts of of approaches. This has been going on for several hundred years, at least. (Depends on how you characterize science precisely.) For this reason, there is a large body of knowledge from which one can work. (No question can be posed in a presuppositionless context.) The interesting and wonderful aspect of science is that it is self-correcting: what we learn about the world is used to feed into our understandings of procedure and method. There is no circularity because it is a case of consilience and mutual correction and support. There is also no regress for much the same reason.
As for the difference between mathematics and factual science, Rostin is quite right - there is a difference. It is best to see mathematics as a fiction, though as a matter of fact even mathematicians who hold a Platonist view do often adopt a coherence theory of truth, whence the problem suggested goes away. (Model theory is more or less an exactification of this idea.)
Finally, the whole issue about false premisses is crucial for the simple reason that false premisses imply both true and false propositions.
(I could go on and talk about how partial truth is useful to avoid dogmatisms, but I'll stop here.)
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One has to provide evidence for the propositions advanced in a deductive argument, or alternatively show that they are plausible in light of (a) their consequences and (b) what consilience can be created.
Scientific research works by using all three sorts of of approaches. This has been going on for several hundred years, at least. (Depends on how you characterize science precisely.) For this reason, there is a large body of knowledge from which one can work. (No question can be posed in a presuppositionless context.) The interesting and wonderful aspect of science is that it is self-correcting: what we learn about the world is used to feed into our understandings of procedure and method. There is no circularity because it is a case of consilience and mutual correction and support. There is also no regress for much the same reason.
As for the difference between mathematics and factual science, Rostin is quite right - there is a difference. It is best to see mathematics as a fiction, though as a matter of fact even mathematicians who hold a Platonist view do often adopt a coherence theory of truth, whence the problem suggested goes away. (Model theory is more or less an exactification of this idea.)
Finally, the whole issue about false premisses is crucial for the simple reason that false premisses imply both true and false propositions.
(I could go on and talk about how partial truth is useful to avoid dogmatisms, but I'll stop here.)