If you limit yourself to deductively valid arguments - as it seems you are - then you cannot do science. Indeed you can have no knowledge at all about any external reality - you cannot even knwo that there is one.
Science takes a more pragmatic view and holds that induction is valid, that there is an external reality and that we can derive data from it via our senses. (Or rather most scientists would - there are other valid viewpoints, notably instrumentalism).
The Bayesian viewpoint offers one validation of induction that - even if you do not buy the whole Bayesian package - at least offers good reason to accept that induction can offer all-but-certain proof (if you have enough data).
™ Version 4.2
