Scientific laws as tools for taxonomy

Many people hold that laws of empirical sciences are general hypotheses whose validity is tested by observations. According to them, these kind of tests are done as follows. Given a law, from a conjunction of this law with some other hypotheses several sentences are deduced. These deduced sentences make assertions about phenomena which should be observed at some specified times and places. Then the validity of these assertions are checked. If these phenomena are observed in fact at the specified times and places, the given law is said to have been confirmed by the test. If not and there is no doubt that other hypotheses are valid, then the law is said to have been refuted by the test. In the case where the law has been confirmed by some test, it can be subjected to another test of this kind. Tests of this kind can be repeated again and again till one day the law is refuted by a test. Then the law is said to have been invalidated by experience. In cases where deductions are made in some empirical sciences, logically or mathematically valid sentences are often among premises of the deductions. But even in the cases where deduced sentences are incompatible with observations, usually people would not say that these logical or mathematical sentences have been invalidated by observations. Why? Because most people are ready to keep the validity of logical or mathematical sentences what may happen in experience. In this sense, these sentences are enjoying the status of a priori valid statements. So, logically or mathematically valid sentences are not counted among laws of empirical sciences by the above mentioned people. In other words, as to any law of empirical science they are not sure that it will never invalidated by any test. For them these laws can not be a priori truths. If they are true, they are a posteriori truths.