Logical analysis of empirical expressions. What is wrong with empiricism, Pavel Materna

The following well-known problem motivated my handling more general problems: As we surely know our pupils and even students are confronted with much more troubles when learning mathematics (and even physics) than when they learn empirical sciences like biology, mineralogy etc. There are many factors that can at least partially explain this phenomenon, I would however mention one factor that is not too frequently adduced: mathematics, logic and much of physics use concepts that are abstract while the empirical sciences seem to support understanding by using expressions concerning (denoting? expressing?) concrete objects.

Therefore the first topic to be explained (or explicated) is: Abstract vs. concrete. The second point will consist of applying the first point to explanation of the troubles with learning mathematics. The third point will ask Logical Analysis of Natural Language how to tell abstract expressions from the concrete ones.

The fourth point will confront the conception described in the foregoing point with the conceptions trying to abandon the distinction between the analytic and empirical expressions. Here it will be shown that empiricism representing this latter conception deprives semantics as applied to Natural language of important features of expressivity.