This is a presentation of Bolzano's ideas on logic, logical semantics, ontology, proof theory, the foundations of mathematics, and certain aspects of the philosophy of nature. Bolzano's world view was a universal one in the sense that philosophy, mathematics, physics, and metaphysics should build upon the same logical foundation. In the pursuit of this encyclopaedic point of view he already recognized many of the essential things to come in logic and the foundations of mathematics.

The application of semantical concepts such as synonymy and interpretation to actual situations of usage gives rise to perplexing problems. One of the few attempts to tackle these problems has been carried out by Arne Naess. Further advances along this line may become possible after a clarification of the basic concepts employed. The discussion centers around empirical synonymy and certain other notions built on this concept by Naess. Possible ways of making the system coherent are indicated.

In his Wissenschaftslehre Bernard Bolzano tried to lay down a logically satisfactory foundation of mathematics and theory of probability. Thereby he became aware of the distinction between the actual thoughts and judgments of human beings, their linguistic expressions and the abstract propositions {Sätze an sich) and their components. This ontological distinction is fundamental in Bolzano's thinking paired with a universal world view in the sense that philosophy, mathematics, physics and metaphysics should be build upon the same logical foundations. Bolzano's enterprise (...) is sketched in the light of examples from his logical semantics, proof theory, number theory, theory of truth and his variation logic. (shrink)