Carnap believed that the difficulty with traditional philosophy lay in the use of concepts that are not useful for science. For Carnap, the scientific legitimacy of these concepts was doubtful, because the sentences containing them do not express facts. Indeed, a logical analysis of those sentences proves that they do not convey the meaning of states of affairs. In other words, theses sentences are meaningless. Carnap explains that to be meaningful, a sentence should be factual. It can be so, for one thing, by being based on experience, i.e. by being formulated with words relating to direct observations. For another, a sentence is factual if one can clearly state what are the observations that could confirm or disconfirm that sentence. After all, Carnap presupposes a specific criterion of meaning, namely the Wittgensteinian principle of verifiability. Indeed, he requires, as a precondition of meaningfulness, that all sentences be verifiable, which implies that a sentence is meaningful only if there is a way to verify if it is true or false. To verify a sentence, one needs to expound the empirical conditions and circumstances that would establish the truth of the sentence. As a result, it is clear for Carnap that metaphysical sentences are meaningless. They include concepts like “god”, “soul” and “the absolute” that transcend experience and cannot be traced back or connected to direct observations. Because those sentences cannot be verified in any way, Carnap suggests that science, as well as philosophy, should neither consider nor contain them.
The logical syntax of language is a formal theory. It is not concerned with the contextualized meaning or the truth-value of sentences. In contrast, it considers the general structure of a given language and explores the different structural relations that connect the elements of that language. Hence, by explaining the different operations that allow specific transformations within the language, the theory is a systematic exposition of the rules that operate within that language. In fact, the basic function of these rules is to provide the principles to safeguard coherence, to avoid contradictions and to deduce justified conclusions. Carnap sees language as a calculus. This calculus is a systematic arrangement of symbols and relations. The symbols of the language are organized according to the class they belong to and it is through their combination that we can form sentences. The relations are different conditions under which a sentence can be said to follow, or to be the consequence, of another sentence. The definitions included in the calculus state the conditions under which a sentence can be considered of a certain type and how those sentences can be transformed. We can see the logical syntax as a method of formal transformation, i.e. a method for calculating and reasoning with symbols.
It is in the logical syntax that Carnap introduces his notable principle of tolerance. This principle suggests that there is no moral in logic. When it comes to using a language, there is no good or bad, fundamentally true or false. In this perspective, the philosopher's task is not to bring authoritative interdicts prohibiting the use of certain concepts. In contrast, philosophers should seek general agreements over the relevance of certain logical devices. According to Carnap, those agreements are possible only through the detailed presentation of the meaning and use of the expressions of a language. In other words, Carnap believes that every logical language is correct only if this language is supported by exact definitions and not by philosophical presumptions. Carnap embraces a formal conventionalism. That implies that formal languages are constructed and that everyone is free to choose the language it finds more suited to his purpose. There should not be any controversy over which language is the correct language; what matters is agreeing over which language best suits a particular purpose. Carnap explains that the choice of a language should be guided according to the security it provides against logical inconsistency. Furthermore, practical elements like simplicity and fruitfulness in certain tasks influence the choice of a language. Clearly enough, the principle of tolerance was a sophisticated device introduced by Carnap to dismiss any form of dogmatism in philosophy.
Clearly, the probability of a statement about relative frequency can be unknown; because it depends on the observation of certain phenomena, one may not possess the information needed to establish the value of that probability. Consequently, the value of that statement can be confirmed only if it is corroborated with facts. In contrast, the probability of a statement about the degree of confirmation could be unknown, in the sense that one may miss the correct logical method to evaluate its exact value. But, such a statement can always receive a certain logical value, given the fact that this value only depends on the meaning of its symbols.
More than 1,000 pages of lecture outlines are preserved that cover the courses that Carnap taught in the United States, Prague, and Vienna. Drafts of his published works and unpublished works are part of the collection.