Final answer:
The development in modern logic regarding propositions and asserting isn't a replacement but an evolution, distinguishing between the content of a proposition and the act of asserting. The theory of truth, particularly the correspondence theory, and the consideration of the speaker's context and intentions, play significant roles.
Step-by-step explanation:
The question you're asking involves the evolution of how propositions are understood in modern logic, as well as their relationship to the act of asserting. The idea wasn't so much a replacement but rather a development in the way philosophers and logicians conceptualize what propositions are and how they function within logical systems. Historically, a proposition in logic is understood as the content of an assertion — in other words, what is being asserted, independent of whether it's spoken or written, and irrespective of the particular linguistic form it may take. The theory of truth most commonly associated with this is the correspondence theory, which posits that a proposition is true when it corresponds with a fact or state of affairs. For instance, the proposition "The cat is on the mat" is true if, in reality, there is indeed a cat on the mat.
However, over time, there emerged a distinction between the content of an assertion (the proposition itself) and the act of asserting that content. The act of asserting involves a speaker committing to the truth of the proposition, and this is a separate matter from the content of the proposition itself. Discussions in philosophy of language and logic have thus broadened to consider the roles of context, speaker intention, and the performative aspects of language. This development enriches our understanding of propositional knowledge, which is about claims that must be capable of being determined to be either true or false. Reading philosophers like David Hume and examining various forms of knowledge, such as propositional knowledge and procedural knowledge, can provide insights into how these ideas evolved. Additionally, looking at Aristotle's interpretation of true statements or exploring Ibn Sina's categorization of propositions reveals the diverse perspectives that historic and modern philosophers have contributed to the subject.