How did rationalists respond to the logical positivist criticism of a priori knowledge?

Logical positivists challenged rationalism by arguing that a priori knowledge is philosophically trivial, claiming such propositions are merely analytic, linguistic, and conventional—essentially definitions that offer no new information about the world.1

Rationalists responded to this criticism with three primary counterarguments:

• Real vs. Verbal Definitions: Rationalists argued that positivists confuse verbal definitions (which describe words) with real definitions (which describe the nature of objects). They maintained that the thought of a concept, such as a straight line, refers to an object rather than just a linguistic label.1
• Conventions in Thought: Rationalists contended that while one may choose different languages to express a proposition, the underlying proposition itself is not a matter of convention. Once the concept of a straight line is established, it is necessarily the shortest distance between two points; this is a logical requirement, not a choice.1
• Non-analytic A Priori Truths: Rationalists challenged the claim that all a priori statements are analytic. They pointed to examples like "whatever is coloured is extended," where the concepts are distinct; the first entails the second, but the statement is not merely a repetition of the subject term.1