Michael Dummett (1925-2011) was from the same generation as Putnam and came to prominence about the same time as he did. Much of his best known work argued that meaning is closely tied to the knowledge a speaker possesses, and this paper (pp. 527-534) is devoted largely to exploring how well or poorly this view fits with the ideas you have seen in Putnam. (Although the paper by Putnam he refers to predates the one you read, it contains very similar ideas.)
Before discussing Putnam, Dummett surveys several other positions, and I’ll add a few comments on what he says.
• Frege operated with a somewhat different scheme of concepts than would be found in analytic philosophy typical of the early 20th century. First, although he is responsible for the rejection of Kant’s claim that arithmetic is synthetic, he did hold that geometry was synthetic and thus accepted the existence of some synthetic a priori truths. Second, he had a concept of meaning, usually translated as “sense” that made finer distinctions than does any idea of synonymy tied to analyticity: when two expressions have the same sense, anyone who understands both should be able to see their sameness immediately while analytic equivalence can require proofs that are far from obvious. Putting the two points together, a priori equivalence, analytic equivalence, and equivalence in sense make successively finer distinctions among expressions.
• That Dummett finds something like Frege’s view of sense in Quine is a little surprising since Quine was famously skeptical about the idea of meaning. Dummett’s way of understanding Quine depends on his own understanding of the significance of a metaphor that is found in Quine’s best known expression of his skepticism about meaning, the paper “Two Dogmas of Empiricism.” There Quine tries to counter a picture of rigid ties of meaning among beliefs by depicting beliefs instead as residing in and responding to a “field of force” whose boundary is experience. Dummett takes relative distance from the experiential periphery (and nearness to differing parts of that periphery) to be a central feature of this metaphor and sees it as supporting the idea of ties to experience that differ from sentence to sentence (contrary to Quine’s claim earlier in “Two Dogmas” that no empirical significance could be assigned to sentences individually).