Talking past each other is an idiomatic expression describing a situation in which people in a discussion proceed at cross purposes. There is a mismatch.

In other words, "those who subscribe to alternative, incommensurable paradigms are bound to a degree to talk past each other."(italics and underline added)

History

The idiomatic expression is an allusion to the interaction between Thrasymachus

Thrasymachus

Thrasymachus was a sophist of Ancient Greece best known as a character in Plato's Republic.-Life, date, and career:...

 and Socrates

Socrates

Socrates was a classical Greek Athenian philosopher. Credited as one of the founders of Western philosophy, he is an enigmatic figure known chiefly through the accounts of later classical writers, especially the writings of his students Plato and Xenophon, and the plays of his contemporary ...

 over the question of "justice" in Plato's Republic I. In their dialogue, neither man addressed any of the issues raised by the other and two different concepts which need not have been disputed are somehow confused.

In common use

In fictional dialogue, when characters "talk past each other, ...[they are said to] expose an unbridgeable gulf between their respective perceptions and intentions. The result is an exchange, but never an interchange, of words in fragmented and cramped utterances..."(italics and underline added)

The phrase is used in widely varying contexts. For example,

• 1917 — Albert Einstein
  Albert Einstein
  Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...
  
   and David Hilbert
  David Hilbert
  David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...
  
   had dawn-to-dusk discussions of physics; and they continued their debate in writing, although Felix Klein
  Felix Klein
  Christian Felix Klein was a German mathematician, known for his work in group theory, function theory, non-Euclidean geometry, and on the connections between geometry and group theory...
  
   records that they talked past each other, as happens not infrequently between simultaneously producing mathematicians."(italics and underline added)

• 2009 — After U.S. President Barack Obama
  Barack Obama
  Barack Hussein Obama II is the 44th and current President of the United States. He is the first African American to hold the office. Obama previously served as a United States Senator from Illinois, from January 2005 until he resigned following his victory in the 2008 presidential election.Born in...
  
  's 2009 speech in Cairo, PBS
  Public Broadcasting Service
  The Public Broadcasting Service is an American non-profit public broadcasting television network with 354 member TV stations in the United States which hold collective ownership. Its headquarters is in Arlington, Virginia....
  
   commentaors discussed the President's address and its potential consequences:

David Brooks

David Brooks

David Brooks may refer to:* David Brooks , American actor and stage director and producer* David Brooks , Australian author of short stories and co-editor for Southerly...

, Columnist

Columnist

A columnist is a journalist who writes for publication in a series, creating an article that usually offers commentary and opinions. Columns appear in newspapers, magazines and other publications, including blogs....

, New York Times: "... I liked it on the whole. You know, if you cover the Middle East

Middle East

The Middle East is a region that encompasses Western Asia and Northern Africa. It is often used as a synonym for Near East, in opposition to Far East...

, you know that there's a lot of shouting there, a lot of people talking past each other. Famously, every group has their own historical narrative which they emphasize while ignoring everyone else's narrative. And I thought Obama did the right thing, which was to go there and give everybody -- everybody's narratives melded into one. Now, it meant he had to squeeze history here and there, but that's fine. He melded it into one so everyone could have a common conversation." (italics and underline added)