This blog post serves to flesh out a small component of one of my recurring concerns: that there is something epistemologically and ontologically special about certain sets of conflicting views (colloquially "disagreements"). I approach this concern by distinguishing between disagreements in the language, and "disagreements" split between the language and the metalanguage.
Consider the following positions, taken between friends Alice and Bob:
Alice: It is raining and cloudy outside.
Bob: It is sunny outside.
Colloquially, we would say that Alice and Bob disagree.
Without diving into the actual fact of the matter, I propose the following formalization for
disagreement: a disagreement
D(X) is the tuple of
<X, ~X> where
X is a statement
"in the language," meaning that
X and its complement both refer to objects in the same formal
Consider a more complicated set of positions:
Alice: Candidate John is the right candidate to vote for.
Bob: It's always wrong to vote for the candidate who will raise taxes.
Given the background knowledge that "Candidate John" is indeed the candidate who will raise taxes,
we would also say that Alice and Bob disagree: their positions boil down to a tuple of
Thus, it's not the case that a disagreement, when vocalized, must be a direct expression of contradicting beliefs: we are content to call beliefs whose entailments conflict "disagreements".
As a relation:
Disagree(Alice, Bob): (Alice's statement entails X) & (Bob's statement entails not X)
But what do we do about this case?
Alice: It is raining and cloudy outside.
Bob: Outside does not exist.
Colloquially, we are again inclined to say that Alice and Bob disagree: after all, their beliefs
are in clear conflict. However, this inclination falls apart under the formalization above:
instead of a tuple of
<X, ~X>, we have something like
<X, ~Language(X)>. In other words:
X, while Bob believes that the statement that Alice's language
exists in (i.e., the system that contains statements like
~X) is not the case. Alice is
in the language, while Bob is in the metalanguage.
Given this, the notion of "disagreement" between these statements becomes tricky: how can Alice "disagree" with Bob when Bob's statement in the metalanguage entails the absence of any sort of meaning (or even the existence of) Alice's statement in the language?
Alice can, of course, produce a statement in the metalanguage that does serve to produce a
disagreement: "Outside exists." But this is a new disagreement, not a resolution of the original
conflict — Alice believes that
X, while Bob's beliefs entail the nonsensibility of even
Under this account, we might revisit our approach to common "disagreements":
Alice: The universe is governed by physical laws.
Bob: The universe is governed by God.
Given the background knowledge that Bob's notion of "God" is one of an omnipotent deity, we can see that we've arrived at another language-metalanguage conflict: Alice would be correct to observe that Bob does not believe that "the universe is not governed by physical laws". Instead, he believes that the notion is nonsense: any "physical law" is purely contingent on God, and so much for any language of physical laws.
More seriously, consider a common refrain among white supremacists: that their opponents are censors, afraid to give them equal standing in a debate lest others are convinced of their position. We can see, in the framework defined above, how this refrain exploits the language-metalanguage divide: white supremacists reject (and know that they reject) the notion of "debate" insofar as they reject the possibility (and, in fact, reality) of being wrong. Thus, there can be no "disagreement" with white supremacists: their statements are statements in a metalanguage, to the effect that my statements in the language (and my own self) should not exist.
I think that this formalization could become central to a formal account of "faithless" or "bad faith" actors: we can see, at the very least, that attempting to present a language-metalanguage conflict as a "disagreement" is a common (if not exclusive) tactic.
I have given relatively little consideration to solutions to this problem. Per the "solipsistic Bob" example, we might think that the correct approach is to promote our own statements into the metalanguage: that the properties associated with Bob's notion of "God" are mutually incompatible, and so "God" does not exist. But, as mentioned, this does not resolve the original conflict. I have no compelling answers.