Summary of my second amendment paper

I've made some promises to some people about trying to summarize my paper about the linguistics of the second amendment. Here is my attempt. The full paper is available here (the website makes you wait 90 seconds before downloading, since I signed up for a free membership; the delay is their way of motivating people to get paid memberships).

The issue is as follows: In the Supreme Court case of D.C. v. Heller (discussed previously on this blog here, here and here), Justice Scalia, author of the majority opinion, and Justice Stevens, author of one of the two dissents, disagree over whether the absence of the word to, bracketed in the following, is semantically significant.

The right of the people to keep and [to] bear arms shall not be infringed.

Justice Stevens reports the intuition that the absence of to supports the conception that the amendment does not protect two separate rights, but rather a single right,

a right to have arms available and ready for military service, and to use them for military purposes when necessary.

Justice Scalia disagrees:

JUSTICE STEVENS resorts to the bizarre argument that because the word "to" is not included before "bear" (whereas it is included before "petition" in the First Amendment), the unitary meaning of "to keep and bear" is established. Post, at 16, n. 13. We have never heard of the proposition that omitting repetition of the "to" causes two verbs with different meanings to become one. A promise "to support and to defend the Constitution of the United States" is not a whit different from a promise "to support and defend the Constitution of the United States."

Both Stevens and Scalia appear to be correct in the judgments that they report, which means that as far as interpreting the Constitition, Stevens is correct and Scalia is incorrect. Scalia makes the error of dismissing an English speaker's intuition about the language of the second amendment by theorizing about linguistics. The purpose of my paper is to show why Scalia's reasoning about linguistics is wrong.

The task, then, is to identify the property of the sentences that makes the presence of to significant in the Constitution, but not significant in Scalia's example sentences. I argue that of the various differences between the sentence pairs (such as the definiteness or indefiniteness of the phrase, and the definiteness and plurality of the object [arms vs. the Constitution of the United States]), the key difference is between right and promise, and the important difference between these two modal nouns is the quantificational force - the fact that right denotes an existential modal noun while promise denotes a universal modal noun.

That the difference is due to right and promise is evidenced by the following sentence pairs, where the sentences are to the extent possible held constant except for right vs. promise, and the presence vs. absence of to.

Right:

a. Workers have the right to unionize and strike

b. Workers have the right to unionize and to strike

Promise:

a. The workers made a promise to unionize and strike

b. The workers made a promise to unionize and to strike

In the case of right, there is a clear truth-conditional difference between the sentences. The (a) sentence does not seem to be asserting an absolute right to strike; rather, the right to do so is contingent on their first having unionized. In the (b) sentence, the right to strike is unconditional.

In the case of promise, there is no such difference. In both (a) and (b) there are two independent promises. If the workers made the promise in (a) and then broke their promise to unionize, their commitment to strike still stands.

So the question is why right is different from promise. As I've suggested, my approach is that it has to do with the quantificational difference between the terms. Right is an existential modal: X has a right to do R if in some possible world consistent with X's rights, X does R. Promise is a universal modal: if X has made a promise to do P, then X does P in every world consistent with X's commitments.

What difference does the quantificational force make? Well, consider the following truth conditions.

a. "A has the right to keep and bear arms" is true iff in some world w in the set W, where W is the set of worlds consistent with A's rights, A keeps arms in w and bears arms in w.

b. "A has the right to keep and to bear arms" is true iff in some world w in the set W, where W is the set of worlds consistent with A's rights, A keeps arms in w, and in some world w' in the set W, where W is the set of worlds consistent with A's rights, A bears arms in w'.

These are different truth conditions. (a) unifies the keeping of arms and the bearing of arms by requiring them to take place in the same possible world, while in (b) they can occur in separate worlds, and are therefore independent rights. But if the quantificational force is existential, the truth conditions come out logically equivalent:

a. "A has made a promise to support and defend the Constitution" is true iff in every world w in the set W, where W is the set of worlds consistent with A's promises, A supports the Constitution in w and A defends the Constitution in w.

b. "A has made a promise to support and to defend the Constitution" is true iff in every world w in the set W, where W is the set of worlds consistent with A's promises, A supports the Constitution in w, and in every world w' in the set W, where W is the set of worlds consistent with A's promises, A defends the Constitution in w'.

This gets us the semantic difference between right and promise, and therefore accounts for our intuitions about the second amendment and Scalia's attempted counterexample. The rest of the paper aims to justify the truth conditions just shown, by arguing for syntactic structures and semantic analysis of these sentences.

In the syntax section of my paper, I argue that the presence or absence of to is probative of a substantial structural difference. So the reason that the right to keep and bear arms means something different from the right to keep and to bear arms is not the lexical semantics of the word to, but the fact that in the former sentence it is just the verbs keep and bear that are conjoined, while in the latter, the full infinitival clause is conjoined. The conjunction is indicated in the following:

a. The right of the people PRO to [keep and bear] arms
b. The right of the people [PRO to keep arms and PRO to bear arms]

[Explanations: PRO is the invisible subject of the infinitival clause; the first instance of "arms" in (b) is phonetically deleted by a process that I can only guess at - it's not a fantastic analysis, but it beats the alternatives.]

Given this syntactic analysis, the logical forms are determined by the semantics as follows. Keep and bear each denote functions from entities (their direct object) to sets of events. So in the sentence John kept his house, the function denoted by keep takes as an argument the entity John's house, and returns the set of events of keeping John's house. I think the semanticists are calling this the neo-Davidsonian or the semi-Davidsonian approach to verb meanings - I've always had trouble keeping these terms straight.

In (a), keep and bear are conjoined. The semantic result is that the truth conditions of each are required. So the meaning of the conjunction is a function from an entity (the direct object of the conjoined verb) to a set of events - the set of events in which the object is both kept and borne.

To takes a set of events as input, and returns a function from entities to sets of worlds in which the entity is the agent of the appropriate type of event in the world. For example, in PRO to keep and bear arms, to takes as its first input the set of events of keepoing and bearing arms, then takes PRO as its entity argument, and returns as the meaning of the infinitival clause the set of worlds in which there is an event of keeping and bearing arms of which PRO is the agent. Ultimately, the truth condition of (a) makes the people the referent of PRO, and compares this set of worlds with the set of worlds consistent with the rights of the people.

The semantic analysis of (b) is more complicated, and requires some creativity of analysis. The meanings of PRO to keep arms and PRO to bear arms are determined straightforwardly - they denote the sets of worlds in which there are events of keeping or bearing arms, respectively, with PRO as the agent of the events.

The challenge is dealing with the conjunction. The ordinary approach to conjoining two sets of worlds would be to create a new set of worlds such that the conditions of both of the sets are met. In this case, the result would be the set of worlds that contain an event of PRO keeping arms and an event of PRO bearing arms. The rest of the semantic analysis would be the same as for (a): PRO would be assigned the meaning "the people," and the set would then be compared with the set of worlds consistent with the rights of the people.

The problem is that this does not match our intuition about the meaning of the sentence. We tend to interpret the right to keep and to bear arms as equivalent to the right to keep arms and the right to bear arms, yet this is not the result of the most straightforward semantic analysis.

The problem seems to be this: in conjunctions such as this one, the conjunction appears to take very wide scope, in effect to be conjoining entire propositions, even if the syntax makes it look like the conjunction is more local. In this case, it is only the infinitival clause that is conjoined syntactically, though semantically it is the propositions that are conjoined. My suggestion is that this syntax/semantics disparity takes place where the conjoined object is an argument rather than a function; that is, when the combinatory operation that the conjoined object participates in is one in which it is "fed into" the meaning of the adjacent object, as in (b), where the set of worlds denoted by the infinitive is one of the arguments of the (denotation of the) word right.
Not, as in (a), one in which the conjoined object takes the adjacent element as an argument, as in (a) where the conjoined verb takes the direct object arms as an argument.

What I propose, then, is that we need a different rule for interpreting conjunctions in situations in which the conjunction is an argument. What I suggest, without presenting a real formal analysis, is that whenever the semantics encounters a conjunction, it assigns it the meaning of the set of conjuncts. So in the case of keep and bear, the meaning is the set consisting of two functions from entities to sets of events, while in the case of PRO to keep arms and PRO to bear arms, it is the set consisting of two sets of worlds.

This set then has the option of either undergoing the traditional conjunction rule and combining with an argument, or of undergoing a new operation and feeding into a function. The new operation consists of creating two separate semantic derivations that are conjoined at the proposition level. So the two sets of worlds in (b) will each, independently, combine with right, yielding a proposition, and those two propositions will be conjoined.

I haven't seen such a procedure suggested before, but it looks like it can handle the syntax/semantics mismatch in the scope of coordination, and it does it without any "looking ahead" by the semantic derivation to see the future interactions of the coordinated object. The derivational mechanism always treats a conjunction the same way - it creates a set of the conjuncts; and what eventually happens to this set is determined by what possibilities exist at the time the conjunction goes to combine with an adjacent object.

Whew. Any questions?