Showing posts with label semantics. Show all posts
Showing posts with label semantics. Show all posts

Wednesday, May 27, 2026

Conversations with Noam Chomsky (2021-2022)

Here are two lengthy conversations that I had with Noam Chomsky on the topics of language, thought and formal semantics. I was very honored to have been able to have these conversations with Noam, who has been a guiding light for me throughout my career.

A Conversation with Noam Chomsky about Formal Semantics (June 25, 2021)

A Conversation with Noam Chomsky about Language and Thought (March 27, 2022)

Saturday, May 10, 2025

A Scope Freezing Effect with Inverse Linking

Abstract: In this squib, I will discuss a scope freezing effect found with inverse linking. I will explain the freezing effect in terms of the theory of negation of Collins and Postal (2012). Then I will discuss the consequences of the scope freezing effect for the theory of inverse linking. 

Version 2 (August 26, 2025)

Version 1 (May 10th, 2025)

Tuesday, April 15, 2025

Quantifier Raising: Entailment and Inverse Scope (Syntax II, Spring 2025)

Consider the following two sentences, each involving an existential quantifier phrase and a universal quantifier phrase.

1.
a. Some boy loves every girl.
b. Every boy loves some girl.

In both cases, we can ask what the possible logical form representations of the sentence are, and what the truth conditions of those representations are. If we adopt the syntactic operation QR, then (1a) with inverse scope yields truth conditions that clearly distinguish it from (1a) with surface scope. The question of whether inverse scope is needed for sentences like (1b) is more intricate. This note goes into these issues in detail.

Applying QR to (1a), there are two logical form representations:

2.
LF1: (surface scope)
[TP <[some boy]1> [TP <[every girl]2> [TP DP1 loves DP2]]
LF2: (inverse scope)
[TP <[every girl]2> [TP <[some boy]1> [TP DP1 loves DP2]]

In these structures, the notation <…> indicates that the occurrence is not pronounced. In LF1, for example, [some boy] has two occurrences, but only the one in subject position is pronounced. Furthermore, in these representations the possibility of VP adjunct is ignored (see Fox 2002 for discussion).

These LF representations can be paraphrased as follows:

3. LF1 (paraphrase): There is some boy who loves every girl.
LF2 (paraphrase): For every girl, there is some boy who loves her.

Now consider the following two situations:

4.
S1: John love Sue, Mary and Kathy.
(and there are no other people or relationships involved)
S2: John loves Sue, Bill loves Mary, Chris loves Kathy.
(and there are no other people or relationships involved)

Calculating the truth value of each LF representation in each situation (actual semantic calculation omitted), we have the following results (SS = surface scope, IS = inverse scope):

5. S1 S2
LF1 (SS) true false
LF2 (IS) true true

This table shows that LF2 (inverse scope) is true in S2, whereas LF1 (surface scope) is not. These truth values provide an important argument for the existence of inverse scope. If inverse scope were not allowed, there is no way we could capture the intuition that (1a) (with structure LF2) is true in S2.

In the theory I presented in class (from May 1977, Fox 2002), inverse scope is accounted for in terms of QR. In inverse scope, the object undergoes QR to a scope position higher than the subject scope position (see LF2 above). Therefore, the data in (5) provides evidence supporting the covert movement operation QR.

This table shows that only S2 distinguishes the two LF representations, S1 does not. Therefore, it is clear that LF1 is stronger, in the sense that whenever LF1 is true, so is LF2, but not vice versa. In fact, using formal semantic tools, it is possible to prove the following:

6. a. LF1 entails LF2 (LF1 ⊨ LF2)
b. LF2 does not entail LF1 (LF2 ⊭ LF1)

When there is an entailment relation like this between two LFs, it is sometimes hard to distinguish them empirically. For example, in 5, both LF representations were true in S1. And so S1 could not be used to distinguish them.

With this background, consider now (1b) above. Applying QR to (1b), there are two logical form representations:

7.
LF1: (surface scope)
[TP <[every boy]1> [TP <[some girl]2> [TP DP1 loves DP2]]
LF2: (inverse scope)
[TP <[some girl]2> [TP <[every boy]1> [TP DP1 loves DP2]]

These LF representations can be paraphrased as follows:

8. LF1 (paraphrase): For every boy, there is some girl who he loves.
LF2 (paraphrase): There is some girl who every boy loves.

Now consider the following two situations:

9.
S1: John loves Sue, Bill loves Mary, Chris loves Kathy.
(and there are no other people or relationships involved)
S2: John love Sue, Bill loves Sue, Chris loves Sue.
(and there are no other people or relationships involved)

Calculating the truth value of each LF representation in each situation (calculation omitted), we have the following results:


10. S1 S2
LF1 (SS) true true
LF2 (IS) false true

In this case, LF2 is stronger than LF1, in the sense that LF1 is true whenever LF2 is true. In other words, we have the following entailment relations:

11. a. LF2 entails LF1 (LF2 ⊨ LF1)
b. LF1 does not entail LF2. (LF1 ⊭ LF2)

Now let’s ask what the evidence is for the inverse scope representation in LF2 of the sentence in (1b). Unfortunately, because of the entailment relations, there is no situation (such as S1 or S2) where LF2 (inverse scope) is true and LF1 (surface scope) is false. This makes it difficult to justify the inverse scope representation purely on the basis of situations where the LF representations are true. Therefore, the question is whether in this case one needs an inverse scope representation of (1b) at all.

To put matters more intuitively, concerning (1b), if it is true that there is some girl who every boy loves (inverse scope) then it is also true that for every boy, there is some girl who he loves (surface scope). So perhaps in this case we could say that only the surface scope representation in LF1 is possible, but it is vague as to whether everybody loves the same girl or not.

We can summarize as follows:

12.
a. Some boy loves every girl.

i. Inverse scope does not entail surface scope.

ii. There is a situation where inverse scope LF is true,
but surface scope LF is not true.

b. Every boy loves some girl.

i. Inverse scope entails surface scope.

ii. If inverse scope LF is true in some situation,
then so is surface scope LF.

Notice that LF1 and LF2 in (7) are not equivalent, and so they are false in different cases (see (10)). In particular LF1 is true in S1 but LF2 is false in S1. This leads to the suggestion that we could use falsity to distinguish the interpretations of LF1 and LF2.

So, given S1, consider the following dialogue:

13. (in S1)
A: Isn’t it strange that every boy loves some girl? (with structure LF2)
Intended: Isn’t it strange that there is some girl that every boy loves?
B: That is false, they all love different girls.

If this were an acceptable discourse it would provide evidence that both LF1 and LF2 are needed for (1b). Since it would show that LF2 (inverse scope) is possible, and is false in a particular situation. Unfortunately, it is not very easy to access the inverse scope interpretation in 13A, and the discourse seems forced.

Another similar way to distinguish LF1 and LF2 is through constructions like “It is false that” and “It is not the case that”. These constructions negate the embedded clause:

14. a. It is false that every boy loves some girl.
Intended: It is false that there is some girl that every boy loves.
b. It is not the case that every boy loves some girl.
Intended: It is not the case that there is some girl that every boy loves.

If LF2 (inverse scope) were a possible representation here, then the sentences would be true in S1. Once again, the facts are not that clear.

There are ways to bring out inverse scope. For example, adding the word particular makes it much easier:

15. a. It is false that every boy loves some particular girl.
Intended: It is false that there is some particular girl that every boy loves.
b. It is not the case that every boy loves some particular girl.
Intended: It is not the case that there is some particular girl that every boy loves.

This kind of sentence where one is negating the inverse scope LF representations suggests that inverse scope is also needed in examples such as (1b).

In summary, based on truth conditions, it is easier to justify an inverse scope LF representation for (1a) than it is for (1b). However, given the clear need for an inverse scope LF representation for (1a), the null hypothesis is that such an inverse scope representation should also be available for (1b). That conclusion leaves open the difficult status of the judgments in (13) and (14).







Tuesday, November 12, 2024

A Merge-Based Approach to the Syntax-Semantics Interface

These notes are based on a career of looking at issues in the syntax-semantics interface, including argument structure, anaphora, negation, quantifiers, coordination, and ellipsis.

Philosophy

1.

Be open to syntax.

Be open to radically syntactic approaches to traditionally semantic and pragmatic issues, no matter how authoritative or how widely adopted the semantic or pragmatic approach might be.

2. 

Semantic operations are defined in terms of syntactic structure. 

In other words, there is no semantics without syntax. As a consequence, all semantic analyses involve important assumptions about syntax. 

3.

Hypothesis: The correct syntactic analysis will have a semantic interpretation that is simple, transparent and uniform (in the sense clarified below in 4-8).

Specific Assumptions

Here are some specific assumptions that help to articulate the above hypothesis.

4.

Semantic operations are simple and limited in type (simplicity).

Semantic operations are as constrained as possible, perhaps only function application and predicate abstraction. Powerful semantic operations such as type shifting, function composition, existential closure and semantic coercion are not part of UG. If an analysis uses such operations, try to think about how to replicate their effects syntactically (e.g., using Merge) and then test the consequences.

5.

Semantic values are simple (simplicity).

The semantic values of lexical items are simple. The more complex a semantic value is, the greater the chance that it should be broken into several different morphemes each with its own simple semantic value. These morphemes will them be merged together in the syntactic derivation.

6.

Variables are represented syntactically (transparency).

If there is a variable x in the semantic representation, then there is a DP in the syntactic representation which is interpreted as the variable x. This constraint forces variables to be introduced into both syntax and semantics via Merge. A simple example is the passive. Since there is a variable representing the agent in the short passive, there must be a DP in the syntactic representation interpreted as that variable. See Collins 2024 for a discussion and references.

7.

Semantic interpretation is uniform (uniformity).

Semantic interpretation is uniform in the sense that a single syntactic structure is not interpreted in two different ways. A single syntactic structure has a single interpretation. 

For example, a DP in a position P, cannot be interpreted optionally as specific or non-specific. To get the two interpretations, something must be different, either the internal syntactic structure of the DP, or the syntactic position of the DP, or both.

8.

Semantic relations and predicates are directly represented in syntactic structure to the greatest extent possible (transparency).

For example, the scope of one quantifier phrase QP1 over another QP2 is represented syntactically in terms of asymmetric c-command at some point in the derivation (not in terms of type shifting one quantifier phrase to given it semantic scope over another). Another example is Rizzi 1997 use of FocP to syntactically represent the semantics of focus.

Of all the assumptions concerning the syntax-semantics interface, (8) is the vaguest and hardest to pin down since the notion of “semantic relations and predicates” is very broad. Furthermore, it may be that (8) follows from the other assumptions in (4-7).

Method

9.

Work out the truth conditions, entailments, presuppositions, scope and other semantic properties. Pay close attention to how the semantic properties vary with varying syntactic configurations. Are there important generalizations about how differences in syntax affect changes in interpretation? 

10.

Work out the syntactic analysis using Merge-based framework. 

(9) and (10) feed into one another. Semantic properties may suggest a particular syntactic analysis (in conformity with (4-8). And the syntactic analysis may suggest investigating certain semantic properties.

11.

Work out the compositional semantics based on assumptions 4-8.

Depending on the audience and venue, it is not always necessary to give the complete compositional semantics. But you should be confident about what the semantic properties of your proposed syntactic analysis are. Your syntactic representation should capture the semantic properties of the construction.

Evaluation

12.

Justify your syntactic analysis using traditional syntactic tests.

You don’t just get to propose syntactic structure free of charge. Since the assumptions in (4-8) are a hypothesis, you need to prove that your proposed analysis is correct or at least better than alternatives. Whatever representation you ultimately come up with, it should be consistent with standard syntactic tests (e.g., constituent structure tests, Binding Theory, islands, distributional tests, agreement, etc.). This is your opportunity to dig very deeply into the syntax of the construction.

13.

Justify your syntactic analysis using cross-linguistic comparisons.

For some topics, it might be easier probe syntactic structure and its semantic interpretation in a different language. In some languages, the morphosyntax of a construction clearly reflects its semantic properties. Investigating such languages can give important clues about the best syntactic analysis cross-linguistically. For example, it is much easier to investigate the syntactic and semantic properties of logophoricity in Ewe, which has a morphologically distinct logophoric pronoun.

14.

Look for the smoking gun.

Does the syntactic approach yield insights into any particular aspect of the problem? Are there interesting empirical predications? Is there a deep theoretical consequence? Try to find something that would convince a disinterested party, or even a skeptic. 

Acknowledgments: I thank Richard Kayne, Paul Postal and Gary Thoms for comments on a draft of this blog post.


Wednesday, June 21, 2023

Papers on Negation and Quantifiers

Here is a series of five papers I have written recently concerning negation, quantifiers and negating quantifiers. They are all syntax/semantics interface papers, with a substantial semantic component. The constant theme throughout is the application of the basic framework of Collins and Postal 2014 to various phenomena. 

Tuesday, May 10, 2022

Scalar Modifiers of Quantifier Phrases (Collins 2022, Glossa)

Abstract: This paper analyzes the syntax and compositional semantics of scalar modifiers of quantifier phrases in expressions like almost every student, absolutely every student and nowhere near every student. The semantics is based on scales (positive and negative) of generalized quantifiers.

Keywords: scalar modifiers, positive scale, negative scale, negative polarity items, endpoint quantifiers

Scalar Modifiers of Quantifier Phrases

Sunday, March 27, 2022

A Conversation with Noam Chomsky about Language and Thought

This interview took place by e-mail starting from November 4, 2021 lasting until November 8, 2021. In some minor cases, the text has been lightly edited, and the order of the questions has been changed.

Cite as: Collins, Chris. 2022. A Conversation with Noam Chomsky about Language and Thought. Ordinary Working Grammarian [Blog].

Friday, June 25, 2021

A Conversation with Noam Chomsky about Formal Semantics

This interview took place by e-mail starting from February 13, 2021 lasting until June 25, 2021. In some minor cases, the text has been edited, and the order of the questions has been changed. I thank Richard Larson for discussions of some of the material from this interview.

Cite as: Collins, Chris. 2021. A Conversation with Noam Chomsky about Formal Semantics. Ordinary Working Grammarian [Blog]. https://ordinaryworkinggrammarian.blogspot.com/2021/06/a-conversation-with-noam-chomsky-about.html

Thursday, April 1, 2021

Sunday, August 9, 2020

The History of Semantics at MIT

This blog post was inspired by a recent Facebook thread on my Facebook page discussing one of Barbara Partee’s talks on the history of formal semantics:


Wednesday, August 1, 2018

Review of Compositional Semantics, by Pauline Jacobson


Review of Compositional Semantics, by Pauline Jacobson

Friday, April 21, 2017