The limits on formal semantics: compositionality, context and truth values

Question

I am a little bit surprised by the principle of composionality in semantics (I'm very new to all of this), which states that the meaning of a complex expression is determined by the meanings of its constituent expressions and the rules used to combine them. When reading stuff like Categorial or Montangue Grammar or Davidson´s account of meaning based on truth values, this principle is a pillar of how meaning is constructed. The problem is that I do not understand why this is not trivially false. I am not thinking of the usual "exceptions" (sarcasm, literary language,...), but about very ordinary not-sarcastic expressions like:

1. I already had dinner

2. I've already read that book

Any competent speaker understand that the first "already" means some hours ago, while the second one can mean "earlier in my life". To know this, seems to me, one needs a detailed knowledge of human habits. An alien who just learned english as a formal system would not be able to adscribe truth-values of any sort to these sentences. Similarly, in

3. I have some of Marie's book at home

4. I have some of Jane Austen´s books at home,

the meaning of the genitive is that of ownership in one case and one of authorship in another. It seems obvious then that the notion of compositionality collapses and it is impossible to assign truth-values to utterances unless we take into account a notion of context that goes widely beyond the usual [speaker, time, place], including common beliefs, cultural items, etc. True, if you consider sentences like "John is running" or "Marie saw that John bought the car that Lucy painted" (which is what you find analysed with painstaking formal detail in books like Gamut's Logic, Language and Meaning), then compositionality seems to work, but these are artificial examples which do not represent ordinary language. Actually, by studying the metaphoric maps common in everyday language (I´m thinking of the contemporary theory of metaphor started by Lakoff in the 80´s), it is easy to derive dozens of common expressions that defy compositionaly in similar ways.

Is it not the case then that semantics does not make sense isolated, without pragmatics? I do not understand that there can really be something "in between" syntax and pragmatics that makes sense on its own.

Answer 1

You raise some valid points regarding the limitations of the principle of compositionality in semantics. It is true that there are many cases in natural language where the meaning of a sentence cannot be fully determined by the meanings of its constituent parts and the rules for combining them. Contextual information, cultural knowledge, and pragmatic considerations often play a crucial role in understanding the meaning of an utterance.

However, it is important to note that the principle of compositionality is not intended to capture the full complexity of natural language semantics. Rather, it is a basic assumption that serves as a starting point for formalizing the meanings of sentences in a systematic way. The principle asserts that the meaning of a sentence is a function of the meanings of its constituent parts and the way they are combined, but it does not deny that other factors may also be involved in determining the sentence's meaning.

In addition, the principle of compositionality is often used in conjunction with other tools and techniques in natural language semantics, such as context-sensitive rules, presupposition accommodation, and implicature. These tools allow us to capture the nuances and complexities of natural language meaning that go beyond the basic principle of compositionality.

Finally, it is true that pragmatics plays a crucial role in natural language understanding. Pragmatics deals with how the context and the speaker's intentions affect the interpretation of utterances. However, pragmatics is not an alternative to semantics but rather an extension of it. Pragmatic considerations can be formalized and incorporated into semantic theories, and many formal semantic frameworks include pragmatic components.

Answer 2

I already had dinner

I've already read that book

The difference is between 'dinner' and 'a dinner'.

The first sentence does not mean that I've already had a dinner, which would mean that at some point in my life I had a meal in the evening. Dinner with article means today's dinner and no other.

The adverb 'already' just means 'at some point in the past' and has the same sense in the two sentences.

The difference comes from 'dinner' versus 'that book'. While the dinner in question is not just anyone of the many dinners I already had in my life but the one and unique dinner I had today. There is no similar indication as to when I read that book.

As far as I can see, my interpretation is entirely based on the meaning of the words involved in the two sentences.

I have some of Marie's book at home

I have some of Jane Austen´s books at home

Jane Austen is a well-known author, Marie isn't. Names are not meaningless tags. They are loaded with what we know about the persons referred to and used by the speaker and interpreted by the audience accordingly.

the principle of compositionality in semantics (I'm very new to all of this), which states that the meaning of a complex expression is determined by the meanings of its constituent expressions (...) I do not understand that there can really be something "in between" syntax and pragmatics that makes sense on its own.

The semantics is not what "makes sense on its own", it is sense itself, so the question is whether the semantics of the whole follows from the semantics of the parts. If you understand the parts, you understand the whole, but understanding the part, for example as 'dinner' versus 'a dinner', or 'that book' versus 'a book', depends on the context and on your own personal experience of th world. The name 'Carpenter' does not by itself refer to any one individual, but it usually does in context, but once you know which Carpenter, you are able to understand what is said about this person.