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Can anyone explain what additional claims can be made for the Principle of Compositionality in regards to a language like Basque?

I understand that Basque is a "free word order" language and the position of subject, object and verb can be permuted.

But how can a speaker know the meaning of a sentence if there is no set syntactical structure?

I'm just getting started with semantics so I hope someone can explain it to me simply.

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    Basque marks the case of noun phrases (e.g. absolutive and ergative case) – brass tacks Jan 12 '18 at 19:04
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    I don't know about the Principle of Compositionality and I don't know about Basque, so I can't answer your question, but maybe the following paper would provide some useful information about how word order in Basque is related to the semantics of a sentence: "Focus and Word Order in Basque", Karlos Arregi – brass tacks Jan 12 '18 at 21:14
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There is a certain meaning, and a sentence constructed in a particular language, obviously, uses the linguistic tools (or instruments) of that language to convey the meaning.

In English, the word order is a tool (one of many) to convey grammatical information. No other tool can replace its function. Hence, "John loves Mary" and "Mary loves John" convey two essentially different meanings (and "loves Mary John" conveys no meaning at all).

In other languages, other tools are used. One of the most typical tools is case system. Using case markers, one can mark subject and object to make the sentence meaningful.
If the case system is developed well enough, the word order (or another tool) can be more or less safely ignored, without losing the meaning.

There are quite a few questions on this site that can shed the light on this phenomenon:

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There's no link between the principle of compositionality and (free) word order. Basque (and many other languages, such as most Indo-European and native American languages) use morphology to indicate grammatical functions whereas word order encodes topic-focus articulation.

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In mathematics, semantics, and philosophy of language, the principle of compositionality is the principle that the meaning of a complex expression is determined by the meanings of its constituent expressions and the rules used to combine them.

You're confused how sentences could have meaning without compositionality. This is probably because word order is the only way you've ever seen it done so you conflate compositionality with word order. Word order is not the only kind of rules you can have for combining constituent expressions. There are rules in free word order languages for combining them, but instead of using word order, they use case marking. It's entirely arbitrary to mark the relation between the words with word order. The only thing that matters is that there is some way it is marked. Furthermore, free word order only pertains to subject, verb, object order, not to the order of all words. There can be word order rules for other constructions of the sentence. For instance, the placement of an adjective might have a fixed word order in a "free word order" language.

Both word order and case marking tag words to show whether they are subject or object. Word order tags a word but it's an invisible tag, because the tag is its place in the sentence. Case marking tags the word by putting a sound on the word.

Free word order does not mean having no set syntactical structure. Basque does not violate the principle of compositionality.

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