Is linguistics a science and if so, how?
Linguistics is a scientific study of humans n language. The scope is broad. This includes the study of etymology, morphology, grammar, semantics, context, phonology, and syntax. Linguistic study covers the function, meaning, and structure of language as it exists in the abstract, in our neurology or at a certain point in history.
Linguistics studies the origin of language(s) as well as the history, evolution and change of language over time. The history of any subject has a sociological aspect, and to that extent a subjective analysis depending on the culture of a people at a certain place and time.
Other subfields are sociolinguistics, psycholinguistics and neurolinguistics. The latter is clearly scientific. With sociolinguistics and psycholinguistics, other factors come into play such as economics and culture. In this case, the linguist looks at the abstract structure of language, the sociological emergence of it, and the contextual, historical and cultural aspects which affect a language at a certain time and place. Even in sociolinguistics, science governs linguistics because speech sounds are now measured on frequency scales and understood in terms of vibrational frequencies.
Linguistics itself is a scientific study, but because it deals with language, it is borrowed by nearly all aspects of human life, including the arts. For example, literary theorists use linguistics in literary analysis. Nonetheless, theoretical and applied linguistics studies have features that are quantifiable in the laboratory.
Ferdinand de Saussure divided the study of linguistics into two categories: langue and parole. Langue is the abstract rules and structure of language and parole is the actual speech acts that occur. So, analogously, langue is the rules of chess and parole are the individual moves in a game. An analysis of each is scientific, but langue is more rigorously scientific because parole (the actual speech acts that occur in history, in a community) must be studied contextually and each context will incorporate sociological, psychological and cultural information. This is not to say that langue is an exact study.
It is not the general system (langue) that changes the evolution of language; it is the individual speech act (parole). So, you can study the abstract structure of language, but to know how it has evolved you have to study the speech acts themselves (and this covers everything from everyday speech to literature and poetry).