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User:Phlsph7/Formal semantics - Methodology

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Methodology

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Formal semanticists rely on diverse methods, conceptual tools, and background assumptions, which distinguish the field from other branches of semantics. Most of these principles originate in logic, mathematics, and the philosophy of language.[1] One key principle involves the analysis of the meaning of a sentence by studying its truth conditions. A truth condition is a specific situation or set of circumstances under which a sentence would be true. For example, a truth condition of the sentence "It is raining" is that raindrops are falling outside. This principle reflects the idea that understanding a sentence requires knowing how it relates to reality and under which circumstances it would be appropriate to use it.[2]

A closely related methodological consideration is the problem of entailment. Entailment is a relation between sentences—called premises and conclusions—in which truth is preserved. For instance, the sentence "Tina is tall and thin" entails the sentence "Tina is tall" because the truth of the first sentence guarantees the truth of the second. One aspect of understanding the meaning of a sentence is comprehending what it does and does not entail.[3][a]

To analyze truth conditions and entailment relations in a precise manner, formal semanticists typically employ model theory. In this context, a model is an abstract representation of a hypothetical situation. Models rely on set theory and introduce abstract objects for all entities in this situation. For example, a model of a situation where Tina is tall and thin may include an abstract object representing Tina and two sets of objects—one for all tall entities and another for all thin entities. Using this approach, it is possible to define truth conditions and mimic linguistic phenomena through mathematical relations between abstract objects, such as the relation of set membership between the object corresponding to Tina and the set of tall objects.[5]

The principle of compositionality is another key methodological assumption for analyzing the meaning of natural language sentences and linking them to abstract models. It states that the meaning of a compound expression is determined by the meanings of its parts and the way they are combined. According to this principle, if a person knows the meanings of the name Tina, the verb is, and the adjective thin, they can understand the sentence "Tina is thin" even if they have never heard this specific combination of words before. The principle of compositionality explains how language users can comprehend an infinite number of sentences based on their knowledge of a finite number of words and rules.[6] Following this principle, formal semanticists connect natural language sentences to abstract models[b] through a form of translation, for instance, by defining an interpretation function that maps the name "Tina" to an abstract object[c] and the adjective "thin" to a set of objects.[9][d] This makes it possible to precisely calculate the truth values of sentences relative to abstract models.[11]

Within formal semantics, there are diverse ways of how to construct models and relate linguistic expressions to them.[12] Some rely on the contrast between grammatical and logical forms. The grammatical form of an expression is the arrangement of words and phrases on its surface, following rules of syntax. The logical form of an expression abstracts away from linguistic conventions to reveal the underlying logical relations at the semantic level.[13] The rule-to-rule hypothesis, proposed by Richard Montague, seeks to bridge the gap between syntax and semantics. It states that for every syntactic rule, governing how a sentence may be formed, there is a corresponding semantic rule, governing how this procedure influences the meaning of the sentence.[14]

To test the adequacy of their theories, formal semanticists typically rely on the linguistic intuitions of competent speakers as a form of empirical validation. For instance, intuitions can be used to assess whether a theory accurately predicts entailment relations between specific sentences.[15]

References

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Notes

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  1. ^ Typically, entailment relations only go in one direction. However, they can also go in both directions if two sentences entail each other, like the sentences "Tina is tall and thin" and "Tina is thin and tall". In such cases, the two sentences are said to be equivalent.[4]
  2. ^ This general method also reflects the externalist theory of meaning common in formal semantics: the meaning of an expression is interpreted as the entities it denotes in an abstract model, without focusing on cognitive processes internal to language users.[7]
  3. ^ This can be expressed symbolically through the use of double brackets. For example, the formula refers to the object denoted by the name "Tina" in the model "M".[8]
  4. ^ In this context, semanticists typically speak of denotation: the denotation of an expression is the entities to which it refers.[10]

Citations

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  4. ^ Winter 2016, p. 16
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  8. ^ Winter 2016, p. 18
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  11. ^ Winter 2016, pp. 24–27
  12. ^
  13. ^
  14. ^
  15. ^

Sources

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  • Stokhof, Martin (2013). "Formal Semantics and Wittgenstein: An Alternative?". Monist. 96 (2): 205–231. doi:10.5840/monist20139629.
  • Janssen, Theo M. V.; Zimmermann, Thomas Ede (2025). "Montague Semantics". The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University. Retrieved 28 May 2025.
  • Matthews, P. H. (2007). "Rule to Rule Hypothesis". The Concise Oxford Dictionary of Linguistics. Oxford University Press. ISBN 978-0-19-920272-0.
  • Kearns, Kate (2011). Semantics (2nd ed.). Bloomsbury Academic. ISBN 978-0-230-23229-7.
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