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Methodology

Unlike other approaches to semantics, formal semantics relies heavily on various formal tools and methods from fields like logic, mathematics, and philosophy of language to analyze meaning. One central assumption is the attempt to grasp the meaning of sentences by studying their truth conditions. A truth condition of a sentence is a specific situation or set of circumstances under which the sentence would be considered true. For example, a truth condition of the sentence "It is raining" is that rain drops are falling outside.[1]

A closely related methodological consideration is the problem of entailment. Entailment is a relation between sentences—called premise(s) and conclusion—in which the truth is preserved. For example, the sentence "Tina is tall and thin" entails the sentence "Tina is thin" because the truth of the first sentence guarantees the truth of the second sentence. One aspect of understanding the meaning of a sentence is understanding what it does and does not entail.[2][a]

To analyze the 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 the entities in this situation. For example, a model of a situation in which Tina is tall and thin may include an abstract object corresponding to Tina and two sets of objects—one for all tall entities and one 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 the object corresponding to Tina being a member of both sets.[4][5]

The principle of compositionality is another key methodological assumption to analyze the meaning of natural language sentences and connect them to abstract models. The principle states that the meaning of compound expressions is determined by the meanings of its parts and the way they are combined. This rule states that by knowing the meanings of the name Tina, the verb is, and the adjective thin, a person can understand the sentence "Tina is thin" even if they have never heard this sentence before. The principle of compositionality explains how language users can comprehend an infinite number of sentences based on their understanding of a finite set of words and rules.[6][7][8][9]

Using this approach, formal semanticists connect natural language sentences to abstract models[b] through a form of translation, for example, by defining an interpretation function that maps the name "Tina" to an abstract object and the adjective "thin" to a set of objects. In this context, they typically speak of denotation: the denotation of an expression is the entities to which it refers.[14][10][15][c] This makes it possible to precisely calculate the truth values of sentences relative to abstract models.[17]

Different approaches to formal semantics propose different ways of constructing models and relating linguistic expressions to them.[13][18][19] Some rely on the contrast between grammatical and logical form. The grammatical form of an expression is the arrangement of words and phrases on its surface, following rules of syntax that can vary between languages. The logical form of an expression abstracts away from linguistic conventions to reveal the underlying logical relations on the semantic level.[20][21] 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 affects the meaning of the sentence.[22][23]

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 example, intuitions can be used to assess whether a theory accurately predicts entailment relations between specific sentences.[24][25]



References

Notes

  1. ^ Typically, entailment relations only go in one direction. However, entailment relations 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.[3]
  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 the abstract model, without focusing on cognitive processes internal to language users.[10][11][12][13]
  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".[16]

Citations

  1. ^ Lappin 2003, pp. 375–376.
  2. ^ Winter 2016, pp. 12–13.
  3. ^ Winter 2016, p. 16.
  4. ^ Winter 2016, pp. 17–18.
  5. ^ Fox 2014, pp. 86, 90–92.
  6. ^ Winter 2016, pp. 28–29.
  7. ^ Lappin 2008, pp. 370, 374.
  8. ^ Stokhof 2013, pp. 208–209.
  9. ^ Fox 2014, pp. 90–91.
  10. ^ a b Winter 2016, pp. 18, 240–241.
  11. ^ Portner & Partee 2002, pp. 1–2.
  12. ^ Partee 2016, pp. 3–4.
  13. ^ a b Lappin 2003, pp. 370–371.
  14. ^ Fox 2014, pp. 86, 90, 93.
  15. ^ Saeed 2009, pp. 309–310.
  16. ^ Winter 2016, p. 18.
  17. ^ Winter 2016, pp. 24–27.
  18. ^ Moeschler 2007, pp. 32.
  19. ^ Fox 2014, p. 92.
  20. ^ Stokhof 2007, pp. 609–611.
  21. ^ Stokhof 2013, pp. 209–210.
  22. ^ Janssen & Zimmermann 2025, § 2.3 Logic and Translation.
  23. ^ Matthews 2007.
  24. ^ Stokhof 2013, pp. 210–213.
  25. ^ Winter 2016, pp. 12–16.

Sources

  • 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.
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