I found that most of the examples of entailment are statements about a third person, but never the speakers themselves. So I wonder what the utterance like "I'm cold." entails?

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This is a pretty broad question. "I'm cold" without any other contextual details entails any number of things. Basically any entailment means "if A, then B; A therefore B".

So if "I'm cold." then

  • I exist.
  • I sense ambient temperatures.
  • The temperature I experience can change.
  • I have a concept of hot/cold.
  • The temperature I am experiencing is in the range of what I would define as "cold".

If you get creative, you could probably come up with a dozen or so more entailments for this simple sentence pretty easily.

One reason entailments are more often about 3rd persons rather than 1st is that there is a distinction between presuppositions and entailments. Speakers have presuppositions, sentences have entailments. So the 1st-person sentence "I'm cold" entails certain presuppositions that the speaker has. And since the speaker and the subject of the sentence are the same, it makes distinguishing entailments and presuppositions a little trickier whereas with 3rd-person sentences, the presuppositions of the speaker do not have a direct impact on the entailments of the sentence.

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