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It is of my understanding that logical statements are either true or false. "Patrick is 32 years old" is a statement that can easily be verified: it is either true or false.

But how does one analyze statements that are subject to someone's opinion, like "It is cold today" or "This is the best restaurant in town"? Do we simply say that for person X that statement is true but for person Y it is not?

Bernard
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bru1987
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    Mathematics doesn't really have a lot to say about loose, subjective comments. Of course, you could measure the percent of responders who assert that "it feels cold". That's a solid numerical value. – lulu Jul 20 '19 at 11:41
  • Certainly, different persons will have different notions of "best" (or even of "town"), but ultimately, the statement "Patrick is 32 years old" is also at least time-dependent isntead of an absolute fact – Hagen von Eitzen Jul 20 '19 at 11:42
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    You might be interested in reading about "fuzzy logic": https://en.wikipedia.org/wiki/Fuzzy_logic – awkward Jul 20 '19 at 12:48
  • Why do you think this is a question about mathematical logic? – Asaf Karagila Jul 21 '19 at 00:47
  • @awkward thank you, I see the relation of that and my question here. – bru1987 Jul 21 '19 at 20:34
  • @AsafKaragila why wouldn't it be? It seemed like a boundary worth exploring – bru1987 Jul 21 '19 at 20:35
  • How do you define, mathematically "opinion"? – Asaf Karagila Jul 21 '19 at 21:41
  • The truth value of each of the sentences "Patrick is 32 years old", "It is cold today" and "This is the best restaurant in town" depends on the given axioms and interpretation, for example, how "cold" and "best restaurant" have been defined and what properties are possessed by the referent of "this". $\quad$ At the risk of being circular: in propositional logic, the interpretation can be thought of as precisely the row in which those three sentences, X,Y and Z, possess the required triple of truth values. $\quad$ Related. – ryang Jul 08 '23 at 05:45

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It depends on what proposition the sentence is expressing. It could be, [Assessor/speaker general] thinks it is cold today which is a simple empirical question. So if Patrick said "It is cold today", then the proposition expressed would simply be, Patrick feels cold today which is true just in case Patrick feels cold today.

Another way you could analyze it is that the definition of "cold" changes depending on the assessor/speaker. So that the sentence "It is cold today" if read/spoken by me expresses the proposition It is less than 60 degrees which is also an empirical question and the proposition is true just in case it is less than 60 degrees.

The second way amounts to saying that such sentences are belief reports. I'm am not saying either is the correct way to analyze such sentences. The correct way to do so is, if I remember correctly, a matter of philosophical debate. So keep that in mind.