Are opinions considered propositions? I was wondering the thought. My textbook says:

A proposition is still a proposition whether its truth value is known to be true, known to be false, unknown, or a matter of opinion.

*

*"It is a nice day" - This is not a proposition

*"All Politicians are dishonest" - This is a proposition

*"The movie was funny" -This is a proposition.


Then wouldn't statement 1 be considered a proposition, especially since it says that being a matter of opinion doesn't change the fact is a proposition? Or maybe this doesn't matter at all?
 A: Let's adopt a predicate-logic perspective.


A proposition is still a proposition whether its truth value is known to be true, known to be false, unknown, or a matter of opinion."


I think your textbook is trying to say that a proposition's truth value is allowed to vary across contexts/interpretations. In this sense, the truth value of the proposition “Jan 1 2020 was a nice day” varies according to the particular location and the definition of “nice day”, as supplied by the context. (This is my best guess as to why it admits a subjective claim as a proposition.)
To be clear: in the above, your textbook is not defining a proposition, nor suggesting that $(x=x)$ is a proposition (despite even having a definite truth value, it technically isn't a proposition; see below).



*

*"It is a nice day" - This is not a proposition

*"All Politicians are dishonest" - This is a proposition

*"The movie was funny" -This is a proposition.



I think your textbook is translating the above natural-language sentences as

*

*$N(x)$

*$\forall x\;[P(x)\to\lnot H(x)]$

*$F(c).$
$c$ is a constant; $x$ is a free variable, so (1) is an open formula, so it is not a proposition (which conventionally means a formula with no free variable).
Summing up: I think your textbook is letting context/interpretation deal with subjectivity, so is not using the latter as a criteria in evaluating whether the three examples are sentences. That "matter of opinion" point above was an unhelpful (complicating) detour; actually, even the typical “A proposition is either true or false but not both” characterisation isn't very clear, because the proposition “for each $x,\;x^2$ is not a negative number” is a proposition, is true in real analysis but false in complex analysis, and has a definite truth value only under a particular interpretation.
A: Just to avoid misunderstandings:
It seems that there is an extra-logical error in the question occurred while carrying over here from the Web source:
Examples for non-propositions:

Examples for propositions:

"It is a nice day" is as proper a proposition as the others are; probably, it is somehow confused with "Have a nice day".
