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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.

  1. "It is a nice day" - This is not a proposition
  2. "All Politicians are dishonest" - This is a proposition
  3. "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?

Mauro ALLEGRANZA
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Dread
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    This is more suited for philosophy stack exchange. To give you a cursory answer however, a proposition is a truth-bearer- an object that is capable of having a truth value. – emesupap Aug 20 '22 at 03:41
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    What textbook is it? – Suzu Hirose Aug 20 '22 at 03:45
  • I personally don't know if I agree if a statement can still be a proposition in a mathematical sense if the truth value is a matter of opinion. But I'm sure someone on here knows more than I do about this. – blakedylanmusic Aug 20 '22 at 03:48
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    i would throw this book into the garbage. – lola Aug 20 '22 at 14:05
  • in particular, you are right that if you adopt the (quite useless) definition of proposition given in the book, the number 1 must be a proposition as much as 3 is. – lola Aug 20 '22 at 14:07

1 Answers1

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  1. "It is a nice day" - This is not a proposition
  2. "All Politicians are dishonest" - This is a proposition
  3. "The movie was funny" -This is a proposition.

I think your textbook is translating the above as

  1. $N(x)$
  2. $\forall x\;[P(x)\to\lnot H(x)]$
  3. $F(c).$

Since propositions do not contain any free variable, (1) is disqualified from being a proposition. On the other hand, $c$ is a constant and (3) is a proposition.

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.

Here, your textbook is not defining a proposition, but just trying to say that a subjective proposition's truth value alternates across contexts; for example, 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”.

Incidentally, this is why the widespread “either true or false but not both” characterisation of a proposition is misleading: “for each $x,\;x^2$ is not a negative number” is a proposition, and is true in real analysis and false in complex analysis (though it does have a definite truth value under each interpretation).

ryang
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  • The day might be "nice" to one person but not "nice" to another person. "It is a nice day" is NOT either true or false to all. – George Ivey Aug 20 '22 at 12:40
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    @GeorgeIvey What's with the caps lock? And your comment is entirely consistent with my Answer. – ryang Aug 20 '22 at 12:55
  • “it is a nice day” has “it”, which in the standard meaning as it’s used in natural language has the same usage as “the” in “the movie was funny”, i.e. it is of type $N(c)$ where c = the present day. – lola Aug 20 '22 at 14:05
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    i understood that you were just attempting at making excuses for the book. i wanted to remark that the book’s example is quite debatable and that the best thing would be to find another book. – lola Aug 20 '22 at 14:43