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So I've come across two different definitions for a proposition,

1. A proposition is a sentence that can be true or false. However, not both simultaneously.
2. A proposition is a sentence that is true or false. However, not both simultaneously.

Let's consider the following sentence,

5x = 20

According to the 1st definition this is a proposition since it can be either true or false depending on the value of x.

According to the 2nd definition this is not a proposition because we don't know the value of x, so we don't know whether it's true or not.

Which of these is the correct definition?

Warning: English is not my first language, so it could be that I understood these definitions incorrectly.

pineappleFrenzy
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1 Answers1

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Many textbooks will use the second definition and, consequently, consider $5x=20$ not to be a proposition.

Personally, I am more with the first definition, and say that

$5x=20$

is a proposition.

Here are some other examples:

"It rains"

I would say that's a pretty clear proposition. Is it true or false? No idea. Depending on where and when we are evaluating it, I suppose.

Even something like

$1+1=2$

Sure, this is true in the 'normal' world of mathematics, but I can define different mathematical worlds where this is false.

In short: the truth- or falsity of a proposition depends on what world we are evaluating it in. But it's still a proposition. Unlike things like:

"It's"

or

"raining"

or

$5x$

or

$=2$

That is, I would say the class of expressions "1+1=2", "5x=20", and "It rains" is quite clearly different from the class of expressions like "1", "rains", and "=", and I would consider the former the class of propositions, and the latter non-propositions

Bram28
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