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It may be a silly doubt, but let me ask this.

What is the difference between a proposition and an assertion?

I know there's a very thin line between the two terminologies, but I'm unable to get that.

Lord_Farin
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Ujjwal Saini
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3 Answers3

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There is a subtle difference between the two:

  1. A proposition is a statement in either a natural or a formal language, for which it makes sense to ask whether it is either true or false.

  2. An assertion is a statement which one claims to be true.

As such, assertions are more restrictive than propositions. For example:

  1. In a logic textbook, we read "It's raining" as an example of a proposition. This is not an assertion.
  2. I look out of the window and say: "It's raining." From the context, it is clear that I am asserting this proposition to be true. Hence, it is an assertion.

The distinction is fine, because everything that is a proposition can also be an assertion, while all assertions are necessarily propositions. So the distinction between the two depends entirely on the context.

Lord_Farin
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    Though whenever I start a paragraph with Proposition., that is certainly something I claim (or assert) to be true (and usually show to be true right away), but neither deserves the merit to be called Theorem. nor is it so subordinate that it should be called Lemma. instead :) – Hagen von Eitzen Aug 24 '15 at 19:05
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    @Hagen A fair point :). I'd edit it into my answer if it weren't already obvious from the tags that OP is talking about logic rather than mathematical practice. – Lord_Farin Aug 24 '15 at 19:07
  • @Lord, Hagen.. thanks! But can you clarify with an example.?that would be very helpful – Ujjwal Saini Aug 24 '15 at 19:12
  • @UjjwalSaini How careless of me not to include one. Here you go. – Lord_Farin Aug 24 '15 at 19:16
  • @Lord_Farin...this is what i was looking for! nice example, now i got this..thanks :D – Ujjwal Saini Aug 24 '15 at 19:26
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    @UjjwalSaini You're welcome. Since you are new, you may not be familiar with the procedure when questions are answered -- see this topic from the help centre. – Lord_Farin Aug 24 '15 at 19:28
  • @HagenvonEitzen, some people classify their proven assertions into lemma/theorem/corollary, others just call everything a proposition. Mostly a matter of taste. – vonbrand Aug 24 '15 at 20:39
  • This is exactly I have been looking for hours. Thank you @Lord_Farin. After the prover confirms something about proposition, it becomes assertion to them and but still can be true or false to the challenger. I mean what if the challenger sees sunny weather through windows after they are told Its raining. In that case the assertion is false. So assertion is subject is based on beliefs of the prover. – tbhaxor Oct 12 '23 at 15:06
  • Also you missed full-stop in the first statement. Does that mean something special? Because grammatically if it is a statement, it must end with full-stop. – tbhaxor Oct 12 '23 at 15:08
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An assertion is a proposition that is claimed to be true.

Proposition P1: The tree is tall
(This might be true or might be false, and it can be just an idea proposed for consideration, apart from anyone's actual beliefs. It may be thought or expressed.)

Assertion A: "The tree is tall."
(This might be true or might be false, but it is a statement of a proposition claimed to be true. Generally, someone purports to believe it and offers it as fact.)

The assertion is itself equivalent to a proposition (P2) about proposition P1:

A = P2: P1 is true. (P2 is the assertion of P1.)

Scott Hatfield
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  • Both are statements.
  • For a Proposition, we can say whether it is true or false.
  • But for an assertion, no chance to be false and definitely it is true.
  • So you can identify that all assertions are prepositions also.
  • But all propositions should not be assertions.
user729424
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Vidu VDS
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    it's my understanding that an assertion is a statement whose maker claims to be true, and the maker could be wrong. – Sajuuk Sep 20 '21 at 10:06
  • Exactly, its up to challenger to prove it true or false. There is a proof by assertion, where prover forces its assertion again and again until there is no challenge to prove it otherwise. It's interesting to look into it. – tbhaxor Oct 12 '23 at 15:15