3

Today in class our professor explained that a proposition is a sentence that declares a fact that either true or false but not both. However, shortly after he defined Atomic Proposition as "No part is a proposition" with an example of a proposition.

After researching around it seems that the two are identical as I can't find any definitions that show differences between the two.

A quick and easy explanation between the two would be awesome as I should have asked him during class.

Thanks!

EsotericLanguage
  • 33
  • See this post for definition and examples regarding predicate logic. – Mauro ALLEGRANZA Aug 27 '19 at 06:46
  • A formula of propositional calculus can be either atomic (i.e. a propositional letter : $P,Q,R$) or "compund" (i.e. containing one or more conenctive : $\lnot P, P \lor Q$). – Mauro ALLEGRANZA Aug 28 '19 at 13:17
  • In the same way, in natural language we may call a proposition atomic if we cannot find a part of it that is again a proposition : "Socrates is a man", while we can call it compund if we can analyze it in parts that are themselves propositions (glued together by conenctives) : "Socrates is a man and Plato is his pupil". – Mauro ALLEGRANZA Aug 28 '19 at 13:19

2 Answers2

3

Consider "Grass is green and snow is white".

This is a proposition, since it makes a claim that is either true or false (in our world, it is true, but in other logically possible worlds, it might be false).

However, this statement is not an atomic proposition, since it has a part (e.g. "Grass is green") that is a proposition.

"Grass is green" itself is an atomic proposition, since there is no smaller part that is still a proposition (e.g. "Grass" is not a proposition).

ferris
  • 13
Bram28
  • 100,612
  • 6
  • 70
  • 118
  • What would be an example of an atomic proposition? Would it just be "Grass is green".

    From my understanding, an atomic proposition is just a proposition without 2 or more parts that are also propositions.

     – EsotericLanguage Aug 27 '19 at 03:36
  • @Zdravstvuyte Exactly ... "Grass is green" has no smaller part that is a proposition itself ... but it is a proposition as a whole. So, it is an atomic proposition. – Bram28 Aug 27 '19 at 03:52
  • @Zdravstvuyte But also note that a proposition that is not an atomic proposition need not have 2 parts that are propositions. "grass is not green" is not an atomic proposition, and yet it has only 1 part "Grass is green" that is a proposition. – Bram28 Aug 27 '19 at 03:53
  • if a proposition is not an atomic proposition does that mean a proposition much contain at least 2 parts that are propositions themselves? – EsotericLanguage Aug 27 '19 at 03:55
  • @Zdravstvuyte No. That's what I tried to show with the example of "Grass is not green". That is clearly a proposition, but not an atomic proposition. But it also does not have 2 parts that are propositions themselves. It has just 1: "Grass is green" – Bram28 Aug 27 '19 at 10:12
  • I think I had a typo and meant to say "an atomic proposition must contain at least 2 parts that are propositions themselves?" – EsotericLanguage Aug 29 '19 at 13:52
  • @Zdravstvuyte No, If a proposition contains two parts that are propositions themselves, then it is certainly not an atomic proposition. An atomic proposition contains no parts that are still propositions themselves. – Bram28 Aug 29 '19 at 14:43
  • I guess I am not understanding this. If "Grass is not green" is not an atomic proposition then what is? as this is a proposition but only has 1 part that is a proposition which is itself. Thank you again for responding as I do appreciate the effort put in towards making me understand the topic! – EsotericLanguage Sep 01 '19 at 04:17
  • @Zdravstvuyte Look at the definition of an atmic proposition provided by your Professor: "No part is a proposition". So, "Grass is green" is an atomic proposition, because any part of it (like "Grass" or "green" or even "Grass is" or "is green") is not a proposition. However, "Grass is not green" is not atomic, because it does have a part, namely "Grass is green" that is a proposition. You keep thinking that for something to not ba an atomic proposition it must have at least 2 parts that are propositions, but that is not true ... and not what your professor said. – Bram28 Sep 01 '19 at 11:06
  • seems like everything makes sense now! Thank you so much for your support. – EsotericLanguage Sep 03 '19 at 23:57
  • @Zdravstvuyte Great, glad I could help! You can accept my Answer by clicking the check mark to the left of it. – Bram28 Sep 04 '19 at 02:24
2

A proposition is a sentence like $p\to(p\to q)$. An atomic proposition is like $p$. Like with atoms, an atomic proposition is the fundamental block from which more complex structures can be built.