What is the difference between a Proposition and Atomic Proposition?

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!

• See this post for definition and examples regarding predicate logic. Aug 27, 2019 at 6:46
• 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 : $\lnot P, P \lor Q$). Aug 28, 2019 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". Aug 28, 2019 at 13:19

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).

• 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. Aug 27, 2019 at 3:36
• @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. Aug 27, 2019 at 3:52
• @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. Aug 27, 2019 at 3:53
• if a proposition is not an atomic proposition does that mean a proposition much contain at least 2 parts that are propositions themselves? Aug 27, 2019 at 3:55
• @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" Aug 27, 2019 at 10:12

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.