4

In An Introduction to Logic by Patrick Suppes, an atomic sentence is defined as a sentence that contains no sentential connective. However, in a later chapter, a sentence is defined as a formula which contains no free variables.

Now if we take a sentence like all apples are red, it could be symbolized as (x)( A(x) => R(x) ) which does contain an implication. So is that sentence an atomic sentence or not?

8

In propositional logic sentence and formula are synonyms.

An atomic sentence is a formula without propositional connectives [see Suppes, page 12].

In predicate logic, sentence and formula have different meaning: a sentence is a formula with no occurrences of free variables [see Def. page 54].

The formal definition of formula for predicate logic is at page 52:

a predicate followed by the appropriate number of terms as arguments is an atomic formula [examples: Px,Rxy].

Formulas are: atomic formula or formulas produced using connectives and quantifiers.

Thus, "Socrates is a philosopher", which can be symbolized with Phil(S), is an example of atomic sentence, while "Every Greek is a philosoper" [ ∀x ( Greek(x) → Phil(x)) ] is not.

4

It is a sentence but not an atomic sentence.

It is a sentence because the all-quantifier binds the free variables and so closes the formula. It is not an atomic sentence because it contains an implication.

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.