PHI 112: Intro to Logic

Waggle Sections

Analysis of Language and the Parts of Sentences.

Let us start from the most basic notion in logic.  In order to understand reasoning, we need to pay special attention to language.  The most basic form of a sentence is an atomic sentence.  These atomic sentences only have grammatical structure.  In English, there are two basic forms of atomic sentences.  This is due to the fact that there are one place verbs and two place verbs in English.  What I mean by a one-place verb is a verb that predicates of some name a predicate.  What I mean by a two-place verb is a verb that sets up some relationship between two names.

A.  Socrates is mortal.

B.  Socrates taught Plato.

Sentence A is an example of an atomic sentence with a one-place verb.

Sentence B is an example of an atomic sentence with a two-place verb.

All other declarative sentences in English are constructed by using logical connectives.  Please note that the type of logic we are studying does not apply to interrogative or imperative sentences.  These more complex declarative sentences are constructed by using one of the eight logical connectives listed in the table below.

Please note that some of these connectives do not have left and right parts.  Negations, for example, are one-place connectives.  Whatever follows the negation connective is called the “negate”.  The identity sentences do not have unique names for the left and right parts.  Both generalizations, technically, are composed of quantifiers and scopes.  These sentences are more complicated than the previous 6 and we will examine them last.  For now, we should assimilate the names of the connectives and their parts for the conditionals, biconditionals, conjunctions, disjunctions, and negations.  We will learn the symbols later in the semester.  For now, just familiarize yourself with these notations so that you will understand them when you encounter them.  We will spend a portion of the course solely on the symbolic notation.

These logical connectives are exhaustive, meaning, there cannot be any declarative sentence in the English language that is not built up from these connectives.  Moreover, we may have sentences with far more complexity than those listed above, but the main connective will be one of the eight.

Example of a basic level logical sentence.

If Socrates is human, then Socrates is mortal.

Example of a more complex sentence with a conditional as the main connective.

If both Socrates is human, and Plato is human, then both Socrates is mortal and Plato is mortal.

Please notice that this second sentence is a conditional, just as in the first sentence.  But, the antecedent is a conjunction, and the consequent is a conjunction.  We could have a sentence with even more structural complexity, but what we should notice is that the main connective will be one of the eight.  Moreover, the sub-parts also will be either atomic or logically complex and if the latter, then built up using one of the eight connectives.