Logic: Meanings

I. Four Types of Sentences

1. Declarative: “Michigan beat Ohio State.”
2. Interrogatory: “Did Michigan win?”
3. Imperative: “Beat Ohio State.”
4. Exclamatory: “Hurrah for Michigan!”

II. Lexical Definitions vs Stipulative Definitions

A lexical definition means the way a word is commonly defined. A stipulative definition is when a word is defined by a person for a specific context or argument. Stipulative definitions can be different from lexical definitions, as long as they are defined clearly, are useful, avoid circularity, etc.

III. Analytic vs Synthetic Statements

An analytic statement is one that’s self-contradictory to deny. Examples: 2+2=4, no bachelors are married. A synthetic statement is one in which it is not self-contradictory to deny. Contingent is another term for this.

IV. A Priori and A Posteriori

A priori (rational) knowledge is knowledge not based on sense experience. This often (though not always; see below) lines up with analytic statements. A posteriori (empirical) knowledge is knowledge based on sense experience. This often (though not always) lines up with synthetic statements.

There are examples of  a posteriori truths that are analytic: “all cats are mammals.” And a prior truths that are synthetic: “the 1 Meter Bar (the reference bar used to set the length of all meters) is 1 meter long.”