Formal Logic: Types, Language, and Statements
Formal Logic
Formal logic deals with the validity of arguments by focusing on their formal aspect. It determines when an inference is well-built, meaning the conclusion is properly deduced from the premise.
Types of Formal Logic
- Logic of Statements: Studies the formal validity of arguments by considering only the truth value (true or false) of each statement. It treats statements as a whole, without analyzing the subject and predicate internally.
- Predicate Logic: Analyzes the internal structure of utterances, focusing on propositions where a property (predicate) is attributed to the subject.
- Logic of Classes: Considers statements as propositions that express ties between individuals and classes. Predicates are analyzed as properties shared by individuals within the same class or set.
- Logic of Relations: Addresses the limitation of other types of logic by incorporating elements, symbols, and rules necessary to express relationships.
The Language of Logic
The language used in everyday conversations, such as English, is called natural language. Natural languages contain ambiguities and inaccuracies, including equivocal terms. To address this, mathematics, physics, and logic use constructed languages. This language is not only artificial but also a formal language. The symbols (p, A, T, r) in formal logic have no inherent meaning, unlike the signs in natural languages.
Logical Language Elements
- Vocabulary: A set of logical symbols, similar to words in a language.
- Lyrics: Represent the set of arguments. For example, “If you ask me, then go” would be: if p then q.
- Signs: Represent the relationship between sentences and terms. For example, “If you ask me, then go” would be: p ? q.
- Formation Rules: Define which combinations of symbols form well-formed sentences, similar to grammar rules in natural languages.
- Transformation Rules: Determine how formulas can be deduced from others, which is the core of logic. These rules are similar to natural language rules, such as converting from active to passive voice.
The Logic of Statements
Also called propositional logic, its purpose is to analyze the relationships between statements, i.e., the connections that allow us to obtain a valid conclusion from premises.
Statements
Only sentences that can be true or false are considered statements. There are two types:
- Simple (Atomic) Statements: Cannot be broken down into other sentences. For example: “John studied philosophy.”
- Complex (Molecular) Statements: Can be broken down into simple statements. For example: “His name is Antonio and his wife’s name is Araceli.”