# Formal Logic

One of the two main kinds of logic. Formal logic deals with the form of an argument rather than its content, and it studies language, deduction and reasoning. It is closely related to mathematics.^{F36}

One of its core rules is *modus ponens* (“the affirming mode”): a technical term sometimes used by students as a brand name for the whole of formal logic, as in “*modus ponens* and all that”. *Modus ponens* is an inference from two premises. The first premise is conditional, consisting of an “antecedent” and a “consequent”; the second premise simply confirms that the antecedent applies in this case. Example:

1. If you get some ducks [antecedent], your slug problem will be resolved [consequent].

2. You are getting some ducks [the antecedent is confirmed].

3. Therefore your slug problem will be resolved [conclusion].

The counterpart to this is *modus tollens* (“the denying mode”), in which a similar first premise is followed by a second premise that denies the *consequent*. Example:

1. If Mary is at home [antecedent], her car will be outside [consequent].

2. Her car is not outside [the consequent is denied].

3. Therefore she is not at home [conclusion].

It sounds banal, but the syllogisms of formal logic are the building blocks of reasoning which—in combination with a series of conditions, affirmed or denied in sequence and in parallel—can develop into a problem-solving capacity of great complexity, used as the logical structure on which artificial intelligence is based.^{F37}

Informal logic is, of course, the junior partner in all this, since it depends on the reasoning of formal logic, and its mixing up of logic and content is exactly what you cannot do with formal logic. On the other hand, without content, logic has no purpose. Formal logic is the road; informal logic is the journey.

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