Discuss the concept of validity in formal logic and provide examples.

In formal logic, validity refers to the property of an argument where the conclusion logically follows from the premises. It is concerned with the structure and form of an argument rather than the actual truth or falsity of the statements involved. An argument is considered valid if it is impossible for the premises to be true and the conclusion false at the same time.

To determine the validity of an argument, we use deductive reasoning and logical rules. These rules are based on the principles of formal logic, such as modus ponens, modus tollens, hypothetical syllogism, disjunctive syllogism, and others. By applying these rules, we can evaluate the validity of an argument.

Let's consider an example to illustrate the concept of validity:

Premise 1: All mammals are warm-blooded.
Premise 2: All dogs are mammals.
Conclusion: Therefore, all dogs are warm-blooded.

This argument is valid because the conclusion follows logically from the premises. If we assume that both premises are true, it is impossible for the conclusion to be false. The argument follows the logical rule of categorical syllogism, which states that if a statement applies to a whole class (all mammals) and a particular member of that class (dogs), then it applies to the relationship between the particular member and the whole class (dogs are warm-blooded).

Now, let's consider an example of an invalid argument:

Premise 1: All cats have tails.
Premise 2: This animal has a tail.
Conclusion: Therefore, this animal is a cat.

This argument is invalid because the conclusion does not logically follow from the premises. Even though the premises are true, it is possible for the conclusion to be false. The logical rule of categorical syllogism cannot be applied here because the premises do not establish a relationship between the whole class (cats) and a particular member of that class (this animal).

In summary, validity in formal logic is concerned with the logical structure of an argument. An argument is valid if the conclusion logically follows from the premises, making it impossible for the premises to be true and the conclusion false simultaneously. By applying logical rules, we can evaluate the validity of arguments and determine their logical soundness.