Validity and Soundness

Valid and Sound Arguments An argument is a series of statements meant to establish a claim. A statement is any explicit declarative statement about a fact. It says that something is (or isn’t) the case. A premise is a statement used in an argument to establish a claim. An argument is valid if its premises necessarily lead to its conclusion. An argument is sound if it is valid and that its premises are actually true. The two arguments by Socrates in The Apology being evaluated are as follows. Argument 1 Premise 1 – If Socrates corrupts the young, they or their relatives will accuse him. Premise 2 – His young followers do not accuse him and neither do their relatives. Conclusion – Therefore, Socrates has not corrupted the young. Argument 2
Premise 1 – Either death is dreamless sleep or death is migration of the soul to some other place. Premise 2 – If the former, then there is no reason to fear death. Premise 3 – If the latter, then there is no reason to fear death. Conclusion – Therefore, there is no reason to fear death.
Symbolic notation and truth tables are great tools to identify validity. In argument 1, the statement that Socrates has corrupted the youth can be abbreviated as ‘Y’. The statement that either his young followers will accuse him or their relatives will accuse him can be translated as – either ‘F’ or ‘R’. In the second argument, the statement that death is dreamless sleep can be abbreviated as ‘D’. The statement death is a migration of the soul to some other place can be abbreviated as ‘M’ and the statement that there is reason to fear death can be abbreviated as ‘F’. When one translates statements into symbolic notation, one must be concerned not to associate with the expressions of the English language; the letters or symbols should be in the purest form of its definition. Symbolic notation is a great time-saver in argumentation. It prevents logical confusion especially when dealing with complex arguments.
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