Core Concepts Symbolic Logic

Argument Indicators

Words or phrases used to indicate that certain propositions are intended to be read as support for some other proposition

Ex: ‘hence’ ‘therefore’ ‘because’

Premise Indicators

Words ot phrases that indicate that we are about to be given premises

Ex: Since, because, for, as, for the reason that, in view of the fact that, etc

Conclusion Indicators

Words or phrases that indicate that the conclusion is about to come

Ex: Therefore, hence, thus, so, it follows that, which establishes that, etc

How do you put an argument into standard form?

Identify the premises and the conclusion, list and number all of the premises and draw a line under the last one, write and number the conclusion under the line

The line will represent the conclusion indicator

The premises of an argument support the conclusion when…

All the premises are ture and the conclusion follows from the premises

An argument is valid …

If and only if it is impossible for premises to be true and conclusion false at the same time

An argument is invalid…

when it is possible for the premises to all be true and the conclusion to be false at the same time

An argument is sound…..

when it is both valid and has all true premises, otherwise it is unsound

An argument is unsound…

When it is either invalid or it has at least one false premise

An argument succeeds in showing that its conclusion must be true when:

All the premises are true and the conclusion follows validly from the premises

An argument form is valid…..

If and only if it is impossible for any argument having this form to have all true premises and a false conclusion

Ex: All Xs are Ys. Z is a X. Z is a Y. It is impossible to come up with values for X Y Z that will make the premises true and the conclusion false

An argument form is invalid….

when it is possible for an argument having that form to have all true premises and a false conclusion

The validity of an argument is…

a function of it’s form, not its content