ABSTRACT
This chapter explains validity theory in the formal logic elements. People found it easy to prove that two forms of the mixed hypothetical syllogism were invalid, that they could not be relied on to give a true conclusion from true premisses. Since, in order for the form to be valid, every proper set of substitutions must yield a valid inference, to show that a form is invalid it suffices to find one set of substitutions which does not yield a valid inference. In formal logic people are not interested in all the rich encrusted variety which occurs in ordinary language. The concern is to dig beneath this variety for the more austere structural elements: and since validity springs from structure, any method for determining it must be concerned with these structural elements. The chapter introduces a few symbolic conventions which will make for easier working.
