Abstract

In this dissertation, I address two main, related problems: Rigorously defining the concept of "logical form" for standard languages of logic, and using it to define the concept of "validity in virtue of logical form", or "formal validity". Proving that formal validity, as so defined, is a type of deductive validity, that is, necessary truth-preservation. ;To define the concept of "logical form" I make use of grammatical substitution, and divide the vocabulary of a language into two parts: the logical and the lexical vocabularies. The logical terms are held fixed, while the lexical terms are open to substitution by terms of the same grammatical category. The specific logical form of a sentence is defined as the smallest class of sentences which contains the sentence and is closed under grammatical substitution. A sentence is defined as "formally true" if its specific logical form is a class of true sentences. ;The main argument that I present is that the definitions of formal validity for sentential and predicational languages capture a type of deductive validity. I use the fact that the substitutional theory of validity equates the formal validity of a sentence to the truth of a second-order generalization of that sentence. I show that if formal validity is appropriately defined, and if the language has the proper grammatical and lexical resources, then these second-order generalizations will be noncontingent. This means that the formal validity of a sentence is a noncontingent matter. Since it can be proven that a sentence being formally valid entails its preserving truth, it follows that a formally valid sentence will be necessarily true. This makes it deductively valid. ;My main result is to show that it is possible to steer a middle course between the textbook writers who claim that all validity is formal, and the skeptic who claims that no validity is formal. This means that I have both positive and negative results: the negative result that formal validity is not all of deductive validity, and the positive result that formal validity is some of deductive validity