This thesis is a contribution to mathematical logic. In the language of predicate calculus, I change the syntactic structure of the atomic formula from a predicate relation on terms, where terms represent individuals, to a verb as a relation on nouns, where nouns represent either individuals or properties. Based on the verb on nouns syntactic structure for atomic formulas, I construct a formal language that has all the properties of a first-order predicate calculus and, furthermore, that can model natural syntax, the syntax of natural languages. While most mathematicians and logicians acknowledge the success of predicate logic for mathematics, some logicians have criticized predicate logic as being unnatural in a sense, in that its syntax cannot adequately model natural syntax. Logicians who refute predicate logic as a logic for natural languages maintain that term logic is the logic of natural languages and models how we actually reason. I show that the constructed formal language is mathematically rigorous enough to be a basis for the language of predicate calculus by constructing a predicate calculus from the formal language. I also show that the formal language is natural enough to model the syntax of term logic by constructing a formal calculus for term logic from the formal language. Theoretical implications of the formal language are found in the fields of mathematics and linguistics. I show how the formal language may be an approach and mathematical framework for the foundations of mathematics and language in general.
