7/25/2023 0 Comments Logic world history![]() = “All trespassers are people who will face prosecution.”.More examples of translation exercises from English into the logical syntax of Aristotelian logic: ![]() Now the subject term denotes a class of people, and not just a bare adjective. “Some disorganized people are teenagers.” To write this in the “logicese” of Aristotelian logic, you need to rewrite the adjective as a plural noun, like so: Adjectives are used to modify nouns, they can’t normally stand alone. The problem is that the word “disorganized” is an adjective, not a noun. This is no longer a grammatically well-formed sentence. If you switch the subject and predicate terms you get this: “ Some disorganized are teenagers”. “Some McDonald’s employees are teenagers” is just as grammatically well-formed as “ Some teenagers are McDonald’s employees”.īut now consider this statement: “Some teenagers are disorganized”. Plural nouns can function either as subject or predicate terms in a categorical statement. That’s what categorical logic was set up to represent. Informally we call this translation from English (say) to “logicese” (by analogy with “Chinese”, “Japanese”, etc.).įor linguistics majors, the main benefit of working through the exercises like this is that they help to make you aware of grammatical and logical features of language that you wouldn’t otherwise pay attention to.įor example, it’s easy to translate “Some teenagers are McDonald’s employees” because both the subject and predicate terms are plural nouns - each denotes a class of objects. One of the more fun activities you do in a symbolic logic class is learn how to translate natural language expressions into the logical syntax of a particular logical system. It’s the fragment of natural language that involves statements with a two-place subject-predicate structure, where the subject and the predicate terms can be represented as classes of objects, and where the logical relations between statements are determined by relations of inclusion, exclusion, and overlap among the classes. So, what is the fragment of natural language whose logical structure Aristotelian logic is able to model? (There are fourteen valid forms in Aristotle’s system. These reflect the subject-predicate structure of a wide class of statements, but certainly not all statements.Ī categorical syllogism is an argument consisting of exactly three categorical statements (two premises and a conclusion) in which there appear a total of exactly three categorical terms, each of which is used exactly twice.Īristotle examined all the logically distinct types of syllogisms that could be created using the basic categorical statements, and identified which are deductively valid and which are invalid. ![]() Or rather, it’s the logic of statements that can be represented in terms of classes of things, and relationships between those classes.įor example,the natural language statement “All cows are mammals” would be represented as a relation between the class of cows and the class of mammals (namely, that the class of cows is a subset of the class of mammals, or equivalently, that all members of the class of cows are also members of the class of mammals).Īristotelian logic gives us tools for representing claims of the following form, which are called “categorical statements”: Aristotelian logic is the logic of classes, or categories - hence, it is often called “categorical logic”. ![]()
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