Question

Write a summary of what is learned in intro to logic using these terms :

Categorical propositions

Categorical syllogisms

Propositional logic

Predicate logic

Answer 1

• Logic is a language for reasoning. It is a collection of rules we use when doing logical reasoning. Human reasoning has been observed over centuries from at least the times of Greeks, and patterns appearing in reasoning have been extracted, abstracted, and streamlined.
• Categorical propositions are the building blocks of categorical logic, which goes back to Aristotle’s fundamental work in the 4th century BC. Aristotle developed his logic as a foundation for science.
• A proposition that relates two classes, or categories, is called a categorical proposition. The two classes in question are denoted by the subject term and the predicate term. Categorical propositions assert that either all or part of the class denoted by the subject term is included in or excluded from the class denoted by the predicate term.
• There are four standard forms of categorical propositions:
• 1. All S are P (A proposition)
• 2. No S are P (E proposition)
• 3. Some S are P (I proposition)
• 4. Some S are not P (O proposition)
• A categorical syllogism is an argument consisting of exactly three categorical propositions (two premises and a conclusion) in which there appear a total of exactly three categorical terms, each of which is used exactly twice.
• One of those terms must be used as the subject term of the conclusion of the syllogism, and we call it the minor term of the syllogism as a whole. The major term of the syllogism is whatever is employed as the predicate term of its conclusion. The third term in the syllogism doesn't occur in the conclusion at all, but must be employed in somewhere in each of its premises; hence, we call it the middle term.
• Since one of the premises of the syllogism must be a categorical proposition that affirms some relation between its middle and major terms, we call that the major premise of the syllogism. The other premise, which links the middle and minor terms, we call the minor premise.
• Consider, for example, the categorical syllogism:

• No geese are felines.
  Some birds are geese.
  Therefore, Some birds are not felines.

• Clearly, "Some birds are not felines" is the conclusion of this syllogism. The major term of the syllogism is "felines" (the predicate term of its conclusion), so "No geese are felines" (the premise in which "felines" appears) is its major premise. Simlarly, the minor term of the syllogism is "birds," and "Some birds are geese" is its minor premise. "geese" is the middle term of the syllogism.

• Propositional logic (also called sentential logic) is logic that includes sentence letters (A,B,C) and logical connectives, but not quantifiers. The semantics of propositional logic uses truth assignments to the letters to determine whether a compound propositional sentence is true.

• Predicate logic is usually used as a synonym for first-order logic, but sometimes it is used to refer to other logics that have similar syntax. Syntactically, first-order logic has the same connectives as propositional logic, but it also has variables for individual objects, quantifiers, symbols for functions, and symbols for relations. The semantics include a domain of discourse for the variables and quantifiers to range over, along with interpretations of the relation and function symbols.