Introduction to Logic 11th ed. When a statement such as “Some politicians are not corrupt” is said to distribute the “corrupt people” group to “some politicians”, the information seems of little value, since the group “some politicians” is not defined. This is not the case for the A and O forms. Conditionals If A then B 7: The Logic of Categories. If not-B then not-A 3:
Since the rule applies to every member of the corrupt people group, namely, “All corrupt people are not some politicians”, the predicate is distributed. In short, for the subject to be distributed, the statement must be universal e. In the process of obversion , we change the quality of a proposition from affirmative to negative or from negative to affirmative , and then replace its predicate with the negation or complement of the predicate. As such, a Venn diagram illustrating any one of the forms would be identical to the Venn diagram illustrating its obverse. This proposition has a truth value — it makes an assertion that could be true or false. Introduction to Logic 11th ed. Some non-P is non-S.
Surprisingly, a large number of sentences may be translated into one of these canonical forms while retaining all or most of the original meaning of the sentence. Since all beetles are defined not to be mammals, and all mammals are defined not to be beetles, both classes are distributed. This is what it means to say that this logical system is a truth-functional logic.
Propositional Logic: The Logic of Statements | The Critical Thinker
If so, this thin,ing called the hypothetical viewpointin opposition to the existential viewpoint which requires the subject category to have at least one member. When a statement such as “Some politicians are not corrupt” is said to distribute the “corrupt people” group to “some politicians”, the information seems of little value, since the group “some politicians” is not defined.
What you learn in propositional logic is the rules for determining the truth values of the following compound claims …. Some non-P is not non-S.
Categorical propositions can be categorized into four types on the basis of their “quality” and “quantity”, or their “distribution of terms”. There are four types of categorical proposition, each of which crihical given a vowel letter A, E, I and O. Conditionals If A then B 7: This is based on the Latin a ff i rmo I affirm cirtical, referring to the affirmative propositions A and Iand n e g o I denyreferring to the negative propositions E and O.
It is usually a collective statement such as ‘all dogs’ or ‘some dogs’.
Home Top Menu Quick Links. The truth of the whole proposition is a function of the truth of the individual component propositions.
A dog is an animal Some dogs are friendly No dog is a cat Propositions may have quality: Predicate and subject The first term in the proposition is the subject. Thunking my commentary notes here students will notice interesting features of these 15 Venn Diagrams that help understand the underlying logical necessity of validity.
A and O converses are seldom true. All cats have four legs. Note that the quantity does not move with the subject or predicate. No non-P is non-S. No S is non-P. From the crtiical proposition “No beetles are mammals”, we can infer that no mammals are beetles. All S is non-P.
Since not all politicians are defined by this rule, the subject is undistributed. The new statement may or may not be equivalent to the original.
An A -proposition distributes the subject to the predicate, but not the reverse. An Introduction 2nd ed. The contrapositive of a categorical proposition is formed by taking the complement of both subject and predicate awio then reversing them.
Since the rule applies to every member of the corrupt people group, namely, “All corrupt people are not some thniking, the predicate is distributed. The contrapositive of any true A or O proposition is also true making it a useful test. Each of the four canonical forms will be examined in turn regarding its distribution of terms.
Definitions Categorical term A categorical term is something that will be categorized, such as ‘dog’ and ‘cat’. Therefore, Some S are not P. Philosophy Critical Thinking And Writing: