Logic Verbal Question
[#permalink]
31 Mar 2015, 17:51
There are three main sub-types of syllogisms: categorical, disjunctive, and hypothetical. This extra credit assignment involves categorical syllogisms. Categorical syllogisms are deductive arguments in which every statement of the argument (all the premises and the conclusion) are categorical statements. Categorical statements are statements that begin with a categorical quantity term (CQ Term). There are four type/kinds of categorical statements. These are established by which of the four types of categorical quantity terms that are used to begin the categorical statement. Here are the CQ terms:
CQ Term Corresponding Abstract Categorical Stmt.
1. All, every All As are Bs.
2. No, none No As are Bs.
3. Some Some As are Bs.
4. Some … not …, not all Some As are not Bs.
Given the following parameters (assumptions), write an arithmetic/algebraic proof (in other words, PROVE) to show the total number of categorical syllogism arguments (= the number of possible permutations or combinations of categorical syllogisms given the parameters below).
Assume that categorical syllogisms are limited to three (3) statements consisting of two (2) premises and one (1) conclusion.
Recall that there are four (4) types/kinds of categorical statements.
How many two premise, one conclusion categorical syllogisms are there? Another way of asking: How many possible permutations are there for three statements with four different kinds of statements?
One must provide in one’s satisfactory answer the total number of permutations, an arithmetic/algebraic proof that proves it is that number.
HINT ANALOGY. This question is similar to asking how many possible PIN numbers there are. Assuming that PIN numbers must be four (4) digits places ONLY, and the only possible digits in each place are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 = 10 digits, how many possible permutations of PIN numbers are there?