What are syllogisms?
A syllogism can be defined as a type of logical argument. However, syllogisms differ from standard logical arguments considerably. As a rule, a traditional logical inference has two basic elements, i.e., a premise and a conclusion. A standard syllogism contains three basic elements, which are two premises and the following conclusion. A typical syllogism is also different from a traditional logical inference in that the conclusion that follows its two premises does not coincide with the supposed result. The conclusion of a syllogism interferes with the minor premise from a major one with the help of mediation.
What constitutes a “formal fallacy?”
The argument whose premises do not support the conclusion in any way and in which the chain of logical conclusions is always wrong is typically referred to as a formal fallacy. When speaking about a formal fallacy, it is important to realize that it does not matter in the given case whether a specific argument is true or false; it might as well be true with a formal fallacy in it. Traditionally, the following pattern is used to demonstrate the specifics of a formal fallacy:
- Logical statement: 1. If A then B. 2. A. 3. Therefore, B.
- Formal Fallacy: 1. If A then B. 2. B. Therefore, A.
Examples of a formal fallacy:
- If one is ashamed, one’s face will turn red. A man’s face is red. Therefore, he is ashamed.
- Some men can drive a car. Mr. Johnson is a man. Therefore, he can drive a car.
What is the difference between Conjunction and Disjunction?
In logical operations, conjunction is used to denote an “and” operand; in other words, it denotes the situation in which both operands (or all those included) are true. In its turn, a logical disjunction, known as “or,” is an operand that shows if one or more of the operands involved is true.
Herein lies the difference between the two operands. In the case of Conjunction, the statement under consideration can be regarded as a universal truth; otherwise, the Conjunction does not make sense. The Disjunction operand works differently; in contrast to Conjunction, Disjunction serves to denote that only some of the operands in question are true, yet not all of them.
From a mathematical standpoint, conjunction can be interpreted as the inclusion of a specific subset into another set. Disjunction, on the contrary, presupposes the exclusion of one of the sets.
How Does Truth Table work?
Often defined as a template for analyzing the forms and relations of the elements in logical expressions, a Truth Table consists of several columns in which a corresponding variable is placed. The final column is left for defining and marking the outcome of a logical operation.
It would be a mistake to believe that a Truth Table can only deliver the results for the operations involving only two variables. On the contrary, as it has been stressed above, the number of types of input variables can be rather big. The result, however, is necessarily restricted to the truth-or-false answer.
It should also be mentioned that a Truth Table allows for dealing with the logical operations that include conjunctions, disjunctions, negations, or implications.
A Truth Table can also help in analyzing the relations between different elements of the logical operation in question, therefore, structuring the task and allowing for a better understanding of the problem.