1	Logic “Come now, and let us reason together, saith the LORD” (Isaiah 1:18)
2	What Is Logic? Logic is the study of methods and principles used in the proper use of reason. Its intent is to assist the student of logic to distinguish between correct reasoning and incorrect reasoning. All human beings employ logic in their daily lives, but a student of logic is more likely to reason correctly than a non-student. The proper use of logic should make thinking easier rather than harder.
3	Definitions Explicit proposition – an expressed statement that directly relates its meaning. Implicit proposition – a proposition which is implied by other propositions, but not expressly stated. Implication – the process of conveying information indirectly without expressly stating the proposition.
4	Definitions Inference – the process of ascertaining information not expressly stated in express statements. (Note: implications are contained within the statements that imply them. Inferences are our own conclusions.) Valid – an argument formed such that if its premises are true, its conclusion must be true. Sound – a valid argument with true premises.
5	Components of Logic Premise – a proposition used as the basis of an argument or inference. Conclusion – a proposition thought to be derived from two or more propositions taken as premises. (Note: conclusions may become premises for other arguments.)
6	Components of Logic Proposition – a statement which has the characteristic of being either true or false. Argument – A series of propositions consisting of two or more premises and at least one conclusion. (Note: in everyday speech arguments are often expressed as enthymemes where either some of the premises or the conclusion is implied.)
7	Simple Arguments Categorical arguments – arguments based on set theory. These arguments consist of a major and a minor premise and a conclusion. Hypothetical arguments – arguments based on conditional statements. The premises of this kind of argument are not called “major” and “minor” premises.
8	Categorical Arguments Four standard forms of propositions: Universal affirmative – All dogs are mammals. Universal negative – No humans are marsupials. Particular affirmative – Some mammals are humans. Particular negative – Some politicians are not liars.
9	Terms All valid propositions consist of three terms. The “terms” of an argument are the major nouns of the argument. In the propositions “All men are mortal” “men” and “mortal” are the terms. The “major term” is the term that exists in the predicate of the conclusion. The “minor term” is the term that exists in the subject of the conclusion. The middle term is not found in the conclusion, but is found in both premises.
10	Major and Minor Premises The Major Premise is the premise that contains the major term. The Minor Premise is the premise that contains the minor term. Note: The Major Premises is usually stated first in an argument, but it is the presence of the major term that makes it the Major Premise, and not its placement in the argument.
11	Validity of Categorical Arguments Must have three and only three terms in the argument. The middle term must be distributed in at lease one of the premises. Terms distributed in the conclusion must be distributed in the premises. At least one of the premises must be in the affirmative. If either premise is negative, the conclusion must be negative. A particular conclusion cannot be drawn from two universal premises.
12	Hypothetical Arguments Made up of a condition and a consequent (If A then B) Truth Table Condition Consequent Result True True True True False False False True True False False True
13	Hypothetical Arguments Valid arguments Modus Ponens affirms the condition. Modus Tollens denies the consequent. Invalid arguments Affirming the consequent Denying the condition (or antecedent)
14	Common Fallacies Argumentum ad Ignorantiam (argument from ignorance) Argumentum ad Populum (appeal to the people) Argumentum ad Verecundiam (appeal to authority) Pititio Principii (begging the question) Complex question
15	Common Fallacies Equivocation – changing a definition during an argument. Division – applying to individuals of a group, that which is true of the group as a whole. Accident – making a general rule from a specific example.