Introduction to Logic

A compilation of the key terms from each week in the course: Introduction to Logic.

Stoicism

A philosophy advocating the repression of emotion and indifference to pleasure or pain. This term is named after the Greek Stoics (dating from around 300 B.C.) who held to such a philosophy. See Acts 17:18.

Belief

A positive mental attitude toward a proposition; something a person accepts as true.

False

Contrary to the mind of God. Something is false if it is something that God would never say.

Implications

That which is suggested by evidence or reasoning. That which follows logically from something else.

Logic/Logical

In accordance with the laws of logic: reasonable.

Rational

In accordance with laws of logic: logical.

True

Conforming to the mind of God. Something is true if it is something that God would say.

Faith

Having confidence in something not perceived with the senses.

Revelation (Divine)

The disclosure of information from God to man.

Knowledge

Knowledge is true, justified belief.

Laws of Logic

Universal, invariant, abstract rules of correct reasoning.

Objective

Independent of the person. Something is objective if it is the same for all people.

Propositional

A truth claim. A proposition is either true or false (though sometimes we don't know which).

Sovereign

Having supreme power or authority and not required to answer to any higher authority.

Special Revelation

The disclosure of information from God to man contained in the Bible.

Emulate

To copy or imitate; to match the characteristics of another.

Qualitatively

Pertaining to the quality, kind, or nature of a thing, regardless of the amount or degree.

Quantitatively

Pertaining to the amount, degree, or number of something.

Sin

Disobedience to God.

Speculation

Conjecture, guess, or hypothesis, without sufficient supporting evidence.

Proposition

A truth claim. A proposition is either true or false (though sometimes we don't know which).

Argument

A series of propositions where the truth of one is said to follow from the others.

Premise

A proposition in an argument that is taken as an accepted fact.

Conclusion

The proposition in an argument that the person is attempting to prove.

Inferences

Opinions formed from evidence; what people reason to be true or likely true from evidence or reason.

Persuasive

The tendency to include belief or behavior in a person. A persuasive argument is one in which most people will accept the conclusion as true.

Deductive Argument

An argument in which the conclusion is certainly true if the premises are.

Inductive Argument

An argument in which the conclusion is likely to be true if the premises are.

Fallacy

A common error in reasoning.

Absolute

Independent of arbitrary standards; being without exception or qualification.

Abstract

Existing in thought as an idea but having no physical or material existence.

Conceptual

Abstract; existing within the mind such as a thought or idea.

Invariant

Not changing over time.

Law of Identity

"A thing is itself" or "If A then A."

Law of Non-Contradiction

The compound proposition "A and not-A" is always false. Or, "You cannot have A and not-A at the same time and in the same sense."

Law of the Excluded Middle

The compound proposition "A or not-A" is always true. Or, "Either A is true, or not-A is true." A proposition always has the opposite truth value of its negation.

Negation

The opposite proposition formed by adding "it is not the case that" to the original proposition.

Omni-Present

Able to exist or exert power at all locations in space at the same time.

Universal

Applicable everywhere.

Extrapolate

To project or expand beyond known data or experiences based on patterns exhibited in known data or experiences; to infer unknown values or properties based on known values or properties.

Justify

To provide reasons for a proposition.

Monotheistic

Pertaining to the belief or conviction that there is one and only one God.

Polytheistic

Pertaining to the belief that there are multiple gods.

Repealed

Removed, rescinded, or annulled. A law that has been repealed is no longer binding.

Contradiction

The negation of a proposition, or the combination of the proposition and its negation. "A and not-A" is a contradiction.

Intuitive

In accordance with our feelings or expectations.

Pragmatic

Practical; based on what works regardless of theoretical considerations, principles, moral implications, or truth.

Self-Refuting

That which shows itself to be wrong. A self-refuting argument is one in which the conclusion is inconsistent with one or more of the premises.

Transcend

To go beyond.

Apparent

Something that appears clear to the eye or mind, though it may not be.

Prerequisites

Those things that are required in advance; that which is necessary to a particular end.

Rhetoric

The art or skill of speaking or writing effectively and persuasively (regardless of considerations of logic or truth).

Subjective

Dependent on the thoughts or feelings of the individual.

Arbitrary

Something that does not have a specific reason.

Cogent

An informal argument is cogent if the conclusion is likely to be true.

Inconsistent

At variance or not compatible. Two things are inconsistent if they do not go well together.

Lexical Definition

The definition of a word found in a dictionary or lexicon.

Stripulative Definition

A declaration of the meaning of a word or phrase that does not already have an established use.

Precising Definition

The definition of a word that is consistent with its lexical definition, but which adds further restrictions for the purpose of clarification or scientific precision.

Theoretical Definition

A stipulative or lexical definition that is associated with a particular scientific theory.

Persuasive Definition

A fallacious definition, not found in any dictionary, that is intended to persuade someone. (Rhetorical definition.)

Referent

The object or idea to which a word points or symbolizes.

Ambiguity

The quality of being unclear in meaning; the capacity to be understood in two or more ways.

Biased

Inclined or prejudiced to a particular position.

Linguistic Token

A written or spoken symbol that represents something else. Words are linguistic tokens.

Formal Logic

The study of the principles of correct reasoning that focuses on the structure (or form) of the argument.

Informal Logic

The study of the principles of correct reasoning which does not focus on the structure of an argument.

Sound

An argument that is valid and also has true premise. A sound argument always has a true conclusion.

Syllogism

A categorical argument containing two premises and one conclusion.

Valid

An argument in which the conclusion follows logically from the premises, regardless of whether the premises are true.

Enthymeme

An argument with an unstated premise or an unstated conclusion.

Fallacy of Ambiguity

A category of logical fallacy in which the argument has used words or phrases in a way that is confusing or vague.

Fallacy of Presumption

A category of logical fallacy in which the argument has assumed something that is unproved or doubtful.

Fallacy of Relevance

A category of logical fallacy in which the conclusion of the argument is not strongly relevant to the premises.

Equivocation

Shifting from one meaning of a word to another within an argument.

Reification

Attributing a concrete characteristic to something abstract.

Fallacy of Accent

Changing the meaning of proposition by placing undue emphasis on a word or phrase.

Collective

The use of "all" that means "all together" or taken as a whole - in contrast to distributive.

Fallacy of Composition

Falsely assuming that what is true of the parts/individuals must also be true of the whole/group.

Fallacy of Division

Falsely assuming that what is true of the whole/group must also be true of the parts/individuals.

Distributive

the use of "all" that means "each and every one" taken separately -- in contrast to collective.

Hasty Generalization

Drawing a generalization from too few specific examples.

Sweeping Generalization

Applying a generalization to an exception.

False Cause Fallacy

The error of attributing a cause-and-effect relationship between two events that do not actually have such a relationship.

Post Hoc Ergo Propter Hoc Fallacy

"After this, therefore because of this." The (false cause) fallacy of assuming that event A caused event B solely on the basis that B came after A.

Cum Hoc Ergo Propter Hoc

"With this, therefore because of this." The (false cause) fallacy of assuming that event A caused event B solely on the basis that the two events occur together.

Begging the Question

Arbitrarily assuming what one is attempting to prove as part of the proof.

Virtuous Circle

An argument that has some degree of unavoidable circularity due to the essential nature of the claim, and yet is self-consistent and non-arbitrary.

Vicious Circle

A way of reasoning that arbitrarily assumes what the person is attempting to prove. Vicious circles commit the fallacy of begging the question.

Hypothetical

Something that is based on speculation or conjecture for the sake of discussion or argument.

Question-Begging Epithet

Using biased (often emotional) language to persuade people rather than using logic.

Complex Question

Attempting to persuade by asking a loaded question.

Fallacy of Bifurcation

Claiming there are only two mutually exclusive possibilities, when there is a third option (or more).

The No True Scotsman Fallacy

The error of defining a term in a biased way that would not be found in a dictionary in order to protect a claim from evidence to the contrary.

Special Pleading

The error of (arbitrarily) using a double standard, especially when the arguer exempts himself from a standard he applies to others.

False Analogy

The error of drawing erroneous inferences from an analogy that is not similar in relevant ways to the topic under discussion.

Slippery Slope Fallacy

Arguing that a given action will set off a chain reaction leading to a particular result, when in reality other factors are likely to prevent that result.

Weak

An informal argument is weak if the conclusion is not likely to be true.

Ad Hominem

Directing an argument against the person making the claim rather than the claim itself.

Abusive Ad Hominem

Arguing that a person's argument is wrong by attacking the character of the person.