Introduction to Logic and Its Concepts

Logic and Inference

• Logic is a tool used to make conclusions, derived from the Latin word "logike" meaning "thinking".
• Inference involves deducing something to form a conclusion.
• Natural Logic refers to common sense or knowledge, whereas Formal Logic is a science that involves correction.
• Material Logic focuses on truth, and Simple Apprehension is an operation of logic that involves a mental act.

Judgement and Reasoning

• Judgement involves affirming or denying something.
• Reasoning is the act of productive inference, and a concept is a mental representation of the essence of a thing.
• Phantasm refers to a depiction or representation of what one is thinking.

Signs and Terms

• A Natural Sign signifies its nature, whereas a Conventional Sign is designated by man.
• A Formal Sign represents the plain essence of a thing.
• Comprehension is the sum total of all notes, and Extension is the sum of "inferiors".
• Concrete terms signify individual things that exist in nature, whereas Abstract terms have no exact existence but still exist.
• Terminus refers to the end of completion, and a Significant Term represents the essence or attribute of a thing.

Definition and Classification

• Definire involves setting limits or boundaries.
• Real terms signify real objects, and a Term is a created idea.
• A Proposition is a declarative sentence or statement that is part of a judgement.
• Proponere means to put forward for consideration.
• Major Term, Minor Term, and Middle Term are terms used in syllogisms, with Major Term as the predicate of the conclusion, Minor Term as the subject of the conclusion, and Middle Term as the term appearing in both premises but not in the conclusion.

Syllogism and Argumentation

• Sequence refers to the interrelation of concepts, which is supported by the truth of premises.
• Reciprocal Identity involves two terms being identical with each other, whereas Reciprocal Non-Identity involves one term being identical with a third term and the other term not being identical.
• The Principle of 'Dictum De Omni' states that what is said of all is true, whereas the Principle of 'Dictum De Nullo' states that what is not said of all is denied universally.

Definition and Analogy

• Definition by Synonym involves defining a term with the same meaning.
• Definition by Example involves presenting a sample.
• Definition by Property involves an attribute essential to the nature of a thing.
• Logical Accident refers to the logical consequences of a situation.
• Analogy involves comparing two things, and Proportionality is based on the resemblance of two things due to their function.

Causality and Attribution

• Attribution involves similarity based on attributes.
• Internal attribution is realized equally, whereas External attribution is realized only by a primary.
• Supposition involves conveying a specific meaning.
• Etymological Definition states the origin of a term.
• Real Definition involves the proximate genus and specific difference.
• Descriptive Definition describes the physical appearance.

Efficient, Material, Formal, and Final Causes

• Efficient Cause refers to the origin of the creator of a thing.
• Material Cause refers to the stuff that makes up a thing.
• Final Cause states the purpose of a thing.
• Formal Cause mentions the form that constitutes a thing.

Identity and Contradiction

• Identical terms have the same comprehension and extension.
• Similar terms have the same extension but not entire comprehension.
• Compatible terms have different aspects but are present simultaneously in the same thing.
• Incompatible terms cannot be present simultaneously.
• Reciprocal terms imply each other.
• Privative terms express the absence of a positive quality.
• Contradictory terms are the negation of a positive quality.
• Contrary terms are opposite extremes of a given category.

Reality and Logical Categories

• Real supposition involves existing truth.
• Logical concepts involve the concept of 2nd intention.
• Imaginary concepts are true only by imagination.
• Metaphorical concepts are true only by analogy.
• Symbolic concepts involve a predicate that speaks of the subject term.
• Material concepts involve letters of the alphabet with definite pronunciation.
• Real concepts involve origin, stating real objects.
• Arbitrary concepts do not exist.
• Immediate concepts involve direct experience.
• Mediate concepts involve information from other sources.

Univocal, Equivocal, and Analogous Terms

• Univocal Terms have one and the same meaning.
• Equivocal Terms have two and several related meanings.
• Analogous Terms apply partly the same and partly different meanings.
• Singular Terms refer to one specific thing or person.
• Universal Terms refer to the total number.
• Particular Terms refer to a portion of the total number.
• Indefinite Terms refer to groups, undetermined, or unspecific.
• Contingent Terms are based on the truth of their content, which is temporary and variable.
• Necessary Terms are permanent and unchangeable.

Categorical and Hypothetical Propositions

• Categorical Propositions are based on the logical form, which is directly and categorically without any condition.
• Hypothetical Propositions involve an "if" condition.
• 'A' Propositions involve all S are P.
• 'E' Propositions involve no S are P.
• 'I' Propositions involve some S are P.
• 'O' Propositions involve some S are not P.

Valid and Invalid Syllogisms

• Valid Syllogisms are based on the truth of their matter.
• Invalid Syllogisms are formally valid but materially invalid.

Qualities of a Good Definition

• A good definition should be short.
• A good definition should be positive.
• A good definition should be adequate.
• A good definition should contain the term in define.
• If one is true, the other is necessary.