Key Definitions: Logic, Reasoning, and Language

Fundamental Concepts in Logic and Language

Language

The human capacity to communicate and express thoughts through a system of signs.

Reason

The ability to combine intellectual concepts and propositions, using intelligence to compare ideas and reality.

Symbol

A sign that bears a similarity to what it represents.

Concept

The idea or understanding we have about something. Every concept can be considered a symbol.

Perception

A feeling or understanding that results from a material impression received by our senses.

Category

The most general concept through which we order, understand, and express reality.

Propositions or Statements

A sentence or phrase—a sequence of words subject to syntactic rules—that asserts something about something.

Reasoning / Argument / Inference

Sequences of propositions used to prove or justify something.

Conclusion

An element within a reasoning, argument, or inference, defined as what is intended to be proven from a premise.

Premise

An element within a reasoning, argument, or inference, defined as the initial data used to substantiate a conclusion.

Functions of Language

The different purposes speakers have when communicating. These include:

• Informing
• Conveying feelings
• Expressing opinions
• Arguing
• Giving orders

Address

A coherent series of words and phrases possessing logical coherence and grammatical structure.

Material Correctness

The truth or falsity of the premises and conclusion within a proposition.

Formal Correctness

The validity or invalidity of a proposition's structure.

Deduction

A method of reasoning that proceeds logically from the universal to the particular. In deductive arguments, if the premises are true, the conclusion must also be true.

Induction

A method of reasoning that proceeds logically from the particular to the universal. In inductive arguments, the premises provide probable, but not certain, support for the conclusion, making it more or less likely.

Analogy

A relation of similarity that exists between different things.

Validity

The correctness or incorrectness of an argument's structure, independent of the truth or falsity of its premises and conclusion.

Strength and Weakness of Inductions

This refers to the degree of support the premises provide for an inductive conclusion. Strong inductions have premises that provide substantial support, making the conclusion highly probable. Conversely, weak inductions have premises that offer insufficient support for the conclusion.

Logic

The science of reasoning, examined from the perspective of its correctness or incorrectness.

Formal Logic

A branch of logic that provides tools for reasoning effectively, irrespective of the specific content or material of the arguments.

Material Logic

A branch of logic that encompasses all dimensions of thought and assesses the internal strength of each argument.

Natural Language

A language where the meaning of words (the lexicon) plays a crucial role.

Logical Language

A language that primarily focuses on grammatical structure.