Logic and Reasoning: Deductive, Inductive, and Semiotics

Understanding Logic and Reasoning

Early Concepts and Ambiguity

• Modes: 1: AB, 2: AB, 3: AB, 4: AB
• Relationships: AC, CA, BC, CB, CA, CB, CA, CB
• Abstract Thought: "A-whole-E is no. Or is it some? Some I is not."

An example of ambiguity: "The pig of the child" (Does this mean "The pig belongs to the child," "The pig is the child," or "The child is dirty like a pig?").

Signs and Symbols: Semiotic Entities

Signs and symbols are semiotic entities with distinct properties. A sign is defined by the relationship between the signifier, the signified, and the interpretant, while a symbol is a graphical representation that can be part of a larger sign system. Both convey ideas effectively in pre-literate or functionally illiterate cultures. However, their utility is not lower among the verbally literate; on the contrary, it is often higher.

Logic: A Formal Science

Logic is a formal science and a branch of philosophy that studies the principles of demonstration and inference.

Reasoning and Argumentation

Reasoning is the outcome of the mental activity of drawing conclusions, a set of propositions linked together that support or justify an idea. Reasoning aligns with the verbal activity of arguing. In other words, an argument is the verbal expression of reasoning.

Types of Logical Reasoning

Logical reasoning refers to the use of understanding to move from some propositions to others, based on what is already known or what we think we know, towards the unknown or less known. We distinguish between inductive reasoning and deductive reasoning.

Deductive Reasoning

Deductive reasoning is a form of reasoning in which, if the premises are true, the conclusion must logically follow and therefore be true. It is impossible to assert the premises and simultaneously deny the conclusion without contradiction.

Reasoning is not deductive when we:

• Generalize from the observation of some cases (this is inductive reasoning).
• Establish comparisons (analogical reasoning).
• Draw specific conclusions from partial or insufficient information, for example: "There are clouds, thus it will rain."

Deductive Reasoning Example (Syllogism)

This type of reasoning is composed of a general universal affirmative major premise, from which a particular affirmative premise is inferred, leading to a particular affirmative conclusion:

• Premise 1: The English are punctual.
• Premise 2: William is English.
• Conclusion: William is on time.

Inductive Reasoning

Inductive reasoning is a form of reasoning that moves from specific observations or instances to a general conclusion. The conclusion is probable, but not guaranteed, even if the premises are true.

Inductive Reasoning Example

• Observation 1: Plastic expands with heat.
• Observation 2: Wood and metal also expand with heat.
• Conclusion: All bodies expand with heat.