Understanding Logical Conjunctions, Definitions, Divisions, and Proofs

Posted on Feb 26, 2025 in Philosophy and ethics

Understanding Logical Concepts

The conjunction is true when both statements are true. The disjunction is false when both statements are false. The exclusive disjunction is true when one statement is true and one is false. The conditional is false if the first statement is true and the second is false. The biconditional is true when both are false or both are true.

Classes can be defined by extension (listing the elements) and compression (expressing their common properties).

Science is an eminently rational and systematic knowledge, and this feature is enabled by the use of the scientific method.

Definitions

To define means to limit. It consists of a definiendum (the term being defined) and a definiens (the definition itself). Definition classes:

Rating Definitions

Clarifies the meaning of the name of the object you want to define. Can be further classified as synonymic or etymological.

Real Definitions

Tells us what something is. It has several forms:

  • Essential: Defined by genus and specific difference. The next genus is a feature that is immediately used to define other objects of different species. The specific difference is the feature that distinguishes the object you want to define from other objects that belong to the same genus.
  • Descriptive: Definition of a property. The property is possessed by all members of a species.
  • Descriptive: A set of characteristics that are neither closely related to genus nor specific difference.
  • Genetic: Tells us how to produce the object to be defined.
  • Causal: Indicates one of the causes producing the object:
    • Final cause: States the aim or purpose for which the object is intended.
    • Efficient cause: States what makes or gives existence to the object.
    • Exemplary cause: According to the model or pattern according to which the object was manufactured.
  • Operational: An experimental procedure capable of being operated, built, or manipulated.
  • Recursive: The object is defined in relation to one or more terms of a numerical sequence.
Laws of Definition

The definiens must be clearer than the definiendum. This law implies the following sub-rules:

  • The definiendum must not be part of the definiens.
  • The definiens should be brief, since a long definition is often obscure and confusing.
  • The definiens must not be negative, except when defining a lack or deprivation.
  • The definiens must apply to all of the definiendum and to it alone. From here we derive:
    • The definiens must not be more stringent than the definiendum.
    • The definiens must not be wider than the definiendum.

Division

Physics: The whole that is divided is physical, in which parts are different from each other. The physical division can be in turn:

  • Quantitative physics: A whole is divided into homogeneous parts.
  • Essential physics: Here it divides a whole into its essential components.
  • Accidental Physics: A whole is divided into its constituent components as an aggregate.
  • Logic: The parties are distinguished by human reason.
  • Moral: The division is primarily a moral whole, whose parts are distinguished but remain united by a moral bond.

Laws of Division

  • It must be complete, i.e., must express all possible parts so that the sum of the parts equals the whole.
  • The parts must be mutually irreducible. Each part has to exclude others.
  • The basis or criterion of the division should not be changed in the process of it.

Proof

  • A priori and a posteriori: The proof a priori is based on the cause to demonstrate the effect. In the subsequent demonstration, we move from the effects to the cause.
  • Rational and experimental: Rational demonstration is based on purely rational speculation. The experimental demonstration is based on experimental data.
  • Directly and indirectly: In the direct demonstration, one starts from the premises and the conclusion is reached. In the indirect proof, also known as reductio ad absurdum, one proves the negation of the thesis that we have submitted a demo.
  • Absolute demonstration and demonstration ad hominem: The absolute proof is valid for any intelligence. In the ad hominem demonstration, one starts from a proposition accepted by the person to whom you want to prove a thesis, although this proposition is questionable or false, to make them reach the opposite conclusion to which they held.
  • Analytical and synthetic: Laboratory tests should be moving from simple to complex. In electrolysis, water breaks down into oxygen and hydrogen. In summary, the process is reversed: check water from hydrogen and oxygen.