Foundations of Logic and Philosophical Knowledge
The Principles of Logic
Logic is an essential instrument that ensures the proper functioning of reason. It is defined as the branch of philosophy dedicated to identifying and validating the forms of thought. Since reasoning is the fundamental way of thinking, logic can be understood as the philosophical discipline that aims to establish formally valid reasoning.
Understanding Arguments in Logic
An argument is a procedure where, starting from a set of comprehensive propositions and utilizing the relationships established between them, we arrive at new knowledge that emerges from the initial statements. In logic, the form of an argument is paramount, not its content. It does not matter if the statements themselves are true or false; what matters is the correctness of the reasoning process.
It is crucial to understand that reasoning itself is not true or false; rather, it is either correct or incorrect. Logic is primarily concerned with ensuring that the process of deduction is sound and valid.
Logical Operators: Connecting Propositions
Operators are symbols used to link propositions, forming more complex statements. Here are the primary logical operators:
The Negator (¬)
Translated as “not,” the negator (symbolized by ¬) is a connector that converts a true proposition into a false one, and vice versa.
The Conjunct (^)
Translated as “and,” the conjunct (represented by ^) is a connector that results in a compound proposition that is true only when all the propositions it connects are true. In all other cases, the compound proposition is false.
The Disjunctor (v)
Translated as “or,” the disjunctor (symbolized by v) has two main forms:
- Inclusive Disjunction: (e.g., “P or Q, or both”) – True if at least one proposition is true.
- Exclusive Disjunction: (e.g., “P or Q, but not both”) – True if exactly one proposition is true.
The Conditional (→)
Matching the structure “if…, then…” (symbolized by →), the conditional is a connector that results in a compound proposition that is not always true. Specifically, it is false only if the antecedent (the “if” part) is true and the consequent (the “then” part) is false. In all other scenarios, it is true.
The Biconditional (↔)
Corresponding to the expression “if and only if” (symbolized by ↔), the biconditional is a connector that results in a compound proposition that is true when both components have the same truth value (both true or both false) and false otherwise.
Attitudes Towards Knowledge
Philosophers have adopted various stances regarding the possibility and nature of knowledge:
Skepticism: Doubting Certainty
Skepticism is the attitude that asserts we cannot achieve exactitude or absolute certainty about things. Early proponents include Thales, Pythagoras, and Heraclitus. There are two primary forms of skepticism:
Radical Skepticism
This extreme form is often summarized in three propositions: nothing exists; if something did exist, we could not know it; and if we could know it, we could not communicate it.
Moderate Skepticism
Exemplified by David Hume, moderate skepticism is evident in its critique of the principle of causality, suggesting there is no inherent cause-and-effect relationship that can be empirically proven. Voltaire also demonstrated a form of wisdom that questioned dogmatic assertions. Moderate skepticism reduces all knowledge to two types of impressions:
- Impressions: Direct information perceived through the senses.
- Ideas: Copies or faint images of those impressions.
According to this view, if there are no initial impressions, then no ideas can be formed.
Dogmatism: Accepting Sensory Truths
Dogmatism, particularly in its moderate or philosophical form, describes the human tendency to spontaneously accept as true whatever is captured through the senses. This natural attitude, however, requires a critical distance to question and discern what constitutes true and false knowledge.
Origins and Limits of Knowledge: Descartes’ Rationalism
Founded by René Descartes, Rationalism is a philosophical current characterized by a firm belief in human reason’s capacity to attain truth, always subject to a rigorous method. For rationalists, reason is the primary source of knowledge, and there is a significant distrust of sensory information.
Reason empowers us to determine what is true or false. Descartes aimed to establish philosophy as a body of knowledge as precise and certain as the sciences of his time. He believed that differences among people are not due to variations in reason itself, as reason is universal; rather, the differences lie in the method applied. To address this, Descartes outlined a method, originally comprising 27 rules, which he later condensed into four fundamental precepts:
Evidence
Accept nothing as true unless it is presented to the mind so clearly and distinctly that there is no room for doubt.
Analysis
Divide each difficulty under examination into as many parts as possible, and as might be necessary for its better resolution.
Synthesis
Proceed in an orderly fashion, beginning with the simplest and most easily known objects, and gradually ascending to the knowledge of the more complex.
Review
Make enumerations so complete and reviews so general that one is certain to have omitted nothing.
Descartes famously expressed his distrust of the senses and sought an indubitable foundation for knowledge, leading to his iconic declaration: “Cogito, ergo sum” (I think, therefore I am).