Core Principles of Logic, Philosophy, and Human Existence
Fundamental Principles of Logic
Modus Ponens (MP)
Given a conditional statement and its antecedent as premises, we can derive its consequent as a conclusion.
Implication Introduction (II)
If, by assuming a proposition A, we can derive another proposition B, then we can conclude that A implies B (A → B).
Conjunction Introduction (CI)
If we have two premises, we can conclude their conjunction.
Conjunction Elimination (CE)
Given a conjunction as a premise, we can conclude any of its individual members.
Disjunction Introduction (DI)
If we have a proposition as a premise, we can add any other proposition disjunctively, and that disjunction will be true.
Disjunction Elimination (DE)
Given a disjunction as a premise, if assuming each disjunct separately leads to the same conclusion, then that conclusion can be inferred from the disjunction. This is also known as Proof by Cases.
Double Negation (DN)
Denying a proposition twice affirms it. A double negation cancels itself out.
Reductio ad Absurdum (RAA)
If assuming the negation of a desired conclusion leads to a contradiction, then the original conclusion must be true.
Stages of Reductio ad Absurdum:
- Assume the negation of the desired conclusion.
- Derive a contradiction from this assumption.
- Conclude that the initial assumption (the negation) must be false.
- Therefore, the original conclusion is true.
Understanding Philosophy
Philosophy is a natural human endeavor, arising spontaneously from our thinking and questioning.
Key Features of Philosophy:
- Totality: It seeks to understand the whole of reality, all being, and all things.
- Ultimacy or Depth: It aims to understand reality with absolute depth, seeking the ultimate foundations, roots, or causes of things and events.
- Rationality: Philosophical knowledge is uniquely human, relying on reason and logical consistency for its explanations.
- Reflective: It involves internal review, revisiting the same content repeatedly with fresh perspectives.
- Critical: It involves testing ideas, thoughts, traditions, and accepted behaviors.
- Speculative or Theoretical: It involves mental contemplation and theorizing, seeking reasons and grounds for knowledge, often for the intrinsic enjoyment of understanding.
Science Versus Philosophy
The purpose of science is more limited and specialized. Science studies the functioning of phenomena and their laws.
Philosophy, in contrast, investigates the essence of things and seeks their ultimate foundations. Philosophy provides broader perspectives on approaches, problems, methods, and theories.
Science provides empirical data and precise knowledge that informs philosophical inquiry.
The Nature of Human Beings
Human beings stand out among living creatures due to their complexity. Humans cannot remain completely passive; their existence in the world constantly prompts them to find appropriate responses.
Unlike animals, only a portion of human responses are fixed by nature. Many crucial responses must be discovered and decided upon by humans at their own risk to act appropriately. Humans are inherently open to the world.
While an animal’s response to stimuli is automatic, a higher animal directs its own behavior, organized by its knowledge of external reality. The human spirit is not merely linked to the world but is profoundly open to it. Humans possess a ‘world’ and can elevate objects from their surroundings into meaningful entities. They have the intentional ability to access all objects.
Humans are also self-aware, enabling them to shape their lives by directing their own behavior. They project their future and are oriented towards the world. Biologically, humans are unspecialized and lack true instincts.
To navigate this situation, individuals possess the capacity for thought. Through this thinking, humans interpret nature and engage with it, which is the root of culture.
Models of Knowledge:
- Formal Scientific Knowledge (Mathematics)
- Experimental Scientific Knowledge (Natural Sciences)
- Philosophical Knowledge