Logical proof: natural rights and the golden rule

 

Proof for the Conclusion:

"A competent individual should have natural rights to live his life as he wishes as long as he respects the rights of others."

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Definitions

1. Competent Individual: A person who possesses the mental and moral faculties to make rational decisions and understand the consequences of their actions.
2. Natural Rights: Fundamental rights inherent to all individuals by virtue of their humanity, not granted by governments or institutions, including life, liberty, and the pursuit of happiness.
3. Respect for the Rights of Others: The principle that one's actions should not infringe upon the equivalent natural rights of others.
4. Autonomy: The capacity of an individual to govern oneself and make decisions free from external coercion or undue interference.

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Self-Evident Axioms / Assumptions

1. All human beings are inherently equal in dignity and worth.
2. Natural rights are universal and inalienable, meaning they cannot be justly removed without violating the moral order.
3. A competent individual is capable of rational decision-making and moral reasoning.
4. The moral principle of reciprocity (the "Golden Rule") is a foundational ethical standard: one should treat others as one wishes to be treated.

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Poly-Syllogism 1

Premises:

1. All human beings possess inherent dignity and worth (Axiom 1).
2. Natural rights are derived from the inherent dignity and worth of human beings (Definition 2).
3. A competent individual, by virtue of being human, possesses inherent dignity and worth (Definition 1).

Conclusion (Theorem 1):
A competent individual possesses natural rights.

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Poly-Syllogism 2

Premises:

1. Natural rights include the right to life, liberty, and the pursuit of happiness (Definition 2).
2. Liberty entails the freedom to make decisions about one’s own life and actions (Definition 4).
3. A competent individual, by definition, is capable of making rational decisions and understanding the consequences of their actions (Definition 1).
4. Therefore, a competent individual is capable of exercising liberty without external interference (Premises 2 and 3).

Conclusion (Theorem 2):
A competent individual has the natural right to live his life as he wishes.

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Poly-Syllogism 3

Premises:

1. The principle of reciprocity (Axiom 4) requires that one respects the rights of others in order to have one’s own rights respected.
2. Natural rights are universal and apply equally to all individuals (Axiom 2).
3. The exercise of one’s natural rights must not infringe upon the equivalent rights of others (Definition 3).
4. A competent individual, by definition, can understand and adhere to the principle of reciprocity (Definition 1).

Conclusion (Theorem 3):
A competent individual should respect the rights of others when exercising his natural rights.

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Poly-Syllogism 4

Premises:

1. A competent individual has the natural right to live his life as he wishes (Theorem 2).
2. A competent individual must respect the rights of others when exercising his natural rights (Theorem 3).
3. Respecting the rights of others ensures that the principle of reciprocity is upheld (Axiom 4).
4. Therefore, the natural rights of a competent individual are contingent upon his adherence to the principle of reciprocity (Premises 2 and 3).

Conclusion (Theorem 4):
A competent individual should have the natural right to live his life as he wishes, provided he respects the rights of others.

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Final Conclusion:

Theorem 5:
An individual who is competent should have natural rights to live his life as he wishes as long as he respects the rights of others.

This conclusion is logically supported by the chain of poly-syllogisms above, grounded in objective definitions, self-evident axioms, and reasoned premises.

In addition:

Axiom 1: A competent individual should have natural rights to live his life as he wishes as long as he respects the rights of others.

Axiom 2: Objectivism holds that individuals have the right to pursue their own life, liberty, and happiness without interference, as long as they do not infringe on the rights of others.

Axiom 3: In laissez-faire/free market capitalism, individuals are free to engage in voluntary exchanges without coercion or interference.

Main Premise: A competent individual should have natural rights to live his life as he wishes as long as he respects the rights of others.

Additional Premises:
4. Objectivism supports the idea that individuals have the right to pursue their own goals and values.
5. Laissez-faire capitalism allows individuals to freely interact in the market based on their own choices and preferences.
6. Respecting the rights of others includes refraining from initiating force or fraud against them.

Theorems:

1. Competent individuals have the natural right to live their lives according to their own choices and values, provided they do not violate the rights of others.
2. Objectivism and laissez-faire capitalism align with the premise that individuals should be free to pursue their own goals and engage in voluntary exchanges without coercion.
3. Upholding the rights of others involves refraining from initiating force or fraud, ensuring peaceful and respectful interactions in society.

Therefore, the conclusion that can be proven using the initial axiom is:
Theorem: Competent individuals have the natural right to live their lives as they choose, respecting the rights of others, in alignment with the principles of objectivism and laissez-faire capitalism.