Basic ethics for a moron I found online who thinks that people should be robbed and that videogames are valid as logical arguments, lets see if this brainlet can even understand it

((Para leitores brasileiros, estou apenas traduzindo alguns argumentos meus para o inglês para compartilhar em um forum, ainda voltarei a postar textos seriamente))

Here I intend to use a definition framework similar to the one used by Gödel in his ontological argument, which is formalized, but still more verbal, and I also intend to explain clearly what I mean by each definition.

Definition 1: x is a potential purpose if and only if x is a possible future world that differs from other possible future worlds due to the behavior of a living being.

Definition 2: x is an action if and only if x consists of a choice among possible purposes.

Definition 3: x is an agent if and only if x acts.

With that, we have a proposition, the fundamental axiom of human action, which will be represented by "P".

P := agents act

Definition 4: x is scarce if and only if x cannot be employed to achieve all possible purposes.

Definition 5: x is a means if and only if x can be employed to achieve possible purposes, and if and only if x is scarce.

In other words, if something can be employed to achieve possible purposes but not absolutely all possible purposes, then we call this something a "means." I will demonstrate here that if x acts, it implies that x employs means to do so, that is, proposition Q, stated as...

Q := agents employ means to act.

The proposition can be proven in a contrapositive manner. Let me explain: If Q were false, it would mean that the agent could achieve all possible purposes, implying that the agent would no longer have any possible purposes left since they would have already been accomplished. Therefore, if Q were false, the agent would not act. Thus...

¬Q⇒¬P

By the law of contraposition, we know that (¬Q⇒¬P) and (P⇒Q) are equivalent. Therefore, P implies Q.

∴ P⇒Q

If P is true, using the logical rule of modus ponens, it is proven that Q is also true (and P is true because it is a tautology).

Definition 6: x is a duty if and only if x is a possible purpose or a set of possible purposes, and if x is the only logically acceptable possible purpose or set of possible purposes for the agent.

Definition 7: x is a legal duty if and only if x is a possible purpose or a set of possible purposes, and if x is the only logically acceptable possible purpose or set of possible purposes for the agent, and if the agent is liable to be prevented from not pursuing x by the use of force or to be punished by the use of force if they do not pursue x.

Definition 8: x is a law if and only if x is a rule that seeks to articulate a legal duty.

Definition 9: x is a legitimate law if and only if x is a rule that articulates a legal duty.

N := the possible purpose x will become real.

Then ◊N would be something like "there exists a possible world in which the possible purpose x will become real," which is equivalent to asserting the possibility of purpose x becoming real. Asserting ¬◊N, in this sense, would be asserting the impossibility of this possible purpose becoming real.

The same applies to B.

B := the possible purpose y will become real.

Definition 10: x and y are mutually exclusive purposes if and only if N⇒¬◊B, and if and only if B⇒¬◊N.

Definition 11: there is a conflict between agents if and only if purposes x and y are pursued simultaneously, and if x and y are mutually exclusive purposes of different agents.

Definition 12: Rule z resolves conflicts if and only if agents x and y are in conflict, and if z states that x can pursue their purpose at the expense of y or that y can pursue their purpose at the expense of x.

Definition 13: Rule x avoids conflicts if and only if no agent violating the rule implies the absence of any existing conflict.

R := legitimate laws resolve conflicts

¬R⇒W

The negation of R will imply another proposition (W), where W is defined according to the notation presented below.

W := there exists a legitimate law y that explicitly states how agents should act in relation to x, and x is something that is not a conflict.

If x is not a conflict, then there are no mutually exclusive purposes between the agent violating law y and the agent creating law y. Therefore, the agent creating the law would not be able to prevent the other agent from violating it, let alone punish them. In that case, it would not be a law. Hence, law y will never exist, the existence of law y is not possible.

W⇒T

T := a legitimate law that explicitly states how agents should act in relation to x if x is not a conflict does not exist.

However, the assertion T is equivalent to the negation of W.

T⇔¬W

Thus, the negation of R implies a contradiction because...

E := legitimate laws avoid conflicts.

If a law does not avoid conflicts, it means that even with no one disobeying it, some conflict is created. If a conflict is being created, then the law is not resolving the conflict. In other words...

¬E⇒¬R

∴ R⇒E

By the principle of contraposition.

M := legitimate laws explicitly state rights to use means.

The above proposition will be proven through a contrapositive argument. The negation of M, ¬M, would imply that there is a legitimate law that dictates how individuals should act (explicitating a legal duty) without explicitly stating rights to use means. However, if it is not through the use of means, there are no conflicts, as without the use of means, the agent can achieve all possible purposes. Therefore, the law would not be resolving conflicts nor addressing the issue that gives rise to them.

¬M⇒¬R

∴ R⇒M

The next proposition to be proven is the proposition...

X := legitimate laws explicitly state rights to exclusive use of means.

It can be directly and easily proven that R implies X, as 1) we already know that R implies M, and 2) if the right to use is not exclusive, the use of one agent of the means will not exclude the use of the other, thus the law will not prevent one of the mutually exclusive purposes from being pursued.

(R∧(R⇒M))⇒X

And now, in this subsection, it only remains to prove one last proposition:

D := legitimate laws explicitly state rights to definitive use of means.

In other words, if an agent has used a means in a manner considered legitimate (approved by the legitimate law), then until they relinquish their right over the means, no one else has the right to use it without their permission.

The proposition D can be proven as follows:

If D were not true, then there would be some legitimate law that explicitly states non-definitive rights to use, but if it did so, agents could use means that other agents had used and, although they may not physically possess them, they would already be employed to pursue some purpose. Thus, it would generate new conflicts in such situations, it would generate conflicts even if followed by everyone, and it would not avoid conflicts.

¬D⇒¬E

∴ E⇒D

Definition 14: Law x explicitly states a right of ownership if and only if x establishes exclusive and definitive rights to use means.

Here we have proposition U...

U := legitimate laws establish rights of ownership.

By the logical law of hypothetical syllogism, following the chain of implications from R, R⇒U, and since negating R leads to contradiction, proposition U is proven by reductio ad absurdum.

Therefore, any created law must necessarily establish rights of private property in order to be legitimate.

Violation of property

Definition 15: Aggression, if person A uses force or uses property x of person B without B's permission, and B neither used force against any third party's property without their permission, nor did others do so, then A's action is an aggression.

If A commits an aggression, it implies that A believes that individuals have the right to commit aggressions.

That will be proven by reductio ad absurdum.

The proposition "Individuals have the right to commit aggressions" will be denoted as A.

The negation of A, denoted as ¬A, is that the person could have been prevented from committing the aggression, and if they were not prevented, they can be punished.

If a person advocates for A, it also implies F (individuals have the right to use force against others).

A⇒F

Now it will be proven that any aggression (violation of private property) can be prevented and punished.

A⇒F

However, F⇒Y

Where Y represents the use of force against aggressors to prevent or punish.

Y, in turn, implies A, as ¬A is that the person could have been prevented from committing the aggression, and if they were not prevented, they can be punished.

Hence, A⇒¬A

A contradiction.

Any defense of A is necessarily incorrect.

And finally, L.

L := legitimate laws prohibit or punish aggression against any private property.

¬L⇒A∨¬U

Since both A and ¬U lead to contradictions,

L is true by reductio ad absurdum.