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Expand Up @@ -109,7 +109,7 @@ Applying estoppel in such a manner perfectly complements the very purpose of dia
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** Applying Estoppel
Let’s apply this theory of estoppel to the case of $A$ punching $B$. Assume that this is the extent of the assault, as the question of defending an ongoing aggression shall be discussed in the next section, $B$ decides that he wants to punish $A$ in an eye-for-an-eye manner by punching him back, or perhaps by hiring a champion, $C$, to punch $A$ if $B$ cannot, or does not want to, do this himself. If $A$ were to challenge this punishment, he would claim that this punching of him is an impermissible action, i.e. that people should be prohibited from punching him. But, $A$ has previously demonstrated that he thinks that he should not be prohibited from punching $B$. In essence, $A$ has pre-supposed that punching people sans-consent is just, and is now explicitly making the claim that its unjust. This is a clearly incoherent position, thus $A$ is estopped from challenging his punishment, therefore we revert back to the simple case of an unchallenged punishment which is per se just.
Let’s apply this theory of estoppel to the case of $A$ punching $B$. Assume that this is the extent of the assault, as the question of defending an ongoing aggression shall be discussed in the next section, $B$ decides that he wants to punish $A$ in an eye-for-an-eye manner by punching him back, or perhaps by hiring a champion, $C$, to punch $A$ if $B$ cannot, or does not want to, do this himself. If $A$ were to challenge this punishment, he would claim that this punching of him is an impermissible action, i.e. that people should be prohibited from punching him. But, $A$ has previously demonstrated that he thinks that he should not be prohibited from punching $B$. In essence, $A$ has pre-supposed that punching people sans-consent is just, and is now explicitly making the claim that it's unjust. This is a clearly incoherent position, thus $A$ is estopped from challenging his punishment, therefore we revert back to the simple case of an unchallenged punishment which is per se just.

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Expand Down Expand Up @@ -154,7 +154,7 @@ Quite commonly it has been observed that argumentation implies that a propositio
> Quite commonly it has been observed that argumentation implies that a proposition claims universal acceptability, or, should it be a norm proposal, that it is “universalizable.” Applied to norm proposals, this is the idea, as formulated in the Golden Rule of ethics or in the Kantian Categorical Imperative, that only those norms can be justified that can be formulated as general principles which are valid for everyone without exception.
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This is because if one is to claim any proposition as being argumentatively valid, said proposition must be rational---what this means is that it must in principle be valid no matter who it is proposed to. To reject this would be to adopt a polylogism; i.e. that a proposition might be true when levied in one argument, but not when levied in another[fn:7]---and it was shown in the first lesson, that polylogism implies contradiction, making it false. So universilisability is therefore a pre-supposition of the very normative discourse that $A$ would be partaking in by attempting to reject his punishment, but the norm that its fine for $A$ to punch $B$ but not for others to punch $A$ is not universalisable---we would be faced with a contradiction if we tried to swap out $A$ for $B$ and hold both norms simultaneously, meaning this norm cannot be applied to everyone:[fn:8]
This is because if one is to claim any proposition as being argumentatively valid, said proposition must be rational---what this means is that it must in principle be valid no matter who it is proposed to. To reject this would be to adopt a polylogism; i.e. that a proposition might be true when levied in one argument, but not when levied in another[fn:7]---and it was shown in the first lesson, that polylogism implies contradiction, making it false. So universilisability is therefore a pre-supposition of the very normative discourse that $A$ would be partaking in by attempting to reject his punishment, but the norm that it's fine for $A$ to punch $B$ but not for others to punch $A$ is not universalisable---we would be faced with a contradiction if we tried to swap out $A$ for $B$ and hold both norms simultaneously, meaning this norm cannot be applied to everyone:[fn:8]

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Expand Down Expand Up @@ -221,9 +221,9 @@ Third, this mind-changing is still a form of particularisation---it's the claim
* $A$ can *only* drop the challenge
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I will re-iterate this point for clarity; what makes a man estopped from challenging a given punishment is that the given challenge would imply a contradiction, meaning it cannot be uttered in an argument. When I perform some action $X$, I thereby pre-suppose by this performance that I think I should do $X$ as opposed to $\neg X$. There is some confusion over this thesis, often I have encountered the counterargument of the man who is smoking and says that he should stop---does this man not believe that he should stop? Is he lying when he says he should stop? That is not necessarily the case. We can indeed imagine a man who is currently engaged in an act of smoking--a man who has chosen to smoke rather than not smoke--who nonetheless believes that he should not smoke. But, this does /not/ establish that he is not also pre-supposing that he should smoke. It is possible for a person two hold two contradictory beliefs at the same time, we call this cognitive dissonance. Consider the anarchist who goes through the labour of demonstrating that taxation is theft and that theft is bad, therefore taxation is bad only to be confronted by his statist opponent who agrees that taxation is theft and that its bad but still asserts that taxation is a good thing that should continue. It is clear to anyone who has encountered stupid people that man is fully capable of holding contradictory theses at the same time. The upshot of this for our smoker is that by choosing to smoke rather than not smoke it must be the case that he believes that he should smoke rather than not smoke, /but/ this does not preclude the possibility that our smoker /also/ believes that he should not smoke---it's just that his belief that he should smoke is in some sense over-powering his contradictory belief.
I will re-iterate this point for clarity; what makes a man estopped from challenging a given punishment is that the given challenge would imply a contradiction, meaning it cannot be uttered in an argument. When I perform some action $X$, I thereby pre-suppose by this performance that I think I should do $X$ as opposed to $\neg X$. There is some confusion over this thesis, often I have encountered the counterargument of the man who is smoking and says that he should stop---does this man not believe that he should stop? Is he lying when he says he should stop? That is not necessarily the case. We can indeed imagine a man who is currently engaged in an act of smoking--a man who has chosen to smoke rather than not smoke--who nonetheless believes that he should not smoke. But, this does /not/ establish that he is not also pre-supposing that he should smoke. It is possible for a person to hold two contradictory beliefs at the same time, we call this cognitive dissonance. Consider the anarchist who goes through the labour of demonstrating that taxation is theft and that theft is bad, therefore taxation is bad only to be confronted by his statist opponent who agrees that taxation is theft and that it's bad but still asserts that taxation is a good thing that should continue. It is clear to anyone who has encountered stupid people that man is fully capable of holding contradictory theses at the same time. The upshot of this for our smoker is that by choosing to smoke rather than not smoke it must be the case that he believes that he should smoke rather than not smoke, /but/ this does not preclude the possibility that our smoker /also/ believes that he should not smoke---it's just that his belief that he should smoke is in some sense over-powering his contradictory belief.

There is a further confusion to be addressed at this point which stems from a conflation between two different senses of the word "ought." To highlight this, consider the statement "it is raining outside, therefore you ought bring an umbrella." Now, there are two ways one could interpret this statement; either (1) ought is being used in its precise logical meaning, or (2) its being used as prudential advice. For (1) it simply does not follow that because it is raining you ought bring an umbrella, at least not without additional steps. For (2) "ought" is being used colloquially, if we were to precisely formulate (2) it would be something like "it is raining outside so if you do not wish to get wet when you go outside a potential means to achieve this goal would be to bring an umbrella." When formulated precisely it becomes clear that when prudential advice is given like this, the statement is really an "is" statement rather than an "ought" statement. This insight will become crucial in the next lesson so I will not stress it too heavily here, but the key takeaway for now is that there is only ought; ought is ought. There doesn't exist different "flavours" of ought in logic, it is a failure of imprecision to mix in colloquial usages of this word.
There is a further confusion to be addressed at this point which stems from a conflation between two different senses of the word "ought." To highlight this, consider the statement "it is raining outside, therefore you ought bring an umbrella." Now, there are two ways one could interpret this statement; either (1) ought is being used in its precise logical meaning, or (2) it's being used as prudential advice. For (1) it simply does not follow that because it is raining you ought bring an umbrella, at least not without additional steps. For (2) "ought" is being used colloquially, if we were to precisely formulate (2) it would be something like "it is raining outside so if you do not wish to get wet when you go outside a potential means to achieve this goal would be to bring an umbrella." When formulated precisely it becomes clear that when prudential advice is given like this, the statement is really an "is" statement rather than an "ought" statement. This insight will become crucial in the next lesson so I will not stress it too heavily here, but the key takeaway for now is that there is only ought; ought is ought. There doesn't exist different "flavours" of ought in logic, it is a failure of imprecision to mix in colloquial usages of this word.

Bringing this back to our criminal, $A$, who wishes to challenge his punishment for punching $B$, he has already demonstrated by his conduct that he thinks punching is a legitimate interaction. If he then states that it is /not/ a legitimate interaction, which is required for him to challenge his punishment, he is in a contradiction. To resolve a contradiction between two statements, one of the statements /has/ to be dropped, because $A$ simply /cannot/ drop the statement that punching is proper, he is left only with being able to drop the statement that punching is improper, but the statement that punching is improper is the one that is /required/ for him to challenge the punishment. Therefore, $A$ /cannot/ challenge his punishment---he is dialogically estopped from doing so.

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