A discussion of Paradoxes

What is a paradox? I'd like to think of it as a theory that seems to be inconsistent, but is justifiably inconsistent. We might think that only theories that are consistent (does not prove a contradiction) ought to be interesting, but there are certain ideas or notions that are just fundamentally intuitive and that one might think we ought to accept. Perhaps the most famous paradox is the Liars paradox, generated by a correspondence theory of truth. If we think that a sentence is true if and only if it corresponds in some sense factually to the reality (and false otherwise), how do we assess whether the statement "this sentence is false" is true?

Paradoxes are useful because they help us assess the really interesting and relevant parts of our argument. Their existence typically drives development in the theory, allowing us to modify our current theory in order to remove such problems. With regards to the liars paradox, one solution is to think that our language can only be considered on different levels, and that a given sentence is only able to make truth valuations of sentences on a lower level. As a result it is not possible for the sentence to evaluate it's own truth. Other solutions we might be looking for are to reject the correspondence theory of truth in favour of a new theory.

On thing to note is that paradoxes typically apply only upon our intuitions and do not really exist in a formal sense, mathematical sense. This is because we typically require a mathematical system to be logically consistent. If it is not, then the paradox causes the Mathematical system to change. Perhaps the most famous example of this is Russells Paradox and it's impact on set theory. Suppose that we think everything is a set, and that there is an axiom that allows us to consider the set of all things that satisfy some property $\phi$. Thus we can consider the set $R = \{x : \neg ( x \in x)\}$, that is the set of things that do not belong to themselves. However, since we assume everything is a set, $R$ must also be a set and thus we can consider whether $R$ belongs to $R$. If we follow our logic, the system is necessarily inconsistent. At least in terms of set theory, our solution is to reject the axiom so that we are able to consider the set of all things that satisfy $\phi$. We are only able to consider the set of all thins that satisfy $\phi$ already considering a bounding set.

Now the paradox that I wanted to discuss today is the Paradox of intolerance. The paradox itself works as follows: it seems that a tolerant person is likely to antagonistic views with regards to intolerance. However this seems to imply that they are acting intolerantly to those that are intolerant, which itself appears intolerant. 

Essentially what we are interested in is whether this is justified. At least according to the paradox it seems as if a tolerant agent should be tolerant to all other agents, regardless of their own tolerance. However intuitively it seems for various reasons, including self preservation, a tolerant agent has a degree of obligation to respond negatively to those that would express intolerance in a manner that causes harm to others. For it seems minimally plausible for someone to be tolerant but wish to prevent a Nazi from killing Jews. 

How ought we respond to the paradox? Well the initial response is to consider tolerance as a bounded concept. One has a right to be intolerant towards those who are they themselves intolerant. However this seems a bit odd : what if the intolerant individual is not causing any harm or what if they barely expressing their intolerant views? Instead perhaps we should modify our theory such that we should only be intolerant to those whose intolerance would negatively affect others around them.

Now consider a slightly more difficult issue. According to our theory above, one is allowed to react intolerantly towards someone who is representing Nazi like views. Thus in this sense we might be allowed to limit their freedom of speech, and not allow them to express their beliefs. Let us call this situation A. Now consider a situation B where anyone who is acting intolerantly towards someone else who is expressing Nazi like beliefs can be silenced by a group one level higher. After all the people who are acting intolerantly with respect to others with Nazi like beliefs are they themselves negatively hurting those around them who are themselves expressing Nazi like beliefs. Whilst I think most peoples intuition is that situation B is wrong, the justification for why it is wrong is not particularly simple. I think most justifications hinge upon the notion that the group who are expressing Nazi like beliefs are inherently wrong, and thus it is fine to silence them. However it is not obvious why this is the case. We could at least imagine a possible world where a Nazi like belief is justified and where there is something fundamentally wrong with silencing them.

Note that in my above argument I think it is important to consider each belief and action separately. We can perhaps express moral values upon each statement, but these moral values do not hold in the modal sense. It is not necessarily necessary the case that certain actions are wrong. By this I mean that it possible that Nazi like views are actually necessarily wrong, but we don't know this yet, and thus for sake of our discussion of universal theories we should take this into account.

Anyway the problem here is that there are those who wish to espouse being tolerant of others views, but wish to justify intolerance in certain cases (notably to those who are already intolerant). I wish to say that there is a fundamental difficulty in assessing whether they are justified in being intolerant of others. Perhaps you think my example of a Nazi like belief is extreme. How about a religious view? If a religious person expresses beliefs that say I am going to go to hell (as a result of their religion, even if they are personally friendly to me), am I justified in being intolerant of them?

 Further difficulties arise because a lot of our judgements about being intolerant of intolerance arise from somewhat utility based arguments; considering the total amount of suffering by allowing an intolerant view to be expressed. Yet many responses are they themselves irrational. Should we justify being intolerant to certain views that cause irrational reactions? How about it is revealed that a significant majority group of people get fundamentally offended each time anyone makes a feminist remark on the news. Should we silence people from making feminist views? Perhaps someone makes the argument that the feminist view is intolerant of those who wish to live in a status quo of a patriarchy. Does this provide me justification?

On final thing to reiterate is that the examples I've used here are simply that: examples. I don't necessarily endorse any of the views espoused here, I have simply chosen them because they seem to correspond to some intuitions. And yes, I have had to make a degree judgement here as to what view is intuitive and what is not. I think that's permissible.

Universal Theory

We might think of Mathematics as to some extent, the generalisation of singular sentences. Most of these sentences possess a certain logical structure, and whilst these singular cases interest us, we would like to understand the general and universal theory behind them. 

As a basic example, we might be familiar with the solution to an equation $5x - 10 = 0$ as being 2. Our method for finding this happened to be by first adding 10 to both sides and then dividing both sides by 5. Now, why is this justified? Mathematically the answer relates to abstract algebra (in particular Rings). More generally, Mathematics allows us to provide a general solution to an equation of the form $ax + b =0$ as being $-\frac{b}{a}$ assuming $a \not = 0$. Why is this useful and important? Well it means that we have a general method that works in every situation (that our conditions apply under). 

Now note that we can have multiple levels of generalisation, and indeed I think there is a very strong reason to do so. Consider the claim 'it is morally wrong to kill the child named Rob'. Suppose for hypothesis that we think this claim to be true. This is a singular instance of a moral claim. However we wish to have something that is a lot more powerful than that. We're obviously not always going to be talking about Rob, we might be talking about George or Ann who may or may not be children. We would ideally want a moral theory that is more universal. A theory where we could make claims such as 'it is morally wrong to kill children' or 'it is morally wrong to kill anyone named Rob'. The more general the claim there is the sense in which it is more useful. In mathematics we wish to remove as many superfluous factors in a given situation as a possible. It is the same in making general philosophical claims. By aiming for generality we are able to only consider the meaningful and salient features. By making the claim that is morally wrong to kill a person we are able to consider a far larger branch of situations. Further we are able to pinpoint that the relevant factor is personhood instead of that person's name. 

However one can make claims that are even stronger than universal. We can make a claim that is necessarily true. The purpose of necessity is that there is a sense in which a claim must always be true. It's not just due to stars aligning in a certain manner. To say that it is necessarily true than killing a person is morally wrong is to commit to the idea that it is not possible in anyway for killing a person not to be morally wrong. In every world and possible situation, the action is wrong. 

Nevertheless, one might argue that our practical situations are individual instances, and that a universal theory misses out on specific factors. I think that for the purpose of justifying our actions, we need to depend on this universal theory. If I kill a child called Rob, maybe we can agree it is morally wrong. however I think that if we wish to punish me, we need some type of explanation. 

If I choose not to hire a woman because she might become pregnant, presumably I have done something wrong. However we must ask why is this the case? What are the salient features of the situation that make it wrong? Perhaps one responds that it is because she is female, but this doesn't seem particular adequate. Why does her gender matter in this situation? Why does it impede on my right to hire people as I wish? So let's go even more general: perhaps it is because as a female she must pay a disproportionate physical price if she does get pregnant and hence it is unfair to punish her. Or perhaps it is because as a female, she is already discriminated against and as a society we wish to move forwards from this. Regardless of the reason, we have managed to analyse the reasons a bit deeper. We are explaining the issue in terms of discrimination or disproportionate costs. It seems under these claims, it doesn't really matter so much if the person is a woman or not, only if they fall under some these categories.

The power of the universals allow us to move forward from just considering the singular case of not hiring a woman. It allows us to explain what the problematic features are, and why they are problematic. In cases of sexism it provides us an explanation for what we can do if the genders were say reversed. It allows us to be consistent with our theory. By considering how our theory functions under different circumstances we are able to provide stronger justification with what we should do in this circumstance.