Modern philosophy seems to have an inclination to mathematics and other scientific disciplines. Even moral philosophy is being "mathematized". Some peer-reviewed articles on the mere addition paradox, for example, utilized complex mathematical concepts just to prove or disprove the paradox. So, is there still a place in modern philosophy for "qualitative philosophers"? What if a philosophy major is not interested in delving in logic, math or anything in between?
The current trends in mainstream academic philosophy in the English-language portion of the world are definitely in the direction of the more quantitative, mathematical, analytic, scientific and experimental. So if this does not interest you, your options are to leave the mainstream, leave academia, leave the English-speaking world, or change the trends.
It's also worth noting that the paradox you referenced is itself intrinsically quantitative and comparative in nature. If you want to move away from quantitative philosophy, you may need to consider different types of questions.
EDIT: You could also leave your philosophy department. Many people who used to be in philosophy have moved into English, Education and Sociology departments. You might see if your university has a program in Cultural Studies or Interdisciplinary Studies. Many of those are havens for people with a less quantitative approach to philosophy.
The meaning of the word "Philosophy" is shifting and increasingly contracts to mean "Analytical, mathematical, scientific philosophy". At least it is the paradigm for academic philosophy and we are right in the middle of the puzzle-solving-phase. The "other" philosophy is still being taught - but as "history of philosophy". Also there are a lot of people researching the old philosophy and try to reconstruct e.g. John Locke's arguments to see if there is still something in it, we can use today. However if you were to publish a paper in the style of "Concerning Human Understanding", you will have a hard time finding a publisher and if you do it probably wouldn't help you gaining reputation. If Socrates lived today he certainly wouldn't be offered a chair of philosophy!
But just because the meaning of the word "philosophy" is shifting doesn't mean, people stopped doing the stuff formerly known as philosophy. They just moved to other departments - as Chris Sunami pointed out. And they still publish - it's just not academically recognized as "philosophy", and in this narrower sense of "philosophy" it indeed isn't (which - I think is - also why there are no eastern/asian philosophers.. In this sense of philosophy, they are simply no philosophers.)
According to Gnostic religious wisdom and traditional science, the prevalent modern infatuation with quantity both in real life -- as in love for material wealth and the craze for technological innovation --, and also in modern scientific tendency -- as a desire to understand and explain everything by reducing it to numerical terms -- is an essential characteristic of the current (and last) phase of the historical cycle of manifestation of the transcendental principle, a phase called Kali-Yoga in Hinduism, and termed as Akhar uz-Zamaan (The End of Time) in Islam and former Abrahamic religions.
The era is marked by sociopolitical disorder, moral decline and corruption as direct consequence of increasing preoccupation with the lowermost manifestation of the transcendental all-inclusive one being who unites all qualities (God) that ends and fully descends in the divisive quantitative material plane of existence that is devoid of any quality and substance.
This will be a prevalent cultural characteristic of our time embraced by the majority until the phase will come into its inevitable exhaustive end (marked by among others global frustration at the state of the things), a turning point from when on the universal ascent towards the transcendental principle will manifest itself in a resurgence of public interest in qualitative virtues and uniting transcendental truth. Other than conditions associated with the fateful and frustrating phase exhaustion, the transition will be also facilitated by inspiration from a minority of men of esoteric wisdom who carry and spread the traditional and gnostic sciences during the era. But the transition will be ultimately led, guided and the ensuing global order finally established by a human being who himself unites in his self all qualitative virtues and has a full affinity with the one supreme principle, hence he himself is only one person who contains all truth, a whole reflection of the all-inclusive principle of existence (or God in religious terms). This messianic leader is identified as ‘Mahdi’ in Islamic End of Time literature and whose equivalent exists in Hindu and other ancient religions.
So you have a dilemma to choose between what is now only a temporary popular trend or what is now an unpopular but a destined prevailing guidance in future, of course, if you can understand and comprehend the esoteric wisdom behind this worldview, for which I recommend you The Reign of Quantity by Rene Guenon which discusses this topic in detail and depth. You may ultimately choose to join theology, religion or anthropology departments in the West where esoteric wisdom and philosophy can be officially studied.
Many people who like to call themselves philosophers do a lot of logic and maths. The vast bulk of this stuff has nothing to do with what used to be called philosophy and it is often wrong.
I can't tell you what you should do, but there are some problems you should bear in mind. If you're not interested in doing something you shouldn't do it. Also, it is not necessary to be in academia to do philosophy. You could have a day job doing something else and do philosophy when you're not working. Also, there is a lot of philosophy that is not formally identified as such and it is often a lot better than academic philosophy.
Academia is largely hostile to doing good philosophy. The problem is that academics like tests. To pass the test you have to give an answer that satisfies the examiner. The examiner is set up as an authority on what is right and an exam is a terrible way of determining what is right or wrong. You have only a limited number of shots (often only one) to persuade the examiner you are right and then you're toast. Creating substantive knowledge requires a lot of back and forth argument so this is a terrible system for finding truth. So either a given academic philosopher hasn't figured this out, or he has figured this out and thinks it is okay to ignore criticisms of stuff he is doing. Either way he is bad at epistemology.
Let's consider the particular case of the mere addition paradox, which is also called the repugnant conclusion:
The problem runs like this. Assume utilitarianism is true (that moral judgements should be made by looking at how much utility they generate), that utility scales with happiness, that you can add up utility of different people and compare these aggregates between populations. Then if you have a lot of people whose lives are barely worth living this would be better than having fewer people who are very happy, but this sounds wrong - this is the mere addition paradox.
Perhaps somebody can come up with some mathematical model in which this conclusion fails, but no such model is necessary because every assumption made in the argument is false.
Let's look at the first assumption. Utility is some sort of measure of pleasure or happiness or something like that. If such a measure is calculable then it follows that there is a closed list of stuff that is relevant to morality. This, in turn, implies that there is a bound on the growth of knowledge and that any problems remaining when the maximum amount of knowledge is reached will never be solved. And there will be problems because at a bare minimum there will be issues of whether different parts of our knowledge can be used together and stuff like that. So then those problems will remain unsolved forever no matter what people do. But if that is true then some things about how to do stuff and how the world works can't be understood. And since the stuff that can't be understood is related to stuff that supposedly is understood in fact that the stuff that is supposedly understood also can't be understood. For example, if everything more than billion light years couldn't be understood, then we couldn't understand anything else either. Light from the incomprehensible stuff would interact with the stuff we supposedly do understand and we wouldn't be able to understand the subsequent behaviour of the stuff we allegedly understand. So then the first assumption in the mere addition argument implies that the whole world is incomprehensible the assumption should be rejected. The mere addition argument can't fly without that assumption so it is false.
The second assumption is too vague because happiness is a vague idea. People can feel happy for bad reasons and different people may use happiness as a label for different sensations. So we can reject the second assumption too.
What about the third assumption? Let's suppose we identify utility as happiness whatever that is. Different stuff can make different people happy and different people are not necessarily talking about the same thing when they talk about happiness, so then you can't place all utility on a single scale and add it up between different people. So the assumption fails. But what if we look at what makes a person's life better in reality? This does not save the assumption. What makes a person's life better is solving problems and different people have different problems with different solutions so you can't put them all on one scale. The fourth assumption has similar problems.
Some philosophy stuff worth reading. "The Open Society and Its Enemies" and "Realism and the Aim of Science" by Karl Popper. "The Fabric of Reality" and "The Beginning of Infinity" by David Deutsch. Ayn Rand's novels and collections of essays. The books of Thomas Szasz and William Godwin. See also
I think the basis of this question is a matter of poor sociological perception.
Every culture's qualitative philosophy assumes that culture's science, but we are unable to recognize those things as science, because we have factored off science into an enclosed discipline. No part of Stoicism was independent of the assumptions common at the time about how natural processes worked. We can look at Aristotle as though he invented 'science', but he is codifying something commonplace to his people, a sort of worship of the forms of language as a guide to understanding, and a basic alchemy. No part of Kant is independent of the religious habits or physical data he had available to him due to his time -- those were his science.
Qualitative reasoning in modern cultures is scientific, because the ordinary furniture of our lives is the product of science and involves accepting scientific theories as data. But I do not see how someone like Daniel Dennett is not still doing completely qualitative philosophy when he uses the science that has gone before him to make decisions about how it is reasonable to describe and structure reasoning.