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When compared to scientific progress as well as other kinds of inquiry, the nature of philosophical progress is different because of a lacking structural methodological process. Williamson argues that in order to make philosophical progress, we should make clear our philosophical intuitions by adopting a methodology that largely depends on mathematics, “one that prizes clarity, rigor, and open-eyed reflection on the sorts of constraints – including logical constraints – that should be held to fix the contours of the debate.” 
Typically, making progress also involves refining and clarifying the initial question, but the relevant refinements and clarifications cannot all be foreseen at the beginning of the inquiry. Classifying questions up front as ‘useful’, or not useful, is not the right methodology to adopt; the clear questions that help improve science emerge in the process of attempting to answer the original rough questions, and would not emerge otherwise. This is another difference between scientific inquiries and philosophical ones: philosophical questions might initially come across as naïve or hopeless. It is only during the process of finding an answer that we give ourselves the opportunity to clarify and specify the questions, and come to the nature and the object of our philosophical investigations.
The nature of the questions that philosophy asks differ even more so, because scientists tend to take their methodologies as a point of departure for their research and inquiries, and therefore as questions that can be answered by methods. Also, they ask specific kinds of questions. Williamson thinks this is a legitimate way of working in the natural sciences. But he also thinks that it would not be a good idea to abandon all other sorts of questions that could not directly be answered by well-developed scientific methods. In fact, sciences never could be that well-developed, if natural scientists left questions for which there is no answer readily at hand unexplored. So what is it then, that Williamson considers to be the obstruction of progress in philosophy? What should we do better?
In philosophy we seem to be stuck because we only have very limited means of answering questions, namely through argumentation and deductive analysis. The progress that we make, is that what needs to be willing to persist even when progress is very slow and may involve setbacks. According to Williamson, we have to go through that crisis before we get anywhere.
Starting from the point that philosophers ask questions, and try to answer them, one thing philosophers need to do according to Timothy Williamson is to provide potential answers to philosophical questions. We have to find ways of distinguishing better and worse answers to these questions. Up to this point I agree with Williamson that accuracy, the courage to be as accurate and precise as possible and to repress the urge to be an entertaining writer, can lead to different insights in theories. ‘Different insights’, rather than ‘better insights’, because I do not agree with Williamson’s arguments on how philosophy should do better. In the next part, I will explain why.
In line with Williamson, I do not consider philosophy a natural science, but I do consider philosophy a science proper. Philosophy does not produce knowledge, but tries to find theories of knowledge by answering questions about the nature of knowledge. Philosophy helps make us understand things and is more concerned with clearing up confusions of concepts than any other scientific field. The answers to these questions (‘what is knowledge?’) are basically philosophical theories. There are different answers possible and philosophers need to formulate these different theories. Next to answering the questions, Williamson mentions that we need to clarify the original inquiry as well, during the search of finding an answer.
Additionally, he states that in order to accomplish progress in philosophy, we must work on the highest level by using the methodologies of logic and math. Williamson claims that since Frege, philosophers have in hand the most powerful conceptual tool of precision, which enables us to formulate hypotheses that can bring clarity and determine the consequences of theories and concepts, better than ever before. Mathematical models serve to show how structures in theories work or do not work, and by using math we can erase semantical paradoxes and create more clarity. By using math and logic as a methodology, we can create at least a structural analysis of what is going on: in the sense that in this way it is much clearer what the underlying premises are of a scientific theory.
For Williamson, this is analytical philosophy at its best. Philosophy “(…) has never been done for an extended period according to standards as high as those that are now available”. The rethinking of philosophical methodology, argues Williamson, involves understanding, at an appropriate level of abstraction, how philosophy is actually done. Williamson seems to call for a high-end philosophy, where its researchers should move slowly, with precaution and precision. So being insistent on trying to make progress in philosophy through mathematical methodology and focusing on the ”highest achievable” through precision and clarity, Williamson loses sight of the nuances and traditions that are so meaningful in philosophy.
My main criticism of Williamson’s approach to philosophy is that he seems to ignore dialectic in his train of thought: it seems that philosophy can only look backwards to judge the quality of its questions, but perhaps the same goes for the question whether math’s methodology is the right way to go. But this is also due to my conception of philosophy: In my opinion philosophy is a separate science, a science that asks questions about methodologies of other sciences, as well as the methodologies of philosophy itself. Williamson clearly sees philosophy as a separate science as well, but for other reasons: because the logical and mathematical conceptual apparatus enables us to perform deductive analyses which allow us to validate or falsify theories and hypotheses on formative grounds, i.e. without explicitly looking at the content. However, you want to show that philosophy can play a supplementary role by asking the right questions, but then the philosophical in itself is more like a methodology. The hardest question to answer is how to judge where we are in philosophy right now: What is the meaning of ‘progress?’
In addition, I agree with Nancy Bauer when she states that philosophical quests have a much higher value than (only) the outcome of the research: Philosophy is not exclusively about the answers or about clarifying meaning and reference. Philosophy is mainly about the quest itself. In my opinion philosophy is also about the process of questioning and critical reflection.
Williamson seems to suggest that philosophy serves a certain purpose and it fails to be philosophy if that purpose is not achieved. One could respond to Williamson that what it means to philosophize well, which is an essential part of philosophy, lies in the value of asking the questions, regardless of the methods used to answer them.  In addition, the intermediate steps taken when trying to answer a question, are in my opinion as valuable as clarifying the question itself: how do you know when the question is at it most clearest? When is ‘progress’ done? And how do you judge progress, or the position we are in philosophy right now? Williamson seems to dismiss this essential part of philosophizing by rejecting philosophical forms that are different from the analytical tradition, while philosophy is a rich discipline of versatility and philosophical questions, paradoxically, require a pluralist approach.
 Williamson, Timothy. Must Do Better, pp. 177–187.
 Williamson, Timothy. Must Do Better, pp. 179.
 Williamson, Timothy. Must Do Better, pp. 178.
 Williamson, Timothy. Past the Linguistic Turn?
 Williamson, Timothy. What Does Philosophy Do?
 Philosophy Overdose. Timothy Williamson on Philosophy.
 Hacker, P. M. S. “A Philosopher of Philosophy.” in The Philosophical Quarterly, pp. 291.
 Bauer, Nancy. “Getting Things Right” in How to Do Things with Pornography, pp. 1- 26.
 Another point of critique involves Williamsons arguments on how philosophy should deal with vagueness in word meaning and reference. Words like ‘many’ and ‘few’ , but certainly also ‘progress’, are excellent examples of vagueness. They are vague quantifiers, colour is an examples of vagueness, and what they behold, how we should interpret them, is a philosophical question by any means in my opinion. Williamson doesn’t discuss this topic in a great detail. Maybe he considers them just as not very structured words yet, that have to be clarified, once philosophy has made progress?
 Bauer, Nancy. “Getting Things Right” in How to Do Things with Pornography, pp. 1- 26.
Edit: Kees Müller.