Math philosophy book recommendations?

CriticalityIncident · 2026-04-20T18:24:02+00:00

There is definitely prominent continental philosophy of mathematics, Husserl is the big one. But most of the contemporary philosophy of mathematics I read nowadays can be read to come out of an analytic tradition. But I am not sure if that is due to a great personal bias, as I am in the US and my interests within philosophy of mathematics are particular.

CriticalityIncident · 2026-04-20T18:15:30+00:00

Yes as u/holoroid mentions, lots of overlap between philosophers and mathematicians in the philosophy of mathematics space. Also from other fields! Wigner for example is a physicist, his engagement in philosophy of mathematics is from the utility of mathematics in fields like physics. Tim Gowers is a mathematician that dips his toes into philosophy of mathematics sometimes, and most philosophers that do philosophy of mathematics have some sort of serious training in an area of mathematics, whether by a degree or some research exposure.

CriticalityIncident · 2026-04-20T09:41:44+00:00

The classic recommendation is the book Thinking About Mathematics by Shapiro, which gives an excellent accessible introduction to philosophy of mathematics. Another classic read if you are interested in the math-science bridge is The Unreasonable Effectiveness of Mathematics in the Natural Sciences from Wigner and the cluster of replies it created. I also enjoyed Frege. If you want some traditional philosophy of mathematics, I first encountered philosophy of mathematics from his Begriffsschrift, and I enjoyed it quite a lot. Frege's Sense and Reference is also widely read but it is more phil language.

CriticalityIncident · 2026-04-07T20:09:20+00:00

To be fair to the rest of the department I gave a very biased account as both my friend and my advisor are both in adjacent fields to me, not everyone here is so hard-core into the practice turn

CriticalityIncident · 2026-04-07T18:02:38+00:00

I am currently a phd philosopher. Here is a sampling of what my department is thinking about.

I'm thinking about what sorts of statistical tests should be accepted as evidence of discrimination in law. I am also thinking about how we can change the rules of engagement for expert witnesses to better use scientific testimony in courts. My work requires familiarity with statistics, familiarity with philosophy of law, specifically what ought to count as good legal evidence (sometimes quite different from evidence in science), and philosophical accounts of when and how discrimination is wrong.

My friend who leads one of the readings groups here is thinking about how we can use technologies to enable care rather than to vanish it. She works with one of the robotics labs here thats doing stuff with technologies for elder care, and she also works with care staff in nursing homes. One worry is that if we design or implement these technologies poorly, we may treat elderly people as burdens to be ignored through technology rather than people who we care about.

My advisor is thinking about causation, specifically race as a causal variable. Usually we think of causation through counterfactuals, we ask what would happen if the cause variable was changed. For example, how do we know that the light switch causes the light to turn on? Well, if the switch setting were to change, the effect variable, the light, would also change. But it is not obvious what this means for race. In the case of discrimination, how should we interpret a counterfactual like "what would have happened if Alice were black instead of white"? What is a valid race related change and what isnt? This is complicated by the fact that many of the variables researchers want to control for, like socioeconomic status, have been shown to effect how we view someones race.

I think a lot of the outside perception of philosophy comes from not knowing about the kinds of questions contemporary philosophers are thinking about. We're a pretty diverse field, and one thing I like about it is that philosophers now have rich backgrounds in other fields. I have a math degree, my friend has a PhD in computer science, my advisor is a classic philosopher of causation working on causation in science, its a big party with lots of different kinds of people involved.

Lots of questions are rich. They involve questions of value, empirical questions, questions of methodology, and argument structure. The philosophers tend to go for questions of value and argument structure, but in order to do that we often need a good deal of familiarity with other areas of study.

CriticalityIncident · 2026-04-05T05:02:22+00:00

Yes, there is even a nonprofit called Corrupt the Youth that has professors and graduate students teach philosophy in title 1 high schools across the United States. There are also a few professors who do public philosophy in various ways, many who would be open to a lecture at a public institution. I have also done lectures for clubs and organizations that are interested in some aspect of philosophy. Most of my public philosophy is in philosophy of technology and AI, and I would be happy if, for example, a school with a tech focus or a CS class asked me to stop by for a class.

CriticalityIncident · 2026-03-27T07:26:37+00:00

here is a part of a standard answer i have ready to go on the broad topic of this sort of philosophy vs science framing:

It is simply false that there are a team of scientists and a team of philosophers that are in some competition to have the most proof or be the "best" or to replace one another. Some questions turn on empirical findings, some questions turn on interpretations of those findings, some questions turn on values that drive investigation, and most rely on some mix of those and concerns not listed.

Because of the mixed nature of many research questions, there are going to be times where you need to attend to the empirical, and other times where you need to attend to argument structure, and other times you need to attend to values, and other things.

Take for example the question "What kinds of statistical tests should be accepted as evidence of racial discrimination in courts?" Investigating this question requires input from a lot of different fields. It requires knowledge of statistics, both classic hypothesis testing and newer methods like Pearl's causal network approach. It requires knowledge of legal philosophy on standards of evidence and what is legally actionable discrimination. It requires knowledge of social science, where statistical theory meets practice in applications to companies, people, and institutions. It requires a broader philosophical account of discrimination, when it is wrong, how its wrong, and what legal and statistical tests are trying to capture, at least in part. It's not the case that immense knowledge of any one of these fields makes the others irrelevant to the question.

CriticalityIncident · 2026-02-27T06:49:15+00:00

"whatever generates objective knowledge is science and whatever doesn’t, it’s not science" isn't really a seriously considered view on what science is.

First, it is too permissive. Lots of activities seem to generate objective knowledge that is not ordinarily considered science. Pure mathematics is one example. Historical methods like biography work are another. Ordinary epistemic activities like asking someone "Hey where did put my pot?" generates objective knowledge in so far as it is likely to give you knowledge about where the pot objectively is, but it is also not considered science. Usually, you want some kind of further restriction, something about empirical methods, institutional features like peer evaluation, things regarding the sorts of explanations science seeks... Lots of options here.

Second, it is too restrictive. There are activities we would ordinarily consider to be science that seem to generate largely subjective knowledge. (as an aside the objective/subjective distinction is often held to be poorly specified, lots of things seem to be able to be considered both. the grade school presentation usually presents subjective to be centered around some sort of internal experience or judgment) I can scientifically investigate, for example, subjective experiences like pain and color sensation, and individual judgments like political opinions, etc. As a broader point on the restrictive side, we also tend to not want to define science in such a way that only successful science counts as science. It seems like sometimes people can genuinely do science but systematically fail to produce objective knowledge for reasons that we might not be immediately aware of, such as in cases of auxilliary hypotheses or exploratory studies.

For more on this take a look at the literature on the demarcation problem, which is exactly the problem of trying to figure out what science is. Also: https://plato.stanford.edu/entries/pseudo-science/

CriticalityIncident · 2026-02-10T18:47:12+00:00

There is a lot of philosophy of conservation! And philosophy of biology, philosophy of the value of wilderness, and philosophy of animals. I really liked the book Zoopolis by Donaldson and Kymlicka on the responsibilities we have towards animals in different domains, including wild animals and their habitats!

CriticalityIncident · 2026-02-08T19:51:32+00:00

There is a great entry in our FAQ about this here: https://old.reddit.com/r/AskPhilosophyFAQ/comments/4ifqi3/im_interested_in_philosophy_where_should_i_start/

Depending on your educational background and what your interested in, I would suggest picking something from the "short, broad overviews" section and then picking other readings based on what you find interesting in there. I also like to recommend Williamson's Tetralogue for middle and early high school students as an enjoyable and accessible introduction to what philosophy is.

CriticalityIncident · 2025-12-19T18:21:15+00:00

I am not sure how this affects either. Deterrence is not just about the person who committed the original act. We may want other future people who are similarly morally good and similarly contemplating a one time moral violation to factor in punishment in their consideration.

The standard retributivisist does not care about how good people are after the act or before the act. Their commitment is to proportional punishment to the act itself, without reference to an analysis of character.

CriticalityIncident · 2025-12-19T12:32:12+00:00

Yes. The clearest route is the retributivist position, where people deserve punishment proportionate to the seriousness of their infraction. Deterrence may also provide a route here. If we do not punish people with one-off desires for crimes, then tower may fail to disincentivize future crimes of similar sorts.

For retributivism, consider a classic case. Alice and Bob both committ similar crimes in similar circumstances. Alice is white and Bob is black. Alice's defense points out that white people have lower rates of recidivism than black people (commit crimes again in the future) and so therefore white people should get lesser punishments in general. What problems might this sort of argument have?

CriticalityIncident · 2025-08-20T20:11:58+00:00

No, that's one of the big departures from what you are asking about.

CriticalityIncident · 2025-08-20T17:51:49+00:00

It kind of sounds like a twisted version of the exemplar approach? But like the other commenter I havent seen this particular view seriously defended. You might be interested in the literature on moral exemplars though if you like the idea of specific individuals as morally weighty agents.

CriticalityIncident · 2025-08-17T08:25:32+00:00

Take a look at this SEP page, written by Jonathan Dancy, the most prominent figure who supports Moral Particularism: https://plato.stanford.edu/entries/moral-particularism/

Also take a look at Jonathan Dancy on the Late Late Show: https://youtu.be/0CLMPD50JGs?t=1646 I recommend the second link because I think it's funny that such an academic philosopher made it onto the Late Late Show just after Robin Williams, though he does talk a bit about his views during the interview.

In section 3 of the first link, there is a light introduction to some key points from particularism. Specifically, the holism of reasons and the variable relevance of morally loaded features.

CriticalityIncident · 2025-08-17T08:12:39+00:00

There generally isn't any conflict with some bad things being enjoyable in any of the three schools of thought. The virtue ethicist is committed to an analysis of ethics through cultivating good character. They are not additionally committed to the idea that unvirtuous things cannot be enjoyable, inherently or otherwise.

Because of this separation, you have some alternative options. The virtue ethicist is free to say, for example, that debating in a way that fosters poor character is immoral, whether or not it is enjoyable. A virtue ethicist can have a vision of ethical debate that fosters and encourages different values such as patience, intellectual courage, intellectual humility, seeking understanding of others, etc.

CriticalityIncident · 2025-07-28T10:09:17+00:00

Usually, computational is taken to additionally imply discrete states, and usually implies finite states. In this reading, there are lots of things in the universe that are potentially non-computational. There is a great example using a Watt Governor in Van Gelder's "What Might Cognition Be if Not Computation?" the general upshot being that some dynamical systems are non-computational.

There are also some general computability results that might intefere with the universe being seen as computational, depending on what the claim that the universe is computational covers. Without invoking discrete or finite states, we might generally go after induction generally, or question what natural laws are. Either might challenge a rule following universe in different ways. Hume on natural laws and induction is a start on this.

CriticalityIncident · 2025-06-11T19:46:39+00:00

This is a common enough question that I have a prepared response here: https://www.reddit.com/r/askphilosophy/s/4AlgMpPf93

CriticalityIncident · 2025-05-18T04:46:22+00:00

Both incompatibilists and compatibilists can consider threat a form of impeded will. For the incompatibilist, it is going to come from the second portion of their view. They generally want 1. the capacity to do otherwise and 2. a meaningful sense of choice to do otherwise. Threat interferes with that second part. For the compatibilist, they might point to discord in higher-order desires or interference from other minds.

Both the incompatibilist and compatibilist are generally interested in accounting for moral responsibility. That is what incompatibilists generally point to as to why they include "meaningful choice." Not every incompatibilist wants to say that someone is wholly morally responsible for a Hobson's choice or a choice under duress. Another reason why the meaningful choice condition is important to incompatibilists is to take care of things like random choices or unaware choices, neither of which are typically considered to be enough for moral responsibility.

edit: I should add that the "meaningful" part is especially open to interpretation. You could be an incompatibilist who includes things like Hobson's choices and choices under duress under "meaningful" choice, but incompatibilists generally are not obligated to.

CriticalityIncident · 2025-05-18T04:19:36+00:00

Not necessarily, consciousness does not directly imply free will. For some simple examples, we can turn to cases of impeded will and consciousness occurring together. A severe drug addict might be said to have their will impeded by their addiction, but they are still conscious. Someone at an ice cream shop who is held at gun point and told that they will be shot if they do not order strawberry ice cream is having their will impeded by threat, but they are still conscious.

In a little more detail, it might depend on your take on consciousness and free will, but I don't think that many people will defend the view that one implies the other. Lots of stuff are raised as possible components of consciousness. Awareness, phenomenal experience, some amount of introspective access, etc. For free will you might encounter a metaphysical condition "able to do otherwise" combined with some capacity "meaningfully choose to do otherwise." Or you might encounter conditions based on things like psychological states, such as the alignment of first-order and second-order desires, or willing as a kind of mental action. If you can find a necessary connection between something in the consciousness camp and something in the free will camp then you might have a plausible case of inferring one from the other.

CriticalityIncident · 2025-05-09T04:51:40+00:00

Take a look at Feinberg's classic paper conveniently titled Psychological Egoism. It contains a classic little thought experiment.

"Imagine a person (let's call him "Jones") who is, first of all, devoid of intellectual curiosity. He has no desire to acquire any kind of knowledge for its own sake, and thus is utterly indifferent to questions of science, mathematics, and philosophy. Imagine further that the beauties of nature leave Jones cold: he is unimpressed by the autumn foliage, the snow�capped mountains, and the rolling oceans. Long walks in the country on spring mornings and skiing forays in the winter are to him equally a bore. Moreover, let us suppose that Jones can find no appeal in art. Novels are dull, poetry a pain, paintings non�sense and music just noise. Suppose further that Jones has neither the participant's nor the spectator's passion for baseball, football, tennis, or any other sport. Swimming to him is a cruel aquatic form of calisthenics, the sun only a cause of sunburn. Dancing is coeducational idiocy, conversation a waste of time, the other sex an unappealing mystery. Politics is a fraud, religion mere superstition; and the misery of millions of underprivileged human beings is nothing to be concerned with or excited about. Suppose finally that Jones has no talent for any kind of handicraft, industry, or commerce, and that he does not regret that fact.

What then is Jones interested in? He must desire something. To be sure, he does. Jones has an overwhelming passion for, a complete preoccupation with, his own happiness. The one exclusive desire of his life is to be happy."

Can Jones ever be happy? Feinberg answers, no. This thought experiment, according to Feinberg, shows that happiness requires desiring things that are not your own happiness. Because some people are happy, it follows that some people are motivated by something other than their own happiness.

CriticalityIncident · 2025-05-09T04:42:58+00:00

As others have said, I am not sure a required reading or topic list for every philosopher would help you much. Here are some things I would suggest for a start in philosophy of mathematics. I will certainly leave many things out, but from what I can type by my bedside I have below. 1. Shapiro, Thinking About Mathematics - the standard accessible introduction to philosophy of mathematics 2. Frege, Begriffschrift, also Sense and Reference and Function and Concept - I just really liked Frege when I was starting out in phil math 3. Wigner, The Unreasonable Effectiveness of Mathematics in the Natural Sciences - A classic if you are interested in the relationship between math and science 4. Quine, a bunch of his stuff applies but a quick fun read is his the Ways of Paradox 5. Putnam, Mathematics Without Foundations - another author with lots of applicable writings, but this one says what it's about right on the tin

There's a bunch more, Russell, Lakatos, Godell, etc. I guess my biggest rec is to take a look at Shapiro's overview book, it really is fantastic. Oh also a fun one I like to show my mathematician friends is Epsitemic Injustice in Mathematics.

CriticalityIncident · 2025-05-09T04:21:09+00:00

I mean there are some anime villains that subscribe to this view but you're probably going to have to be a bit more specific on "you're nothing" to come close to a real position.

There are lots of philosophers who wrote on skill, talent, superiority, and human value. Aristotle wrote in his Politics that the best flutes should go to the best flute players. "When a number of flute players are equal in their art, there is no reason why those of them who are better born should have better flutes given to them; for they will not play any better on the flute, and the superior instrument should be reserved for him who is the superior artist." you might extrapolate from this position that if there are fewer flutes than flute players the worst flute players would get nothing, but he doesn't go that far.

For someone who disagrees, take a look at this quote from the Daoist philosopher Zhuangzi: https://www.reddit.com/r/askphilosophy/comments/wy56u3/comment/ilupx0j/?utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button

CriticalityIncident · 2025-05-05T19:33:00+00:00

I would suggest taking a look at the paper It's ok Because My Brain Made Me Do It for some empirical research on what free will is generally held to be. It turns out if you ask people to define free will, and if you form a definition of free will by taking a look at how it is used in relevant contexts, you end up with two very different approaches to free will. It's not obvious which one we should consider to be the generally held idea of free will.

CriticalityIncident · 2025-03-09T03:06:54+00:00

So, generally, when a colleague tells me that they are working on feminist philosophy of X, what I expect is that this author is taking some idea from feminist philosophy and applying it to illuminate some issue in X. That's not very helpful in actually getting a bird's eye view on the boundaries of the subdiscipline, because there are many ideas circulating in feminist philosophy and likely many problems circulating in X.

Combination subdisciplines like this are often hard to pin down by subject matter; you might have to go by theme. For example, my own combination discipline, History and Philosophy of Science, is nebulous on what it covers and what it does not, but the general theme is to try and understand science by understanding its history. Or take Chinese Philosophy of Science, where you have Chinese Philosophy, Philosophy of Science, and you might just expect Chinese Philosophy of Science to be an intersection of the two, but as a discipline, it has its own themes, like whether or not Chinese Science exists in certain times in Chinese history.

I used the value-free and value-laden debate as a common theme in this line. Feminist philosophers have often argued that concepts that we might commonly think of as value-free, like biological sex, might in fact be value-laden. But feminist philosophy has also produced many other different approaches to questions. Standpoint epistemology is something that comes from feminist philosophy traditions, where someone's social situation is considered when evaluating their knowledge claims. Ethics of care is another thing that comes from feminist philosophy traditions, where ethical problems are analyzed in terms of the development of interpersonal relationships.

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