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I'm a mathematician who has taken an interest in philosophy in the past few years. I want to start with the 17th-century rationalists (mainly Descartes, Spinoza, and Leibniz) and move forward in time through the empiricists (Locke, Hume) to Kant, Hegel, and then the 19th century. I'm aware of how broad this "program" is, so to narrow it down a bit, I should clarify that I want to grasp the big ideas and do not intend to delve into every detail of each thinker. Moreover, I'm specifically interested in ideas related to epistemology and the philosophy of science, some political philosophy, and, to a lesser extent, metaphysics.

One of my problems is that I don't know good resources, such as textbooks, other than SEP, and moreover, I don't have a "syllabus" to follow (things like, should I read this whole book or only chapters such and such?).

Another problems is that, not being a trained philosopher, I lack basic study skills (should I take notes, make summaries, discuss on forums?).

I found this entry that has some useful tips, but it's still a little detached from my goal.

Any suggestions/advices would be appreciated.

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  • yeah, you just need a reading list, and - arguably - to be shouted at sometimes, idk. you can take maybe oxford cambirdge continuing education classes on-line, if you want to get a sense of how stupid you are. hth
    – user66760
    Commented Jul 23, 2023 at 23:13

12 Answers 12

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If you want to study the philosophers of the 'modern' era, by which philosophers mean roughly from Descartes to Kant, then by all means read the primary works themselves. The main texts are:

  • Descartes: The Meditations; Discourse on Method.
  • Spinoza: Ethics.
  • Leibniz: Monadology; New Essays on Human Understanding.
  • Locke: An Essay Concerning Human Understanding.
  • Berkeley: Philosophical Works (edited by M. Ayers).
  • Hume: Treatise on Human Nature.
  • Kant: Critique of Pure Reason; Critique of Practical Reason; Critique of Judgment.

As a mathematician you might well be interested in Frege, who was hugely influential in our modern understanding of philosophy of language, logic, and philosophy of mathematics. Peter Geach and Max Black's book, Translations from the Philosophical Writings of Gottlob Frege, covers some of his writings.

The Stanford Encyclopedia of Philosophy and the Internet Encyclopedia of Philosophy both have good articles on these philosophers.

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  • Thanks for the comment! I specially appretiate the list of texts as I often find it hard to make selections, specially of the more prolific authours. Reading directly from the sources was my first instinct; I do however feel that sometimes you need someone to explain some terminology that has a history of its own (e.g. the word "substance" in Descartes and Spinoza). Maybe I can use SEP and IEP for that.
    – hamath
    Commented Jul 22, 2023 at 22:08
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Welcome!

As someone who has been on a steady diet of self-study over the last 4 years coming from a mathematics/computer science background, I would encourage you to conduct a survey of books about philosophers written by philosophers. For instance, I own Kant: A Very Short Introduction which was written by Roger Scruton, an esteemed philosopher in his own right. Simon Critchley has done one on Continental philosophy, and so on. The reason for this might be understood as that the works in themselves do not simply or adequately delineate "the big ideas" or what constitutes historical context, and professional philosophers often provide useful normative characterization of the materials. In fact, something like the Critique of Pure Reason is not only dense and difficult to understand (G.J. Matley has a glossary of Kant terminology online), but the concepts themselves are often subtly defined differently starting with Ancient Greeks, and then borrowed and repurposed over the centuries.

In short, having professional guidance helps, particularly when there are multiple interpretations of works. After Kant's death, for example, German philosophers immediately engaged in a process of reinterpreting his work in their own manner. So, to your self-study, I would also suggest a reading of one or two general histories of philosophy to provide context to the work. In mathematics, we are often raised in an environment that places a philosophical presumption of the universal objectivity of terms. Euclid's definitions in Elements are fairly easy to understand to this day, but the basic terminology of epistemology, ontology, and metaphysics are much more open to interpretation, and so Cartesian introspection, empiricism in its various forms might be seen in a different light with the an understanding of the evolution of philosophy immediately prior, during, and after the linguistic turn which are done in a way that raises the profile of the philosophy of language in conducting what might be considered exegesis.

What I'm pushing as an answer is the idea that just like its an act of ignorance to read the US Constitution, as an example, without the Federalist Papers or having an overview of history, so too reading the Western Canon without having a general understanding of philosophy more broadly is likely to stymie a logically consistent understanding of the work. As for method, I would simply suggest writing out your thoughts, articulating questions, and then answer them yourself in conjunction with resources like encyclopedias, dictionaries, and communication with others, this being one of a number of forums dedicated to philosophy.

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  • Thanks! In fact, the first sentence of your last paragraph is precisely one of my motivations for seeking for help here. I tried with some of the "Very Short Introduction" summaries but not all of them succed in introducing the subject to the nonexpert. However, I think that the general point is a good one, maybe I'll have to fine-tune a little the references.
    – hamath
    Commented Jul 22, 2023 at 22:14
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    In working out one's own perspective (by questioning) reason is what is used, hence the relevance of Kant's critique. I started with Heidegger & Derrida and have come back to Kant. Commented Jul 24, 2023 at 0:11
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Resources for self-teaching philosophy

In response to questions like these, I always recommend The Story of Philosophy by Will Durant. The book, nearly a century old, holds up very well. Durant is an engaging writer, and his survey of the discipline is an excellent resource for those, like you, who "want to grasp the big ideas and do not intend to delve into every detail of each thinker."

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  • That's a nice reference, thank you! It kind of goes well with some suggestions from the other comments.
    – hamath
    Commented Jul 22, 2023 at 22:15
  • +1 @Hamath I also often recommend Will Durant for 'first readings' requests
    – Rushi
    Commented Jul 24, 2023 at 2:29
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You might like this answer: A newbie's highly thought-upon plan for starting philosophy

I'd say, read core texts. Research and write notes about topics. Then write essays, ideally with feedback, like by giving answers here.

I think it's important to frame what you think philosophy is for, what it's about. I make my case for it being a toolbox, that helps us get 'unstuck' and into a place where we can think productively and creatively, here: (Why) is this negative outlook on the concept of philosophy misguided? This great essay, for me, puts it even more clearly: Nāgārjuna, Nietzsche, and Rorty’s Strange Looping Trick.

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    Thanks for the reply. Your last comment is particularly interesting, I haven't really thought about it.
    – hamath
    Commented Jul 22, 2023 at 14:22
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    @hamath: It doesn't need to be a final verdict, your answer will doubtless change wuth study. But it is foundational & shapes understanding of the subject. I give Socrates a defining role: philosophy.stackexchange.com/questions/88852/… The status of math is a pivotal question, which shapes much else; you might be interested in my take: 'The Unreasonable Ineffectiveness of Mathematics in most sciences' philosophy.stackexchange.com/questions/92058/…
    – CriglCragl
    Commented Jul 22, 2023 at 15:29
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A couple of comments.

• You are not actually doing philosophy if you merely read and understand arguments and counter-arguments. Rather… assuming the case in which you are thinking about a position that is wrong… you have to actually do the mental work of reaching out from a position, logically, to find tenets that your opponent would accept, that disagree with their position. ([Please respect my/any IP here.] That is “divergent” thinking; “convergent” thinking allows you to work out whether or not a position disagrees with your existing position, but does not reach out to find grounds for determining the answer.)
For example… utilitarianism is the species of consequentialism [the view that an action is right or wrong according to its consequences] that holds that an action is right or wrong according to the “happiness” it results in. The [if I may] “obvious” objection is that this does not express moral rules (to which the counter is that the pertinent “happiness” is rule-based). The non-“obvious” objection -- and this is my point here -- is that one tends to think of “good” actors; the weakness is that an evil actor will (arguably) be made “happy” by evil… from which it follows that what we want to know is what should cause happiness… which takes us back to square one. [Tangentially, we can observe that we already know [or not] what a good actor would desire.] The point is that you have to be doing the work that would [hopefully!] enable you to think of such objections, to be doing philosophy.

• I think of the overall body of philosophical thinking like a binary tree index (which can just get deeper and deeper). There is a paper, and there are papers that agree or disagree, and there are counters to those, and so on, hierarchically. The point is that… to stop at any depth-point is to assume that this is the right answer (or just that one is not going to delve deeper into the topic, regardless). An example here is the concept of having true beliefs. It appears entirely reasonable to think that a true belief is one that corresponds with reality. However, there is the objection that this is a category error; {reality} and {beliefs about reality} are of different kinds… and so it begins… !

• Related to the previous point… [one of my lecturers observed that] in respect of any new “concrete” question [such as the ethics around some new medical technology]… the [actually] correct answer appears within the first year or so, as a rule (as opposed to this taking a long time and being hard to follow).

• Since I’m here, I shall issue my standard dire warning. From inside, postmodernism is an exciting exploration of the nature of truth, and beliefs, and mind, and all sorts of exciting things. From outside, postmodernism is the rejection of antithetical thought, and truth, and meaning. Engaging with postmodern “thinking” WILL wreck your brain. You have been warned.

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Sounds like you're MUCH more rigorous than this, but there's a YouTube channel that gives nice, but concise introductions/overviews of individual philosophers.

It couldn't take the place of reading the actual texts, but it might be a way to prep for doing so.

https://www.youtube.com/@OverthinkPodcastPhilosophy

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  • Thanks! I believe that podcasts and YouTube videos are a good complement for the actual reading so your suggestion is much appreciated.
    – hamath
    Commented Jul 23, 2023 at 10:39
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Great Question. The others have given some good suggestions, but I would like to add my two cents worth. I would personally recommend reading the Bible as it is the basis for a lot of philosophy (not only western, but it features significantly in western philosophy). If you want a justification for that, the book "The air we breathe" by Glen Scrivener is quite good. I greatly enjoyed reading it myself.

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I tell this story occasionally. I was, through no direct fault of my own, an arrogant philosophy undergraduate, despite failing philosophy. Eventually, after I graded at a low 2ii in an exam in which I assumed I had solved the riddle of induction, I snapped, and I asked the lecturer to look at the paper again. He replied, and I didn't understand a word he said; he apologised. Anyway, at the start of the next year someone managed to convince me that their research was trendy ("cutting edge"), and suddenly I was able to learn from what he was saying in class (to the point of realising I could not do any better than him), and both work out and judge arguments that appear in print.

tl;dr

You need a reading list, but you also need humility.

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Aside from some concrete tips, á la Sophie's World or following podcasts (hey, how about "The Partially Examined Life" from that list, which has an entertaining yet educating format intended to introduce people to philosophers while requiring zero previous knowledge), in my opinion philosophy lends itself greatly, and much more so than any other topic, to a DIY approach. Start with any random media you can find, and then branch out to the topics that interest you.

It is much too broad and deep (and conflicting) to cover all of it systematically, I would not try that at all. Try to understand the history of where a certain philosophical theory comes from - that will make it much more easy to entertain a modicum of understanding. And aside from a general top-down overview, which obviously always helps, and which you can acquire from many books or other media, figure out what interests you and proceed into those directions on your own, maybe guided by references from the other resources you already consumed.

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To a much greater extent than with other disciplines, any philosophical critique, summary, commentary or curriculum is itself a philosophical statement, and inevitably non-identical with the philosophy of the original(s). In addition, many of the originals are more accessible than the studies of them. (Descartes' Meditations, for example, are quite lucid, easy to read and understand, and brief.) For that reason, self-guided self-study of primary materials is not a bad idea, or at least, a good-enough place to start.

Your list of philosophers isn't bad, but for a mathematician in particular I would start with Plato--at least the Meno, which is quite brief--and swap out one or more of the Empiricists for Pascal. But of course, that betrays my own philosophical prejudices.

As far as techniques of reading philosophy, even these are themselves infected by philosophical biases. Plato was read one way for hundreds of years before Plotinus rescued an entirely different (and to my mind, much superior) way of accessing his work. Conversely, deconstructionist readings of philosophy claim no allegiance to the original intentions of the author at all. The most common academic approach is the close read, which focuses on the fine details of the logical arguments. My own favored approach, however, is quite different: I read philosophy quickly, without seeking to understand each detail, and wait to apprehend the deeper meanings in what Wittgenstein called the "silence" (a method that might not work for anyone else). In summary, therefore, I urge you to be bold in seeking your own path through philosophy, without neither apology nor trepidation.

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  • Many thanks for the comments, I'll certainly give Plato a fair shot. I believe I betrayed the purpose of my post by confessing my "mathematicianship". In fact, I'm interested in philosophy as a side activity from my professional/academic endeavours. I have a follow up question regarding the techniques: how do I know that I'm not simply getting a completely wrong idea about this or that philosopher? I understand the deconstructionist idea but I do tend to think that there are somewhat canonical interpretations of a text and one can more or less attempt to grasp them.
    – hamath
    Commented Jul 29, 2023 at 19:49
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    There are definitely canonical interpretations--but no guarantee those are correct. As I mentioned, Plato was radically reinterpreted centuries after his death, and many, including myself, believe the "neo-Platonic" interpretation is the more correct one. Conversely, interpretations of Hegel experienced a sharp and never fully resolved "right/left" schism shortly after his death. // I won't discourage you from reading commentaries and critiques, but read the originals first--and don't take the orthodox views as gospel truth. Commented Jul 30, 2023 at 2:46
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Well, like ya I'm a noob in philosophy and though I kinda sorta love the queen of the sciences (mathematics), I don't think the feeling is reciprocated in any way, form or shape.

I have what is but an inkling of how math works ... I'm familiar with the basic operations (+, -, ×, ÷, ^) and I'd like to submit a request to you, which you're at full liberty to ignore.

Math simplifies or so I'm told. Could you, after you feel the time has come for ya ta say "Consummatum est!" in re yer tryst with sophia share some of yer (mathematical) insights with us?

To give ya a an idea of what I'm getting at ...

  1. -Theism = Atheism (like positive & negative numbers)
    So, obviously ...
  2. Theism + Atheism = 0 (Like +2 + -2 = 0). You'll probably see a lot of this around.
  3. Natural Theology = Religion + Empiricism.

Bonam fortunam (broken Latin for Good Luck) homo viator

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    Hi there! Thanks for the reply. I would be glad to share some insights as soon as I have something somwhat interesting to say, which I guess will require that my "tryst with sophia" extends for at least a reasonable bit. For the time being I do feel obliged to say that, even if it is true that simplification is part of Math, I guess that the more profund functioning of it has to do with finding regularities and patterns and, probably to more interesting in this realm of sophia, to try to come up with the appropriate structures with which such patterns can be propely described.
    – hamath
    Commented Jul 29, 2023 at 19:36
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The Blog of the APA has a series of posts where instructors publish their class syllabi: https://blog.apaonline.org/category/syllabus-showcase/ . One may find useful references there.

Also The Daily Idea website, https://thedailyidea.org/ , has syllabi and introductory reading lists for many philosophical topics.

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  • Great resource, thanks!
    – hamath
    Commented Jul 27, 2023 at 18:03

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