How to start learning philosophy and overcome my bias towards mathematics?

Question

I am interested and curious about philosophy, especially topics like morals, justice, ethics, etc. I want to read books that explain the philosophy behind them. However, I am very ignorant and I don’t know anything about philosophy, so I have no idea what the different branches or ideologies or schools of thought are in philosophy like (nihilism, absurdism ,fatalism etc ). Sometimes one is too ignorant to even know for what he/she should ask, and this is me I have no idea about philosophy and don't know what to ask for, Is there a roadmap or list of topics? If not then what to learn and how to know what to learn next?

I also want your advice/thoughts about my problem with reading philosophy, novels, etc.

I always wanted to read and I like reading in general, but I avoided reading many topics like history, philosophy, etc. because I think they are greatly influenced by opinions, beliefs, religion, etc. and I cannot be sure of their validity or accuracy. The idea that in every one of these topics there is an opinion and an opposite opinion, and to reach the truth I had to dig up in 10,000 books, made me hate to read any of them. This has been my problem for more than four years and still to this day. I decided to stick to reading scientific books like physics books because they are less opinion-based and biased. Then I switched all my reading to math books because they are the least biased. I like the idea of proof and rigorous math, so I avoided reading any non-mathematical book.

Although I still prefer to learn pure math, I want to learn more things like philosophy, for example.

Can you please recommend me some books or resources that can introduce me to philosophy in a clear and objective way? How can I overcome my fear of reading topics that are not purely factual or logical?

Answer 1

As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.
Einstein

1. I suggest you reflect on this quote of Einstein.
2. Then try to probe into what you are running away from when you say you have a bias towards math.
3. That probing (can) lead to what will be your own authentic entrée into philosophy.

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As a counter weight to Einstein there is also Gauss, widely considered the greatest amongst mathematicians

When a philosopher says something that is true then it is trivial. When he says something that is not trivial then it is false.

If you can hold and grapple with both Einstein and Gauss together, great!
If not with your inclinations and questions I say, Start with Einstein

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As a specific recommendation for a person with your proclivities I'd suggest Zen and the Art of Motorcycle Maintenance which is a an exploration of the "romantic" vs the "classical" outlooks with the author very much on the classical side.

I suspect you will find you share the orientation of the author...

And also the dangers!

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Added Later

I am rather bewildered on the upvotes on this. Especially since it was not meant to be an answer at all — at first I thought only to put the Einstein in a comment.

But its really not an answer; it just shines a light on the question that is (hopefully) clearer than the question.

So here's another answer that should help you to explore the question in many more dimensions.

Answer 2

Philosophy is intrinsically about things where there's no clear, objective and universally acclaimed answer. So it's impossible to avoid opinions, even when coming up with a reading list. Every person is going to recommend a different one. I'll give you mine, specifically for you (but I can't pretend it's objective):

• First, I'd recommend any good beginner text on symbolic logic. It's at the nexus of mathematics and philosophy, so it would be a good point of overlap with your prior studies (as well as being arguably the least subjective topic in philosophy, at least if you stick to the standard logics). It will also help you understand the structure of philosophical arguments.

• Next, I'd recommend Plato, because he's the most important and central figure in Western philosophy, and nearly everyone who came after him was influenced by him. There's a lot of Plato, but Meno would be a good introduction (it's short, and on the topic of mathematics). Apology and Republic are his most famous and influential works.

• Next I'd do Descartes' Meditations. They are short, easy to read, and hugely influential. Plus, Descartes was heavily interested in the same thing you are--what can we know for sure? In some ways, this work can be seen as a direct answer to your question "How can I overcome my fear of... topics that are not purely factual or logical?" (Descartes was also a master mathematician, whose invention of the Cartesian plane revolutionized the field.)

If you start with those, it will give you a good foundation for understanding anything else you might read after that. I won't include many follow-ups because I suspect your philosophical tastes and mine don't coincide, but if you're open to reading something VERY different, I'd recommend Laozi's Dao De Jing.

All of the above should be freely available online in multiple different translations.

Answer 3

What can help you with overcoming this problem is reminding yourself that you still have to ACT in the world. So you already have some moral, ethical and general philosophical framework, but it is not conscious yet.

So while the world might have many more shades of grey than a mathematical proof, you are already forced to engage with it. The question is do you want to do this on autopilot mode or do you want to expand your consciousness and be able to engage, understand and ultimately improve your own philosophical framework. If you do there is no way around "getting your hands dirty" and confront the ambiguity and the uncertainty which comes with the world.

Answer 4

There really are two approaches you can take. You can find more trust in philosophy or less trust in mathematics.

I'd recommend Douglas Hofstadter's book, Gödel, Escher, Bach: an Eternal Golden Braid, often referred to as GEB. It is a study of logic and math, and in particular the issues that arise when trying to demonstrate the validity of logic using logic.

It's a fascinating read that shows the triumph of mathematics and its immaculate precision, and at the same time the price that is paid. There are things that mathematics can prove that it cannot prove (within a particular set of rules), and they abound more often than we might like.

After that, one starts to realize that the reason math based stuff seems so un-opinionated is that people you listen to mostly agree on the opinions so you don't see them as easily. Then, after that, you start to see that there are indeed contrary opinions out there. It was just easy to ignore them.

Answer 5

Depending on the type of philosophy, it may overlap with mathematics.

My college major was theoretical mathematics. I got a minor in philosophy. In the college I attended at least, the view was that logical philosophy and foundational mathematics were intertwined to the to the point that many classes dealing with one or the other was cross-listed as both mathematics and philosophy.

In other words, at least assuming you accept the view that the line between the philosophy of logic and foundational mathematics is blurry, then there is a lifetime's worth of serious philosophy you can do without really even leaving mathematics.

Even in non-mathematical areas of philosophy, a mathematical leaning may serve you well.

If you truly want to overcome a bias towards mathematics, you certainly can. There are definitely serious philosophers with little knowledge of mathematics.

But you may find that it will serve you well. Even in areas of philosophy that are less intertwined with mathematics, mathematical training (in the sense of proofs, not in the sense of arithmetic) may serve you well. Almost every philosophical endeavor will involve making and supporting arguments. You may be appealing as your foundational materials to evidence from the physical world or even to intuition rather than axioms and prior proofs in some areas of philosophy, but they will still be sensitive to whether or not your arguments are well reasoned and well structured. A background in mathematics (at least of the kind dealing with proofs) is likely to serve you well in that.

As a practicing lawyer now, I sometimes appeal to legal philosophy (especially on appeals, less so in trial court). I structure those arguments in a way very similar to the way I would structure a mathematical proof and use similar techniques even though I rely on prior precedent instead of axioms and prior proofs.

Answer 6

Regarding there being no conclusive answers in philosophy (which is an overexaggeration, for example: the so-called "Hume's problem of induction" is generally accepted as being what it is, i.e. a simple fact about the relation between evidence and theory), I think that Wittgenstein was in some sense right when he said that in some sense all philosophical puzzlements are pseudo-problems. Not in the sense that they're irrelevant or that they're impossible to discuss (Wittgenstein, whether he liked it or not, spent his whole life on these questions) but rather in the sense that some of them (ex. "How can there be free will in a determined world?") are how to think about x questions and not is x *really* there questions. Philosophy is in this sense an exercise in imagination and in this way it's similar to mathematics - but unfortunately philosophers too often confuse imagination with a mere fantasy, (luckily!) unlike mathemathicians.

Philosophical debates aren't unlike scientific debates in the aspect that the justification for any position isn't ever conclusive or convincing for everyone. But philosophy doesn't have the pragmatic dimension which our natural scientific understanding has and thus the plurality of options might seem like there is absolutely no agreement (although that's too sometimes the case). And often only once the dust settles it becomes clear what the debate was all about (that's one of the problems with many philosophers' insistence on the history of the subject). Usefulness motivates agreement.

My reccommendation would then be to understand philosophical debates not as disagreements over fundamental, untimely questions but rather as an attempt to better understand the puzzling problem, exactly to dissolve the dichotomy on which it is based. Often this is a self-perpetuating cycle where one vocabulary (to use a Rortyan term) gets replaced by another, less problematic one which however also has its distinctive issues. In this way the history of philosophy is crucial, because it reconstructs the path along which, driven by the failure of our everyday understanding to answer some antinomies and paradoxes inherent to it, leads through various "shapes of consciousness", as Hegel would say, to what we have now. Simply put, just because most people won't become vegans after reading a paper of Peter Singer's, however brilliant argumentatively, doesn't mean that there's no difference that philosophy can make.

Getting to the point - there are some book reccomendations:

1. Daniel Bonevac, Deduction - if you know mathematical logic most of it won't be in any way revelatory (it might even be banal), but it discusses questions relevant to philosophical logic (ex. modal logic)
2. Robert Brandom, Tales from the Mighty Dead - if you're interested in the history of philosophy; Brandom discusses ideas of various thinkers from a perspective which appreciates the manner in which they introduce new ways of thinking about various issues, even if their answers weren't very good.
3. John Haugeland, Artificial Intelligence: The Very Idea - the first chapter discusses some central innovations of the Enlightenment in the same way in which Brandom does; The book is of course quite outdated now, but Haugeland was both a competent philosopher and historian of the subject and a working programmer so it's a great read.
4. Willard Van Orman Quine, Two Dogmas of Empiricism - a must-read if you care at all about twentieth century thought (and it's hard not to); for an elaboration of similar themes: W.V. Quine, Pursuit of Truth (technically, Quine's magnum opus is Word and Object, but it's a difficult read - a good introduction, if you're nonetheless interested, is Eve Gaudet's Quine on Meaning or Gil Harman's articles named Quine on Meaning and Existence)
5. Ludwig Wittgenstein, Philosophical Investigations - gives more questions than answers and isn't very well written but if you know barely any philosophy it can be revelatory

Answer 7

My other answer was not really an answer. Because there was an unusual interest in it, I thought Id make a real answer... or at least come closer to it.

A first short answer is don't force yourself. If your sibling likes the Beatles and you like Beethoven, neither needs to like the other. More pertinently if one of you is drawn to experimental physics and the other to theoretical physics there need be no reckoning as to which is superior. So if you like math and not history or philosophy there is no reason per se to try modify that.

However you clearly also have a nagging suspicion that you are missing out on something. Speaking personally, as a teacher its always a dilemma when to tell a student to focus on their strengths and when on their weaknesses. After all any typical university program begins by focusing on lacks ie weaknesses in their required core courses and then on to strengths in the electives, projects, theses etc.

So below, I have made tables that try to enumerate the different facets of the two sides. The line down the middle is really not straight, its not a line. Its really more wiggly, curvy, even concave and generally confused.

Nevertheless there are two sides as you intuitively guess. If you find yourself definitely preferring the one side for one row it does not mean you should prefer the same for all the others.

^{The links that are there are for the harder to find entries and not the ones that will easily appear on wikipedia, SEP, IEP etc}

Facets

Classical	Romantic
Necessary	Contingent
a priori	a posteriori
analytic	synthetic
Platonic	Empiric
Rationalism	Empiricism
Laws of Science	Scientific Data
Logos	Mythos
Materialism/physicalism	Idealism/solipsism Buddhism/New Age/"Woo"
Buddhism (psychology)	Hinduism (mythology)
Positivism	Hermeneutics Phenomenology
Analytic model	Simulation models
Functional programming	OO programming
Truth	Paradigm
Proof	Evidence
Identity x2 - y2 = (x + y)(x-y) cannot be unsolved...necessarily	Equation x2 - 5x + 6 = 0 can be solved...possibly
Possible worlds	This world
Timeless world	World in time
Math	Physics
Physics	Economics Anthro/Psycho/Socio
STEM	Humanities
Conventional "western" medicine	Alternative medicine
Theoretical Physics	Experimental Physics
Pure math	Applied math
Anglo American Analytic Philosophy Logical Positivism	Continental Post-modernism Existentialism Absurdism
Conservative	Progressive

People

Classicist	Romantic
Voltaire	Rousseau
Sokal	Derrida
Logicism-Frege	Psychologism-Mill
Popper	Kuhn
Einstein	Edison
Kant	Herder
Chomsky	Whorf
Richard Dawkins	Deepak Chopra
Carnap	Heidegger
Johnson	Berkeley

I'm sure you'll find if you explore the rows above that in some cases you already align/belong on the "other side".

Answer 8

Aim for sophisticated disagreement, not necessarily truth

I always wanted to read and I like reading in general, but I avoided reading many topics like history, philosophy, etc. because I think they are greatly influenced by opinions, beliefs, religion, etc. and I cannot be sure of their validity or accuracy.

As a teaser, I quote from David J. Chalmers's Why Isn’t There More Progress in Philosophy?:

Advocates of a view learn what extra commitments they need to take on to avoid the arguments. Bad versions of a view are rejected and sophisticated versions are developed in their place. This leads to a sort of negative progress where areas of philosophical space are eliminated, but only in small fragments at a time. It is rare for a major general view (materialism or dualism, compatibilism or incompatibilism, utilitarianism or deontology) to be eliminated in this way. Instead, there are large surviving fragments involving the views needed to avoid the arguments [...]. The same sort of elimination, fragmentation, and refinement often recurs at these lower levels. The views that survive yield a sort of fractal structure to philosophical space, akin to the Mandelbrot set with its intricate complexities at all levels, but in which large regions of space are rarely eliminated entirely.

So while it shows that philosophy is much influenced by opinion or "judgement calls", it's not that arguments are completely powerless. We get at least this sort of progress: sophisticated disagreement (as Chalmers calls it).

The idea that in every one of these topics there is an opinion and an opposite opinion, and to reach the truth I had to dig up in 10,000 books, made me hate to read any of them.

You very likely won't reach the truth in all philosophical questions that you tackle, except through some special grace or luck. What you aim for is sophisticated disagreement.

And for this you don't have to read 10,000 books. In theory, one good, non-opinionated introduction about a philosophical field suffices.

The mathematically educated can begin with philosophy of mathematics

Can you please recommend me some books or resources that can introduce me to philosophy in a clear and objective way? How can I overcome my fear of reading topics that are not purely factual or logical?

I guess I'd start with something from philosophy of mathematics, so one learns that not even in mathematics, everything is purely "logical", and there are "different schools" (e.g. intuitionism) and hidden, unexamined assumptions.

There's a bit of an odd book, Philosophical Perspectives on Infinity by Graham Oppy, in the sense that it is mostly philosophy of mathematics but also a bit philosophy of religion. So it bridges those areas of which one is supposed to be very rational and the other quite the opposite.

I'd start with that, in your special case, if you're interested in infinity at all. It should be easily accessible, with your mathematical background knowledge.

Plato

After that, one could read arguably the most important philosopher in the Western tradition, Plato. Maybe the dialogues Theaetetus and Meno (and read the SEP articles for them, they're good to check if you understood everything). Theaetetus is about knowledge, Meno more about mathematical knowledge, and an important Platonic doctrine, the "recollection" of innate knowledge.

René Descartes

I don't know if one should read René Descartes' Meditations soon after that, though in university education one usually begins with this work. Descartes' quest for absolute certainty and the highly questionable method he employs to get out of his radical skepticism had a discouraging effect on me. It reeked of futility. As a beginner, you're kind of left alone with his unnerving skeptical arguments, since you aren't in a position to refute them – they just feel very wrong. So it's easy to take away the message that philosophy is an idle, sophistical exercise.

Still, it's the foundational work of modern philosophy, and especially interesting since Descartes sent the manuscript to luminaries of his time, and published their objections and his replies to them.

So I guess, read the Meditations, but with the correspondence.

C. S. Peirce

Because of the sense of futility Descartes instilled in me, I really liked C. S. Peirce's critique of Cartesian philosophy in Questions Concerning Certain Faculties Claimed for Man and Some Consequences of Four Incapacities.

⚠️ But a warning: while I think they are understandable for a beginner, Peirce uses very few of Kant's technical terms (the "transcendental object"), so one has to look that up somewhere

Answer 9

Try to have fun and get a feeling for what is going on in the field. Philosophy has some intense formal areas (logic and so on), but large swaths of it can be very "light" (in a positive sense) compared to mathematics.

I'd suggest two media that are near and dear to my heart:

• The book Sophie's World by Jostein Gaarder. It is appropriate for teenagers, but in no way only a children's or young adult book. It is absolutely great for adults as a first introduction to philosophy. It uses a cheerful little story to embed introductions to many classical philosophers in somewhat of a dialogue structure, which is an old-time staple of antique philosophers.
• The podcast The Partially Examined Life, which is given by three trained philosophers and tackles its topics in a very informative, yet also entertaining (while not ludicrously so) manner. They actually give reading recommendations for every podcast session; that means that you can read something before listening (and the reading "homework" is usually publicly available on the 'net; and relatively short). It is still digestible for laymen but much deeper than Sophie's World.

For completeness sake: the standard reference for philosophic terms is the Stanford Encyclopedia of Philosophy. I find it not so entertaining to read, often, but sometimes philosophical terms have a very technical meaning where it makes sense to see what the "professionals" interpret into them.

In total: to get into philosophy, just start consuming it in whatever way you like. Whenever you pick up something that seems interesting to you, divert into that direction. While the two sources given above give you a structured approach, there is no drawback to just read what interests you and find your own journey.

Answer 10

Some days ago there was a similar question concerning a reading list for philosophy, see some answers at philosophy books.

I agree that books from mathematics are the least opinion based from all books. Mathematical books are structured as follows:

• Some motivation,

• then theorem or proposition,

• finally the proof.

Proofs in mathematical textbooks are free from opinions, they are just correct and rely on logic.

But apparently one should not restrict reading only mathematical books because of the only reason, that they are free from statements which rely on opinions.

The present platform deals with questions from philosophy. The platform is full of opinions from different viewpoints. Often these opinions do not agree.

The point of philosophy is to ask meaningful questions and to elaborate arguments for possible answers. That's a useful capability.

Answer 11

Humanity is always seeking for "THE" (factual) ANSWER, but fail to understand that this is not the goal.

Define this.. define that.. What do you think is "insert super generic term"?

So if you are too attached to the logical (like i was) i would recommend a book that is more in the "halfway" between racional and feeling.

Art of Love by Erich Fromm, talks about our "favorite" super generic term, love, and paints it as the last obtained basic necessity of the man.

When we think that reached the apex of reason, we crave to be part of something bigger.. and then.. we love

Answer 12

The reason philosophy isn't as easy to accept is because you don't have a starting point that you trust. A set of axioms, like math.

However, I advise you to start with some. The Biblical history is common for everyone except Aryans, Native Americans, and the derived races (which do indeed derive from different origins than most of us). The good news is that the Hebrew story of our history gives you power -- whether you're a woman or a man -- because it states that you're on a journey of knowledge. Further, it says you can become equal to GOD. Admittedly, the Devil said this to us, but the snake cannot speak on its own. These words must have been built from the Spirit side of GOD and cannot be false.

So, best to start where your ancestors did and continue the journey.