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Philosophy as Math-Like Thinking (jessylin.com)
70 points by gsjbjt 60 days ago | hide | past | web | favorite | 33 comments

"Philosophy is a way to address these questions more systematically -- it takes our fuzzy concepts and intuitions and makes them rigorous... In metaphysics, for example, when we talk about ontology, we try to formalize our natural intuitions for objects"

This is only true of certain types of philosophy -- analytic philosophy and its brethren in the 20th and 21st Centuries, and some systematic philosophers of earlier times.

Nietzsche is one of the most well-known counterexamples. Writing in an intuitive, aphoristic style, he was far from interested in any kind of systematization or formalism.

The playfulness of Derrida and the approaches of some other of the Postmodernists are also the antithesis of what this article claims philosophy is about.

The Pre-Socratics and Socrates himself were not interested in systematization or formalism either. Neither was most Eastern philosophy.

Philosophic interest in formalizing only rears its head in philosophy towards the end of the 19th Century with Frege and the logical-positivists (themselves ancestors to the Analytics) who followed him.

There's plenty of philosophy that just isn't interested in this.

On the other hand, if what the author is getting at is that philosophers tend to examine the questions and subjects that interest them in a deeper way than most other non-scientist do, then I would agree with that.

A lot of Platonic dialogues and Aristotle's works are pretty rigorous like analytic philosophy. Plato also has a mythical and literary element to his dialogues, but there is also logical rigor and careful distinction. Arguably, there is a reason for the literary setting of the logic in the dialogues, more than just 'make it readable.'

And if you want overboard rigor, look to the scholastics. Aquinas is nothing if not methodical. Duns Scotus gets inordinately detailed in his distinctions.

I would argue that rather than being typical, the Nietszche/Derrida/etc. continental sort of philosophy is just one half of the historical philosophy coin. The best philosophers have gone hand in hand with logical rigor and literary poise.

Derrida is a lot closer to literature than it is to philosophy, including Nietzsche. He’s a charlatan that uses cryptic language to make his writing seem serious and profound. Not unlike Jacques Lacan and Aleister Crowley.

Lacan is actually surprisingly rigorous or, at least, methodical. It's just, if you attempt to talk about what preconditions language and language like structures using language, you necessarily enter a metadiscourse. (Having read Lacan in philosophy was actually of help to me to come up with some algorithms as a programmer.)

If Lacan could be methodical (and I don't think he did), it would be much in the same way psychotics can be methodical.

> you necessarily enter a metadiscourse

It's quite possible for metadiscourse to be also intelligible. No reason to write like a lunatic.

I think, much of the reception of Lacan is specific to the language, language as in translation. E.g., mind that the early US reception is somewhat unfortunate due to the translation. On the other hand, the German edition tends to be a bit pompous, probably in order to establish the text in the context of the German academic discourse of the time. (Especially the Ecrits are about unreadable at times.) The Seminars, however, are, at least in the original, colloquial, slowly spoken, trying to find appropriate words for where there are none. And he's developing a methodology of his own, for sure. He even tried to express them conclusively in mathematical formulars and diagrams ("mathemes" – yes, we may have to put an emphasis on "tried"). If you have a look at Seminar II (Le moi dans la théorie de Freud et dans la technique de la psychoanalyse, 1954-1955), you even may observe that he entertained relationship with the cybernetic community, there are also traits of Rosenblut, contemporary mathematics… And, not to the least, some of Lacan's concepts seem to have shown up in FMRI findings of the last years.

Edit: If we entertain for a moment Marx's thought of history being the natural history of mankind, we may assume that this natural history sediments into technological artifacts, for short, technology, machines. If we also assume some value for the concept of the moi, we may conclude that we put some of a resemblance to our own into these machines. There's a mutual inheritance in the description. And machines, which are are also kind of sediments of algorithms or symbolic forms in their own, adhere – at least to some degree – to the same preconditions. (This, BTW, is a great way of looking at 2001, A Space Odyssey.) There's something to be learned from exploring either of them. However, we may have to find appropriate methodology for each of them, according to the specific scope. Since the venture of describing the preconditions of the human psyche equals the endeavor of describing a scope from within this very scope, we also encounter Boges' paradox of the map at 1:1 scale, which doesn't do for a description. What to do about it? Necessarily, we'd have to resort to some analogies, but, at the same time, we'd have to invalidate them, in order to not fall prey to ontology. What's left? Probably a system which is built more on resonance than on conclusive description, entertained by the mutual relations and suspense of the various concepts, which, at the same time, provides proper meaning to these concepts. Some sort of a bootstrapping process. We try to talk about meaning and its constraints by the very process of making meaning. Which, BTW, is totally conclusive with post-structuralist epistemology, as long it is internally conclusive. (Mind that this is for the most in the 1950s and 1960s, at the height of the linguistic turn. – And it's a generation of French academics who were, at least to some extent, formed by the confrontation with Hegel and Heidegger, and by the example of Lévi-Strauss.)

I've read different translations, I've have been part of a prestigious Lacanian psychoanalytic society that's a direct descendant of his original - physical - school in France. At its best Lacan's works is an interesting form of literature, at it's worse it's indistinguishable from pseudo-science and charlatanism. His followers are basically mystics and cultists.

If you read Aleister Crowley you will get to the same point: "this is so incomprehensible that it must have meaning. And after years of decyphering, there it is, actual meaning!".

Human beings are genetically formed to see patterns. If I generated a list of grammatically correct phrases combining random words, people would find meaning there too.

I'd say, if it makes sense as a system and you can make sense by it and in it, it must be a system, at least. If we may further make predictions, which prove to hold (compare the FMRI findings mentioned above), and/or add explanation to what was previously unexplained, there may be even some value to it. :-)

Supposing that a random word generator is a worthwhile source of valuable knowledge, and if you're willing to concede that Lacan is/was just as good as a random word generator, then YES, Lacanian psychoanalysis is a valuable epistemological framework.


> a random word generator is a worthwhile source of valuable knowledge

Is obviously valse!

I guess, we won't come to terms on this subject.

(I, on the other hand, do not understand, why certain economists are supposed to make any sense, just because their words are easily intelligible.)

P.S.: I should specify (previously supposing this was obvious from context), I'm distinctively talking about Lacan in terms of metapsychology and not as a psychoanalytical framework in the strict, therapeutical sense. Yes, here we may have to make a distinction. I'm not too sure, if I would prefer a Lacanian therapy. (Probably not.)

To me, Lacanian therapy was surprisingly good, not because of Lacanian psychoanalysis makes any sense, but because Lacanian circles attract some of the most intelligent psychotherapists.

Psychology, as a science, is a very practical, statistical, straightforward field. Research does require intellectual sophistication, but psychotherapy is largely the application of proven prophylactic you better not mess too much with.

Some of the smartest psychologists tend to flock to the set of references that most eludes them.

So Lacanian psychology may be a good choice because smart people give the best advice.

> He’s a charlatan that uses cryptic language to make his writing seem serious and profound.

A common criticism, to be sure; but not one with much evidence behind it. For instance, here's a good review of one of his better books, _The Politics of Friendship_: https://www.newyorker.com/books/second-read/what-jacques-der...

> It’s taken me years to read “The Politics of Friendship.” As I’ve inched my way through it, lines here and there have sent me to Derrida’s other writings, or have spurred my mind to chase random memories. I fix on the parts that sing, and I try to catch the gist of the parts that are too complicated for me. The book’s main appeal is the opportunity it provides to follow along as someone grapples with an ephemeral part of human experience. Doing so has come to feel more and more poignant as I have made my slow progress. At times, it seems as though Derrida is describing a bygone way of being, one racked with less anxiety about the bonds that tie us together. In an era of social media and fluid, proliferating channels of communication and exchange, the idea of friendship seems almost quaint, and possibly imperiled. In the face of abundant, tenuous connections, the instinct to sort people according to a more rigid logic than that of mere friendship seems greater than ever.

That doesn't sound like a charlatan. It sounds like a difficult author that few people have the patience or incentive to engage with -- like Heidegger or Wittgenstein, who somehow eschew the "charlatan" label while being much more technically demanding.

If your prose is obtuse enough in just the right way, you can come off as profound and let people read all kinds of things into your words that are not really there.

This is like saying ''if you use enough math symbols, you can come off as profound and let people think you are proving things which arent really proving". Which is of course ridiculous, just like your premise is.

I've noticed that lots of people, and especially those with a background in STEM, seem to have lots of difficulty with any works written for specialists in humanities disciplines, preferring to pretend like the writing is the problem, not their lack of reading skills (because being able to read and interpret and understand specialist works is a skill above being able to read words) and knowledge of the discipline. On the other hand, when people go ''i cant read this math book meant for grad students, this book is bad'', they go ''well yes, its because you lack the expected knowledge that the math builds on''. But they do expect to be able to pick up books written by philosophers for philosophers without having to understand everything the book is in dialogue with.

Just to give you some info: I have a mater's in literature and a bachelor's degree in film. I am well-versed in humanities and have a knack for it. I'm not even that good at math and technical stuff. Still think Derrida is a charlatan.

this still comes off as somewhat uninformed. just for comparison's sake i recommend trying to read Hegel, who is one of the more celebrated philosophers yet one regarded as one of the worst writers. one of the things that Hegel argues is that to understand a philosophy you must understand the philosophy that come before it meaning that individuals who commit to studying philosophy are better equipped to understanding.

you finding Derrida cryptic(which can describe much of the post modern french) is understandable, but calling him a charlatan makes little sense, you at that point would be calling much of the discipline a charlatan discipline. though in the contemporary his philosophies are frequently cited to be argued against, his concepts such as deconstruction of philosophy brought much to the table.

congratulations on your accolades but they don't really seem like rigorous studies to help you understand academic philosophy.

I appreciate your generosity, but my previous experience in humanities don't come even close to being "accolades.

You're entirely right in thinking I have no real academic credentials in philosophy. I just wanted to point out where I was coming from since most people on Hacker News have a STEM background and you might have been making that assumption about me.

So I thought this information might be relevant for your argument. It turns out it is not, which is totally fine.

> Nietzsche is one of the most well-known counterexamples. Writing in an intuitive, aphoristic style, he was far from interested in any kind of systematization or formalism.

I mostly agree with Lukacz account[0] that Nietzsche’s philosophy was actually a kind of knowing obfuscation of imperialist violence, dressed up in aphorism to make it all seem somehow heroic.

While he’s not of the analytic strain, his book “The Destruction of Reason” (from which the below is excerpted) is an excellent rebuttal of this kind of irrationalism in continental philosophy, from Nietzsche to Heidegger to Late Wittgenstein (all of which also informed Derrida).

[0] https://www.marxists.org/archive/lukacs/works/destruction-re...

> You learn to find an isomorphism between the concepts in your brain and someone else’s.

Coming from a math background myself, this is a really great way to relate philosophy to something I'm used to thinking about. So many times in conversations I've noticed that people talk about the same fundamental ideas but use different language and constructs to express them, and end up thinking (mistakenly) they disagree with each other.

I had similar thoughts after finishing an engineering ethics course. Everything is an argument. Strong arguments often demonstrate their superiority over alternatives. The more dimensions the problem context has (or, of course, the more alternatives), the more difficult this becomes. Luckily, arguments can usually be abstracted to ethical frameworks or philosophical traditions.

Sometimes these wrappers are easier to reason about. Sometimes, if the problem context is a foreign government's pending social credit system whose design and implementation is clouded by deceit and unknown consequences, all we can do is turn to Aristotle and ask, "[How] can we teach others to be good citizens?"


Don't take philosophy for the math-like thinking. Take math for that. Take it for the cool readings, discussions, and qt existentialist girls rarely found in compilers.

Philosophy is more than just cool readings. You have book clubs for cool readings. Philosophy is for learning critical thinking (just like math is, just both in different and complementary ways), evaluating arguments made by others, forming arguments on your own and thinking those arguments and their consequences through to the very end.

Take both math and philosophy, as both enrich your life and aren't interchangeable.

'Philosophy is like math's ne'er-do-well brother. It was born when Plato and Aristotle looked at the works of their predecessors and said in effect "why can't you be more like your brother?" Russell was still saying the same thing 2300 years later.' ~pg

Not sure it is. And I think the paper argue more about rigorous thinking and expressing it.

I've read a fair bit of philosophy, and I think the approach this post describes is often problematic.

They try to treat concepts as if they were like mathematical symbols that they can reason precisely with. The problem is when they don't understand the concepts involved well-enough to be able to treat them in this way. This is often the case, given that the subject-matter is in philosophy.

So you end up with a situation where it looks like they're drawing conclusions in a rigorous fashion, but where it's actually a kind of garbage-in-garbage-out situation.

Precision is really important. But you have to acknowledge the level of precision that your level of understanding affords. Trying to be more precise than that makes things worse.

It is the argument and the process that counts. The destination is never satisfactory. Like a tourist who enjoy the train (of thought) journey. Get out and and onto another.

There is no answer. Those have answer like Maths or Physics is not superior but just left. What remains are the hard part. And we left with only with signpost and past journeys.

Philosophy is post-thinking. Nothing like maths.

I’d be interested to hear book recommendations that discuss “fuzzy thinking” and how to avoid it.

Not entirely the point of the book, but I found that the first chapter of Gödel, Escher, Bach: An Eternal Golden Braid (which discusses formal systems, symbol manipulation and how that relates to thinking) was a catalyst for me to tighten up my thinking processes.

Hooray! This section of "Rationality: AI to Zombies" deals with exactly that:


I’ve read some po-mo stuff (like Baudrillard). Terms are constantly used without clear definitions, and rather than a logical progression of thoughts it’s a snaggle of metaphors. That kind of reading is very thought-provoking, but it’s the antithesis of math.

I feel the same way about reading math (without ever studying it).

What math are you reading? All of the math textbooks I’ve read, in university, begin each section with a precise definition and then proceed to examine the implications. Theorems begin with a precise statement of the hypotheses and conclusion before proceeding to the proof.

If you’re trying to read math on Wikipedia, without having studied it, you’re going to have a bad time. Wikipedia’s math pages are better used as a reference to remind you of what you already know and give you a jumping-off point for related topics. They are not meant to teach you math.

This person confuses philosophy with what anglosaxon barbarians consider philosophy...

Math is just a branch of philosophy which is not constrained by reality.

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