5 ms·

Philosophy as Math-Like Thinking

70 points by gsjbjt 7y ago

pmoriarty 7y ago
"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.
- yters 7y ago
  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.
- bananamerica 7y ago
  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.
  - masswerk 7y ago
    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.)
    - bananamerica 7y ago
      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.
      - masswerk 7y ago
        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.)
- claudeganon 7y ago
  > 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-reason/ch03.htm https://www.marxists.org/archive/lukacs/works/destruction-re...
stiglitz 7y ago
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.
- cam_l 7y ago
  I feel the same way about reading math (without ever studying it).
  - chongli 7y ago
    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.
zozbot234 7y ago
'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
- ngcc_hk 7y ago
  Not sure it is. And I think the paper argue more about rigorous thinking and expressing it.
jpster 7y ago
I’d be interested to hear book recommendations that discuss “fuzzy thinking” and how to avoid it.
- hliyan 7y ago
  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.
- justinpombrio 7y ago
  Hooray! This section of "Rationality: AI to Zombies" deals with exactly that: https://www.lesswrong.com/s/7gRSERQZbqTuLX5re https://www.lesswrong.com/s/7gRSERQZbqTuLX5re
mwlp 7y ago
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.
- FranzFerdiNaN 7y ago
  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.
derex 7y ago
> 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.
romwell 7y ago
Math is just a branch of philosophy which is not constrained by reality.
jamesrcole 7y ago
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.
ngcc_hk 7y ago
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.
coldtea 7y ago
This person confuses philosophy with what anglosaxon barbarians consider philosophy...

70 points by gsjbjt 7y ago

"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.

yters 7y ago
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.
bananamerica 7y ago
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.
- masswerk 7y ago
  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.)
  - bananamerica 7y ago
    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.
    - masswerk 7y ago
      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.)
claudeganon 7y ago
> 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-reason/ch03.htm https://www.marxists.org/archive/lukacs/works/destruction-re...

stiglitz 7y ago

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.

cam_l 7y ago
I feel the same way about reading math (without ever studying it).
- chongli 7y ago
  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.

zozbot234 7y ago

'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

ngcc_hk 7y ago
Not sure it is. And I think the paper argue more about rigorous thinking and expressing it.

jpster 7y ago

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

hliyan 7y ago
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.
justinpombrio 7y ago
Hooray! This section of "Rationality: AI to Zombies" deals with exactly that: https://www.lesswrong.com/s/7gRSERQZbqTuLX5re https://www.lesswrong.com/s/7gRSERQZbqTuLX5re

mwlp 7y ago

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.

FranzFerdiNaN 7y ago
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.

derex 7y ago

> 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.

romwell 7y ago

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

jamesrcole 7y ago

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.

ngcc_hk 7y ago

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.

coldtea 7y ago

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