Congrats on your new publication! I think mathematics is different from philosophy in the following ways:
1. The reality-correspondence of mathematics happens to be very high, in a pretty-hard-to-dispute way. Mathematics is a study of a subset of formal games. We can imagine living in a world where mathematics-as-studied doesn't have much correspondence with reality. (Fortunately) that's not the world we live in. Instead we live in a world where (primarily non-mathematicians) publish papers like "Unreasonable effectiveness of mathematics in the natural sciences" (https://www.maths.ed.ac.uk/~v1ranick/papers/wigner.pdf). By what some would consider strange and fortunate coincidence*, mathematics-as-understood-by-humans happen to describe the world we live in very well.
2. Mathematicians convince each other. Almost completely. There are some exceptions on the edges of math (C in ZFC or non-constructive proofs), but it's usually things that are considered minor to most laymen. You'll never have embarrassing situations like the difference between consequentialism and deontology (something that most laymen can easily grasp and understand is important) being hotly contested centuries later. Genuine mathematical progress is made much more regularly, and at much faster timescales, than philosophical progress.
* I have a slightly crankpotish and not very well-developed theory that the best explanation here is anthropics, incidentally.
But philosophy also has corresponds to reality in important ways. It tells us about the ultimate nature of reality and how we should live. Philosophers also convince each other--there are no logical positivsts these days. Mathematicians convince each other more, but that's mostly because philosophers only spend time considering the unresolved questions. Can you elaborate on the anthropics point?
>Mathematicians convince each other more, but that's mostly because philosophers only spend time considering the unresolved questions.
I'm sympathetic to the overall argument, but I don't think this is the only reason why there's a difference between philosophy and math.
Broadly, it's hard to find situations where mathematicians aren't marching in total lockstep. You might find some disagreement about whether a certain unproved theorem is true or false--but even then, they'll unanimously agree that the theorem hasn't been proven yet. Moreover, virtually every time somebody puts forward an attempted proof, the mathematicians will reply in unison, "No, the proof isn't valid" or "Yes, the proof is valid, this problem is now solved" and move on. And there's total agreement on a vast body of existing mathematical work--no mathematician thinks that group theory or differential geometry are wrong or deeply flawed.
In contrast, that sort of unanimity is rare in philosophy. Philosophers disagree all the time over whether moral realism or physicalism or some other claim has been decisively proven. When somebody puts forward an argument, philosophers don't usually agree on whether the argument is valid--they sometimes do, but it's pretty rare. You get 100% lockstep agreement in a handful of situations, yes, but the extent of the difference is huge: You can get a Master's in math by only learning concepts that every mathematician agrees on, but if you tried the same in philosophy, you'd have a hard time making it through a single course!
I won't speculate about what causes this difference, but there *is* a difference that can't be explained by choice of focus, and I think it's a large part of why the fields are perceived differently.
Re: anthropics, I think observers, especially of the level of sophistication necessary to ask questions about the unreasonable effectiveness of mathematics, are much more likely to exist in mathematically simple worlds. Life (if it's even possible to form life) in sufficiently complex/chaotic worlds will not get a sufficiently smooth gradient for complex intelligence for there to be a sufficiently large premium for intelligence/consciousness.
> Mathematicians convince each other more, but that's mostly because philosophers only spend time considering the unresolved questions.
That's true of maths too :)
Maths is just very trendy, because STEM, and oh, and woah, sometimes it's useful. And it's relatively easy to desenzitivize mathematicians to almost all of their math-related preconceptions. (But of course, if you get a lot of math constructivists/finitists and ask them to what they think of proofs involving transfinite induction .. they might have some objections. Or maybe not. No one ever saw an extant constructivist :D Okay, maybe bad example.)
But in philosophy it seems people are a lot more motivated in certain set ways, folks like their own theories and models, and spend most of their time on trying to come up with arguments that revolve around those.
Probably math is more strictly connected. Simpler. (Likely because it's more structured, so its legibility - or lack thereof - is more evident.) Less opportunity for inserting unseen complexity. Philosophy relatively is less mature in tool use. (Or at least it seems that there are a bunch of disconnected questions, and ... most of them are not well modeled. Most of it lives in just a few people's head. Language is not very efficient to let other people get "up to speed", etc.)
... and again, fanciness. How come whatever abstract shit Grothendieck come up with was noteworthy? (Many math papers are about considering some totally new problem in some abstract space. How come other math people even read it?) How come the saga of the `abc conjecture` became big news on mainstream news, even though what seems to have happened is that someone produced hundreds of pages of gibberish? Is it because there are a lot more mathematicians and math-adjacent people? Is it because somehow "progress" in math is just the "default mindset"?
Philosophy could be sexy too. After all it has the best open problems ... impossible ones!
>Philosophers also convince each other--there are no logical positivsts these days.
Or, it could be that logical positivism functions as a "scissor" theory. Those who think it's obviously wrong will continue to do philosophy. Those who are more favorable to logical positivism will develop a negative attitude towards philosophy and self-select out of the field into other domains of discourse. Nobody will be left defending it because everybody favorable to it already left, and everybody else disagrees with it so there's not much to talk about. The people who disagree with logical positivism might even say that they successfully "convinced" each other that it is wrong, due to an insensitivity to the empirical sociological factors that influence their nonempirical field.
The NSA has many mathematicians on staff! So does Google, State Farm, JP Morgan Chase etc.. But they don't have any philosophers on staff. I wonder why?
...
(Actually, hot take, all these places do have philosophers on staff. We just call them lawyers.)
I feel like much of the way philosophy advances is *via* deference. People who have "sophisticated" arguments, or sounding smart etc. Whereas mathematics is much more about having proofs that in theory anybody can follow along (smarter people just follow them faster).
In practice, mathematicians defer too, but only in much more hyperspecialized and specific subfields (eg topologists might defer to number theorists in areas not covered in a first- or second- year grad course, and vice versa). But philosophers end up needing to defer at much earlier levels (eg SIA vs SSA, or even consequentialism vs deontology) for any "progress" to be made in advancing the field.
I think mathematicians probably defer less, but that's because in math there's less disagreement--mostly for the reason I described in response to your last comment .
I will use your comment to shamelessly signal that much like the average layperson knows nothing about consciousness, so too is the average philosopher of mind mostly clueless about what methods work in studying consciousness. A priori conceptual gap arguments like p zombies don't prove anything interesting, let alone metaphysical about human cognition, and illusionism is an existing position in philosophy of mind that entirely dissolves bankrupt approaches like dualism that don't contribute anything to understanding the mind, besides entangling its practitioners in silly knots.
On first read, this post feels like utter nonsense. The reason that people venerate complicated math is because people using that math are able to vaporize cities and travel to the moon.
If your arguments from psychophysical harmony could summon angels, then they would be obvious.
Is there any other field which makes predictions that are *absolutely* untestable? Maybe the social sciences, but they aren’t highly regarded either.
Most of math is untestable! So is most of history! So is most of biology! I wasn't suggesting that math and philosophy were equally valuable, just that they were both mysterious and hard to make sense of if one is an outsider.
What are you talking about? Most of math is obviously testable! Can you name one kind of math that is not testable? (One which a layperson would, as you argue, hold in a higher regard than philosophy).
I believe this for two big reasons
1. People who use very complicated math can make cities vanish in balls of radioactive fire.
2. I am not aware of any substantial debate that happens in the mathematical community whenever a result is published. Either the proof is valid, or a logical mistake is found fairly quickly and everyone agrees that a proof is invalid. Now I don’t claim to be any sort of expert on the field, but this is my impression from reading a few dozen articles on various mathematical proofs, including some seemingly useless and very complicated proofs on Tao’s blog.
“History” being untestable is patently false. You can visit the concentration camps and check the work of translators. Can you name one part of history that is not testable but held in more regard than philosophy?
If what you mean by testable is they say things that people can think about and conclude are true, well of course they're all testable. So is philosophy. But there's no experimental verification of mathematical claims. Of course, with philosophy you're more easily able to just flat out reject the other guy's assumptions, but the same is true of history. Some arguments in history, like for the holocaust, are knock-down, others are not.
Bulldog. There is experimental verification of mathematical claims. It happens when the atomic bomb vaporizes a city.
I am flabbergasted at how you have continuously managed to ignore this point. What am I missing?
Edit: This quote from Orwell is decisive:
> In philosophy, or religion, or ethics, or politics, two and two might make five, but when one was designing a gun or an aeroplane they had to make four. Inefficient nations were always conquered sooner or later, and the struggle for efficiency was inimical to illusions. Moreover, to be efficient it was necessary to be able to learn from the past, which meant having a fairly accurate idea of what had happened in the past.
Sometimes math has results that are applicable and those results are experimentally verified. Other times--as in, for instance, some kinds of higher level math, topology would be a good example--there aren't anything resembling empirical verifications.
It seems like you're now admitting that the overwhelming majority of math is applicable, save for a few very in the weeds categories in pure math.
I will note, based on 45 seconds of google searching, that Topology seems to have plenty of real-world applications:
> Roughly, if you have a data set representing, say, a fingerprint, and you want to recognize it, then you'd associate some numbers ("presistent betti numbers") to it as follows: If 𝑋 is a collection of data points on ℝ2, let 𝑋𝛿 denote a 𝛿-thickening of 𝑋, i.e., union of neighborhoods of radius 𝛿 of the points in 𝑋⊂ℝ2
If you vary 𝛿, the topology of 𝑋𝛿 will change, but if you vary 𝛿 at a certain speed, you can look how much time it takes for 𝑋𝛿 to change it's topology. For example, you could look at the betti numbers of 𝑋𝛿 and see how long they stay the same. Among the betti numbers 𝑏𝑛 of 𝑋𝛿 the one which stays same the longest amount of time is called the persistent betti number. For example, if our data set is a bunch of point cluttered around the unit circle, 𝑏1=1 would stay for a long time. This "persistance" data lets you identify different data sets.
I will freely admit that I do not understand most of this. What I do understand is are two sentences wheer the author says that this is actually used to identify fingerprints, and also that it has broader applications to analyze data sets.
That is a real-world application, and one that yields experimentally vertfiable results!
I agree that once you get to the level of axioms and never-observed infinities, math is much closer to philosophy.
I guess this is just not what I think of when I hear “math”. I tend to think of all the ways in which much more concrete applications of the subject are used in every day life. The overwhelming majority of actually done math does not involve counting angels dancing on a pinhead (isn’t the answer obviously 7?).
I don’t think philosophy in the sense that Bulldog uses it here is used in daily life or in important industries at all.
If a certain kind of math is "untestable" - i.e. that it has no relationship to reality - then this is signposted somehow. "Assume A, B, and C are true, then..." is both obviously fair enough and obviously unlike philosophers. Philosophers don't say, "assuming that consciousness is not an emergent property of matter, then..." They say "consciousness must not be an emergent property of matter, because..."
1. On every important philosophical topic, philosophers disagree, producing a multitude of differing and mutually contradictory views
2. Most or all of these mutually contradictory views must be incorrect
3. All of these mutually contradictory views are supported by sophisticated philosophical arguments produced by extremely smart philosophers.
4. Therefore, the existence of a sophisticated argument by an extremely smart philosopher purporting to establish some conclusion is not a good reason to accept said conclusion
Disagree https://www.philosophyetc.net/2012/10/unreliable-philosophy.html. The empirical premise is just wrong--nearly all philosophers now reject logical positivism, for instance. I also think that you can, with sufficient carefulness, beat the crowds. Most people are wrong about politics but that doesn't mean I'm wrong about it.
- The regret rate on deference to mathematicians is effectively zero. Mathematicians will defer to arbitrary mathematicians (and in fact lay people will defer to arbitrary mathematicians) with a regret rate that is essentially zero. They believe that if they picked a mathematician out of a hat, who produced a claim that they did not understand, and then sat down with them for a few years of lectures they would come away convinced that they were right. This is not true of philosophers.
- Insofar as mathematicians agree a lot because they deal with the known and philosophers the unknown, the overwhelming majority of mathematical questions that lay people (and mathematicians) encounter are fully known, whereas the overwhelming majority of philosophical questions that lay people (and philosophers) encounter are in the realm of the unknown, which leads them to trust mathematicians more as a class.
- Semi-related to the above, the vast majority of mathematics that a lay person encounters is "falsifiable" via experience. If many of these claims were false, we wouldn't have atom bombs and so on. Mathematics becomes untestable in theory at the far reaches of academic mathematics where few dare to venture. However, in 100% of places where the lay person encounters mathematics, they can confirm it works with 100% accuracy. This is not true of lay encounters with philosophy. If all philosophers at every level were just making stuff up the average lay person would see very little change in their lives.
- Mathematics has, to most lay people's knowledge, never encountered revolutions where previously established facts were overturned.* The mathematicians of 1600 were just as correct as the mathematicians of today. A lay person, seeing previous ideas repeatedly overturned, may conclude that the entire field is whatever happens to be fashionable at the time. * Sure, questions like "can you take the square root of negative one" was updated at some point - just add "in R" to all the previous claims - but in general mathematical updates are much kinder to previous theories than in other fields.
Lay people place a lot of trust in the falsifiability of science, either by actual experiment or by observational checks, neither of which most philosophical arguments are conducive to. Science outruns experiment when we cannot run actual experiments due to constraints on time or scale (we cannot go back millions of years in time to look at dinosaurs, or watch a universe evolve in a bottle for billions of years, or generate a particle with a quadrillion electron-volts in a lab). In this case scientists attempt to generate "observationally falsifiable" theories about past events: for example, if one theorizes an asteroid ended the Permian era, we can go looking for a huge hole in the ground or a layer of asteroid dust in geological rock layers. Historical theories make predictions as well, though with much less precision. If we don't find one, that's evidence against the theory. Even for physics theories we cannot observe scientists try mightily to find downstream predictions about how a theory of supersymmetry, not directly testable, might imply that a particle being smashed in a lab might have certain properties.
In the far reaches of cosmology or quantum gravity where no experiment is even slightly feasible, physics does indeed become effectively unfalsifiable by experiment or observation. In these cases physicists steal most of their credibility from math: the mathematics is nicer if the universe works this way; this approach tends to work where we can observe it and so we (philosophically) infer that it probably works that way where we can't observe it as well. But it also so happens that when you reach these far fields, physics becomes open to the "what if they're just making all that shit up" criticism which does in fact get leveled by lay people and contrarian physicists alike.
Philosophy in most cases, relies on thought experiments that are not amenable to experiment or even observational verification, which lay people place a great deal of trust in when choosing what theories to believe.
>One who was not well-versed in mathematics would be skeptical of the existence of successful mathematical arguments. Mathematicians couldn’t convince lay people of controversial mathematical conclusions if they had to argue for them step-by-step—the only reason they can do so is that mathematicians are treated as experts worth deferring to.
There is a catch. Advances in highest-order mathematics have demonstrably led to the creation of a computer, a nuclear bomb, space travel and other mind-blowing things. Proposition in highest-order philosophy... well, it's not even obvious if much positive philosophical progress has occurred in the last couple of centuries, whether what we have counts as "advances". No matter how clever a philosophical argument is, another philosopher will probably not bite it. This doesn't really happen in mathematics too often.
Most of technical, counter-intuitive and jargon-laden writing is incredibly boring to most people, but at least mathematics has something to show for it.
Re: footnote 1. Which paper makes you say that Lewis was a moral anti-realist? I've read all his papers that have been collected into volumes, and I don't recall anything that would make me apply that meta-ethical position to him.
Do you take the same attitude to continental philosophy? While I think analytic philosophy is a bad field, I think continental philosophy is worse in pretty much every way. Phenomenology, panoptican, semiotics, existentialism... I consider these all practically explicitly obscurantist topics that are meant to create an illusion of understanding when there isn't much substance to anything that gets written about in these fields. To the extent that you agree with my dismissal of continental philosophy, why not be skeptical of analytic philosophy in the same way? I remember the joke post about hating Camus that I think should bias you towards skepticism.
>doing so requires understanding something about philosophy of mind
That's a rather euphemistic way of saying "requires believing in dualism".
>I’ve discussed the zombie argument against physicalism with tons of philosophically ignorant lay people. Almost none of them buy it (interestingly, they are more moved by Mary’s room).
The difference is that mathematicians have a method for proving things that leads to convergence, which philosophers don’t seem to have.
And anyone who has taken high school level geometry knows what proving something mathematically means at a basic level. So I don’t know why you think people don’t have the faintest idea of mathematical reasoning.
Mysteriousness is not an inherent property of some fields or arguments. it's a property of a mind in correspondance to something that this mind does not properly understand. One of the advantage of studying math in university is that you experience how math that initially appears to be mysterious, complex and opaque is actually simple to the point of self evidence. I don't think that philosophers of consciousness can say the same about their titular subject.
Celebration of mystery is celebration of your own ignorance. And I feel that you are doing a fair share of it in this post: Mathematics is mysterious and repected; philosophy is also similarly mysterious, therefore we should respect it on par with mathematics. This is a poor way to reason about anything. Stuff can be confusing simply because it's flowerly nonsense without any substance. And, sadly, lots of conventional philosophy is like that.
As a person who has been in love with philosophy since my teens, I understand that it's a hard thing to swallow. It felt so good to be able to derive the same answers to open philosophical problems that some acclaimed philosophers had done. Abandonning the idea that I was doing some actually impressive cognitive labor felt painful, as if I was justifying all the people who failed even to engage with the argument properly. But one has to grow up eventually. If lots of philosophy is nonsense I want to believe that lots of philosophy is nonsense. I won't hold to beliefs I do not want.
> Imagine that mathematics was not a well-developed discipline but instead, we argued about math the way we argue about philosophy. There would be no rigorous framework or assumption that some people are experts—instead, people would just try to beat each other over the head with arguments.
In that case treating math with as much respect as we are treating philosophy now would be justified. WIthout a rigorous framework it's unclear who is right and who is wrong, no way to separate valuable knowledge from useless falsehoods, therefore no optimization process for truth and therefore no value in expertise beside hollow appeal to authority.
The correct question to ask is why math and natural sciences are formalized and therefore respected while philosophy is not so much. There are several good reasons for it. One of the most prominent is that as soon as some kind of formalization or falsification becomes possible for some philosophical domain, it stops being philosophy and joins the realms of science. Therefore, we have an evaporation dynamics, where the best philosophical ideas are not credited to philosophy anymore, and when people say "philosophy" they mean all the rest - poorly falsifiable and non-formalized semantic games, appealing to intuitions.
There is also an opposite evaporation where people who are very much philosophers in everything but name, who do important work progressing our understanding of philosophical questions refuse to participate in the conventional institution of philosophy, refuse to embrace the title of philosopher, and prefer to associate with more respectful disciplines instead. While people who are ready to embrace the identity of a philosopher are selected for accepting the usual philosophical arguments whether they are crazy or not. And therefore knowing that the majority of philosophers support some kind of position on some question becomes very much not a useful signal about whether this position is true or even whether the questuin itself even makes sense. And of course if you disagree with just one particular philosopher its not a signal at all - with all likelihood there is another philosopher with whom this philosopher disagrees about this exact question.
Some philosophy, notably analytical , is formalised.
Formalization is a insufficient to prove correctness -- particularly soundeness. A formal argument can be checked for validity , but still depends on the soundness of its premises.
Philosophy is unique in being a)fairly intimidating and abstract (unlike the rest of the humanities) and b) relatively unemployable (unlike STEM).
People have limited bandwidth for abstract intellectual topics, and even smart, abstract-thinking people can’t be expected to patiently wait for philosophical ideas to click when they need to spend their brain power on getting a job. Philosophy’s PR problems seem kind of complicated, and maybe some of the problems are intrinsic to the discipline itself, but I can’t help thinking they would mostly go away if there was some way to pipeline Phil majors into 6 figure professions.
Nice job on the Synthese article. I disagree with it in a number of places, simplest of which is that you sometimes say "all alternatives to SIA have feature X" when you really just mean "SSA has feature X." Most relevantly, you seem to think all non-SIA views imply strong evidence for some sort of doomsday scenario. But there's a large family of SSA-like anthropic principles on which it's at best very weak evidence, and the evidence doesn't get arbitrarily strong as the "large" world possibility gets larger and larger in terms of the number of people therein.
No, I meant all alternatives to SIA have feature X. If one is a Bayesian and finds out that they're early, because being early is more strongly predicted on theories according to which there are fewer people, they get a big update against big worlds.
They may get an update against big worlds (like SSA does), but not all variants of SSA imply a big update. Some imply a tiny update, whose magnitude doesn't depend much on the number of people involved.
They all apply a big update if you have a uniform prior across the people you might be prior to confirming your identity. Suppose I'm considering between two hypotheses: first that there are 10 million people and second that there are 100 quadrillion people. I discover I'm in the first 10 million people. Well then I'll get evidence the odds of which is 10 billion times as strongly predicted on the first hypothesis. Therefore, if the only way for humanity to be destroyed before having 100 quadrillion people is for me to get a royal flush in poker, I can be super confident that I will get a royal flush.
>They all apply a big update if you have a uniform prior across the people you might be prior to confirming your identity.
I'm confused. SSA, and variants of SSA, definitionally don't use uniform priors across all people you might be. They may involve uniform priors among people *within* concrete possible ways the world could be, but not among people across such ways. Moreover, there are variants of SSA which uphold this within-concrete-world uniformity and which don't automatically imply strong updates to small worlds (only weak updates).
SSA is perfectly consistent with having a uniform prior across the people you might currently be. For instance, suppose that there are 3 people created but I know nothing about them. SSA is consistent with having a credence of 1/3 in being each of them!
Suppose God flips a coin; if it's heads, he creates one person, and if it's tails, he creates two people. SSA is indifferent between the two people in the tails world (this is what I mean by uniformity within a concrete possible world), but it weighs the one guy in the heads world twice as highly as any of the individual people in the tails world. So it's not uniform among people *across* possibilities.
(To be clear, "concrete possibility" here means worlds where the values of all random variables in play have been completely fixed. In my above example, it would be the outcome of the coin toss.)
Congrats on your new publication! I think mathematics is different from philosophy in the following ways:
1. The reality-correspondence of mathematics happens to be very high, in a pretty-hard-to-dispute way. Mathematics is a study of a subset of formal games. We can imagine living in a world where mathematics-as-studied doesn't have much correspondence with reality. (Fortunately) that's not the world we live in. Instead we live in a world where (primarily non-mathematicians) publish papers like "Unreasonable effectiveness of mathematics in the natural sciences" (https://www.maths.ed.ac.uk/~v1ranick/papers/wigner.pdf). By what some would consider strange and fortunate coincidence*, mathematics-as-understood-by-humans happen to describe the world we live in very well.
2. Mathematicians convince each other. Almost completely. There are some exceptions on the edges of math (C in ZFC or non-constructive proofs), but it's usually things that are considered minor to most laymen. You'll never have embarrassing situations like the difference between consequentialism and deontology (something that most laymen can easily grasp and understand is important) being hotly contested centuries later. Genuine mathematical progress is made much more regularly, and at much faster timescales, than philosophical progress.
* I have a slightly crankpotish and not very well-developed theory that the best explanation here is anthropics, incidentally.
But philosophy also has corresponds to reality in important ways. It tells us about the ultimate nature of reality and how we should live. Philosophers also convince each other--there are no logical positivsts these days. Mathematicians convince each other more, but that's mostly because philosophers only spend time considering the unresolved questions. Can you elaborate on the anthropics point?
>Mathematicians convince each other more, but that's mostly because philosophers only spend time considering the unresolved questions.
I'm sympathetic to the overall argument, but I don't think this is the only reason why there's a difference between philosophy and math.
Broadly, it's hard to find situations where mathematicians aren't marching in total lockstep. You might find some disagreement about whether a certain unproved theorem is true or false--but even then, they'll unanimously agree that the theorem hasn't been proven yet. Moreover, virtually every time somebody puts forward an attempted proof, the mathematicians will reply in unison, "No, the proof isn't valid" or "Yes, the proof is valid, this problem is now solved" and move on. And there's total agreement on a vast body of existing mathematical work--no mathematician thinks that group theory or differential geometry are wrong or deeply flawed.
In contrast, that sort of unanimity is rare in philosophy. Philosophers disagree all the time over whether moral realism or physicalism or some other claim has been decisively proven. When somebody puts forward an argument, philosophers don't usually agree on whether the argument is valid--they sometimes do, but it's pretty rare. You get 100% lockstep agreement in a handful of situations, yes, but the extent of the difference is huge: You can get a Master's in math by only learning concepts that every mathematician agrees on, but if you tried the same in philosophy, you'd have a hard time making it through a single course!
I won't speculate about what causes this difference, but there *is* a difference that can't be explained by choice of focus, and I think it's a large part of why the fields are perceived differently.
Re: anthropics, I think observers, especially of the level of sophistication necessary to ask questions about the unreasonable effectiveness of mathematics, are much more likely to exist in mathematically simple worlds. Life (if it's even possible to form life) in sufficiently complex/chaotic worlds will not get a sufficiently smooth gradient for complex intelligence for there to be a sufficiently large premium for intelligence/consciousness.
> Mathematicians convince each other more, but that's mostly because philosophers only spend time considering the unresolved questions.
That's true of maths too :)
Maths is just very trendy, because STEM, and oh, and woah, sometimes it's useful. And it's relatively easy to desenzitivize mathematicians to almost all of their math-related preconceptions. (But of course, if you get a lot of math constructivists/finitists and ask them to what they think of proofs involving transfinite induction .. they might have some objections. Or maybe not. No one ever saw an extant constructivist :D Okay, maybe bad example.)
But in philosophy it seems people are a lot more motivated in certain set ways, folks like their own theories and models, and spend most of their time on trying to come up with arguments that revolve around those.
Probably math is more strictly connected. Simpler. (Likely because it's more structured, so its legibility - or lack thereof - is more evident.) Less opportunity for inserting unseen complexity. Philosophy relatively is less mature in tool use. (Or at least it seems that there are a bunch of disconnected questions, and ... most of them are not well modeled. Most of it lives in just a few people's head. Language is not very efficient to let other people get "up to speed", etc.)
... and again, fanciness. How come whatever abstract shit Grothendieck come up with was noteworthy? (Many math papers are about considering some totally new problem in some abstract space. How come other math people even read it?) How come the saga of the `abc conjecture` became big news on mainstream news, even though what seems to have happened is that someone produced hundreds of pages of gibberish? Is it because there are a lot more mathematicians and math-adjacent people? Is it because somehow "progress" in math is just the "default mindset"?
Philosophy could be sexy too. After all it has the best open problems ... impossible ones!
>Philosophers also convince each other--there are no logical positivsts these days.
Or, it could be that logical positivism functions as a "scissor" theory. Those who think it's obviously wrong will continue to do philosophy. Those who are more favorable to logical positivism will develop a negative attitude towards philosophy and self-select out of the field into other domains of discourse. Nobody will be left defending it because everybody favorable to it already left, and everybody else disagrees with it so there's not much to talk about. The people who disagree with logical positivism might even say that they successfully "convinced" each other that it is wrong, due to an insensitivity to the empirical sociological factors that influence their nonempirical field.
If one philosophy is right about those things, the others must be wrong....
The NSA has many mathematicians on staff! So does Google, State Farm, JP Morgan Chase etc.. But they don't have any philosophers on staff. I wonder why?
...
(Actually, hot take, all these places do have philosophers on staff. We just call them lawyers.)
Mathematicians also spend their time considering unresolved questions! But then they resolve them.
I feel like much of the way philosophy advances is *via* deference. People who have "sophisticated" arguments, or sounding smart etc. Whereas mathematics is much more about having proofs that in theory anybody can follow along (smarter people just follow them faster).
In practice, mathematicians defer too, but only in much more hyperspecialized and specific subfields (eg topologists might defer to number theorists in areas not covered in a first- or second- year grad course, and vice versa). But philosophers end up needing to defer at much earlier levels (eg SIA vs SSA, or even consequentialism vs deontology) for any "progress" to be made in advancing the field.
I think mathematicians probably defer less, but that's because in math there's less disagreement--mostly for the reason I described in response to your last comment .
>The reality-correspondence of mathematics happens to be very high, in a pretty-hard-to-dispute way.
It's obviously extremely low. If the inverse square law is correct, then the inverse cube, quartic, etc, ad infinitum, literally, laws are wrong.
But the reality correspondence of maths is much easier to establish.
Really felt the Goff comment. You host Sean Carroll once and your comment section becomes a hellscape of illiterate materialists.
I will use your comment to shamelessly signal that much like the average layperson knows nothing about consciousness, so too is the average philosopher of mind mostly clueless about what methods work in studying consciousness. A priori conceptual gap arguments like p zombies don't prove anything interesting, let alone metaphysical about human cognition, and illusionism is an existing position in philosophy of mind that entirely dissolves bankrupt approaches like dualism that don't contribute anything to understanding the mind, besides entangling its practitioners in silly knots.
Great piece! 👏
On first read, this post feels like utter nonsense. The reason that people venerate complicated math is because people using that math are able to vaporize cities and travel to the moon.
If your arguments from psychophysical harmony could summon angels, then they would be obvious.
Is there any other field which makes predictions that are *absolutely* untestable? Maybe the social sciences, but they aren’t highly regarded either.
Most of math is untestable! So is most of history! So is most of biology! I wasn't suggesting that math and philosophy were equally valuable, just that they were both mysterious and hard to make sense of if one is an outsider.
What are you talking about? Most of math is obviously testable! Can you name one kind of math that is not testable? (One which a layperson would, as you argue, hold in a higher regard than philosophy).
I believe this for two big reasons
1. People who use very complicated math can make cities vanish in balls of radioactive fire.
2. I am not aware of any substantial debate that happens in the mathematical community whenever a result is published. Either the proof is valid, or a logical mistake is found fairly quickly and everyone agrees that a proof is invalid. Now I don’t claim to be any sort of expert on the field, but this is my impression from reading a few dozen articles on various mathematical proofs, including some seemingly useless and very complicated proofs on Tao’s blog.
“History” being untestable is patently false. You can visit the concentration camps and check the work of translators. Can you name one part of history that is not testable but held in more regard than philosophy?
Biology is testable. See vaccines.
If what you mean by testable is they say things that people can think about and conclude are true, well of course they're all testable. So is philosophy. But there's no experimental verification of mathematical claims. Of course, with philosophy you're more easily able to just flat out reject the other guy's assumptions, but the same is true of history. Some arguments in history, like for the holocaust, are knock-down, others are not.
Bulldog. There is experimental verification of mathematical claims. It happens when the atomic bomb vaporizes a city.
I am flabbergasted at how you have continuously managed to ignore this point. What am I missing?
Edit: This quote from Orwell is decisive:
> In philosophy, or religion, or ethics, or politics, two and two might make five, but when one was designing a gun or an aeroplane they had to make four. Inefficient nations were always conquered sooner or later, and the struggle for efficiency was inimical to illusions. Moreover, to be efficient it was necessary to be able to learn from the past, which meant having a fairly accurate idea of what had happened in the past.
Sometimes math has results that are applicable and those results are experimentally verified. Other times--as in, for instance, some kinds of higher level math, topology would be a good example--there aren't anything resembling empirical verifications.
It seems like you're now admitting that the overwhelming majority of math is applicable, save for a few very in the weeds categories in pure math.
I will note, based on 45 seconds of google searching, that Topology seems to have plenty of real-world applications:
> Roughly, if you have a data set representing, say, a fingerprint, and you want to recognize it, then you'd associate some numbers ("presistent betti numbers") to it as follows: If 𝑋 is a collection of data points on ℝ2, let 𝑋𝛿 denote a 𝛿-thickening of 𝑋, i.e., union of neighborhoods of radius 𝛿 of the points in 𝑋⊂ℝ2
If you vary 𝛿, the topology of 𝑋𝛿 will change, but if you vary 𝛿 at a certain speed, you can look how much time it takes for 𝑋𝛿 to change it's topology. For example, you could look at the betti numbers of 𝑋𝛿 and see how long they stay the same. Among the betti numbers 𝑏𝑛 of 𝑋𝛿 the one which stays same the longest amount of time is called the persistent betti number. For example, if our data set is a bunch of point cluttered around the unit circle, 𝑏1=1 would stay for a long time. This "persistance" data lets you identify different data sets.
I will freely admit that I do not understand most of this. What I do understand is are two sentences wheer the author says that this is actually used to identify fingerprints, and also that it has broader applications to analyze data sets.
That is a real-world application, and one that yields experimentally vertfiable results!
Source: https://math.stackexchange.com/questions/1616770/why-do-we-need-topology-and-what-are-examples-of-real-life-applications
It's a stackexchange post, but there seem to be many similiar posts of roughly the same substance.
Are you using testable to mean empirically testable.
I agree that once you get to the level of axioms and never-observed infinities, math is much closer to philosophy.
I guess this is just not what I think of when I hear “math”. I tend to think of all the ways in which much more concrete applications of the subject are used in every day life. The overwhelming majority of actually done math does not involve counting angels dancing on a pinhead (isn’t the answer obviously 7?).
I don’t think philosophy in the sense that Bulldog uses it here is used in daily life or in important industries at all.
If a certain kind of math is "untestable" - i.e. that it has no relationship to reality - then this is signposted somehow. "Assume A, B, and C are true, then..." is both obviously fair enough and obviously unlike philosophers. Philosophers don't say, "assuming that consciousness is not an emergent property of matter, then..." They say "consciousness must not be an emergent property of matter, because..."
1. On every important philosophical topic, philosophers disagree, producing a multitude of differing and mutually contradictory views
2. Most or all of these mutually contradictory views must be incorrect
3. All of these mutually contradictory views are supported by sophisticated philosophical arguments produced by extremely smart philosophers.
4. Therefore, the existence of a sophisticated argument by an extremely smart philosopher purporting to establish some conclusion is not a good reason to accept said conclusion
Disagree https://www.philosophyetc.net/2012/10/unreliable-philosophy.html. The empirical premise is just wrong--nearly all philosophers now reject logical positivism, for instance. I also think that you can, with sufficient carefulness, beat the crowds. Most people are wrong about politics but that doesn't mean I'm wrong about it.
Why people trust mathematicians:
- The regret rate on deference to mathematicians is effectively zero. Mathematicians will defer to arbitrary mathematicians (and in fact lay people will defer to arbitrary mathematicians) with a regret rate that is essentially zero. They believe that if they picked a mathematician out of a hat, who produced a claim that they did not understand, and then sat down with them for a few years of lectures they would come away convinced that they were right. This is not true of philosophers.
- Insofar as mathematicians agree a lot because they deal with the known and philosophers the unknown, the overwhelming majority of mathematical questions that lay people (and mathematicians) encounter are fully known, whereas the overwhelming majority of philosophical questions that lay people (and philosophers) encounter are in the realm of the unknown, which leads them to trust mathematicians more as a class.
- Semi-related to the above, the vast majority of mathematics that a lay person encounters is "falsifiable" via experience. If many of these claims were false, we wouldn't have atom bombs and so on. Mathematics becomes untestable in theory at the far reaches of academic mathematics where few dare to venture. However, in 100% of places where the lay person encounters mathematics, they can confirm it works with 100% accuracy. This is not true of lay encounters with philosophy. If all philosophers at every level were just making stuff up the average lay person would see very little change in their lives.
- Mathematics has, to most lay people's knowledge, never encountered revolutions where previously established facts were overturned.* The mathematicians of 1600 were just as correct as the mathematicians of today. A lay person, seeing previous ideas repeatedly overturned, may conclude that the entire field is whatever happens to be fashionable at the time. * Sure, questions like "can you take the square root of negative one" was updated at some point - just add "in R" to all the previous claims - but in general mathematical updates are much kinder to previous theories than in other fields.
But people also take history very seriously, as well as science, and none of those things are true of those fields.
Lay people place a lot of trust in the falsifiability of science, either by actual experiment or by observational checks, neither of which most philosophical arguments are conducive to. Science outruns experiment when we cannot run actual experiments due to constraints on time or scale (we cannot go back millions of years in time to look at dinosaurs, or watch a universe evolve in a bottle for billions of years, or generate a particle with a quadrillion electron-volts in a lab). In this case scientists attempt to generate "observationally falsifiable" theories about past events: for example, if one theorizes an asteroid ended the Permian era, we can go looking for a huge hole in the ground or a layer of asteroid dust in geological rock layers. Historical theories make predictions as well, though with much less precision. If we don't find one, that's evidence against the theory. Even for physics theories we cannot observe scientists try mightily to find downstream predictions about how a theory of supersymmetry, not directly testable, might imply that a particle being smashed in a lab might have certain properties.
In the far reaches of cosmology or quantum gravity where no experiment is even slightly feasible, physics does indeed become effectively unfalsifiable by experiment or observation. In these cases physicists steal most of their credibility from math: the mathematics is nicer if the universe works this way; this approach tends to work where we can observe it and so we (philosophically) infer that it probably works that way where we can't observe it as well. But it also so happens that when you reach these far fields, physics becomes open to the "what if they're just making all that shit up" criticism which does in fact get leveled by lay people and contrarian physicists alike.
Philosophy in most cases, relies on thought experiments that are not amenable to experiment or even observational verification, which lay people place a great deal of trust in when choosing what theories to believe.
>One who was not well-versed in mathematics would be skeptical of the existence of successful mathematical arguments. Mathematicians couldn’t convince lay people of controversial mathematical conclusions if they had to argue for them step-by-step—the only reason they can do so is that mathematicians are treated as experts worth deferring to.
There is a catch. Advances in highest-order mathematics have demonstrably led to the creation of a computer, a nuclear bomb, space travel and other mind-blowing things. Proposition in highest-order philosophy... well, it's not even obvious if much positive philosophical progress has occurred in the last couple of centuries, whether what we have counts as "advances". No matter how clever a philosophical argument is, another philosopher will probably not bite it. This doesn't really happen in mathematics too often.
Most of technical, counter-intuitive and jargon-laden writing is incredibly boring to most people, but at least mathematics has something to show for it.
Re: footnote 1. Which paper makes you say that Lewis was a moral anti-realist? I've read all his papers that have been collected into volumes, and I don't recall anything that would make me apply that meta-ethical position to him.
Oh oops—I’ll fix
Do you take the same attitude to continental philosophy? While I think analytic philosophy is a bad field, I think continental philosophy is worse in pretty much every way. Phenomenology, panoptican, semiotics, existentialism... I consider these all practically explicitly obscurantist topics that are meant to create an illusion of understanding when there isn't much substance to anything that gets written about in these fields. To the extent that you agree with my dismissal of continental philosophy, why not be skeptical of analytic philosophy in the same way? I remember the joke post about hating Camus that I think should bias you towards skepticism.
>doing so requires understanding something about philosophy of mind
That's a rather euphemistic way of saying "requires believing in dualism".
>I’ve discussed the zombie argument against physicalism with tons of philosophically ignorant lay people. Almost none of them buy it (interestingly, they are more moved by Mary’s room).
Maybe it's just a better argument.
I agree, although I also think one could reasonably believe both a) philosophy should be respected and b) academic philosophy should be defunded
The difference is that mathematicians have a method for proving things that leads to convergence, which philosophers don’t seem to have.
And anyone who has taken high school level geometry knows what proving something mathematically means at a basic level. So I don’t know why you think people don’t have the faintest idea of mathematical reasoning.
Mysteriousness is not an inherent property of some fields or arguments. it's a property of a mind in correspondance to something that this mind does not properly understand. One of the advantage of studying math in university is that you experience how math that initially appears to be mysterious, complex and opaque is actually simple to the point of self evidence. I don't think that philosophers of consciousness can say the same about their titular subject.
Celebration of mystery is celebration of your own ignorance. And I feel that you are doing a fair share of it in this post: Mathematics is mysterious and repected; philosophy is also similarly mysterious, therefore we should respect it on par with mathematics. This is a poor way to reason about anything. Stuff can be confusing simply because it's flowerly nonsense without any substance. And, sadly, lots of conventional philosophy is like that.
As a person who has been in love with philosophy since my teens, I understand that it's a hard thing to swallow. It felt so good to be able to derive the same answers to open philosophical problems that some acclaimed philosophers had done. Abandonning the idea that I was doing some actually impressive cognitive labor felt painful, as if I was justifying all the people who failed even to engage with the argument properly. But one has to grow up eventually. If lots of philosophy is nonsense I want to believe that lots of philosophy is nonsense. I won't hold to beliefs I do not want.
> Imagine that mathematics was not a well-developed discipline but instead, we argued about math the way we argue about philosophy. There would be no rigorous framework or assumption that some people are experts—instead, people would just try to beat each other over the head with arguments.
In that case treating math with as much respect as we are treating philosophy now would be justified. WIthout a rigorous framework it's unclear who is right and who is wrong, no way to separate valuable knowledge from useless falsehoods, therefore no optimization process for truth and therefore no value in expertise beside hollow appeal to authority.
The correct question to ask is why math and natural sciences are formalized and therefore respected while philosophy is not so much. There are several good reasons for it. One of the most prominent is that as soon as some kind of formalization or falsification becomes possible for some philosophical domain, it stops being philosophy and joins the realms of science. Therefore, we have an evaporation dynamics, where the best philosophical ideas are not credited to philosophy anymore, and when people say "philosophy" they mean all the rest - poorly falsifiable and non-formalized semantic games, appealing to intuitions.
There is also an opposite evaporation where people who are very much philosophers in everything but name, who do important work progressing our understanding of philosophical questions refuse to participate in the conventional institution of philosophy, refuse to embrace the title of philosopher, and prefer to associate with more respectful disciplines instead. While people who are ready to embrace the identity of a philosopher are selected for accepting the usual philosophical arguments whether they are crazy or not. And therefore knowing that the majority of philosophers support some kind of position on some question becomes very much not a useful signal about whether this position is true or even whether the questuin itself even makes sense. And of course if you disagree with just one particular philosopher its not a signal at all - with all likelihood there is another philosopher with whom this philosopher disagrees about this exact question.
Some philosophy, notably analytical , is formalised.
Formalization is a insufficient to prove correctness -- particularly soundeness. A formal argument can be checked for validity , but still depends on the soundness of its premises.
https://iep.utm.edu/val-snd/
Philosophy is unique in being a)fairly intimidating and abstract (unlike the rest of the humanities) and b) relatively unemployable (unlike STEM).
People have limited bandwidth for abstract intellectual topics, and even smart, abstract-thinking people can’t be expected to patiently wait for philosophical ideas to click when they need to spend their brain power on getting a job. Philosophy’s PR problems seem kind of complicated, and maybe some of the problems are intrinsic to the discipline itself, but I can’t help thinking they would mostly go away if there was some way to pipeline Phil majors into 6 figure professions.
You're familiar with Katja's SIA doomsday argument right? https://meteuphoric.com/2010/03/23/sia-doomsday-the-filter-is-ahead/
(warning: I remember finding it depressing when I first read it, but I've now forgotten why)
I address it in the paper!
Nice job on the Synthese article. I disagree with it in a number of places, simplest of which is that you sometimes say "all alternatives to SIA have feature X" when you really just mean "SSA has feature X." Most relevantly, you seem to think all non-SIA views imply strong evidence for some sort of doomsday scenario. But there's a large family of SSA-like anthropic principles on which it's at best very weak evidence, and the evidence doesn't get arbitrarily strong as the "large" world possibility gets larger and larger in terms of the number of people therein.
No, I meant all alternatives to SIA have feature X. If one is a Bayesian and finds out that they're early, because being early is more strongly predicted on theories according to which there are fewer people, they get a big update against big worlds.
Only if you believe that you could be born at some other time, which you really should not.
They may get an update against big worlds (like SSA does), but not all variants of SSA imply a big update. Some imply a tiny update, whose magnitude doesn't depend much on the number of people involved.
They all apply a big update if you have a uniform prior across the people you might be prior to confirming your identity. Suppose I'm considering between two hypotheses: first that there are 10 million people and second that there are 100 quadrillion people. I discover I'm in the first 10 million people. Well then I'll get evidence the odds of which is 10 billion times as strongly predicted on the first hypothesis. Therefore, if the only way for humanity to be destroyed before having 100 quadrillion people is for me to get a royal flush in poker, I can be super confident that I will get a royal flush.
>They all apply a big update if you have a uniform prior across the people you might be prior to confirming your identity.
I'm confused. SSA, and variants of SSA, definitionally don't use uniform priors across all people you might be. They may involve uniform priors among people *within* concrete possible ways the world could be, but not among people across such ways. Moreover, there are variants of SSA which uphold this within-concrete-world uniformity and which don't automatically imply strong updates to small worlds (only weak updates).
SSA is perfectly consistent with having a uniform prior across the people you might currently be. For instance, suppose that there are 3 people created but I know nothing about them. SSA is consistent with having a credence of 1/3 in being each of them!
Suppose God flips a coin; if it's heads, he creates one person, and if it's tails, he creates two people. SSA is indifferent between the two people in the tails world (this is what I mean by uniformity within a concrete possible world), but it weighs the one guy in the heads world twice as highly as any of the individual people in the tails world. So it's not uniform among people *across* possibilities.
(To be clear, "concrete possibility" here means worlds where the values of all random variables in play have been completely fixed. In my above example, it would be the outcome of the coin toss.)