In my view one of the most glaring indictments of the way philosophy and other humanities are taught and practiced is the senseless insistence on reading original works by the great masters. This is most apparent in the continued consumption of Plato, Hobbes, Aristotle and the like in philosophy but can be equally well be seen in the reverance for Chaucer, Shakespeare or other literary classics. To my horror this reverence for the original works is even being promoted in economics. So even though I gave a short reply in the comments at overcoming bias when this issue came up I’ve been meaning to discuss the question in more detail.

For the moment I’d like to set aside the issue of literature for another post and focus on subjects like philosophy and economics where (at least in theory) the aim is to genuinely progress towards a (more) accurate/useful understanding. Since I find it genuienly perplexing why one would ever feel the need to read the originals rather than the digested and improved material found in modern expositions as one does in math of physics I’ll quote Tyler Cowen’s justifications for returning to the original thinkers. Obviously these don’t represent every possible justification but they are the best justifications I’ve ever heard.

First though I’d like to be perfectly clear that the issue under consideration is whether there is some pedagogical benefit to reading original thinkers as opposed to modern summaries (of either the original thinker or simply the current state of the discipline). There is no accounting for taste so if you simply have some Plato fetish or like the way reading Plato makes you feel sophisticated you might find it more enjoyable to read Plato rather than more modern work just as someone else might prefer to have their philosophical arguments interspersed in Harry Potter slash. Also if your interest is in original historical research then influential works are a reasonable thing to read¹ but again the question at hand is the benefit of reading original works by great thinkers to the advancement of the discipline itself not it’s history or the practitioners feelings of sophistication. With this point clear let’s examine what Tyler Cowen has to say point by point.

1. Secondary sources are unreliable and they do not capture or understand many of the original insights. To remove it from the distant past, what I get from John Rawls or Robert Nozick is quite distinct from what I get from their distillers.

So what? The standard isn’t whether a latter distillation captures the exact content but whether it’s a more effective way to gain understanding. Reading a modern calculus book is extremely different from reading the original Newton. Newton’s notions of infinitesimals and fluxions have been excisced wholesale and replaced with the modern notions of limits and epsilon-delta proofs and that’s a huge improvement in the ability of calculus books to convey understanding.

2. Truly great thinkers require numerous distillers. Can you read just one book on Keynes? No. So you have to read a few. Shouldn’t one of these then be Keynes himself? Yes.

This presupposes the goal is to understand what Keynes thought. Keynes was a brilliant economist but he was just as human as the rest of us and some of his ideas were simply confused or poorly thought out. The benefit of later distillers is to transmit the insights while avoiding the confusions, so no, one of these shouldn’t be Keynes himself.

I mean imagine Keynes was really a highlander and was still alive and at the height of his intellectual powers. Who would it be more beneficial to read the 1936 Keynes or the 2010 Keynes who has used the intervening years to excise the confused parts of The General Theory and find more lucid explanations of the key insights? Surely it’s the 2010 Keynes who would (likely) provide the better explanation (if you disagree would you go back to his half-assembled notes? Further?). Yet surely if Keynes could improve on his own work than (as the goal is to convey economic ideas not Keynes personal beliefs) surely others could as well, especially when the benefit from the collaboration and exchange of ideas provided the academic discipline.

3. The errors of top thinkers are often more interesting and instructive than their successes. Distillers have a hard time capturing these errors and their fruitfulness.

But that’s the wrong comparison. The right comparison is whether it’s more useful to build upon the work of past greats and digest this new material including the mistakes made by those who have built upon the great thinkers of the past than to spend time digesting the errors of the past. Obviously if it was costless one would read every book on the subject but the key question question is would the time spent exploring the errors made by Keynes be better spent exploring later work that builds upon his insights.. The reason it’s so tempting to advocate reading originals is that we don’t properly take into account the opportunity costs incurred reading those originals.

Moreover, given that there is only so much time for students (or professors) to devote to learning a subject either one must give up totally on the idea of making progress or admit that it’s sometimes more effective to substitute modern materials for some works of great thinkers. Hence this argument either proves too much (progress is impossible because it’s always better to learn from the mistakes of past great thinkers) or proves nothing at all since we continuously make beneficial trade offs of replacing originals with more modern works.

4. We often read great thinkers not to learn what they understood but also to set our minds racing and to find interesting new questions. Great thinkers are usually better at supplying this service than are their distillers.

Again this assumes that the job of the distiller is to summarize the original author. A good analysis book doesn’t summarize Newton it digests his insights and presents them as part of a grander theory. Reading a modern analysis book does a much better job a posing interesting new questions than does reading Newton.[^empirial]

Moreover, I suggest this is largely a placebo effect. One is told that the reading great thinkers in the original is particularly inspiring so we search for questions to inspire us. We would probably do equally well if told that Joyce’s Ulysses conveyed deep economic questions. If you doubt this consider the stunningly large number of people who, despite not being religious, claim to derive deep moral messages and insights from the bible despite it’s blatant encouragement of genocide, rape, and every other kind of brutality imaginable.

5. Sometimes the value is in having read common sources and benefiting from the commonality per se. Great thinkers are usually more focal than any of their distillers and thus reading them is a good input for discussions with others.

OFten this is simply false as influential textbooks and articles are often just as widely read. More importantly by virtue of the novelty of their ideas original thinkers are usually lacking in clarity meaning the same work is usually interpreted in a host of different ways.. However, even if true this argues for more canonical books. In mathematics this issue is solved by the publication of various yellow books that provide a common base for everyone to use as a reference and there is no reason not to do the same for other subjects.

6. Original sources often help you challenge or reexamine your world view or intellectual ethos. Distillers very often pander to that world view, while pretending to challenge you.

Given their status as influential originals the content in these works has largely been either incorporated into your modern world view or people have developed standard objections. I know my world view (or even philosophical position) has never been threatened by the original work of an past great thinker but often it’s been shaken by a new argument or idea from a modern source.

7. Consider a simple comparison. You can read either Adam Smith’s two major books or any ten or even twenty books on him, toss in articles if you wish. It’s a no-brainer which you should choose.

Right, neither. Who the hell cares what some dude named Adam Smith thought. Given the choice between reading a modern economic textbook and any of Adam Smith’s books I know which one I would choose and it’s the same thing we always choose for undergraduates.

8. The best distillers often are original sources in their own right (and in part unreliable expositors), such as in Charles Taylor’s excellent book on Hegel.

Again the false dichotomy. Instead of trying to find out what Hegel said we should be finding out what is true (which in the case of Hegel will involve simply ignoring him).

9. Distillation works best in very exact sciences, such as physics and mathematics. If you rely on distillation for an inexact science, you will do best at capturing its exact parts. You will be left with a systematic bias, and knowledge gap, regarding its inexact parts.

So it’s only when you can’t actually go out and check whether going back to read the original works by great thinkers that it’s beneficial? That’s awful suspicious

Stepping back for a moment I would point out the fact that there are many different mutually contradictory disciplines of theology (every major world religion has one). Thus regardless of your religious views (and especially if you are an atheist) you must admit that there are academic disciplines which are totally bullshit. Now I would point out that in virtually all instances of theological study the original work of prior influential (but not prophets or otherwise supernaturally gifted) theologians is regarded as similarly important to read in the original.

Hence, we must all admit there are situations where academic disciplines are convinced of the important of reading influential past thinkers in the original despite even though it provides no actual benefit. Conversely in all those disciplines where we have reliable quantatative measurements of progress (with the obvious exception of history) returning to the original works of past great thinkers is decidedly unhelpful. Therefore at the very least anyone who wishes to claim that reading past great thinkers in the original (be it Plato, Keynes, Aristotle or whomever) has a substantial argumentative burden to meet and until they do the assumption should be against spending time doing so.

So browsing the web this morning I came across this amazing blog largely focused on the author’s (apparently a philosophy grad student somewhere) continentalist approach to Godel’s incompleteness theorem. Rather than describe the content I’ll just include his last post.

Perhaps this will be my last post here? A simple reiteration of negative Platonism, situating its significance in the context of awakening from the wrong expectations performed so thoroughly and unconsciously in the second Critique.

To put it once again with maximal simplicity: The diagonal is what relates, without religious/imaginary synthesis, our mathematical/cognitive and ethical/existential lives.

We already live in both places: in consistency through calculation and consciousness, in completeness through care and the unconscious. What we suffer from, as both theoretical inadequacy and ethical alienation, is an inability to relate these in a way that makes sense and is good.

Thus it has suddenly become possible, after long stagnation, to say something rigorous and suggestive, something that opens logoi both mathematically lucid and existentially thick (again without synthesis: it’s a matter of bridges and transitions, not of sovereign unities or systems) about the fundamental Socratic question: which knowledge, which part, of knowledge, would do us any good?

At stake here is exactly what gets talked about, prephilosophically, as “the meaning of life”. It is good philosophical practice to avoid this question until one has something real to say about it, and instead, to work the problem from either side. But it is not good practice, once the relation has become clear, to remain squeamish about naming it: Idea of the Good, Diagonalization.

Note, if you read the rest of the blog it’s totally clear that he really means diagnolization in the sense of the mathematical technique employed by Godel. Moreover, he seems to genuienly understand the mathematics (Godel’s theorem is a result in a meta-system describing provability in some formalized system) so what’s going on here is surely not mathematical confusion. It’s the philosophy that’s totally fucked (I’m pretty confident now that it’s not a hoax).

However, to be fair to this blogger, he isn’t some isolated crank, but rather a participant in a ‘respectable’ philosophical tradition. Indeed, one of the famous philosophers he references, Alain Badiou is even more incoherent. While he would almost certainly quibble with the description given on wikipedia if the following is even remotely accurate he might as well be spouting gibberish.

Badiou’s use of set theory in this manner is not just illustrative or heuristic. Badiou uses the axioms of Zermelo–Fraenkel set theory to identify the relationship of being to history, Nature, the State, and God. Most significantly this use means that (as with set theory) there is a strict prohibition on self-belonging; a set cannot contain or belong to itself. Russell’s paradox famously ruled that possibility out of formal logic. (This paradox can be thought through in terms of a ‘list of lists that do not contain themselves’: if such a list does not write itself on the list the property is incomplete, as there will be one missing; if it does, it is no longer a list that does not contain itself.) So too does the axiom of foundation — or to give an alternative name the axiom of regularity — enact such a prohibition (cf. p. 190 in Being and Event). (This axiom states that all sets contain an element for which only the void [empty] set names what is common to both the set and its element.) Badiou’s philosophy draws two major implications from this prohibition. Firstly, it secures the inexistence of the ‘one’: there cannot be a grand overarching set, and thus it is fallacious to conceive of a grand cosmos, a whole Nature, or a Being of God. Badiou is therefore — against Cantor, from whom he draws heavily — staunchly atheist. However, secondly, this prohibition prompts him to introduce the event. Because, according to Badiou, the axiom of foundation ‘founds’ all sets in the void, it ties all being to the historico-social situation of the multiplicities of de-centred sets — thereby effacing the positivity of subjective action, or an entirely ‘new’ occurrence. And whilst this is acceptable ontologically, it is unacceptable, Badiou holds, philosophically. Set theory mathematics has consequently ‘pragmatically abandoned’ an area which philosophy cannot. And so, Badiou argues, there is therefore only one possibility remaining: that ontology can say nothing about the event.

For any readers familiar with set theory the part about drawing ethical maxim’s from Cohen’s method of forcing might be even more amusing. Sure, he is hardly the first continental philosopher I’ve read who should be properly regarded as a crackpot but when it’s about my subject (mathematical logic) it just makes the point all the more clearly.

Now reading this sort of BS is kinda amusing but I do have a broader point. Despite being essentially indistingushable from the sort of crank theories that pop up from physics crackpots all the time the people publishing this stuff are still seen as respectable, even acclaimed, philosophers. If philosophy wants to be a serious intellectual discipline it needs to take the same hard line that they physicists do about crackpots, even if it means tossing out entire university departments.

The physicists wouldn’t simply sit quietly and say nothing about a crank being allowed to teach physics courses, nor attend conferences or journals that treated them as respectable researchers. Moreover, were they to do so the progress of the discipline, and certainly the public understanding of physics, would be greatly harmed. My point is ultimately that it’s not enough for analytic philosophers (particularly tenured ones) to sit back and privately dismiss all this crap as rubbish. They have a positive duty to denounce these people as cranks and eliminate them from the field. Failing that they have a duty, even if it imperils funding, to demand departments be split and otherwise clearly distingush what they do from what the continental crankpots do.

To be clear not everyone one might classify as a ‘continental philosopher’ should be deemed a crank. Despite being notoriously confusing Kant surely is not. Mere error or poor writing is not enough to be a crank. However, neither the blurriness of the line or our inclinations to charity are an excuse for tolerating obviously incoherent gibberish as valid philosophy. Since it’s notoriously difficult to conclusively establish that some convoluted continental style ‘argument’ lacks any reasonable interpretation the burden should be on the person presenting the apparent gibberish to convince others they are merely really poor writers with a meaningful point.

So lately I’ve been reading a bit of Overcoming Bias and Less Wrong. While the posts on these sites are always interesting they frequently, especially at Less Wrong, seem to promote a sort of cult of rationality. Of course I too value reaching the right conclusions instead of the wrong ones and am broadly sympathetic with the goal of ameliorating the negative effects of psychological shortcuts that interfere with our utility but alot of the content on these sites seems to go much further than this. For example consider these posts by Robin Hanson and Eliezer Yudkowsky. Underlying these remarks seems to be the assumption that there is some kind of objective standard of (perfect?) rationality to which we could aspire that would somehow capture our intuitive notion of rationality as distinct from merely being lucky. While I rarely see rationality so earnestly venerated as it is on these two sites the same assumption pervades much of analytic philosophy and many puzzles and papers simply take it for granted that there is some well defined notion of rational thinking/belief(I’ll leave act rationality out of this for the moment). However, despite being an extremely useful tool in describing common situations and deciscions it’s long been my view that, when considered in full generality, rationality isn’t even a coherent concept.

To explain what I mean we first need to go back to Quine’s seminal paper Two Dogma’s of Empiricism. Even though I think Carnap clearly had the better of the argument about analyticity¹ I want to give Quine credit for pointing out to me the way in which the concepts we use depend on our background assumptions (how we model/conceptualize things) for their very coherence. Just as the concept of an equivalence class stops making sense once you start talking about non-transitive relations so too do many of our scientific and everyday notions cease to be well defined when we no longer accept the assumptions they were defined with respect to.

Stealing an example from Quine consider the Newtonian concept of kinetic energy. A good Newtonian physicist would have said that the kinetic energy is defined to be .5mv² where m is the object’s mass and v it’s velocity. However, kinetic energy is obviously also intended to be in some sense a measure of the work it would take to stop that object. Since these two notions coincide on the Newtonian picture there isn’t any problem. So long as we believe (or even use as an approximation) Newtonian physics there isn’t any question as to which is the right definition of kinetic energy. We are simultaneously committed to the concept capturing both notions. What Quine observed is that once we abandon the Newtonian conceptual framework there isn’t really any objective fact about which commitments we should honor and which we should discard. If scientists had responded to special relativity by using kinetic energy to describe the Newtonian formula and started theorizing about the conservation of Eisensteinian smenergy we couldn’t really accuse them of having made a mistake. Just as there is no right way to extend the notion of an equivalence class to non-transitive relations there often isn’t any right way to extend our scientific or everyday concepts outside of the frameworks they were conceived in.

The upshot of all this, in my view, is that our most useful concepts often presuppose certain assumptions. When these assumptions no longer hold the concepts themselves may cease to be coherent. So keeping this in mind let’s take a look at the assumptions that give rise to our concept of rationality.

Without going into too much detail I think it’s fairly safe to assume that a major (primary?) grip on (belief) rationality comes by way of postulating that people hold various beliefs where we take those beliefs to behave in some loose way like propositions. In other words we gloss over complexities like the effect of context and social situation on the views people express and simply pretend they either do or don’t believe some claim. Of course you can embelish this view a great deal and allow people to believe things in varying degrees or even take them to merely have some transitive implication relation. However, we can only stretch these concepts so far before they become unwieldy and useless, something we all implicitly recognize when we hesitate to attribute beliefs to ethnic groups, countries, or our computers.

So what? It’s hardly news that some aspects of people’s behavior won’t be well described by idealizing them as having something like beliefs. However, the point I want to press home is that rationality isn’t a property that big fleshy globs of atoms have. Rationality, is a concept grasped in terms of a certain kind of idealization about human behavior. It’s a useful concept and useful idealization but it’s still a type error to think of it as a property that applies to actual physical beings. We frequently forget this because in most contexts there is an obvious “right” way to idealize someone as an agent with certain beliefs so we talk about people having irrational beliefs and find it useful. However, it’s important to remember this shorthand only makes sense as long as this kind of idealization makes for a decent model of human behavior. Just like it’s simply confused to talk about the Newtonian kinetic energy of a particle traveling at .999c there are situations in which idealizing people as having something like belief is such a bad way to model their behavior that talking about rationality is similarly confused.

But the situation for a viewpoint independent concept of rationality applicable to real people only gets worse once you realize just how sensitive the ascription of rationality is to the way we choose to idealize the situation. Choosing to idealize a split brain patient as a single agent will yield very different judgments about his degree of rationality than idealizing his actions as the result of two seperate agents with distinct beliefs. It’s not that one of these idealizations is wrong and the other right (what could that even mean?) but just that in certain contexts one will be more useful than the other. And it’s not just split brain patients, Frued and many others have often taught that people were better modeled as the result of several competing agents or personalities. To really drive home the dependence of ascriptions of rationality on your choice of model just try to work out how you could make a principled application of the concept to a network of partial autonomous, partially integrated AIs.

My point is that it’s not just that we can’t ever be fully rational. It’s that the very notion as applied to living breathing people isn’t even coherent. Rationality is a concept that lives in an abstract idealize realm populate by agents possesing something like beliefs. It’s only applicable to real creatures insofar as this kind of idealization is useful and people largely agree on how it should be done. Step beyond that and it just doesn’t make sense anyone. I also think this realization can help alleviate some of the confusion over various paradoxes like the surprise quiz but that’s another post.

It’s not uncommon on the blogs I read to see people objecting to some kind of government action as inconsistent with libertarianism. As a mild example consider this post critiquing the idea of letting bankruptcy judges modify mortgage obligations. More extreme examples are easy to find and usually characterized by strident, but unsupported, declarations that such and such is in principle unacceptable government intervention. Now I happen to agree it would be a mistake to hand bankruptcy judges the general power to renegotiate mortgages¹ but the problem is that referencing libertarianism does nothing to support this argument nor virtually all of the other arguments it is invoked to support. You can no more justify specific governmental interventions by saying you are a libertarian than you could justify federal funding for giving beanie babies to the poor by saying you are a democrat.

Before we can see this we first need to eliminate the spectre of principled libertarianism from the discussion. Many self identified libertarians seem to take the position that the government is absolutely forbidden from interfering in certain vaguely defined kinds of private behaviors no matter what the consequences. However, it’s no accident that, apart from Ayn Rand’s Dexedrine fueled rantings², the deontological restrictions on acceptable government are always left vague or unexplored. Given any supposed inviolable libertarianesque restriction on governmental behavior it’s easy to create a hypothetical where the impact of this principle is so repugnant no one would endorse it. You think the government ought not to ever seize private property solely to distribute the benefits more broadly? What if that property was billions of doses of the only cure for a devastating global plague and the owner was dead seat on destroying them? Would anyone really oppose government seizure of property in that circumstance?

Sure, some people will bite the bullet and endorse deontological moral theories but the rules they endorse don’t resemble the sort of governmental restrictions libertarians have in mind. Given the consistent failure of anyone to articulate a remotely attractive inviolable set of libertarian restrictions on the government we can dismiss any supposed principled libertarian objection to governmental action unless it comes with an attractive articulation of those inviolable restrictions. In other words you can’t just insist that there is some unstated but intuitively compelling rule out there which prevents the government from doing what you find objectionable and expect others to just take it on faith.

Once we accept that in theory severe enough consequences can justify what libertarians would otherwise see as objectionable government interference the whole argumentative structure shifts. The libertarian can no longer say, “that policy would violate personal property it’s unacceptable,” he admits that sometimes the government must do just that. Instead he must argue that the consequentialist benefits of the policy aren’t sufficient to balance the harms to liberty. Indeed, it would be perfectly reasonable for a libertarian to say, “I think that 2 accidental deaths per thousand people is a reasonable price to pay to be free of gun regulations but not 3 per thousand.”³. However, this kind of argument is never made since it saps the appeal to libertarianism of all it’s appeal. Whatever valuations you place on liberty seem arbitrary and the argument is mired in the same kind of consequentalist quibbles that an purely pragmatic objection would face.

Of course a sophisticated libertarian would instead say that libertarianism is a formula for producing good policy outcomes. On this view it’s not that protecting liberty necessarily has some kind of intrinsic value but that when liberty is protected good consequences tend to result. This kind of libertarian tends to emphasize the effectiveness of private property and the market economy in creating wealth and alleviating suffering and try to parlay this into an argument against whatever policy they are currently opposing. That argument might be enough to suggest we should default to a libertarian approach but it isn’t enough to counter specific claims that this policy will lead to beneficial results. After all it’s only in most cases that the libertarian approach is superior but the other side has given specific arguments to the effect that in this case government intervention would be beneficial. If the argument in favor of this specific policy is valid then it should be enacted as one of the few exceptions to the superiority of the libertarian approach. If the argument is shown to be invalid then the reference to libertarianism does no extra work in rejecting the policy. All that being a libertarian does for the author or audience is arm them with the conviction that there is probably a flaw in the arguments for some governmental intervention. It doesn’t resolve them from the responsibility to pinpoint those flaws.

Perhaps the best case that someone could use to bring a general libertarian philosophy to bear on a specific question of policy is to argue that people are irrationally biased toward governmental intervention and against the, usually better, libertarian solution. If the libertarian can convince us that we lack the facilities to rationally evaluate arguments for this policy he can leave us with nothing but the raw general preference for libertarian solutions to guide us. In other words if we are no better evaluating specific policy arguments in our native language than in esperanto we might as well follow the same strategy in both cases and always guess the more libertarian solution is better. Unfortunately, at best this gets us a vague, “well it’s more likely than not that intervention will be bad,” which is far weaker than the conclusion the libertarian in the debate desires. Moreover, it’s simply implausible to believe that we can somehow rationally evaluate the argument that on average the libertarian policy tends to be superior but can’t gain any greater information about the better solution in any specific case. After all if we can’t tell what policies tend to work and which don’t how did we ever conclude that the libertarian policies were preferable in most instances in the first place?

Ultimately one should be a (sophisticated) libertarian only if in most cases the arguments for the libertarian style solution are compelling. One justifies being a libertarian by reference to many specific arguments for the superiority of the libertarian solution. You can’t justify rejecting an argument for a specific government intervention because you are a libertarian.

There are important questions about the appropriate role of government in encouraging healthy behavior. As a free society we should have deep reservations about forcibly taking people’s money and using it to tell them how they should live, even when we are sure that would make for a better society. History is replete with examples of tyrannical majorities wasting resources and even fueling crime combating`harmful’ behavior. Thus we already have plenty of reason to tread carefully when legislation to discourage tobacco use, encourage exercise or promote a healthy diet is proposed. However, I have a much more fundamental question. Is it even preferable to have a society where people live longer?

At first glance this seems to be a truly stupid question. After all it’s bad when people die early. Isn’t it? Well, I certainly don’t want to die and neither do most people but that misses the point. We all die eventually and even if we personally want to put off death as long as possible can we truly say that a society where the average life span is 90 years rather than 70 is a better place? Would a society where the average life span was 200 years be even better? What sort of life span would be optimal?

It’s tempting to answer ‘infinite’ and certainly it would be wonderful if we could all retain our youth for forever and never have to grieve over lost friends and family. However, for the immediate future this simply isn’t possible. No healthy diet or prudent lifestyle can reduce the (average) number of friends we must mourn¹ and no amount of yoga or wheatgrass smoothies can prevent old age from taking it’s toll. Moreover, suppose we really could increase our lifespan indefinitely. At least for the next century or so we would have to virtually stop reproducing to avoid outgrowing our resources.

Ultimately we can’t simply say ‘life is good so we want more of it.’ Almost certainly such a policy would actually demand we divert money from healthcare into programs encouraging reproduction. As a society we’ve already reached the conclusion that it’s better to maintain a relatively small population that can live well than to expand into a great multitude that can barely make do. But rationally applying this insight to this question suggests that investing in longer life spans might not make sense.

Certainly we feel greater pain when someone is snatched from life too early and so we certainly shouldn’t stop pursuing more effective treatments to save people who might otherwise be struck down in the prime of life. Nor would we want to create distress or anger by denying people treatment. However, researching ways to further prolong our life span would likely introduce greater variability (some people die of heart attacks at 65 others make it to 130) and thus prolong the time people would have to endure the loss of loved ones as well as the sense of tragedy and anger at their deaths. Other things being equal a society is better if people spend a smaller proportion of their lives old and frail and since extending old age is unlikely to make people substantially happier (on average²) investing in technologies to lengthen our lifespan seems counterproductive. Of course we should look for technologies that let people be healthy and fit for a greater fraction of their lives and if we are able to make 80 feel like 55 that might justify more investment in keeping people alive till 80.

The observation that merely putting off death is not necessarily a desirable end in and of itself also has substantial consequences to what kind of charity and aid is best to give to the third world. However, that will have to wait for another post.

So in a recent post I pointed out how unreasonable it was to assume that aliens advanced enough to transfer their consciousness into computers would have motives or behaviors anything like what the current human species does. Of course there is an implicit assumption here that a simulation of our brain process on a computer would be just as conscious as we are (the strong AI hypothesis). Here I argue that this isn’t really true. Of course I don’t doubt that artificial conscious beings can be constructed. There is nothing magical about conception, if we manufactured nerve cells in the lab and put them together in a brain it wouldn’t be any less conscious than you or I. However, this doesn’t mean that the particular means by which our brain performs it’s calculation is irrelevant to consciousness. As I shall argue here we actually have pretty good reason to believe that simply simulating what the brain does on a microchip as we know them ¹ is unlikely to give rise to any experiences no matter how faithfully it might reproduce the behavior of that brain². This is a pretty long post so I continue below the break.

(more…)

So my fiance Sharon Berry posted a very early (like 2 years early) draft of her thesis on a wiki here. The broad question she is addressing is how we can come to have accurate mathematical knowledge which I figured might be of interest to some people who check out the philosophy part of my blog. I also figured I’d take this chance to share my own thoughts on the subject. However, to give credit where credit is due I would never have really thought through these issues if Sharon hadn’t brought up the subject and many of the ideas are really hers. However, I take them in a very different direction than she does.

The really short version of my attitude to the problem of mathematical knowledge is “What Problem?” I mean obviously mathematical knowledge is subject to the same skeptical doubts that other forms of knowledge are but I’m unconvinced that there is any particular problem unique to mathematical knowledge. More specifically I would say that mathematical knowledge is nothing but a limiting case of other sorts of knowledge so it poses no problem over and above the problem of understanding the meaning and our knowledge of other sorts of statements. Of course explaining meaning is a notoriously difficult problem in it’s own right but I’m tempted to think that it’s a hopeless problem. Ultimately one must merely take meaning to be a primitive concept but that’s another discussion.

I need to get back to working on my thesis so I won’t give more than a very very quick sketch of my thoughts here but roughly I take it there are two primary reasons one might think that mathematical knowledge requires special explanation.

1. The Benacerraf problem: How could we come to know anything about numbers if they don’t have causal powers, we don’t interact with them and so forth.
2. How could it be that our mathematical theories turn out to be useful in the way they are.

Platonism and Reference

So if one accepts a platonic theory of mathematical meaning then there may indeed be special problems about mathematical knowledge. That is if the meaning of a statement like 2+2 =4 is really that some special 2 object out there bears a certain relation to itself and the four object one might wonder how it is that we come to know about these platonic objects. However, I’m inclined to simply turn the question around and ask whether the platonic theory in question provides any reason to think that “2″ refers to something we would ‘recognize’ as an integer or whether it could (logically not metaphysically) be that 2 refers to the concept of bunny rabbits and all our statements about arithmetic are really nonsensical. If the platonic interpretation of mathematics tells us that the reference of two must really behave like 2 to qualify as the correct reference then we know exactly how we come to have true beliefs about the numbers — because if our beliefs weren’t largely true we would be talking about something else[^enough]. On the other hand if we don’t have any restrictions about what sort of platonic object 2 might refer to then we aren’t justified in adopting this kind of theory in the first place.

Unfortunately the debate about Platonism and competing philosophies of mathematical largely distracts from what I think are the important issues. As I’ve argued previously Platonism in and of itself says very little about mathematics. What the last paragraph as well as my previous post on the issue emphasize is that it isn’t really Platonism that is doing the work it is your theory of reference. Really on it’s own Platonism says nothing very significant¹, it’s the means by which our talk maps to particular platonic objects that really does the work in the theory. This raises the obvious question of what we even mean when we say that the reference of a certain term is such and such. Are we merely making a claim about dispositions and talk or are we invoking some real metaphysical relation. While Platonism provides a good motivation to consider the issue I think a proper examination of this question of what sort of thing the meaning relation is in the first place illustrates the non-problem of philosophy of mathematics in general.

Platonic Realism About Reference

There are two ways one could understand claims about meaning and reference One could think that the relation of meaning is a truly objective notion with metaphysical substance. That is that the relation between words/mental states/speaking contexts is some and references/meanings is something like a platonic entity in it’s own right. On such a theory it is presumably logically possible (but not metaphysically) that when I say “2″ it really (by virtue of this objectively existing meaning relation) refers to rabbit. In other words the meaning of word is a notion much like the moral status of an action under on a realist moral theory.

Just as with moral realism I think the appropriate response to this notion of meaning is to challenge that it counts as meaning at all. Ultimately there is just this relation out there mapping situations/worlds/utterances/mental states/whatever to references/intentions but why should we think this picks out what we talk about when we use the term meaning? Additionally on this sort of platonic realism about meaning we don’t have any reason to actually believe that we really do have knowledge. After all maybe the objective meaning relation isn’t what we think it is at all and what we take to be true statements aren’t true at all.

One might still be tempted to insist that obviously we have knowledge thus the fact that this theory can’t explain this fact is a puzzle requiring explanation. However, this simply gets things backwards and implicitly rejects the very assumptions of the theory itself. If we accept this sort of theory we need to just bite the bullet and say we don’t know if we really know anything and thus how we know things doesn’t require explanation. Personally I think our intuition that our usage determines meaning is a good reason to reject this sort of theory but in either case this leaves no special problems for mathematics. Of course you might try and say that the mapping between statements and meanings/references must obey certain restrctions but this does no good at all since of course any actual map will have some facts that are true of it but this does nothing to offer us reason to think we have any knowledge of what they are.

Naturalist Theories of Meaning

I think a much more promising approach² is to jettison all the metaphysical baggage and start from the assumption that meanings, ultimately must be defined in terms of sounds, dispositions, actions and other arrangements of matter. That is nothing special or magical goes on with meanings. They are just a concept introduced to organize very complicated descriptions of human behavior in terms of atoms and physical laws. Thus the ultimate standard against which we judge a theory of meaning is it’s predictive accuracy and theoretical utility (how well does it work with other models we wish to use). In some sense already this approach should suggest that there shouldn’t be any deep paradoxes in terms of meaning. After all we are confident that the description of human behavior at the level of atoms is consistant thus any apparent difficulty at the level of meanings either reflects a confusion on our part or a poor choice of definition.

To put the point a bit differently we should think about a theory of meaning much the way we think about thermodynamics as derived from statistical mechanics. Yes, it can be a powerful theory with useful concepts and important impacts but ultimately just as debates about whether entropy is the log of the number of possible states holding X,Y and Z fixed or just X and Y doesn’t reflect any fundamental fact about the universe but a definitional choice we make that is judged on it’s utility. Thus theories like fictionalism or formalism shouldn’t be understood as making different philosophical claims but rather judged simply on their utility in predicting how people actually use words. Indeed one might very well conclude that different models are most appropriate in different circumstances.

Ultimately then the question about how we can come to have mathematical knowledge is largely a non-question. I can point to the actual ways that mathematicians prove theorems and reach conclusions and that right there shows how we come to have mathematical knowledge. Still one might ask but why are the results of our proofs actually true? However, this has a totally trivial answer. The reason that proofs give us true mathematical results is that every step of the proof is truth preserving. Indeed we can go through this and using the fact (in the meta-language) that A and B is true if and only if A is true or B is true show that the methods mathematicans use to reach theorems really do produce true theorems. Asking for anything more is a demand to know why logic is true. Obviously at a very basic level we have to just assume that logic is true (see Quine’s arguments about this point in his discussions of radial translation) so it’s unclear what is left to be explained at all.

To put the point slightly differently it’s contradictory to worry about how we get mathematics correct. Either the question tells us how we have reason to believe we do get mathematics right, in which case it tells us the answer or it offers no such explanation and we have no need to explain a phenomena that we don’t have reason to accept as true.

Usefullness of Mathematics

This finally brings us to the question of why mathematics turns out to be useful. One might think that it’s surprising that the results of mathematics tells us useful things about the world. Certainly in one sense it is surprising, but that’s the sense in which the understandability of the world is surprsing, i.e., that induction works. While it may appear that mathematics directly makes predictions about the world (if I have two apples in my bag and place another two apples into my bag I have four apples in my bag) in fact it’s only the combination of mathematical theorems with contingent bridge laws that makes these predictions (apples don’t appear or disappear when I place more of them together). One might try and minimize the significance of these bridge laws by saying something like “So long as apples don’t appear or disappear the number of apples in my bag is the number of apples I added minus the number I removed.” However, this merely begs the question by working in our expectation that the plus operation on the natural numbers describes how objects behave into the definition of appear or disappear. I could equally well claim that apples were disappearing and reappearing all the time but if they didn’t do so we could see that adding n apples to a bag with m apples in it results in a bag with n x m apples in it.

In fact the usefulness of something like mathematics is an easy consequence of a well known theorem in recursion theory. Supposing we have a language complex enough to express arbitrary procedures³ then that language will contain infinitely many different ways to state the same procedure, some subset of which will be possible to construct a verification that they are equivalent. In other words no matter how weird your language is you can’t get around the fact that some things will turn out to be non-obviously equivalent which suggests that it will be useful to have a means to identify at least some of them.

Usefullness and Knowledge

The final worry is that one might try and link the two concepts and ask how it is that we come to have mathematical knowledge that yields useful results. Thus even if we don’t have abstract reasons to believe that the syntactic manipulations of mathematicians meet some independent standard of being true we do notice that they let us build rockets and cure disease and the like. Thus one might think the utility of mathematics requires some explanation.

Once again though I think a careful examination of the question reveals it to be a non-worry. If by mathematics you merely mean the sort of thing that mathematicians do then it’s undeniable that what counts as mathematics is partially determined by what is useful. While many types of mathematics are very abstract the subject in the large is influenced by what has solved problems presented by the world. This point is made even more forcefully if you try to define mathematics as any abstract rule based manipulation of symbols. After all under such a definition certain types of astrology would qualify which most assuredly is not useful. Similarly any other means by which you tried to formally define the problem is likely to either reduce to triviality or not call our for any explanation at all.

This was a pretty hurried and scattered explanation of my thouhts so hopefully people ould follow it. If you are confused but curious about what I’m trying to say anyway feel free to post a comment or ask me via email

There is a great article over on the New York Times about recent psychological studies of moral impulses. Perhaps the most interesting point in the piece was the observation that people’s emotions strongly demand they make distinctions they can’t rationally justify and appear not to really be rationally justifiable at all but that individuals with damage to the relevant emotional centers in the brain revert to being utilitarians. This is interesting because the sort of unjustified moral antipathy toward things like consequence free incest, using parts of an American flag as a bathroom rag or directly (as opposed to indirectly) killing one to save others bear a great resemblance to the moral judgements of earlier ages we now repudiate. It’s the same type of disgust we have at consequence free incest that makes others demonize homosexuality or (at least in the past) interracial marriage and the same distaste we might feel at using the American flag to wipe toliets still gives rise to laws against insulting the prophet in much of the muslim world.

Now the only reason we shouldn’t toss moral philosophy out as useless is that we believe that by formulating simple unifying theories about what’s moral we can refine our judgements. In other words moral theorizing only makes sense if you believe that by rational considerations we can identify and discard the sort of things we now recognize as moral superstitions (like objecting to autopsies). Yet if we know that the same unjustified instinctive reactions that demand punishment without deterrent value or cringe at pure hedonic pleasure are responsible for the misguided morals of the past surely these sorts of emotional pulls must be discounted in our moral theorizing. Given the further evidence that people fall back to being utilitarians once the misleading effect of these emotional reactions has been swept aside it would seem that utilitarianism is the only real candidate for a good moral theory.

In other words if we believe in moral philosophy at all and join with the rest of society in rejecting many of the odious moral notions of the past we must explain what caused these prior moral beliefs to go bad and avoid applying the same methods in the present. If the scientific work shows that what the beliefs we now find objectionable had in common was their grounding in this emotional part of the brain this gives us good reason to discount these emotions as a basis for our current moral theories. If science also tells us that in the absence of these misguiding emotions we end up being utilitarians then it seems we must either repudiate moral philosophy as a reasonable inquiry or accept some form of utilitarianism.

One of the principle arguments both for our confidence in the application of our physical theories to unobservable situations¹ and the reality of the postulated objects is that our physical theories are particularly simple. The background idea is that when we approximate a function by fitting points or some other general method we expect to get a complex unwieldy object back thus the simplicity of our physical theories shows they aren’t just good approximations based on lots of data points but somehow really get at what is happening. However, I’m skeptical that our intuitions about simplicity are correct. In particular I worry that our idea of what’s simple is deeply influenced by what we find useful. To explain further let me offer an example.

Suppose you are given a box that lets you dial in any² number between 0 and 1 and returns some output value between 0 and 1 within some experimental error³. If after trying many values you derive a polynomial with 25 coefficients that lets you very closely approximate the average result⁴ for a given input you probably wouldn’t think you’d hit on anything deep about the operation of the box. In fact you’d probably guess that greater precision (averaging over more tests) would reveal subtle distinctions between your approximate function and the true value. On the other hand if after the same number of tests it appears that sin(x) is an equally good approximation you might think this was the true function and expect this to be born out by further experiments. You might even make hypothesises about the box’s mechanism on this basis.

My worry is that those theories we take to be simple and elegant really aren’t simple at all. For instance is it really the case that sin(x) is a simpler function than some 25 term polynomial with integer coefficients between 1 and 10? The obvious way to answer this is to ask how many symbols it takes to define each function but this answer depends on what we take to be our primitive terms. To put the point more formally the Kolmogorov complexity of a string depends on our choice of a universal prefix-free machine. However, it’s reasonable to think that so long as we pick one system to represent out theories in and stick with it then it will function as a useful measure of a theories complexity⁵.

However, in practice we never really fix one system and insist on writing all our theories in terms of it. When people discovered that the sin function was frequently useful in describing physical systems they stuck it into their toolkit. They didn’t stick with whatever previous system they had been using and include the definition of sin(x) in all of their theories. Yet if our idea of what a simple theory is changes in response to what seems to make good predictions we no longer have a good argument for the truth of our theories. If it had turned out that a parametrized solution to the equation y^3+x*y=x^2 had been widely useful in physical theories instead of solutions to x^2+y^2=1 then it would probably have been those functions rather than cos(x) and sin(x) that we regarded as elementary functions.

I don’t doubt that evolution has endowed us with a notion of simplicity that works well in everyday macroscopic scenarios. What I’m skeptical of is the claim that the abstract mathematical theories that underlie particle physics and cosmology are really especially simple. Certainly it’s true that they can be expressed in a form that strikes us as elegant and appears simple but they only do so by making use of many layers of abstraction. I’m not so sure that if we examined the mathematical framework for quantum mechanics written out as a formal statement in PA it would still strike us as particularly simple.

In short I’m worried that we underestimate the power of additional layers of abstraction. Sure, the mathematical concepts used in modern physics are the result of a series of definitions and abstractions each one of which strikes us as simple and elegant but the essential question is whether alternative theories giving similar agreement with the data would admit a similar chain of definitions. Given that no real work (to my knowledge) has been done about the additional complexity each layer of abstraction brings to a theory what reason do we really have to be confident about the simplicity of physics?

In philosophy it is common to take strong intuitions about a subject as reason to believe what we intuit as true. For instance in moral philosophy we generally take our intuition that abducting bums and torturing them to death is wrong to weight against any moral theory that concludes the opposite. Now how these intuitions could give us the proper sort of epistemic access to moral facts is a classic problem in meta-ethics and analogous problems are equally famous in areas like philosophy of math, counterfactuals and many more but I want to try to approach this problem a bit differently¹. Suppose you are dosed with a drug and this altered state of consciousness provokes an extremely strong moral intuition. Does this intuition still give one reason to believe it’s conclusion is true? Is it just as good as a sober intuition? If not why not?

For concreteness sake let’s assume that every time you take MDMA² you have an outflowing of love and sympathy which makes the death penalty or any retributive (as opposed to deterrent or preventative) punishment seem to be a horrible moral abomination³. Or even just that you know that if you were to take the drug you would feel this intuition. Now intuitively one wants to say in these cases that such a drug induced intuition doesn’t count or at least counts much less but why? Well one reason we might wish to exclude such intuitions is the worry that there would be too many of them. Indeed if you believe experiences (or whatever intuitions are) supervene on local physical state (e.g. brain state) then your likely to think that some kind of brain intervention could create any moral intuition desired⁴. But this isn’t a (sound) argument that these intuitions aren’t equally valid it’s merely a wish that they aren’t. It would be nice to have access to moral facts but we can’t discredit the possibility that none of our intuitions, drugged or otherwise, give us any evidence just because we don’t like it.

A more promising approach is to observe that we don’t credit the sensory experiences of inebriated people to the same degree we credit those of sober folks and argue that philosophical intuitions work similarly. While this sounds good the problem is that it’s just not true that we always trust sober perceptions more than chemically altered ones. For instance if a perceptual task requires great focus we very well might prefer the observation of someone taking a small dose of amphetamines than that of a sober person⁵. Certainly imagine drugs or other brain alterations that would improve our perceptual accuracy in some ways even while they might impair it in others. Thus it’s not that we have a blanket rule about trusting sober observations more, rather, we merely induct on prior observations about perceptual accuracy in different states. Without an independent check on moral facts we don’t have any reason to take our normal sober brain states as more reliable in this regard than others⁶.

More broadly one might observe that even without knowing anything about drugs or the effects of brain injuries one would probably believe that most modifications to the brain would degrade, rather than improve our perceptual abilities. However, we only believe this because we have reason to believe that evolution has tuned our brain for perceptual accuracy. Given a situation where we have reason to believe evolution would have tuned our perceptions to get an incorrect, rather than correct, result⁷ we should believe that random alterations to our brains would be likely to improve the result. After all if your brain is a reliable mispredictor (when X occurs we perceive ~X) then any alteration in that behavior would have to be an improvement. Thus whether or not we should assign a higher probability to our normal sober intuitions being correct or those induced by brain changes depends on whether or not we have reason to believe evolution favored accurate or inaccurate intuitions.

When our intuitions are not subject to an external check I really don’t think we have any reason to give more weight to our actual intuitions than those we would have if our brains were altered. In the particular case of moral intuitions I would argue that if anything we have reason to believe that our intuitions are, if anything, less reliable than those selected at random. We have plenty of meta-moral intuitions like ‘all people deserve equal moral consideration’ yet there seems to be no shortage of examples where evolution has favored more concrete intuitions in conflict with these principles, e.g., people tend to have different moral reactions when it’s a family member’s life on the line than a strangers. Thus any analysis that gives more weight to our actual intuitions than other possible ones must acknowledge the existence of evolutionary pressures to have inaccurate moral intuitions while their are both in principle (moral facts would seem to lack causal powers) and pragmatic (continued failure to show otherwise) reasons to think there isn’t any evolutionary pressure for our moral intuitions to match up with true moral facts.

I think this actually establishes an extremely strong negative result. In the absence of a plausible naturalized epistemology of morality (or philosophy of math, or knowledge of possible worlds) it’s irrational to use our intuitions as evidence. Without any justification of why our actual intuitions are more likely to be valid than any of those intuitions we could have had it’s an outright error to treat them as stronger evidence for their claims than the fact that we could have had some other intuition. However, even if you aren’t willing to take it this far it raises some very interesting questions. One that seems particularly challenging for the meta-ethicists is the following:

Suppose theoretical analysis (or survey of galactic civilizations) reveals that our moral intuition about the importance of life is actually an improbable fluke and evolution tends to equip any sentient being with the intuition that it’s the future of someone’s genetic line (or their happiness) that is morally salient not whether they live or die. Does that give us reason to believe that death isn’t morally salient? If not how can it be rational to believe something about moral facts on the basis of an accident without any connection to these facts?