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Is Physics Simple?

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?


  1. For instance inferences we draw about cosmology based on particle physics developed under substantially different physical conditions. While a physicist might claim that the situation in a distant star is quite similar to some test in an accelerator (or more accurately dissimilar in understood ways) what they are really saying is that it’s similar to the distant situation in the relevant ways. Our understanding of virtually all processes we haven’t directly tested is based on the assumption that our current theories aren’t just a really good fit to the data in a particular range but actually hit on deep invariants about the rules of nature. 

  2. More accurately it lets you dial in any number with a finite decimal expansion. You can choose the length of the decimal expansion but it takes longer to dial in .234823482348 than it does to dial in .234. 

  3. For each input value there is a ‘true’ output value and the observed outputs are normally distributed around the true value. 

  4. You test the same input value many times average the observed outputs and compare to your prediction. 

  5. Formally if K(u) is one complexity measure and C(u) is another then there is a constant D such that K(u) < C(u) + D and K(u)+D >C(u). Thus the only cases where C and K will disagree about which theory is more complex is when it’s a sufficiently close call. 

Drugs And Intuitions

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?


  1. I won’t say in a new way since I bet someone has raised this point before in some obscure journal article I’ve never read. 

  2. Otherwise knows as E or ecstasy. Users of this drug usually experience an extremely heightened sense of empathy and have feelings of love for almost anything. 

  3. Yes, this is quite plausible, even likely. 

  4. One could have the interesting view that certain sorts of intuitions just aren’t (physically? metaphysically?) possible. For instance you might believe there just isn’t any experience of feeling that torture and murder are morally obligatory. Or you might adopt some externalist framework that simply refuses to count any local state of affairs as being this sort of intuition. However, given that we often encounter people with pretty fucked up moral intuitions this response seems unmotivated and implausible. Besides, once you admit that people apparently have false moral intuitions you still have the same problem as to when an apparent moral intuition should be taken seriously. 

  5. The military provides bomber pilots with small doses of amphetamine because they have seen that sleepy pilots are less mentally capable than those on amphetamines. 

  6. Note that just because a drug interferes with one sort of perception or ability doesn’t mean it doesn’t improve others so we can’t bootstrap from the fact that altered states are often seen to produce less accurate perceptual reports to the conclusion that they produce less accurate moral intuitions. Besides, even if you reject this point it seems likely that sufficiently targeted brain interventions could avoid degrading perception or even improve it while creating whatever moral intuition you desire. 

  7. Say the case where something moves with great rapidity to always stay in our blind spot. I suspect there are even better examples out there where evolution has actually ‘tried’ to trick us into perceiving false things (maybe about the amount of suffering felt by our enemies or the sexiness of our sexual partners in certain circumstances). 

Science Journalists: Does The Public Even Have A Chance?

I’m listening to an interview on KQED’s forum (local NPR station’s call in show) with science journalist Timothy Ferris. Apparently he just wrote a new book about amateur astronomy which I don’t doubt is well researched and accurate but as people called in he apparently felt the need to opine on time travel and quantum mechanics ‘scientific’ matters and I was appalled. Since he’s also written a book called “The Whole Shebang” his misleading answers can’t be explained as mere failure to research. However, I’m inclined to think that in this case the fault lies with the physicists themselves (either for doing bad philosophy or using mislead metaphors.

It started with someone bringing up the Fermi paradox (why haven’t advanced alien civilizations contacted us yet). The host then steered the question towards whether this was an argument against time travel as well (failure to see time travelers). Timothy Ferris replied that he didn’t find it very compelling because he expects time will be lack a deck of cards so that if you go back in time of forward in time you end up in one of many possible pasts or many possible futures. While he admitted it was just his expectation he clearly conveyed the sense that it was a possibility that experts would take seriously.

I happen to think the very idea of something being time travel requires that we go back into the past not merely enter some universe that looks like the past.1 However, let’s set this point aside. I suspect the journalist was referencing some approaches to quantum mechanics that go by the name of sum over histories or multiple histories. Possibly he meant to refer to many minds or many worlds theories. The problem is that traveling to an ‘alternate’ past doesn’t even make sense in any of them. Supposing it was true and even meaningful that we have multiple histories in this QM sense we would have multiple presents as well. What the hell would it even mean for a person, who is really a superposition, to visit one component of a prior superposition? Pure many worlds theories only really make sense2 if we understand them as collapsing down to a many mind’s theory and it certainly isn’t clear what it would mean for a mind that rides atop the superposition to time travel by itself, certainly not in the sense of some dude from the future appearing.

That’s confused and I was annoyed that he said it with such apparent authority but what really got my goat was when he talked about how interesting it would be if we ended up with quantum computers since we couldn’t explain their processing power with just one universe and would have to say that they use other universes to do their computations. This is just a lie that is being pushed on the public. The fundamental laws of nature could just offer us an oracle that computer anything we wanted as fast as we want. For all we know there is some special experiment we can do that reveals the true bits of 0′ (the set of the halting problem). Worse this is certainly not anything scientists have or can test. It is purely unjustified bad philosophical speculation that misleads the public.

I’m not sure whether to be mad at the people who promote this crap or applaud the physicists for great PR. Maybe we should just adopt this for math. Push the whole confusion about Godel’s theorem a bit more and try selling the Banach-Tarski paradox as a proof that “space is an illusion.”

Bit about quantum computer


  1. Merely assigning a prior t-coordinate to certain states don’t make them time travel. For instance if we invent FTL travel and by the standard Lorentz transform (special relativity) we find that are time coordinate has decreased but we are unable to ever affect events which causally affect us or even be present at them we haven’t engaged in time travel. This can happen without abandoning the Lorentz transform at all. It will just appear in some reference frames that effects precede their causes but you can just postulate an absolute reference frame where causes always precede effects if you want. 

  2. If you just say multiple worlds you haven’t actually said anything. You have just named the projections of the universe onto specific coordinates of some basis in your Hilbert space ‘universes’ but mere terminology can’t be an interpretation of quantum mechanics. 

Philosophical Naivety: Labeling and Substance

UPDATE: Fixed some wording, added clarification at the bottom.

Consider a philosophical debate between two materialists over whether a virus is alive. Philosopher A advances the hypothesis that any organism capable of manipulating it’s environment to copy itself is alive. Philosopher B counters that Shakespeare’s “Macbeth” has this property as it’s induces people to produce reproductions of the work and instead argues that a being is alive only if it doesn’t require outside intervention to duplicate itself. Philosopher A counters with an example of a plant that humans have cultivated for long enough that it is now incapable of reproduction without intentional human intervention.

Now we can imagine this debate continuing as both philosophers refine their theories as to what constitutes life but no matter how long they argue in this fashion they can’t hope to reach any substantive conclusions. Why? Because they didn’t disagree about anything but word usage at the outset. As materialists they both reject the notion of some elan vital that we might add to our fundamental ontology to ‘explain’ what counts as alive and what doesn’t. As far as the virus goes they would both accept the biologists explanation as to how it reproduced they only disagree on how to label this event. Now there are certainly times it makes sense to argue about labeling but we naturally expect such debates to take a very different form. In particular when people merely disagree about how we should term something they will usually sidestep the debate eventually and simply qualify their wording. When people disagree on how in fact people are inclined to use words they tend to either shrug and move on or to start pulling out real empirical data1. In no case where people understand themselves to be merely debating a matter of labeling would we expect them to argue about the issue for decades in reputable journals with no hint that they view themselves as debating some empirical fact about usage or pragmatic fact about what would make for good usage.

Unfortunately there seems to be no shortage of arguments in philosophy that can’t be explained as anything other than a confusion of a question of terminology as a substantive question2. There are a host of examples but let me give a couple

Is formalism or fictionalism the right philosophy of math?

Now there is (arguably) a genuine substantive question as to whether mathematical Platonism is true. Is there or is there not a realm of platonic objects out there? And if you believe in a substantive notion of reference (reference facts aren’t ontologically reducible to physical/mental facts) whether or not that is what we refer to with mathematical talk. However, when we get down to debates between functionalism and fictionalism things suddenly become much more unclear.

Neither theory disagrees about what in fact mathematicians assert nor makes any fundamentally different metaphysical suppositions. Nor do the two theories compete on genuine empirical predictions. Neither theory attempts to best predict what in practice people will tend to assert about mathematics. So in what sense can there be said to be a substantive question at issue here? And if not why believe these two interpretations are in opposition to each other?.

The “Proper” Conception of Evidential Support

In formal epistemology there seems to be a great deal of ink spilt arguing over what the ‘proper’ notion of confirmation is. Now Brandon Fitelson has always (at least to my eyes) pushed for a ‘there is no fact of the matter’ resolution to many debates in this area so I wouldn’t accuse him of making this sort of mistake but this paper of his gives a nice picture of what sorts of arguments are at play in the area. In particular there seems to be a long lasting dispute as to what the ‘right’ notion of confirmation turns out to be. Is it a three place relation between evidence, theory 1 and theory 2 or is it a two place relationship between evidence and a hypothesis?

Now I would be most surprised if anyone in this debate thought confirmation was an substantive notion (but I’ve been wrong about this sort of thing before), that is that when we assert that evidence E favors hypothesis H we aren’t just asserting some fact about probabilities, models or events but actually claiming that there is some special ‘confirmation’ property in our ontology that adheres to that particular relation but not to others that we might have chosen instead to term confirmation and that. Yet if we aren’t being ontologically liberal like this it would seem that all this debate about what is the ‘right’ notion of confirmation seems silly. We can all agree on the formal consequences of each notion and just set aside the contentious terminological question3.

Is Welfare Desire Satsifaction or Utility Maximization

I mention this because it was the argument that first made me realize that many of these debates couldn’t be substantive. While many people want to add an extra ontological fact to explain morality few people are inclined to indiscriminately add ontological entities for subsidiary moral concepts like welfare yet they are perfectly happy to debate the issue as if it were substantive.

In particular many people argue about whether we maximize welfare by maximizing utility or by maximizing desire satisfaction (or something else) as if it was a separate question we resolve prior to figuring out what is morally good. However, short of proposing a new fundamental property or relation it would seem that the debate over what increases someone’s welfare is merely a terminological question.

Kripke’s Causal Theory of Reference for naturalists

I debated about including this one since some people who buy into Kripke’s theory believe it as a genuine substantial claim. That is they add extra fundamental objects to their ontology (references, meanings etc..) and make the substantial claim that somehow our intuitive explanations of words in terms of other words track these objects and that as a real ontological fact it turns out that the reference of our word is determined by it’s causal history.

However, many of the people who take these theories seriously would call themselves naturalists or physicalists and would balk at the suggestion that by endorsing Kripke’s theory they were making grandiose metaphysical claims that couldn’t possibly be explained in terms of anything physics could in principle ever discover. Presumably as a physicalist one should accept the fact that there is nothing more to speech acts than certain configurations of matter and that there is no free floating metaphysical object ‘the reference’ that exists over and above the configuration of matter. As I’ve argued before it’s absurd for a good naturalist/physicalist to have a horse in the internalist/externalist debate except insofar as one turns out to be a genuinely better empirical predictor of future events.

My thesis is that there is a strong bias towards taking mere disputes about terminology and assuming that they are substantive. Not only is it a tempting fallacy to fall into on it’s own but it also creates for a much more interesting seeming discussion. It seems much more significant to say that one is figuring out the nature of life than to admit one is merely debating what we should call “life.” In any case whatever the reason it seems that this is a common fallacy that I see in philosophical discourse and one we should guard against. There are more than enough substantive arguments to keep philosophers busy and some of these non-substantive arguments are worth having as well but which arguments we take to be persuasive will be very different once we understand it is merely a terminological debate. Importantly once we accept that many of our debates are merely terminological we can no longer assume that there is any tension between things like internalism and externalism or different measures of confirmation.

As an aside I think this is in some sense the issue between Carnap and Quine over the nature of analyticity but that’s something for another post.

CLARIFICATION: I don’t want to claim that these debates couldn’t be rendered substantive. Really all I want to claim is that they are not naively substantive questions so using a standard of argumentation suited to this assumption is in error. I don’t mean to say that we need to abandon these questions only that we should figure out what we are trying to say and what it would take to establish our claim before we try to argue for one side or another.

Also I’m not convinced that any particular philosopher is making this error. It often seems that when I talk to any given philosopher about the matter they have some complex alternative interpretation of the claims at issue that either recognizes them as not substantive or renders them so through some non-obvious interpretation. It’s entirely possible that this is merely a process error but at the very least something is wrong when people adopt the form of a substantive argument for notions that don’t seem like they could be substantive without giving an indication as to what way it is (non-obviously) substantive (least different people think they are debating different questions). What I really want to do hear is not so much to advance my particular theory as to what is going wrong but to call attention to the fact that something seems really out of wack (or have someone give me a satisfactory explanation as to why it is not).


  1. Even when they are debating on some sort of idealized limit of what people would say given better knowledge we would still expect arguments of the form: surveys show that when people are told how a virus reproduces they are no longer willing to call it life. 

  2. I would like to define a substantive question as one that involves a disagreement as to fundamental objects in one’s ontology (understood to include fundamental relations and properties of these objects) and a question of terminology to be one where both parties would agree on every description and question phrased in terms of fundamental objects in their shared ontology but nevertheless disagree about the matter. However, this is likely to be controversial and I don’t need it for my claim. 

  3. Yes, there has been some interesting work on what sort of confirmation measure people actually employ but from the form of argument employed it seems clear that this debate is not primarily an empirical effort to create a predictive theory of how people actually judge confirmation. If so being simple and accurate wouldn’t be so important. 

If Saddam Can Do It Why Can’t We?

This is a quesiton that has been bothering me for awhile so you’ll have to excuse me if I’ve already said this but why can’t we keep peace in Iraq like Saddam did?. Now obviously the answer seems to be that we choose not to do so, probably if we tortured innocent people, rewarded corrupt officials who repressed their people for us and otherwise behaved like dictators do all over the world we could oppress the Iraqi people just like Saddam managed to do. The question I really want to ask is whether it’s reasonable for us to refuse to behave like Saddam.

In particular many liberal’s beliefs about Iraq consist of the following two views:

  • Invading Iraq was a horrible mistake that made the average Iraqi much worse off than they were under Saddam, often with the clear implication that a civil war or some other sort of massive bloodshed is inevitable.
  • If we could do something for the Iraqis we should but we can’t so we should just leave now.

I realize this doesn’t summarize all liberal’s beliefs about the war (certainly not mine). Some people believe (unreasonably IMO) that things will get much better once we leave and there might be some who even believe the Iraqis are better off now than they were under Saddam but I get the sense that the two views I summarized represent at least a significant percentage of mainstream liberals.

Don’t they entail that we should stay in Iraq but just clamp down just like Saddam did? For those of you who doubt we could do this all we would need to do is pick some local strongman and use our troops as muscle to help him establish himself as Saddam 2. Heck, maybe we could even keep our hands clean by just giving him implicit support and training his forces.

So why shouldn’t we kill a few innocent people now to save many more from a potential civil war? Or was the initial invasion actually a good thing?

Are We Living In A Computer Simulation?

Philosophers and stoned college students have long been intrigued by the idea that we could be living in some kind of simulation but I was surprised to see this idea mentioned in the New York Times 1. The NYT article summarizes this paper by philosopher Nick Bostrom who has also created a webpage with links to background reading, depictions of simulation scenarios in the media2 and even someone’s wiki about ‘simulism’3. The paper, while interesting and notable for getting into the New York Times, doesn’t say anything really new. It merely fleshes out the argument that if we believe that simulated individuals would have real experiences and that it is likely that humans will create many simulations of humanities past then you should assign a high probability to the proposition that you are actually being simulated.

While my intuition is that the idea behind this argument is correct I think the argument Professor Bostrom gives isn’t quite right. In particular the focus on what human civilizations are likely to do and ancestor simulation seems all wrong. There is no reason why totally alien beings could not simulate people nor to believe that our simulated universe resembles the real one in which the simulation is running much less that we are an earlier stage of the simulators history. Later I might think about how to fix this point but what made me want to write this post was the comment in the NYT that you could get out of the argument by either denying strong AI (a simulation wouldn’t be conscious) or by assigning a low probability to the chances that human beings will progress far enough to run such simulations.

This reminded me of the post I wrote a year ago about Sleeping Beauty in The Matrix arguing that a widely accepted solution to the sleeping beauty problem also implied we should believe the universe creates infinitely many individuals with the same memories and experiences as we have. Of course intuitively I think the conclusion of this argument is total crap but it’s tough to figure out why it’s wrong4. In short I think there is something very subtle going on in these sort of arguments that I don’t yet understand. If I ever figure it out I will post but until then I’m remaining skeptical.


  1. Thanks to the berkeley philgrads list for the pointer. 

  2. Even mentions my favorite book, Permutation City. I wonder if this book influenced him at all in thinking there was interesting philosophy to be done here. 

  3. I don’t have high hope for this since it is open to edits by the general public without an obvious standard like that possessed by an encyclopedia but it’s kinda nifty that it’s out there. 

  4. One new thought is that if I worked everything out in experience moments, i.e., pretend that at each waking you are a randomly chosen experience from the pool of total experiences. While this might solve the problem I posed since repeating the whole universe doesn’t change the proportion of experiences in some state it might also suggest that you should believe everyone else is a zombie. I need to think more about it. 

Tarski’s Definition of Truth

In an earlier post post I reviewed the mathematical significance of Tarski’s definition of truth and promised that I would explain why it is philosophically useless in a later post. I wasn’t sure anyone was interested and never got around to making that post but thanks to a comment I’ve finally gotten around to this post.

Briefly Tarski’s ‘defines’ truth by endorsing the following scheme (called the T-schema) for every sentence S:

‘S is true’ if and only if S

To take the canonical example:

“‘Snow is white’ is true” if and only if ‘Snow is white’

Now I don’t dispute that this scheme indeed holds (perhaps even necessarily) for the concept truth. I’m even willing to grant that this scheme may ‘define’ truth in some sense but what I dispute is that it tells us anything significant about truth.

Although we normally expect a definition to explain1 the concept in question not all definitions do so. For instance consider the definition of a ‘good action’ as “an action one morally ought to take.” While such a definition might explain the term ‘good action’ to someone who didn’t speak the language or help organize a philosophical theory in no way could it be said to explain what a good action was or give us a grip on the nature of morality. That is the definition merely reveals trivial linguistic connections between words that all make use of the same underlying opaque concept.

Tarski’s definition of truth is just the same. Sure if one didn’t know how to translate the English word ‘true’ into German communicating the T-schema in English could help your listener realize that ‘wahr’ was the correct translation. However, the T-schema only manages this by bootstrapping off the fact that your listener already understands assertability in English. In other words all the T-schema expresses is the connection between the predicate ‘true’ and assertability. In order to find the fact that “‘Snow is white’ is true” if and only if ‘Snow is white’ enlightening you must already understand what it means for snow to be white. If you don’t see this just imagine a linguistic practice where uttering ‘Snow is white’ conveyed your disbelief in the whiteness of snow. In that case the the word defined by the T-schema would have the same meaning as our word ‘false’.

When philosophers ask “What is truth?” they don’t want to know when they should term a sentence ‘true’ supposing they already know when to endorse it as fact. Rather they want to know what it means to assert something as fact, e.g., what is the relationship between ‘Snow is white’ and the external world. Tarski’s ‘definition’ of truth does nothing to explain truth in this sense, it is up to other theories like the correspondence theory of truth to answer this question. The T-schema (in a philosophical context) only illustrates the obvious and trivial relationship between asserting a sentence and asserting that sentence is true. As I outlined in my previous post on the subject Tarski’s definition of truth is a substantial mathematical contribution but it just doesn’t cut much philosophical ice.

Note that nothing I’ve said here conflicts with the deflationist position that the T-schema is the only thing that can be cogently said about truth. I actually find this position quite appealing but the substance of this view is not that the T-schema says something substantial about truth but that there isn’t anything substantial to say about truth. Intuitively this seems right because you must already understand what it means to assert things to even make sense of any other proposal but I haven’t thought about it enough to be totally convinced.


  1. I’m using explain here in a totally informal fashion, i.e., a definition explains the concept if it satisfies philosophical curiosity about what it means. I don’t mean to imply any connection with the idea of explanation from philosophy of science. 

Tarski's Definition of Truth:

Content Externalism: Not Even Wrong

This is still a bit rough around the edges but I wanted to finally get this argument out there.

There are two possible views one might have about content (mental, linguistic or whatever). One view holds that there are certain events/relations/objects that intrinsically have certain content. That is what makes certain objects/states express content is a brute ontological fact. Searle’s belief that certain sorts of experiences just come with satisfaction conditions is a good example of this view. At the most basic level some components of the experience posses content like properties directly not as a consequence of any other facts about them. Alternatively you might not add content to your fundamental ontology and instead try and layer it on afterwards. For instance any attempt to define content in terms of counterfactual dispositions or other non-content bearing property. Let us call the former view content non-reductionism (CNR) and the later view content reductionism (CR). Note that the CR/CNR distinction is almost exactly analogous to the debate about ontological reducibility/irreducibility for experiences.

Generally any physicalist will hold CR as they obviously will be reluctant to add content to their fundamental ontology. While not logically required anyone who believes in content externalsim (e.g, supporters of the causal theory of reference) or is otherwise a proponent of broad mental content will endorse CR. Though some philosopher might endorse a crazy view like the extended mind hypothesis and thus reasonably hold both CNR and externalism it is a very rare and extreme view. The original and primary aim of most externalist theories is exactly to explain what gives rise to content they tend to be an alternative to views which hold that content is a fundamental constituent of reality.

In short most popular modern theories of content (Searle excepted) and almost all proponents of externalist theories of meaning endorse CR. This is particularly ironic as CR is incompatible with there being any fact of the matter about content externalism or a substantive dispute between internalism and externalism. Ultimately CR forces one to view content as a mere convenient approximation, much like classical physics and the supposed content it talks about is, like the rigid body, merely a useful idealization.

By definition content is not a part of the fundamental ontology under CR. Thus any statements about content are either fictional/formal (like mathematical statements about ideal objects) or reduce to a claim about objects in the fundamental ontology. Assuming that content claims aren’t totally formal then any physicalist must believe that claims about content are really heavily disguised claims about physical events. For instance the Kripke causal theory of reference must be interpreted as a (very high level) statement about the behavior of point particles (or strings or whatever). Already this should give one reason to doubt the more categorical claims about content as almost always high level approximate theories have exceptions.

In such a situation what it is for some theory of content, like Kripke’s causal theory of reference, to be ‘correct’ is simply to make accurate predictions. Since none of these theories aspire to give exact predictions about fundamental particle we can only evaluate it’s virtue as a convenient approximation as we do with classical mechanics. For the physicalist content externalism is only as good as the physical predictions it makes. In other words Kripke’s theory of reference is (approximately) ‘true’ if it gives accurate predictions of when people say, “Ohh yah he was referring to the such and such Socrates,” plus similar reactions.

Understood in this fashion we have no good evidence for content externalism. I tend to think our best predictive theory is the semi-internalist fold theory. But regardless of where you think the evidence lies the best theory of content would be an empirical matter to be studied by psychologists/anthropologists/social scientists. It doesn’t even make sense to employ the sorts of thought experiments about twin earth commonly used to argue for content externalism since the possibility that content externalism is literally true isn’t even on the table. Besides these thought experiments would now come out against content externalism. For instance it’s absurd to make the predictive claim that people wouldn’t (eventually) respond to swamp man as if he really was referring (even with words he has never heard).

Now I expect a few objections at this point. One might claim that content externalism is an idealization and these thought experiments shows the internal coherency of the idealization. However, once we know a theory (like classical mechanics) to be literally false purely theoretical virtue takes a back seat to pragmatic value and the theory fails in it’s original intent either way. Also one might try and claim that content externalism was merely a definition of reference, i.e., saying it is a fully formal theory. Yet if so this whole area of philosophy is not only misdirected but actually misleading. Content externalism would then be a pretty uninteresting branch of mathematics with fancy names that tricked us into thinking it was saying something about pre-theoretical notions of content or meaning.

The argument goes through just as effectively only assuming CR rather than full on physicalism. It doesn’t matter whether we have to reduce claims about content to fully physical properties or to some other (non-intrinsically contentful) set of properties. In either case it just doesn’t make any sense to talk about theories like content externalism being ‘true’ in any sense other than an approximate or trivial one. They certainly aren’t saying what they intuitively claim (there are actual states that have content prior to the theory and the theory describes how that content works).

The upshot of all this is that there are pretty much three choices we can take as philosophers when dealing with content.

1) Give up Kripke and Davidson and (like Searle) accept that content is really a basic constituent of reality.

2) Give up the idea of content as anything but a folk concept and leave it to the scientists to generate/test theories about how we actually assesses content.

3) Accept that we can only give approximate predictive type theories and try to come up with a simple theory describing actual human/societal norms about assigning content. Effectively we would be doing much the same thing that people do when they compile the rules of grammar. There is nothing ‘true’ or deep about the rules of grammar but a precise agreed upon statement can be helpful as might also a catalog of the societal norms about ascribing content. This too might require experiments.

Humean Causation and Strong AI

So discussing one of my favorite books (Permutation City by Greg Egan) it dawned on me how to formulate a (limited) form of an argument I’ve long found convincing. I will, of course, assume that there is an objective fact about whether certain items have experiences and that people do and tables do not, i.e., rejecting Panpsychism.

In any case take the (far too) widely assumed thesis of strong AI, namely that any two processes that execute the same calculations will have the same experiences. For instance any computer that simulated the human brain would have all the same experiences as that person. Note that this is much stronger than merely saying we could build some machine that simulated the human brain and had the same experiences as it tells us that it doesn’t matter how we simulate it.

Now in order for this thesis to make sense we must have some notion of when a certain physical device implements a given calculation. Of course the natural way to phrase this is in terms of some kind of counterfactuals. However, this means that we would need to buy into a substantive notion of physical cause. There would need to be an extra meta-physical entity that somehow makes one description of the actual events in the universe the ‘true’ laws that really support counterfactuals while other predictively equivalent ones are wrong. Note that being a Lewis style realist about possible worlds is not sufficient either as you would need to believe that the closeness relation was somehow real/had metaphysical backup as well.

In fact if we are Humans about causation it seems that there is no hope for us. Since there is no (objectively) privileged statement of the laws we can transform any actual result into a computation. If we want to conclude that the decay of an atom implements a certain calculation we just decide what the output of the computation should be (say 1) and pick an equivalent (in our world) formulation of the physical laws that says (assuming the atom did decay) the atom decays if and only if the output of the computation is a 1. Obviously if we want to break up some complex computation into many small pieces we surely can. In particular we can interpret the random thermal motion of a table to be the simulation of a brain.

Now perhaps you will try to object that simple descriptions of the laws are somehow privileged. Even if so it seems you still need some fact which makes them objectively privileged. If all being simple amounts to is that human beings take a certain attitude toward them you haven’t gotten very far. It would appear that the very intuitions that motivate the strong AI view, namely that there isn’t extra spooky non-physical facts that determine what events cause experiences, is undermined as the very position sees to require we have these non-physical facts about what the ‘right’ way to write the physical laws is.

Probably this argument has been made in some form before but it occurred to me today and I’m stalling on my math.

Random Moral Intuition

What follows is a vague explanation of why I think utilitarianism and other simple moral theories that clash with our intuitions are the best moral theories.

Compare the following situations:

Case 1:

A mother of Siamese twins is dedicated to seeing that they have the chance to live a normal life. When doctors in the US refuse to attempt separation surgery because they think the chance of success is too low this mother flies them to a country where they will attempt the operation. If asked she defends her choice by saying, “Any chance, no matter how small, of giving my kids a normal life is worth it.”

It’s my intuition that most people wouldn’t hold this person morally culpable if their children end up dieing. Especially if the mother was a former Siamese twin herself who has strong feelings about how bad it is to grow up that way.

Case 2:

Same situation except in this case the mother can’t find any doctor willing to perform the surgery (the babies only have one hear) so the mother carefully researches painless ways to induce death and eventually gives the babies an overdose of Valium and morphine killing them. Here she defends her actions by saying that her kids are better off dead than growing up as conjoined twins.

It is my intuition that most people would find the mother to be morally blameworthy in the second situation, no matter how genuienly she believes she is doing a kindness. Yet these two reactions seem impossible to reconcile in any plausible (consequentialist) moral theory that tries to only tweak our moral intuitions.

What seems odd about the situation is that standard (my intuition is that case 2 is fine) intuitions are apparently drasticly discontinuous in this case (I’m sure there are better standard examples that illustrate this better). So long as their is a realistic chance of successfully separating the children it doesn’t matter how small this chance turns out to be. Yet any rational individual who prefers any wager between S and D to U, no matter how bad the odds for S must prefer D to U. Surely it can’t be right that taking every instance of the wager between living separated and dieing is morally acceptable but that actually taking the straight out trade between death and an unsuccessful operation is a huge moral harm.

Of course people are likely to object that the ‘realistic’ requirement effectively functions as a bound on how bad a wager you can take. Perhaps it does but not in a way that is particularly useful. For starters this realistic requirement doesn’t seem sensitive to the badness of the condition being avoided. If we make the lives of the Siamese twins 10 times worse the realistic chance threshold doesn’t seem to shift. So long as the act seems like a plausible attempt to separate the children people are okay with it but as soon as it is a clear preference for death rather than this sort of life people reject it. Worse, the realistic requirement doesn’t seem to track real probability. Even if we had a statistician come on TV and explain that in reality the chances for success were astronomically low so long as one of the common cognitive biases we have in evaluating probability made it feel plausible that the operation might be a success I suspect people would still be okay with the choice.

While it’s not a convincing argument these points strongly suggest that what matters is the mother’s intention rather than anything about the actual chances for success or failure that our moral intuitions are tracking. So long as the mother is intending to take a big risk with her children’s lives so they can have a brighter future we are okay with it but once it becomes clear the mother prefers her children to die we reject her actions. Already this seems troubling, how can it be morally acceptable for the mother to have the intention to take any bet of this form no matter how bad but not to accept the rational consequence of these beliefs? Even taking the ‘realistic’ restriction seriously this means the mother is implicitly valuing death as only a slightly worse consequence than living with the disability. But then what happens if her next pregnancy results in children who face a life that is significantly more horrible than these children? Surely we can’t combine the acceptable belief about the first children, with a fact about how much worse the lives of her new children will be to get the ‘unacceptable’ conclusion that she should kill these children.

Now while these intuitions don’t seem to make any sense as serious moral considerations (even in a deontic sense as they seem to punish rationality) they make perfect sense as applied social rules. As a pragmatic manner we aren’t going to be able to agree on risks and harms well enough to second guess the trade offs people choose. However, there is a strong need to prevent people from doing dastardly things under the guise of moral tradeoffs. We don’t want people to get away with putting their aged rich father down when he is unconscious with probably correctable problem on the grounds that any chance of brain damage is worse than death.

If this was an isolated example that would be one thing but this seems to be characteristic of our moral intuitions. Our intuitions just don’t seem to make sense as guides to abstract moral rules, rather they are pretty clearly rules of thumb that when applied in common situations give good results. The upshot of this is that it seems deeply mistaken to try to closely track these intuitions in developing our moral theory. Rather then trying to avoid clashes between our moral theories and intuitions in unlikely cases (killing depressed people on isolated dessert islands) we should be trying to come up with the moral theory with the best theoretical virtues (simplicity etc..) that explains what our moral intuitions have in common when applied in standard circumstances.

In other words we should be looking at very simple theories (like utilitarianism) that capture our intuitions at an extreme level of abstraction (don’t hurt people) rather than trying to closely track each twist and turn of our intuitions. The fact that our theory disagrees with intuitions in uncommon cases is really no problem at all. There was no hope that our moral intuitions could be a close guide to any ‘real’ theory so the fact that our theory radically disagrees with our intuitions in uncommon situations isn’t a failure at all. In particular it seems deeply wrong to twist our theories like Rawls does to make sure they don’t disagree too much with intuition. The explanation that perhaps what morality is about is making the best selfish decision if you were to be randomly assigned to be some individual in society is a good start but we should then take that theory and see where it goes (I think it implies utilitarianism) not try to back fit it to our intuitions so it comes up with the ‘right’ answers.