Straight from Wikipedia.

I just had to stare at this a while.  We can have papers published about this, we really ought to be able to get papers published about Friendly AI subproblems.

My favorite part is at the very end.

Trivialism is the theory that every proposition is true. A consequence of trivialism is that all statements, including all contradictions of the form "p and not p" (that something both 'is' and 'isn't' at the same time), are true.[1]

[edit]See also


  1. ^ Graham Priest; John Woods (2007). "Paraconsistency and Dialetheism"The Many Valued and Nonmonotonic Turn in Logic. Elsevier. p. 131. ISBN 978-0-444-51623-7.

[edit]Further reading

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Challenge: Now find a trivialist philosopher who disagrees with your criticism.

What criticism?

The incredulous stare?

I find that one particularly hard to argue with.
I was being serious -- I can't tell what that stare means. The explicit claim, "FAI research is more inherently valuable than trivialism research," is clear, but that's not a criticism of trivialism. As far as I can tell, EY believes many serious research fields are less valuable than FAI research.
The primary statement of trivialism, as I understand it: "(X and ¬X) for any possible value of X Therefore, P(X|A) = P(¬X|A) = 1. Therefore, for any evidence A, Value of Information = 0." Personally, I think they have successfully found the ideal philosophy of perfect emptiness. [Insert disdainful status signal]
Exactly! Status signals aren't valid arguments!
I agree. I think this was obvious, but I'm also not quite clear on what the real criticism is. It doesn't seem like trivialism is useful at all, but usefulness is not correlated to truth according to the priors of proponents of trivialism (or at least, I expect that to be true). I just accept that the hypothesis does not match the evidence according to my own models and current model-forming strategies (some of which I was presumably born with and are there because ancestors which happened to have those traits had more children) and that as such should be discarded. It also doesn't produce any value within my best estimate of my utility system, and I attribute utility to a belief or theory producing value in said system... so we're back to "This is ridiculous" full circle.
It isn't practically useful, no. But from a politico-philosophical standpoint, if dialetheism can't distinguish itself from trivialism, nobody will bother to study it. By analogy, a running joke in some mathematics circles involves people studying Hoelder continuous functions with parameter greater than one. As it turns out, all such functions are constant. However, before one knows that fact, there is a very nice research program that can be run proving all sorts of interesting properties of such functions, e.g., they are all smooth (which would be unexpected to such a mathematician, as when the parameter is one they are not even differentiable everywhere). Such a research program is ultimately useless, but only after one knows the critical fact. As for the overwhelming amount of empirical evidence against trivialism, this is covered in the dissertation. However, a shorter argument one could give is that humanity will likely only ever "observe" the truth value of finitely many propositions. That subset is of measure zero in the set of all propositions, i.e., practically no evidence. Since trivialism necessarily rejects the law of non-contradiction, observing finitely many false sentences does not imply that all sentences are not true. For example, perhaps it's just much harder to "observe" that the sentences we've observed to be false are also true, as would be the case if, say, proving their truth required a proof of length 3^^^3.
Also: ¬(P(X|A) = P(¬X|A) = 1) Therefore, for any evidence A, Value of information > 0. Contradictions are not failure conditions in trivialsim.
I wasn't positing this as a failure condition within trivialism, but of trivialism. According to what I'm seeing here, a perfectly trivialist agent sees no difference between the truth of dying when shooting themselves in the head, the truth of not dying when shooting themselves in the head, and the truth of dying and not dying when being alive. No imaginable action can have any effect on the world, because everything is true, and so there's no real reason to do anything, including living. This too is true, as is the opposite, to said agent. Basically, a trivialist assigns the null hypothesis over whether to care or not about the universe and themselves? Everything is true, but that doesn't consist in a reason to not act? Everything is true when it lets you write a paper and get grant money, but otherwise some things can safely be considered false for the purposes of living a normal life? How convenient can question-begging get? Can I become a billionaire doing nothing but this? ("Yes, that's true." says the trivialist) The way I see it, trivialism rejects logic and any kind of possibly imaginable rule for the purposes of writing philosophy papers, but conveniently ignores itself whenever it's time to go home or eat or live a perfectly normal life just like they would if some possible things were actually false.
Lots of strawman in there- especially with the assumption that trivialism implies meta-trivialism. Doesn't the strict rationalist have trouble with the truth value of statements conditioned on false statements? You are looking for a philosophy which tells you what the indicated course of action is. That means that trivialism is poorly suited for you. You are looking for a philosophy because you want your philosophy to tell you what you should do. That means that trivialism is the perfect philosophy for you to practice. Trivialism is not nihilism, and only a perfect trivialist could believe that it was. As a final koan: Why are the characteristics of trivialism that you list negative? So what? Why does that matter?
Sorry, not my intention to strawman. It is alien to me. No. Not bayesians, at any rate. What's an "indicated" course of action? How is it different from "what you should do", below? What does trivialism predict? What does it tell us to do? Does trivialism let me predict anything more accurately than any other theory? A single instance of one thing that it would predict more accurately and/or reliably in reality than any other theory would make it instantly much less worthy of derision. At present, it is to me nothing more than a humorous thought experiment similar to "This sentence is false."
When you try to make predictions, use a philosophy that performs predictions well. Bayesian rationality provides many useful tools to determine what the expected results are, but no tools to determine which expected result to choose. Trivialism provides tools more well suited for deciding in the absence of information.
Whoa whoa whoa. Too much inferential distance. I don't even have the slightest remote idea of where to begin imagining how trivialism could possibly be used or imply anything even remotely like a tool for "choosing" anything. Is there a "Learn Trivialism the Hard Way" thing somewhere that would help me bridge the gap between "X is true for all X" and actually choosing an action, a belief, anything at all? I'm obviously not going to gain much just from the wikipedia page, and googling doesn't seem to provide anything useful either.
It is going to rain and it is not going to rain. Do you bring your umbrella? Personally, I am not a trivialist, because there are no arguments which convince me that trivialism is superior to the blended philosophy that I haphazardly adhere to. That could be because I don't understand it well enough to internalize it, or it could be because trivialism isn't a robust philosophy. Either way, as long as you are trying to use information to make informed choices, you aren't well served by trivialism. Trivialism is best used to make trivial choices; in pure trivialism all choices are trivial. If you believe that a choice is nontrivial, you are not trivialist.
Is it then strawman to say that a good trivialist sees no important distinction between the decision to jump off a cliff and the decision to not jump off a cliff? After all, it is true that they can fly and it is true that they cannot fly - and if I'm interpreting your umbrella example correctly, this should imply that they might as well act as if they did fly with certainty.
Is that line of though the absolute best line description of trivialism as you understand it? What the pure, complete trivialist decides does not have much bearing on what an outside rationalist observer observes. It is true that if the trivialist decides to jump off the cliff, they will not jump off the cliff. A hybrid trivialist rationalist might say "I can fly and I cannot fly. Since I can fly, I gain utility x from jumping off a cliff. Since I cannot fly, I gain negative utility y from jumping off of a cliff. My expected utility from jumping off of a cliff is x-y. This line of thought is neither pure trivialism nor pure rationalism.
Then one merely smiles back.

It's probably not a good idea to laugh at people until you've at least heard their arguments. It is at the very least very bad signaling for an intellectual community to dismiss a small body of work because a sentence on Wikipedia (source unknown) makes it sound silly.

Remember that LW sounds pretty silly on Rational Wiki.

I think Wikipedia's Trivialism page already contains a comprehensive list of its supporting arguments.
Here is the abstract for the dissertation linked on Wikipedia. It argues that it is impossible to reject trivialism, as there are no alternatives to trivialism. It furthermore argues that common refutations of trivialism are incorrect for various reasons. I'm not sure any of that refutes what you just said. The paper is offered freely on the page.
Yea. My personal guess would be that the people in question were never even exposed to a lot of hidden (correct) assumptions we have that makes it so obviously silly, like the nature of things like math, "statements" and "truth". EDIT:: I'm apparently not all here today and sprouting bull**, sorry.

You mean that the graduate student of the philosophy of logic doesn't know about things like math and theories of truth? That seems unlikely to me.

Adding to this, it seems more likely that they were exposed to critiques of those assumptions, and put more stock in those critiques than we do.

We can have papers published about this, we really ought to be able to get papers published about Friendly AI subproblems.

Are you implying that you are trying to get papers published about Friendly AI subproblems and having difficulty?

Pfft, I don't see what's so funny about the end. If it had been , alright, that would have been somewhat ironic at least, but )? Nobody was even arguing against that.

I saw "You can help Wikipedia by expanding it." as the amusing ending...

Trivialists are!
But they weren't. Trivialists certainly do assert that ) is true, and so is
A trivialist would insist that "Trivialists argue ) is false" is true. Believing that you're arguing something isn't quite the same as arguing something, but I wanted to point out that under trivialism, trivialists think they're arguing for and against all propositions simultaneously.

In college I was part of the cult of Alfred the Duck. It was a religion with five or so members, formed when our founder decided to take False as an axiom, and also drew a little picture of a duck. Using the holy T=F axiom, it's easy to prove that Alfred the Duck knows all and sees all, and that everything both exists and doesn't exist. It actually worked pretty well as a religion. (There was also something about welcoming alien invaders, but I think that was a different religion.)

That seems to be a practical accomplishment of trivialist philosophy.

Something like this?

To paraphrase something Eliezer said to me in person, "Here's one more thing philosophers have written more papers about than reflective decision theory."

I am a proponent of Wednesdayism. "Wednesdayism is the view that true is true and false is false except, crucially, on Wednesdays."

Is Wednesdayism true or false on Wednesdays?

Strict Wednesdayism is undefined on Wednesdays. Orthodox Wednesdayism is false on Wednesdays. Reformed Wednesdayism requires you to personally decide if it is true on Wednesdays.

False, but true on all the other days.
What does this imply for Last Wednesdayism?

The Kabay dissertation is interesting in a bizarre way.


My own view is that this argument is as convincing as an argument for any philosophically interesting position, and so should be taken seriously. Trivialism should not be treated as a special case in this regard. Philosophers have committed to claims on the basis of a lot less.

If you leave out the phrase "and so should be taken seriously", I'd agree with that.

It was definitely worth skimming through. Two... well, not really questions, but thoughts:

  1. How does trivialism differ from assuming the existence of a Tegmark IV universe?

  2. A spectral argument given in defense of trivialism in the dissertation runs like this:

a. Natural language is inconsistent.

b. Therefore, by explosion, every sentence in natural language is true.

c. Every classical proposition may be interpreted in natural language.

d. Therefore, classical logic is inconsistent.

The error in the argument is actually quite subtle!

Tegmark IV is the space of all computable mathematical structures. You can make true and false statements about this space, and there is nothing about it that implies a contradiction. You may think that any coherent empirical claim is true in Tegmark IV, in that anything we say about the world is true of some world. But being true in some world does not make it true in this world. If I say that the sky is green, I am implicitly referring to the sky that I experience, which is blue. That is, I am saying that the sky which is blue is green. So I'm contradicting myself, and the statement is false. You don't even need to think of alternate universes to reason through this. After all, some planet in our galaxy surely has a green sky. It all looks shaky, but most obviously, just because every classical proposition may be interpreted in natural language doesn't mean that every natural language proposition may be interpreted in classical logic. In particular, the aspects of natural language that make it inconsistent probably can't be translated into classical logic. After all, that's why we invented classical logic in the first place. Did these points come up in the dissertation?
From one of Tegmark's pop sci papers: Trivialism induces a mathematical structure, and so is contained in the level IV multiverse. I think there's some meta-level confusion in the rest of the first part of your comment. It's not clear to me how this claim affects the argument. Asserting the negation of the converse of (c) doesn't imply anything about (c). The argument is not central to the dissertation. He reports it from a trivialist to establish the existence of at least one trivialist.
Because even if we assume the existence of every mathematical structure, we are still assuming that they are coherent. Mind you, there are consistent models of some paraconsistent logic (even in set theory), but there is no model of the theory of all sentences. This is pretty standar model theory: the class of models of the total theory is empty (viceversa: the theory of the class of all models is empty). Anyway, assuming trivialism is uninteresting (as the name correctly imply ;)): we still can play a formal game that mimics the difference between truth and falsity.
I'm not sure why level IV would restrict itself to standard model theory. In a tri-valued logic (i.e., all propositions are either true, false, or both), there are non-trivial models of trivialism.
Trivialism would not respect Tegmark IV's subsections which comply with our model of logic.
I read this sentence differently than its author intended, I think:
It makes sense; as he lays out in the first section, it isn't clear why dialetheism is different from trivialism. If they weren't different, then a good part of his advisor's field would become trivial! Taking on a willing grad student to devote time to separating the two is just good politics.
Imagine all well-formed logical statements, stretching out in an infinite list. Each of these statements are to be marked "true" or "false." For each possible marking, there is a shortest set of rules that generates that marking. Those rules are "rules of logic" you'd be following if that was how all the statements were to be marked true or false. Trivialism is a particularly simple rule: "mark all true." Dialetheism points to a category of markings, where both A and not-A are true for some A - and thus points to a category of rules that generate such patterns.
This is one form of trivialism; the dissertation also uses it to mean something like "whatever marking you place on the list, every item is marked true (but also possibly marked something else)."
I wonder ... when he signed the declaration on page 4, what was he asserting?
Wow. I've actually used all but one of those arguments (the principle of sufficient reason one) as reductios against various things.

Trivialists think "Trivialists think trivialism is false" is true.

Trivialists think "Trivialists think "Trivialists think ... is true" is false" is true.

That must be a hoax. Tell me it's a hoax! [takes a look at the references] No, it isn't a hoax. What the ...

Unfortunately, that's just another canary. A daily reading of all the front-page "science news" articles (for, say, two weeks) should numb you enough through sheer numbers of ridiculously silly papers and experiments that stuff like this doesn't really surprise you anymore.

Graham Priest interview with Julia Galef and Massimo Pigliucci on paraconsitency and dialetheism:

Does anyone know if trivialism has to be interpreted as "every sentence is at least true" or as "every sentence is true and only true"?

Every sentence (or rather, proposition) is both true and false, since "false" is defined here to mean having a true negation (and all negations are established as being true.) So for P to be both true and false would be for both P and ~P to be true, or, deflatively, for it to obtain that P and ~P. If (alternatively) neither P nor ~P - as might sometimes be the case according to intuitionists - we would say that P is neither true nor false.
If false is defined as the property of having a true negation, than under trivialism there's no real semantic distinction between true and false, since there's no property that can distinguish between the set of true and false propositions. This is of course to be expected, but I was curious if trivialism could be interpreted as a system that poses significant distinctions of truth values: for example, one that postulates that some propositions can be true and false, but not necessarily all of them: some of them could just plainly be true. I know that such a system can be formally coherent (after all, there is one that is isomorphic to classical logic), but I'm interested if it has been used in that way. But this, I get, is not trivialism.
In that case it's not trivialism anymore, but there are nonclassical logics where some (but not all) propositions are true and false; indeed such things are considerably more popular than trivialism (for what I presume to be obvious reasons.) Graham Priest, for instance, is constantly pointing out that if you drop the principle of explosion it's very easy to have the Liar's Paradox be simultaneously true and false without implying that Socrates simultaneously is and isn't mortal. You get correctly, yes.

I think my brain just imploded.

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I don't think that you think that your brain just imploded.

sighs This is why, when one studies philosophy, one does well to pretty much ignore anyone who claims that the universe is completely knowable a priori.

In fact, given the number of sets of axioms from which one can derive statements, pretty much any argument that hinges primarily on a priori claims is probably mistaken. (Note: This is an a posteriori claim.)

May I add that a failure to ignore these people is a very bad sign for a student: no one (or at least no one significant) has ever claimed this!
Oh, and Plato.
Spinoza: His views are tricky, because of his particular brand of monism. You're right that we should generally take the 'Ethics' as a work of a priori reasoning, but nevertheless he considered our knowledge of the contents of nature to be empirical knowledge: in order to know that there is a knife on the table, my mind has to interact with the 'mind' of the knife, and this involves physical contact. Plato: The trouble with saying something like this about Plato is that he neither deployed the a priori/a posteriori distinction, nor had views similar to ours about knowledge. And he predates the very idea of deductive logic. For Plato, knowledge was distinct from 'correct opinion' in being unchangeable. This means that knowledge was necessarily not about nature. However, it doesn't follow from this that the knowledge is a priori. So in dialogues like the Meno or the Phaedo, Plato claims that we have access to knowledge of things like geometry through recollection. If we take him literally, then this could not be in any way a priori knowledge: recollection is firmly an experience (remember, 'a priori' doesn't refer to innate knowledge, or knowledge that is temporally prior to experience). There's plenty of room to take him less literally, of course.
Ah, but in the case of Spinoza, you can't get real 'empirical knowledge' because to get 'knowledge' of the knife on the table, you'd have to learn the entire causal history of the knife on the table. Otherwise, you don't have knowledge, you have something like an incomplete modification of an idea. So the only way he can have knowledge is a priori reasoning, which is why he relies so heavily on his axiomatic system. I'll grant you Plato did not use this distinction, but while recognition allows us to access knowledge, Plato does claim that we already "have it" in some sense. I suppose that makes it debatable whether or not the knowledge is truly a priori: generally we take ourselves to lack knowledge, rather than to have it and not recognize it. Still, if we run with that idea: I might not be remembering some detail at a given moment. My mom's hair-color, for instance. Nevertheless, we would say that I have knowledge of my mom's hair before I 'recollect' it. Similarly, if we have the knowledge before we have the experience that allows us to recollect the knowledge, that would make the knowledge itself a priori.
As to Spinoza, you make a good point, though using Spinoza's (or Plato's) refined sense of what 'knowledge' is as opposed to the everyday claims we would today call 'knowledge' (e.g. I know that the sky over Chicago is clear today) seems to me to go against the spirit of your initial complaint: neither Plato nor Spinoza thinks you can 'know everything about the universe a priori' in our sense of 'know'. If they do believe that, then it is because they have a much stricter understanding of what knowledge is. It's not as if they think they can deduce the existence of my pen from a priori axioms.
Point taken, but I would point out that both Plato and Spinoza think that our everyday claims about knowledge don't map onto reality, so they can't talk about what we 'know' in the everyday sense of 'know.' They don't think that is a valid way to talk about knowledge at all.
Kant claimed one could know most of the interesting things a priori, even if one couldn't know everything.
I don't think that's true. Much of the point of the first Critique was to vindicate experience as a source of knowledge, for which he thought he needed to appeal to certain synthetic a priori propositions (like causality). When we at LW appeal to causality as a necessary part of the map, but not necessarily a part of the territory, we are making a similar move. Kant was the great enemy of metaphysics. About morality, you're largely right, though a fair bulk of his writing on morality consists of discussions of social practices and law.