Things philosophers have debated
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
[edit]References
- ^ 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
- Paul Kabay (2008). "A defense of trivialism". PhD thesis, School of Philosophy, Anthropology, and Social Inquiry, The University of Melbourne.
- Paul Kabay (2010). On the Plenitude of Truth. A Defense of Trivialism. Lambert Academic Publishing. ISBN 978-3-8383-5102-5.
- Luis Estrada-González (2012) "Models of Possibilism and Trivialism", Logic and Logical Philosophy, Volume 21, 175–205
- Frederick Kroon (2004). "Realism and Dialetheism". In Graham Priest, J. C. Beall, and Bradley Armour-Garb. The Law of Non-Contradiction: New Philosophical Essays. Oxford University Press. ISBN 978-0-19-926517-6.
- Paul Kabay (2010). Interpreting the divyadhvani: On Why the Digambara Sect Is Right about the Nature of the Kevalin. The Australasian Philosophy of Religion Association Conference
- Bueno, O. V. (2007). "Troubles with Trivialism". Inquiry 50 (6): 655–667. doi:10.1080/00201740701698670.
- Priest, G. (2000). "Could everything be true?". Australasian Journal of Philosophy 78 (2): 189–195. doi:10.1080/00048400012349471.
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Comments (76)
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."
Then one merely smiles back.
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?
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.
To paraphrase something Eliezer said to me in person, "Here's one more thing philosophers have written more papers about than reflective decision theory."
Are you implying that you are trying to get papers published about Friendly AI subproblems and having difficulty?
The Kabay dissertation is interesting in a bizarre way.
Heh.
If you leave out the phrase "and so should be taken seriously", I'd agree with that.
I wonder ... when he signed the declaration on page 4, what was he asserting?
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)."
It was definitely worth skimming through. Two... well, not really questions, but thoughts:
How does trivialism differ from assuming the existence of a Tegmark IV universe?
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.
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.
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.
Graham Priest interview with Julia Galef and Massimo Pigliucci on paraconsitency and dialetheism:
http://rationallyspeaking.blogspot.de/2012/11/rationally-speaking-podcast-graham.html
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 Phys.org "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.
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?
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"?
Both.
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.