By the way, “It seems” and “arguably” seem a bit less defensive than “I think” (which is purely subjective). Arguably.
cubefox
Karma: 1,969
I hear a lot of scorn for the rationalist style where you caveat every sentence with “I think” or the like.
I think e.g. Eliezer (in the sequences) and Scott Alexander don’t hedge a lot, so this doesn’t necessarily seem like a rationalist style. I do it a lot though, but I fairly sure it makes readability worse.
We don’t need to shave ahead of time anyway (we can do it when the pandemic is already here), so it doesn’t compete with mental resources now.
Impressive write-up! As a follow-up question, what’s currently your favorite (hypothetical) explanation for the actual main cause of high obesity rates? Some environmental contaminant? Something else?
Yes, with Hilbert proof systems, since those have axioms / axiom schemata. (In natural deduction systems there are only inference rules like Modus ponens, no logical axioms.) But semantically, a “primitive” identity symbol is commonly already interpreted to be the real identity, which would imply the truth of all instances of those axiom schemes. Though syntactically, for the proof system, you indeed still need to handle equality in FOL, either with axioms (Hilbert) or special inference rules (natural deduction).
These syntactical rules are weaker in FOL however than the full (semantic) notion of identity. Because they only infer that all “identical” objects have all first-order definable predicates in common, which doesn’t cover all possible properties, and which holds also for weaker forms of equality (“first-order equivalence”).
Eliezer mentioned the predicate “has finitely many predecessors” as an example of a property that is only second-order definable. So two distinct objects could have all their first-order definable properties in common while not being identical. The first-order theory wouldn’t prove that they are different. The second-order definition of identity, on the other hand, ranges over all properties rather than over all first-order definable ones, so it captures real identity.
But I’m pretty sure all instances of the axiom schema
(for any FOL-definable predicate in our theory) are already implied if we, as is customary, assume as logic FOL+identity, i.e. first-order predicate logic with a primitive logical predicate for identity. So in that case we don’t need the axiom schema. (And in second and higher order logic we need neither an axiom schema nor a primitive relation, because in that case identity is already definable in pure logic, without any theory, so we have a logical identity relation without having it to add as a primitive.) If we just assume FOL alone, adding this axiom schema to a particular first-order theory makes sense, but I conjecture that it is not equivalent to full (primitive or second-order definable) identity, similar to how the axiom schema of induction is not equivalent to the induction axiom, which requires second-order logic.
I don’t know about category theory, but identity can’t be defined in first-order logic, so it is usually added as a primitive logical predicate to first-order logic. Adding infinite axiom schemas of the sort you showed above don’t qualify as a definition, which has to be a finite biconditional. But identity is definable in pure second-order logic. Using Leibniz’s law, one can define
Intuitively, and are defined identical iff they have all their properties in common. Formally, there is always a subset of the domain in the range of and which for any object contains only . This guarantees that the definition cannot accidentally identify different objects.
For instance, are the symbols “1” = “2″ in first order logic? Depends on the axioms!
Yes and that is because in predicate logic, different names (constant symbols) are allowed to refer to the same object or to different objects, while the same names always refer to the same object. This is similar to natural language where one thing can have multiple names. Frege (the guy who came up with modern predicate logic) has written about this in an 1892 paper:
Equality gives rise to challenging questions which are not altogether easy to answer. Is it a relation? A relation between objects, or between names or signs of objects? In my Begriffsschrift I assumed the latter. The reasons which seem to favour this are the following: a = a and a = b are obviously statements of differing cognitive value; a = a holds a priori and, according to Kant, is to be labelled analytic, while statements of the form a = b often contain very valuable extensions of our knowledge and cannot always be established a priori. The discovery that the rising sun is not new every morning, but always the same, was one of the most fertile astronomical discoveries. Even to-day the identification of a small planet or a comet is not always a matter of course. Now if we were to regard equality as a relation between that which the names
a' andb’ designate, it would seem that a = b could not differ from a = a (i.e. provided a = b is true). A relation would thereby be expressed of a thing to itself, and indeed one in which each thing stands to itself but to no other thing. What is intended to be said by a = b seems to be that the signs or namesa' andb’ designate the same thing, so that those signs themselves would be under discussion; a relation between them would be asserted. But this relation would hold between the names or signs only in so far as they named or designated something. It would be mediated by the connexion of each of the two signs with the same designated thing. But this is arbitrary. Nobody can be forbidden to use any arbitrarily producible event or object as a sign for something. In that case the sentence a = b would no longer refer to the subject matter, but only to its mode of designation; we would express no proper knowledge by its means. But in many cases this is just what we want to do. If the signa' is distinguished from the signb’ only as object (here, by means of its shape), not as sign (i.e. not by the manner in which it designates something), the cognitive value of a = a becomes essentially equal to that of a = b, provided a = b is true. A difference can arise only if the difference between the signs corresponds to a difference in the mode of presentation of that which is designated. Let a, b, c be the lines connecting the vertices of a triangle with the midpoints of the opposite sides. The point of intersection of a and b is then the same as the point of intersection of b and c. So we have different designations for the same point, and these names (point of intersection of a and b,'point of intersection of b and c’) likewise indicate the mode of presentation; and hence the statement contains actual knowledge.It is natural, now, to think of there being connected with a sign (name, combination of words, letter), besides that to which the sign refers, which may be called the reference of the sign, also what I should like to call the sense of the sign, wherein the mode of presentation is contained. In our example, accordingly, the reference of the expressions
the point of intersection of a and b' andthe point of intersection of b and c’ would be the same, but not their senses. The reference ofevening star' would be the same as that ofmorning star,′ but not the sense. (...)He argues that identity expressed between names is a relationship between their “modes of presentation” (senses/meanings) rather than between their names or reference object(s). This makes sense because different names can be synonymous or not, and only if they are we can infer equality, while in the latter case whether they are equal or unequal has to be established by other means.
Oh, apparently I misinterpreted the meaning of “bowing out”, as I’m not a native English speaker. Anyway, I just want to register my opinion that I thought the “not worth getting into?” react was good in itself.
Doesn’t “not worth getting into?” sound better than “bowing out”?
I’m probably also misunderstanding, but wouldn’t this predict that large production models prefer words starting with “a” and names starting with “I” (capital “i”)? Because these letters are, simultaneously, frequently-used words in English. Which makes it likely that the tokenizer includes the tokens ” a” and ” I” and that the model is incentivized to use them.
This is an excellent clarification of an important topic!
I also have noticed in the past his sometimes unusually hostile/gaslighting/uncharitable/unproductive war-of-attrition discussion style when he disagrees with someone, described here in detail by habryka. Including his aggressive/escalating voting behavior in simple one-to-one disagreements, also mentioned by habryka. (I also wondered whether sock puppet accounts or specific “voting friends” are involved, but as far as I see habryka didn’t mention these exist, which is some evidence that they don’t.) I have not seen anyone else act like that, so I don’t think this is a case of just “banning people who voice criticism”. There are countless people posting outspoken criticisms without remotely employing an unconstructive style like that.
Reading now that this has been going on for many years, including temporary bans, I believe this is a psychological property of his personality, and likely not something he can really control. Similar to how some people have a natural tendency to voice disagreements in friendly and productive manner, but the other way round.
To say that Eliezer is a moral realist is deeply, deeply misleading.
No, it is not at all misleading. He is quite explicit about that in the linked Arbital article. You might want to read it.
Eliezer’s ethical theories correspond to what most philosophers would identify as moral anti-realism (most likely as a form of ethical subjectivism, specifically).
They definitely would not. They would immediately qualify as moral realist. Helpfully, he makes that very clear:
Within the standard terminology of academic metaethics, “extrapolated volition” as a normative theory is:
Cognitivist. Normative propositions can be true or false. You can believe that something is right and be mistaken.
He explicitly classifies his theory as cognitivist theory, which means it ascribes truth values to ethical statements. Since it is a non-trivial cognitivist theory (it doesn’t make all ethical statements false, or all true, and your ethical beliefs can be mistaken, in contrast to subjectivism) it straightforwardly classifies as a “moral realist” theory in metaethics.
He does argue against moral internalism (the statement that having an ethical belief is inherently motivating) but this is not considered a requirement for moral realism. In fact, most moral realist theories are not moral internalist. His theory also implies moral naturalism, which is again common for moral realist theories (though not required). In summary, his theory not only qualifies as a moral realist theory, it does so straightforwardly. So yes, according to metaethical terminology, he is a moral realist, and not even an unusual one.
Additionally, he explicitly likens his theory to Frank Jackson’s Moral Functionalism (that is indeed very similar to his theory!), which is considered an uncontroversial case of a moral realist theory.
An illusion is perception not accurately representing external reality. So the perception by itself cannot be an illusion, since an illusion is a relation (mismatch) between perception and reality. The Müller-Lyer illusion is a mismatch between the perception “line A looks longer than line B” (which is true) and the state of affairs “line A is longer than line B” (which is false). The physical line on the paper is not longer, but it looks longer. The reason is that sense information is already preprocessed before it arrives in the part of the brain which creates a conscious perception. We don’t perceive the raw pixels, so to speak, but something that is enhanced in various ways, which leads to various optical illusions in edge scenarios.
I assume the minimum number was put into place in order to prevent another method of gaming the system.
I think it’s trainable mainly in the indirect sense: If someone has a lot of social grace, they can pull off things (e.g. a risque joke in front of a woman) that would be perceived as cringe or creepy in people with significantly less social grace. These latter people can become less cringe/creepy by learning not to attempt things that are beyond their social grace capabilities. (Which reduces their extraversion, in contrast to treating anxiety, which boosts extraversion.)
I think already children show significant differences in social grace. I remember a kid in elementary school who got bullied a lot because of his often obnoxious behavior. He had both very low social grace and very low social anxiety. I assume with time he learned to become less outgoing, because that wasn’t working in his favor. Outgoing behavior can be scaled down at will, but social grace can’t be easily scaled up. Even people who are good at social grace don’t explicitly know how to do it. It’s a form of nonverbal body/intonation language that seems to be largely innate and unconscious, perhaps controlled by an (phylogenetically) older part of the brain, e.g. the cerebellum rather than the cortex.
Of course that’s all anecdotal and speculation, but I would hypothesize that statistically the level of social grace of a person tends to stay largely the same over the course of their life. The main reason is that I think that lack of social grace is strongly related to ASD, which is relatively immutable. It seems people can’t change their natural “EQ” (which includes social grace) much beyond learning explicit rules about how to behave according to social norms, similar to how people can’t change their natural IQ much beyond acquiring more knowledge.
You might be surprised to learn that the most prototypical LessWrong user (Eliezer Yudkowsky) is a moral realist. The issue is that most people have only read what he wrote in the sequences, but didn’t read Arbital.
Human moral judgement seem easily explained as an evolutionary adaptation for cooperation and conflict resolution,
That’s not true: You can believe that what you do or did was unethical, which doesn’t need to have anything to do with conflict resolution.
and very poorly explained by perception of objective facts. If such facts did exist, this doesn’t give humans any reason to perceive
Beliefs are not perceptions. Perceptions are infallible, beliefs are not, so this seems like a straw man.
or be motivated by them.
Moral realism only means that moral beliefs, like all other contingent beliefs, can be true or false. It doesn’t mean that we are necessarily or fully motivated to be ethical. In fact, some people don’t have any altruistic motivation at all (people with psychopathy), but that only means they don’t care to behave ethically, and they can be perfectly aware that they are behaving unethically.
Unfortunately I think social grace can only be trained to a small degree, for reasons similar to ASD not being curable. Some people just have a natural social grace, others are much more socially awkward, and removing their social inhibitions too much may make them “cringe” or even “creepy”.
Not sure whether you know this, but on Twitter roon mentioned that GPT-5 (non-thinking? thinking?) was optimized for creative writing. Eliezer dismissed an early story shared by Altman.