Is Eliezer strawmanning positivism here? He says that all statements are defined by experimental predictions in positivism, but positivism also leaves room for logical deductions. So you could end up with empirical statements far removed from any observation. The statement, "Chocolate cakes rarely materialize spontaneously," constrains future observation. But from that it follows that the odds of a cake just now materializing in the center of the sun are low. Because to say that something happens rarely, is to say that there is a low probability of it happening at any given time and place.
Or does logical positivism also forbid generalizations of that kind?
It also seems that any accurate model, predicting what we can expect from the sun in the future, would, as a side effect, predict how likely it is for cakes to form. For example, our model of the sun is based on the theory that it's made of matter like we find on earth, playing by the same rules.
I think you're right. Even Ayer's painfully naive version of positivism would not have said Eliezer's sun cake sentence was meaningless; certainly that's not what you'd get from the views of Carnap or Neurath. But perhaps Eliezer was more interested in talking about Ayer's fanboys than about the major logical positivist philosophers, and there certainly are people who discover Ayer's verification principle (or Popper's falsification principle) and immediately develop an extreme overconfidence in its ability to simply dissolve all manner of problems.
I don't understand what it would mean for logical positivism to be true/false. What should I expect to experience differently in each case?
Eliezer's post is about verificationism specifically. Are you intending to raise the traditional question of whether verificationism is itself verifiable? If so, the standard answer is that verificationism is intended to be a logical principle, so no, it is not verifiable, and in fact not empirically meaningful. What would you expect to experience differently if the axiom of choice were true or false?
Are you intending to raise the traditional question of whether verificationism is itself verifiable?
I'm just trying to understand the statement Eliezer is making in this post.
What would you expect to experience differently if the axiom of choice were true or false?
I don't think the axiom of choice is a first-order tautology so you wouldn't call it true or false. It could be inconsistent within certain popular theories in which case for each inconsistent theory I would expect the the negation of the conjunction of the axiom of choice and the theory to eventually appear in an enumeration of first order validities.
Today's post, No Logical Positivist I was originally published on 04 August 2008. A summary (taken from the LW wiki):
Logical positivism was based around the idea that the only meaningful statements were those that could be verified by experiment. Unfortunately for positivism, there are meaningful statements that are very likely true and very likely false, and yet cannot be tested.
Discuss the post here (rather than in the comments to the original post).
This post is part of the Rerunning the Sequences series, where we'll be going through Eliezer Yudkowsky's old posts in order so that people who are interested can (re-)read and discuss them. The previous post was The Comedy of Behaviorism, and you can use the sequence_reruns tag or rss feed to follow the rest of the series.
Sequence reruns are a community-driven effort. You can participate by re-reading the sequence post, discussing it here, posting the next day's sequence reruns post, or summarizing forthcoming articles on the wiki. Go here for more details, or to have meta discussions about the Rerunning the Sequences series.