I used "ontology" here to mean the definitions in your model. E.g. boojums, snarks and monsters in the examples above. If you wanted to update your model itself based on observations and remain within the Bayesian framework, you'd have to have had the foresight to anticipate doing so, and provided a collection of different models with a prior over them.
You are right. Thank you for the correction, and I like your description which I hope you don't mind me using (with credit) when I edit this post. My error was not realizing that P(boojum(x)|snark(x)) is the marginal probability for one particular row in the table. Even though the syntax is (hopefully) valid, this stuff is still confusing to think about!
and he similarly thinks about the dummy variable of the quantifier that way, and so how could all these different cats have the same propability?
I'm not quite sure how Chapman is interpreting these things, but what you are describing does sound like a reasonable objection for someone who interprets these probabilities to... (read more)
This is an excerpt from a longer article I wrote, where I go into much more depth on many of the ideas here.
In his blog post, Probability theory does not extend logic, David Chapman goes through a number of examples which he claims don't make sense, and therefore Bayesian 1st order logic is dead in the water. I'm now going to take up Chapman's challenge to make his examples well posed, i.e. syntactically valid (only one way to blindly parse the math) and with a reasonable interpretation of what is going on.
Through his "Challenge" problems, Chapman wants to demonstrate that arbitrary nesting of probabilities mixed with quantifiers does not parse, and that... (read 5246 more words →)
The arguments for Bayesian epistemology embodying rationality. It would be helpful to see this position elucidated all in one place.
tristanm writes "I’ve noticed a recent trend towards skepticism of Bayesian principles and philosophy ... which I have regarded with both surprise and a little bit of dismay, because I think progress within a community tends to be indicated by moving forward to new subjects and problems rather than a return to old ones that have already been extensively argued for and discussed." These extensive arguments and discussions about this topic seem to be scattered about LW and other sites. It would help Bayesian proponents to have a standard sequence to point to, especially if they think the issue is settled.
I'm being too vague with my use of the word "model". By "model" I just mean some set of possibilities that are grouped together. For instance in machine learning, a model is a parametrized function (which can be regarded as a set of functions each indexed by a parameter). A set of different models is also a model (just more possibilities). Maybe this is not the best word to use.
In the case of Solomonoff induction, some of those programs might contain logic that appear to simulate simple environments with 3D space containing stuff, such as chairs and cars, that interact with each other in the simulation as you'd expect. I'd say the... (read more)