How compatible are Bayesianism and Objectivism?

It is unclear what is meant by Bayesianism, but statistical decision theory relying on Bayes Theorem does not prescribe a loss function. If one objects to a utilitarian loss function, they do not, per se, object to Bayesianism. One can use a loss function consistent with Rand's morality.

But I think that there is a different, and deeper, inconsistency between Objectivism and Bayesianism - the latter allows for A and ~A to be true simultaneously. I have seen some say this is not the case, and that assigning non-zero truth values to both A and ~A simultaneously is due entirely to ignorance. But I have heard this point argued with (see well know frequentist-bayesian debates. I also thing the objective-subjective debate within the Bayesian community is relevant).

I suppose it is possible that objective Bayesianism and Objectivism are consistent. I don't know enough about the two to say for sure.

Does anyone know how Objectivism deals with uncertainty and/or randomness? Does it allow for a truth value between 0 and 1?

Post 41

Saturday, March 31, 2012 - 8:41am

Before answering this, I will first explore Bayesianism somewhat. Talking about it helps. This not only helps readers, it helps me to get my thoughts clear. I went to a webpage to refresh my memory (see link below), and what follows draws very heavily from that webpage.

Bayesianism, in its simplest form, is about what I would call "2nd-level" probability calculation -- where the probability of the occurrence of one single event hinges on the assumed fact of the occurrence of another single event. It's a conditional probability. The primary question asked and supposedly answered is:

What is the probability of A, given B? [What is the probability that the event "A" will occur, assuming that the event "B" has already occurred?]

Now, this question can be restated as: p(A; given B) and that is the value that we are trying to discover. In order to get an answer to this, you'll need to start with a few notes. You will need:

--the default (or "prior") probability of event A: .......................................................................... p(A)
--the probability that you would have gotten event B along with the occurence of event A............ p(B; given A)
--the default (or "prior") probability of event B: ........................................................................... p(B)

Let's use a concrete example. Here's the one given on the webpage linked to below:

Marie is getting married tomorrow, at an outdoor ceremony in the desert. In recent years, it has rained only 5 days each year. Unfortunately, the weatherman has predicted rain for tomorrow. When it actually rains, the weatherman correctly forecasts rain 90% of the time. When it doesn't rain, he incorrectly forecasts rain 10% of the time. What is the probability that it will rain on the day of Marie's wedding?

In this concrete example, p(A) is the default probability that it will rain on any given day -- the historical "frequency" of rain in that area. p(B) is the probability that the weatherman would have predicted rain on any given day. And what we want to discover is the probability it will rain, given that the weatherman predicted rain, which is: p(A; given B). We require just one more contingency: the probability that the weatherman would have already predicted rain, given that it, in fact, does rain on any particular day, which is p(B; given A).

Here's the formula:

p(A; given B) = [ p(B; given A) ] x [ p(A) ]
________________________________
.......................... p(B) .............................

Taking just the right side of the equation, we have:

... [ p(B; given A) ] x [ p(A) ] ...
________________________
.................... p(B) ...................

p(B; given A) is the probability that the weatherman successfully predicts rain before it actually does rain, and this guy gets this right about 90% of the time, so the value for that variable is: 0.90.

p(A) is the default probability that it will rain on any given day, which is 5 days per calender year, which is: 5/365, or 0.014.

p(B) is the default probability that the weatherman will predict rain on any given day. Let's calculate it. It rains 5 days a year and, when it does, the weather predicts rain 90% of the time -- so that is already 4.5 days a year (or 4.5/365, or 0.012) that the weatherman will predict rain. Also, it doesn't rain for 360 days out of the year but, unfortunately, the weatherman accidentally predicts rain 10% of the time during those days -- so that is 10% of 360 days which is 36 days a year (or 36/365, or 0.099). Now we can add these 2 probabilities together to get the default probability -- no matter what day it is -- of the weatherman predicting rain:

p(B) = 0.012 + 0.099 = 0.111

Now, armed with every variable in the right side of the equation, we can plug them in and calculate the probability of rain tomorrow:

p(A; given B) =

... [ p(B; given A) ] x [ p(A) ] ...
________________________
.................... p(B) ...................

=

... [ 0.9 ] x [ 0.014 ] ...
__________________
........... 0.111 .............

=

0.114

Conclusion:
So there is an 11.4% chance of rain tomorrow, given the background frequency of rain in the area, along with the prediction of rain by the weatherman, and further updated by the past success of the weatherman in getting this particular prediction right.

The first problem I have with Bayesianism, in its simplest form, is that it assumes virtual omniscience with regard to the notion that the probability of one event is always and only updated by the occurrence of one other event (rather than by a panalopy of inter-related events, all working together to give rise to an eventual outcome). In the above example, the only thing thought to affect the probability of rain on a given day is the forecast of a single weatherman in the area. His action is assumed to be the only thing that can help you arrive at a probability of rain. This is not a terrific advance over the prior situation of simply counting the days it rains, and using that relative frequency to predict the chance of rain. Also, I have a problem with the basic fact that it is "frequentist". In order to come up with default (prior) probabilities -- you simply count. This is induction via enumeration and is a process that, itself, is highly suspect. I'll stop there to gather my thoughts.

Ed

Source:
http://www.stattrek.com/probability/bayes-theorem.aspx

(Edited by Ed Thompson on 3/31, 8:52am)

Post 42

Sunday, April 1, 2012 - 9:28am

Mr. Stern,

But I think that there is a different, and deeper, inconsistency between Objectivism and Bayesianism - the latter allows for A and ~A to be true simultaneously. I have seen some say this is not the case, and that assigning non-zero truth values to both A and ~A simultaneously is due entirely to ignorance.

Bayes' advocates are often pragmatists who do not worry if probabilities (e.g., of A and ~A) correspond to a stable reality with identity, because they do not believe that there is a stable reality with identity. Stephen Hawking once said that if something isn't measured, then it doesn't exist -- implying that humans bring existents into existence ex nihilo, simply by formalized investigation. It's likely that Baye's advocates reify their decision theory algorithms into something that has even more reality than reality does. It sounds like your experience of their reactions can be chalked up to them going through some hand-wringing, because they got caught being pragmatic without rationally legitimacy.

It reminds me of Aristotle's sea battle. You cannot now say whether there exists a sea battle tomorrow, because tomorrow has no actual existence today. There is only the present moment, and a whole bunch of un-actualized potentiality.

I suppose it is possible that objective Bayesianism and Objectivism are consistent. I don't know enough about the two to say for sure.

I think that it may be possible to qualify Bayesianism so much that it could be made consistent with Objectivism, but this might involve stripping traditional Bayesianism down to less than half of the usual assumptions it makes. It'd be an interesting research topic and it'd be great if some aspiring student took it up as a graduation thesis!

Does anyone know how Objectivism deals with uncertainty and/or randomness? Does it allow for a truth value between 0 and 1?

In Objectivism, uncertainty is an epistemological condition rather than a metaphysical aspect of reality. Even apparent randomness is an epistemological condition -- and not a metaphysical aspect of reality. True randomness violates the Law of Causality (which is the Law of Identity, applied to actions). Even so, an observer's estimate of a truth value can be between 0 and 1, even if there is no such fact of reality that corresponds to such a "partial truth." For instance, take the parable of Schrodinger's Cat (from quantum mechanics). The cat in the box is either dead or alive, but is not ever half-dead, or half-alive.

So there is room from an observer's standpoint to make probability estimates based on epistemological concerns, as long as everyone understands that there are no partial-truths in reality -- so that a truth value of, say, 0.45, for some event is just an aspect of estimation. In Introduction to Obectivist Epistemology, the notion of imaginary numbers is brought up. Imaginary numbers have no correspondence to anything in reality but can be utilized epistemologically in order to accomplish some scientific tasks. On that note, imaginary numbers I believe were categorized under the broad heading: concepts of method -- to allow for the human use of imagined things in order to accomplish a real (non-imagined) purpose.

Ed

Post 43

Monday, April 2, 2012 - 5:51am