- how
*should*one think about probability?

There is some collection of "usual topics" in the philosophy of probability, which I don't intend to engage directly; rather, the list below contains questions that seem potentially more fruitful.

Being a "naive empiricist" who thinks one should learn abstract concepts from real world instances, rather than a "naive Platonist" who thinks one can gain insight into the real world by logical arguments from first principles, causes me some difficulties with this material -- after all, one can't really apply empiricism to "should" questions. The difficulty is well illustrated by Taleb's The Black Swan: The Impact of the Highly Improbable; to quote from my my rather long review

*
Much of the book is
rhetoric about empiricism, with a remarkable lack of actual empiricism, i.e.
rational argument from data. *

(xxx under construction)

- Whenever we think about "the chances of" something, we are consciously recognizing unpredictability or uncertainty. But not every situation where we consciously recognize unpredictability or uncertainty is a situation where we habitually think in terms of chance, even qualitative (likely/unlikely) chance. So: within contexts of unpredictability or uncertainty, under what further conditions do qualitative probability statements make sense?
- Both mathematicians and philosophers tend to jump quickly to the "interpretation of quantitative probability assertions" issue below. I find it useful to go slower and first discuss Probability as a qualitative spectrum. In particular, how is probability similar to or dissimilar from other aspects of the world for which we habitually compare instances on some "more than or less than" scale without having any ready way of measuring quantitatively?
- At many places on this site I repeat a desire to avoid being drawn into the traditional Interpretations of Probability debate on what meaning one should attach to a statement like "the chance that team A beats team B in tomorrow's game is 60%". So I'm not going to attempt to write anything systematic, merely recording scattered comments on the usual philosophical interpretations of probability. (not yet written)
- Instead of the usual
"how large is the role of chance in Life, the Universe, and Everything?"
let me ask
in what real-world contexts do we tend to overestimate, or to underestimate, the role of chance?.
(xxx not yet written)
.............

- A broad range of calculations rely on what I call the
local uniformity principle;
this principle seems intuitively reasonable, but it's hard to
say
**why**it seems reasonable.

(xxx under construction)

- A qualitative sense of likelihood, for instance a conscious recognition of some future events as likely and some as unlikely, is part of the common sense that the human species is endowed with.
- Whenever we think about chance, we are consciously recognizing unpredictability or uncertainty. But not conversely. There are many settings where we recognize unpredictability but do not naturally think in terms of chance.