Philosophical background to the Probability and the Real World project
This is the cover page for the "philosophy" part of the
Probability and the Real World project.
I am using the word "philosophy" rather casually to mean
and all this material is intended as conceptual background to the overall project of
critically articulating the connection between mathematical probability and
empirically testable aspects of the real world.
- 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
Much of the book is
rhetoric about empiricism, with a remarkable lack of actual empiricism, i.e.
rational argument from data.
Our philosophy topics
Here are the topics I will emphasize.
Clicking on links within these pages will take you on detours of unpredictable
In all of this I am not claiming new insights or advocating some crazy theory of my
own; rather, I seek to present a different focus and emphasis than I have seen
(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.
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
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.