The role of the bet, although virtual, in the sense
of `as I would be called to bet', is crucial to make
clear distinctions between different concepts that could
otherwise be confused.
Belief Vs imagination, beliefs Vs wish,
subjective Vs arbitrary: the role of the
coherent (virtual) bet
To conclude this subsection, when somebody claims something
on the basis of arguments that you do not clearly understand,
follow Kant's suggestion and
ask him/her to bet for money. And, if it is a claim in favor
of new/extraordinary physics only based
on a p-value, don't hesitate to cash, as nicely
shown in the comic of figure 2,
appeared immediately after the recent (in?-)famous result on
- We can imagine something, just combining ideas
(even ``the New Jerusalem,
whose pavement is gold and walls are rubies'' - on this
issue a reference to Hume is a must, T.126.96.36.199),
but, nevertheless, we could not believe it.
- We should also be careful not to confuse what we
wish with what we do belief. I would like
to win the highest prize playing at a lottery, but I
don't believe I will. Similarly - and this is well
stated in proposition (2) - I think everyone working
in frontier science would be very happy if something
really new `appears', such that it forces us to
change our vision of the world. But before we
can accept something like that we really need
much experimental evidence, obtained in different ways
with different techniques.
- Finally, it is a matter of fact that
`` Since the knowledge may be different with different persons
or with the same person at different times, they may anticipate
the same event with more or less confidence, and thus different numerical
probabilities may be attached to the same event.''
It follows that probability is always conditional
probability, as again well stated by Schrödinger,
`` Thus whenever we speak loosely of `the probability of an event,'
it is always to be understood: probability with regard to a certain
given state of knowledge,''
i.e. has always be understood as , where
stands for a given status of information, that changes
with persons (subjects) and time.
Hence a probability assessment
has always to be meant as
This is the meaning of the adjective subjective
attached to probability, that has nothing to do
with arbitrary. Once again, thinking in terms of bets,
instead of noble but empty ideals of `objectivity' that can easily
drift to `metaphysics', helps to distinguish
what is really arbitrary from sound rational beliefs.
(But, besides the humorous side, I invite my colleagues to reflect
on the fact the general public is not by definition stupid and
there is an increasing number of well educated tax payers who
are starting to get tired of fake claims.)
A comic from xkcd, on
superluminar neutrino, valid for any fancy claim.