Belief Vs imagination, beliefs Vs wish, subjective Vs arbitrary: the role of the coherent (virtual) bet

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.

• 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[15], T.1.1.1.4), 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.''[26]

  It follows that probability is always conditional probability, as again well stated by Schrödinger[26],

  `` 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. $P(E)$ has always be understood as $P(E\,\vert\,I)$, where $I$ stands for a given status of information, that changes with persons (subjects) and time. Hence a probability assessment has always to be meant as
  
  $$P[E\,\vert\,I_s(t)]\,.$$
  
  
  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.

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[27], appeared immediately after the recent (in?-)famous result on superluminar neutrinos[28].

Figure: A comic from xkcd,[27] on superluminar neutrino, valid for any fancy claim.

(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.)