Reading  “The Logic of Modern Physic” by P.W. Bridgman.

Some comments.

 

Mario Di Bacco

Scuola di Alta Formazione Biostat, Polo Universitario, Asti (Italy)

 

 

I transcribe some sentences drawn from the essay [1] of the eminent physicist P.W. Bridgman. Each of them is shortly commented for putting those general ideas in the specific contest of Probability Theory and Statistical Inference.

It is worth to notice that Bridgman’s book is quoted by the B. de Finetti ([2], pag. 93) and, more recently, by F. Lad ([3] …..) with regard to the operational definition of Probability.

Indeed, here the sentences.

 

 

(1) We shall accept as significant our common sense judgment that there is a world external to us … [Introduction, page XI].

 

Comment

 

In the jargon of Probability Theory any “Event” is a concept derived from empirical experience and from it alone. Therefore, Bridgman’s premise is also a necessary premise to any reasoning on probability.

 

 

 

(2) … when experiment is pushed into new domains, we must be prepared for new facts, of an entirely different character from those of our former experience [Chapter I, page 2].

 

Comment

 

Analogously, in the logic of the support (e.g. Hacking [1] pages 122-5) there is place for “surprise”. By taking into account Bridgman’s assertion and by relating it to Bayesian inference, “non-informative prior” (NIP) must be a significant concept. Indeed, I think that the classical objections to NIP are overcome if I say “assume NIP when you expect that any piece of information that you get makes the action that you shall choose (= your decision) less risky.

 

 

 

(3) In general, we mean by any concept nothing more than a set of operations: the concept is synonymous with the corresponding set of operations (page 5).

 

Comment

 

“Probability” is a significant concept only if all interested parties know the same set of operations – use the same device – to assign probability to event E, whatever E is. In fact, if Pat claims Pr(E)=p, all his interlocutors realize that p is the numerical representation of Pat’s opinion on. “E is true” and each of them should give the same value p to “E is true” if they were in the same state of information as their friend Pat. However p is not more than the summary of the personal information on event E! If all interlocutors – or almost all – agree to Pr(E)=p, then p could be the objective probability for “E is true”.

 

 

 

(4) … the operations which enable two events to be described as simultaneous involve measurements on the two events made by an observer so that “simultaneous” is, therefore, not an absolute property of the two events and nothing else, but must also involve the relation of the events to the observer (page 8).

 

Comment

 

In line with Bridgman’s view, statements like “Pr{E}>Pr{F}” or “in sequence (E1, E2, … En, …) the events are exchangeable” do not describe properties of the events, but report the opinion of interlocutor I, an opinion which might of might not be shared by the other parties.

 

 

 

(5) If a specific question has meaning, it must be possible to find operations by which an answer may be given to it. It will be found in many cases that the operations cannot exist, and the question therefore has no meaning (page 28).

 

Comment

 

A concept describes an event – say, E – if and only if there exists, at least in principle – i.e. it can be coherently conceived –, an empirical process which will definitely be able to establish that E is true or, alternatively, false. Indeed the medieval alchemists could say “E is an event if and only if there exists the “aurum argumentum” to conclude on its “truth” or “falsity”.

 

 

 

(6) If the statement of arithmetic [2+2=4] is to be an exact statement in the mathematical sense, the “object” must be a definite clear-cut thing which preserves its identity in time with no penumbrae. But this sort of thing is never experienced (page 32).

 

Comment

 

Transferring the above sentence on our field – that of statistical inference – it should be accepted that any statistical datum is an ill-determined thing. Consequently the “only right” inference should be a “fuzzy-inference”. Unfortunately, it appears that such an inference is still to be invented.

 

 

 

(7) The savage is satisfied in explaining the thunderstorm as the capricious act of an angry god. The physicist demands more, and requires that the familiar elements to which we reduce a situation be such that we can intuitively predict their behaviour (page 38).

 

Comment

 

According to Bridgman’s view, inference on “A is true” given “B is true” using Pr{A/B} is able to predict (i.e. “to tell in advance”) just whether in the real world things go according to A or not. Indeed, it seems that Bridgman is a “true empiricist” who does not take in account Hume’s warnings. On the contrary de Finetti [3] claims that Pr(A/B) simply updates coherently your initial option on A.

 

 

 

References

 

[1]   Bridgman, P.W. (1927): The Logic of Modern Physic. The MacMillan Company, New York.

 

[2]   Hacking, J. (1965): The Logic of Statistical Inference. At Cambridge Univ. Press, Cambridge.

 

[3]   De Finetti, B. (1937): La Prévision: Ses Lois Logiques, Ses Sources Sbyectives. Ann. Inst. H. Poincaré, 7, 1-68.