-1
$\begingroup$

Can the following point of view be traced back to a particular publication by Poincaré? In Section 3.1 of Gravitation, by Misner, Thorne and Wheeler, the authors write:

Here and elsewhere in science, as stressed not least by Henri Poincare, that view is out of date which used to say, “Define your terms before you proceed.” All the laws and theories of physics, including the Lorentz force law, have this deep and subtle character, that they both define the concepts they use (here B and E) and make statements about these concepts. Contrariwise, the absence of some body of theory, law, and principle deprives one of the means properly to define or even to use concepts.

The reason I'm so interested in this: I do still encounter that "out of date" view.


Looking for clues I checked the Stanford encyclopedia of Philosophy entry for Poincaré, which has

Poincaré and Hilbert propose a radically new view of geometry. They hold that all that we can say about the meaning of ‘point’, ‘straight line’, ‘distance’, etc. is that which we have stated in the axioms or principles of the system, and that geometry is not a set of truths about some previously known objects. Thus Poincaré formulates a new view of geometric theories, that geometry does not express true or false propositions and that there are no special objects which geometry studies. Rather, geometry is just a system of relations that can be applied to many kinds of objects.

It comes close to what is raised in MTW, but it's not quite there, it seems. It may well be, of course, that more was attributed to Poincaré than was ever in Poincaré's actual writings.


Here is a longer quote from 'Gravitation', by Misner, Thorne and Wheeler's Section 3.1, The Lorentz force and the electromagnetic field tensor:

At the opposite extreme from an impulsive change of momentum in a collision (the last topic of Chapter 2) is the gradual change in the momentum of a charged particle under the action of electric and magnetic forces (the topic treated here).

Let electric and magnetic fields act on a system of charged particles. The accelerations of the particles reveal the electric and magnetic field strengths. In other words, the Lorentz force law, plus measurements on the components of acceleration of test particles, can be viewed as defining the components of the electric and magnetic fields. Once the field components are known from the accelerations of a few test particles, they can be used to predict the accelerations of other test particles (Box 3.1). Thus the Lorentz force law does double service (1) as definer of fields and (2) as predicter of motions.

Here and elsewhere in science, as stressed not least by Henri Poincare, that view is out of date which used to say, “Define your terms before you proceed.” All the laws and theories of physics, including the Lorentz force law, have this deep and subtle character, that they both define the concepts they use (here B and E) and make statements about these concepts. Contrariwise, the absence of some body of theory, law, and principle deprives one of the means properly to define or even to use concepts. Any forward step in human knowledge is truly creative in this sense: that theory, concept, law, and method of measurement—forever inseparable—are born into the world in union.

Later in the book this point is raised again: that laws and theories of physics are both laws/theories of physics and operational definitions of the concepts that the laws make statements about. See Section 12.3 in 'Gravitation'.

$\endgroup$
9
  • $\begingroup$ The Lorenz force law as a definer of fields an a predictor of motions. Is this the same as a law and an operational definition? $\endgroup$ – Deschele Schilder Jul 18 at 8:56
  • $\begingroup$ Is it really thought that acceleration can find place without sudden impulse changes like in collisions? This is of no relevance to you question of course but Im curious. Where do you see the view described in MTW (contested by Poincare) in modern science? Who had the quoted (outdated) view? $\endgroup$ – Deschele Schilder Jul 18 at 9:04
  • $\begingroup$ Was the view "define your terms before you proceed" out of date? And what follows the view of MTW? $\endgroup$ – Deschele Schilder Jul 18 at 9:09
  • $\begingroup$ "Define your terms before you proceed" Why is this outdated and were do you still see it? Do the terms just arise while proceeding? So not before? $\endgroup$ – Deschele Schilder Jul 18 at 9:21
  • $\begingroup$ The reason I'm so interested in this: I do still encounter that out of date view Is that good or bad? $\endgroup$ – Deschele Schilder Jul 18 at 9:43
2
$\begingroup$

A good account on genesis of the modern view of definitions (as opposed to the definitions-first Aristotelian one) is Fontanella, Axioms as Definitions: Revisiting Poincaré and Hilbert. Perhaps the clearest expression of it from Poincare comes from his response to Russell Sur les principes de la géométrie: réponse à M. Russell, Revue de Métaphysique et de Morale, 8(1) (1900) 73–86:

"If one wants to isolate a term and exclude its relations with other terms, nothing will remain. This term will not only become indefinable, it will become devoid of meaning."

In Science and Hypothesis (1902), when speaking of geometry, he links the idea to his famous conventionalism:

"The axioms of geometry are therefore neither synthetic a priori intuitions nor experimental facts. They are conventions. Our choice among all possible conventions is guided by experimental facts; but it remains free and is only limited by the necessity of avoiding every contradiction [...]. In other words, the axioms of geometry (I do not speak of those of arithmetic) are only definitions in disguise."

Although it is an implication, I doubt that Poincare explicitly stated in the digested didactic manner of MTW that we shoud stop asking for terms to be defined before proceeding.

$\endgroup$
1
  • $\begingroup$ I assume M. T. and W. were inspired by Poincaré's ideas. I will definitely keep using the MTW statement, but i'm thinking of omitting the allusion to Poincaré, to emphasize that the statement speaks for itself. Once I became aware of the law-is-operational-definition nature of science I started recognizing it. Example: Ohm's law counts as a law of physics, and Ohm's law is also an operational definition of what qualifies as 'resistance'. There is only one way to define electric resistence: by referring to Ohm's law. Proof that Ohm's law isn't circular reasoning: experimental corroboration. $\endgroup$ – Cleonis Jul 20 at 20:24

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.