# [FOM] R: Is there a compendium of examples of the "power"of deductive logic?

Antonino Drago drago at unina.it
Wed Dec 14 18:11:25 EST 2005

```John McCarthy:
> It is possible to introduce mass, force, and acceleration separately,
> so that F = kma, where k is a constant, becomes experimentally
> testable.  Later units can be chosen so that k = 1.
>
> Namely: Introduce mass as weights, the key fact being that when two or
> more bodies are combined, the mass of the combination is the sum of
> the masses of the constituents.

It is well-known that mass force and acceleration cannot be introduced
separately. Indeed what John McCarthy introduces is the notion of statical
force, but not dynanical
force; and
the notion of force is just the notion needed for transpassing from statics
to
dynamics.
Thus, a vicious circle is inherent in f=ma. Newton "solved" the
question by appealing to the notion of density, by disregarding the fact
that beforehand one has to define density independently from mass. Mach
tried to solve the question by making use of the third principle for
defining mass; the cost is the loss of a principle .
One more vicious circle is in the notion of inertial reference frame, which
is the frame where the inertial principle holds true. But the inertial
principle holds true only in inertial reference frame. The problem did not
belong to Newton's system which appealed to an absolute space. Thus, he had
no need of defining the notion of time independently of inertia principle;
but in the modern formulation of dynamics this definition constitutes one
more vicious circle with the inertial frame.
About the inertia principle I suggest to read N.R. Hanson: "Newton's first
Law. A Philosopher's door in Natural Philosophy", in R.G. Colodny (ed.):
Beyond the edge of certainty, Prentice-Hall, 1965, 6-28.
A further analysis is my: "A Characterization of Newtonian Paradigm" in P.B.
Scheurer, G. Debrock (eds.): Newton's Scientific and Philosophical Legacy,
Kluwer Acad. P., 1988, 239-252. Every time a physical theory starts a
deductive theory, it puts a principle abstract in nature, then a second
principle corrects this abstractness; this configuration is the same that
Berkeley denounced in infinitesimal analysis, i.e. a double fault. The more
manifest instance of this double fault in deductive theory in physics, is
the theory of thermodynamics, where the second principle corrects the full
validity of the first one (equality between heat and work in a cycle) by
bounding the conversion of heat to work to a maximum efficiency (hence heat
is no more said to be equal to work, but equivalent to work).
Greetings
Antonino Drago
via Benvenuti 5
Castelmaggiore Calci Pisa 56010
tel. 050 937493
fax 06 233242218
-----Messaggio Originale-----
Da: "" <jmc at steam.Stanford.EDU>
A: <fom at cs.nyu.edu>
Data invio: mercoledì 14 dicembre 2005 7.37
Oggetto: Re: [FOM] Is there a compendium of examples of the "power"of
deductive logic?

> Introduce force using the static equilibrium of strings pulled by
> springs or weights.  The key fact is that forces add vectorially.
>
> Acceleration is based on measurements of position and time.  Time