Re: Revised Tautology FAQ - Thread-2

Friar Broccoli wrote:
On Aug 17, 5:14 am, nos...@xxxxxxxxxxxxxxxx (J. J. Lodder) wrote:
David Hare-Scott <sec...@xxxxxxxxxx> wrote:
On the whole it's good. If you are aiming at an explanation for the
non-technical but educated layman (tha's me) the tone and level seems right.
One problem that I noticed. I have snipped the rest to make it clearer.
This bit:
Tautologies are True by definition and
may be characterised as follows:
.....
- not dependent on empirical testing (observations from the real
world)
......
contradicts this bit
Thus, being a tautology, does not immunize a
statement from being falsified by observation.
I think I know what you are driving at but as it stands it's just a
contradiction.
The friar is not clear in his mind on the disticttion
between mathematical equations and physical ones.

F = ma as an axiom in a mathematical formulation of Newton's theory
and F = ma as an economical description of thing observble
are entirely different things conceptually,
even though they look just the same.

(I'll try to come back to this point)

Yes, I would VERY much like more input on this point/issue.
The distinction between physical reality and the formulations
that people use to describe them is central to many of the points
I am trying to make.

An algebraic equation, devoid of interpretation (semantics), cannot be falsified. Indeed, it cannot even be meaningfully employed in mathematics.

Devoid of interpretation, F = m a is no more falsifiable than X = y z, or r = s t, or any one of same structure without a supplied semantics. In fact, without an interpretation, even the equals sign "=" is meaningless. (Would intelligent aliens from another planet, though scientifically far more advanced than humans, know what it means without being told?)

In mathematical logic, we learn how to provide an interpretation (semantics) for each term and operator in a mathematical statement, that maps each term to its allowed set, and each operator to the axioms that define it. To begin with, F, m, and a are considered by physicists to be real numbers, and "=" to mean equality. The axioms of equality are taken to be the Peano postulates for the equality relation.

Science provides interpretations that go further and ostensibly match up with quantities observable in the real world. So they interpret F to mean physical force, m to mean mass, etc. Then they assert that F = m a accurately depicts the behavior of phenomena in the real world. But that assertion can be falsified, and in fact the Theory of Relativity falsified it for very high speeds and masses.

Electrical engineers freely work with complex numbers to describe real-world phenomena, showing that it's highly important to get the semantics well defined.



--
Steven L.
Email: sdlitvin@xxxxxxxxxxxxxxxxxxx
Remove the NOSPAM before replying to me.

.

Relevant Pages

  • Re: Revised Tautology FAQ - Thread-2
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