Re: Incommensurability of Mathematical Logic and Scientific Logic
- From: jem <xxx@xxxxxxx>
- Date: Wed, 02 Nov 2005 08:43:03 -0500
AllYou! wrote:
"jem" <xxx@xxxxxxx> wrote in message news:X3M9f.19$ii.12@xxxxxxxxxxxxx
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Daniel Weston wrote:
Pentcho: I agree with you completely. To state it another way, math is
metaphor. Or the map is not the territory. Or the description is not
the thing described.
What often happens is that people are so math orientated that they
anthropomorphisize math. They give some math procedure a name, then
state that the math procedure so named is the cause of some physical
event. Such as, "gravity is caused by the curvature of spacetime".
These people are totally blind concerning this logical error. Kepler's
planetary laws of motion do not cause the planets to move the way they
do.
Your problem is you don't know where the dividing line is between map and territory. Planets are elements of a model, and the logical rules that govern their behavior within models can certainly be considered to cause that behavior.
Rules are man's best guess at predicting the behavior of the elements of the model, and as such, those guesses cannot cause anything to happen to anything.
The behaviors of the elements of a model don't have to be guessed; they're entirely defined.
The behaviors of the elements of a model will be as they will be observed. The rules man devises about those behaviors are his predictions of future observations based upon past observations. Predictions can't cause anything to happen to anything.
Models are completely distinct from the real-world measurements they're designed to reproduce. Models are hypothetical worlds where everything is *defined* to work in a specified manner. The worth of a model lies entirely in how well the defined hypothetical measurements of the model match up with actual real-world measurements. Physics makes no attempt to speculate about the "causes" for real-world measurements, because no sense can be made of such speculations.
Models are completely distinct from real-world measurements because there's no way to ascertain what the real world is, or even whether or not it exists.
A real-world exists. Physics defines it as the collection of all measurable phenomena.
To claim, as you do, that there are two sets of
measurements (i.e., that of the defined hypothetical measurements and that of real world measurements) is pure folly. Please provide an
example of two such meansurements and how we'd match them.
A weather model indicates that real-world devices called thermometers will register 20 degrees Celsius when other real-world devices called clocks register noon. Hold a clock and a thermometer side by side so that both readings are visible simultaneously. When the clock reads 12:00, check to see whether the thermometer reads 20.
Can you identify what's from the model and what's from the real-world?
All we have are observations, and we use those observations to build a model of what we believe might be an accurate reflection of a real world, should one exist.
Where "accurate reflection of a real world" means that predicted measurements match actual measurements (within suitable tolerances).
The real-world *is* the measurements - of course it exists.
The worth of the model lies in it's abiltiy to
reliably predict future
and retrodict past
observations, and those predictions are based
upon past observtions,
Those predictions/retrodictions are based entirely on a model. The extent to which the formulation of the model relied on past observations is irrelevant.
and speculations as to the causes of those
observations. IOW, we observe the Earth in orbit around the Sun,
We've observed certain affects on certain measuring instruments (e.g. eyes, clocks, sextants, etc.), and built a model containing entities called Sun, Earth and orbit.
we
predict that this orbit will continue along a certain path,
We've *defined* the paths of the Earth and Sun (model entities), and translated those paths into numerical results that are expected to match the readings on particular real-world instruments.
and we base
this prediction upon the observations we've made which result in speculation as to the cause.
The prediction is based solely on the model; no speculation is needed in order to designate a cause within the model.
The worth of our model lies in the
reliability of those predictions.
It lies in the correctness of the predictions. .
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