Re: Incommensurability of Mathematical Logic and Scientific Logic


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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.



Physics is only about building models of what we observe. Reality is a philosophical issue, not a scientific one.


"Reality" is simply the name for what's observed (i.e. natural phenomena).


What's observed is what's observed. What's real is a philosophical issue because we have no idea if what we observe is real.

How can it be so hard for you to grasp such a simple idea? When what is real is defined to be what is observed, it necessarily follows that what we observe is real.


But that definition is


incorrect.

Reality: "The quality or state of being actual or true." Reality is not what we observe because there's no way to know if what we observe is true to the exclusion of every other possibility. How do you know if you observe the color red, the there's not something wrong with your eyes? How do you know the two events occurred simultaneously even if you observed that to happen? We used to believe with all the convictions we could muster that we could observe simultaneity, but now we know we cannot. Did reality change? Reality is singularly true, so it cannot have changed, yet by your standard, we observed it, so it was real.

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?



Now I see what you meant. You think physics is about building models of what will happen in the future,


Physics is about building models that make predictions (which are not limited to the future).


I said guess, you say prediction. Same thing. So must we build a model for the purpose of making predictions (guessing), if the rules by which the model operates define the behavior of its elements?

Creating the rules is what's meant by building the model.

You cannot have it both ways. In another thread, you said that rules can cause physical events to occur, and now you're claiming that man creates the rules. So which is it? Which definition of rules are you using now? Are rules created, or do rules occur naturally?


 but that physics can determine what the
real world is in the present.


The real-world is the collection of nataural phenomena - all phenomena. Talking about a "real world in the present" hardly makes sense.


That implies that we know that what we observe are *real* phenomena. You're going in circles again.

You're right about that, because you keep taking this discussion around in circles. In Physics, what's real *is* what's observed. That's not conjecture; it's definition.

From dictionary.com 
Reality:  The quality or state of being actual or true.

Where's your defintion?

All we have are observations. We hope
and claim that those observations are caused by real phenomena, but that's sheer philosophical speculation.

The observations are the phenomena, and all phenomena are real (what else would they be?). No speculation is involved.

The notion of reality is not about perception at any point in history, it's about an absolute truth. That's the definition of real.


We have observations, and we 
use those to build a model.  That's pretty much it.

>   Well, I hate to break this to you, but

that's not what's meant by physics being used to build models. As I've said, all we have at any given present time are observations.


Didn't I hear you say that time didn't exist? Never mind, that's rhetorical, but yes, Physics is concerned only with observations (the "present time" qualifier is inappropriate).


Time is not physical. That doesn't mean that there's no past, present, and future as concepts of the human mind, and in order to effect communication with you, I've got to use terms with which you can identify.



>   Physics

isn't concerned about if what we observed really happened or not.


Anything observed *really* happened; it's nonsensical to suppose otherwise.


It's philosophical to suppose that it did. Much of what we thought we observed in the past turned out to be inconsistent with more thorough observations.

Everything that was observed, was observed. 

Correct.  Reality has nothing to do with it.

> And so for you to be correct, you'd have to agree that
reality changed.

No observation was or will ever be corrected, since there is no conceivable way in which that could be done.

Well, if we observed what was real (singularly true), then what we observed would never change.


> But if you believe in the concept of reality, then it
can't change. IOW, at one point, man's best observation was that the sun orbited the Earth, and the planets moved in the sky in irregular patterns. Is that what was *really* happening simply because that's what the sum total of our observations told us was real? 

Sun and Earth are elements of models, remember?  So is orbit; so is sky.
What has evolved are the models (i.e. the pictures of reality), not reality.

that's my point. At one moment in time, we observed one thing, and then later, we came to know that we observed another. for your definition to be valid, reality would have to change. But it does not.


> Or are we so
arrogant that what we claim to observe *now* is real, and what we observed in the past was a mistake?

You're very confused. 

"The quality or state of being actual or true."  The confusion is yours.

>   We

have no way of knowing if our lying eyes, or any devices we've invented *really* happened as we observed them.


You are hung up on the concept of "real", and you're giving it unwarranted significance. It's just a label for what it is that Physics studies.


Real implies a singular and absolute truth.

Nonsense, it implies its definition, and in Physics, "singular and absolute truth" is not it. 

The quality or state of being actual or true


> It's not just a term in
physics, it's a concept which has no place in physics.

Do you think "measurable phenomena" has a place in physics? 

Yes.

Assuming you do, then taking "real" to be synonymous with "measurable phenomena", gives it a place in Physics.

But taking it so is invalid. If pigs could fly on their own, they wouldn't be pigs.

>   To claim that we do is to close

off a whole set of possibilities. Even AE claimed that no observer has a valid claim over any other observer about what *really* happened.


Physics has procedures to arrive at consensus re. observations/measurements (i.e. the experiments which give rise to observations are required to be repeatable), but it makes no sense to try to differentiate between things that "really" happened and things that happened, but not "really".


Agreed. That's why the concept of reality should not be brought to bear in physics. No differentiation is required.

"Reality" is brought in because it's the object of attention - the raison d'etre for doing Physics. 

The quality or state of being actual or true

We make observations, and
build a model based upon those observations. That model is reliable to the extent that predictions made based upon the model are consistent with subsequent observations.


The more observations we make, the more
reliable the model becomes.

This would be an interesting issue to explore, but not at the level that we're at. 

Because you're confused.

> That's it.

We make observations, and we build a model of what reality is.


Yes, but what reality *is*, is fully contained in the observations and measurements of natural phenomena (e.g. a "good" model with planets doesn't suggest that planets are in any sense real).


How do you know that your observations are fully and absolutely consistent with the one and only truth?

What's a "one and only truth"? 

Reality.  The quality or state of being actual or true


Now, we
can use that model to make the sorts of predictions you spoke of, but as far as physics is concerned, all we have is the model, and reality has nothing to do with anything.


Understanding reality (i.e. the world we inhabit) is the *sole* purpose for doing Physics. Reality has everything to do with Physics.


As I said, by building an ever increasingly reliable model, we hope that the model gets increasingly closer to what we hope is a reality, but that's as much as we can do. Physics is just a tool.

Physics isn't a tool; physics is a discipline whose goal is to achieve an understanding of our world (i.e. of reality). Physics uses mathematics and logic as tools in an effort to reach that goal. 

tomato............tomato.  We invented it to help us.  Tool.

Within the world
of physics, we build models. Outside the realm, we use the model to speculate about reality. This is a physics NG, and you have no business considering reality while you're doing physics. While you're doing physics, just stick to building the model.

Aargh! 

The quality or state of being actual or true

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).



No. We can only hop our model is accurate. But there's no way of knowing that at all.


Sure it can be known. There'd be no reason for going to the trouble of building models, if it couldn't be known. Accurate models are the ones whose predictions aren't wrong.


The reliability of a model is determined by the degree to which predictions made based upon it are consistent with observations.



>   All we can do is build the mot reliable model

possible.


Provided that "reliable" is interpreted as "correctly predicting measurements". 


Reliable is the degree to which predictions agree with observations.


The real-world *is* the measurements - of course it exists.



Maybe, maybe not, but that's a philosophical issue, not a scientific one.


It's not an "issue" at all; it's a definition.


It's an assertion, and a bad one.

Do you even know what a definition is? It's the substitution of one word or phrase for another word or phrase. So if I say e.g. substitute the term "real-world" for "collection of measureable phenomena", that's a definition, not an assertion. 

The quality or state of being actual or true


  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.



Ignoring the past to make predictions is nothing more than sheer random guessing.


It's irrelevant how a good model comes about. If a Ouija board was created that correctly predicted all measurements, it would be the end of Science.


I agree. But whereas we've tried the Ouija board and it's proven to be unreliable, we build model based upon observations, and if we use that
model to make predictions, then by definition, *past* observations were the only relevant factor. So to claim that relying on the past is irrelevant is simply false.


>   I base my prediction that the rock will hit the Earth, how

fast it will get there, and the force with which it will impact, when I let it go based upon past observations. Those observations are in no way irrelevant to those predictions.


People who build models generally are aware of past observations, and usually consider them during the building process, but the point is that needn't be the case; only the end product is relevant, not the manner of production.


As I said, building a model without regard to the past would be sheer guesswork.

So what. 

So that contradicts your assertion that models have nothing to do with the past.

> Give me one example of a valid scientific model which was not
based upon past observations. Just one.

Try producing a coherent description of what it means for a model to be "based upon past observations". 

I knew you couldn't do it.

> 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.



There's nothing in what I've said that's contrary to this. So why'd you post it?


Because I believe that you view Earth, Sun and orbit as more than elements of a model. 


Within the realm of physics, I do not.


 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.



We can define a path all we want, but the observation will be the observation, and natural phenomena will ignore any definition created by man. It will be what it will be, and all we can do is match our prediction of what it will be to what it is in order to value the worth of our model.


That's right, but without the definition there'd be no prediction.


But the fact remains that neither the definition nor the prediction will effect the path.

"Path" is an model entity; it's obviously effected by its definition. 

It is what it is.  A definition is an invention of man.

It will be what it will be. Tell me this, would there
be any definitions or predictions without man? Would the path still be the path?

There would be no path, since there'd be no model.

The model is an invention of man too. We created it, remember? We create models based upon observations. There's be no reason for a model if we could play with reality. <sigh>


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.



Well, of course we base all of this upon the model. There's nothing in that proposition that's contrary to what I said.


Yes there is, because for you, "cause" is what effects phenomena, and my proposition claims that causes exist only in models.


Here's the thing. There is a reality (one absolute truth)

That's not what reality means in Physics. 

The quality or state of being actual or true

> which our
limited science and limited intellect and limited ability to make accurate measurements prevents us from ever knowing.

What sense does it make to believe that there's something we can never know?

It is what it is. We don't believe it because there's a purpose in believing it, we believe it because we do.



> However, because
we're curious about that which affects us, we set out to conduct observations of everything physical. Physical is defined as anything which is capable of affecting our senses, either directly, or indirectly.

If you want to start your own discipline, you're free to create your own definitions; if you want to discuss Physics, you're not. 

The quality or state of being actual or true


So we endeavor to build one, giant, integrated model of everything physical. As we evolve, not only does the model grow, but portions of become increasingly more reliable. Reliability is defined as the extent to which predictions made based upon the model are consistent with observations.

So what of predictions? Predictions are more than simple trend analysis based upon observations. While we can predict the path of the Earth

Models don't predict the "path of the Earth"; they predict the readings on specific instruments. "Path" and "Earth" are entities of models where they're used to logically infer the predictions.

as
it orbits the Sun fairly reliably based upon this method, the only way we were able to predict what would happen with the first nuclear explosion was to take all of our observations of all relevant natural phenomena, and combine that with what you, yourself claim is the whole point of science, and that's a better understanding of that which affects us. In short, it's the cause. What causes a rock to fall to the Earth when I let it go, and will whatever causes that to happen be a factor in what causes the nuclear explosion?

"Falling rocks" and "nuclear explosions" are elements of models. What causes them to behave as they do are the postulates of the model (i.e. their behavior is defined).

You've repeatedly claimed to understand the distinction between real-world and model, yet you continually demonstrate otherwise. 

The quality or state of being actual or true

So we take our speculations as to what cases that which we observe, together with other data which our model yields, and we developed a prediction of what will happen.



So what remains here are two things. First, is your claim that the *rules* we've developed to explain the operation of the model, in themselves, can affect the operation of the model. Well, you'll have to
explain to me what a rule is in that context,

The rules of a model are the rules of logical inference together with the model's postulates.

because the elements of
the model with behave as we find them behaving,

The only place you can "find" how the model elements are behaving is within the model, and they way they're *always* found to behave is as they've been defined to behave.

There is no always. There is just more and more evidence to demonstrate reliability.



and no rules written by
man will affect them.

You're not even close to understanding how Physics' modelling process works. You need to spend a lot more of your time listening than talking. 

The quality or state of being actual or true

Second is your claim that science is somehow capable on knowing one, absolute truth. Clearly, it is not.

I have no idea what "absolute truth" even means, so it's certainly not any claim that I've made.

The quality or state of being actual or true 

.

Relevant Pages

  • Re: Incommensurability of Mathematical Logic and Scientific Logic
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  • Re: Incommensurability of Mathematical Logic and Scientific Logic
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  • Re: Incommensurability of Mathematical Logic and Scientific Logic
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  • Re: Incommensurability of Mathematical Logic and Scientific Logic
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