Ken G,
I had said the same thing you did. That our Current level of mathematics is an approximation. It's accurate- but imperfect.

Irrelevant to the fact that (Call it a platonic view all you want) the reality that exists does exist. That is not an assumption.
Mathematics is a way of describing that reality.
This, too, is not an assumption.

Apparently not, or you would not have claimed that reality is completely logical.
That statement is only logical if by "flawed" you mean "violate their own rules". That would be a silly interpretation of that word, tautologically impossible. A reasonable meaning for "flawed" is "does not exactly correspond to reality". This is the meaning I have been using. But now I'm confused if you disagree, or if you "already knew" that.
If they are not convincing to you, there is little more I can do. I find them quite convincing.
As we cannot reach "consensus" on whether or not there are problems with interpreting reality mathematically, I guess we must conclude this is not a scientifically answerable question. Oh, that problem establishes my position anyway.
In all cases, I have shown the fallacy in your claims of fallacy. There is no more I can do than that. See previous remark.

I have said that so many times I am blue in the face. And you think I'm "shifting" in some way? No, all that is shifting is what you are imagining me to say. This is a summary of what I have been saying:

1) science is the study of reality, not the study of mathematics
2) mathematics has proven an invaluable tool in science
3) mathematics defines its own rules, so cannot be "wrong" by its own rules
4) reality does not always obey our mathematics, so mathematics can be "wrong" when applied to reality
5) we can work for better postulates, find their ramifications, and compare to observations of reality. That's science. But the authority is the observations, not the postulates, and we already know we will face fundamental limitations using this approach. The limitations include the fact that science must make models of reality, which are different from reality, and the mathematics appears in the models, not the reality. Hence the various fundamental limitations we face when making models (the need to make a subject/object dichotomy, the limit of our intelligence, the need to use words, the need to make idealizations, etc.) will always be there in any mathematical axiomatic systems we dream up to describe reality, so they will always limit how well the mathematics works on reality.

If any part of that was unclear before, or if you think I have "shifted" from this view in any way, I hope this has been clarified now.

No, you are mistaken. What you did was say "That would be like me confronting 19th century classical mechanics with electromagnetism, to claim that theoretical physics is gibberish. " That means you were accusing me of using an inconsistency to establish gibberish, which logically would require me to equate those two. Yes or no? As I do not equate them, and indeed it would be wrong to do so, your accusation is logically fallacious-- I can point to an inconsistency and use it to show naught but an inconstency, and indeed I would. Can we at least agree on what simple logic is?

The difference is, you do not need to "unravel" the inconsistencies, you only need to learn how to live with them. That has been the core of a large part of this debate about the differences between science and mathematics, in fact.

My point is, we already knew that. We only imagined otherwise when we lost track of what we were really doing, and of course relativity is no different.

I would say the contradiction has been illuminated, not unravelled. The "knot" is still there, but we see it that much more clearly.
How do you make sets? Made just like that. I fail to see why that is "substantive", please elaborate.

__________________
If we understood everything going on in the head of a pin... we still wouldn't know not to step on the pointy end.

People think the problem with models is that they are limited by our minds, but the greater problem is that our minds are limited by our models.

You were right about this one. It's not the excluded middle fallacy. It's a version of the liar's paradox, in other words of Russell's paradox.

But does it "exist in reality"? Or only in our imagination? What could it possibly mean for such a statement to exist? I say that such statements tell us little about logic (they are not accepted as propositions in modern logic), and even less about the physical world. It's such word games that best fit the description of "mere intellectual games" you've been trying to slap on mathematics.

The question you mention is deeply unrealistic, unphysical. You are the one who seems to be getting lost from reality with his wild flights of abstraction, not mathematicians.

But I'll play along for a while. The "fuzziness" you speak of is not something that exists (objectively) in reality. It exists in our minds, which are not used to seeing quantum mechanical objects, and therefore accept a certain fuzziness in their concepts of "Achilles" and "the turtle". When you shower in the morning and some of your hair falls down the drain, I'm sure you don't think that you're losing a piece of yourself, though strictly speaking -- in an idiotically strict sense -- one could legitimately argue precisely that. In short: even in a best case scenario, your example proves nothing about reality, only about the imprecision of human perceptions of reality.

Fair enough, but then I'm going to need to ask you what you meant, exactly, by the statement I contested:

What on Earth were you trying to say with this? What makes any of that "illogical"?

See above.

If the radius is 0.5 units, then the circumference will be pi units long.

Precision? Who said anything about precision? I am fully aware that physical measurements are limited to a certain number of decimal places, but an object is not the same as the measurements of that object. Measurements are merely, in your own terms, "projections" of reality.

Yes, that is exactly what you have done. You can waffle all you like, but this much is clear.

__________________
"All your bias are belong to us." Ara Pacis
"A witty saying proves nothing." Voltaire

You really haven't been paying attention, have you? No, that's not how you make a set. "Set" is a technical term in modern mathematics. A thing must satisfy a certain number of conditions before we call it a set. One of those conditions is that a set cannot be an element of itself. The examples you gave are not sets.

__________________
"All your bias are belong to us." Ara Pacis
"A witty saying proves nothing." Voltaire

Nothing that is comprised of words "exists in reality", obviously. All words are models, even the word "reality". Such are the limitations we cannot escape, I'm sorry to have to be the one to tell you this.Obviously not, see the above difference between "words" and "existence". The point is, fuzziness is indeed something we need to model reality effectively. You seem to think "mathematics" is some separate thing handed to us by logic, or by reality. No, it is neither-- it is whatever we make it, whatever rules we invent for it. And we choose how we make those rules-- often to mimic or model reality, but not always. Either way, it's still mathematics-- and it's still not reality. Fuzziness is just another something we need to address in our models to get them to work, it's just another thing we fashion in the image of our familiarities.
You don't seem to realize that "quantum mechanical objects" are also in our minds. Ergo, "fuzziness" is not so distinguishable. Indeed, fuzziness is a crucial aspect of quantum mechanical objects (a la wave functions in a position basis).

I find it strange that you think we have any means of interacting with reality other than "imprecise human perceptions". We do not, that's the point. So there is no way to make the separation you claim, between the limitations of our perceptions and the limitations of what we can prove about reality.
I never said it was "illogical", in the sense you appear to mean (contrary to logic), I said it did not project onto logic. If you don't see that difference, I'm not sure what I can say to draw it out. Some things project poorly onto logic, other things quite well, but nothing completely, except of course logic itself. Is that not obvious?

I was asking for reality, not a mental syllogism. Weren't you the one saying imagination "doesn't count" as reality, so it doesn't need to be logical? But now you imagine a circle and claim it is real? I'm confused how you distinguish what needs to be logical, and what doesn't.
True, but so are "objects"! That's the point.

__________________
If we understood everything going on in the head of a pin... we still wouldn't know not to step on the pointy end.

People think the problem with models is that they are limited by our minds, but the greater problem is that our minds are limited by our models.

A point I have made many times is that mathematics defines its own rules to avoid contradictions, purely out of choice by mathematicians. When it ran into trouble with "set", it found a new definition. That doesn't surprise me at all, it's a very nice mathematical game. Chess is nice too. But what I am looking at is our means for conceptualizing reality, and the limitations of logic on that, not the contortions that mathematics can go through to avoid contradictions. So if you say the technical meaning of "set" doesn't allow my construction, I will simply define a technical meaning that does, and call it a "gleezbo". How is the mathematics I'm doing any different from yours? It isn't, it just leads to contradictions. Even mathematics can lead to contradictions-- do you deny it? Do you not realize that there is nothing in mathematics itself that rules out contradictions, it is only the way we choose to do it which avoids them?

__________________
If we understood everything going on in the head of a pin... we still wouldn't know not to step on the pointy end.

People think the problem with models is that they are limited by our minds, but the greater problem is that our minds are limited by our models.

The mathematics is exact, its usefulness in modeling reality is what is imperfect. If you are saying that, then we agree completely.
True, it's not an assumption, it's a tautology.If by "describe" you mean "model" or "approximate", then again we have no disagreement. We would only disagree if you mean what has been said in this thread, that to work reality has to be built mathematically so "describing" it means, in effect, reverse engineering its structure. That's how we like to imagine science, but a surprisingly large number of people seem to actually believe it-- with no evidence beyond that it works to adopt that picture. That's the "religion" part I referred to-- many people feel it works to adopt that picture as well. If you can't demonstrate or falsify it, it just ain't science.

__________________
If we understood everything going on in the head of a pin... we still wouldn't know not to step on the pointy end.

People think the problem with models is that they are limited by our minds, but the greater problem is that our minds are limited by our models.

I think we are agreeing at odd angles.

If that makes sense.

The way I see it is that we Currently are employing mathematics imperfectly. In order to use what we have to describe our observations.

But if we were able to factor in every factor- the mathematics and the product- would be Perfect. It would describe observation- Perfectly.
We would be able to predict- Perfectly.

I don't know how many years (Millions?) It would take for us to attain that. But the very existence of the Universe strongly suggest that such is possible.
Imagine Unlimited calculating power, intellect and resources- and claim then it's still impossible- that would require divine intervention for the Universe to work.

I am asking what are the models or projections you speak of in regards to science and mathematics and how is it that they are models or replicas of something else? Are Newton's ink markings a model?

It is the notion that math and science produce some sort of copy of reality that I question. It suggests that the world is not understandable, but somehow a copy of it is.

Models are every bit as real as what they model.

In the example, I was simply carrying six bags into the house two at a time. I'm trying to look at science, math, and grocery shopping in the wider context of and as human activities and then asking, “Is there really a model here in the sense suggested by philosophy? (That is, in a dichotomized sense where there is a “reality out there” and a “subjective copy in here.”) Or are there just activities that we execute more or less well and that work out more or less well for us?”

In carrying the bags in, I did not attend to their atoms or molecules, but it doesn't follow then that what I did attend to was not real. Training and experience, including mathematical drills, changed me into someone who could carry grocery bags in, more often than not, efficiently and without risking muscle strain or dropping bags. There is more to reality than that, of course, including the atomic, but that doesn't make my achievement a model, projection, or copy of the atomic facts.

Let's look at something that more easily qualifies as a model. I can step outside to see if it is raining and then bring an umbrella if it is. Or, I can build a computer system that models the weather from an array of temperature, pressure, humidity sensors and so on. Then I can check the computer's predictions and bring an umbrella if it forecasts rain.
Is the computer system “not reality”? No. It is every bit as real as the rain. Is it a copy or replica of weather? No, not in this case. We just talk about it that way. Electronic components are not weather systems.

Stepping outside to check for rain and grabbing an umbrella puts my behavior, so to speak, in control of the rain falling on me. Grabbing an umbrella based on the computer's prediction, on the other hand, puts my behavior in control of temperature, pressure, humidity, and so on. That's what the computerized forecasting system allows—when the system works. It doesn't always work to my advantage (in either case), but that doesn't mean there is a non-reality (subjective) that is isolating me from a reality (objective). I deal with reality in either case. My skills, techniques, and equipment are just sometimes in need of improvement.

I think you want to look at the failure case, when the prediction fails, to suggest that there must be a non-real shadow rain system that I grabbed my umbrella in response to. But it was just an electronic computer and sensor array. A real one that failed for real reasons that made me really suffer by causing me to drag around an umbrella all day when I didn't need to. (That is, reality didn't afford me the luxury of hiding protected and isolated behind a subjective model. It always seems ready to knock some sense into me when I don't act the right way.)

That I think is the part we agree on.
That's the "odd angle". I would say that not only do we have no evidence that is true, we have considerable evidence that it isn't. It just sounds like a quasi-mathematical religion.
I think that exact argument has been used to advance the existence of a supreme being.That sounds similar to what Lonewulf said, but it doesn't follow from any scientific discoveries, it is pure faith. I see no reason why "mathematically calculated" vs. "divinely controlled" are the only possibilities. Why can't it just be what it is?

__________________
If we understood everything going on in the head of a pin... we still wouldn't know not to step on the pointy end.

People think the problem with models is that they are limited by our minds, but the greater problem is that our minds are limited by our models.

How so? What evidence do you have that suggests that the universe cannot be described mathematically?
I would say that we have a very simple piece of evidence: Cause and effect.
Similarly, it can be used to claim there can be no supreme being.
What I said demonstrates a Universe which is not ruled by Divine Intervention- but by cause and effect.
This is the second time you have said "no evidence."
How do you make this claim considering:
Quantum Mechanics-
Newtonian Physics*-
Celestial Mechanics*-
Fluid Mechanics-
Heck... Even Chaos theory!


* These two show much easier predictive value than the others- But all rely on cause and effect. No intelligence required.
Exactly- It IS what it IS.
The fact that it is a working system demonstrates that it is describable.
If it was unworking- or seemed unfathomable- then we would (And have in millenia past) chalk it up to Divine Intervention.

Words are not models. The command, "I'll have a Big Mac and a large fry" is not a facsimile of a Big Mac hamburger and french fries. I live in a society where speaking those words in the right contexts brings food (or a reasonable facsimile thereof!) my way. The words function in the wider context of such human interaction.

No.
NoNoNoNoNO....

This is all wrong!


.



It's Burger King where you can get fast food "my way."

Big Macs are lovin' it.

They fill all the textbooks, that's what the textbooks contain once you can interpret their meaning.
No, they are somethign real, that you are modeling as "ink markings. " But their meaning is a physics model.