AstroAg17 said:

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Yeah I'm not following. I get what you're trying to say but I don't think your premises actually lead to your conclusions. "Math exists" doesn't necessarily mean that all mathematical expressions have a physical representation (unless you're TexAg91, then that's exactly what it means). The ability to express something mathematically is not more significant than the ability to express something in words. You seem to be implying that everything which can be described exists. I think that's nonsense, at least as far as our universe is concerned.

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Yeah, you should see this cool Mandelbrot object I've got here. It's so complex!

TexAgs91 said:

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k2aggie07 said:

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So you're just substituting "as of yet unknown" for "mysterious"?

That's cheating.

It's an article of faith that it is not mysterious and only undiscovered, versus undiscoverable.

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I am not a follower of "God of the Gaps".

We rarely see anything that doesn't follow the laws of physics. And when we do, we update the laws when needed. As you know these updates are only really made if they're able to make a prediction (repeatedly and by different scientists) according to the scientific method. So yes, there's dark matter and dark energy. They are detectable and make up a very large percentage of the universe, but we don't really know for sure what they are.

Given science's stellar track record to understand things once thought to be magic, why would I think that the story behind dark matter and dark energy would be any different?

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Have you ever considered that a physical law could be both super natural and repeatable?

Relavent to this thread, I was reading the book "the will power instinct" about human will and it mentions a few cases where a person's behavior was dramatically changed after damage to the brain. It is evident that there is some physical component to decisions making that occurs in the brain and when you remove a part of the inputs or processor (the brain) the output (decisions) change.

And damaging a computer hardware may adversely affect how a program runs. Does that mean the program is part of the hardware?

It doesn't exist outside of or apart from the hardware? It's generated solely from within the hardware?

AstroAg17 said:

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Can you bring it closer? I can't make out the details.

Tegmark believes there's a universe where the Mandelbrot fractal exists, doesn't he?

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I don't think so. It's an interesting mathematical object, that's about it. Although it's infinitely complex, it's not complex in a way that allows for life or any complex physics. And it's only 2D and there's no time. So pretty dull as far as universes go.

bmks270 said:

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Have you ever considered that a physical law could be both super natural and repeatable?

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Doesn't supernatural mean beyond the laws of nature?

AharonovBohm effect: a charged particle is affected by an electromagnetic field even though it has no local contact with that field
Bell's theorem: Why do measured quantum particles not satisfy mathematical probability theory?
Double-slit experiment: Matter and energy can act as a wave or as a particle depending on the experiment.
EinsteinPodolskyRosen paradox: Can far away events influence each other in quantum mechanics?
Extinction paradox: In the small wavelength limit, the total scattering cross section of an impenetrable sphere is twice its geometrical cross-sectional area (which is the value obtained in classical mechanics).[3]
Hardy's paradox: How can we make inferences about past events that we haven't observed while at the same time acknowledge that the act of observing it affects the reality we are inferring to?
Klein paradox: When the potential of a potential barrier becomes similar to the mass of the impinging particle, it becomes transparent.
Mott problem: Spherically symmetric wave functions, when observed, produce linear particle tracks.
Quantum LC circuit paradox: Energies stored on capacitance and inductance are not equal to the ground state energy of the quantum oscillator.[citation needed]
Quantum pseudo-telepathy: Two players who can not communicate accomplish tasks that seemingly require direct contact.
Quantum Zeno effect: (Turing paradox) echoing the Zeno paradox, a quantum particle that is continuously observed cannot change its state
Schrdinger's cat paradox: According to the Copenhagen interpretation of quantum mechanics, a cat could be simultaneously alive and dead, as long as it remains unobserved.
Uncertainty principle

This seems as much a consequence of your worldview as my definition of contemplate is accused of being mine.

And anyway even given your definition, if the software exists in another structure it still exists and can malfunction due to the hardware it is "installed" on.

If our consciousness existed outside of our physical reality (the hardware of the universe of which we are part) there would be no way of knowing if it existed on other hardware, in another reality.

Forget all computers. Focus on one.

Even if I accept your definition of "real", just because the software is completely absent on one computer doesn't mean it doesn't exist somewhere else.

And that software can be introduced to that same computer from outside the system. Yes?

So why can't that happen with our universe? And what's more how would you ever know if it was or wasn't?

k2aggie07 said:

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You're coming at it from the wrong angle.

What does a computer program do with a paradox? Nothing. It can't do anything because the paradox is both true and false at the same time. It's like dividing by zero, you get an error.

Anyway, darg, the subject is open and not really of my inventing:
http://www.iep.utm.edu/lp-argue/

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It's an interesting read. It kind of reminds me of the omnipotence paradox. Or the ontological argument. In general I have a hard time believing that this kind of word-play can lead to any fundamental truth about reality, even though I can't put my finger on exactly what I find wrong about the argument. Some of the objections I had to the argument are stated in that very article -- some of the objections I had are probably too infantile to be addressed and I'm just not well-versed enough in this stuff to see what's wrong with them. Either way I remain unconvinced that a human mind is not a sophisticated computer, though.

That said, let's say for the sake of argument I buy Lucas' argument. How does one jump from the fact that the human mind is not an S-computer to free will?

I remember the first time I encountered some logical paradoxes I said the same thing. "These are just word games and don't mean anything." It's a humbling experience. Logic is real, at least as real as math and any other model we use to interact with reality on a predictive basis (so...all of them).

I just think that determinism implies consistency... and I think the human mind is capable of true inconsistency. So I don't think humans are deterministic.

Put another way, I can't envision a way to make a computer behave in a truly inconsistent fashion, just as you can't make it truly random.

So assuming we're working with a formal system subject to the incompleteness theorem why does determinism imply inconsistency of the system rather than incompleteness?

Do you personally believe that the universe is governed by a set of physical laws that are deterministic and that humans are outside of that law? Or do you believe that nonorganic stuff is nondeterministic as well?

k2aggie07 said:

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Logic is real, at least as real as math and any other model we use to interact with reality on a predictive basis (so...all of them).

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Sure, but typically mathematics that we consider physically meaningful is grounded in empirical fact. This doesn't seem to be.

Can you describe a computer that is not a formal system? Or a computer that is not deterministic?

For any deterministic system, it will have a fixed and unconditional output for a given input. Can you elaborate a way to have such a system and have it not be a formal system?

Or are you implying that the machine of the brain is incomplete, in that there are inputs for which there is no defined output? Wouldn't that violate determinism in and of itself?

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Do you personally believe that the universe is governed by a set of physical laws that are deterministic and that humans are outside of that law? Or do you believe that nonorganic stuff is nondeterministic as well?

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I think that reality exists and the models we apply to interact with reality are both subject to reality and underdefine reality. You're putting the cart before the horse.

I suspect all of our models are wrong in a deterministic sense in that they are all based on assumptions that are probably incorrect in certain scales or frames of reference.

On the other hand, I also believe that there are realities beyond that which we have observed so far as humans, and I think it's foolish to limit our definition of "real" to things which currently exist inside the field of knowledge.

Piffle. There's all kinds of abstract mathematics that do not have any direct physical parallels.

Is the Banach-Tarski paradox "useful" or "real" or "grounded in empirical fact"?

I'm not aware of the banach-tarski paradox being physically meaningful, though.

k2aggie07 said:

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Can you describe a computer that is not a formal system? Or a computer that is not deterministic?

For any deterministic system, it will have a fixed and unconditional output for a given input. Can you elaborate a way to have such a system and have it not be a formal system?

Or are you implying that the machine of the brain is incomplete, in that there are inputs for which there is no defined output? Wouldn't that violate determinism in and of itself?

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I'm not sure what this is a reply to, or how this relates to what I said. I'm not denying that a computer is a formal system. I suppose the advent of a quantum computer may give you a computer that is not deterministic in the "hard" sense.

What have I said that requires that I show an example of a deterministic, non-formal system?

I'm not sure that physically realizable and noncomputable from a formal system are contradictions.

Or any paradox for that matter. Paradoxes arising is a great way for us to know our premises need tweaking, not that reality is fundamentally absurd and that we should ignore contradiction.

k2aggie07 said:

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I think that reality exists and the models we apply to interact with reality are both subject to reality and underdefine reality.

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I'm not sure what this means.

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I suspect all of our models are wrong in a deterministic sense in that they are all based on assumptions that are probably incorrect in certain scales or frames of reference.

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That might be true. Do you believe that we have a good sense for what those frames of reference are? Or at the very least that we have an idea of some frames of reference where those models correctly apply? For instance, I assume when you drive you are comfortable believing that the laws of Newton describe the behavior of your car in the past, present and future sufficiently well

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On the other hand, I also believe that there are realities beyond that which we have observed so far as humans, and I think it's foolish to limit our definition of "real" to things which currently exist inside the field of knowledge.

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I'm not sure anyone wants to limit reality to our field of knowledge. But if it does not interact with anything physical at least on some level I would be comfortable calling it "not real."

Sigh. Yet you use an a priori assumption to say that the metaphysical consciousness can't interact with the physical through our minds. Even though we have literally no idea how this works or why.

I would say that a quantum computer being non-deterministic would be pretty interesting and would match what a previous poster said about consciousness being an emergent phenomenon. I also think at that point both sides would be equally right or equally wrong b

k2aggie07 said:

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Sigh. Yet you use an a priori assumption to say that the metaphysical consciousness can't interact with the physical through our minds. Even though we have literally no idea how this works or why.

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Where have I made this claim?

You. Y'all. Sorry I got three people comin at me from different angles.

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I just think that determinism implies consistency... and I think the human mind is capable of true inconsistency. So I don't think humans are deterministic.

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What about chaotic systems though? Change a few input variables by a small amount and you'll get very different outputs. Even though they are deterministic, they appear to be inconsistent if you can't accurately tell the difference between input conditions from one run to the next. The human brain with its 100 trillion connections is a chaotic system.

Are you using chaotic as a synonym for "exceedingly complex"? Chaotic is kind of your version of God of the gaps, no?

I think there's a problem with determinism and intelligence, and the problem runs like this:

1. A determinant system by definition must have a 1:1 mapping between input configurations, state, and output configurations. Meaning it is truly consistent.

2. That means these inputs and outputs can be characterized (in theory, whether or not that is practical is not relevant). Because it is consistent, that characterization could be written axiomatically, i.e., a determinant system would be a formal system. If it is determinant, it can be modeled, and if it can be modeled, it would be modeled by math.

3. All formal systems are either incomplete or erroneous. Godel's two incompleteness theorems say that first, there will always be statements within a system that are not provable within the system; and second, that a system cannot prove its own consistency. Therefore this system will either be inconsistent or incomplete.

Conclusion / Discussion.

4. It is possible to conceive of inconsistencies which cannot be axiomatically described. Therefore the system (in this case, our minds) is at least capable of envisioning axiomatically impossible things. So the system may be inconsistent.

Is the axiomatically governed system our algorithm, i.e., how we consider / process information? If so, how do you axiomatically represent thinking or considering a paradox?

Or is the axiomatically governed system our output? If so, a paradox presents the opportunity for multiple solutions for a given input, and state -- this is inconsistency, i.e., indeterminance.

5. Alternately, the system could be provably consistent for areas it has a mapping, but incomplete. Again, consciousness is capable of envisioning things that are as of yet unmapped. These new areas may be consistent, but the system will never be provably determinant because there exists always the necessity of an incomplete system which means each new mapping will either be consistent and not the last one, or inconsistent and the last.

Therefore the human mind cannot be universally consistent or determinant, only conditionally determinant at best.