If anything this seems like an argument for even less philosophy in physics.
Mathematical models are simply not equal to real world, even if we use models in an attempt to approximate, so that we can do useful things. Mathematics can never truly model reality. The best it can do is a caricature, and not the real thing.
Without solid philosophy to guide the scientists who drive the scientific institutions, the sciences fall stagnant, because it is philosophy that is the very bedrock and lifeblood of the scientific endeavour, in all fields. Without philosophy, that endless hunt and search for meaning and understanding, we lose our way.
While I don't disagree with your overall point, this claim is pure conjecture. Ironically, it depends on your philosophy of mathematics. If most physicists were mathematical Platonists, then your argument based on this claim falls apart.
There are exactly zero real physical systems that can be modelled with perfect accuracy to any indefinite point in the future.
Physics is made of limited toy models of complex systems. It makes accurate predictions over limited timescales under limited conditions.
That's it. That's all you get.
The limited accuracy doesn't keep the predictions from being useful over human-friendly timescales.
But it takes an unrealistic act of hubris to believe physics does more than this, and that after a few hundred years of effort its predictions and frameworks are already perfectly accurate and perfectly correct.
You're talking about simulation not modelling, which is what I and the GP are talking about. Totally different basket of fish. A model can 100% accurately represent the underlying system, and yet be practically incomputable. Intractability or incomputability are not hallmarks of modelling failure.
Furthermore, you can't dismiss an a priori argument that reality is mathematical by an appeal to empiricism. In such a world, empiricism is itself a mathematical process.
Simulations are one form of model. So to call simulations a different basket of fish is a mistake. Every model attempts to predict the outcome of something.
Nor can you say that reality is mathematical as an a priori argument or knowledge. It is simply a claim that is open to dispute. You are now dipping into philosophy. What would be much more accurate is that mathematics is a very useful tool in developing models of the universe around us. Certainly, there are various mathematical streams that give interesting insights in the physical world around us. But just because they are useful doesn't mean that they are correct.
Not true. Solomonoff induction is an algorithmic process that can reproduce any underlying computable function merely from sampling its outputs. This is a formalization of the scientific process, which means on a long enough timeline, science will converge on a 100% accurate model.
> Simulations are one form of model.
That's not the distinction I was making. The OP said there are "zero physical systems that can be modelled with prefect accuracy to any indefinite point in the future".
Let's unpack this in a mathematical context where there can be no ambiguity:
1. The universal Turing machine (UTM) is a model of computation.
2. I can never actually build a UTM because there is no such thing as an infinite tape.
3. The UTM is a 100% accurate model of computation, in that, any other form of computation can be translated to a UTM with some overhead.
4. I cannot simulate a UTM with perfect accuracy to any indefinite point in the future because I don't have an infinite tape.
So here we have a 100% accurate model that cannot be simulated as the OP said, so these two properties simply aren't entangled as the OP implied. Hopefully that clarifies the distinction I'm trying to make, namely that the accuracy of the model has nothing to do with our ability to simulate it to arbitrary precision. Modelling is simply different than simulating, even though we can simulate models.
> Nor can you say that reality is mathematical as an a priori argument or knowledge. It is simply a claim that is open to dispute. You are now dipping into philosophy.
Yes, it's a claim, but it's not one I was making. The OP said that "mathematics can never model reality" is not a conjecture, but "empirical fact".
And yet, existence is consistent with the hypothesis that reality is mathematical. Given this, empiricism would itself be a mathematical process, which directly contradicts the OP's point. So the OP's point is simply not objectively true, which is how he presented it.
You then go into comparing a non-physical entity as an example of a physical system. Universal Turing Machines are an idealised entity. It cannot match, in any way, any physical system in a 100% accurate way. So saying that you cannot simulate an idealised model of computation as the means of saying that that we have a 100% accurate model that cannot be simulated is logically circular.
It does not make the distinction you are trying to make. Simulations are models and all models are idealised. So simulations cannot never be 100% accurate as no model can be 100% accurate of physical systems.
As far as "reality is mathematical" and empiricism, you are the one claiming that empiricism is mathematical in nature when it is a philosophical viewpoint and you are claiming that the OP is claiming empiricism.
The problem you are forgetting is that every theory and every model are idealised representations of the universe about us. Whether or not we are able to successfully use mathematics to describe all that we find is another matter entirely.
When scientists, both experimental or theoretical, say that their theories or models on any the subject are correct, they are misleading themselves and everyone else. Every model and theory is inaccurate. All make assumptions that ignore the reality that they are investigating.
I have said this before, just because a theory or model gives some predictive ability to what one may see, it doesn't mean that that the theory or model is correct. Too many people, including the scientists that promote a theory or model, get so caught up in being right that they forget that the theory and model is only something that we can use to try and understand what is going on about us in the universe.
I used to have no problems with biological evolutionary theory and models. However, after reviewing the results of experiments in the field, it became obvious that something was really wrong with the model (models) being used. The results did not support what was being promoted.
I used to have no problems with various things like the "big bang" or "black holes" or "neutron stars" or even general relativity, until I started to look at what was being seen in actual experiments and the problems with the underlying assumptions to the theories being used. Anomalous results that were being found and ignored. The ad hominem attacks of those who did not ascribe to the "consensus" theories and models really lead me to investigate the basic assumptions being used.
All that I see is a growing problem in science where it is no longer about developing an understanding of our universe but "follow the party line" or be anathema and be excommunicated. To those who know their history, the Inquisition is alive and well today.
Science is a tool we can use to gain some understanding. Philosophy is a tool we can use to gain understanding. We should be capable of putting these tools in our toolbox and using them accordingly. But to those who only have a hammer, then everything is a nail.
Any process which would converge on a 100% accurate model would suffice. A universally agreed upon definition is not necessary. Some such processes will simply converge more quickly than others.
> So saying that you cannot simulate an idealised model of computation as the means of saying that that we have a 100% accurate model that cannot be simulated is logically circular.
I don't think youve understood the example if this is your summary of my argument. My argument proves that even given 100% accurate model, simulability is a completely separate property. Accuracy is necessary but not sufficient. Accuracy is also achievable, as was mathematically proven in Solomonoff Induction.
> So simulations cannot never be 100% accurate as no model can be 100% accurate of physical systems.
This is either incorrect or wildly speculative. Either way, these two claims are not entangled, ie. simulations can be inaccurate for reasons other than the accuracy of the model.
> As far as "reality is mathematical" and empiricism, you are the one claiming that empiricism is mathematical in nature when it is a philosophical viewpoint and you are claiming that the OP is claiming empiricism
No I'm not. I suggest you reread it again, and keep in mind that since we don't know the fundamental structure of reality, the OP's claim that the conjecture is empirically false is a universal claim that must be true regardless of the structure. His claim is false in a mathematical universe as I explained, ergo his claim is simply false. See, avoiding silly arguments like this is why people need philosophy.
> I have said this before, just because a theory or model gives some predictive ability to what one may see, it doesn't mean that that the theory or model is correct
No one has made that claim.
Simulation is a model and as such is not a "completely separate property". You raise the "mathematically proven" Solomonoff induction process. Yet you do not state the limitations to such a process and the simple fact that it is about computability and for all intents and purposes completely impractical for any study of reality.
There are many simulations that are not computable.
You have a belief that a model is possible to be 100% accurate. You will need to demonstrate that belief. Every model and theory makes some assumption and simplifications about the subject matter for which it is applicable.
You make an assumption that mathematics is capable of describing the universe accurately. Yet mathematics is an idealised system with its own assumptions as to what is true.
This is no way means that the universe itself is mathematical, nor does it mean that mathematics can describe the universe. I have no problem with models and theories being useful but all fail in some area of applicability.
The fundamental error you are making is the assumption that humans can understand. We can gain some understanding but we do not understand. There is a big difference here.
I'll say it again, science (even mathematics) is not about finding the "truth" but is about creating workable models and theories that we can use. If you want "truth" then study philosophy and religion.
Every experiment performed in the search for a more workable model and theory always gives rise to more questions. Many times, those questions can be "swept under the carpet" because those questions lead to question the firmly held belief in the model and theory being investigated.
You cannot declare that the OP's claim is simply false since he talking about the universe and not a "mathematical universe". Your claim that the universe is a mathematical universe is supposition on your part.
When you claim that a model or theory is capable of being 100% accurate then you are making the claim that the model or theory is correct.
It is interesting that you recognise that we don't know the fundamental structure of reality, yet you make the claim that it is mathematical. Please take a step back and also recognise that mathematics is a useful tool to help develop useful models and theories. Don't give authority to mathematics and the theories and models that come out of it. Keep in mind that they are useful "tools" only.
The discussion is about physics and philosophy and the interaction between the two. Those who have claimed that physics doesn't need philosophy have forgotten or have never looked at the specific philosophical underpinnings involved in the current crop of models and theories in use across every field of scientific study and investigation. Those philosophical viewpoints have dictated where the various models and theories have gone.
Have a look at your own fundamental belief system and ask yourself "How would I look at the universe around me if my basic belief was different?" Understand that your philosophical and religious viewpoint colours how you interpret the results of experiments, colours what experiments you will perceive and how you will develop your theories and models. If you are an Atheist, you will see things in a variety of ways. If you are a Buddhist, you will see things differently. This will happen whether you are a Hindu, a Daoist, a Moslem, a Christian, a Wiccan, or any of the various religious or philosophical systems.
Honestly, I'm having trouble understanding how I can explain this more clearly, because I literally provided you with a reference to a mathematical proof that this is possible. Convergence on truth is already a well known of applying Bayesian probability, and Solomonoff Induction places this process on a rigourous formal footing from first principles. This fact you keep saying is a conjecture that I need to demonstrate has already been demonstrated.
> Simulation is a model and as such is not a "completely separate property".
Yes, it is. That's literally what "necessary but not sufficient means". Indecidability in a formal system is a property of having enough power to represent addition and multiplication, it simply does not follow from either addition or multiplication alone.
> This is no way means that the universe itself is mathematical, nor does it mean that mathematics can describe the universe.
And that's pure conjecture. You have no way to prove this, and if you were at all familiar with the philosophy of mathematics, you'd know why Platonic and other forms of mathematical monism are actually preferred at the moment.
> You cannot declare that the OP's claim is simply false since he talking about the universe and not a "mathematical universe". Your claim that the universe is a mathematical universe is supposition on your part. [...] It is interesting that you recognise that we don't know the fundamental structure of reality, yet you make the claim that it is mathematical
No, you've once again failed to understand the argument being made, and frankly, I don't see any point in repeating myself further. I've laid out all of the facts that have been debated many times in philosophy, and now it's up to you to put aside whatever bias is driving you to continuously misinterpret my words.
That’s a strong and sweeping claim about a varied field, much of which is only concerned with experiments. Do you have anything like support for your claim? Remember that most of physics isn’t the highly popularized version of theoretical physics you may be familiar with.
Mathematical models are simply not equal to real world, even if we use models in an attempt to approximate, so that we can do useful things. Mathematics can never truly model reality.
No... shit? That’s why physics is dependent on observation and experiments, and why there is a division between physics and mathematics. We’re talking over the internet because of the concrete, useful things brought to us by physics.
The best it can do is a caricature, and not the real thing. Without solid philosophy to guide the scientists who drive the scientific institutions, the sciences fall stagnant, because it is philosophy that is the very bedrock and lifeblood of the scientific endeavour, in all fields. Without philosophy, that endless hunt and search for meaning and understanding, we lose our way.
How is philosophy in any way a cure for this imagined loss of rigor? The problem with physics according to you is a divorce from reality, and your solution is something even more abstract, less amenable to rigor, and famously fluid?
Huh?!
This point seems to be lost on a bunch of physicists these days who wallow in their derivations and forget that the fundamental revolution in modern science was the empirical method. The silly philosophers who got overthrown never knew it.
Animals understand "the empirical method". Experimentation, pattern inference, cause and effect... Aristotle may have described it, but like most of the rest of the interaction of philosophy and science it's a post-hoc formalisation, mostly good for convincing philosophers that scientists are doing something reasonable.
That's why they should learn some philosophy of science.
Here's a philosophy-free formulation of science: (i.e. one where scientists don't have to know any philosophy)
- People set up symbol games with rules, that produce symbols.
- They also set up physical machines that produce symbols.
- When they match, they're happy.
I think that does a good job of capturing why physics was able to progress so well without concurrent progress in philosophy. At the end of a day, a physicist will have a number on their scratch paper and a number on the meter and the goal is to get them to match. Mainly the role of philosophy is to guard them from any distractions that would confuse them away from doing that, and perhaps to bend their brains into coming up with good symbol games.
Philosophy informs these questions. For instance, a scientific process modelled on Solomonoff induction would give you more insight on what kind of games you should set up and why, which games are better than others for the same symbol outputs and why, to what extend modifying a game is a valid approach, etc.
If you have multiple matching symbol games, maybe just either prove them mathematically equivalent (a la matrix mechanics and Schrodinger's equation), or if they aren't equivalent, write them both down and keep an eye on them until you develop an experiment that can distinguish between them. As far as I can see, that remains within the paradigm of "go forth and match the symbols."
But your rules provide no guidance to do so, which would require philosophy.
> As far as I can see, that remains within the paradigm of "go forth and match the symbols."
Absolutely, I'm not suggesting changing the spirit of the basic empirical game you outline, merely that a different set or a few additional rules would permit you to generate better games more efficiently. Blind trial and error would eventually work too, but we ideally want to converge on accuracy and precision as fast as possible. What this means in practice is a philosophical question worth answering.
It seems suspicious that this is classified as philosophy - it has an empirical foundation! You can even design experiments to test these "theories of metascience:" just check to see how fast the scientists that work according to them produce successful theories. So it sounds like what you're advocating for is a human science (i.e. very difficult to design experiments, but fundamentally based on empiricism), as opposed to a branch of philosophy.
Roughly speaking, the division I am making here goes: experiments plus arguments makes science, arguments without experiments makes philosophy. In this context, I can say, "scientists are only (professionally) interested in experiments and therefore uninterested in philosophy." However if something involves empiricism but is also labeled philosophy, that's just language and I gladly concede that scientists might be professionally interested in it.
I'm very skeptical that such a foundation would work faster or achieve more optimal results than an analytical approach. You can keep going meta, but so can I, and the analytical approach will always outpace the empirical one.
> Roughly speaking, the division I am making here goes: experiments plus arguments makes science, arguments without experiments makes philosophy.
I suppose it depends what you classify as "arguments". Science traditionally produces theories that provide predictive power, but also explanatory power. This latter aspect is often overlooked, but it's essential since it provides insights into further possible experiments. If your "arguments" includes an ontology for scientific theories, then I could agree with your breakdown, but notice that an ontology overlaps with philosophical inquiry.
Also, there's a new and growing branch called "experimental philosophy" which includes experiments that test intuitions on philosophical questions, so it's still not quite clear cut!
It sounds like you're describing and empirical meta-approach: that we should pick the approach that goes the fastest. I'm not proposing that analysis be thrown away, just that it is and should be controlled by empiricism (at every meta-level). Essentially, I'm arguing that science applies to itself recursively: if you take empiricism as axiomatic, then science can "choose" its own philosophy, just like it chooses its theories: empirically.
>Also, there's a new and growing branch called "experimental philosophy" which includes experiments that test intuitions on philosophical questions.
In that vein, you could claim that all philosophy is empirical: An Enquiry Concerning the Principles of Morals was plain evidence that Hume's brain had produced certain beliefs about morals. So, is philosophy of science an exploration of its namesake, or an exploration of the brains of philosophers of science? I say, whenever it has empirical grounding (in the success of science), it works like science and tells us things about how to do science, and when it's inwardly-focused it is just information about how philosophers' brains work.
>but also explanatory power
As far as I can tell, explanations are stories that make our brains feel comfortable with the procedures that we use to predict things. Why? Because perfect stories will be discarded without a second thought if another completely unpalatable theory comes along with better predictive power. Story-sentences about this stuff (for example, "the virtual particles pop in and out of existence in the vacuum") carry as much information about our brains as they do about the universe that they're supposedly describing.
It's not at all clear what "take empiricism as axiomatic" even means. This itself consists of a few a long-running philosophical debates:
https://plato.stanford.edu/entries/constructive-empiricism/
https://plato.stanford.edu/entries/rationalism-empiricism/
https://plato.stanford.edu/entries/logical-empiricism
> Because perfect stories will be discarded without a second thought if another completely unpalatable theory comes along with better predictive power.
I disagree. Newton's theories are still widely taught despite their inaccuracy, because their predictive power suffices and their explanatory power is superior to more accurate but sophisticated theories.
Furthermore, there's a good reason why the foundations of quantum mechanics are still hotly debated in some circles, despite the fact that such debates will have little practical impact on most practicing physicists. And such debates over explanatory power have yielded valuable insights into QM, like Bell's theorem which resulted from Bell's interest in the de Broglie-Bohm theory, and numerous other no-go theorems.
Certainly a theory with superior predictive power will be employed for predictions, but it will immediately launch an effort to provide a coherent explanatory framework.
The philosophy of science I am arguing for is empirically testable: so, as far as I can see that makes it science as opposed to philosophy.