From Sabine Hossenfelder, author of *Lost in Math: How Beauty Leads Physics Astray,* at her blog Back(re)action:

It occurred to me some years ago, however, that there is a much simpler example for how reductionism can fail. It can fail simply because the extrapolation from the theory at short distances to the one at long distances is not possible without inputting further information. This can happen if the scale-dependence of a constant has a singularity, and that’s something which we cannot presently exclude.

With singularity I here do not mean a divergence, ie that something becomes infinitely large. Such situations are unphysical and not cases I would consider plausible for realistic systems. But functions can have singularities without anything becoming infinite: A singularity is merely a point beyond which a function cannot be continued.

I do not currently know of any example for which this actually happens. But I also don’t know a way to exclude it.

Now consider you want to derive the theory for the large objects (think humans) from the theory for the small objects (think elementary particles) but in your derivation you find that one of the functions has a singularity at some scale in between. This means you need new initial values past the singularity. It’s a clean example for a failure of reductionism, and it implies that the laws for large objects indeed might not follow from the laws for small objects. More.

Note her qualification:

It will take more than this to convince me that free will isn’t an illusion, but this example for the failure of reductionism gives you an excuse to continue believing in free will.

Of course, the critical question isn’t whether Hossenfelder does or doesn’t believe free will to be an illusion. Daniel Dennett believes consciousness to be an illusion. It’s a high stakes game.

The point she makes that is worth noting is that the laws of physics don’t rule out free will. But that is just a well for the laws of physics because, if Dennett is right and consciousness is an illusion, then the “laws of physics” probably are too. The concept of evidence has been rendered powerless.

Her explanations are admirably concise and free of question-begging.

*See also:* Sabine Hossenfelder: Particle physics now belly up. As it happens, her book is a solid string of 1’s at Amazon

Neuroscientist: Free will is an illusion but we should believe we have it

Neuroscientist debunks hype about no free will, etc.

GP, Mike Pence and Free Will

At Physics Central: How human beings can have free will as complex, purely physical systems

Do the defects of real numbers open the door to free will in physics?

and

How can we believe in naturalism if we have no choice?

Indian thinker Ashish Dalela has a series of articles on his blog on free will, in which he brings up similar points about reductionism — in the later posts he’s looking at things from Indian philosophy, but in his first essay, he makes the argument on how science itself is built on the axiom of choice.

This is a quote from the second part of the first article:

—

“Rationality is a Bottomless Pit

Let’s suppose that we are able to define some meta-factors that in turn decide which criteria such as sexual orientation, economic prestige, and social status, must be given what weight, and those weights can help us define the real problem to be solved, which can then be solved rationally.

But you quickly find that the choice of the meta-factors is itself questionable. How do we know that meta-factors are rational, and not merely our choices? By choosing those meta-factors, therefore, you don’t solve the problem of choice because someone is soon going to shake you up asking: Upon what deeper principles does this ground of human rationality stand?

Clearly, this is a cascading, recursive, logically bottomless pit. If you are going to use reason to explain all actions, but your rational system depends upon a choice of axioms (regardless of what those axioms are), then you haven’t truly solved the problem of choice until you explain how you arrived at the axioms themselves. As you try to explain those axioms by postulating more axioms, you end up in a bottomless pit of recursive reasoning.

There is only one way out of this bottomless pit: you must find a single axiom using which you can explain all rational action. This axiom must not be free will because you cannot postulate something to explain that very thing, and you cannot have more than one axiom because anything more than one still leaves room for choice. The only way to explain free will based on reason is if your rational system itself has only one axiom, and that axiom is not free will.

Now, if you actually try to go down this path, you will face a very simple problem: How do we reduce all reasoning to a single axiom plus logic? Isn’t the conclusion of a single axiom always that axiom no matter how many times you apply logic to it? For example, if you have a single letter ‘A’ in your alphabet, you can form statements like AAA, AAAA, AAAAA, etc. You are not adding any information to the system by repeating the same thing over and over. In effect, you now have the reverse problem of how to explain diversity.

If you happen to have more than one axioms – say two alphabets ‘A’ and ‘B’ – then you can create statements such as ABABAB, or AAABBB, but you are now again faced with the problem of choice: should the letter A be followed by the letter B or another letter A? Note that you can start with a set of axioms and reasoning takes you in different directions producing different conclusions. The conclusion you produce is not just an outcome of logic, but also the direction. This direction is itself not logical, and if you arrive at a conclusion you have a choice embedded in it.

In short, if you traverse this path, you will be frustrated. You will find that either you make no progress, or your progress actually depends on making some choices, which are not in turn dictated by anything that you knew previously – i.e. they aren’t rational. You might be tempted to terminate this exercise by postulating free will as an axiom! Such a postulate seems better when you have spent some time on the problem and found that it has no exit.

Whether or not the axiom of free will is true, is beside the point. I’m not suggesting (at least not yet) that free will is an axiom, or should be an axiom in your reasoning. I’m only saying that either you have that axiom as part of reasoning or you cannot produce reasoning.

The Axiom of Choice

The critics of free will reduce choice to rationality. But, unfortunately, rationality is a bottomless pit. No one has so far been able to define that fundamental basis on which rationality itself rests, or define how we must all reason, and which dimensions must be given how much weight. I’m not talking about the big questions of ethics, morality, goodness, beauty, etc. I’m saying that even in the most rigorous of sciences – logic, mathematics, and computation – we still don’t know what the foundation of rationality is.

The only thing that we know is this: logic alone is inadequate to produce rationality, so we need to have some fundamental ideas to create rationality. These ideas are called axioms in a formal system. But whatever basic axioms you choose, it is eventually your choice which cannot be rationalized.

To illustrate this point, we only need to take a closer look at the elementary mathematical problem of trying to order an unordered set of objects. We all know that to count objects, we must order them: one, two, three, four, five, etc. To order these objects, we must pick one object, and call it the first, followed by another object and call it the second, and so forth. The problem of counting thus reduces to the problem of ordering, and the problem of ordering reduces to the problem of choice: How do you pick the first object?

You might say: Well, I’m going to pick the objects rationally by measuring their physical properties: height, weight, speed, etc. But, which property among height, weight, or speed, are you going to measure first? If you are going to order the objects, then you must perhaps first order them by height, then by weight, then by speed, etc. You might also order them by speed, weight, and height. How do you decide what to measure first?

The point is that whenever you have a set of unordered objects, the ordering requires the choice of a method — ?e.g. measuring height before weight, and measuring weight before speed, etc. If you cannot make that choice, and try to derive it from some other rational reasoning, you end up with another set of axioms using which you must order height, weight, and speed, but to perform this ordering, you must first order those axioms themselves.

Given these problems, set theorists decided to postulate the Axiom of Choice. This axiom says that there are infinitely many ways in which we can order an unordered set of objects (i.e. label them as first, second, third, etc.) and we will assume that there is a way we can pick from among these methods of ordering. Let’s not worry about how an individual method orders, or how we arrive at one of the many possible methods—i.e. let’s not try to rationalize this choice and reduce it to more fundamental things—because we can see that this reduction in turn needs more axioms and choices.

Choice Isn’t A Human Problem

The key takeaway is this: choice is not merely a human problem and therefore does not only occur in relation to the decisions we need to make. Rather, it occurs in every attempt to order—i.e. distinguish and count—things. If we cannot distinguish and count, we cannot know, and if we cannot know that there many things, how do we form theories about those things?

We get around the problem by postulating choices; whether that postulate is true or false is beside the point. The key point is that if you are going to count things to formulate theories about nature, then you need choices. These theories may eventually describe the human body and brain and that description might appear to reduce our body and brain to the rational theory. However, that reduction does not eliminate choice, because we already made choices in formulating the theory. Since there are many ways in which we could have formed the theories (using different axioms) the mechanism we suppose explains our brain itself depends upon our original choices.

The only way we can totally eliminate choices is if there is a universal theory of nature that depends upon a single axiom which is not free will. However, that single axiom—as we saw above—will not explain diversity. The theory of a single axiom—even if it exists—will be incomplete. If, however, you decide that an arbitrary theory without the axiom of free will is the ultimate natural theory that also explains free will, your claim would be inconsistent since you made a choice of axioms to deny that there are choices.

A Dilemma for Reductionism

The reductionist reduces free will to rationality. The rationalist then reduces reasoning to computing. The computer scientist then reduces computing to a logical machine, which the physicist reduces to atoms and molecules, which a mathematician reduces to a mathematical theory (about Hilbert Spaces), which reduces to the idea of functions, which reduces to an ordered set of numbers. Now we have done all the reducing we know how to do today, and we are faced with the problem of how to order an unordered set of objects. This ordering itself needs a method which cannot be decided rationally, and must be chosen. Once you choose that method in ordering, you can see that at each successive level of reduction you must make similar choices.

You meet your destiny on the road you take to avoid it.

The dilemma of reductionism is the choice between a bottomless pit and the Axiom of Choice. If you are going to choose a bottomless pit, you not only have a lot of explaining left to do, but also that you are not being self-consistent: you are making a choice but denying that one is possible. If instead you are going to choose the Axiom of Choice, at least you are logically consistent because your action only affirms that choices are possible.

The key point is that if you want to be entirely rational, then you must axiomatize choice. If, however, you deny choice, then you are not only left with a bottomless pit, you are also logically irrational.

I’m still not insisting that free will is true! I’m only saying that if we are going to be rational about it, then we must accept free will as a unique, fundamental, and irreducible concept.”

https://www.ashishdalela.com/2015/11/12/do-we-have-free-will/

Reductionism is baseless – singularity or not and there’s no conflict between physics and free will:

1. No, we do not know the laws. We just know instances of those laws and we have been wrong in the past about those laws.

2. The laws cannot be known with certainty from as many discrete observations as you want

3. We know with certainty that 100% determinism fails ever since quantum mechanics effects were first observed. This invalidates your: “what you do tomorrow is already encoded in the state of the universe today”?

4. In the equation Outcome due to X% Determinism + Y% Quantum Indeterminacy + Z% Free Will + K% Unknown where X+Y+Z+K = 1, We Do Have Free Will if Z > 0 no matter how small Z is. You’re on mission impossible trying to demonstrate Z = 0

5. You’re not thinking through the implications of you being just a probabilistic automaton.

6. As I explain http://nonlin.org/free-will the default view on Free Will should be ‘FW is true’ because we feel it in us and in the actions of all other.

7. We clearly see the difference between inert objects that do not have Free Will and alive organisms that do. You can include in the first category the most advanced AI and the dead (formerly alive), and in the second the simplest bacteria and slime mold.

tarmaras as to:

It might interest you to know that ‘the problem of how to order an unordered set of objects’ shows up in quantum mechanics. Specifically, in regards to (quantum) contextuality we find that, in the quantum world, the property that you discover through measurement is not the property that the system actually had prior to the measurement process. What you observe necessarily depends on how you carried out the observation.,,, and,,, Measurement outcomes depend on all the other measurements that are performed – the full context of the experiment.

Contextuality means that quantum measurements can not be thought of as simply revealing some pre-existing properties of the system under study.

And as Anton Zeilinger states in the following video, “what we perceive as reality now depends on our earlier decision what to measure. Which is a very, very, deep message about the nature of reality and our part in the whole universe. We are not just passive observers.”

Thus the ‘axiom of choice’ is built into quantum mechanics and reveals itself through, as Ashish Dalela found in his line of reasoning, how we choose to order our measurements.

As Ashish Dalela noted, “This ordering itself needs a method which cannot be decided rationally, and must be chosen.”

As to Hossenfelder’s observation that

It might please Hossenfelder to know that her intuition that “the laws for large objects indeed might not follow from the laws for small objects” is now proven.

Specifically, the failure of reductive materialism to be able to explain the basic form of any particular organism occurs at a very low level. Much lower than DNA itself.

In the following article entitled ‘Quantum physics problem proved unsolvable’, which studied the derivation of macroscopic properties from a complete microscopic description, the researchers remark that even a perfect and complete description of the microscopic properties of a material is not enough to predict its macroscopic behaviour.,,, The researchers further commented that their findings challenge the reductionists’ point of view, as the insurmountable difficulty lies precisely in the derivation of macroscopic properties from a microscopic description.”

And as to Hossenfelder’s observation that “It occurred to me some years ago, however, that there is a much simpler example for how reductionism can fail. It can fail simply because the extrapolation from the theory at short distances to the one at long distances is not possible without inputting further information.”

It might further please Hossenfelder to know that her intuition that “the extrapolation from the theory at short distances to the one at long distances is not possible without inputting further information” is confirmed, at about the 41:00 minute mark of the following video, by Dr. Jonathan Wells.

Dr. Wells, using a branch of mathematics called category theory, demonstrates that, during embryological development, information must somehow be added to the developing embryo, ‘from the outside’, by some ‘non-material’ method.

To provide further evidence for information coming into the developing embryo ‘from the outside’, it is also important to note that quantum correlations somehow arise from outside spacetime, in the sense that no story in space and time can describe them,,,

And these quantum correlations which somehow arise from outside spacetime, are now found in molecular biology on a massive scale. In every DNA and Protein molecule,,,

Thus in conclusion, the reductive materialistic framework of Darwinian evolution is found to be grossly inadequate for explaining how any particular organism might achieve its basic form. Moreover, to state what should be glaringly obvious, since neo-Darwinian explanations are grossly inadequate for explaining how any particular organism might achieve its basic form, then neo-Darwinian speculations for how one type of organism might transform into another type of organism are based on pure fantasy and have no discernible experimental basis in reality.

Whereas, on the other hand, Theism, especially with these recent breakthroughs in quantum biology,,,

,,,is found to be very well supported in its claim that God has formed each of us in our mother’s womb.

Verses: