Can there be "non gap" arguments against reductionism?

Question

Reductionism is the idea that any scientific theory can be eventually reduced to the laws of physics. For example the laws of biology can be reduced to chemistry, which in turn can be reduced to the laws of physics. Implicit in this is that there is a hierarchy of theories, and to reduce a theory to the laws of physics, all one has to do is reduce it to a theory that has already been reduced (which would then be considered lower in the reduction hierarchy).

In a larger sense, reductionism can be seen as a form of positivism: Anything that can be explained or discussed rationally can be eventually broken down to mathematical, logical and empirical statements, which in turn can be broken down into laws and statements of physics.

There are 2 opposing positions to this one:

• Not everything can be reduced to the laws of physics because there is more to the world than the physical (i.e. Cartesian Dualism).
• The world is only composed of physical/material objects and events (there is no supernatural), but we will never be able to reduce them to the laws of physics - for example we will never be able to reduce mental states to just a description of neurons. I've seen this view described as naturalism, emergentism, supervenience, among others.

My questions are the following:

1. Disregarding the possibility of supernatural, are there any arguments against reductionism other than gap arguments (i.e. arguments based on the fact that we haven't been able to reduce some particular theory to a lower one yet)?
2. Is such an argument conceivable at all, where we can definitively prove that reductionism doesn't hold, as opposed to simply listing theories that we haven't been able to reduce yet?

Answer 1

People would like to think that since the number of concepts involved needs to be kept small, that the specific statement of all laws of physics, is, at any given moment, expressible in some many-sorted first-order logic.

(More directly, this is related to "Henkin semantics" on higher order logics, where if you accept limitations on what quantifiers consider, you can safely use second-order language in a way that is no more risky than first-order language. I would suggest that the way science tests and defines things requires its quantifiers to have Henkin semantics.

But I think that to get consensus a scientific principle must be even more stringent about its referents -- it needs to be prescriptively clear about the 'sorts' of things to which any given claim applies, or such a claim will not be demonstrable (much less falsifiable). This reduces it to a sub-recursive type theory and makes it a many-sorted first-order system.)

The need for higher orders of logic arises largely in mathematics and psychological arenas, where things or people can refer to themselves. But then a lot of those things are second-order by nature, and some of them should be irreducibly second-order.

If those irreducibly second-order ideas are somehow real, then physics will not be able to encompass them. Physics and biology are unlikely to be able to explain why we imagine space should be infinitely divisible, for example. Notions like infinity, the continuity of space, and other deep mathematical anchor points do not seem to arise from their survival value. They are not supported by actual physics. They do little but waste our time thinking about them. And they seem to arise far too late to be evolved.

As Terrence McKenna points out, many of us live in a world of linguistic structure more than material implications (especially those who often visit a psychedelic state.) And very little of that linguistic structure is truly first order. Grammarians have tried to establish an adequate set of parts-of-speech, which is basically a many-sorted first-order classification of words as functions or propositions, for a very long time, and lots of usages still escape our modern Natural Language Processors.

Philosophy's ongoing obsession with finding a materially plausible meaning for 'meaning' is a perfect example. We can come close by encoding meaning as use and action (a la Wittgenstein's games), or by encoding meaning as a matrix of relations between abstract referents with deep commonly-reoccurring psychological underpinnings (a la Lacan's master signifiers), but neither of those is truly reducible to statable rules.

At the same time, these linguistic constructs also do not seem accidental. They have made for easier development of engineering and legal structures in many places. This implies some force of simplicity or cogency of thought that acts as a force on our intellectual development.

You can presume that the drive toward simplicity and elegance itself survives by wasting the energy of those who are not driven to simplify. But that does not explain how the simplifications themselves come to exist. Thinking creates ideas bigger than reality all the time, and we use those to genuine effect.

And as we use them, we enter an order of complexity in our reasoning that is beyond what can be encapsulated by the kind of rules we prefer in science. Science hopes the world is describable in first-order statements, perhaps with a second-order sorting. But our mathematics, as a linguistic structure, is not. So a statable theory of the world is not capable of predicting our mathematics and other pure linguistic objects, or their future development.

Answer 2

It depends very much on what you mean by “can be reduced”.

In the sense of one level being a theoretical consequence of another level, sure, chemistry is already ~100% reduced to physics: chemical bonds are just sharing of electrons, and they are likely or not depending on the properties of the atoms, in particular the permitted electron energy levels (quantum physics, i.e. you need quantum physics for this particular reduction).

But in the sense of practical predictions, the distance between these abstraction levels is too great. It's the old discovery that even almost trivially simple systems can exhibit unlimited complexity. For example, it has been proved that an exceedingly simple 2-state 3-symbol Turing machine is universal, i.e. that it can do any arbitrarily complex computation.

As a more simple physical example, while the behavior of two gravitationally attracted bodies in empty space can be practically predicted to any desired degree of accuracy, arbitrarily far into the future, the behavior of three bodies, called the three body problem, is in practice not predictable.

Still, they just follow simple physical law: it's the emerging behavior that's so complex, so exponentially dependent on small variations, that it's effectively not predictable.

The odd thing about complex behavior is that we often can see large scale patterns in it, and then make probabilistic (statistical) predictions at that level: higher level laws.

This is how chemistry emerges at a higher level of abstraction than physics, and how climate emerges at a higher level of abstraction than weather (which in turn, and so on).

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In other news, …

I find it noteworthy that the notion of practically irreducible complexity is not one of the "two positions" you list, namely (1) the supernatural and (2) the view that some things just can't be understood. If there ever was false dichotomy it must be this, with both branches just childish nonsense. Is it really true that modern adult philosophers in general think one has to choose between the childish nonsense options (1) and (2)?