Reductionism and Unity in Science

One problem encountered when physicists talk to philosophers of science is that we are, to quote George Bernard Shaw out of context, divided by a common language. A prime example concerns the word “reductionism”, which means different things to the two communities.

In the 20th Century the Logical Positivist philosophers were engaged in a highly normative program of specifying how they thought academic enquiry and science should be conducted. In 1961, Ernest Nagel published “The Structure of Science”, in which he discussed how high-level explanatory concepts (those applying to complex ensembles, and thus as used in biology or the social sciences) should be related to lower-level concepts (as used in physics). He proposed that theories at the different levels should be closely related and linked by explicit and tightly specified “bridge laws”. This idea is what philosophers call “inter-theoretic reductionism”, or just “reductionism”. It is a rather strong thesis about linkages between different levels of explanation in science.

To cut a long story short, Nagel’s conception does not work; nature is not like that. Amongst philosophers, Jerry Fodor has been influential in refuting Nagel’s reductionism as applied to many sciences. He called the sciences that cannot be Nagel-style reduced to lower-level descriptions the “special sciences”. This is a rather weird term to use since all sciences turn out to be “special sciences” (Nagel-style bridge-law reductionism does not always work even within fundamental particle physics, for which see below), but the term is a relic of the original presumption that a failure of Nagel-style reductionism would be the exception rather than the rule.

For the above reasons, philosophers of science generally maintain that “reductionism” (by which they mean the Nagel’s strong thesis) does not work, and on that they are right. They thus hold that physicists (who generally do espouse and defend a doctrine of reductionism) are naive in not realising that.

“The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble.”     — Paul Dirac, 1929 [1]

The problem is, the physicists’ conception of reductionism is very different. Physicists are, for the most part, blithely unaware of the above debate within philosophy, since the ethos of Nagel-style reductionism did not come from physics and was never a live issue within physics. Physicists have always been pragmatic and have adopted whatever works, whatever nature leads them to. Thus, where nature leads them to Nagel-style bridge laws physicists will readily adopt them, but on the whole nature is not like that.

The physicists’ conception of “reductionism” is instead what philosophers would call “supervenience physicalism”. This is a vastly weaker thesis than Nagel-style inter-theoretic reduction. The physicists’ thesis is ontological (about how the world is) in contrast to Nagel’s thesis which is epistemological (about how our ideas about the world should be).

Contra theologian Roger Trigg on the nature of science

Roger Trigg is a senior theologian and philosopher. His new book, “Beyond Matter”, is soon to be published by the Templeton Press, part of the wealthy Templeton Foundation whose aim is to produce a religion-friendly version of science.

An excert from the book promotes a view of science that is common among philosophers. Those of us with a scientistic perspective see it as erroneous, and yet, since Trigg’s account of science is widely accepted, it is instructive to rebut it.

Trigg argues that science rests on metaphysical assumptions:

What then has to be the case for genuine science as such to be possible? This is a question from outside science and is, by definition, a philosophical — even a metaphysical — question. Those who say that science can answer all questions are themselves standing outside science to make that claim. That is why naturalism — the modern version of materialism, seeing reality as defined by what is within reach of the sciences — becomes a metaphysical theory when it strays beyond methodology to talk of what can exist. Denying metaphysics and upholding materialism must itself be a move within metaphysics. It involves standing outside the practice of science and talking of its scope. The assertion that science can explain everything can never come from within science. It is always a statement about science.

This view can be summarised by the “linear” schematic:

One can see why theologians like this account of science. If it were really true that science rested on metaphysical assumptions then science would be in big trouble, since no-one has ever proposed a good way of validating metaphysical assumptions.

Basics of scientism: the web of knowledge

A common criticism of science is that it must make foundational assumptions that have to be taken on faith. It is, the critic asserts, just one world view among other, equally “valid”, world views that are based on different starting assumptions. Thus, the critic declares, science adopts naturalism as an axiom of faith, whereas a religious view is more complete in that it also allows for supernaturalism.

This argument assumes a linear view of knowledge, in which one starts with basic assumptions and builds on them using reason and evidence. The fundamentals of logic, for example, are part of the basic assumptions, and these cannot be further justified, but are simply the starting points of the system.

Under scientism this view is wrong. Instead, all knowledge should be regarded as a web of inter-related ideas, that are adopted in order that the overall web best models the world that we experience through sense data.

Any part of this web of ideas can be examined and replaced, if replacing it improves the overall match to reality. Even basic axioms of maths and logic can be evaluated, and thus they are ultimately accepted for empirical reasons, namely that they model the real world.

This view of knowledge was promoted by the Vienna Circle philosophers such as Otto Neurath, who gave the metaphor of knowledge being a raft floating at sea, where any part of it may be replaced. As worded by Quine:

The unity of maths and physics revisited

A major part of scientism is the idea that maths and logic are not distinct from science, but rather that they arise from the same fundamental root — they are all attempts to find descriptions of the world around us. The axioms of maths and logic are thus equivalent to the laws of physics, being statements of deep regularities of how the world behaves that enable us to describe and model the world.

My article advocating that mathematics is a part of science was recently posted on Scientia Salon. This was followed by an article by Massimo Pigliucci which took the opposite line and criticised the return of “radical empiricism”.

In response I wrote about the roots of empiricism, defending the radical empiricism that Pigliucci rejects. That post was getting rather long, so I have hived off parts into this post where I return to the distinction between mathematics and science. This is essentially a third part to my above two posts, countering various criticisms made on Scientia Salon.

To summarise the above arguments in two sentences, my critics were saying: “Well no, mathematics is anything but studying physical objects. It is the study of abstract concepts”, whereas I was saying, “Yes, mathematics is the study of abstract concepts, abstract concepts that are about the behaviour of the physical world”.

I have argued that maths and logic and science are all part of the same ensemble, being ideas adopted to model the world. We do that modelling by looking for regularities in the way the world works, and we abstract those into concepts that we call “laws of physics” or “axioms of maths” or of logic. Thus axioms of maths and logic are just as much empirical statements about the behaviour of the world as laws of physics. In part one I discussed other possible origins of mathematical axioms, while in part two I discussed the fundamental basis of empirical enquiry.

That leaves several possible differences between maths and science, which I address here:

The roots of empiricism: Hume’s fork, and the divide between knowledge “by observation” and “by reason”

Scientia Salon recently published my article advocating that mathematics is best regarded as a part of science. In reply to “scientism week”, Massimo Pigliucci wrote an article criticising “the return of radical empiricism”. The collision of “scientism week” with “anti-scientism week” generated a lot of energy and comments!

Massimo Pigliucci’s article is well worth reading, being a clear exposition of the relevant ideas. He traces the issues back to Hume’s famous fork, in which Hume declares that:

All the objects of human reason or enquiry may naturally be divided into two kinds, to wit, Relations of Ideas, and Matters of fact and real existence.

The “relations of ideas” category is taken to include mathematics and logic, where knowledge is “discoverable by the mere operation of thought”, while the “matters of fact” category contains science, where knowledge derives from empirical data.

Kant rejected Hume’s empiricism and sought to establish the primacy of reason. He adopted the term “a priori” for knowledge that does not derive from experience, in contrast to “a posteriori” knowledge which does. A related concept is that of “analytic” statements, which follow from the definitions of the terms, contrasting with “synthetic” statements that describe how the world is.

This notion of a fundamental epistemological divide holds today, and is at the heart of resistance to the idea that mathematics, logic and science are a unified whole.

In reading Pigliucci’s article I agree with much of what he says, but, to me, he seems to miss the main arguments for the essential unity of the different domains of knowledge. I will thus outline how I see the roots of empiricism, and then consider the supposed divide between knowledge “from reasoning” versus knowledge “from observation”.

Applying falsifiability in science

Falsifiability. as famously espoused by Karl Popper, is accepted as a key aspect of science. When a theory is being developed, however, it can be unclear how the theory might be tested, and theoretical science must be given license to pursue ideas that cannot be tested within our current technological capabilities. String theory is an example of this, though ultimately it cannot be accepted as a physical explanation without experimental support.

Further, experimental science is fallible, and thus we do not immediately reject a theory when contradicted by one experimental result, rather the process involves the interplay between experiment and theory. As Arthur Eddington quipped: “No experiment should be believed until it has been confirmed by theory”.

Sean Carroll recently called for the concept of falsifiability to be “retired”, saying that:

The falsifiability criterion gestures toward something true and important about science, but it is a blunt instrument in a situation that calls for subtlety and precision.

Meanwhile, Leonard Susskind has remarked that:

Throughout my long experience as a scientist I have heard un-falsifiability hurled at so many important ideas that I am inclined to think that no idea can have great merit unless it has drawn this criticism.

Defending scientism: mathematics is a part of science

While the term “scientism” is often a rebuke to those considered to be overstepping the proper boundaries of science, plenty of scientists will plead guilty to the charge so long as they get a say in how the term is defined. The “scientism” that I defend is the claim that, as far as we can tell, all human knowledge is empirical, deriving from empirical contact with reality. Further, that empirical reality seems, as far as we can tell, to be a unified whole, and thus our knowledge of reality is also unified across different subject areas so that transitions between subjects are seamless.

What we call “science” is the set of methods that we have found, empirically, to be the best for gaining knowledge about the universe, and the same toolkit and the same basic ideas about evidence work in all subject areas. Thus there are no “other ways of knowing”, no demarcation lines across which science cannot tread, no “non-overlapping magisteria”.

A related but different stance is expounded by philosopher Massimo Pigliucci in his critique of scientism [1]. Pigliucci instead prefers the umbrella term “scientia”, which includes “science, philosophy, mathematics and logic”. This sees mathematics and logic as epistemologically distinct from science. Indeed Pigliucci has remarked:

it should be uncontroversial (although it actually isn’t) that the kind of attention to empirical evidence, theory construction, and the relation between the two that characterizes science is “distinctive enough” … to allow us to meaningfully speak of an activity that we call science as sufficiently distinct from … mathematics.

Mathematics is a huge area of knowledge where science has absolutely nothing to say, zip …” [2]

In this piece I argue that mathematics is a part of science. I should clarify that I am taking a broad interpretation of science. Nobody who defends scientism envisages science narrowly, as limited only to what is done in university science departments. Rather, science is conceived broadly as our best attempt to make sense of the empirical evidence we have about the world around us. The “scientific method” is not an axiomatic assumption of science, rather it is itself the product of science, of trying to figure out the world, and is now adopted because it has been found to work.

A scientism defence of Logical Positivism

Like everyone else I read Ayer’s Language, Truth and Logic as a teenager and, like many people of a scientific bent, I loved it. The Logical Positivism that it espoused can be summarised as the claim that knowledge is of two types: (1) logical reasoning from axioms, such as used by mathematics; and (2) claims about the universe that can (in principle) be verified empirically. Anything else — such as metaphysics — is literally meaningless.

Logical Positivism is generally held to have been refuted (following criticisms from notables such as Quine, Popper and others), and as stated in its original form that is a fair assessment. However, its general thrust can be defended as sound. Indeed, Logical Positivism was a forerunner of what today gets called scientism, and interpreting it as scientism it is very much alive.

First, a defender of scientism would subsume the first type of knowledge, the “logical reasoning from axioms”, into the knowledge that derives from empiricism and can be empirically verified. Afterall, the reason that we adopt our basic axioms of logic and mathematics is because they work — they give results that apply to our universe. Where else would we have got them from?

What does “existence” mean?

During a recent online discussion I discovered, somewhat to my surprise, that there is no general agreement on what the word “exist” means. Everyone has an intuitive understanding of it but when it comes to an explicit definition of the word there is no consensus, and indeed philosophers have written a vast literature on the topic of ontology, or what exists.

Dictionaries don’t really help; for example Oxford Dictionaries gives a nicely circular set of definitions:

Exist: 1. have objective reality or being
Reality: 1. the state of things as they actually exist
Being: 1. existence.

Of course physicists have a perfectly good operational definition: something exists if it is capable of making a detector go ping. Try arguing that, however, and you’re immediately accused of materialism, physicalism, scientism, being blind to possibilities beyond a very narrow world-view, and a host of similar sins (I plead guilty to at least the first three).

Disagreeing (partially) with Sean Carroll about what is science

Sean Carroll talks a lot of sense on the nature of science, and in a recent post gave a definition of “science” that focuses on the methods and attitudes of science. He wrote:

Science consists of the following three-part process:
1. Think of every possible way the world could be. Label each way an “hypothesis”.
2. Look at how the world actually is. Call what you see “data” (or “evidence”).
3. Where possible, choose the hypothesis that provides the best fit to the data.

It’s a good operational definition, separating a scientific attitude from a pseudo-scientific or religious attitude, although the process needs to be iterative, with the hypothesis of step 3 then being tested against new data; and I would add in Feynman’s maxim: try hard to see whether you are fooling yourself, remembering that yourself is the easiest person to fool.

Later in the article, however, I start disagreeing with Carroll about what is and isn’t science. He says: