Monday, February 26, 2007

The Metaphysics of the Scientific Method

Part 1: The Failure of Deductivism
Part 2: The Failure of Logical Positivism
Part 3: Falsificationism
Part 4: The Metaphysics of the Scientific Method

In the previous three parts of this series I talked about what the Scientific Method is, and addressed the procedural objections. I'd like now to discuss the metaphysical objections.

Metaphysics is the bullshit "opinion journalism" of philosophy. One important topic in metaphysics is what constitutes "proof" and "truth". It's difficult, then, to talk about proving anything metaphysical or finding metaphysical truth without running into obvious self-referential paradoxes.

One issue in science which presents metaphysical difficultly is the correspondence between valid theorems of a rigorous scientific theory and observations, i.e. statements of perception in natural language. Since we don't directly understand natural language with any degree of logical rigor (a rigorous grammar or theory of semantics is a scientific theory about how minds operate), the correspondence is arbitrary.

The arbitrariness isn't a big issue in practice. Science gets off the ground in the first place because we use it to investigate just those observations that we all commonly assent to, and thus are caused (in theory) by objective reality. Also, the "deeper" our scientific theories go, the more abstracted they are from reality, the simpler the observations become. At the most esoteric, the actual observations consist mostly of reading numbers off a dial, a task suitable for even graduate students. (I kid!)

More worrisome metaphysical objections concern the obvious observation that the premises are entirely invented. Logic preserves the truth of the premises to the conclusions. But where are we if our premises are not merely dubious but arbitrarily guessed at? The whole idea seems absurd on its face.

Deductivism, though, requires absolutely perfect premises. There's no middle ground; there's no such thing as an almost perfect premise. That's why mathematical premises are definitional in nature; an abstract definition can be absolutely perfect--at the expense of not talking about anything but itself. A straight line, for example, is the shortest distance between two points just because that's how we define "straight line".

Errors in premises get amplified: If we commit all our epistemic resources to substantiating our premises, and we don't do so perfectly, we will create a deductive edifice that undetectably veers farther away from a description of reality, as Aristotle and the medieval scholasticists show us.

Once we've abandoned commitment to the perfection of our premises, there's no additional harm in simply making them arbitrary guesswork and turning the bulk of our epistemic resources elsewhere. Happily, logic gives us a way to do so.

We can use the logical technique of modus tollens: if the consequent of an implication[1] is false, then either the antecedent is false or the implication is false[2]. Consider the canonical syllogism:
P1: Socrates is a man
P2: All men are mortal[3]
C: Socrates is mortal
In this case, if we were to know that Socrates were not mortal, then we would know that one of the premises was false.

That's how the scientific method works: pick some premises (more or less) arbitrarily, derive some theorems from them, and test to see whether the derived theorems are true--in other words, do people assent to the observation that corresponds to the theorem. If the derived theorem is false, then go back and change the premises and try again, since we know one or more of the premises must be false.

I warned you in part 2 that we were going to have to abandon certainty, and this method indeed does not give us the certainty we find in deductivism. It might well be true that Socrates himself is mortal, yet false that he is a man (other beings than men are mortal) or false that all men are mortal (Socrates unluckily didn't get the immortality gene). We can thus call some theories false with absolute certainty, but we cannot ever call one true with absolute certainty.

The scientific method treats truth like sculpture in the old joke: If you want to sculpt an elephant, take a block of wood and remove anything that doesn't look like an elephant. Or, as Sherlock Holmes put it, "When you eliminate the impossible, whatever remains, however improbable, must be the truth."

We could, I suppose, simply follow Stephen Hawking's lead and dispense with the notion of "truth" with regard to scientific theories:
[A] scientific theory is a mathematical model that describes and codifies the observations we make. A good theory will describe a large range of phenomena on the basis of a few simple postulates and will make definite predictions that can be tested.[4]
A theory is a "model" that "makes predictions", not a statement of truth. But I think Hawking is being a little disingenuous here, perhaps so as not to distract his work in physics by picking fights with philosophers.

Hawking's disingenuity, though, does not really match our intuitive, prosaic notions about truth. When I give testimony in court, I do not swear to give only a robust model which makes testable predictions; I swear to tell the truth. When my auto mechanic tells me I need a new $800 flux capacitor, I want to know if it's true that the old one is broken. When the milk smells bad, I know it's true that it's spoiled. When I buy Viagra on the internet, I want to know if it's true that... well, you get the picture.

Constructing models that make predictions turns out to match very closely with our intuitive, prosaic notions about truths of ordinary reality. Even better, where they don't match, we find our notions about ordinary reality are actually false. It seems very difficult to equal the scientific method in this regard.

Yes, we could insist on absolute certainty. But we'd be pretty much limited to nihilism at worst, and at best mathematics and theology, entirely uncontaminated by any sort of notions about the world we actually live in.

In Zen and the Art of Motorcycle Maintenance, Robert M. Pirsig observes that the scientific method gives us no rigorous means (indeed no means at all) of determining which of the infinity of hypotheses we wish to test. He constructs an elaborate Metaphysics of Quality to address this issue. Pirsig argues that things and ideas have an intrisic Quality which we are capable of observing directly.

I think Pirsig misses the mark, at least on an epistemic basis; the issue of which hypotheses to test seems a task more suited to psychologists rather than philosophers. I don't know that we should even be "surprised" (in the statistical sense) in the first place at the pace of scientific progress.

The overall metaphysical issue is: Is the scientific method deterministic? Is there only one exactly true scientific way to describe the physical world?

The scientific method is at least partially deterministic. Absent any controversy over how to correlate the derived theorems of some hypothetical system to actual observations (a controversy which rarely arises in practice) it's definitely true that the notion of the fitness of a theory to some set of observations is very--if not perfectly--deterministic, deterministic in a way that something like theology isn't.

But is there exactly only one science? Popper argues that we can determine in probabilistic terms how close any particular theory is to The Truth, i.e. the perfect scientific theory; Carnap (and others) rebut him effectively. In part 5, I'll argue that the notion of "the perfect scientific theory" is itself incoherent.

[1] An "if antecedent then consequent" statement is an implication.

[2] Also known as the law of contrapositive: if A then B entails that if not B then not A.

[3] Stated as an an if... then...: "If someone is a man, then he is mortal."

[4] Hawking, Stephen W., The Universe in a Nutshell, Bantam Books, 2001, p. 31


  1. The two teaser strands coming out of this post, the determinism of the scientific method and your gnomic remarks on Truth and the perfect scientific theory seem to be pointing towards a table toppling insight next time, so I hope but I am not sure these remarks are directed towards what you are trying to say.

    Saying that the scientific method is partially deterministic seems self-evidently true as it is used as a tool for prediction. At its strongest this would support this premise:

    If a) science were 100% reliable for predicting cause and effect then b) reality is deterministic.

    The existence of a perfect scientific theory which revealed the entire workings of reality would presumably mean that reality was deterministic.

    Yet the moment a) begins to crumble can we really say that real meat and bones determinism is so undefeatably in the running as it was before? Maybe we can, but partial determinism seems so vague as to be useless.

    None of this is of course criticizing your brilliant and exceptionally lucid analysis, but more asking for your to put your cards on the table a bit more as to where you stand on the free will/determinism debate.

  2. Thanks for the "brilliant" and "exceptionally lucid". I blush.

    I don't know if my further insights will be "table toppling", though.

    If a) science were 100% reliable for predicting cause and effect then b) reality is deterministic.

    In this essay, I'm talking about "determinism" in a very different way. I'm talking about a sort of "semantic" determinism: the meaning of a scientific theory is deterministic and thus everyone agrees what a scientific theory means.

    I'm drawing the contrast not between determinism and free will, but between the deterministic meaning of scientific theories and the non-deterministic meanings we find in, for instance, theology or the worst sort of philosophical metaphysics.

    Now that you've prodded me, though, I think I'll write soon on the determinism and predictability of reality itself.

    As to where I stand about free will, my position can be summarized quite simply: After all my reading and thinking, I'm no closer to understanding what "free will" actually means--even to the extent of knowing whether I myself have "free will". I thus conclude that, barring some profound new insight, the term is meaningless.

  3. Larry,

    You write, "I'm talking about a sort of "semantic" determinism: the meaning of a scientific theory is deterministic and thus everyone agrees what a scientific theory means." It is not true that the meaning of scientific theories is always clear. From its inception until today, quantum mechanics has been interpreted and re-interpreted in many incompatible ways! While what is called the Copenhagen Interpretation has emerged as the dominant one, it has had no shortage of objectors. In this case, what is agreed upon is how to apply the mathematical formalism. Its meaning, however, remains a topic of disagreement.

  4. Touché. Still, there's eight skitty zillion kinds of meaning.

    The empirical meaning of even something as refractory as QM is entirely deterministic: It tells us exactly what to expect in terms of experimental result.

    The philosophical interpretation of that clear, deterministic meaning is another matter entirely.

  5. Larry,

    "The empirical meaning of even something as refractory as QM is entirely deterministic: It tells us exactly what to expect in terms of experimental result."

    Not quite. Forgive me for pressing my point.

    As you may already know, quantum mechanics makes only statistical predictations: one cannot, with a quantum-mechanical theory, predict what really will happen. In particular, the state of a system is represented by an abstract vector in (an infinitely dimensional) Hilbert space, written as a "ket" |A>. From a state vector |A>, it is possible to calculate all possible results of performing an experiment on the system it describes. How to mathematically extract that information and impose it on experimental setups.

    The main interpretative question is what our vector |A> really denotes -- does |A> capture all of the physical facts as many scientists have thought? This is not purely a philosophical question either; if state vectors (wavefunctions) like |A> do not exhaustively characterize the systems they are meant to describe, then there must exist a class of hidden variables which does.

    Obtaining a correct interpretation of quantum mechanics and whether it makes a claim to completeness is empirically important -- if we know that it is only meant as an incomplete description of nature, then we can seek out superior alternatives. In fact, Einstein famously argued that properly understood quantum mechanics does not purport to exhaustively describe nature. As a result, he sought to discover a correct hidden variable theory.

    I think all this illustrates the interconnectedness of intellectual disciplines emphasized by Quine. There are no sharp boundaries between speculative metaphysics and empirical science, and they certainly blend together at this point. The idea that we can neatly separate conceptual and empirical questions has been forcefully criticized by Quine, a critique which culminates in his attack on the analytic/synthetic distinction.

  6. Whoa! I meant to say: How to mathematically extract that information and impose it on experimental setups is understood.

  7. One of the really nice things about having smart readers is that I discover explanations which seem entirely obvious to me are in actuality matters of controversy, and offer me an opportunity to clarify my thinking.

    I'm speaking of "determinism" in a very narrow sense: the empirical predictions of a scientific theory, whatever they happen to be, are deterministic in the sense that they are derived from the hypotheses by formal logical deduction.

    Whether any such theory is phenomenologically complete, or how well the formalism coheres with our other knowledge are horses of entirely different colors.

    There is no ambiguity at all about what QM says about the probabilities regarding observations of ensembles. In this extremely narrow sense, QM is unambiguous and "deterministic".

  8. Timmo,

    I suspect I'm not quite getting your real point here.

    I'm not at all disputing that Quantum Mechanics appears to be incomplete. At the very least, it does not at all cohere with General Relativity; by itself this incoherence argues strongly for incompleteness.

    So is Quantum Mechanics The Truth? Is General Relativity The Truth? Well, they each fits certain observational facts extremely well. In this sense, they are small-tee truthful, but probably not as good (fitting more facts with fewer total premises in an entirely coherent way) as some theory or theories as yet undiscovered.

    If we consider truth as a number, representing not distance from The Truth as Popper would have it but by fitness to facts, there's no contradiction.


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