April 1998

by Jon Blumenfeld

Part I

Can science survive the current cultural, academic, and philosophical trend towards a postmodernistic world in which truth has no objective meaning?

For those who follow a philosophy of reason and critical thinking, no idea is more important than the Scientific Method. It is the tool we use to unlock the world, and we try to use it in every instance we can, from science and the world around us to the less concrete ideas of morality and ethics. Recently a new breed of philosophers has arisen who call reason ‘just another religion’ that is no better than any other way of thinking; they tell us (and the world) that we are just as well or better served by irrationality and randomness as we are by our ordered, empirical, Scientific Method. Where do these claims come from, to what extent are they valid, and where do they go wrong? What are the consequences of rejecting reason? Moreover, can the Scientific Method be saved?

Over the years, philosophers, many in the vanguard of scientific progress, have examined the philosophical underpinnings of the Scientific Method, and have often found, to their dismay and ours, that it cannot be derived from philosophical first principles alone. Far from being crackpots, pseudoscientists, or ‘anti-scientists,’ they are some of the most respected figures in the history of science. David Hume (1711 – 1776), Nelson Goodman (currently Professor Emeritus of philosophy at Harvard), WVO Quine (also at Harvard) and Kurt Gödel (1906 – 1978), among many others, have all investigated the questions of reason and provability, and have all reached surprising, and seemingly unsatisfactory, results. From these results have risen the so-called ‘postmodern’ ideas of relativism and irrationality, which trace their origins through Paul Feyerabend and Thomas Kuhn back to Karl Popper; by and large it is a twentieth century, post World War II phenomenon.

What is meant by the statement that reason (or the Scientific Method) cannot be derived from philosophical first principles? The Scientific Method itself is made up of several components; to show that the method itself is ‘provable,’ each component must be provable, and the proofs must be devoid of any external, ‘real-world’ information, because we’re trying to derive our result from self-evident ‘first principles’ without carrying in any non-axiomatic assumptions. For this reason, we are restricted to the tools of logic and set theory. If these tools provide us with a proof, we are home free, but if they produce the opposite, a ‘disproof,’ we’re in trouble. Surprisingly, sometimes the result is in between – we arrive at the conclusion that a proof or disproof is impossible.

Perhaps the two most important pillars of the Scientific Method, in which we attempt to generalize our observations of the world into rules with the power to predict future observations, are ‘Induction’ and ‘Completeness.’ ‘Induction’ is the principle that allows us to generalize our observations from a set of examples; this contrasts with ‘deduction’ which is a process by which conclusions are reached using iron-clad, axiomatic rules (a typical example is the famous syllogism ‘All men are mortal. Socrates is a man. Therefore Socrates is mortal’. This is deductive because it uses hard and fast logical rules to go from known ‘true statements’ to an inescapable conclusion. In fact, the truth of the relation is independent of the real world truth-value of the statements – it can be converted to symbolic logic or set theory without altering its truth-value at all. Thus, all members of the set A are members of the set n [Set A is a subset of set n]. x is a member of set A, therefore x is a member of set n. This is equivalent to the syllogism, in which set A is ‘all men’, set n is ‘all mortals’, and x is ‘Socrates’. The syllogism is deductively true, even though in the real world, Socrates may not have existed at all).

Induction, mathematically, is a two step process. First, we must prove that if some generic example (call it n) is true, it follows logically that the next generic example (n+1) must also be true. From this we can construct a chain which covers all possible examples, and then all we need to do is to show that some real example, some base case, is true. Once we have our base case and our ‘chain’ rule, we have everything we need for an ‘inductive’ proof (For example, to prove that all positive numbers are greater than 0, we can say the following: If n is greater than 0, then n+1, which is greater than n, must also be greater than 0. We know that 1 is greater than 0, so 1+1=2 must be greater than 0. If two is greater than 0, 3 must be greater than 0, etc… for all positive numbers. Okay, a pretty trivial example, but you get the point).

‘Completeness’ is the idea that a system will produce ONLY true statements and is capable of producing ALL true statements. Arithmetic, for instance, would be complete if its system a + b = x could produce all true sums. Together, induction and completeness should give us everything we want out of the Scientific Method, because with both of them acting together, we can generalize the results of our experiments, and we would know that every truth in the universe could be reached using our tried and true experimental method. Unfortunately, as we shall see, neither induction (in the real world) nor completeness follow from logical and set-theoretical first principles.

David Hume

David Hume, the great Scottish Humanist, was one of the first modern philosophers to investigate the question of induction. Hume examined the concept of cause and effect. Imagine a situation in which we observe two events, call them a and b. Every time we see event a, it is immediately followed by event b. In addition, we never see event b, unless it is immediately preceded by event a. Can we say that event b is caused by event a? Hume’s startling conclusion was that the only evidence we have linking the events is our experience, that we cannot deduce effects from causes through reason. This goes to the heart of induction, and therefore to the heart of the Scientific Method. If we cannot show that effects follow causes through reason alone, we have lost the first part of our induction, in which the truth of statement n+1 follows logically from the truth of statement n. We are left only with our base case, taken from experience. In fact, we may have any number of base cases – we may see the sun rise every morning, and we may inductively reason that the sun will rise tomorrow morning, and we may be right, but we cannot prove this using logic and set theory alone.

Kurt Gödel

At the turn of the century, Bertrand Russell and Alfred North Whitehead attempted to collect everything that was known about mathematics into one giant tome, the Principia Mathematica. Their intent was to show the beauty and completeness of modern mathematics, but they found themselves stumbling over an ancient paradox. What is the meaning of the following self-contradictory statement: “This statement is false”? If the statement is true, then it must be false, but if it is false, then it must be true, and so on ad infinitum. Russell came up with the idea of introducing ‘meta-language’ – no system should be allowed to talk about itself; only the meta-language could talk about the system. Unfortunately, paradoxes kept cropping up in the meta-language, and so a meta-meta-language was needed to talk about the meta-language, and a meta-meta-meta-language, and on and on forever. Gödel investigated this phenomenon and came up with another startling result, which is now known as Gödel’s Incompleteness Theorem:

To every w-consistent recursive class k of formulae there correspond recursive class-signs r, such that neither v Gen r nor Neg (v Gen r) belongs to Flg(k) (where v is the free variable of r).

You’re stunned, aren’t you? In plainer English, what Gödel is saying is that :

All consistent axiomatic formulations of number theory include undecidable propositions.

Still not quite there? What this ultimately means is that in any system at all which is sufficiently complex as to be useful, there will be true statements that are unprovable. For instance, in the mathematical system of Principia Mathematica, consider the statement

This statement of number theory does not have any proof in the system of the Principia Mathematica.

This statement is undecidable using the Principia, and so it is true. Remember now, the Principia was intended to codify all of mathematics, and yet here is a true statement which is unreachable mathematically. The consequences of this are profound, not just for mathematics, but for all systems, including the Scientific Method. Take a look at figure 1. The area labeled T is the set of all true statements, and this includes everything in the figure except for the contents of the circle labeled F. In that circle are all false statements. The circle S represents a system, let’s call it the Scientific Method. Inside the circle are all the statements produced by the system. Notice the overlap with the circle F, and the fact that the circle does not enclose all of the area T. The question mark in the overlap is due to a further consequence of the incompleteness theorem – the fact that we can’t prove the consistency of the system; we can’t prove that no false statements can be produced. The upshot of Gödel’s theorem is that a system (like science) can neither be relied upon to produce all true statements, nor can it be proven never to produce a false one.

Karl Popper, Paul Feyerabend, and Thomas Kuhn

So the foundations of Scientific Method are not provable from first principles. Where do we go from here? The answer for a new breed of philosophers was to discard reason altogether. Karl Popper was fond of addressing groups by saying ‘I have come to criticize the Scientific Method. Unfortunately, there is no such thing as the Scientific Method.’ Thomas Kuhn came up with the idea of ‘paradigms’ in which major changes in thought cause sudden shifts not just in theory but in the whole way we look at the universe; we change so much, in fact, that our new world view becomes ‘incommensurable’ with our old world view. Because of this, we cannot even compare new ideas with old. Attempts were made to incorporate this into the Scientific Method by saying that new ‘paradigms’ may be ‘incommensurable’ with old ones, but they are not ‘untranslatable’; furthermore, each ‘paradigm shift’ brings us closer to the objective truth – closer to being right. Kuhn himself rejected this by saying that it was unclear (and could not be proven) that one paradigm is any better or any ‘truer’ than any other; they are merely different. Paul Feyerabend, an iconoclast and gadfly, put forward the idea that no theory, no matter how outlandish or irrational, should be discarded or left unstudied. Theories improve themselves by playing off other theories, and all ideas should be allowed this interplay so that knowledge as a whole can advance, the irrational along with the rational. For Feyerabend, theories need not be reasonable or even consistent (internally or externally) to be of value. ‘The only principle which does not inhibit progress is: anything goes’ (italics his). Thus was ‘relativism’ born, the philosophy that no system or idea is better than any other.
Keep in mind that Feyerabend and Kuhn reached the height of their popularity in and around the 1960’s, a time when the ordered, established ways of doing things were automatically suspect, in which new scientific theories (such as quantum mechanics) were challenging the very nature of reality as we thought we knew it, and in which new ways of thinking and living were sweeping through the world, particularly among the intelligentsia and in academia. Just as relativistic eastern religions were attractive to the new ways of thinking, so were relativistic scientific philosophies, which to many seemed to better fit the new modes of thought; this was the beginning of the ‘New Age’, and new philosophies were needed.

PART II

At the end of Part I, we were left with major objections to the scientific method and the rise of Relativism. We asked what were the consequences of relativism, and could we save the Scientific Method?

First, the consequences: A new breed of philosophy rose up around the idea of relativism, and a new breed of philosophers carried the banners of post-modernism, deconstructionism, radical multiculturalism, social constructionism, critical race theory, and radical feminism, just to name a few. All of them are based on one central theme: either there is no objective reality or we cannot objectively observe it, and so concepts like truth, reason, and rationality are mere social constructs, usually created to maintain the status quo, which usually benefits white (or European) males.

In practical terms, what are we talking about? This article would be incomplete without some amusing but ultimately chilling quotes, so here goes:
Duke University English department head and Law professor Stanley Fish contends that “like ‘fairness,’ ‘merit,’ and ‘free speech,’ Reason is a political entity,” an “ideologically charged” product of a “decidedly political agenda.” He has also said simply that “There is no such thing as intrinsic merit.” Professor Houston Baker, Jr., of the University of Pennsylvania (elected president of the Modern Language Association in 1991) has written that “reading and writing are merely technologies of control. [They are] martial law made academic.” Radical Feminist Andrea Dworkin defines marriage as a legal contract which sanctions rape. Thinkers like these often reject the normal standards of criticism of their work; in the words of another radical feminist, Catherine MacKinnon:

“If feminism is a critique of the objective standpoint as male, then we also disavow standard scientific norms as the adequacy criteria for our theory, because the objective standpoint we criticize is the posture of science. In other words, our critique of the objective standpoint as male is a critique of science as a specifically male approach to knowledge. With it, we reject male criteria for verification.”

Truth is subjective and political; the door is open for anyone’s favorite brand of irrationalism, from alternative medicine to New Age spiritualism, from ‘no-context’ literature to science as politics.

THE WAY OUT

Induction

How the heck do we get out of all this? Can we answer the objections to the scientific method and perhaps restore our concept that there is an objective universe out there, and that we can measure it and try to model it?

Let’s go back and take a look at the problems we had with the scientific method. The first was the problem with induction, which is the logical process we want to use to create general rules from our observations. We recall that David Hume, the Scottish philosopher, told us that we cannot assume that one event causes another just because we always see one preceding the other, even if the second event always follows the first one – this is only our experience of events, and therein lies the problem. Hume tells us that we have only a record of past sequences of events, but we can’t prove that it will always happen that way.

The man who begins to get us out of this is Harvard philosopher Nelson Goodman. To answer Hume, he asks another question: Just what are we trying to get induction to do? Deduction, the other kind of proof, works because of the rules we use to define it – we say that logical and set theoretical rules take us from axioms to conclusions which are iron clad – that’s deduction. Goodman says that this is merely a definition of deduction, so of course it works, because we have defined it that way. In the case of induction, we are asking too much if we want axiomatic-type proofs. What we need is to check our definition, and when we do we find that induction should work to generalize exactly the sets of observations we’ve been trying to get it to prove all along, because that’s the definition of induction. Now, this may seem circular, and Goodman is well aware of that. Ultimately, like logic and set theory in the case of deduction, the underlying rules need to be examined and codified. The problem now, which Goodman calls ‘The New Riddle of Induction,’ is in defining those underlying rules, which will tell us which kinds of observations can be generalized, and this turns out not to be trivial at all. Goodman starts out by saying that the problem is now one of confirmation, or finding out which observations confirm, or provide evidence for, which hypotheses.

What Goodman comes up with is a theory of confirmation and projectibility which tells us what kinds of hypotheses can be formulated and what kind of evidence is needed to confirm those hypotheses. The process is one of evidence gathering and testing, searching for repeatability and generality, in which evidence for a hypothesis is built up over many observations… hey! Wait a minute! Isn’t that the scientific method itself? So induction and the scientific method are saved when we realize that we are not asking for axiomatic proofs but rather for an accumulation of evidence to confirm our hypotheses.

Incompleteness

GØdel’s incompleteness theorem, which states that no axiomatic system can be relied on to reach every true statement, and furthermore cannot be proven to always produce true statements, was the second major objection to the scientific method.

What we need to remember is that applying GØdel’s theorem does not eliminate the truth value of statements derived in a system – the truth is still the truth, even if our systems are sometimes incapable of proving it. Moreover, the incompleteness theorem most certainly does not give me, you, or anyone else the right to select what we want to be true. Define as the truth that you can fly, and then try flying off the top of the Empire State Building, and see how long your ‘truth’ holds up (so to speak). The incompleteness theorem puts limits on the kinds of problems that can be solved systematically, but it does not throw systems into the relativistic ‘anything goes’ abyss prepared by the post-modernists.

Social Construction

On the other hand, scientists bring all kinds of cultural baggage to the table, and they make models of the world that cannot fail to incorporate their preconceptions; moreover, science is infamously conservative – how long did it take to convince the world that the earth goes around the sun, or that bacteria (or even meteors) exist? It is clear that we are social creatures living in a world of social constructs, and we really have changed our conceptions of scientific truth over the years, from flat earth to spherical, from geocentric to heliocentric, from classical Newtonian to the modern relativity/quantum mechanics duality, which we’re getting ready to give up (or enhance) in favor of a unified field theory.

Let’s examine the process by which the ‘truth’ supposedly changes. Jacques Derrida has said that we use rational processes most of the time, but that occasionally we ‘step outside’ our rationality, and make an irrational adjustment to our worldview – very much like Thomas Kuhn’s ‘paradigm shifts.’ Is this process really extra-rational? If we could merely remake the truth to conform to our social preconceptions, why would we ever make such a shift? Wouldn’t it be easier just to stay in our comfortable old world, with our comfortable old assumptions, and never allow anything to challenge us? The process of change must be a rational one, in which our natural tendency to conservatively ‘stick to our guns’ is finally forced to move by a rational analysis of the irrefutable, unchangeable evidence that accumulates. When our social constructs come into conflict with our observations, it is the social constructs that must change, not the truth. We can now concede the point that even our scientific theories are social constructs, but they are subject to the rules of confirmation by evidence, and they must change in response to new evidence – they cannot change the evidence itself. In this accumulation of evidence and confirmation is the answer to Kuhn’s objection that no paradigm can be shown to be closer to the ‘truth’ than any other – the old paradigm has its set of evidence, and the new one must encompass not only the old evidence, but new evidence as well. It must, by definition, explain more than the old paradigm. In fact, these shifts do not carry us from one ‘world’ to another, creating an uncrossable gulf in which we are unable even to communicate with the ‘old’ world, caught in a different paradigm – it’s just the natural progression of science, changing the models we make to explain the world we see, but leaving the world itself unchanged.

We can go even farther, if we want to. If scientific theories are social constructs subject to testing against observations, why aren’t our other social constructs subject to the same kind of analysis? Can it be that our supposedly irrational (or extra-rational) ideas, the ones that govern our social interactions, can be looked at as scientific theories that get tested against real-world observations? We’re willing to admit that any given theory has an element of cultural presupposition to it, but that it must respond to an accumulation of evidence if it is flawed. Don’t we apply the same process to our social interactions? Take slavery, for example. The ‘received’ view (to Europeans) 300 years ago was that black-skinned people were really soulless animals, which superior Europeans could use like cattle or horses; that God had put them here for just that purpose. Over time, the inexorable weight of evidence built up until the social construct of African inferiority finally had to be abandoned, until today’s ‘received’ view is that skin color or geographic origin is irrelevant to innate humanity. It was the social construct that changed, not the objective truth.

Are we closer now to a belief that reflects the objective world of right and wrong? Absolutely. Our social constructs are just like scientific theories, and every day we are confronted with evidence for or against those theories; like conservative thinkers who took years to accept relativity, we have an urge to maintain the status quo, but ultimately we cannot change the underlying truth in order to support our prejudices. Occasionally, backwards steps are made, such as the shameful era of eugenics and social Darwinism of the early years of this century, ideas that were exploited in the horror of the holocaust, but once again rationality rode to the rescue and those ideas were dropped from the mainstream. Good and Evil, right and wrong, science and pseudoscience – in the end, the overall direction is still progress toward truth via the rational application of reason.

References:

1) Feyerabend, Paul, ‘Against Method’, third edition, Verso, New York, 1993.
2) Feyerabend, Paul, ‘Killing Time, The Autobiography of Paul Feyer abend’, The University of Chicago Press, Chicago, 1995.
3) Goodman, Nelson, ‘Fact, Fiction, and Forecast’, fourth edition, Harvard University Press, Cambridge, Massachusetts, 1983.
4) Hofstadter, Douglas, ‘Gödel, Escher, Bach, An Eternal Golden Braid’, Vintage Books, New York, 1980.
5) Hume, David, ‘On Human Nature and the Understanding’, edited, with a new introduction, by Antony Flew, Collier Books, New York, 1962.
6) Quoted in Farber, Daniel A. and Suzanna Sherry, Beyond All Reason, The Radical Assault on Truth in American Law, Oxford University Press, New York, 1997, p. 25
7) Quoted in Beard, Henry, and Christopher Cerf, The Official Politically Correct Handbook and Dictionary, Villard Books, New York, 1992, p. 10
8) Quoted in ibid, p. 108
9) Quoted in Farber, p. 26
10) Goodman, Nelson, Fact, Fiction, and Forecast, Fourth Edition, Harvard University Press, Cambridge, Massachusetts, 1983.
11) Hofstaeder, Douglas, Godel, Escher, Bach, An Eternal Golden Braid, Vintage Books, New York, 1980.
12) Collins, Jeff, and Bill Mayblin, edited by Richard Appignanesi, Introducing Derrida, Totem Books, New York, 1996.

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