Category Archives: Scientific Method

Concentration

Those writing about logic emphasize with good reason the creative power of concentration, although they tend to ignore a variety that might appropriately be called cerebral polarization or sustained concentration—that is, steady orientation of all our faculties toward a single object of study for a period of months or even years. The thinking of countless brilliant minds ends up sterile for lack of this ability, which the French call esprit de suite. I could cite dozens of Spaniards with minds finely suited to scientific investigation who retreat discouraged from a problem without seriously measuring their strength, perhaps just at the moment when nature was about to reward their eagerness with the anxiously awaited revelation. Our classrooms and laboratories are full of these capricious and restless souls who love research and suffer through mishaps with the retort or microscope day after day. Their feverish activity yields an avalanche of lectures, articles, and books—upon which they have lavished a great deal of scholarship and talent. They constantly exhort the garrulous throng of dreamers and theorizers with the indispensable need for observing nature directly. Then, after long years of publicity and experimental work, those closest to them (their satellites at the prestigious yet mysterious meetings where the great preside) are asked about the discoveries of the master. The allies are forced to confess shamefacedly that the great burden of talent, combined with the virtual impossibility of summarizing in a nutshell the extraordinary magnitude and range of the work undertaken, make it impossible to state what partial or positive progress had been made. These are the inevitable fruits of negligence or excessive lack of focus, not to mention childish, encyclopedic ostentation. This approach is inconceivable today, when even the most renowned scholars specialize and concentrate in order to produce. But enough of this; we shall deal later with bad habits of the will.
To bring scientific investigation to a happy end once appropriate methods have been determined, we must hold firmly in mind the goal of the project. The object here is to focus the train of thought on more and more complex and accurate associations between images based on observation and ideas slumbering in the unconscious—ideas that only vigorous concentration of mental energy can raise to the conscious level. One must achieve total absorption; expectation and focused attention are not enough. We must take advantage of all lucid moments, whether they occur during the meditation following prolonged rest; during the super-intense mental work nerve cells achieve when fired by concentration; or during scientific discussion, whose impact often generates unanticipated intuition like sparks from steel. Most people who lack self-confidence are unaware of the marvelous power of prolonged concentration. This type of cerebral polarization (which involves a special ordering of perceptions) refines judgment, enriches analytical powers, spurs constructive imagination, and—by focusing all light of reason on the darkness of a problem—allows unforseen and subtle relationships to be discovered. If a photographic plate under the center of a lens focused on the heavens is exposed for hours, it comes to reveal stars so far away that even the most powerful telescopes fail to reveal them to the naked eye. In a similar way, time and concentration allow the intellect to perceive a ray of light in the darkness of the most complex problem.

The comparison just made is not, however, entirely accurate. Photography in astronomy is limited to recording faint though preexisting stars, whereas intellectual work is an act of creation. It is as if the mental image that is studied over a period of time were to sprout appendages like an ameba— outgrowths that extend in all directions while avoiding one obstacle after another—before interdigitating with related ideas.

The forging of new truth almost always requires severe abstention and renunciation. During the so-called intellectual incubation period, the investigator should ignore everything unrelated to the problem of interest, like a somnambulist attending only to the voice of the hypnotist. In the lecture room, on walks, in the theater, in conversation, and even in reading for pleasure, seek opportunities for insight, comparisons, and hypotheses that add at least some clarity to the problem one is obsessed with. Nothing is useless during this process of adjustment. The first glaring errors, as well as the wrong turns ventured on by the imagination, are necessary because in the end they lead us down the correct path. They are part of the final success, just as the initial formless sketches of the artist are a part of the finished portrait.

When one reflects on the ability that humans display for modifying and refining mental activity related to a problem under serious examination, it is difficult to avoid concluding that the brain is plastic and goes through a process of anatomical and functional differentiation, adapting itself progressively to the problem. The adequate and specific organization acquired by nerve cells eventually produces what I would refer to as professional or adaptational talent. As a motivator of the will itself, this brain organization provides the energy to adapt understanding to the nature of the problem under consideration. In a certain sense, it would not be paradoxical to say that the person who initiates the solution to a problem is different from the one who solves it. This is an obvious and simple explanation for the astonishment proclaimed by all investigators on discovering the simple solution so laboriously sought. “Why didn’t I think of this at the outset!” we exclaim. “There was so much confusion traveling down roads that led nowhere!”

If a solution fails to appear after all of this, and yet we feel success is just around the corner, try resting for a while. Several weeks of relaxation and quiet in the countryside brings calmness and clarity to the mind. Like the early morning frost, this intellectual refreshment withers the parasitic and nasty vegetation that smothers the good seed. Bursting forth at last is the flower of truth, whose calyx usually opens after a long and profound sleep at dawn—in those placid hours of the morning that Goethe and so many others consider especially favorable for discovery.

Travel has the same virtue of renewing thought and dissipating tiring preoccupations by furnishing new views of the world and transmitting our store of ideas to others. How often the powerful vibration of the locomotive and the spiritual solitude of the railway car (the “just rewards of humanity,” as Descartes might say) suggest ideas that are ultimately confirmed in the laboratory!

Now that scientific research has become a regular profession on the payroll of the state, the observer can no longer afford to concentrate for extended periods of time on one subject, and must work even harder. Gone are the wonderful days of yore when those curious about nature were able to remain withdrawn in the silence of the study, confident that rivals would not disrupt their tranquil meditations. Research is now frantic. When a new technique is outlined, many scholars immediately take advantage of it and apply it almost simultaneously to the same problems—diminishing the glory of the originator, who probably lacks the facilities and time necessary to gather all the fruits of his labors, and of his lucky star.

As a result, the coincidences and battles of priority are inevitable. It is clear that once an idea becomes public it joins the intellectual atmosphere that nourishes all of our minds. Because of the functional synchronization that governs minds prepared and oriented toward a particular subject, the new idea is assimilated simultaneously in Paris and Berlin, in London and Vienna—in virtually the same way, with similar developments and applications. The discovery grows and develops spontaneously and automatically like an organism, as though scholars are reduced to mere cultivators of the seed planted by a genius. The magnificent flowering of new information is observed by all, and naturally everyone wishes to gather for themselves the splendid blossoms. This explains the eagerness to publish most laboratory studies, even when imperfect and incomplete. The desire to arrive first results at times in shallowness, although it is also true that feverish anxiety to reach the goal first wins the prize for priority.

Be that as it may, it is unwise to become disenchanted if someone arrives ahead of us. Continue work undaunted; in time our turn will come. That eminent woman, Madam Curie, provides an eloquent example of untiring perseverance. After discovering the radioactivity of thorium, she was unpleasantly surprised to learn that the same observation had been announced a short time earlier by Schmidt in the Wiedermann Annalen. Far from disheartened, however, she continued her research uninterrupted. She analyzed new substances with the electroscope, including uranium oxide (pitchblende) from the mines of Johann Georgenstadt, and its radioactivity proved four times stronger than that of uranium itself. Suspecting that this very active material contained a new element, she undertook (with the assistance of M. Curie) a series of ingenious, patient, and heroic experiments that were rewarded with the discovery of a new element, the remarkable radium. Its properties inspired a great deal of further work that has revolutionized chemistry and physics.

In Spain, where laziness is a religion rather than a vice, there is little appreciation for how the monumental work of German chemists, naturalists, and physicians is accomplished—especially when it would appear that the time required to execute the plan and assemble a bibliography might involve decades! Yet these books have been written in a year or two, quietly and without feverish haste. The secret lies in the method of work; in taking advantage of as much time as possible for the activity; in not retiring for the day until at least two or three hours are dedicated to the task; in wisely constructing a dike in front of the intellectual dispersion and waste of time required by social activity; and finally, in avoiding as much as possible the malicious gossip of the café and other entertainment—which squanders our nervous energy (sometimes even causing disgust) and draws us away from our main task with childish conceits and futile pursuits.
If our professions do not allow us to devote more than two hours a day to a subject, do not abandon the work on the pretext that we need four or six. As Payot wisely noted, “A little each day is enough, as long as a little is produced each day.”
The harm in certain things that are too distracting lies not so much in the time they steal from us as in the enervation they bring to the creative tension of the mind, and in the loss they cause to that quality of tone that nerve cells acquire when adapted to a particular subject.

Of course we don’t recommend the elimination of all distractions. However, those of the investigator should always be light and promote the association of new ideas. A stroll outside, contemplating works of art and photography, enjoying scenes such as monuments in different lands, the enchantment of music—and more than anything else the companionship of a person who understands us and carefully avoids all serious and reflective conversation—are the best ways for the laboratory worker to relax. Along these lines, it is wise to follow the advice of Buffon, who justified his abandon in conversation (which displeased many of those who admired the nobility, along with his elegant writing style) by noting: “These are my moments of rest.”

In summary, all great work is the fruit of patience and perseverance, combined with tenacious concentration on a subject over a period of months or even years. Many illustrious scholars have confirmed this when questioned about the secret of their creations. Newton stated that he arrived at the sovereign law of universal attraction only by constant thinking about the same problem. According to one of his sons, Darwin achieved such a high degree of concentration on the biological facts related to the principle of evolution that for many years he systematically deprived himself of all reading and contemplation unrelated to the goal of his thoughts. Buffon said unreservedly, “Genius is simply patience carried to the extreme.” To those who asked how he achieved fame he replied: “By spending forty years of my life bent over my writing desk.” As a final example, it is widely known that Mayer, the genius who discovered the principle of energy conservation and transformation, dedicated his entire life to this concept.
Thus, it is clear beyond doubt that great scientific undertakings require intellectual vigor, as well as severe discipline of the will and continuous subordination of all one’s mental powers to an object of study. Harm is caused unconsciously by the biographers of illustrious scholars when they attribute great scientific conquests to genius rather than to hard work and patience. What more could the weak will of the student or professor ask than to rationalize its laziness with the modest, and thus even more lamentable, admission of intellectual mediocrity! Not even biographers with the good sense of G.L. Figuier are immune from the regrettable trend of extolling beyond reason the mental gifts of famous investigators. Careful thought should make them realize how discouraging this can be to their readers. On the other hand, many autobiographies wherein the sage presents himself full-length to the reader provide an excellent moral tonic, showing weaknesses and passions, lapses and triumphs. After reading autobiographies that fill the soul with hope, you might well say: “Even I can be a painter!”

Well, it’s been some time since I’ve posted anything serious.  Now that I’m studying for exams though I naturally turn back to something distracting while hopefully being somewhat productive in this distraction.

I’ve been watching videos from the Beyond Belief conference at the Salk Institute over the past week or two.  One word:  Yes.  That yes is a fully positive endorsement of this conference and a hope for many more to come.  That said, I’ve been searching for post-BB commentary and came across an opinion piece by Sam Harris.  The wonderful exchange between Scott Atran, Sam Harris, and others on Edge not included (and highly recommended), there seems to be a general glossing over of some thoughtful commentary.  Glossing turned to spin in Harris’ piece posted as an op-ed on the Council for Secular Humanism website.  Let’s take a closer look:

Recently, I attended a three-day conference at the Salk Institute, organized by The Science Network. The conference was titled, Beyond Belief: Science, Religion, Reason, and Survival and was conducted as a town-hall meeting before an audience of invited guests. Speakers included Steven Weinberg, Harold Kroto, Richard Dawkins, and many other scientists and philosophers who have been, and remain, energetic opponents of religious unreason. And then there were other esteemed participants and audience members who proved themselves to be eager purveyors of American-style religious bewilderment.

And the spin begins…

It was a room full of bright, scientifically literate people—molecular biologists, anthropologists, physicists, engineers—and yet, three days were insufficient to force agreement on whether or not there is any conflict between religion and science.

You mean, after hundreds of years of debate on science and religion, this three day conference didn’t solve the relationship between these two massive enterprises?  You’re kidding!

While at Salk, I witnessed scientists giving voice to some of the most unctuous religious apologies I have ever heard. It is one thing to be told that the pope is a great champion of reason and that his opposition to embryonic stem cell research has nothing to do with religious dogmatism; it is quite another to be told this by a Stanford physician who sits on the President’s Council on Bioethics.

Oh, what’s that in your pocket Sam?  Oh yes, it’s a bunch of embryonic stem cells.  You love to whip those little guys out whenever you have a chance.  Mr. Harris, your characterization of Dr. William Hurlbut’s comments (and note that you only named people on your side of the argument throughout this piece) is quite inappropriate Hurlbut’s comments did not center on stem cells.  Hurlbut’s comments were in the spirit of having an understanding of any given dogma before criticizing it.  And not just a read through with untutored eyes.  A skeptical read, but a read open to more than a literal interpretation.  This seems to me something you would want more people, believers or not, to do.  Further, for someone seemingly so familiar with Buddhist traditions, it seems rather odd that the distinction between esoteric (Vajrayana) and exoteric (Mahayana) texts and practices has not even popped up in the midst of discussion.  And what about the ideals of a Bodhisattva?  Prajna (wisdom), virya (warriors spirit), and upaya (skillful means)?  Mr. Harris’ argument certainly shows plenty of warriors spirit but seems to be lacking skillful means.

Over the course of the meeting, I had the pleasure of hearing that Hitler, Stalin, and Mao were examples of secularism run amok,

No. Examples of dogmas as or more deadly than religion.

that the doctrines of martyrdom and jihad have nothing whatsoever to do with Muslim terrorism,

Just watch the back-and-forth between Sam Harris and Scott Atran to see that this is not so.

that people can never be argued out of their beliefs because we live in an irrational world,

Another hyperbolic comment!  Scott Atran’s comments were to the effect of dealing with rationality in a fundamentally irrational world, not that it is a lost cause to challenge people on contentious beliefs.

that science has made no important contributions to our ethical lives,

Stop Sam.  Stop!  Listen to yourself!  Anyone who cares enough to know what was actually said can download the entire conference.  Doing so, and particularly after watching Susan Neiman’s talk, one sees a different ethos.  One that welcomes empirical data and wishes for more empiricism in informing ethical and moral decision making but contending that this tells us what ‘is’ while the ‘ought to be’ remains impoverished by such means.  Far from being one sided, this was then challenged by the Churchlands with thoughtful criticism.  It’s a great exchange of ideas, apparently so great Mr. Harris has kindly cherry picked it from his memory and squashed it on the floor.

and that it is not the job of scientists “to take away people’s hope”—all from atheist scientists, happily trading in the most abject and paralyzing shibboleths of academic political correctness.

Heck, even Richard Dawkins said he would not challenge someone’s beliefs on their deathbed…

There were several moments during our panel discussions that brought to mind the final scene of Invasion of the Body Snatchers—people who looked like scientists, had published as scientists, and would soon be returning to their labs nevertheless gave voice to the alien hiss of religious lunacy at the slightest prodding. In case anyone thought that the front lines in our culture wars could be found at the entrance to a megachurch, I am here to report that we still have considerable work to do in a nearby trench.

For all the frustration I felt at this meeting,

…receiving thoughtful criticism of your arguments, being called on repeated arguments and abuse of language…

it seemed like the perfect forum in which to resolve the centuries-old collision between reason and faith. If reputable scientists cannot be made to agree that there are important intellectual and moral differences between knowing something and pretending to know it, we are doomed.

Argumentum ad Bacculum.

Happily, the meeting at Salk will be convened again next fall. Perhaps then it will be possible to rule out the Virgin Birth of Jesus as a valid scientific hypothesis.

Sam continues, giving four questions he’d like answered.  Unfortunately I do not have the time to go through this and formulate a thoughtful response.  Biochemistry awaits…

I’ll finish off by pointing out that as much as Sam Harris argues for corrections of ‘problems of discourse’ and ‘intellectual honesty’ during the Beyond Belief conference, he seems to take these concerns off like a coat as he takes the time to write pieces like this which perpetuate the problem of discourse and veil what actually happened.  Despite this opinion piece though, Harris made some very good points at the Salk.  There is every reason to challenge beliefs that can reduce someone to resembling something like this.  And for all the heavy arguments and bruised egos, it is quite stimulating to watch or listen to the proceedings, particularly Neil de Grasse Tyson’s equally inspiring and hilarious lecture, and I would encourage anyone who has made it this far in the post to check it out.  Certainly don’t take this post as the word on the conference, and equally so, do not take Mr. Harris’ opinion as a full synopsis either.

P.S.  Has anyone found any articles by Sam Harris in a scholarly science journal or a poster at a conference?  I can’t seem to find any.

it’s about time i started to put some excerpts from the neuroethics book edited by judy illes.  here’s another wonderful ditty from chapter 11:  a picture is worth 1000 words, but which 1000? 

italics are mine.

…from ch. 11 in Neuroethics

What constitutes a ‘significantly greater’ activation than another, is in a way, in the eye of the beholder… lowering the threshold will create more regions that are statistically significant, whereas raising the threshold will reduce the number of significant regions. The choice of the threshold is largely determined by convention among researchers, rather than absolute standards. Reporting brain activation patterns is therefore primarily a statistical interpretation of a very complex dataset, and may be interpreted differently by different researchers. (Canli and Amin 2002)

YES!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 

While group averages are vital for achieving acceptable signal-to-noise ratios, individual differences, from both anatomical and functional variability may become diluted and overshadowed (Beaulieu 2001; President’s Council on Bioethics 2004). When dealing with single-subject data, as is the case for presurgical planning, it is often desirable to minimize false-negative voxels in order to avoid erroneously excising potentially healthy tissue (M. P. Kirschen et al., under review). Outside the clinical setting, we can easily extend these considerations to any analytic objective set to pinpoint activation areas for function in individuals:

…the image of an activation pattern from a poorly designed study is visually indistinguishable from one based on an exemplary study. It takes a skilled practitioner to appreciate the difference. Therefore, one great danger lies in the abuse of neuroimaging data for presentations to untrained audiences such as courtroom juries. What can be easily forgotten when looking at these images is that they represent statistical inferences, rather than absolute truths. (Canli and Amin 2002)

YES!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 

Lastly, the interpretability of fMRI activation maps is dependent on how the data are displayed. The colour-coded statistical maps are usually overlaid on high-resolution anatomical MR images to highlight the brain anatomy. There are several media for displaying these composite images. The most rigorous is to overlay the functional data onto single anatomical slices in any imaging plane. While this is the most comprehensive means of examining the data, it is often difficult to localize the activations to a particular region, given a particular scan plane, and researchers are limited in the number of slices they can include in a publication or lecture. Alternatively, the activation maps can be presented on a three-dimensional rendered brain. While this technique gives good visualization of prominent external brain structures, internal regions like the hippocampus or basal ganglia are not well characterized on these models. Researchers often use both of these techniques to examine data, but ultimately choose the one that best highlights the main results of the study for presentation.

Since basic research is usually done to infer characteristics bearing on populations, the extension to individual applications is challenged by a scarcity of normative data that can support, for example, conclusions of abnormal activation (Rosen and Gur 2002). There are risks that measures will vary between individuals or that the meaning of data compared with normal individuals will be difficult to establish. Abnormality and predictive validity could even be more problematic in the context of real-world behaviours, especially those that are potentially value laden or culturally determined (Illes et al., 2003).

What follows is an excerpt from chapter 11 of Karl Popper’s lucid and, as far as I’m concerned, inspiring book Conjectures and Refutations. Unfortunately I have only had the opportunity to read this chapter, but mark my words, by the end of this summer I’ll have the rest of Popper in my brain. The title of the chapter is ‘The Demarcation between Science and Metaphysics’ and the excerpt was gleaned from section 2, titled ‘My own view of the problem’.

// It was in 1919 that I first faced the problem of drawing a line of demarcation between those statements and systems of statements which could be properly described as belonging to empirical science, and others which might, perhaps, be described as ‘pseudo-scientific’ or (in certain contexts) as ‘metaphysical’, or which belonged, perhaps, to pure logic or to pure mathematics.

This is a problem which has agitated many philosophers since the time of Bacon, although I have never found an explicit formulation of it. The most widely accepted view was that science was characterized by its observational basis, or by its inductive method, while pseudo-sciences and metaphysics were characterized by their speculative method, or as Bacon said, by the fact that they operated with ‘mental anticipations’—something very similar to hypotheses.

This view I have never been able to accept. The modern theories of physics, especially Einstein’s theory (widely discussed in the year 1919), were highly speculative and abstract, and very far removed from what might be called their ‘observational basis’. All attempts to show that they were more or less directly ‘based on observations’ were unconvincing. The same was true even of Newton’s theory. Bacon had raised objections against the Copernican system on the ground that it ‘needlessly did violence to our senses’; and in general the best physical theories always resembled what Bacon had dismissed as ‘mental anticipations’.

On the other hand, many superstitious beliefs and many rule-of-thumb procedures (for planting, etc.) to be found in popular almanacs and dream books, have had much more to do with observations, and have no doubt often been based on something like induction. Astrologers, more especially, have always claimed that their ‘science’ was based upon a great wealth of inductive material. This claim is, perhaps, unfounded; but I have never heard of any attempt to discredit astrology by a critical investigation of its alleged inductive material. Nevertheless, astrology was rejected by modern science because it did not fit accepted theories and methods.

Thus there clearly was a need for a different criterion of demarcation; and I proposed (though years elapsed before I published this proposal) that the refutability or falsifiability of a theoretical system should be taken as the criterion of its demarcation. According to this view, which I still uphold, a system is to be considered as scientific only if it makes assertions which may clash with observations; and a system is, in fact, tested by attempts to produce such clashes, that is to say by attempts to refute it. Thus testability is the same as refutability, and can therefore likewise be taken as a criterion of demarcation.

This is a view of science which takes its critical approach to be its most important characteristic. Thus a scientist should look upon a theory from the point of view of whether it can be critically discussed: whether it exposes itself to criticism of all kinds; and—if it does—whether it is able to stand up to it. Newton’s theory, for example, predicted deviations from Kepler’s laws (due to the interactions of planets) which had not been observed at the time. It exposed itself thereby to attempted empirical refutations whose failure meant the success of the theory. Einstein’s theory was tested in a similar way. And indeed, all real tests are attempted refutations. Only if a theory successfully withstands the pressure of these attempted refutations can we claim that it is confirmed or corroborated by experience.

There are, moreover (as I found later), degrees of testability: some theories expose themselves to possible refutations more boldly than others. For example, a theory from which we can deduce precise numerical predictions about the splitting up of the spectral lines of light emitted by atoms in magnetic fields of varying strength will be more exposed to experimental refutation than one which merely predicts that a magnetic field influences the emission of light. A theory which is more precise and more easily refutable than another will also be the more interesting one. Since it is the more daring one, it will be the one which is less probable, But it is better testable, for we can make our tests more precise and more severe. And if it stands up to severe tests it will be better confirmed, or better attested, by these tests. Thus confirmability (or attestability or corroborability) must increase with testability.

This indicates that the criterion of demarcation cannot be an absolutely sharp one but will itself have degrees. There will be well-testable theories, hardly testable theories, and non-testable theories. Those which are non-testable are of no interest to empirical scientists. They may be described as metaphysical.

Here I must again stress a point which has often been misunderstood. Perhaps I can avoid these misunderstandings if I put my point now in this way. Take a square to represent the class of all statements of a language in which we intend to formulate a science; draw a broad horizontal line, dividing it into an upper and lower half; write ‘science’ and ‘testable’ into the upper half, and ‘metaphysics’ and ‘non-testable’ into the lower: then, I hope, you will realize that I do not propose to draw the line of demarcation in such a way that it coincides with the limits of a language, leaving science inside, and banning metaphysics by excluding it from the class of meaningful statements. On the contrary: beginning with my first publication on this subject, I stressed the fact that it would be inadequate to draw the line of demarcation between science and metaphysics so as to exclude metaphysics as nonsensical from a meaningful language.

I have indicated one of the reasons for this by saying that we must not try to draw the line too sharply. This becomes clear if we remember that most of our scientific theories originate in myths. The Copernican system, for example, was inspired by a Neo-Platonic worship of the light of the Sun who had to occupy the ‘centre’ because of his nobility. This indicates how myths may develop testable components. They may, in the course of discussion, become fruitful and important for science. In my Logic of Scientific Discovery I gave several examples of myths which have become most important for science, among them atomism and the corpuscular theory of light. It would hardly contribute to clarity if we were to say that these theories are nonsensical gibberish in one stage of their development, and then suddenly become good sense in another.

Another argument is the following. It may happen—and it turns out to be an important case—that a certain statement belongs to science since it is testable, while its negation turns out not to be testable, so that it must be placed below the line of demarcation. This is indeed the case with most important and most severely testable statements—the universal laws of science. I recommended, in my Logic of Scientific Discovery, that they should be expressed, for certain purposes, in a form like “There does not exist any perpetual motion machine’ (this is sometimes called ‘Planck’s formulation of the First Law of Thermodynamics’); that is to say, in the form of a negation of an existential statement. The corresponding existential statement—‘There exists a perpetual motion machine’—would belong, I suggested, together with ‘There exists a sea-serpent’ to those below the line of demarcation, as opposed to ‘There is a sea-serpent now on view in the British Museum’ which is well above the line since it can easily be tested. But we do not know how to test an isolated purely existential assertion.

I cannot in this place argue for the adequacy of the view that isolated purely existential statements should be classed as untestable and as falling outside the scientist’s range of interest. I only wish to make clear that if this view is accepted, then it would be strange to call metaphysical statements meaningless, or to exclude them from our language. For if we accept the negation of an existential statement as meaningful, then we must accept the existential statement itself also as meaningful.

I have been forced to stress this point because my position has repeatedly been described as a proposal to take falsifiability or refutability as the criterion of meaning (rather than demarcation), or as a proposal to exclude existential statements from our language, or perhaps from the language of science. Even Carnap, who discusses my position in considerable detail and reports it correctly, feels himself compelled to interpret it as a proposal to exclude metaphysical statements from some language or other.

But it is a fact that beginning with my first publication on this subject (‘Ein Kriterion des empirischen Charakters theoretischer Systeme’, Erkenntnis, 3, 1933, pp. 426 ff., now in The Logic of Scientific Discovery, pp. 312-14, see also Sections 4 and 10), I always dismissed the problem of meaninglessness as a pseudo-problem; and I was always opposed to the idea that it may be identified with the problem of demarcation. This is my view still.