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“In opposition to common sense I dare to imagine some movement of the Earth; … since mathematicians have not (yet) agreed with each other, I was moved to think out a different scheme …; by supposing the Earth to move, demonstrations more secure than those of my predecessors (could) be found for the revolutions of the… spheres… all (celestial) phenomena follow from this (supposition).” Nicholas Copernicus, On the Revolutions of the Heavenly Spheres, Preface and Dedication to Pope Paul III.1

There, too often, the matter is left, B feeling that A is profoundly unclear about what he is asking for, and A reckoning that B’s refusal to have his difficulty indicates only a lack of depth and a narrowness of technique. A’s position is quite shocking, despite the fact that many discussions (both inside and outside philosophy) often come perilously close to it. Because if you and I can never know whether we are having the same experience in those situations where we both confront, e.g. a stoplight, and respond by saying “Red,” then we can certainly never know whether we are having the same experience when we are looking at triangles, or chairs, or tables, or other people, or any of the other philosophical furniture of the external world. To have the doubt which A expresses just is to entertain the most radical kind of solipsism, although many seem to have had the former without explicitly entertaining the latter. It is hardly satisfactory to point out here, as some recent philosophers, like B above, seem to have thought it sufficient to do, that the question is not a soluble one. This is precisely what A is claiming. Discussions often conclude therefore in agreeing that the difficulty is insoluble and then proceed to construct theories as to how it is that A and B ever manage to agree upon so much in the world, despite their disagreements about “basic” visual experience. Here words like “convention”, “agreement”, “stipulation”, and “ostensive”, are exercised rather heavily. We can, apparently, never really know that we have the same “inner” visual experiences. But we can, by various sorts of arbitrary agreements and conventional decisions, proceed to act as if we do have the same experiences. The value of the agreements and decisions is assessed pragmatically. If we can all succeed in managing our affairs in the world by agreeing that X and deciding that Y, then in so far do we rely on X and Y.

Consider ‘Hume’s dictum’: that from a necessary proposition nothing contingent follows — and vice versa. The effect of this on speculative metaphysics is devastating, although few practicing metaphysicians realize how utterly their position has been devastated. I will spell this out by drawing the profound logical moral of Hume’s dictum.

As Marcus Aurelius once said: “Those who come on the third night during rain, are truly lovers of wisdom.” It isn’t absolutely certain that he said that, but there is some scholarly dispute about it. Last night I considered the shaping of an idea. The idea was this: that flight might be thought of as a scientifically understandable, objectively tractable, and practically achievable phenomenon. Through the sorts of work that Newton and the other ideal hydrodynamicists accomplished, they did shape such an idea, the idea of a discipline concerned with the dynamics of gases like air. Tonight we won’t talk about the shaping of an idea, but rather the idea of a shape. And the shape we will be discussing tonight by slow degrees will be nothing other than the airfoil shape which, as shapes go, seems to me one of the more influential that we have had in our time. There is evidence in Leonardo’s little tract on the flight of birds which indicates that he understood something of the curvature in a bird’s wing. It can even be supposed that he was not wholly in the dark concerning the air flow over the top side of such a convex shape, though this is just conjecture. However, you must remember Sir George Cayley, the man who made the remarkable statement that the whole problem in aerodynamics is simply to make a surface support a given weight by the application of power to the resistance of the air. Shortly after he made that statement, he considered what he called the concave wing of a bird. He explained its purpose as follows: “the air being obliged to mount along the convexity of the surface, creates a slight vacuity immediately behind the point of separation.” What he means by vacuity behind the point of separation is a topic we will be considering shortly. But Cayley said this in 1809, almost 100 years before the actual advent of powered flight. His passing reference to the slight vacuity above the wing appears to our 20-20 hindsight as the vision supreme in the story of flight. Because this is truly the germ of the full explanation of what all air foils are meant to do. Whether they flop or are rigid or whether they rotate horizontally as helicopter blades do or spin vertically as do orthodox propeller blades.

“F is a good reason for C”, if true at all, could not but have been true — even when F and C are contingent. Much in this claim is true. Much is misleading. Let us sort this out and, en route, discuss a certain pattern of inference, and “the problem of induction”.

Contemporary Psychological Behaviorists argue against the existence of mental events in ways that are but little more refined than those of Watson, Lashley, and others forty years ago. The orthodox case stated by today’s psychologists against the possibility of a science of mental events is inconclusive. This is because their attack is usually based on factual considerations, instead of being, what it ought to be, a conceptual analysis of the idea of a mental event. This article seeks to disclose some weaknesses in the standard pattern of attacks on Introspection. It does this by defending the latter (i.e. Introspection) against such factually-orientated criticisms as those of Watson, Lashley, Hull and Skinner. It then challenges Introspection as it should be attacked; not externally with counterfacts, but internally with demonstrations of what is untenable in the very concept of a science of private events called “mental”.

The trial of Galileo has long been used by historians, by philosophers, and by scientists as a classic example of intellectual martyrdom, resembling somewhat the trial of Socrates. Since that is the way “the Galileo story” is usually represented, it turns out replete with villains and heroes. The scenario depends on who the scriptwriter happens to be.

A loose analogy relates the work of Laplace and Hilbert. These thinkers had roughly similar objectives. At a time when so much of our analytic effort goes to distinguishing mathematics and logic from physical theory, such an analogy can still be instructive, even though differences will always divide endeavors such as those of Laplace and Hilbert.

An agnostic maintains himself in a state of perfect doubt concerning God’s existence, a position I regard as unsound. The agnostic achieves his equipoise of dubiety only by shifting his ground where logic requires him to stand fast.

In thirty years the science of elementary particles has made few achievements compared with its unsuccessful essays. The recent works of Schwinger, Tomonaga, Feynman and Dyson, however, have had some success.1 We have here a hint that progress is being made on the formal side of the discipline — though even this work is profoundly disturbing in some of its purely mathematical aspects.2 There could be no better time to review the situation from a physical and philosophical standpoint, even if this proves to be an over-ambitious undertaking.

My objective here is vulnerable to some spurious semantics. I aim to delineate how the development of physical theory in the later nineteenth century was essentially dependent on the reflections and discoveries of Chemists, Biologists and Mathematicians. But when one alludes to some professional Chemist or Biologist as having affected the history of physics, it can always be countered “to that extent he was doing physics, he was being a physicist”. Thus when Urey helped to separate U235 from U238, and when he invoked theoretical thermodynamics to determine the age of the solar system, he might be said then to have been doing physics – despite being a Nobel laureate in chemistry. And when Pauling applied quantum theory to studies of complex substances, and when he considered the rotation of molecules in crystals – he too was apparently being a physicist, although, again, a Nobel laureate in chemistry. So also of great moments in the work of Nernst, Boltzmann, Helmholtz, Faraday, Young… and so on. That is, one can always say that whatever helps physics is physics. But this is 20–20 hindsight focused to the point of tautology. For it suggests that a Biologist might one day awaken with the pronouncement “I think I’ll do some physics today”; a Chemist or Mathematician might muse “this problem will put demands on the physicist in me”. The history of science can be thus chopped up only by destroying the organic interplay between disciplines, an interplay which constitutes the very pulse of scientific research. The picture of disciplines rigidly fixed as to content, and of scientists as compartmentalized thinking machines – both pictures are unreliable reflections of the ways in which problems and their solutions have actually shaped the history of science. Just as being a ‘natural philosopher’ in the seventeenth century was not identical with being a theoretical physicist in the twentieth, so also the divisions between biology, chemistry and physics in the nineteenth century may not always have been drawn along the same lines as we should sketch them today. In short, one must be an historian when tracing the lines of development through nineteenth century science. Not everything that is embraced today in physics texts began in physics labs, or in the minds of professional physicists. Therefore, I propose to correlate the contributions of scientists now known to us as important in the histories of chemistry and biology-with moments in the development of nineteenth century physics. Should one then choose to dub all such individuals as really physicists, a la bonne heure.

If I can imagine X, then X is not logically impossible. If X can be thought, then “X” is consistent. If one could draw a picture of X, then “X” is not self-contradictory.

As Marcus Aurelius once said: “Those who come on the third night during rain, are truly lovers of wisdom.” It isn’t absolutely certain that he said that, but there is some scholarly dispute about it. Last night I considered the shaping of an idea. The idea was this: that flight might be thought of as a scientifically understandable, objectively tractable, and practically achievable phenomenon. Through the sorts of work that Newton and the other ideal hydrodynamicists accomplished, they did shape such an idea, the idea of a discipline concerned with the dynamics of gases like air. Tonight we won’t talk about the shaping of an idea, but rather the idea of a shape. And the shape we will be discussing tonight by slow degrees will be nothing other than the airfoil shape which, as shapes go, seems to me one of the more influential that we have had in our time. There is evidence in Leonardo’s little tract on the flight of birds which indicates that he understood something of the curvature in a bird’s wing. It can even be supposed that he was not wholly in the dark concerning the air flow over the top side of such a convex shape, though this is just conjecture. However, you must remember Sir George Cayley, the man who made the remarkable statement that the whole problem in aerodynamics is simply to make a surface support a given weight by the application of power to the resistance of the air. Shortly after he made that statement, he considered what he called the concave wing of a bird. He explained its purpose as follows: “the air being obliged to mount along the convexity of the surface, creates a slight vacuity immediately behind the point of separation.”1 What he means by vacuity behind the point of separation is a topic we will be considering shortly. But Cayley said this in 1809, almost 100 years before the actual advent of powered flight. His passing reference to the slight vacuity above the wing appears to our 20-20 hindsight as the vision supreme in the story of flight. Because this is truly the germ of the full explanation of what all air foils are meant to do. Whether they flop or are rigid or whether they rotate horizontally as helicopter blades do or spin vertically as do orthodox propeller blades.

Socrates said those who come at the second night are truly lovers of wisdom. It isn’t certain that Socrates ever said that, but it is quite clear that it is the sort of thing that he might have said, and if he had I would have quoted him tonight. Last night we considered the discovery of the air, and what this meant for the History of aerodynamic theory and the development of the concept of flight. This evening I want to discuss the shaping of an idea. The idea is this: flight is a subject matter which can be treated objectively and scientifically and consideration of this idea might sooner or later actually lead to the construction of a proper flying machine. Erwin Schrodinger once said “Nature will tell you a direct lie if she possibly can”. Nature told such a lie to Daedalus and to Icarus; nature told the same lie to the Chinese Emperor Shun and to the Saracen of Constantinople. And nature also told that lie to Leonardo Da Vinci. The lie was this: all birds flap their wings; therefore flapping wings are somehow essential to flight. Further, any theory of flying through air requires the idea of flapping as a primary premise in the argument. In that collection of notes and random jottings that remain of the literary works of Leonardo, we find something resembling a monograph on the flight of birds, a tract written in 1505.1 Here, Leonardo was quite sympathetic to the Aristotelian doctrine of antiperistasis which we considered last night. It is the doctrine that a body moving through air is assisted in its forward progress by the circulation of those particles separated by the arrowhead which come around behind and impinge on the aft section of the arrow. But after 1505 Leonardo lost his sympathy for this theory. From that point on he saw air as fundamentally a factor of resistance, something that tended to slow moving objects down, and thought that this was due to a property of air which Galileo and others later referred to as condensibility. Today we would call it compressibility.

A subtitle for this paper might have been ‘Creation, Conservation and the Cloak of Night’ — for it is these semantical knots in the reticulum of contemporary cosmology which I shall seek to unravel, or at least to re-knot. Clearly, much of the fabric of scientific cosmology is rent and torn by sharp breaks in exposition and by jagged misunderstandings of philosophical principle. I may come to grief on these same reefs, but the course must be sailed.

There is but one question before us: can a philosopher utilize historical facts without collapsing into the “genetic fallacy”? If he can, will his analyses be improved?

From what is contingent nothing necessary follows. And from what is necessary nothing contingent follows. Let us call this ‘the Hume-Leibniz dictum’. These theses never occur full-blown in Hume or Leibniz, but the dictum is implicit within the philosophies history has come to associate with these thinkers.

The earliest tracts of Aristotle to reach the reviving West were the logical works - the Logica Vetus - rendered into Latin by Boethius during the sixth century. A good deal of Boethius’ work in mathematics and astronomy, as well as his Commentaries on the logic of Aristotle and Porphyry, were available in the earliest middle ages. In the early twelfth century Aristotle’s Posterior Analytics - part of the Logica Nova - were translated into Latin. Then in 1126 Adelard of Bath translated the fifteen books of Euclid’s Elements from the Arabic into Latin. In short, logical studies, and the analysis of cogent argumentation, were themselves responsible for much of the intellectual quickening which we now recognize as the medieval revival of learning. The Schoolmen were very early aware of the logical distinctions to be drawn between knowledge of facts and appraisals of valid argument. They knew the difference between factual proofs and logical consistency. And they realized that consistent consequences might be shown to follow from factually untrue premises. They could also detect logical inconsistencies in arguments generated invalidly from factually true premises. These distinctions, pellucidly clear in Aristotle’s own works, reinforced the cleavage between (1) the dogmatic Truths which had been injected into the ‘Christianized’ cosmology of The Philosopher, and (2) the logical and mathematical consistency so obvious in the treatises of Ptolemaic astronomy.

Copernicus calculated with respect to the distances and periods of Mercury as follows. Consider the diagram in Figure 69a. The inside circle represents Mercury’s orbit; the outer circle, the earth’s. Clearly, from the earth Mercury should always be seen close to the sun ‘oscillating’ to either side of it. E1 and M1 denote the earth and Mercury when the latter is farthest to the west. The angular distance between the two bodies at this time averages out as about 23°.61

Imagine Mars to have been observed at intervals (following opposition) equal to one, two, and then several orbital periods of that planet. It is obvious that Mars will always be at the same intersection of celestial coordinates during these observations - at the same position in its orbit. Meantime the earth will be occupying different position, since the orbital periods of earth and Mars are different.

My objective here is vulnerable to some spurious semantics. I aim to delineate how the development of physical theory in the later 19th century was essentially dependent on the reflections and discoveries of Chemists, Biologists and Mathematicians. But when one alludes to some professional Chemist or Biologist as having affected the history of physics, it can always be countered “to that extent he was doing physics, he was being a physicist”. Thus when Urey helped to separate U235 from U238, and when he invoked theoretical thermodynamics to determine the age of the solar system, he might be said then to have been doing physics — despite being a Nobel laureate in chemistry. And when Pauling applied quantum theory to studies of complex substances, and when he considered the rotation of molecules in crystals — he too was apparently being a physicist, although, again, a Nobel laureate in chemistry. So also of great moments in the work of Nernst, Boltzmann, Helmholtz, Faraday, Young… and so on. That is, one can always say that whatever helps physics is physics. But this is 20–20 hindsight focused to the point of tautology. For it suggests that a Biologist might one day awaken with the pronouncement “Ithink I’ll do some physics today”; a Chemist or Mathematician might muse “this problem will put demands on the physicist in me”. The history of science can be thus chopped up only by destroying the organic interplay between disciplines, an interplay which constitutes the very pulse of scientific research. The picture of disciplines rigidly fixed as to content, and of scientists as compartmentalized thinking machines — both pictures are unreliable reflections of the ways in which problems and their solutions have actually shaped the history of science. Just as being a ‘natural philosopher’ in the 17th century was not identical with being a theoretical physicist in the 20th, so also the divisions between biology, chemistry and physics in the 19th century may not always have been drawn along the same lines as we should sketch them today. In short, one must be an historian when tracing the lines of development through 19th century science. Not everything that is embraced today in physics texts began in physics labs, or in the minds of professional physicists. Therefore, I propose to correlate the contributions of scientists now known to us as important in the histories of chemistry and biology — with moments in the development of 19th century physics. Should one then choose to dub all such individuals as really physicists, a la bonne heure.

U. J. J. Leverrier was a colossus of nineteenth-century science. But for philosophers and historians his work has lain largely undiscovered; a suboceanic mountain beneath the scientific sea. We have surrendered 1859 to another giant. This is indeed the year of the watershed; it divides history into everything which went before, and everything which has flowed to us since. But 1859 is not only the year of The Origin of Species. It is also when Leverrier announced his ill-starred “hidden planet hypothesis” to account for the precession of the perihelion of Mercury. The very discovery of this aberration is itself due to Leverrier. Its negative consequences for history of science are at least as great as was the positive work of Darwin.

It may disarm the gentle reader to learn that I am not a trained theologian. Although once religious, and a serious student of ‘The Arguments’ for the existence of God, the writer has had no explicit academic preparation for an essay like this one. These pages, then, must be construed as the good natured testament of a reluctant disbeliever — whose studies in logic, analytical philosophy and philosophy of science have ground the lenses through which he looks at life and death, perhaps never again with the innocence once possible.

Is there such a thing as a ‘Logic of Discovery’? Do we even have a consistent idea of such a thing? The approved answer to this seems to be “No”. Thus Popper argues (The Logic of Scientific Discovery) “The initial stage, the act of conceiving or inventing a theory, seems to me neither to call for logical analysis nor to be susceptible of it”, (p. 31.) Again, “… there is no such thing as a logical method of having new ideas, or a logical reconstruction of this process”, (p. 32.) Reichenbach writes that philosophy of science “… cannot be concerned with [reasons for suggesting hypotheses], but only with [reasons for accepting hypotheses]”. (Experience and Prediction, p. 382.) Braithwaite elaborates: “The solution of these historical problems involves the individual psychology of thinking and the sociology of thought. None of these questions are our business here.” (Scientific Explanation, pp. 20, 21.)

Perplexities concerning Scientific Theories persist because the usual ‘singled valued’ philosophical analyses cannot do justice to the problematic features of so complex a semantical entity. The components of theories are like law statements, and like models and hypotheses, being conceptual entities which are used in a variety of ways—not all of these being always compatible with the others. Thus many physicists characterize the classical laws of motion, as if they functioned in a definitional way.1 But sometimes these laws seem remarkably empirical.2 Others characterize such laws as ‘conventional’; they shape entire disciplines much as the rules shape the game of chess.3 Law statements are not exclusively any one of these — definitions, factual claims or conventions. They are all these things.

In his early book Reality, Paul Weiss says interesting and important things. Some remarks however, besides being interesting and important, require further examination. The following quotation is a case in point.