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Warn moderators| Author : | Topic: causality | Bottom |
| saucer admin Posts : 673 A Good Tautology is Hard to Find!  |
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| saucer admin Posts : 673 A Good Tautology is Hard to Find! |
- Introduction The eclipse of causality in 20th Century thought is one of the leading characteristics of this Dim Age. A revolt against causality began with influential 18th Century philosophers, notably Hume and Kant. The revolt grew throughout the 19th Century and, in the late 19th and early 20th Century it reached physics, where it gave rise to the two central theories of 20th Century physics: relativity and quantum mechanics. This may raise some hackles; for while quantum mechanics' disdain for causality is not the least controversial, relativity is usually regarded as a causal theory, a haven of sanity compared to quantum mechanics. Unlike quantum mechanickers, relativists don't crusade against causality; indeed, they occasionally appeal to it. Relativity's sins against causality are more subtle, but no less devastating. Causality and Measurement Relativity's link to the revolt against causality is the movement called positivism, as exemplified in physics by Ernst Mach (of Mach number fame). Mach's inspiration was the French philosopher Auguste Comte, who originated and named positivism. (Comte was also busy in ethics; he coined the term "altruism.") Mach's influence on physics in general, and on Einstein in particular, is well known. Positivism rejects causality. According to positivism, causal thinking is merely a pre-scientific relic. Modern science is mathematical; its results are expressed in equations. But these equations merely report what is observed, namely that certain quantities are equal; they say nothing about causes. Since equations are the whole content of modern science, and since they are merely descrïptions, and not causal explanations, modern science need not be concerned with causes. Science has advanced beyond causality, and may now discard it. This positivist argument is a classic example of the fallacy of the stolen concept. The concepts of "measurement" and "quantity" (not to mention "equation!") rest on causality. To see this, recall that we can only identify quantity by means of measurement, that measurement is a process of counting equal units, and that our only guarantee of equal units is causality. (For the logical necessity of equal units, see my essay, Time, clocks and causality, especially the section "Units, arithmetic and identity: Experimenting on children.") The logical requirement of equal units is truly elementary, a matter of everyday experience. For example, it would be ridiculous to measure lengths using a bar of Jello because the length of a bar of Jello would vary with a myriad of causes between measurements; it would not provide equal units. A steel tape provides a better standard because its length varies less than the length of a bar of Jello, and in a more predictable fashion, according to known causes such as tension and temperature. The speed of light in a vacuum provides an even better standard, being unaffected by the run of the mill causes which affect steel tapes and bars of Jello. The less the changes in one's standard, the more accurate one's measurements. An absolutely accurate standard would have to be immutable, utterly immune to causal influences: it would have to be acausal. Since nothing real is acausal, measurement requires one to discover the causes which may change one's physical standards, and to correct for them. Immutable standards are not found lying about in nature; one constructs an immutable standard by defining a physical standard according to the best causal knowledge available, and by correcting for its variations. One can validate one's measurements and identify quantities only by reference to causality. Causality is prior to quantity. This may seem an audacious conclusion, but only in theory. It reflects the universal practice of all who perform measurements, from household cooks to Bureaus of Standards. All of them ensure that their standards are immutable by eliminating as far as possible all the causes which could change them and, in the last resort, by correcting for those changes which are unavoidable. It is only this painstaking care to construct immutable standards which renders measurements meaningful. Contrary to the assertions of positivists, causality is essential to mathematical science. Mathematical science may not dispense with causality; all of mathematical science--all the equations, laws, theorems and so on--rests on causality! Only complete and precise understanding of the causal influences on one's measuring standards can give meaning to one's measurements. Those measurements in turn give meaning to the equations based on them. It is usual these days to regard a physical theory as no more than the equations it uses, but this is not true. Equations rest on and summarize a vast body of measurements; those measurements are no more valid than the standards by which they were made; and the standards are no more valid than the causal knowledge by which they were defined. That causal knowledge (or error) is the essence of a physical theory; wildly different physical theories can have a great many equations in common. If a measuring standard varies who-knows-how, then the quantities measured by means of it vary who-knows-how, and the equations connecting those quantities mean who-knows-what. This is precisely the bog in which relativists have mired themselves; their doctrine of curved space is symptomatic. Rigidity and Space "Curved space" is a staple of 20th Century thought. Space warps are a cliche of science fiction. Generations of science students have tried to make sense of curved space, and succeeded only in warping their minds. Curved space is taken for granted among the learned; if you protest that curved space is absurd, they roll their eyes and shake their heads pityingly. But what the heck does "curved space" mean, and how does it measure up against the principle of immutable units? Instruments of geometry Geometry seeks to measure objects. It deals with such questions as, "How big is this thing here? How far is this thing here from that thing yonder? Which is bigger: this thing here, or that thing yonder?" The answer to them all is straightforward in principle: grab a measuring stick and go find out. A gas, a liquid, or a bar of Jello will not make a suitable measuring stick. If your measurements are to be valid, you will need a measuring stick which doesn't shrink, expand, shiver, bend or etc. as you move it from place to place. You need a measuring stick which is immutable in these respects, one which is rigid. Measurement requires an immutable standard, and geometrical immutability is rigidity. Rigidity is prior to geometric quantity. This is no new thing, as is shown by the traditional instruments of geometry: the compasses and straight-edge. The distance marked off by compasses is assumed not to change as the compasses are translated and rotated; the continued straightness of the straight edge is similarly assumed. All of classic geometry rests on the assumed rigidity of compasses and straight edges. These rigid instruments are the traditional standards of length and straightness. If any particular compasses and straight-edge are discovered not to be rigid, that just means they are not adequate to the task we demand of them, and we must find better ones or apply corrections as needed. This much is apparent to any beginning student struggling with slipping compasses and sagging straight-edges. The geometer assumes rigidity in proving his theorems, but the experimenter must ensure the rigidity of his standard by reference to causality. Given rigid standards, the theorems of geometry enable us to compare near things with far things without actually moving the things, by defining units, counting them and performing calculations. We can meaningfully calculate only because our units are rigid. Unfortunately, the classic system of geometry forumulated in Alexandria by Euclid (fl. ca. 300 BC) is silent on the issue of rigidity. Thereby hangs a tale. Axiom of parallels Euclid succeeded in deriving the geometrical knowledge of his day from five geometrical axioms and five "common notions." (A common notion is a principle common to all sciences, e.g., "if equals be added to equals, the results are equal," and "the whole is greater than a part.") The manifest success of Euclid's system in fields ranging from carpentry to astronomy testifies that there are no contradictions among Euclid's axioms, but it has never been clear whether all the axioms were necessary to the system. Could one of them be discarded, derived from the other axioms, or replaced with a simpler axiom? Euclid's first four axioms are simple and obvious, so attention focused on his fifth axiom: the axiom of parallels. There are various formulations of Euclid's fifth, but one of the simplest states that precisely one straight line can be drawn parallel to a given straight line, through any point not on the given line. There are a number of problems with this axiom. It is messy--its self-evidence is not obvious. Worse, it is negative; it refers to what will not be found where you can never look--i.e., that two lines will not meet at infinity. Thinkers have long been queasy about Euclid's fifth axiom. There is clear evidence that issues involved in the axiom of parallels were discussed in Aristotle's school. (This evidence was collected in a Scientific American article, published in the 1970s or 80s, on non-Euclidean geometry in Aristotle. I would welcome the exact reference.) Euclid was probably connected with Aristotle's school, and he himself had qualms about the axiom of parallels, as shown by the fact that he used it sparingly; he proved his first 28 propositions without invoking it. Euclidean or non-Euclidean? In the 18th Century, some geometers set out to test the axiom of parallels by denying it and checking if a contradiction would result. The axiom of parallels can be denied in two different ways, either by saying that no parallel to the given line can be drawn, or by saying that more than one parallel can be drawn. In the 19th century it was found that both denials led to internally consistent non-Euclidean systems when combined with the other Euclidean axioms. It was soon recognized that two-dimensional non-Euclidean systems applied to curved surfaces rather than planes--provided one was willing to accept the violence this did to the idea of a straight line. But what of the three-dimensional case? Could it be that real, observed, physical space was non-Euclidean, and therefore in some sense curved? Since the three (kinds of) systems contradicted one another, they could not all be true. A decision between them was required, but on what basis? Mathematicians (under the influence of bad philosophy) had come to regard coherence, or logical consistency, as the standard of geometrical truth. But for this problem, coherence was apparently a non-starter: in terms of the accepted axioms, all the systems were equally coherent. This was taken to mean that logic could not decide the issue. Furthermore, measurement could not decide between systems. Euclid's system was obviously consistent with all measurements that had been made, but to exclude all non-Euclidean geometries would require infinitely precise measurements, and infinitely precise measurements are not to be had. With logic and measurement ruled out, a consensus grew (egged on by philosophical irrationalism) that any decision between systems would be arbitrary. There was progress when Gauss (1777-1855) discovered the intrinsic geometry of surfaces. He found that the shape and curvature of a surface (in Euclidean space) could be discovered by measurements of length made entirely in that surface. For example, surveyors on the Earth can deduce from their surface measurements that the Earth is approximately spherical. This showed that questions of straightness or curvature can be settled in some contexts by an appeal to a standard of length. Riemann (1826-1866) generalized Gauss' result to show that a "curvature" of higher dimensional spaces could be defined by measurements made solely within them. He found that these measurements characterized the many-parallel class of non-Euclidean geometries as an infinity of spaces of constant negative curvature, the no-parallel class as an infinity of spaces of constant positive curvature, and Euclidean geometry as a unique space of constant zero curvature. This neatly displayed all the contending systems on a continuum of curvature, but it raised the daunting prospect of yet more infinities of non-Euclidean spaces of non-constant curvature! Apparently Riemann had only compounded the muddle by introducing new infinities of contending geometries. In fact, he had all but settled the issue; all he lacked was the philosophical principle of immutable units. Euclid wins! How does Riemann's work enable us to select the correct system of geometry? I cannot resist remarking that when--amid infinities of candidate geometries with curvatures which range from minus infinity to plus infinity--and amid further infinities of candidates with curvatures which vary in more ways than you can imagine--there is precisely one, single, unique system with a constant curvature of precisely zero--then it might as well be emblazoned with flashing neon signs and loudspeakers blaring out, "Pick me! Pick me!" But this is not my argument. Riemann's measurements are based on "metrics." A metric is a certain function of position that Riemann was able to define for each of the candidate systems, and which is that system's standard of measurement. In the Euclidean case, the metric is independent of position and yields ordinary length. In non-Euclidean cases, the metric varies with position. It is precisely this variation which expresses the "curvature" of the space; a space is "curved" only if its metric varies with position. If we now appeal to the principle of rigid units, this settles the issue of flat vs. curved space! For we have just seen that curved spaces have standards of length which change with mere change of position, and the principle of rigid units forbids this! I.e., curved space diddles the standard of length, and so must be rejected. The rejection of curved space is neither arbitrary nor dependent on physical measurement: it is logical. Only in Euclidean geometry is there a standard of length which does not change with position, i.e., which is rigid. Flat, Euclidean space is the system of geometrical measurements made with rigid units. Curved space is simply a system of measurements made with squidgy units. (E.g., Jello measuring sticks.) That is the trivial secret behind the gaudy curtain of curved space theories. Despite the mighty theatrics, there is nothing behind the curtain but a dishonest little man who refuses to admit that he fudged the units. Absolute length Riemann's work serves as a reductio ad absurdum of curved space, but it is much more useful than that. Once you grasp that curved space implies variations in your measuring sticks, you can recognize Euclidean geometry as a logical standard for judging real measuring sticks. If your measurements show space to be "curved," you can validly deduce that your measuring sticks are not rigid--even if you have no other evidence of their variations. Then you can ask, "What causes them to vary?" By adopting the logical standard of Euclidean space you can discover causes which a curved space theory would whisk behind the curtain of "space curvature." Furthermore, there is a mathematical transformation which reduces a general Riemannian system to a Euclidean one. The transformation to Euclidean geometry reveals the variations in the measuring sticks, and the lengths in the Euclidean system are lengths. In other words, we can extract knowledge of absolute lengths from our measurements even if our physical measuring sticks are not rigid! This transformation is a precise mathematical form of the common sense thought that we don't need absolutely rigid sticks, provided we can figure out how they vary. It tells us that we can figure out how they vary, so that we can make absolute length measurements. Notice the logical order involved. First, we must demand rigid units. Then we can select Euclidean geometry as the only system in which there are rigid units. Then we can identify deviations from Euclidean geometry as signs of systematic errors in our measurement standard. Then we can discover and correct for such errors. The principle of rigid units is the keen sword that slashes the Gordian knot of curved space. Just as we can cite contradiction as proof of an error in logic, and as we can cite dilatory time as proof of an error in time measurement, so we can cite curved space as proof of an error in length measurement. (For the case of absolute time, see Time, Clocks and Causality.) We can surmise that variations in other standards will reveal themselves by similar signs. As we identify such signs for one standard after another, we will demonstrate the absolute nature of measurement in field after field--in terms specific to each field. Our warrant in each case will be the laws of identity and causality, and the principle of immutable units. Axiom of rigidity, or a new common notion? It is now clear that the axiom of parallels can be replaced. By insisting on a rigid standard of length, we single out precisely that set of theorems which was derived by means of the axiom of parallels. In other words, the non-obvious, negative axiom of parallels can be demoted to a theorem, and replaced by an axiom of rigidity. But an axiom of rigidity would simply be an application to geometry of the principle of immutable standards which is common to all measurement. Therefore it would be better to make this explicit by invoking the principle of immutability as a new common notion. Code breaking Where does all this leave curved space theories? It leaves them with neither an epistemological nor a geometrical leg to stand on! Relativity has encoded (encrypted!) its physical content in terms of curvaceous space and dilatory time. This procedure is not merely odd, but flat out wrong--as wrong as constructing a theory out of contradictions. Freeing modern physics from the 20th century hash of syncopated clocks, Jello compasses and squirming straight-edges will be a massive job, but we can leave to it physicists. The rest of us can heave a sigh of relief as we abandon the hopeless task of trying to imagine curved space. And the next time someone tries to sell us an option on curved space, we can roll our eyes and shake our heads pityingly! We can also use our new understanding of space to draw some long overdue distinctions. Space, Void and Vacuum Space, void and vacuum are usually regarded as synonyms for emptiness, but this will not be an empty discussion. Quite the opposite! By drawing distinctions between space, void and vacuum, we are able to re-affirm that reality is full, that it is a plenum. This re-affirmation is no mere philosophical nicety, of concern only to those who take an eccentric interest in obscure issues of metaphysics. It points to a neglected physical reality of fathomless importance for human knowledge and action. Space: a concept of method Space is often supposed to be a sort of box in which existence is placed, or a sort of insubstantial stage on which the drama of reality unfolds. These notions have the fatal flaw of making space into something prior to existence or apart from existence. But nothing exists apart from existence, so these notions boil down to the idea that space is simply emptiness, non-existence. Men tend to think of space as a box because they think of it as metaphysical--as something which is intrinsic, which exists independently of consciousness. We draw a firm distinction between space and the entities in space, from yon cat to stars and galaxies. We distinguish space from all the "stuffs" which may "fill" space. But if space is regarded as metaphysical, these distinctions leave it with nothing whatever that it can be but a shadowy, unperceived box or stage. The puzzle is instantly resolved by recognizing that space is not metaphysical, but epistemological. Space is a product of human method just as numbers and concepts are products of human method. Like them, space does not exist independently of consciousness; like them it is neither arbitrary nor intrinsic: it is objective. Space is a grid of reference lines which we imagine to be constructed according to geometrical method. We imagine these lines to run through reality in the same way that we imagine lines of latitude and longitude to overlay the globe of a planet. We construct them to help us to visualize geometrical measurements. One indication that space is a concept of geometrical method is that it grew up with geometry. In Aristotle's pre-Euclidean time, geometry was relatively new; and Aristotle is silent on the subject of space. Instead, he speaks of "place," which he defines in terms of bodies: "the innermost boundary of the containing body." (Phys., IV, 4) Only after geometry had won men's confidence did they boldly extend their reference lines through the entire universe. The concept of universal space was the result, as was our modern ability to define "place" in terms of our reference lines, and thus explicitly to relate all parts of the universe to each other. Another indication that space is a concept of method is the fact that the controversy between flat and curved space is a controversy over method; should geometry employ rigid units or squidgy units? If you employ rigid units, then you construct a flat space. If you use squidgy units that vary with position, you construct a curved space. The allegedly unknowable changes in your units are revealed by the flatness or curvature of the resulting space. (See above.) Space is an epistemological construction, a product of human method. This lets us solve the puzzle that although every fragment, scrap and particle of the universe is in space as in a box, yet the universe itself is not in space. The reason is that we draw our boxes in the universe. The universe is not in space, space is in the universe. Our reference lines do not affect real things; they are, after all, imaginary. Lines of latitude and longitude cannot trip you; you cannot stumble over the equator. Even if you resort to squidgy units and take pains to draw your lines around rocks, you still cannot stumble over your lines, but only over the rocks. Space is not a cause because space is not an entity. It is idle to debate the infinity of the universe by appealing to concepts of space. Some curved spaces are indeed finite; but that depends on your choice of units, and your choice of units cannot dictate to reality. Indeed, those who employ a finite space must face the jibe that their space is too small for reality, leaving some parts unmeasured! Flat space on the other hand cannot be too small for reality. When you use rigid units, you can extend your grid as far as the universe extends--and the universe is boundless. Existence exists everywhere, and flat space enables us to extend our lines everywhere. Everywhere is somewhere! Employing flat space, you can draw your lines in any directions you wish, passing through any points you wish, because flat space is based on rigid bodies, and they are rigid under translation and rotation. Flat space is thoroughly and completely acausal. No space is a cause, but in addition, flat space is not subject to causes. Nothing whatever can curve, bend, deflect or tangle our flat space reference lines, for the simple reason that we exclude causes by employing rigid units. Flat space is utterly acausal; we know it is, because that's the way we made it. Our use of acausal, flat space does not hamper our discovery of real causes: it makes it possible. Curved space can hide causes behind the squidginess of its units, but flat space is the incarnation of a null hypothesis. It embodies an assumption of rigidity, of acausality. Any discrepancy between geometrical knowledge of rigid bodies and physical measurements of a real body implies that the real body is not rigid. That's our cue to ask, "What caused that?" Void: an epistemological error "Very well," you may ask, "if space is our visualization of geometry, what are we to call a place from which everything has been removed?" The name for this notion is "void," but like the unicorn, there ain't no such animal! If everything were to be removed, what would be left would be nothing. As Parmenides pointed out about 2500 years ago, and as Ayn Rand reminded us more recently, there is no nothing. To say that a void exists is to say that there is a place where non-existence nevertheless exists. Void is absurd--an epistemological error, a figment. There is something everywhere; reality is full. It has no "gaps." This conclusion has puzzled thinkers since ancient times, and their struggles are instructive. If reality is full, how can we see gaps all over the place? To perceive a number of entities is to perceive that they are separate; to see this cat and yon dog is to see a gap between them. Faced with this, Parmenides himself lapsed into collectivism and rationalism: he declared that there are no separate entities, that our senses deceive us; there is only a mystic unity: The One. Ancient atomists sought to preserve individuality and the evidence of perception by ditching Parmenides' axiom: they declared that everything is made up of atoms and the void, and that void--non-existence--exists every bit as much as the atoms! Their desperate expedient was doomed from the start, for a trivial exercise in logic will extract from it the same rationalistic, collectivist conclusion: "Void is nothing, and void separates the atoms; so nothing separates the atoms. So all is One, and individuality is mere sensory illusion." Atomists raised the specter of a real void, and it has haunted the outer reaches of science ever since. Parmenides and the atomists share the error that perceptual gaps are voids. They differ only in the way they use the error. Parmenides says, contrary to perception, that gaps do not exist; because voids do not exist, and gaps are voids. The atomists insist, contrary to the axiom of existence, that void exists; because gaps exist, and gaps are voids. The solution is to admit--on the warrant of perception--that perceptual gaps exist, and--on the warrant of the axiom of existence--that gaps are not nothing: something exists between perceived entities. What is it? Void is not an option, and space is no answer. Space is merely our system of reference lines. Our new question is "What is the stuff through which we draw those lines between entities?" This stuff is prior to our lines, prior to space. What's the stuff? Rationalists may as well leave right now, for this question cannot be answered by deduction; we have no premises from which the deduction could proceed. The only positive fact we know about our "stuff" is that it exists, and you cannot deduce what a thing is from the premise that it is something. To learn more, you must observe more. Bricks, to air, to vacuum, to ...? Suppose we observe a cat and a dog on opposite sides of a brick fence. What is between them? Obviously there are bricks between them. That's no problem for anyone: we all know that bricks exist. But if we remove the bricks from between our critters, they don't merge into the mystic unity of The One. They are still apart; they are still distinct entities. Now what's between them? You might hazard the suggestion that there is air between them. Congratulations! That recognition marks a great and difficult advance of science. The existence of air was not always obvious; as late as Alexandrian times, experiments demonstrating the reality of air were thought to be necessary. After all, air is shapeless, colorless, invisible, non-dog, non-cat, non-etc. If you focused on these negatives, you would be led to think that air is mere void. But you would be wrong; there is air between our cat and dog; air exists. Gradually, by further observation and experiment, man learned that air is not a fundamental, elemental constituent of reality. Rather, air is made of entities: air is a mixture of molecules, which are made up of atoms, which are made up of subatomic particles. But those particles aren't merged into mystic unity; there is something between them. What is it? In the context of knowledge sketched above, the answer is vacuum, or if you prefer, ether. The descrïption of vacuum involves even more negatives than the descrïption of air; but no list of negatives, however long, can justify the conclusion that vacuum is void: void is a mere figment. To the contrary, we have positive evidence for the existence of vacuum, namely, the separateness of particles. There is vacuum between particles: vacuum exists. If we look ahead to a hypothetical future, it may turn out that vacuum, too, is made up of some kind of entities. Then the axiom of existence will oblige future scientists to ask what exists between those entities. Or, if future scientists find they can remove even vacuum from a vessel, then the axiom of existence will oblige them to ask what exists between the walls of the vessel. Or, perhaps, vacuum will turn out to be elemental, a primary constituent of reality. Only further evidence can decide the issue. Vacuum What can we say about vacuum? Not much, but some. Vacuum transmits electrical and magnetic forces with a time delay which depends on distance. Vacuum transmits gravitational force. If one assumes that gravitational force travels through vacuum at the speed of light and is aberrated like light, one arrives at the correct orbit for the fast-moving planet Mercury. (Paul Gerber published this calculation in 1898. See Petr Beckmann's "Einstein Plus Two," Sec. 3.1) Vacuum transmits light and, near massive bodies, it deflects light. Certain kinds of clocks run more slowly as they move faster through vacuum. Particle masses increase with their speed through vacuum. These facts are all certified by uncontroversial experiment. They are conventionally "explained" in terms of relativistic space-time curvature, but such explanations are worthless. Curvaceous space and dilatory time are means to delude yourself by using squidgy measuring sticks and inconstant clocks. What delusion might one seek by means of variable units? Relativists choose their variable units to maintain the delusion that vacuum does not exist. I'm not guessing about this; it is implicit in their procedure. They begin by denying a real vacuum--in their jargon, an "ether" or "preferred reference frame"--and they derive units which vary precisely as required by that dogma. Their fudged units obediently conceal much of the evidence for vacuum. (The evidence that they have fudged the units--namely, their curved space and inconstant time--remain manifest to all who look.) Relativists' denial of vacuum revives the irrational metaphysics of the ancient atomists, for it amounts to the assertion that non-existence exists between particles. We can now understand why relativists must postulate the speed of light in vacuum to be a universal constant. They equate vacuum with void; and if vacuum were nothing, there would indeed be nothing which could change the speed of light in vacuum! Relativists have no grounds to be smug about this fragment of consistency, for it comes at a terrible price: it banishes reason and causality from physics. Just as a void would be unable to cause any change in the speed of light, it could not cause light to have a speed, and certainly could not cause it to have one particular speed rather than another. Instead of regarding the motion of light in vacuum as an experimental fact to be explained by its causes, relativists must regard it as a metaphysical miracle, forever and in principle inexplicable: absolutely causeless. Indeed, light itself and all forces between particles become miraculous; for they would have to propagate through a void, i.e., through nothing at all! To equate vacuum with void is to spawn an endless torrent of contradictions, for void is itself a contradiction. Back in reality, variations in the speed of light in material media are commonplace; they cause the everyday effect of refraction. Refraction between air and glass or plastic makes eyeglasses work, and refraction between air and water makes a stick which is partially immersed in water appear sharply bent at the water surface. Refraction between warmer and cooler air causes the "heat waves" that you can see over a paved road on a sunny day. There is positive evidence that vacuum (or ether) is pretty much like any other medium, being affected in specific ways by specific causes. For example, starlight passing near the sun is deflected from its usual course. The straightforward conclusion is that vacuum is a refracting medium, i.e., that the speed of light in vacuum is reduced near massive bodies. It's high time for physicists to expel the void from their minds, and to admit that vacuum exists. They will then be free to standardize their measuring sticks, to steady their clocks, and to use these tools to study vacuum. There's no telling what they'll find! The potential of vacuum studies for human progress and prosperity is boundless. Vacuum occupies most of the volume of the universe, and even most of the volume of every atom of ordinary matter. If men can devise methods to make this ubiquitous stuff (or stuffs!) serve human purposes, what might they achieve! Michael Miller, Calgary, February, 1999. Courtesy: quackgrass.com - --Last edited by saucer on 2008-02-18 22:48:30 -- |
| saucer admin Posts : 673 A Good Tautology is Hard to Find! |
- Aristotle on Causality First published Wed 11 Jan, 2006 Each Aristotelian science consists in the causal investigation of a specific department of reality. If successful, such an investigation results in causal knowledge; that is, knowledge of the relevant or appropriate causes. The emphasis on the concept of cause explains why Aristotle developed a theory of causality which is commonly known as the doctrine of the four causes. For Aristotle, a firm grasp of what a cause is, and how many kinds of causes there are, is essential for a successful investigation of the world around us. * 1. Introduction * 2. The Four Causes * 3. The Four Causes in the Science of Nature * 4. Final Causes Defended * 5. The Explanatory Priority of Final Causes * 6. Conclusion * 7. Glossary of Aristotelian Terminology * Bibliography * Other Internet Resources * Related Entries 1. Introduction Aristotle was not the first person to engage in a causal investigation of the world around us. From the very beginning, and independently of Aristotle, the investigation of the natural world consisted in the search for the relevant causes of a variety of natural phenomena. From the Phaedo, for example, we learn that the so-called “inquiry into nature” consisted in a search for “the causes of each thing; why each thing comes into existence, why it goes out of existence, why it exists” (96 a 6-10). In this tradition of investigation, the search for causes was a search for answers to the question “why?”. Both in the Physics and in the Metaphysics Aristotle places himself in direct continuity with this tradition. At the beginning of the Metaphysics Aristotle offers a concise review of the results reached by his predecessors (Metaph. I 3-7). From this review we learn that all his predecessors were engaged in an investigation that eventuated in knowledge of one or more of the following causes: material, formal, efficient and final cause. However, Aristotle makes it very clear that all his predecessors merely touched upon these causes (Metaph. 988 a 22-23; but see also 985 a 10-14 and 993 a 13-15). That is to say, they did not engage in their causal investigation with a firm grasp of these four causes. They lacked a complete understanding of the range of possible causes and their systematic interrelations. Put differently, and more boldly, their use of causality was not supported by an adequate theory of causality. According to Aristotle, this explains why their investigation, even when it resulted in important insights, was not entirely successful. This insistence on the doctrine of the four causes as an indispensable tool for a successful investigation of the world around us explains why Aristotle provides his reader with a general account of the four causes. This general account is found, in almost the same words, in Physics II 3 and Metaphysics V 2. 2. The Four Causes In the Posterior Analytics, Aristotle places the following crucial condition on proper knowledge: we think we have knowledge of a thing only when we have grasped its cause (APost. 71 b 9-11. Cf. APost. 94 a 20). That proper knowledge is knowledge of the cause is repeated in the Physics: we think we do not have knowledge of a thing until we have grasped its why, that is to say, its cause (Phys. 194 b 17-20). Since Aristotle obviously conceives of a causal investigation as the search for an answer to the question “why?”, and a why-question is a request for an explanation, it can be useful to think of a cause as a certain type of explanation. (My hesitation is ultimately due to the fact that not all why-questions are requests for an explanation that identifies a cause, let alone a cause in the particular sense envisioned by Aristotle.) In Physics II 3 and Metaphysics V 2 Aristotle offers his general account of the four causes. This account is general in the sense that it applies to everything that requires an explanation, including artistic production and human action. Here Aristotle recognizes four types of things that can be given in answer to a why-question: * The material cause: “that out of which”, e.g., the bronze of a statue. * The formal cause: “the form”, “the account of what-it-is-to-be”, e.g., the shape of a statue. * The efficient cause: “the primary source of the change or rest”, e.g., the artisan, the art of bronze-casting the statue, the man who gives advice, the father of the child. * The final cause: “the end, that for the sake of which a thing is done”, e.g., health is the end of walking, losing weight, purging, drugs, and surgical tools. All the four (types of) causes may enter in the explanation of something. Consider the production of an artifact like a bronze statue. The bronze enters in the explanation of the production of the statue as the material cause. Note that the bronze is not only the material out of which the statue is made; it is also the subject of change, that is, the thing that undergoes the change and results in a statue. The bronze is melted and poured in a wax cast in order to acquire a new shape, the shape of the statue. This shape enters in the explanation of the production of the statue as the formal cause. However, an adequate explanation of the production of a statue requires also a reference to the efficient cause or the principle that produces the statue. For Aristotle, this principle is the art of bronze-casting the statue (Phys. 195 a 6-8. Cf. Metaph. 1013 b 6-9). This is mildly surprising and requires a few words of elaboration. There is no doubt that the art of bronze-casting resides in an individual artisan who is responsible for the production of the statue. But, according to Aristotle, all the artisan does in the production of the statue is the manifestation of specific knowledge. This knowledge, not the artisan who has mastered it, is the salient explanatory factor that one should pick as the most accurate specification of the efficient cause (Phys. 195 b 21-25). By picking the art, not the artisan, Aristotle is not just trying to provide an explanation of the production of the statue that is not dependent upon the desires, beliefs and intentions of the individual artisan; he is trying to offer an entirely different type of explanation; an explanation that does not make a reference, implicit or explicit, to these desires, beliefs and intentions. More directly, the art of bronze-casting the statue enters in the explanation as the efficient cause because it helps us to understand what it takes to produce the statue; that is to say, what steps are required to produce the statue. But can an explanation of this type be given without a reference to the final outcome of the production, the statue? The answer is emphatically “no”. A wax cast is made for producing the statue. The bronze is melted and poured in the wax cast. Both the prior and the subsequent stage are for the sake of a certain end, the production of the statue. Clearly the statue enters in the explanation of each step of the artistic production as the final cause or that for the sake of which everything is done. In thinking about the four causes, we have come to understand that Aristotle offers a teleological explanation of the production of a bronze statue; that is to say, an explanation that makes a reference to the telos or end of the process. Moreover, a teleological explanation of the type sketched above does not crucially depend upon the application of psychological concepts such as desires, beliefs and intentions. This is important because artistic production provides Aristotle with a teleological model for the study of natural processes, whose explanation does not involve beliefs, desires, intentions or anything of this sort. Some have contended that Aristotle explains natural process on the basis of an inappropriately psychological teleological model; that is to say, a teleological model that involves a purposive agent who is somehow sensitive to the end. This objection can be met if the artistic model is understood in non-psychological terms. In other words, Aristotle does not psychologize nature because his study of the natural world is based on a teleological model that is consciously free from psychological factors. (For further information on the role that artistic production plays in developing an explanatory model for the study of nature, see Broadie 1987, pp. 35-50.) One final clarification is needed. By insisting on the art of bronze-casting as the most accurate efficient cause of the production of the statue, Aristotle does not mean to preclude an appeal to the beliefs and desires of the individual artisan. There are cases where the individual realization of the art obviously enters in the explanation of the bronze statue. For example, one may be interested in a particular bronze statue because that statue is the great achievement of an artisan who has not only mastered the art but has also applied it with a distinctive style. In this case it is perfectly appropriate to make reference to the beliefs and desires of the artisan. Aristotle seems to make room for this case when he says that we should look “for general causes of general things and for particular causes of particular things” (Phys. 195 a 25-26). Note, however, that the idiosyncrasies that may be important in studying a particular bronze statue as the great achievement of an individual artisan may be extraneous to a more central (and more interesting) case. To understand why let us focus on the study of nature. When the student of nature is concerned with the explanation of a natural phenomenon like the formation of sharp teeth in the front and broad molars in the back of the mouth, the student of nature is concerned with what is typical about that phenomenon. In other words, the student of nature is expected to provide an explanation of why certain animals typically have a certain dental arrangement. We shall return to this example in due course. For the time being, however, it is important to emphasize this important feature of Aristotle's explanatory project; a feature that we must keep in mind in trying to understand his theory of causality. This theory has in fact been developed primarily (but not exclusively) for the study of nature. 3. The Four Causes in the Science of Nature In the Physics Aristotle builds on his general account of the four causes by developing explanatory principles that are specific to the study of nature. Here Aristotle insists that all four causes are involved in the explanation of natural phenomena, and that the job of “the student of nature is to bring the why-question back to them all in the way appropriate to the science of nature” (Phys. 198 a 21-23). The best way to understand this methodological recommendation is the following: the science of nature is concerned with natural bodies insofar as they are subject to change, and the job of the student of nature is to provide the explanation of their natural change. The factors that are involved in the explanation of natural change turn out to be matter, form, that which produces the change, and the end of this change. Note that Aristotle does not say that all four explanatory factors are involved in the explanation of each and every instance of natural change. Rather, he says that an adequate explanation of natural change may involve a reference to all of them. Aristotle goes on by adding a specification on his doctrine of the four causes: the form and the end often coincide, and they are formally the same as that which produces the change (Phys. 198 a 23-26). This is one of the several times where Aristotle offers the slogan “it takes a man to generate a man” (for example, Phys. 194 b 13; Metaph. 1032 a 25, 1033 b 32, 1049 b 25, 1070 a 8, 1092 a 16). This slogan is designed to point at the fundamental fact that the generation of a man can be understood only in the light of the end of the process; that is to say, the fully developed man. What a fully developed man is is specified in terms of the form of a man, and this form is realized in its full development at the end of the generation. But this does not explain why it takes a man to generate a man. Note, however, that a fully developed man is not only the end of generation; it is also what initiates the entire process. For Aristotle, the ultimate moving principle responsible for the generation of a man is a fully developed living creature of the same kind; that is, a man who is formally the same as the end of generation. Thus the student of nature is often left with three types of causes: the formal/final cause, the efficient cause, and the material cause. However, the view that there are in nature causes besides material and efficient causes was controversial in antiquity. According to Aristotle, most of his predecessors recognized only the material and the efficient cause. This explains why Aristotle cannot be content with saying that formal and final causes often coincide, but he also has to defend his thesis against an opponent who denies that final causality is a genuine mode of causality. 4. Final Causes Defended Physics II 8 contains Aristotle's most general defense of final causality. Here Aristotle establishes that explaining nature requires final causality by discussing a difficulty that may be advanced by an opponent who denies that there are final causes in nature. Aristotle shows that an opponent who claims that material and efficient causes alone suffice to explain natural change fails to account for their characteristic regularity. Before considering how the defense is attempted, however, it is important to clarify that this defense does not perform the function of a proof. By showing that an approach to the study of nature that ignores final causality cannot account for a crucial aspect of nature, Aristotle does not thereby prove that there are final causes in nature. Strictly speaking, the only way to prove that nature exhibits final causality is to establish it on independent grounds. But this is not what Aristotle does in Physics II 8. Final causality is here introduced as the best explanation for an aspect of nature which otherwise would remain unexplained. The difficulty that Aristotle discusses is introduced by considering the way in which rain works. It rains because of material processes which can be specified as follows: when the warm air that has been drawn up is cooled off and becomes water, then this water comes down as rain (Phys. 198 b 19-21). It may happen that the corn in the field is nourished or the harvest is spoiled as a result of the rain, but it does not rain for the sake of any good or bad result. The good or bad result is just a coincidence (Phys. 198 b 21-23). So, why cannot all natural change work in the same way? For example, why cannot it be merely a coincidence that the front teeth grow sharp and suitable for tearing the food and the molars grow broad and useful for grinding the food (Phys. 198 b 23-27)? When the teeth grow in just this way, then the animal survives. When they do not, then the animal dies. More directly, and more explicitly, the way the teeth grow is not for the sake of the animal, and its survival or its death is just a coincidence (Phys. 198 b 29-32). Aristotle's reply is that the opponent is expected to explain why the teeth regularly grow in the way they do: sharp teeth in the front and broad molars in the back of the mouth. Moreover, since this dental arrangement is suitable for biting and chewing the food that the animal takes in, the opponent is expected to explain the regular connection between the needs of the animal and the formation of its teeth. Either there is a real causal connection between the formation of the teeth and the needs of the animal, or there is no real causal connection and it just so happens that the way the teeth grow is good for the animal. In this second case it is just a coincidence that the teeth grow in a way that it is good for the animal. But this does not explain the regularity of the connection. Where there is regularity there is also a call for an explanation, and coincidence is no explanation at all. In other words, to say that the teeth grow as they do by material necessity and this is good for the animal by coincidence is to leave unexplained the regular connection between the growth of the teeth and the needs of the animal. Aristotle offers final causality as his explanation for this regular connection: the teeth grow in the way they do for biting and chewing food and this is good for the animal. One thing to be appreciated about Aristotle's reply is that the final cause enters in the explanation of the formation of the parts of an organism like an animal as something that is good either for the existence or the flourishing of the animal. In the first case, something is good for the animal because the animal cannot survive without it; in the second case, something is good for the animal because the animal is better off with it. This helps us to understand why in introducing the concept of end (telos) that is relevant to the study of natural processes Aristotle insists on its goodness: “not everything that is last claims to be an end (telos), but only that which is best” (Phys. 194 a 32-33). Once his defense of the use of final causes is firmly in place, Aristotle can make a step further by focusing on the role that matter plays in his explanatory project. Let us return to the example chosen by Aristotle, the regular growth of sharp teeth in the front and broad molars in the back of the mouth. What explanatory role is left for the material processes involved in the natural process? Aristotle does not seem to be able to specify what material processes are involved in the growth of the teeth, but he is willing to recognize that certain material processes have to take place for the teeth to grow in the particular way they do. In other words, there is more to the formation of the teeth than these material processes, but this formation does not occur unless the relevant material processes take place. For Aristotle, these material processes are that which is necessary to the realization of a specific goal; that which is necessary on the condition (on the hypothesis) that the end is to be obtained. Physics II 9 is entirely devoted to the introduction of the concept of hypothetical necessity and its relevance for the explanatory ambition of Aristotle's science of nature. In this chapter matter is reconfigured as hypothetical necessity. By so doing Aristotle acknowledges the explanatory relevance of the material processes, while at the same time he emphasizes their dependency upon a specific end. 5. The Explanatory Priority of Final Causes In the Physics Aristotle builds on his general account of the four causes in order to provide the student of nature with the explanatory resources indispensable for a successful investigation of the natural world. However, the Physics does not provide all the explanatory resources for all natural investigations. Aristotle returns to the topic of causality in the first book of the Parts of Animals. This is a relatively independent and self-contained treatise entirely devoted to developing the explanatory resources required for a successful study of animals and animal life. Here Aristotle completes his theory of causality by arguing for the explanatory priority of the final cause over the efficient cause. Significantly enough, there is no attempt to argue for the existence of four fundamental modes of causality in the first book of the Parts of Animals. Aristotle clearly expects his reader to be already familiar with his general account of the four causes as well as his defense of final causality. The problem that here concerns Aristotle is presented in the following way: since both the final and the efficient cause are involved in the explanation of natural generation, we have to establish what is first and what is second (PA 639 b 12-13). Aristotle argues that there is no other way to explain natural generation than by reference to what lies at the end of the process. This has explanatory priority over the principle that is responsible for initiating the process of generation. Aristotle relies on the analogy between artistic production and natural generation, and the teleological model that he has developed for the explanation of artistic production. Consider, for example, house-building. There is no other way to explain how a house is built, or is being built, than by reference to the final result of the process, the house. More directly, the bricks and the beams are put together in the particular way they are for the sake of achieving a certain end: the production of the house. This is true also in the case of natural generation. In this context Aristotle' slogan is “generation is for the sake of substance, not substance for the sake of generation” (PA 640 a 18-19). This means that the proper way to explain the generation of an organism like animal, or the formation of its parts, is by reference to the product that lies at the end of the process; that is to say, a substance of a certain type. From Aristotle we learn that Empedocles explained the articulation of the human spine into vertebrae as the result of the twisting and turning that takes place when the fetus is in the womb of the mother. Aristotle finds this explanation unacceptable (PA 640 a 19-26). To begin with, the fetus must have the power to twist and turn in the way it does, and Empedocles does not have an explanation for this fact. Secondly, and more importantly, Empedocles overlooks the fact that it takes a man to generate a man. That is to say, the originating principle of the generation is a fully developed man which is formally the same as the final outcome of the process of generation. It is only by looking at the fully developed man that we can understand why our spine is articulated into vertebrae and why the vertebrae are arranged in the particular way they are. This amounts to find the role that the spine has in the life and flourishing of a fully developed man. Moreover, it is only by looking at the fully developed man that we can explain why the formation of the vertebrae takes place in the particular way it does. (For further information about the explanatory priority of the final over the efficient cause, see Code 1997, pp. 127-143.) Perhaps we are now in the position to understand how Aristotle can argue that there are four (types of) causes and at the same time say that proper knowledge is knowledge of the cause or knowledge of the why (APost. 71 b 10-12, 94 a 20; Phys. 194 b 17-20; Metaph. 981 a 28-30). Admittedly, at least at first sight, this is a bit confusing. Confusion dissolves when we realize that Aristotle recognizes the explanatory primacy of the final/formal cause over the efficient and material cause. Of course this does not mean that the other causes can be eliminated. Quite the contrary: Aristotle is adamant that, for a full range of cases, all four causes must be given in order to give an explanation. More explicitly, for a full range of cases, an explanation which fails to invoke all four causes is no explanation at all. At the same time, however, the final/formal cause is the primary cause and knowledge of this cause amounts to knowledge of the why. There is, however, a caveat to be considered when interpreting this claim. Aristotle is not committed to the view that everything has all four causes, let alone that everything has a final/formal cause. In the Metaphysics, for example, Aristotle says that an eclipse of the moon does not have a final cause (Metaph.1044 b 12). What happens when there is no final/formal cause like in the case of an eclipse of the moon? An eclipse of the moon is deprivation of light by the interposition of the earth which is coming in between the sun and the moon. The interposition of the earth, that is, its coming in between the sun and the moon, is to be regarded as the efficient cause of the eclipse. Interestingly enough, Aristotle offers this efficient cause as the cause of the eclipse and that which has to be given in reply to the question “why?” (Metaph. 1044 b 13-15). The example of the eclipse of the moon suggests that Aristotle's view is something like this: in each and every case there is some cause that is the primary cause about which one needs to know in order to have proper knowledge or knowledge of the why, and where there is a final/formal cause, this is the cause that one needs to know, but where there is not, the efficient cause may fill its role. This may explain why Aristotle can confidently say that “we claim we know each thing when we think we know its primary cause” (Metaph. 983 a 25-26. Cf. Phys. 194 b 20). 6. Conclusion Natural investigation was a search for answers to the question “why?” before and independently of Aristotle. A critical examination of the use of the language of causality by his predecessors together with a careful study of natural phenomena led Aristotle to elaborate a theory of causality. This theory is presented in its most general form in Physics II 3 and in Metaphysics V 5. Here Aristotle argues that a final, formal, efficient or material cause can be given in answer to a why-question. Aristotle further elaborates on causality in the rest of Physics II as well as in Parts of Animals I. Here Aristotle explores the systematic interrelations among the four modes of causality and argues for the explanatory priority of the final cause. In so doing Aristotle not only expands on his theory of causality; he also builds explanatory principles that are specific to the study of nature. Aristotle considers these principles an indispensable theoretical framework for a successful investigation of the natural world. He expects the student of nature to have mastered these principles before engaging in the investigation of any aspect of the natural world. Although Aristotle's theory of causality is developed in the context of his science of nature, its application goes well beyond the boundaries of natural science. This is already clear from the most general presentation of the theory in Physics II 3 and in Metaphysics V 5. Here the four causes are used to explain human action as well as artistic production. In addition, any theoretical investigation that there might be besides natural science will employ the doctrine of the four causes. Consider, briefly, the case of Aristotle's Metaphysics. Here Aristotle is seeking wisdom. Part of the argument of the Metaphysics is in an attempt to clarify what sort of wisdom Aristotle is seeking. Suffice it to say that Aristotle conceives of this wisdom as a science of substance that is, or is a part of, a science of being qua being (for further information about this argument, see the entry Aristotle's Metaphysics, especially Sections 1 and 3.) What is important is that this science consists in a causal investigation, that is, a search for the relevant causes. This helps us to understand why the most general presentation of Aristotle's theory of causality is repeated, in almost the same words, in Physics II 3 and in Metaphysics V 5. Although the Physics and the Metaphysics belong to two different theoretical enterprises, in both cases we are expected to embark on an investigation that will eventuate in causal knowledge, and this is not possible without a firm grasp of the interrelations between the four (types of) causes. 7. Glossary of Aristotelian Terminology * account: logos * art: technê * artisan: technitês * cause: aitia, aition * difficulty: aporia * end: telos * essence: to ti ên einai * form: eidos * generation: genesis * goal: telos * knowledge: epistêmê * necessity: anankê * principle: archê * substance  usia* why: dia ti, dioti * wisdom: sophia Bibliography General survey * Frede, M., “The Original Notion of Cause,” in J. Barnes, M. F. Burnyeat, M. Schofield (eds.), Doubt and Dogmatism: Studies in Hellenistic Epistemology (Oxford 1980), pp. 217-249, reprinted in M. Frede, Essays in Ancient Philosophy (Oxford 1989). * Hankinson, J. R., Cause and Explanation in Ancient Greek Thought (Oxford 1998). The Four Causes * Annas, J., “Inefficient Causes,” Philosophical Quarterly 32 (1982), pp. 311-322; reprinted in T. Irwin (ed.), Classical Philosophy. Collected Papers (New York/London 1995), pp. 11-27. * Bogen, J., “Moravcsik on Explanation,” Synthese 28 (1974), pp. 19-25. * Code, A., “Soul as Efficient Cause in Aristotle's Embryology,” Philosophical Topics, 15 (1987), pp. 51-59. * Code, A., “The Priority of Final Causes over Efficient Causes in Aristotle's Parts of Animals,” in W. Kullmann and S. Föllinger (eds.), Aristotelische Biologie (Stuttgart 1997), pp. 127-143. * Freeland, C., “Accidental Causes and Real Explanations,” in L. Judson (ed.), Aristotle's Physics: A Collection of Essays (Oxford 1991), pp. 49-72. * Hocutt, M., “Aristotle's Four Becauses,” Philosophy 49 (1974), pp. 385-399. * Matthen, M., “The Four Causes in Aristotle's Embryology,” in R. Kraut and T. Penner (eds.), Nature, Knowledge and Virtue: Apeiron: Special Issue 22.4 (1989), pp. 159-180. * Moravcsik, J. M., “Aristotle on Adequate Explanations,” Synthese 28 (1974), pp. 3-17. * Moravcsik, J. M., “What Makes Reality Intelligible? Reflections on Aristotle's Theory of Aitia,” in L. Judson (ed.) Aristotle's Physics: A Collection of Essays (Oxford 1991), pp. 31-48. * Moravcsik, J. M., “Philosophic Background of Aristotle's Aitia,” in M. Sim (ed.), The Crossroads of Norm and Nature. Essays on Aristotle's Ethics and Metaphysics (Boston 1995), pp. 237-246. * Mure, G. R. G., “Cause and Because in Aristotle,” Philosophy 50 (1975), pp. 356-357. * Schofield, M., “Explanatory Projects in Physics 2.3 and 7,” Oxford Studies in Ancient Philosophy Supplementary Volume 1991, pp. 29-40. * Sprague, R. K., “The Four Causes: Aristotle's Exposition and Ours,” Monist 52 (1968), pp. 298-300. * van Fraassen, B., “A Re-examination of Aristotle's Philosophy of Science,” Dialogue 19 (1980), pp. 20-45. Art and Nature * Broadie, S., “Nature and Craft in Aristotelian Teleology,” in D. Devereux and P. Pellegrin (eds.), Biologie, Logique et Métaphysique chez Aristote (Paris 1990), pp. 389-403. This article is printed with the title “Nature, Craft, and Phronesis in Aristotle,” Philosophical Topics 15 (1987), pp. 35-50. * La Croce, E., “El concepto aristotelico de tecnica,” Ethos 4 (1976/77), pp. 253-265. * Jacobs, W., “Art and Biology in Aristotle,” in G. C. Simmons (ed.), Paideia, Special Aristotle Issue (New York 1978), pp. 16-29. * Solmsen, F., “Nature as Craftsman in Greek Thought,” Journal of the History of Ideas 24 (1963), pp. 473-496; reprinted in F. Solmsen, Kleine Schriften (Hildesheim/New York 1963), pp. 332-351. Teleology and Necessity * Balme, D., “Teleology and Necessity,” in A. Gotthelf and J. G. Lennox (eds.), Philosophical Issues in Aristotle Biology (Cambridge 1987), pp. 275-286. * Bolton, R., “The Material Cause: Matter and Explanation in Aristotle's Natural Science,” in W. Kullmann and S. Föllinger (eds.), Aristotelische Biologie (Stuttgart 1997), pp. 97-126. * Boylan, M., “Mechanism and Teleology in Aristotle's Biology,” Apeiron 15 (1981), pp. 96-102. * Boylan, M., “The Place of Nature in Aristotle's Teleology,” Apeiron 18 (1984), pp. 126-140. * Bradie, M., Miller, F. D., “Teleology and Natural Necessity in Aristotle,” History of Philosophy Quarterly 1984, pp. 133-146. * Byrne, C., “Aristotle on Physical Necessity and the Limits of Teleological Explanation,” Apeiron 35 (2002), pp. 20-46. * Cameron, R., “The Ontology of Aristotle's Final Cause,” Apeiron 35 (2002), pp. 153-179. * Charles, D., “Aristotle on Hypothetical Necessity and Irreducibility,” Pacific Philosophical Quarterly 69 (1988), pp. 1-53; reprinted in T. Irwin (ed.), Classical Philosophy. Collected Papers (New York/London 1995), pp. 27-80. * Charles, D., “Teleological Causation in the Physics,” in L. Judson (ed.), Aristotle's Physics: A Collection of Essays (Oxford 1991), pp. 101-128. * Cooper, J. M., “Aristotle on Natural Teleology,” in M. Schofield and M. Nussbaum (eds.), Language and Logos (Cambridge 1982), pp. 197-222, reprinted in J. M. Cooper, Knowledge, Nature and the Good: Essays on Ancient Philosophy (Princeton 2004), pp. 107-129. * Cooper, J. M., “Hypothetical Necessity,” in A. Gotthelf (ed.), Aristotle on Nature and Living Things, pp. 150-167, reprinted in J. M. Cooper, Knowledge, Nature and the Good: Essays on Ancient Philosophy (Princeton 2004), pp. 130-147. * Cooper, J. M., “Hypothetical Necessity and Natural Teleology,” in A. Gotthelf and J. G. Lennox (eds.), Philosophical Issues in Aristotle Biology (Cambridge 1987), pp. 243-274. * Friedman, R., “Matter and Necessity in Physics B 9, 200 a 15-30,” Ancient Philosophy 1 (1983), pp. 8-12. * Furley, D. J., “What Kind of Cause is Aristotle' Final Cause?,” in M. Frede and G. Stricker (eds.), Rationality in Greek Thought (Oxford 1999), pp. 59-79. * Gotthelf, A., “Aristotle Conception of Final Causality,” Review of Metaphysics 30 (1976-77), pp. 226-254, reprinted with additional notes and a Postscrïpt in A. Gotthelf and J. G. Lennox (eds.), Philosophical Issues in Aristotle's Biology (Cambridge 1987), pp. 204-242. * Gotthelf, A., “The Place of the Good in Aristotle's Teleology,” in J. J. Cleary and D. C. Shartin (eds.), Proceedings of the Boston Colloquium in Ancient Philosophy, vol. 4 (1988), pp. 113-39. * Gotthelf, A., “Understanding Aristotle's Teleology,” in R. Hassing (ed.), Final Causality in Nature and Human Affairs (Washington DC 1997), pp. 71-82. * Johnson, M. R., Aristotle on Teleology (Oxford 2005). * Lewis, F., “Teleology and Material/Efficient Causes in Aristotle,” Pacific Philosophical Quarterly 69 (1988), pp. 54-98. * Nussbaum, M., “Aristotle on Teleological Explanation,” in M. Nussbaum, Aristotle's De motu animalium, (Princeton 1978), pp. 59-99. * Owens, J., “The Teleology of Nature,” Monist 52 (1968), pp. 159-173, reprinted J. R. Catan (ed.), Aristotle: The Collected Papers of J. Owens (New York 1981), pp. 136-147. * Pellegrin, P., “Les ruses de la nature et l'eternité du mouvement. Encore quelques remarques sur la finalité chez Aristote,” in M. Canto-Sperber and P. Pellegrin (eds.), Le Style de la pensée. Recueil des textes en hommage à Jacques Brunschwig (Paris 2002), pp. 296-323. * Quarantotto, D., Causa finale, sostanza, essenza in Aristotele, Saggi sulla struttura dei processi teleologici naturali e sulla funzione dei telos (Napoli 2005). * Sauvé Meyer, S., “Aristotle, Teleology, and Reduction,” Philosophical Review 101 (1992), pp. 791-825; reprinted in T. Irwin (ed.), Classical Philosophy. Collected Papers (New York/London 1995), pp. 81-116. * Sorabji, R., Necessity, Cause and Blame (London 1980), pp. 143-174. * Wieland, W., “The Problem of Teleology,” in J. Barnes, M. Schofield, R. Sorabji (eds.), Articles on Aristotle (London 1975), pp. 141-160; originally published as chapter 16, “Zum Teleologieproblem,” of Die aristotelische Physik (Göttingen 1962). Special Topics * Bodnár, I., “Teleology across Natures,” Rhizai 2 (2005), pp. 9-29. * Boeri, M. D., “Change and Teleology in Aristotle Physics,” International Philosophical Quarterly 34 (1995), pp. 87-96. * Fine, G., “Forms as Causes: Plato and Aristotle,” in A. Graeser (ed.), Mathematics and Metaphysics in Aristotle (Bern 1987), pp. 69-112. * Furley, D. J., “The Rainfall Example in Physics II 8,” in A. Gotthelf (ed.), Aristotle on Nature and Living Things (Pittsburgh 1985), pp. 177-182, reprinted in D. J. Furley, Cosmic Problems (Cambridge 1989), pp. 115-120. * Furley, D. J., “Aristotle and the Atomists on Forms and Final Causes,” in R. W. Sharples, Perspectives on Greek Philosophy (Aldershot/Burlington 2004), pp. 70-84. * Gaiser, K., “Das zweifache Telos bei Aristoteles”, in I. Düring (ed.), Naturphilosophie bei Aristoteles und Theophrast. 4th Simposium Aristotelicum (Heidelberg 1969), pp. 97-113. * Gotthelf, A., “Teleology and Spontaneous Generation: A Discussion,” in R. Kraut and T. Penner (eds.), Nature, Knowledge and Virtue: Apeiron: Special Issue 22.4 (1989), pp. 181-193. * Kullmann, W., “Different Concepts of the Final Cause in Aristotle,” in A. Gotthelf (ed.), Aristotle on Nature and Living Things (Pittsburgh 1985), pp. 170-175. * Lennox, J. G., “Aristotle on Chance,” Archiv für Geschichte der Philosophie 66 (1984), pp. 52-60; reprinted in J. G. Lennox, Aristotle's Philosophy of Biology (Cambridge 1999), pp. 250-258. * Lennox, J. G., “Teleology, Chance, and Aristotle's Theory of Spontaneous Generation,” The Journal of History of Philosophy 20 (1982), pp. 219-238, reprinted in J. G. Lennox, Aristotle's Philosophy of Biology (Cambridge 1999), pp. 229-249. * Lennox, J. G., “Material and Formal Natures in Aristotle's De Partibus Animalium,” in J. G. 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| ferme Posts : 85 |
Aristotle was not the first person to engage in a causal investigation of the world around us... ferme |
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