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| SELF-EVIDENT TRUTH | |||||||||||||
This basic skepticism started with Humes "Enquiry Concerning Human Understanding" [1749; Clarendon, Oxford: 1955; Open Court, La Salle, Ill.: 1988.] However, Hume did not prove this position, he only said "it seems to me." The generations of philosophers who have followed him assumed, one must suppose, that such a proof was an example of the certain knowledge they could not attain. As we have said, philosophers consider only universal propositions. These propositions may be empirical, dealing with the experimental world, or abstract; and they may be established a priori, from first principles, or a posteriori , from the evidence. Thus there is a four-cornered diagram:
Many philosophers would make the diagram symmetrical by putting "No" at the bottom of the ABSTRACTIONS column, but in fact there must be a posteriori knowledge of abstractions; one can hardly prove a theorem until one has guessed at it, probably from coming across examples. Fermats Last Theorem is known only a posteriori . (The theorem is that an + bn = cn, where a, b, c, and n are integers, is true for no value of n greater than 2. Fermat was found dead in 1637, having made a note that the proof was simple, but no-one else has found it.) Calvin C. Clawson, in The Mathematical Traveler: Exploring the Grand Theory of Numbers [Plenum Press, New York: 1994] records that the proof was set forth in 1993 by Andrew Wiles of Princeton University; on his account, it was anything but simple. Indeed, it was originally defective, according to Simon Singh, Fermats Enigma [Walker, New York: 1997.]Plainly, the denial of the possibility of episteme stands upon the belief that theories about abstractions and theories about empirics are exclusive. If we think about existential theories, this indeed seems plausible. The particular propositions "Some fractions cannot be expressed in decimals" and "Some adult birds cannot fly" are quite distinct; the former can be explained with paper and pencil, the latter may be greeted with "I dont believe it" (except in New Zealand.) However, we all know that a play can have both characters who are immortal and characters who are mortal. An equation can include both imaginary numbers (containing the square root of -1) and real numbers. Can a scientific theory, a law, not apply both to empirics and abstractions? It can indeed. Physicists and even engineers are known to perform imaginary experiments, asking themselves "What would happen if . . . ?" The engineers compare the efficiency of the engines they can build with the efficiency of a "reversible engine," one which could first compress and then expand a gas but return to the original starting point (in a real engine, heat will leak out, and friction will turn work to heat; these changes are irreversible.) A perfect gas, and a reversible engine, are examples of abstractions. Thus the classification of propositions is quite different from Table 3.1, as shown in Table 3.2. There are universal and particular propositions: of the former, some apply both to empirics and to abstractions (these are self-evident truths) and of the latter, some apply neither to empirics nor to abstractions (these are myths.) Although we have heard it asserted that "No concrete proposition is self-evident" [Oliver Wendell Holmes, Jr., "The Path of the Law," 10 Harvard Law Review 457, 466 (1897)], self-evident truths have been known for many centuries. The very discoverer of induction æ i.e. of arriving at universal propositions a posteriori æ Francis Bacon, the Lord Chancellor of England, considered that a law founded only upon observations was "exposed to danger from one contradictory instance" (that is to say, falsifiable) and, for the courts, "utterly vicious and incompetent". [Novum Organum: 1620; Advancement of Learning, Oxford, England: 1974; Encyclopaedia Britannica, Chicago: 1990] Even before that, late in the sixteenth century, Galileo propounded his law of gravity. Contrary to the accounts in the school-books, he did not drop a cannon ball and a musket ball from the Leaning Tower of Pisa. Rather, he imagined that the cannon ball fell faster than the musket ball, and asked himself what would happen if he tied the two together. If the musket ball falls slower, tying it to the cannon ball must slow the latter down: but the additional weight of the musket ball must make the cannon ball fall faster . . . Reductio ad absurdum, it is inconceivable that the two fall at different rates. But, we hear, a pound of lead falls faster than a pound of feathers. To see that Galileos law of gravity is unassailable, we must re-word it as a purely logical proposition, IF . . . THEN . . . . Now it becomes, IF equal masses fall at the same rate, THEN all masses fall at the same rate. Notice that, if it proves æ as quantum mechanics suggests æ that matter falls faster than anti-matter, then the IF will not be satisfied for a gram of matter compared to a gram of anti-matter, and so Galileos law of gravity will still stand unshaken. Thus we see that there is at least one logical proof that governs the material world (what Kant would have called a synthetical statement true a priori.) Let us note that Hume (quoted at the opening of this chapter) was not as ignorant as those who have parrotted his conclusion. He explicitly limited the subjects of which, he held, there was only conjectural knowledge to those concerning cause-and-effect. And those propositions are not self-evident; Galileos law of gravity says nothing about forces or other causes. Today, intellectuals and pseudo-intellectuals alike are heard to evoke
the Second Law of First of all, it applies only in a closed system: if energy can enter the system from outside, as by the sun shining on our planet, then the Second Law does not apply. It indeed seems as if order has appeared where we are; we have been taking electric power out of Niagara Falls for about 100 years. Second, it has an exception æ Maxwells Demon. James Clerk Maxwell asked himself whether it were possible to reverse the process of mixing hot water and cold water together, and getting warm water. And he saw the possibility of dividing the water tank into two, and having a little door in the partition, controlled by a demon. The demon would close the door whenever he saw a hot, fast-moving molecule approaching, and open the door whenever he saw a cold, slow-moving one coming. Then, eventually, the molecules on the demons side of the door would be hotter than those on the other side. Thus the Second Law can indeed be broken æ where there is intelligent life. The theory of Maxwells Demon is of the first importance. One demon might take a long, long time to order a cloud of molecules; can we use several demons instead? We can, if two conditions are satisfied. First, all the demons must agree which is to be the hot, and which the cold, side. Second, all the demons must act independently; each one uses his own judgment. This is a general law of sociology: a society creates order only if individuals enjoy information and independence. (A good example is the red-yellow-green traffic signal: if the drivers know that the green wave moves at, say, 50 m.p.h., they can use this information to avoid being delayed, but if they do not know, then the lights reduce the traffic flow.) The converse is also true; society fails if individuals are bereft of information and independence. Todays society is rich in examples of this theory bearing fruit, of individuals being prevented from getting information and acting independently. Notice that the Second Law, and its refinement of Maxwells Demon, are self-evident truths; the Second Law can be proved with paper and pencil, any scientist who proposed to do an experiment to test it would be utterly discredited. What, you may well ask, about the First Law of Thermodynamics? The First Law says that energy is conserved, only what goes in can come out; therefore, no engine can have an efficiency of more than 100%. But this is only an empirical law, an ordinary scientific theory; it was disproved (and modified) when we found it possible to transform matter into energy. However, the Second Law is a better scientific law: it says that no engine can have an efficiency of more than (T1 - T2)/T1, which is distinctly less than 100%. Thus we see that a self-evident truth can be even more informative, more improbable, more exposed to falsification, than ordinary guess-and-test science. In 1968, I was present at the first proclamation of a self-evident truth. At the annual meeting of the International Society for Terrain-Vehicle Systems, in Essen, Germany, Professor Alan Reece of Newcastle-upon-Tyne University explained the long-familiar phenomenon that the tangential (shear) stress on the surface of a wheel rolling through a weak soil changes direction at the depth where the normal (compressive) stress is a maximum. His thesis was that, where the compression needed to fail the soil forwards is less than that needed to fail it backwards (near the front of the contact) it fails forwards, creating a backwards shear: and, contrariwise, where the compression needed to fail it backwards is less . . . Where the two compressions are equal, there is no shear. There is even another branch of mathematics, or philosophy, called dimensional analysis, which asserts that every scientific law can be expressed in words alone, without reference to any standard at all; the observer using metric units and the observer using customary units must arrive at the same equations. And this prediction has been satisfied by every scientific theory throughout the centuries; indeed, no scientist or engineer would give an instants credence to any equation that was not "dimensionally homogeneous." Thus we know, a priori , that there does not exist an equation connecting unemployment, a pure number, with inflation, a rate (viz. having the dimension t-1.) This means that, when we establish communication with Alpha Centauri, their science will be the same as ours; they will agree with us that one volume of oxygen combines with two volumes of hydrogen. (Actually, they will reverse the "one" and the "two," because the names "acid-bearer" and "water-bearer" were wrongly assigned in the beginning of our chemistry.) Far from science having been discredited, it can claim to be finding universal truth. The classical scholars believed that political questions, questions concerning the whole community, could be solved solely by reasoning a priori from agreed axioms. (The term political question is now used narrowly, to mean a question with more-than-one equally good solutions, such that it needs only a majority in favor, e.g. whether to YIELD to those on ones right or those on ones left; the contemporary term for a question where all [reasonable] men must agree is a justiciable question.) Plainly, the number of questions affecting the whole community becomes less and less as the community becomes larger and larger. One city may be asking whether to heat, or to cool, the city hall, or whether to erect a new building; other cities have other concerns. At the other extreme, there are few or no questions that concern all the people of the world (until the astronomers theories come true, and an asteroid is found on a collision course with Earth.) It is intended to show that, once we consider rather large communities æ counties and states æ the only
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W‚ÑBÜ’ãÇ2éá‡,§fÿóHÚÉ®ÄsËócy!ǃe≤ȬSx8ÄÑp„ÁhMm ®„0hÅoH=;¶ÜphÜLHá9≤Ös8ŒXX|zHu%hÎ !ìß5CÕÖ≥¨Û0âGôñ∆œx¨7ô&)∫pé∏•ÄG+…5 M¿íí8Vïflkë¶Ìº•R™Úî8ájÄÿ`èªs⁄ yPƒùªp˃ ênûºyÙ*“õgQ£={ıu‰hè>|˘Ó°ºgÚû«é UñÏà2&>}0˛K≤,ôflΩù The States where the presidential electors meet and ballot, but merely follow the results of the general election, badly need to compel the electors to follow the deliberative procedure laid down by the U. S. Constitution, i.e. to meet in closed session (and to keep no records of the choices of individual electors.) Then we would see the most respected persons in the counties being chosen as electors, and these people would not be easily swayed by advertising or by the media. Here again we can see that the legislature will not act æ the electoral college, comprising the elite of the State, would eclipse the legislature in prestige if not in power æ so that the counties need to amend the constitutions of their States. Only four of the State constitutions (Georgia, I, 1 [11A]; Indiana, I, 19; Maryland, XXIII; Oregon, I, 16) explicitly acknowledge the responsibility of the jury to rule upon both the facts and the law (other States concede it in libel and sedition cases.) The amendment recommended by the Fully Informed Jury Association is as follows:
My own position is that "motives" (hate, etc.) are irrelevant; one is entitled to be judged by ones actions (intentional acts) and nothing else. Further, "degree of harm" is relevant only to civil suits for damages; a criminal jury is not entitled to consider whether a bombing killed one or one hundred people, only what the accused intended. Finally, "evaluation" implies an opinion, a subjective matter. The second sentence should be cut to " . . . may include jury scrutiny of the statute itself." The States in general urgently need to recognize that illiteracy is widespread, and adopt a literacy test for voting. (The mere existence of a test would, one suspects, discourage those with little grasp of English from going to the polls.) If one needed to be literate in order to vote, the people would, plausibly, no longer allow their children to be badly educated. One might imagine that the State legislatures would readily effect this reform æ to say that literacy is not required by voters is to say that the public affairs can be entrusted to the ignorant. However, because those not literate in English are a substantial minority, it may be that this reform too can only be effected by the counties. The Short TermThe structural reforms discussed above would, clearly, take one, two, or more decades to enact. A state constitution can, one trusts, be amended only by the consent of the counties, and it takes time for the counties to reach a consensus. (This is, in fact, an optimistic estimate; in some States, office-holders are not excluded from sitting in a convention, so that reform of the constitution is virtually impossible.) However, there are measures that could be attempted by the ordinary political process: an obvious example would be choosing a legal tender. Another would be requiring each county to pay the State for the custody of any prisoners convicted in the county (it would be highly injudicious to make this an amendment to the State constitution, because it would implicitly authorize the State to establish a prison.) An important remedy that could be adopted county-by-county is to authorize the county attorney to defend any person accused by the U. S. on account of crimes alleged to have been committed in the county: the reason why U. S. prosecutions are so fearful is that vanishingly few of the citizens can afford the cost of preparing and presenting a defense, and also litigating an appeal. Ideally, the county would undertake the defense only where the U. S. is acting without authority, i.e. where the crime charged does not violate the rights of the people of every State. This should not prove a heavy burden on the tax-payers; once the citizens collectively were paying for the defense of the cases, the grand jury would be likely to give greatly more attention to the evidence than it does now. The importance of this reform should not be discounted. Contesting a case in the U. S. courts is so expensive that corporations, which have to report profits and losses to stock-holders, regularly settle a case that they could, in law, defend; if the U. S. seizes a thousand or a million dollars, that money must come from either the users of the corporations output, or the owners of the corporations stock. Once the county has discovered how expensive such defenses are, the citizens might perhaps pay more attention to the reform of U. S. legislation. Reasonably, the county attorney could be required to defend all cases (in State as well as U.S. courts) where a citizen has been accused by non-republican officers æ either unelected officers, or State officers acting within a county. However, this reform would be difficult to institute (because the county officers have a vested interest in convictions) at least until the counties have been required to pay the State to keep their prisoners. Reform in one or another county appears to be plausible, for two reasons. Firstly, the legislative house of a county is less likely to be composed of career public servants than is that of a State; presumably, persons surviving in the market-place æ eating only by the consent of those with whom they trade as equals æ are relatively enlightened and informed. Secondly, the counties are, more nearly than the States, in competition with one another to attract people and corporations to take up residence; it is easier to move to another county than another State. |
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Thermodynamics to prove
that one or another thing cannot be done. This is a very general law indeed; it says that
order gives way to randomness (so that you always can tell whether you are watching the
real world or a record running backwards æ friction and such
natural effects must be consuming work and developing heat.) Unfortunately, very, very few
of the people who quote the Second Law know about its limitations. 
