1、T→O，O，所以T。自己用真值表验证。
This inference is obviously wrong. “T→O is true” if and only if “it is not the case that T is true and O is false.” When O is true, then no matter what T is, T→O is always true, so O being true is of no help in judging whether T is true or false. On the contrary, the inference “T→O, ¬O, therefore ¬T” is correct.
However, the analogy “T→O, O, therefore T” is not suitable for describing actual scientific explanation. Actual scientific explanation is usually still fairly rigorous—though not “absolutely correct,” at least in general it is more worthy of belief than this obviously mistaken logical inference.
In reality, more reliable scientific explanations can be compared by analogy to other forms of logical inference:
The first kind is the one mentioned above: “T→O, ¬O, therefore ¬T.” Another form is “¬T→¬O, O, therefore T.” This kind of inference is mainly applicable to explanations of phenomena and facts. For example: “If bats were birds, then they should have feathers; bats do not have feathers. Therefore bats are not birds.” “If the earth were not round, then sailing endlessly in one direction on the surface would not bring you back to the starting point; sailing endlessly in one direction may return you to the starting point. Therefore the earth is round.” And so on.
In addition, the scientific explanation discussed here mainly refers to explanations of scientific theory itself, that is, how to demonstrate that scientific theory itself is reasonable and reliable. At this point, it is not appropriate to oversimplify scientific theory by comparing it to a single proposition “T.” A scientific claim itself is at least of the form “if T then O,” or “when T, O can be observed,” which is to say, its complexity should at least be represented in the form “T→O.” At this point, the line of reasoning for scientific theory is more like: “When the condition T is actual, O results always accompany it; therefore T→O,” or rather “the situation in which T is true and O is false never occurs.” Of course, deriving “¬O never accompanies T” from “O always accompanies T” is an imperfect inductive method, but if we temporarily set aside Hume’s problem, then the line of inference here is that “¬(T∧¬O), therefore T→O” is itself logically correct.
However, a simple formula like “T→O” can at most serve as a scientific claim such as “water freezes below 0 degrees” (that is, “if water is cooled below 0 degrees, it will freeze”), “concentrated sulfuric acid releases heat when dissolved in water,” and so on. Compared with the explanatory object analogized by a single proposition “T,” “T→O” can be analogized to some regular real situation, not merely a single, individual fact. But “scientific theory” is by no means so simple.
Whether we call science a “theoretical system” or a “grand narrative,” in short, scientific theory is a huge whole. If we merely focus on using one assertion to explain another assertion, one formula to derive another formula, or using science to explain a single event, then it would even be less vivid and effective than a fairy tale. However, the reliability of science is and must be manifested through its whole. In the sentence “T→O, O, therefore T,” the most appropriate role played by scientific theory is neither T nor T→O, but the word “therefore” itself. In fact, in logical notation, “therefore” is better written as ├S, with “O├S T→O” meaning that, taking O as a premise and proceeding through derivation under S, one can obtain the conclusion T→O. This S contains an entire set of axioms and a series of rules of inference.
Let us reconsider the two kinds of scientific explanation above from this perspective:
The first kind is the explanation of phenomena and facts. The original meaning of “T→O, O, therefore T” can be described as “T├S O (or expressed as ‘├S T→O,’ that is, ‘T→O’ is an internal theorem), O, therefore T” (here “therefore” is in the metalanguage.) This of course is not an inference of first-order logic, but the question is whether the “therefore” here is justified. In other words: “If a proposition confirmed to be true can be explained by another proposition through a scientific theoretical system, then that other proposition is true.” Is this inference justified? Obviously, it is not rigorous. For example, both “O∧T├S O” and “O∧¬T├S O” are correct, yet the two propositions O∧T and O∧¬T are contradictory. That is to say, multiple hypotheses can all derive a certain reality. The task of science is to provide the “best” hypothesis that can explain reality, thereby making people believe that it is the most appropriate one. Here, too, one still has to consider the problem from a holistic perspective: the more ideal situation is that—even though T├S O and R├S O may both hold when T and R are contradictory, T and R can also derive many other conclusions besides O; for example, R├S X, X∧¬T├S Y, and Y is false. Then R∧¬T is false. If we are able to examine all premises that can derive O and that contradict T, and find that they will all lead to conflict with some other known facts besides O, then it is perfectly reasonable for us to therefore regard T as true!
It should be noted: what has just been described is the line of thought for using O to explain T. In other situations, we only know that O has occurred, and the task assigned to science is to seek a certain T as the cause of O, so as to explain why O’s occurrence is reasonable. In such a case, it is sufficient to say that proving T to be true and “T├S O” is enough to establish the reasonableness of O’s occurrence; it is not necessarily required to prove why only a unique T could lead to O. In fact, the premises supporting the reasonableness of O are indeed not unique. For example, the causes that may lead to “the stone is hot” may include “sunlight shining on it” and “burning it with fire,” and countless others. But once we point out the fact that the stone is inside a hot furnace, then the reasonableness of the phenomenon “the stone is hot” has already been sufficiently supported. At this point, we are not required to further demonstrate that “the stone is hot” was not caused by sunlight or some other reason; in fact, sunlight may also have played a small role in making this stone hot, or perhaps not, but what more could those facts contribute to resolving our original puzzlement about “why is this stone hot”? Our confusion was already satisfactorily resolved the moment we saw the furnace!
Further, the reasonableness of scientific theory itself is also manifested in its wholeness. The first demand on scientific theory is that it should explain as many phenomena as possible. If before us there are two candidate theories, T and R, and if all conclusions derivable from R can also be derived from T, but there are some phenomena that can be derived from T but not from R, then T will be the better choice. That is, “T├S O; R├/ SO; O, therefore T is more effective than R”—this line of thought is quite natural. And when several theories have similar explanatory power, according to the principle of simplicity, one will generally choose the most concise one to accept; once a certain theory is accepted, it will also become part of the edifice of science S.
In addition, whether it is a phenomenon or a hypothesis, if a proposition conflicts with the existing scientific system—that is, “T├S ⊥”—then T is usually regarded as wrong. Otherwise, the forced rewriting or even overturning of S will cause more phenomena that were previously well explained to lose a satisfactory explanation. In other words, while rewriting S may indeed give a more satisfactory explanation of T, it sacrifices its original reasonable explanation of countless other phenomena. Therefore, unless one can find an entire set of fairly complete ways to rewrite or replace S, we would rather tolerate a few temporary loopholes on the east wall than tear down the whole west wall just to patch those few small holes!
To sum up, the reasonableness of science is less grounded in the vague “objectivity” or “reality” than it is manifested in its wholeness. We must acknowledge that science is indeed more reliable and more credible than myth, and the main reason is precisely that science is more “grand” than myth.
2 a.m., May 18, 2006
In a crowded Plato Cafe where a football match was being shown, in the empty private room that had only me in it
2、龙存在吗？原子存在吗？两者有何相同与不同？
Both “dragons” and “atoms” are things that people have “constructed.” The difference is that the former is a mythic construction, while the latter is a scientific construction. We
mostly concede that mythic construction is unreal; the question is whether the object of scientific construction is “real”? What is “real”?
As for “real,” I will discuss it more in the next question; here let me just talk about dragons and atoms.
In a certain sense, discussing “Do atoms exist?” seems somewhat outdated. Of course, having “seen” atoms with advanced instruments still does not entirely dispel doubts about whether atoms exist. Still, modern science has a more typical case that is suitable for comparison with “dragons,” namely “quarks.”
Quark theory is exceptionally brilliant in describing the more than one hundred dazzling “elementary particles” using only six kinds of quarks. Yet we cannot “see” what a single quark looks like. This situation is quite similar to the early case of “atoms”—it likewise brilliantly explained phenomena such as chemical change and Brownian motion, but people could not “see” a single atom. However, technological progress eventually enabled us to “see” individual atoms (the meaning of this “seeing” will be discussed later), whereas quarks are different.
Because soon after quark theory was proposed, it was accompanied by another hypothesis, namely the so-called “quark confinement”—that is, quarks always come in pairs or triplets, and we will never “see” an isolated quark. This claim was not based on a lack of confidence in future technology, but on very reasonable scientific reasoning: if quantum vacuum fluctuations are real (already supported by experiments), and energy can transform into material particles (also supported by experiments), then suppose we attempt to knock out an isolated quark. The instant this quark is “knocked out,” it will immediately combine with a pair of quark and antiquark produced by quantum fluctuations in the surrounding space, find a new “partner,” and become a new particle. Therefore what we might observe will never be a single quark!
“Quarks exist” and “quarks are invisible” are both scientific theories (at least scientific hypotheses), and these two even appeared together as different parts of a whole quark theory. The reason scientists favor quark theory can only be stated as: “Quark theory perfectly explains the phenomena; quark theory has no serious contradictions with the existing scientific system; quark theory is very concise.” To put it simply, the advantages of quarks lie less in being “real” or “objective” than in being “practical,” “harmonious,” and “beautiful.”
One issue that needs further discussion is: what exactly does it mean to “see”? “Seeing stars before my eyes when I’m dizzy,” “seeing a piece of cheese in front of me,” “seeing some cells through a microscope,” “through a cloud chamber, ‘seeing’ the tracks of particles,” “inferring the existence of quarks through the behavior of particles” — what is the difference among these descriptions? In fact, like inferring quarks, declaring that one has “seen particles” from “seeing the tracks of particles” is also an indirect kind of “inference”! So is looking at things through a microscope, telescope, or magnifying glass “direct”? Those mirrors are only instruments after all.
Strictly speaking, the status of a magnifying glass is not quite the same as that of a microscope or an astronomical telescope, because the objects observed through a magnifying glass can also be observed with the naked eye. We can often compare the scene seen through a magnifying glass with the scene “directly” seen by the naked eye, and from this infer that a magnifying glass always helps us enlarge what can be directly seen a little, while still preserving the original appearance of the object—at least this inference is as credible as the inference from “sunlight—stone heat” to “sunlight—brick heat.” However, astronomical telescopes and optical microscopes are a little different: we have no way to observe, without tools, the objects that can be seen with the help of these tools, but we are still willing to believe in the reality of the objects we see through microscopes and telescopes. This is because we can quite naturally make an analogy: what is presented when a magnifying glass enlarges things by two times appears to be real, and the principle on which microscopes and magnifying glasses depend is the same (lenses and optical principles). Since doubling the image is real, then enlarging by twenty times, two hundred times, and so on by the same principle is naturally also real. This kind of reasoning also seems very reliable—at least as credible as the analogy from “sunlight—stone heat” to “sunlight—brick heat.”
Electron microscopes, cloud chambers, and so on are again different, because it is difficult to use people’s everyday sensory experience to make analogies to them. In this regard, referring back to the previous subquestion, what we are actually doing in reasoning is: “If this is an electron, then according to scientific theory, it will cause the instrument to display in such-and-such a way; the instrument does in fact display in such-and-such a way; explaining it with electrons is the best (concise, non-contradictory) explanation. Therefore, this is an electron.” This inference cannot be said to be “absolutely correct,” but it is undoubtedly quite credible and reliable.
Going further, what is an “electron”? “Electron” is a noun invented by people, just as people use “bird” to designate those animals with feathers, and “sun” to designate that thing that rises in the east and sets in the west every day. One could also say that “electron” is simply the designation for a certain kind of thing that always causes instruments to display in such-and-such a way. If that is the definition of “electron,” then when we see instruments displaying in such-and-such a way and say that we have “seen” electrons, there is no problem. But the problem is that electrons were not originally defined in this way. Rather, they were first introduced as a mathematical tool, and only afterward did people design corresponding experiments to observe them according to the properties they “should” have.
In a certain sense, it is precisely because electrons were constructed first and experimentally confirmed later that the “reality” of electrons becomes more credible. If we at least believe that “there must be some real thing that causes instruments to display in such-and-such a way,” and, before any experiment is performed, to rely entirely on luck to “guess” the experimental result correctly seems unlikely. So since electron theory perfectly “predicted” the experimental result, this theory is extremely credible—thus it is quite natural to believe that the mathematically constructed “electron” and the thing that caused the instrument to display in such-and-such a way are one and the same thing. Of course, whether there must necessarily be some “real” thing behind a phenomenon is another matter, and not easy to say.
Scientists of any stance must admit that in the world of elementary particles, one can no longer rely entirely on everyday intuition as analogy. Of course, the reason elementary particles are called “particles” is that in many respects they can be compared with the impression of rigid little spheres in the macroscopic world. However, when we say strange things like “a particle is also a wave” and “the spin number of certain particles means they must rotate through two full turns before returning to their original state,” then we can no longer understand them by relying on everyday impressions. The behavior of particles can only be described in mathematical language—descriptions like “it must rotate through two full turns before returning to its original state” can only be understood in a mathematical sense. So does a world describable only in mathematical language exist? Is it real? The answer depends on one’s attitude toward mathematics. For Platonists and Pythagoreans, admitting that “the physical world is merely depicted by mathematical models” by no means means that the physical world is “not real enough,” because precisely the world described by mathematical language is the most real. Of course, this is not the case for non-Platonists. Fortunately, the entire mainstream course of modern science is precisely the continuation of a revived Platonism, thereby sparing us a great deal of trouble.
In this sense, observations of quarks, like observations of those particles, can probably also be said to “indirectly” “confirm” quark theory by observing the behavior of particles—that is, indirectly “seeing” quarks.
By the way, the “constructive” character of quark theory is far more typical than that of electrons and the like. In fact, quark theory did alter the original scientific system—for example, it had originally been believed that a particle’s charge could only be an integer, but quarks carry fractional charges. A more typical example is this: quark theory seems to violate the Pauli exclusion principle! Three identical quarks can occupy the same location, which is not allowed! Therefore, entirely out of the need to preserve the Pauli exclusion principle, people forcibly endowed quarks with three kinds of “color.” Quantum mechanics based on quark theory is thus called quantum chromodynamics. But apart from ensuring that three otherwise identical quarks can sit together without violating the Pauli exclusion principle, quark “color” seems to have no other meaning at all! The “color” constructed for quarks is not quite the same as the construction of atoms, electrons, and so on, because the construction of the latter has the purpose of “saving the phenomena,” or at least of providing an explanation for the phenomena; whereas quark “color” is constructed not in response to any particular phenomenon, but entirely for the sake of preserving the existing theory. What this purpose reflects is precisely the “integrity” of science: a new theory must always, as far as possible, remain in harmony with those old theories that are still very useful, even if they actually show some signs of disharmony. Yet one can still rely on ingenious constructions or on proposing new hypotheses that are as simple as possible to bridge the gap. This is also something often done in the development of science. Some artificial bridging techniques are later discarded—for example, the continual addition of “wheels” to the Ptolemaic system; while some hypotheses used for bridging are later “confirmed”—for example, the “neutrino” added in order to preserve the conservation of angular momentum; and still other supplementary hypotheses—for example, quark “color”—seem neither easy to confirm further (because they do not provide any additional testable predictions), nor easy to falsify. So then, even if one can grudgingly say that quarks are real, is quark “color” real as well? —It seems more appropriate to speak of “practicality”!
Whether real or practical, in the final analysis the objects of science are things that value “cost-effectiveness.” Science seeks to explain the greatest number of problems with the fewest assumptions. As for myth, rather than saying that myth’s explanations fail to achieve the kind of “cost-effectiveness” science has, it is better to say that myth stories simply do not care about cost-effectiveness at all. Myths would gladly invent a vivid and moving legend for every phenomenon. They do not pursue universalization, nor do they require verifiability for their explanations. As a “construction” of myth, “dragon” certainly is not more “real” than “quark,” and is even less convenient and practical than quark. For example, a dragon can of course, together with other legends, form a mythic narrative system, but the “integrity” of this system is far inferior to that of science—altering or deleting stories about dragons has little effect on stories about the Seven Fairies, but altering the theory of elementary particles is enough to force the rewriting of all physics, and even chemistry, biology, and so on. Moreover, the “precision” of myth goes without saying: whether a dragon has two claws or four claws hardly affects the whole mythic narrative at all, but if the description of quark mass were changed by even 1%, that would be intolerable.
By the way, many times we habitually use “real” and “material” interchangeably, and we say that dragons are immaterial while atoms are material. Yet the concept of “matter” in the contemporary world is quite vague! Just casually opening a dictionary, including even a fairly good dictionary of ideas, one often finds the definition of “matter” itself ambiguous—for example, “refers to anything that has mass and can be perceived and measured; all matter is composed of atoms, and atoms are composed of elementary particles.” (The Hutchinson Dictionary of Ideas) We first say that “matter” is just atoms, and then turn around and say that atoms are matter; this, moreover, preloads the concepts of “mass,” “perceptible,” and “measurable” into “matter,” making the concept of “matter” even more obscure. Sometimes we speak of the properties of “matter,” saying that matter is objective reality; at other times we use matter to determine other things, as when we say atoms are material. But what exactly “matter” refers to is very hard to say clearly. In fact, the modern concept of “matter” itself seems to be a scientific construction, just as that “definition” suggests: it is called matter because it can be “quantified,” “observed,” and scientifically “measured and calculated.” In fact, when we say that something is “material,” we are in effect saying that it is “something that can be brought under science as an object”! (For the evolution of the concept of matter, see the article “The Expansion of Matter.”)
Early morning of May 18, 2006
In the large empty private room at the Plato Cafe, which was packed full while a football match was being shown, and where I was the only one present
3. What is scientific realism and instrumentalism? After reading Chapter 4, and in light of your own knowledge of the natural sciences, do you lean toward scientific realism or instrumentalism in science? Please give a brief explanation.
The answer you get depends on the way the question is asked—that is a very good point. The wording of many questions is itself full of hidden traps. A typical form is “Do you like father or mother?” Another classic question takes the form: “Would you rather be run over and killed by a car or by a train?” When we ask “Do you lean toward A or B,” we often confine the respondent’s thinking to the difficult choice between A and B, without prompting them to consider whether there is a possibility of combining the two or of having other alternatives. In philosophy, people are also sometimes shut off from thought by poorly framed questions, the most famous example being the choice between “materialism” and “idealism” — at one time, in the field of Chinese philosophy, the world seemed to consist of only three kinds of people: materialists, idealists, and those wavering between the two. The naiveté of this habit of putting hats on people goes without saying.
Still, even materialism and idealism are at least a pair of concepts on the same level; if two concepts are originally about problems on different levels, then it is even less appropriate to put them together and ask someone to “choose,” for example, “Do you lean toward eating sweets or wearing black clothes?” Such a question is even more incomprehensible.
There is also another special situation: although A and B are problems on the same level, and indeed seem logically to be mutually exclusive, the demand to choose between them is still inappropriate! For example: “Are you going to confess or not?” “Are you something or are you not something?” —the first question implies that you have already done something wrong, while the second is playing word games; for these questions one should simply refuse to answer. Similarly, a question like “Are you a materialist or a non-materialist?” also seems to be one that may as well be “refused” as an answer.
So what, exactly, is the relationship between “realism” and “instrumentalism”?
As for what “realism” and “instrumentalism” actually mean, that is very hard to say clearly. In the Dictionary of Western Philosophy in Chinese and English, both terms are emphasized as “family resemblance concepts.” In other words, no clear definition can be given—indeed, it is hard even to find a single trait shared by all “realists”!
As a stopgap measure, one may refer to Chalmers’s description: “A realist will claim that the aim of science is to arrive at true theories about the observable and unobservable world, interpreting truth in the common-sense way as correspondence with the facts.” (What Is This Thing Called Science?, Hebei Science and Technology Press, p. 340) This description is still pretty good. Unlike some overly simplistic descriptions, realism is not equivalent to materialism, nor is it necessarily epistemological. One can believe in realism even while acknowledging that human cognition is forever limited. The key words for judging whether something is realism are not “matter” or “cognition,” but “truth.” Of course, both scientific realists and anti-realists agree that the aim of science is truth in some sense (as Chalmers puts “global anti-realists,” who oppose “truth” in any sense, “to one side”). In short, realists believe in the existence of absolute “truth,” and believe that scientific theories are approaching that “truth”
Translated from the Chinese original with AI assistance. The original text is authoritative.
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