The two posts contained nearly 10,000 Chinese characters of my own contributions—almost as much as the original text and all the other comments combined. Even I, reading it back, felt I had been far too presumptuous. Still, fortunately the teachers are all good people, so they should be able to indulge me. Although I don’t usually browse forums, being able to write a couple of comments on a blog while at the same time exchanging views with people I admire or look up to is a very pleasant feeling.
The “double-negation” principle and examples
http://blog.sina.com.cn/u/485ea879010003k7
2006-05-28 18:27:46
The “double-negation” principle and examples
Liu Huajie
“Correctness is neither sufficient nor necessary for science.” A few years ago I expressed a similar idea, and friends even quoted it, but I never expected it to arouse the strong dissatisfaction of some people, who may have thought it damaged the image of science. Dissatisfaction is dissatisfaction, but no one has really refuted this formulation.
In ideological terms, or in the eyes of scientific realists and scientism advocates, science is unquestionably the synonym of correctness. There is indeed a close connection between science and correctness. But science and correctness cannot be equated. “1 + 1 = 2,” “Wen Jiabao is the current premier of our country,” “east is not west,” and so on are all correct, but they are not science; this shows that correctness is not sufficient for science. In addition, according to Popper’s view, science is science because, in principle, it is falsifiable; historical sciences, from the standpoint of the present or the future, are usually wrong—such as Ptolemaic astronomy and Newtonian mechanics. They are wrong by today’s lights, but they were indeed standard sciences, and some are still widely used today. The premises of many scientific models are fundamentally wrong, such as the ideal gas model, but these models are extremely useful and can be used for calculation and prediction; they are the finest examples of science. This shows that correctness is not necessary for science. Reasonability is of course another matter, but correctness is neither sufficient nor necessary for science.
In real society, many connections are indeed very important, but they are still neither sufficient nor necessary. This matter of “science/correctness” prompted me to conceive a more universal “double-negation” principle: for the complex connections between many things in the real world, we can hardly characterize them using necessary or sufficient conditions in the purely logical sense; in fact, many seemingly obvious necessary-and-sufficient relations, when examined closely, turn out to satisfy neither, hence the summary “neither this nor that.”
Actually, the earliest occasion on which I considered the double-negation principle was many years ago, when I saw the magazine *On Argumentation* and listened to a lecture by Mr. Chen Jiaying, whose gist was “philosophy is argumentation.” Argumentation is obviously very important for philosophy. This should be especially advocated in view of the current state of the Chinese philosophical world. However, according to the logical-empiricist requirement for defining concepts (giving an “intension,” that is, necessary and sufficient conditions), “philosophy is argumentation” is only a prejudice and cannot be a precise definition. For there is philosophy that does not emphasize argumentation (at least not strict argumentation in the modern sense), such as Lao-Zhuang philosophy (which is obviously pretty good philosophy), and this shows that argumentation is not necessary for philosophy. On the other hand, things that emphasize argumentation are not necessarily philosophy; for example, mathematics places great emphasis on argumentation, but mathematics is not philosophy, which shows that argumentation is not sufficient for philosophy. In sum, argumentation is neither sufficient nor necessary for philosophy.
I had one of my students look into the safety of GMO (genetically modified organisms) and the issue of the “substantial equivalence principle.” I once asked him to consider: a) Is this principle sufficient for the safety of GMO foods? b) Is this principle necessary for the safety of GMO foods? c) When the unsafe “result” is caused by a “small amount,” does this principle fail? Ordinary so-called toxins usually act strongly in tiny doses, such as potassium cyanide; you don’t need much of that stuff. A certain poisonous protein may need only a very small amount to cause death. How does this principle handle such cases?
The result of our discussion seemed to be that the “substantial equivalence principle” is an extremely important principle and also the only principle recognized by the FDA and others, but it still has many loopholes. As far as the safety of GMO is concerned, it also has a double-negation problem: it is neither sufficient nor necessary for safety.
At a gathering of “Hometown Folks” in Beijing on May 25, 2006, Jiang Xiaoyuan and others spoke at length about the relationship between marriage and love. This too touched on the double-negation principle. We all, independently and in unison, voiced the helpless conclusion that “love is neither sufficient nor necessary for marriage.” A marriage with love is of course wonderful, but marriages without love also exist in large numbers. At the same time, lovers do not necessarily end up together. The former says it is not necessary; the latter says it is not sufficient. Of course, ideally, we can still require love and marriage to be closely connected. But normativity is one thing, descriptivity (positivity, empiricality) is another; this is also the difference between the traditional philosophy of science and SSK in their perspectives on science.
What is the relationship between “being admitted to a famous university” and “becoming accomplished”? Clearly, that too is “double-negation.”
I suspect that the “double-negation principle” has considerable universality, though of course it is not necessary. “Double-negation” is a paradox derived from the very core of strict logical thinking; it shows that logic and reality differ considerably, that “importance” does not equal “necessary-and-sufficientness,” and may even have nothing to do with it at all. Even the most basic sufficient and necessary relations require special caution when applied in real society; in many cases, the logical sufficient or necessary relations that are claimed (or implied) do not actually exist. If you don’t believe it, everyone can use the “double-negation principle” to analyze many leaders’ speeches or some famous people’s arguments. You can also use the double-negation principle to analyze the very common sentences in social life of the type “as long as… then…” and “only if… will…”
In fact, up to now I still haven’t found a genuine counterexample.
Who can provide a counterexample for us to discuss?
First draft, 2006-05-28
Article comments
The following comments by netizens only represent their personal views, and do not represent Sina’s views or stance
[Anonymous] Lao Jiang
2006-05-29 10:21:56
Hehe, let me offer a “meta-double-negation” proposition:
Logical inference is neither necessary nor sufficient for real-world practice. Though it is very important.
[Anonymous] Gu Cu
2006-05-29 13:16:48
My anti-scientistic stance Teacher Liu should already know, but I still often have to say good things for science, so I’d like to provide a counterexample and see:
I very much agree that “correctness” is neither sufficient nor necessary for science, but I think it is “important” to science. What I want to raise is: is “pursuing correctness” actually necessary for science?
“Absolute correctness” is impossible to achieve, but being impossible to achieve does not mean it need not even be pursued, or that it is impossible to pursue. I once used a purified-water factory as an example: no matter how excellent the process for making pure water may be, it can never produce water that is “absolutely pure”; the products of a pure-water plant are always water mixed with impurities such as air. But if a factory does not “pursue purity,” then does it still deserve to be called a pure-water factory? If the boss says, “Well, no matter what, carbon dioxide can’t be completely removed anyway, so I might as well put more in”—then what he makes is carbonated water, not pure water. Consumers are still able to distinguish pure water from soda.
Although there is no absolutely pure water to use as a reference, there is a relative standard for what counts as pure water and what counts as impure. Pure water produced by processes from two hundred years ago is no longer acceptable today, but what remains unchanged is this: if a factory does not hope that the water it produces is “the purer the better,” then it does not deserve to be called a pure-water factory; at most it is a beverage factory. That, I’m afraid, would not change under any conditions.
So the question is: although there is no “absolute correctness,” is there “relative correctness”? That is of course a question. But if we admit that there is “relative correctness,” then if an “undertaking” does not regard “correctness” as “good”—that is, if it does not “pursue correctness”—can that undertaking deserve to be called “science”? Art does not pursue correctness, so it is certainly not science; and some religion and philosophy also pursue correctness, so pursuing correctness is not a sufficient condition for science, but can it be said to be a necessary condition?
Here I am speaking of science as an undertaking. Certainly some individuals may have made some progress without demanding that they “pursue correctness,” and these advances may be absorbed into “science”; but the reason certain things can be absorbed into science is still that science is about “pursuing correctness.”
“Only by pursuing purity does one deserve to be called a pure-water factory”; “only by pursuing correctness does one deserve to be called science”—do these count as counterexamples?
[Anonymous] Gu Cu
2006-05-29 14:05:09
Actually, saying that science must “pursue correctness” is precisely a way of opposing the idea that science is “correctness.” A philosophical comparison may help:
Philosophy is precisely the “love of wisdom,” that is, the “pursuit of wisdom.” From the outset, lovers of wisdom are distinguished from sages—those who think they possess wisdom and show it off and flaunt it—are not philosophers, or at least not good philosophers (they too regard wisdom as “good,” but only because they think they already possess it). Philosophers are precisely those who “know that they do not know.” It is precisely because they do not know what wisdom is, or even what the standard for wisdom is, that they pursue, question, and seek.
Science originates from philosophy. The wisdom pursued by philosophy includes truth, goodness, beauty, and other meanings, whereas science developed from the line of “seeking truth” alone; that is why we say science, religion, art, and philosophy all arrive at the same destination by different routes. Just as philosophy is the “love of wisdom,” science ought to be the “love of truth,” the pursuit of truth, the pursuit of correctness. Good science is precisely not supposed to self-identify as truth or correctness, just as with the distinction between lovers of wisdom and sages: if you use yourself as the standard of truth or correctness and show off and boast about it, then it is not good science. So I think proposing that science is “the pursuit of correctness” is quite important.
[Anonymous] ME
2006-05-29 18:49:26
Very good. I very much agree with your statement that “science pursues correctness,” just as philosophy loves wisdom.
I agree with your comparison between philosophy and science.
But there is still one question: how do we define “relative correctness”? I have thought about this before too, but I haven’t worked it out. Apart from defining good and bad, and differences of degree, at the sociological level, can this question be discussed more deeply at the cognitive level?
The philosophy of science has discussed “verisimilitude,” but that also seems untrustworthy. I have also considered using measure theory and probability theory from real analysis to describe this kind of thing, but I still haven’t figured it out.
[Anonymous] Gu Cu
2006-05-29 23:20:08
As for “relative correctness,” first, let’s step back a little: even if one says that there is no standard for relatively comparing “which is more correct,” science should still be “the pursuit of correctness,” just as philosophers have different standards—or even diametrically opposed ones—for what wisdom is, but the questions of what the definition of wisdom is and what the standard for wisdom is are themselves part of the “pursuit of wisdom.” One may say that the standard of truth in the development of science is changing, but the adjustment of the standard of truth itself is also part of the pursuit of truth. In short, science takes “truth” as its aspiration; this is not contradictory even when one cannot clearly say what the standard for measuring truth actually is.
Of course, we do feel that science is indeed “progressing,” and this feeling is very real. The development of philosophy and art, comparatively speaking, does not give people such a sense of “progress.” “Progress”—at least in the sense of making people feel progress, making people feel as though they are getting closer and closer to truth—is a characteristic of science; this cannot be denied. Why does the development of science produce such a strong sense of “progress”? This is a question that cannot be avoided.
I think science has at least two obvious directional forms of “progress”:
First, the total accumulation of experience expands. Things that ancient people could see, encounter, and observe are mostly also within modern people’s reach, but the things and places modern people can observe and touch are clearly more numerous than those available to ancient people. If knowledge comes from experience, then modern people’s “experience” should be richer than that of ancient people. Although modern people’s perspective on nature may cause them to forget many things, on the whole it is hard to deny the proposition that modern people’s experience is richer.
Second, there is the integrative power over experience. Modern science hopes to explain more phenomena with fewer theories; various empirical data are organized as part of a vast scientific whole, connected with one another and supporting one another. Ancient people would never have imagined that the laws behind the sun rising in the east and setting in the west and an apple falling to the ground could be the same.
The points just mentioned are the highlights, that is, measuring scientific progress by the standard of a “system”: the more “systematic,” the more “correct.” “Systematic” includes the two meanings above: “vastness” and “connectedness/coherence.” This is speaking of scientific progress in broad terms. And here I am using science to explain what “correctness” means, which may well lead to a circular explanation—science pursues correctness, while correctness is in turn determined by science… but this is also a helpless expedient. Because science is also supported by certain beliefs—for example, belief in the unity and harmony of nature, belief that the more universal something is, the closer it is to truth; in other words, belief that “the more science progresses, the closer it gets to correctness”—this is a fine belief, just as with faith in God, and there is absolutely nothing objectionable about such a belief. Precisely because the foundations of science need to be supported by “belief,” science should also show tolerance and understanding toward other forms of belief, such as religion. That is my thought.
In addition, one of science’s great virtues lies precisely in its “sense of progress,” or progressiveness, because other human undertakings such as religion, art, and philosophy do not give people anything close to science’s “sense of progress.” Thus science naturally becomes a proud achievement of human wisdom. Human wisdom is also part of nature; like the profound starry sky, human wisdom is lovely and wondrous as well. I myself absolutely do not hate humanity; while praising nature, I also praise human wisdom. So science, as an achievement that can be praised, is also very lovely and worthy of respect. It seems I’ve wandered far off the topic……………
[Anonymous] Li Xia
2006-05-29 23:42:39
This is a very original idea; in this way, many things that were thought to be sacred are restored to their original appearance! I’ll casually give two examples on the spot:
Branded clothing is neither necessary nor sufficient for a person’s temperament. (positive example)
Water (air, food, and all other necessities that sustain life) is both necessary and sufficient for life. (counterexample)
[Anonymous] ME
2006-05-30 07:01:06
Hello, Li Xia!
I’m very interested in counterexamples. However, I can still find little problems.
1) In your parentheses you used the term “necessary,” which is somewhat special, and already carries the meaning of a necessary condition.
2) Water itself may be necessary for life (this also needs careful study), but it is not sufficient. In other words, just giving my dog water to drink would not sustain its life. So half of your counterexample already doesn’t hold according to this point.
3) Is water necessary for life? This is complicated. For life on Earth, perhaps there is a good case to make (though not entirely; see below). If there are other life-forms in the universe, they may not need water. Digital “artificial life” needs water even less.
What can be argued is that life on Earth can also be sustained without drinking water. For example, by drinking milk! Or by eating more of any substance containing H2O.
In short, the particular term “water” is too restrictive. Then would changing the formulation avoid this kind of problem? No, it still wouldn’t. Language is limited, and any restriction has loopholes. So much so that, in the strictest sense, we have to admit that “water is not necessary for life.” Note that this sentence does not contradict the following situation: some substance containing H2O is used to sustain a certain kind of life.
[Anonymous] ME
2006-05-30 07:04:06
Also, regarding one item in Li Xia’s parentheses:
Food is obviously not necessary for life either. One can sustain life by injecting nutrients, since no length of time was specified.
Of course, food is also not sufficient for life; even with abundant food, people still die.
[Anonymous] Gu Cu
2006-05-30 09:32:16
Finding necessary conditions is actually not hard. If I change the wording a bit, and say “energy intake is necessary for life” and “energy consumption is necessary for the operation of a machine,” there should be no doubt about that, right~?
[Anonymous] Li Xia
2006-05-30 13:14:51
Greetings to Teacher Huajie and all the friends above!
This is truly a very interesting question. Coming back from class and seeing everyone’s suggestions, I think they are very good. It is indeed somewhat difficult to find a standard, strict counterexample, but I still want to try one for everyone’s criticism: one thing needs to be made clear, namely that the validity of the double-negation principle is also based on human cognition. In other words, the search for counterexamples is also limited to the bounds of human cognition; otherwise it would be meaningless.
A. Genes are both necessary and sufficient for life.
The difficulty in counterexamples lies in finding the satisfaction of sufficient conditions. For example, the above example can be stated as: if genes exist, then life certainly exists; conversely, if life exists, then genes must exist (the sufficient-condition part). I won’t say more; these are some ideas that occurred to me on the spur of the moment!
Greetings to all friends above!
[Anonymous] Gu Cu
2006-05-30 17:07:07
The gene example is obviously inappropriate. The key question is: what does “gene” refer to? If gene refers to DNA segments, then clearly life forms such as viruses, which use RNA as their genetic material, have no genes. If one says gene broadly refers to all genetic material, then it would be better to say “heredity is both necessary and sufficient for life,” otherwise one cannot make clear what “gene” actually is. Also, why does the existence of genes necessarily imply the existence of life? If you “draw out” the DNA molecule from a cell in a test tube, does a single DNA strand count as life? A single DNA strand is just a segment of information; without RNA and without protein, it cannot replicate, it is dead, and does not count as life—then is it no longer a gene?
In science it is not hard to find sufficiency either; let me give one example: “a temperature difference is both sufficient and necessary for heat transfer.”
[Anonymous] Gu Cu
2006-05-30 17:14:40
Speaking in terms of human cognition at present, there are still many assertions of sufficiency and necessity in science. Let me give another example: “a changing electric field is both sufficient and necessary for the generation of a magnetic field.” But discussing these examples seems rather pointless.
[Anonymous] Li Xia
2006-05-30 17:52:52
Brother Gu’s example is indeed beautiful. I’ve learned something!
I don’t agree with your view. I think looking for such examples is meaningful. The reason is this: if the “dual non-” principle proposed by Hua Jie is only a minority case, then this principle cannot break through the encirclement of traditional consciousness; conversely, if the cases of something being both sufficient and necessary are only a minority, then the dual non- principle becomes highly significant. It shows us the blind spots in our understanding of certain sacred things. If science is like this, then what else is there that, in our imagination, is both sufficient and necessary?
Let’s start with science! Hahahahaha
Greetings to friends!
[anonymous] Song Ge is here
2006-05-30 22:10:45
Li Xia is here to join the fun too 🙂
I’ve written two books. Will you come get them, or should I mail them to you?
As for the dual non-principle, let me add one more:
Meat is neither sufficient nor necessary for health!
[anonymous] Song Ge
2006-05-31 00:15:14
Suddenly I thought of Song Ge’s beard. It’s been a long time since we met; I miss it very much. If there’s a chance, let’s definitely have a couple of drinks together! Please, brother, send me your masterpiece. Recently I haven’t had time to go out of town; I’ve been teaching inside the walls all the time! Hahahahaha, greetings again!
[anonymous] ME
2006-05-31 08:10:47
Approximate sufficient conditions seem plentiful in science. But that’s useless. Right now let’s stick to the hard line and keep it strict. Then it becomes hard to find.
Song Ge’s example is very good. I’ll take it in.
Gu’s rebuttal to the gene example is very good. However, regarding the example you proposed that seems rather strict—“A changing electric field is both sufficient and necessary for producing a magnetic field”—I still think there is a problem.
The necessity is questionable. Can a magnet lying motionless there, by itself, produce a changing electric field?
[anonymous] Gu Bo
2006-05-31 09:54:12
As far as human knowledge currently goes, “a changing electric field is both sufficient and necessary for producing a magnetic field” is correct. The reason a magnet lying there motionless has a magnetic field is that the electric charges inside are moving directionally—because of the special molecular structure of the magnet, the directions of the electrons’ motion inside have a unity, and thus they accumulate and superimpose to produce a macroscopic magnetic field. In essence, it is still the principle that “moving electric charges produce a magnetic field.” So-called electric current producing a magnetic field is still the principle that a moving electric field produces a magnetic field.
Up to now, science has not discovered or recognized a “magnetic monopole”; if there were magnetic monopoles, then it should not be said that they produce from a moving electric field. But for the moment, this sufficient-and-necessary condition is correct.
[anonymous] ME
2006-05-31 10:58:45
It can still be questioned 🙂
“Moving electric charges produce a magnetic field” and “a changing electric field is sufficient and necessary for producing a magnetic field” — are they the same thing?
According to current science, there are four basic interactions in the world (weak, strong, electromagnetic, gravitation). For us humans, electromagnetic interaction is the broadest; our macroscopic world is basically controlled by it. In theory, “electric charge” and its motion are everywhere—so why isn’t there a magnetic field everywhere? The microscopic electron-motion explanation of magnetic phenomena is only a useful hypothesis. For the dual-non conditions we are discussing now, the microscopic level and the macroscopic level cannot be mixed together. When we say “field,” we are discussing the issue on the same plane (level). Where is the “changing electric field” produced by a motionless magnet?
Old Jiang
2006-05-31 11:13:07
Brother Gu is no ordinary person.
For a practice like science, both description and norm are important. Hua Jie does not seem to be much concerned with normativity.
Brother Li Xia, I can’t buy your masterpiece in the bookstore. Shouldn’t you mail me a copy?
Hua Jie’s positive claim is not clear enough and should be defined more strictly. The title of this article might perhaps be changed to “‘Sufficient and Necessary’ and ‘Important.’”
[anonymous] Gu Bo
2006-05-31 11:59:19
Teacher Jiang has spoken too much… I’m just relying on being young and a little presumptuous, and I hope the teachers will forgive me. Everyone can just call me Little Gu.
Questioning scientific assertions is endless; if one really wanted to question all the way down, one could question causality and so on. If one says those scientific explanations are all “hypotheses,” then what is not a hypothesis? That seems a bit too far. In any case, explaining macroscopic phenomena through microscopic phenomena is effective and credible. The reason there isn’t magnetic field everywhere is that most microscopic magnetic effects cancel each other out. The electromagnetic unification theory is precisely about explaining all magnetic fields as electric fields; it is indeed very successful and very credible, as credible as the first and second laws of thermodynamics. Can one also question “consuming energy is a necessary condition for maintaining mechanical operation”? — Of course one can, but is it worth taking that seriously all the way? I think we should still accept things when it is time to accept them. When discussing different topics, the degree of insistence on skepticism varies. When questioning the foundations of human cognition as Hume did, one really can doubt to the end—but didn’t Hume still believe in habit?
In real life, in everyday language, there are no truly strict “sufficient and necessary” conditions. If one wants to explain this view, then perhaps one may as well moderately acknowledge that there are some strict things in science. If, right from the start, one questions away any sense of “strictness” whatsoever, then coming back to discuss strictness in everyday language would seem pointless. If one wants to point out that some statement is incorrect, one must assume that there are some correct—at least more correct, more strict, more reliable—statements. If one does not limit one’s skepticism and denies all “correctness” and “strictness,” then saying that a certain assertion is incorrect loses persuasive force. For things that are equally open to questioning, there is a clear difference between “electromagnetism” and the assertion that “the moon is not made of green cheese.” In ordinary discussion, some bottom-line things in scientific assertions should and deserve to be acknowledged—for example, “a perpetual motion machine is impossible,” and so on. And the microscopic explanation that electric charge motion produces macroscopic magnetic fields really does seem seamless, ironclad… At a certain point, “stop questioning and accept the consensus” ought to be a healthy attitude; only then can questioning other assertions be prevented from descending into chaos. Otherwise, questioning everything and denying everything is equivalent to denying nothing at all.
wildflora
2006-05-31 12:18:07
What you said is all correct. But when discussing philosophical problems, we have to “play dumb” a little. It’s best to start from some premise and keep reasoning forward until we encounter a predicament and can no longer advance. In fact, doing this does not mean that we truly believe in any specific claim; we are simply asking questions—and then asking again. Comrade Hume actually did not believe in the reasoning of abstract understanding, and in life he was just like us. But only this kind of training in the process of reasoning gets the philosophy label attached to it. Hume’s theory of human nature, on the other hand, had little influence on later generations; it was his philosophy (the kind of thinking he opposed) that later generations valued. We should learn from Quine. But “Two Dogmas of Empiricism” is a model of philosophy.
The good thing about dialectics is that it liberates thought. The bad thing is that it doesn’t get very far.
But in reality, people’s dialectics—ideology even more so—has not played out its liberating function, while the problem of not getting very far is very real. Analytic philosophy looks ridiculous at the outset, but it proceeds step by step and does indeed enrich people’s understanding in the details.
wildflora
2006-05-31 12:21:11
Old Jiang:
Sorry. Brother Li Xia’s book has been sitting in my car trunk all this time. I think I told you when we were going to Běilínsì, but then forgot to give it to you. Next time be sure to remind me to ask for it. Are you coming to Professor Lin’s lecture tonight? Also, my apologies to Li Xia.
[anonymous] Li Xia
2006-05-31 14:05:31
Hahahahaha, Brother Hua Jie, it’s really lively here! It could become a salon. Old Jiang and Song Ge are both here; meeting at eight tonight! Hahahahaha. In response to Teacher Hua Jie’s suggestion: learn from Comrade Hume! Learn from Comrade Quine! And by the way, commemorate the Dragon Boat Festival!
Also, Brother Gu has made one very good point! “Pursuing correctness”—in my view, at least, this is a posture of science! It makes me think of van Fraassen’s statement: the aim of science is to provide us with theories that have empirical adequacy; acceptance of a theory is only connected with the belief that the theory has empirical adequacy.
If treated this way, then science does not possess the sacredness that Chinese people’s beliefs have endowed it with; instead, it comes closer to the true state of science. Science is only a convenient tool for us in facing the world. There is no need to do everything in the name of science. We can have the name of morality, the name of history, and the name of beauty; then such a society would be one of fairness and democracy. It would also break the dogmas of thought!
The significance of Hua Jie’s dual non-principle lies precisely here! If it can be proved that science is neither, in the ordinary sense, necessary nor sufficient, then this seemingly correct assertion is undermined from the very bottom of our faith in science. So finding counterexamples is not easy, and that is also a sign of the success of this principle. Conversely, if counterexamples are easy to find, then that instead proves that Hua Jie’s dual non theory has serious difficulties.
I have class this afternoon, so let me stop here for now! Wishing all friends good fortune! Happy holiday!
Hahahahaha, off to class!
[anonymous] Old Jiang
2006-05-31 17:08:45
I can’t go tonight, because I still have to go teach—who told you you were unlucky enough to teach at Tsinghua?
What Brother Gu said above seems to have mixed up two different levels.
1. If you want skepticism to be meaningful, you must first affirm. This is correct and profound. It states the meaning of language.
2. “When questioning on the basis of human cognition as in Hume, one really can doubt to the end—but didn’t Hume still believe in habit?” This is about the difference between theory and practice. What we are doing here is theory, where logical rigor matters, not practical effectiveness.
[anonymous] Gu Bo
2006-05-31 18:04:45
Teacher Jiang is right. “If you want skepticism to be meaningful, you must first affirm.” — that is exactly what I wanted to say.
However, I still have another opinion: we should not get trapped in the binary opposition of “theory-practice,” as if we are either discussing issues in terms of practical effectiveness or else just playing with theory, and as if when talking theoretically one must necessarily be talking under absolute logical rigor. One pole is talking practicality and effect; the other is talking theory and logic; when talking about effect, one must see it through to the end, and if one wants to talk logic, one must also see it through to the end—are there only two mutually exclusive ways to play? That is where I disagree.
Even if we are talking theory, the theory of logic and the theory of science are two different levels. One cannot explain scientific theory clearly from logic alone, but if that means that only one choice remains—talking about things in terms of utility—that is too absolute.
Must “playing theory” mean carrying logical rigor through to the end and never relaxing it?
Even playing theory alone can have logical ways of playing, scientific ways of playing, and philosophical ways of playing; similarly, talking only about practice can have pragmatic ways of speaking, instrumentalist ways of speaking, dialectical ways of speaking, and so on.
When discussing logic, one demands rigor—when discussing science, one values reliability—when discussing philosophy, one emphasizes reasonableness—when discussing practice, one pursues effectiveness, and so on—these are different levels. Logical rigor supports scientific reliability, but even if absolute logical rigor cannot be achieved, one can still distinguish reliable from unreliable when discussing science; even without fully conforming to science, one can still discuss whether something is reasonable in philosophy. Likewise, pointing out that a certain assertion is unreasonable in philosophy does not necessarily require a complete return to logic for analysis. One’s not being absolutely rigorous in logic can be a reason why a philosophical assertion or an assertion in everyday life is unreasonable, but one need not always cling to this too deeply. Different contexts of discussion and different targets call for different ways of playing theory.
My mention of Hume was not expressed clearly. I probably meant that one need not always doubt all the way to the end.
http://blog.sina.com.cn/u/485ea879010003lj
(continued)
II. The roots and significance of the widespread existence of dual-non sets
I think I should first make a summary and then continue the discussion below.
Summary of the previous section:
Regarding the “dual non-” issue, Professor Jiang Xiaoyuan immediately provided two new supporting examples: “Wealth is neither sufficient nor necessary for happiness; talent is neither sufficient nor necessary for success.” Xiaoyuan also pointed out: “Theoretically, there should be infinitely many sets, forming a ‘dual non-’ set.” It seems necessary to accumulate a collection of common dual-non combinations, and their significance can be discussed later.
Tian Song added: “Meat is neither sufficient nor necessary for health!” This happens to match Song Ge’s current theory and practice of ecological vegetarianism.
Jiang Jinsong then offered a “meta-dual-non” proposition: “Logical reasoning is neither necessary nor sufficient for real-world practice. Of course, it is very important.” It has a faint whiff of Feyerabend.
Li Xia offered one positive example and one negative example. “Branded clothing is neither necessary nor sufficient for a person’s temperament (positive example).” “Water (air, food, and all necessities for sustaining life) is both necessary and sufficient for life (negative example).” Li Xia then tentatively proposed a counterexample: “Genes are both necessary and sufficient for life.” However, both of these counterexamples were immediately and rather easily refuted.
Comrade Gu Bo considered the dual-non issue from multiple angles (the part involving the nature of science is very complicated, so I won’t discuss it here), and seemed to conclude with ease: “As far as human knowledge currently goes, there are still many sufficient-and-necessary assertions in science. Here is another example: ‘A changing electric field is both sufficient and necessary for producing a magnetic field.’ But discussing these examples seems to be rather pointless.” I replied: “The necessity is questionable. Can a magnet lying motionless there, by itself, produce a changing electric field?”
Comrade Gu elaborated: “As far as human knowledge currently goes, ‘a changing electric field is both sufficient and necessary for producing a magnetic field’ is correct. The reason a magnet lying there motionless has a magnetic field is that the electric charges inside are moving directionally—because of the special molecular structure of the magnet, the directions of the electrons’ motion inside have a unity, and thus they accumulate and superimpose to produce a macroscopic magnetic field. In essence, it is still the principle that ‘moving electric charges produce a magnetic field.’ So-called electric current producing a magnetic field is still the principle that a moving electric field produces a magnetic field. Up to now, science has not discovered or recognized a ‘magnetic monopole’; if there were magnetic monopoles, then it should not be said that they produce from a moving electric field. But for the moment, this sufficient-and-necessary condition is correct.”
I argued as follows: “‘Moving electric charges produce a magnetic field’ and ‘a changing electric field is sufficient and necessary for producing a magnetic field’—are they the same thing? According to current science, there are four basic interactions in the world (weak, strong, electromagnetic, gravitation). For us humans, electromagnetic interaction is the broadest; our macroscopic world is basically controlled by it. In theory, ‘electric charge’ and its motion are everywhere—so why isn’t there a magnetic field everywhere? The microscopic electron-motion explanation of magnetic phenomena is only a useful hypothesis. For the dual-non conditions we are discussing now, the microscopic level and the macroscopic level cannot be mixed together. When we say ‘field,’ we are discussing the issue on the same plane (level). Where is the ‘changing electric field’ produced by a motionless magnet?”
Following Professor Jiang’s line of thought, there really are many “dual non-” sets. In pure natural science, if one insists on finding dual-non sets, it may be a bit more difficult (but not impossible to find them!). But in the everyday world, in natural language, dual-non phenomena do indeed exist universally.
Why do people describe relations that originally do not have sufficient-and-necessary conditions as sufficient-and-necessary conditions, or at least imply them?
That is an interesting question. I will not answer it for the time being, but instead explain from the standpoint of philosophy of science why dual-non sets are so widespread.
I think there are at least two roots for the emergence of dual-non sets at the level of philosophy of science: (1) ceteris paribus clauses; (2) underdetermination, or multi-realization.
As for (1), because the “all else being equal” assumption is usually not guaranteed, sufficient conditions are difficult to describe. Take striking a match as an example: such a simple thing, yet it cannot be stated perfectly. No matter how strictly one describes the premises, loopholes can still be found that prevent the match from igniting after frictioning the match head. There are many reasons: insufficient force, dampness, no oxygen in the surroundings, and so on.
As for (2), underdetermination means that empirical evidence and data do not fully determine hypotheses and theories. A scientific hypothesis at a certain moment can be made compatible with the data available at that time, but this does not mean that other viable hypotheses do not exist. It is entirely possible that there are several, or even infinitely many, hypotheses that can equally well fit the existing data. This shows that hypotheses are not necessary with respect to data. In principle, any specific hypothesis is not necessary. (Of course, this is not how things work in reality; we are proceeding along the path of mathematical logic.) “Multi-realization” is a concept from philosophy of mind and cognitive science, and it can also be borrowed to illustrate non-necessity.
In sum, ceteris paribus provides an infinite source of non-sufficiency, while underdetermination or multi-realization provides multiple possibilities for non-necessity. Put together, the two can roughly explain why the sufficient-and-necessary conditions of habit are actually imprecise and problematic.
What is the significance of questioning with “dual non-”?
It is a mode of thought, a critical method, a liberating method, and a “methodology of creation” that is conducive to innovation.
Creation means bringing forth something out of nothing; there was originally no concrete, practical method to use, but there is still methodology. Why do dual non- claims help innovation?
The first step in innovation is to think what others have not thought, to raise doubts where no doubt is born. A few examples:
(1) paper – printing – books;
(2) rockets – spacecraft;
(3) eating – living;
(4) making fire – heating;
(5) socialist revolution – living a good life;
(6) memorizing vocabulary and grammar – learning English;
Among other things, books need not be printed on paper, as with e-books. In theory, spacecraft too need not be propelled by “fire”; they can also be driven by ejecting compressed gases or solids at normal temperature outward. One can also imagine human beings living without eating, for example by injecting nutrients; or, even further, making people completely digitalized, supplying only energy (for instance, only electricity). According to a certain reductionist line of thought, spending a great deal of time eating all sorts of delicacies is sheer fuss and bother; just give everyone a few kilowatt-hours of electricity every day and that’s that. Leaders and cadres who eat more could just be given a few more kilowatt-hours. Apartment buildings need not burn boiler fuel either; solar energy would do. And so on.
Li Xia also spoke of other meanings.
Article comments
The comments below by netizens represent only their personal views, and do not represent the views or positions of Sina.com.
[Anonymous] Guhu
2006-05-31 14:37:35
The question I want to raise is: what position does Liu Laoshi want to express? If what he wants to express is that “there are many examples of double non,” “double non is widespread,” “people often take relations that are not in fact both sufficient and necessary conditions, and present them as, or imply that they are, sufficient and necessary conditions”—
If what he wants to express is that meaning, then there is no need to reject every sufficient and necessary condition; the skepticism is too excessive. If you question everything, that is equivalent to questioning nothing. Even in philosophical discussion, one pays attention to the relation with the preceding and following context and with the situation; philosophy can and should doubt everything, but that does not mean that in discussing any issue one should doubt everything.
If one says that there are no sufficient conditions or necessary conditions at all, and rejects any example of necessary and sufficient conditions, then explaining why “people often take relations that are not in fact both sufficient and necessary conditions, and present them as, or imply that they are, sufficient and necessary conditions” becomes far too easy—because there is no truly sufficient and necessary condition in the world at all, so whenever anyone mentions a necessary and sufficient condition, it must be improper. But in that case, the original meaning of the double non principle is actually weakened.
It might as well be admitted: there are indeed some occasions where declaring something to be a sufficient or necessary condition of something else is appropriate—only with appropriate usage can there be inappropriate usage; if no matter how you use it it is inappropriate, then the problem lies with the term itself, not with the inappropriateness of its use. So what exactly does Liu Laoshi mean? Does he want to rule out any possibility that these two terms can be used properly, or is he mainly trying to reveal their frequent misuse in reality? If our emphasis is on the latter, then appropriately accepting some rational formulations about sufficient and necessary conditions is actually support for our position rather than a negation of it.
[Anonymous] Guhu
2006-05-31 15:11:36
If even among the many propositions of natural science one cannot find a single example of proper use of “sufficient and necessary,” that is unfavorable to our position rather than favorable!
If there are no examples of “sufficient and necessary,” then I can say this: I admit that in everyday language “sufficient and necessary” may be logically imprecise, and that saying “sufficient and necessary” is merely a habitual usage. I say that what I mean by “meat is sufficient and necessary for health” is roughly the same as what is meant by “a changing electric field is sufficient and necessary for generating a magnetic field”—I admit that neither is absolutely strict, and both can be questioned, but I say that “a changing electric field is sufficient and necessary for generating a magnetic field” is pretty scientific, isn’t it? Pretty reliable, isn’t it? Saying “meat is sufficient and necessary for health” is not absolutely reliable, but that’s fine; anyway, what I mean is that it is about as credible as “a changing electric field is sufficient and necessary for generating a magnetic field”! Maybe “sufficient and necessary” isn’t a good expression, but in any case, you tell me what relation there is between a changing electric field and a magnetic field~? Whatever relation you say they have, I’ll say that meat and health have that same relation…
—But is that the meaning our position wants to achieve? Are we trying to challenge electromagnetism? Or are we mainly just trying to reveal the improper uses in everyday life?
We should admit that saying “meat is sufficient and necessary for health” and saying “a changing electric field generates a magnetic field” belong to different levels of rationality—Liu Laoshi also talked about “levels”; even if there is no clear boundary between macro and micro, he can still say that they are “two levels.” Then here I need to emphasize even more the question of “levels”: “meat is sufficient and necessary for health” and “a changing electric field generates a magnetic field” are precisely matters of different levels. When we want to emphasize exposing the irrationality and inappropriateness of “meat is sufficient and necessary for health,” it is important to acknowledge the rationality and appropriateness of “a changing electric field is sufficient and necessary for generating a magnetic field,” otherwise we will fall into confusion of position.
[Anonymous] Lao Jiang
2006-05-31 17:23:49
[Jiang Jinsong, for his part, offered a “meta-double non” proposition: “Logical inference is neither necessary nor sufficient for real practice. Of course, it is very important.” It has a faint touch of Feyerabend.]
My meaning of “meta-double non” is:
1. At the logical level, I support little Gu.
2. At the level of scientific practice, I support Hua Jie, namely [I think the root of the double non set lies, at the level of philosophy of science, in at least two things: (1) ceteris paribus clauses; (2) underdetermination or multi-realization.]
3. At the methodological level, I support Hua Jie; one should break the necessity of common connections, while of course also acknowledging a certain high probability of common connections. (This level only occurred to me after seeing Hua Jie’s new formulation.)
*****************************
The key to this issue is that necessary and sufficient conditions are a logical relation, whereas the important relations we often speak of are practical associations, with situations and backgrounds, with relative and utilitarian criteria of judgment, and so on. Hua Jie’s emphasis on the inconsistency between the two is meritorious.
This is the reason I want to label my double non as “meta” double non.
[Anonymous] Lao Jiang
2006-05-31 17:34:09
I’ll construct one more “self-reflexive double non” proposition:
Prove that “correctness” is neither necessary nor sufficient for “science,” though it is very important;
and prove that the more general “importance” is neither necessary nor sufficient, though it is very important;
These results, for the purpose of criticizing scientism,
are neither necessary nor sufficient, though they are very important.
[Anonymous] Guhu
2006-05-31 18:45:50
I have no proposition contrary to Liu Laoshi’s at all; in fact, my purpose is to support Liu Laoshi.
What I am proposing is:
Propositions such as “wealth is neither sufficient nor necessary for happiness; talent is neither sufficient nor necessary for success”—these are quite enough to discuss in ordinary language.
And propositions such as “DNA is neither sufficient nor necessary for life” are quite enough to discuss on the basis of current scientific knowledge.
As for “energy difference is the necessary and sufficient condition for heat transfer,” “a changing electric field is the necessary and sufficient condition for generating a magnetic field,” and so on, these are propositions supported by current science, and can only be rebutted in the logical sense of not being absolutely strict (I do not think one must necessarily rebut them)
Liu Laoshi said—everyone can use the “double non principle” to analyze many leaders’ speeches or some statements by famous people. One can also use the double non principle to analyze the very common sentences in social life such as “as long as … then …” and “only if … then …”.
—If one is talking about the misuse of “sufficient and necessary” in social life, then there is no need to brandish Ockham’s razor, let alone Hume’s fork.
The idea that “if saying ‘sufficient and necessary’ is inappropriate even in the most mature scientific statements, then how much more so in everyday life” seems quite reasonable; but in fact, over-questioning mature scientific statements not only does not help clarify the claim that “it is often misused in everyday life,” it actually weakens the force of that claim.
“More wealth definitely means more happiness” and “conservation of energy” are both “questionable” under strict logic; but if you place them on the same level and rebut both with logical strictness, then you weaken the force of the rebuttal of “more wealth definitely means more happiness.” It is beneficial to question both separately, but it is best to discuss them in different ways. And in our discussion just now, no distinction was made. My point is that when rebutting “more wealth definitely means more happiness,” one need not dig too deeply into logic.
[Anonymous] Guhu
2006-05-31 22:39:58
As for the question “why do people take relations that are not originally sufficient and necessary conditions and present them as, or imply that they are, sufficient and necessary conditions?” let me offer a few random thoughts.
I think this reflects some problem of our era; it is hard to say precisely what, so for the moment let us call it “logicism” (logic supremacy?); it can be understood as part of scientism, or one of its forms.
Just as scientism always consciously or unconsciously views any issue through the lens of science, the characteristic of logicism is that it gets trapped in logical thinking and cannot extricate itself.
For example, scientism cannot accept things that are hard to measure and cannot be analyzed quantitatively or qualitatively—that is, things that science cannot make clear—and either rejects them or forcibly simplifies them. Logicist thinking, by contrast, is that all words must be fitted into logic, and concepts that logic cannot make clear are often forcibly simplified.
Take concepts such as “important” or “closely connected”: how are they to be explained in logic? They cannot be made clear! What logic can make clear are things like “sufficient condition,” “necessary condition,” “either-or,” and so on; these concepts are easier to enter into people’s thinking. So naturally people often, without realizing it, use those logically clear and easily accepted concepts to understand relations that are logically obscure. What is an “important” relation? Hard to tell! But a necessary and sufficient relation is very clear, so people become more inclined, more accustomed, to using “necessary and sufficient relations” to understand relations between things!
Especially in the wake of the tremendous success of mathematical logic, logicism has become particularly widespread. Just as with the “reductionism” of science—emphasizing that various real-world problems should first be reduced to scientific problems, biology to chemistry, chemistry to physics, as though only theories reduced to physics count as profound, and only discussing problems with physics is the highest level—another reductionist route ends at logic: reducing all sorts of real-world and philosophical problems to logic, especially to mathematical logic, as though unless they are reduced to logic they are not profound enough, do not count as doing theory.
I do not oppose reductionism. As a huge system, science has physics as its foundation, and it is indeed extremely important; the effort to reduce other theories to physics is not wrong, only it should not be absolutized. And when discussing philosophy, in order to ensure that one’s views are coherently linked, one also needs to organize thought and form a system; logic is the most fundamental and indeed very important, but it too should not be absolutized, as though for any specific topic one must drag it into logic or else it is not forceful enough—that would go too far.
Sufficient, necessary, if and only if, if…then…, only if…, and so on, were originally all part of everyday language; but after the rise of logic, these concepts seem to have become the exclusive property of logic! It seems that “sufficient and necessary” can only be discussed in logic or mathematics, and that the right to use these words reasonably in everyday language has to be stripped away!
“Only through effort can one gain something,” “As long as one works hard, one will gain something”—how “healthy” these everyday expressions are! Is the usage here inappropriate? In everyday language, and even in scientific theory, can one not find a single counterexample to the double non principle? This is a sad thing; it shows that the right to use concepts such as “as long as…then…,” “only if…then…,” and “necessary” has been monopolized by logic.
I think that what the double non principle reveals is not so much an error of everyday language as the limitations of logical thinking.
[Anonymous] Guhu
2006-05-31 23:05:46
Let me summarize, and then get back to my paper…
Liu Laoshi’s double non principle may be trying to say that “necessary and sufficient conditions” are “imprecise” under any circumstances; in this respect I agree with Liu Laoshi.
But what I have been talking about is that “necessary and sufficient conditions” are often used “inappropriately.”
Arguing from “imprecision” casts too wide a net. And in my view, although not absolutely strict, “sufficient and necessary” has many appropriate uses.
For example, I think it is inappropriate to say “correctness is necessary and sufficient for science”; whereas it is appropriate to say “the pursuit of correctness is necessary for science.”
It is inappropriate to say “DNA is necessary and sufficient for life”; whereas “energy difference is necessary and sufficient for heat transfer,” and “a changing electric field is necessary and sufficient for generating a magnetic field,” are appropriate.
It is inappropriate to say “money is necessary and sufficient for happiness”; whereas it is appropriate to say “knowing contentment is necessary and sufficient for enduring happiness.”
It is inappropriate to say “genius is necessary and sufficient for achievement”; whereas it is appropriate to say “effort is necessary and sufficient for obtaining results.”
It is inappropriate to say “being logically absolutely strict is necessary and sufficient for speaking appropriately”; whereas the statement, “If one wants to doubt meaningfully, one must first affirm,” is appropriate.
……
[Anonymous] ME
2006-06-01 01:41:27
Haha, that’s putting it too heavily!
I never expected myself to happen to bump into some extremely general truth; I’m just practicing. I also believe sufficient conditions may exist, but what I have seen before me mostly does not stand up to scrutiny.
My current task is to pick at bones; if there are no bones, I’ll look for them! If there really are a few propositions that withstand scrutiny, then we can turn around and study what such propositions are like and what features they have.
I also truly hope that people will readily bring out a pile of counterexamples, so that the double non principle is limited to a very small scope. But for now, it still hasn’t been limited.
[Anonymous] Guhu
2006-06-01 02:26:29
The key question is: with what do you want to scrutinize them? If you use Hume’s fork, if you use radical skepticism, then what under heaven could possibly withstand scrutiny? Even the law of excluded middle can be scrutinized! If you scrutinize everything, you will in turn greatly diminish the meaning of scrutiny. Who can refute Hume’s fork? Too difficult! If you do not place some self-limitation on the tools you use to “scrutinize,” then that is far too overbearing; others will not even have the chance to raise counterexamples.
“How contentment is sufficient and necessary for enduring happiness,” “how an energy difference is sufficient and necessary for heat transfer”—how are such propositions to be scrutinized? (I know they can be scrutinized; if you asked me to scrutinize them, I could too. The question is, what sort of method are you using to scrutinize them? Is such scrutiny merely a slide into skepticism? What help, exactly, does questioning provide to making constructive suggestions?)
Radical skepticism can never be refuted. Picking at bones to the absolute limit will inevitably land one in skepticism; does Liu Laoshi’s stance of “if there are no bones, still look for them” already lean toward radical skepticism?
Skepticism is no fun.
wildflora
2006-06-01 14:01:23
It’s nothing more than insisting on reason and not on bullying. If people think a certain step has a problem, then stop; one can stop at any time and consider it carefully. One cannot decide in advance whether one should stop or not.
“Knowing contentment is sufficient and necessary for enduring happiness” makes quite a bit of sense in real life, but it is clearly not strictly sufficient and necessary. Everyone can check this for themselves.
The sufficiency of “an energy difference is sufficient and necessary for heat transfer” is inappropriate, for example with containers A and B: the gases in A and B have different temperatures, but there is a non-heat-conducting partition between them.
If this seems a bit unreasonable, then one can raise a stronger rebuttal: an energy difference in physical terms also does not necessarily lead to heat transfer. For instance, electrons orbiting a nucleus have different energies, there is an energy difference among them, but in a stable atom, the phenomenon of heat transfer generally does not occur.
You may say that this is a special case. But then the original situation may have many special cases. If no limitations are added, then speaking casually becomes problematic in the strict sense.
I’ll repeat once more: picking at bones does not mean that, in an everyday sense, I doubt ordinary propositions. I am only, in the strict sense, picking faults in propositions that are claimed to have no problems whatsoever. If people are not speaking absolute correctness in a strict sense, then naturally there is no need for us to make trouble for them.
Also, note that while proposing the double non principle, I have repeatedly emphasized “double non, but the relation is still very important.” This means I am not blindly skeptical and negative.
The discussion above is a small experiment. Since it is an experiment, of course one must go all the way.
[Anonymous] Guhu
2006-06-01 18:02:01
I very much support Liu Laoshi’s doubly non critique; my small disagreement is only that I hope Liu Laoshi will keep his position steady. Liu Laoshi’s understanding of the “meaning” of the doubly non critique gives one a sense of déjà vu; in that final passage, where he says it is “a method of criticism,” “a method conducive to innovation,” and so on, replacing the double non principle with the phrase “critical spirit” leaves the meaning almost entirely unchanged.
The problem is: is advocating the double non principle just advocating a critical spirit, merely another way of expressing advocacy of the critical spirit? That is not some new idea; many scientists say the same: critical spirit is critical, creative, and scientific spirit. Of course, when many people talk about critical spirit, they also mention that “acceptance” is equally important for science.
Critical spirit is very important, and I very much support advocating it; I also very much support advocating reflection on people’s misuse of “sufficient and necessary”; but if the two are mixed together and advocated, then I do not support it. In that case, why not just directly advocate critical spirit? Wouldn’t that be more straightforward?
The double non says neither sufficient nor necessary, so as long as one puts forward a proposition of sufficiency or necessity, it is a counterexample: is “consuming energy is necessary for maintaining mechanical operation” still not a counterexample?
I feel that Liu Laoshi’s saying “up to now no truly counterexample has yet been found” has a bit of the flavor of “there is no rival under heaven,” and resembles the skeptic’s lament that “I cannot find a single sentence that is truly strict.”
Since this is an experiment, since examples of double non come in infinitely many sets, and since quite a few double non examples have already been found, then offering a few more positive examples would not contribute much, so I try hard to provide the teacher with opposing opinions; I hope you will forgive me.
[Anonymous] ME
2006-06-01 19:49:43
Exactly. Posting this here is precisely in the hope that all kinds of heroes will throw bricks. Little Gu is excellent; everyone has a very good impression of you, and your assignments are also written very well. Lao Jiang of “Frog” U is even more appreciative of you.
Advocating a critical spirit is good; in a certain sense, I do not oppose advocating a conservative spirit either. This thing called science both emphasizes conservatism (I once wrote a piece titled “Science Also Has Conservatism,” see the book “Templet Buddha”) and emphasizes innovation.
“Double non-” is meant to make doubt concrete in one particular respect; speaking in general about a spirit of doubt, people would seem not to know where to begin. One could also concrete the spirit of doubt in many other ways. As for “why not just put it directly as the spirit of doubt—it would be more straightforward,” in my view, that would no longer attract people into discussion! Perhaps people have already heard “the spirit of doubt” so often that they’ve gone numb.
Doubt is not the goal. “So far no truly counterexample has been found” — I wouldn’t dare say that. This matter is rather complicated. I believe there must be counterexamples (if there were none, that would be strange indeed), and probably quite a lot of them; it’s just not easy, for the moment, to produce one that is clean and elegant. As for whether a certain counterexample is really a counterexample, I want to convince myself first. The above discussion does contain an element of quibbling; it’s only a first round of doubt, and if that doesn’t work, then I’ll turn around and accept it.
I will list all the counterexamples everyone has tried, for further discussion. Of course, supporting examples should also be treated even-handedly.
[anonymous] Gu Chu
2006-06-01 22:06:17
Thank you, teachers, for the encouragement :）
Let me strengthen the explanation of the counterexample I raised.
“Energy difference is necessary and sufficient for heat transfer” — this was due to an error in my own copying. What I originally proposed was “Temperature difference is sufficient and necessary for heat transfer” — this example is more appropriate. Because “temperature” and “heat” are both macroscopic statistical concepts, it is meaningless to speak of temperature or heat for a single particle. Therefore, when discussing heat transfer, it is reasonable and legitimate not to consider the quantum world. Ideal objects that do not transfer heat do not exist; between objects with an energy difference that are not infinitely far apart, there must be heat transfer. One can also add “objects in contact,” and then change the later “heat transfer” to “heat conduction.” This proposition is in fact also one formulation of the second law of thermodynamics. Of course it can be questioned — I’ll question it first myself: because the second law of thermodynamics is a statistical law, only a matter of “extremely high probability.” For all the air in a room suddenly gathering into one corner, or heat flowing from a low-temperature object to a high-temperature object, in theory neither is impossible.
“Consuming energy is necessary for maintaining mechanical operation” — in other words, perpetual motion machines are impossible. For a first-kind perpetual motion machine, this is just another way of stating the law of conservation of energy. This belief is quite reliable, and under ordinary circumstances it should not be questioned. If one insists on questioning it, that is of course possible; I’ll “self-execute” that one too. First, in quantum mechanics the law of conservation of energy is a corollary of “time-translation invariance,” that is, doing an experiment at one time and doing it at another time, if all other conditions are the same, will yield the same result. Likewise, spatial translation invariance implies conservation of momentum, and rotational invariance implies conservation of angular momentum. However, those translation invariances are not beyond question; for example, the result of spatial mirror symmetry, “parity conservation,” has already been overturned. Many people are precisely unwilling to question what seems to be the immovable symmetry of a spatial mirror, and therefore could not imagine that parity might actually not be conserved. The discovery of parity nonconservation was precisely a creation born of bold questioning. In addition, in Mayer’s era, conservation of energy had in substance already been replaced by conservation of mass-energy.
“A changing electric field is necessary and sufficient for generating a magnetic field” is also fairly reliable, but if magnetic monopoles exist, then it should not be explainable by a changing electric field.
Add another one: “Imbalanced force is a necessary and sufficient condition for accelerated motion.” If one restricts oneself to non-quantum mechanics, this proposition seems quite reliable; still, let me self-execute it as well. In fact, here there is a verbal sleight of hand that makes it hard to refute, because in classical mechanics the concept of “force” is rather mysterious and quite vague. In fact, it is precisely by looking at an object’s accelerated motion that people speak of force; the so-called measure of force is defined by “one newton equals the force that produces an acceleration of 1 meter per second squared on a mass of 1 kilogram.” The concept of force is very clear in formulas, but what on earth is force itself? It cannot be explained clearly. The ambiguity and mystery of the concept of “force” itself are already worth questioning and questioning again.
Let me offer another positive example: “The law of excluded middle (the law of noncontradiction and the law of identity) is neither sufficient nor necessary for a logical system.” In fact, one should first bring up a counterexample: “A proposition is not false; this is a necessary and sufficient condition for that proposition being true.” This can be put forward as a counterexample, but I have also already self-executed it: why can’t “┐┐p←→p” be questioned? Someone did question it, and further proposed so-called intuitionistic logic, many-valued logic, and other different logical systems, which greatly promoted the development of logic and also had extremely significant implications for reflection on the philosophy of logic.
Even “A←→A” can be questioned; indeed there are logicians who question it, but that is really too much quibbling, and not very interesting anymore. For example, how can one say “1=1”? One is on the left side of the equals sign, the other on the right side; how can the left equal the right? Left ≠ right, so 1 ≠ 1……
[anonymous] Gu Chu
2006-06-02 19:51:56
Even though everything I previously offered has been self-executed, I still regard them as counterexamples. Being questionable does not mean being wrong; there is no “absolute correctness,” and there is also very little “absolute wrongness.”
“‘Questionable’ is neither sufficient nor necessary for ‘wrong’.”
— Relativity, thermodynamics, and electromagnetism can all be questioned, but they are not, at least for now, wrong. And some assertions simply don’t give you the chance to question them, for example: “As long as you absolutely believe what I say, then what I say will come true; only if you absolutely believe what I say will what I say come true. — Faith is the necessary and sufficient condition for efficacy.” When confronted with this kind of assertion that toys with verbal技巧, the moment you doubt it, you are unbelieving, and thus lose the qualification to question it… but what he says is still wrong!
Let me offer another rather meaningful positive example: “Darwinism is neither sufficient nor necessary for scientific evolutionary theory.”
— Evolutionary science is not entirely obedient to Darwinism, and doctrines that are obedient to Darwinism are not necessarily science. Teacher Liu will surely understand what I mean here. In the present day, Darwin has almost become a synonym for evolution theory, and people indeed often confuse Darwinism with the necessary and sufficient condition for biological evolution theory. The significance of the positive example offered depends on whether people really do commonly treat two things as a necessary and sufficient condition, while the claim that there is a necessary and sufficient relation between those two things is indeed false — if a view widely held is not only questionable but actually wrong, then that is a splendid positive example.
wildflora
2006-06-03 00:09:52
Agreed. For some people, then, questioning Darwin is like digging up their family’s ancestral grave. Darwin was very clever, and made some brilliant conjectures, but after all he belonged to the nineteenth century. And unfortunately, in the nineteenth century, what people accepted as evolutionary theory was basically not the kind of evolutionary theory Darwin was talking about.
Translated from the Chinese original with AI assistance. The original text is authoritative.
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