On Politics, Media, and Information (Column 9)

With God's help

David Frenkel, one of the sharpest and finest writers I know, once wrote a column about some remarks by Ehud Barak (see here). Please read that column (it is also recommended to read his other columns published on the Walla site). All that remains for me after that is merely to explain the logical background to his remarks.

The Credibility of Politicians

Read it? Excellent. So why did I think of that column precisely now? Frenkel dealt there with an empty statement (one of many) by Ehud Barak (one politician among many), then the defense minister. And behold, there is nothing new on the western front (Ashkenazic version for the Torah-observant public: this Torah shall not be changed ("this Torah shall not be changed")): it turns out that our new defense minister these very days, Avigdor Lieberman, God bless him, is for some reason exposed to the same criticism. Lieberman, who was known as an uncompromising security hawk, immediately upon entering office let loose several remarks that point to an ideological reversal, almost to the point of becoming a pure political dove. Anyone who was surprised, please stand up (except for a few Meretz and Labor people who demonstrated against the appointment of the fascist as defense minister. They are surely surprised). I am not even speaking of the great trust he is showing toward our prime minister (Netanyahu), after having previously explained that he was a complete nonentity, a liar, and corrupt, someone one could not trust even with running a kiosk.

This, of course, was clear long before Lieberman entered office. But unfortunately I cannot even boast of my rare political wisdom, since almost everyone around me estimated that this is what would happen long before the appointment became known. On further thought, I also do not attribute much informational importance to Lieberman's latest remarks (the dovish ones). Just as he was not a hawk, he is not now turning into a dove. If it suits him, his statements will change back within a week or a month. In any case, there is no connection whatsoever between the statements and what he will actually do. Therefore the whole matter is not really important.

Some will say that this is even legitimate, since this is politics, and who at all attributes importance—let alone credibility—to politicians' statements?! At best, perhaps one can estimate the general direction in which a politician leans, and even that under a very limited warranty. But everyone understands that there is no real connection between what he says and what he will do or say in the future. As Frenkel writes, a politician's statements are in fact almost devoid of any informational payload. This is mere lip movement. But have no fear, I do not intend here to grind once again through the battered question of the credibility of political declarations. No sober person has taken them to heart for a long time.[1] That is the moral question, and I will not deal with it. I want to discuss here a logical aspect of the topic, namely the futility of this talk, and this is where our acquaintance David Frenkel enters the picture. The question is why there is public interest in politicians' statements. Why interview them at all? Why do we all listen, and what should we do instead? So here is my Guide for the Perplexed for our confused generation.

On Speech and Information

There is a well-known joke about Richard Nixon: what is the clear indication that Nixon is lying? Simply that he is moving his lips. Take what he says and infer the opposite. If he says there were no wiretaps in Watergate—then there were. If he says war will not break out—then it probably will. If he says housing prices will fall—then they will probably rise. If he says he opposes a peace process with the Palestinians—then he will probably create one. If he says that Netanyahu is a nonentity, then he is about to join his government. Oops, without noticing I moved from Nixon to the Mediterranean basin. But here there is already a serious mistake. That transition is utterly wrong. To explain this, I need to enter briefly into a logical-philosophical topic.

The Liar Paradox

The source of this famous paradox is in the New Testament, where a Cretan solemnly declares, "All Cretans are liars." But if they are all liars, then he himself, as a Cretan, is also a liar. If so, the Cretans are actually truth-tellers. But then he too is a truth-teller and the sentence is true, and then they are all liars, and so on.

At first glance, an inescapable logical loop. But no—that is not so. There is a way out, because the negation of the sentence "All Cretans are liars" is that not all of them are liars, that is, there is at least one who tells the truth. Let us assume it is his neighbor upstairs. Then the loop stops: indeed, not all Cretans are liars, because his upstairs neighbor is not a liar. But he himself is indeed a liar, and therefore the sentence he uttered (that all Cretans are liars) is false, and the matter is settled.

All right, so when is it a paradox? Perhaps when that same Cretan says, "I am a liar." Here, seemingly, there is no escape. Not true, at least if the meaning of that sentence is "I always lie." If we now examine the loop again: X says, "I always lie," but if so then this sentence too is false, and therefore it is not true that he always lies. But here one can say that this is untrue because in some sentence he uttered yesterday he did not lie, even though this sentence is indeed false. Here again the loop stops.

The conclusion is that a genuine paradox is created only when one says something like this: "This sentence is false." Or more precisely: (A): Sentence (A) is false. Here the claim no longer contains any generalization (an all-inclusive logical quantifier), and therefore there is no escape from the logical loop created. What is the meaning of this loop? That no truth value can be assigned to this sentence. If it is true, then it is false, and if it is false, then it is true. Thus, when Reuven says to me, "This sentence is false," there is no truth value that can be attached to this sentence. In other words, one may say that this sentence contains no information.

Does a false sentence contain information? Certainly. The claims of a pathological liar contain exactly the same information as the claims of a serial truth-teller. The only difference is that in the two cases the decoding software by which we get from the claim (the input) to the information (the output) is different. With a serial truth-teller, the information is the content of the claim, and with a pathological liar the information is the negation of the content of the claim. Thus, if you want to know which of two roads at an intersection you should take, you can ask a serial liar and do the opposite of what he tells you, or ask a serial truth-teller and do as he instructs you. In both cases you will receive full and reliable information.

The great problem is what to do when the person standing before you is someone about whom you do not know whether he is a liar or a truth-teller. In such a situation, apparently, you have no way to extract the information from him. He is much worse than a liar, for his statements are not informative at all. But it turns out that information can be extracted even from a person about whom we do not know whether he is a liar or not, provided that you ask the question correctly. Surely everyone knows the riddle about an intersection with two roads, at each of which stands a person, and we know that one is a liar and the other a truth-teller, though we do not know who is who. We want to know which road we should take to reach our desired destination (heaven). Alternatively, there is one person standing there and we do not know whether he is a liar or a truth-teller. In such a case one formulates a complex question that both a liar and a truth-teller will answer in the same way. For example: "If I were to ask you which is the correct road, what would you answer me?" If he is a liar, he would lie to me about the road but then lie again about what he would answer me to that question, so overall he would tell the truth. But a truth-teller would also answer this question truthfully. Thus, when you arrive at the intersection and ask this question of any person who is standing there, whether you know or do not know what sort of person he is, you will always receive a truthful answer. You should do exactly what he tells you. Thus the words of the liar and the truth-teller contain the same information.

One may wonder why we do not extract the truth in this way from every thief. Let us simply ask him in interrogation what he would answer if we asked him whether he is a thief or not. After all, we would always receive the true answer. So why do we need police investigators at all? Logicians should suffice. To understand this, one must remember that the thief is not always so strong in logic. Think of a situation in which a person stands at the intersection who is a bit weak in logic, and he does not know what he ought to answer on the assumption that he is a liar or on the assumption that he is a truth-teller. After all, there is no physiological obstacle to his moving his lips and lying when we ask him what he would answer if we were to ask him. True, both the liar and the truth-teller are supposed to answer us truthfully on this question, but he never studied logic and chooses to lie. The meaning of such an answer is that this person is neither a pathological liar nor a serial truth-teller, but rather a zig-zagger. Sometimes he tells the truth and sometimes not. For example, he would lie if I asked him which road is the correct one, but now he chooses to tell the truth when asked what he would do if I asked him that. Or vice versa, of course. A zig-zagger is an uninformative person. You can get any answer from him to any question.

Incidentally, there is an article by Yael Cohen in the journal Iyyun, in which she proposes a logical algorithm that extracts the truth from every person, including a zig-zagger. It is a complex algorithm and I will not enter into it here, but at the practical level it suffers from the same problem as the previous algorithm. The disconnect between physiology and logic. Her algorithm too is based on logical analysis that demands consistency from every person (that he not fall into contradictions). You can be a liar or a truth-teller or a zig-zagger, but you must be consistent. But what prevents our respondent from not being consistent? Simply answering in a way based on a contradiction, contrary to Yael Cohen's logical calculus. If so, we can relax. There is no logical polygraph that will replace police investigators.

On Statements and Information

To summarize, we have seen that both a liar and a truth-teller are completely informative. Reliable and complete information can be extracted from their words, and therefore there is a point in asking them questions and hearing what they answer. As we saw, even the zig-zagger can be informative in that sense. But the words of an inconsistent person are, by definition, devoid of informational content. There is no point in asking such a person questions, and of course not in interviewing him. We simply will not learn anything from what he says, since there is no connection whatsoever between his words and the truth. So what is the point of talking to him or listening to him?

Here we arrive at the mistake I made above in moving from Nixon (the metaphorical one) to our politicians. Nixon did us a favor and lied all the time. Such a person is certainly worth listening to, since his statements are completely informative. We merely need to hear what he says and understand the opposite from it. But our politicians are not liars, and not even zig-zaggers, but simply inconsistent. Their words are not lies but something random and arbitrary, and therefore they lack any correlation with the factual situation.

When someone like Yitzhak Shamir tells you that, yes, he did promise—but he did not promise to fulfill it—what sense is there in listening to his promises? If he were a liar, then I could persuade him to promise not to fulfill it, and then everything would be excellent. In such a situation I would always know what to expect, and I would know how to conduct myself in dealing with him (for example, persuade him to promise not to give me a budget, and then I can rest easy). But as long as he does not promise to be either a liar or a truth-teller, but merely says X and does Y with no connection between the two, his promises have no meaning, and indeed his speech in general.

Anti-Paradox

Seasoned politicians employ another non-informative technique, which we shall now examine. As is well known, the Delphic oracle used to issue vague answers, so that any check whether they had been fulfilled or not would allow us to fit the prophecy to the facts. If someone emphatically predicts to you that Israel's economic situation will improve in the foreseeable future (see the so-called "sciences of forecasting"—modern useless sorcery drawing a professor's salary), he is an oracle, not a prophet. There is no way to test his words, since one can always say that the situation improved in some respect, or alternatively that if we wait a little longer that same "foreseeable future" will arrive and then the situation will improve. His statement is not falsifiable, and therefore it is not informative. There is a rule in Jewish law that testimony must be capable of being refuted, and people have already noted that there is a parallel here to Popper's scientific requirement that scientific theories be falsifiable.[2] Oracles issue vague prophecies that can be interpreted in several ways, and therefore they are not falsifiable. This is the tactic adopted by every self-respecting baba (folk mystic), and lo and behold, plenty of fools explain to you that his prophecies are constantly being fulfilled in wondrous fashion. Politicians too issue noncommittal and general statements, and as such there is no way to catch them in a lie (and even if there is—as we know—their words were taken out of context).

The logical model for this technique is what I called in my article (Paradox and Anti-Paradox in Jewish Law), an anti-paradox. Consider the following sentence: (B): Sentence (B) is true. What is the status of this sentence? If we assume that it is true, then it is indeed true; but even if we assume that it is false, it indeed comes out false. That is, this sentence admits two opposite truth values: both true and false, and both are consistent.

To clarify the uniqueness of such a sentence, let me say that an ordinary claim admits only one of the truth values. For example, if I say "The current president of the United States is Barack Obama," I examine the content of the claim against the state of affairs in the world that it describes. If there is a correspondence, then the sentence is true; and if not, it is false. By contrast, a paradox admits no truth value (for if it is true then it is false, and if it is false then it is true). That is, it is neither true nor false. An anti-paradox, unlike those two, admits both truth values together—true and false.

What is the meaning of such a sentence? Is it informative? Certainly not. One cannot learn any information from it whatsoever, since it is a sentence that can be seen as true or as false. Moreover, this sentence asserts nothing beyond a word game about itself, and therefore by its very meaning (if it has one) it adds no information for us. This is Delphic-oracle-style ambiguity, which, as noted, is often found in the toolbox of our cousins, the politicians.

Implications and Applications

We thus learn that logic provides a very useful array of tools for politicians, for commentators, and also for us simple listeners. Politicians can use them to convey a minimum of information by means of a maximum of words and interviews. Journalists and commentators can offer cautious and utterly valueless interpretations of their words,[3] and we may perhaps sometimes understand what on earth is going on here. How does this work? Naive people think that if one hears something in the news one should simply reverse it (roughly in the spirit of lay opinion is the opposite of Torah wisdom — lay opinion is the opposite of Torah wisdom). Mistake! There is a hidden assumption here that we are dealing with pathological liars (and that I also know the quality of the journalistic report about the politician's statements).

The prescription is as follows: a journalist who wants to make use of what we have learned here can plan his moves when he comes to interview a political figure. Suppose, for example, that he wants to find out whether his interviewee supports the gas framework. If he is dealing with a liar, he should ask him whether he supports the gas framework, and write the opposite of the answer he receives. If he is dealing with a truth-teller (an endangered species), he should write down the answer he receives verbatim. If he is dealing with a zig-zagger, that too poses no problem: he should ask him, "If I were asking you about the gas framework, what would you answer me?" But if he is dealing with someone inconsistent, there is no point in conducting the interview.

Various journalists and commentators offer us a substitute. As expert commentators, they will explain to us the hidden intentions of the interviewee, and thus his words will become informative as if by magic. But it seems to me that even if we ignore their own character (see the previous note below), they have no tools with which to do so. Interpretation must rely on prior experience and knowledge. If we have examined the politician before and seen that he always lies, we know how to interpret his answer to the current question. The same is true if we have found that he tells the truth, or even if he zig-zags (provided that we asked the right question: what would you say if I were to ask you…). But if we are dealing with someone inconsistent, and that is probably the situation in most cases, then there is no way to interpret his words and understand their meaning. This is not a matter for experts or people of experience. It is an impossible task. Thus, for example, when Lieberman says that he is in favor of some peace process now taking shape, or alternatively when he announces that he will eliminate Haniyeh within two days and all of Gaza in the half hour after that, this statement adds no information for us. So what is the point of quoting it, analyzing it, demonstrating against him or for him, voting for him or against him, or at all listening to all this unnecessary nonsense? That is the essence of David Frenkel's point.

Instead of interviewing political figures, it seems to me preferable to interview poets, thinkers, or just ordinary folk. But so long as we are dealing with facts, one should make sure that the interviewees are either truth-tellers or consistent liars, or in the worst case zig-zaggers. But one must be very careful of inconsistent people. Another possibility is not to deal with facts at all, but with various literary and artistic creations. I always liked it when, at the top of the news, they inform us with astonishment that the president of the state declared in his speech that those who fell, by their death, commanded us to live, or alternatively that the State of Israel is wonderful (the dream of generations realized), or that our youth are promising and have much more in them than people think they do (a Shimon Peres speech; that was on the news yesterday, I am not making this up), or that the State of Israel will respond severely at a time and place of its choosing, and so on.

People may wonder why 'news,' which are supposed to bring facts to our attention, tell us that those who fell commanded us through their death to live, or that in Peres's opinion our youth have more in them than people think they do. But on second thought, it is actually very clear. We saw that a considerable portion of statements of a factual character in the news are not informative at all. It is therefore no wonder that our wise news editors chose to fill the broadcasts with claims that do not even pretend to be factual. An incomparably wise decision—it's just a shame that they still leave a few factual claims in place. I expect that as we progress further, the newsreaders will recite poems by Dalia Ravikovitch, stories by Dostoevsky, and in the facts corner they will read entries from the Encyclopaedia Britannica for Youth.

An Optimistic Ending

But do not say there is nothing to hope for. There is light at the end of the tunnel. True, producing politicians who speak the truth is probably a vain hope, but what we have learned here shows that to the same extent we can aspire to politicians who are liars or zig-zaggers (but at least consistent ones). As we have seen, this will give us exactly the same amount of information (provided that the interviewers ask the questions in the correct form: what would you answer if I were to ask…), and perhaps that has some chance, doesn't it?…

[1] Although the number of sober people in our society is apparently not large enough, to my regret, those do not need my column, and my column is unlikely to help the others.

[2] See the article by Yemima and Hanina Ben Menachem in Akdamot (see here) and more.

[3] We have not dealt here with the credibility of journalists. One should understand that the logic of journalistic reporting on a politician's statement is astonishingly complicated. For that one already needs a master's degree in the science of the informational vacuum. Such a situation is somewhat parallel to an intersection with two roads, at each of which stands a person, and you have no idea whether there are two truth-tellers, two liars, or one truth-teller and one liar, and who is who. Now you hear from one of them what the other said. He claims that the road on the right is the correct one. Exercise for the advanced reader: does this statement contain information?