Definitions

Technical Discussion and Philosophical Progress

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In The Structure of Scientific Revolutions (p. 19-21), Thomas Kuhn remarks on the tendency of sciences to acquire a technical vocabulary and manner of discussion:

We shall be examining the nature of this highly directed or paradigm-based research in the next section, but must first note briefly how the emergence of a paradigm affects the structure of the group that practices the field. When, in the development of a natural science, an individual or group first produces a synthesis able to attract most of the next generation’s practitioners, the older schools gradually disappear. In part their disappearance is caused by their members’ conversion to the new paradigm. But there are always some men who cling to one or another of the older views, and they are simply read out of the profession, which thereafter ignores their work. The new paradigm implies a new and more rigid definition of the field. Those unwilling or unable to accommodate their work to it must proceed in isolation or attach themselves to some other group. Historically, they have often simply stayed in the departments of philosophy from which so many of the special sciences have been spawned. As these indications hint, it is sometimes just its reception of a paradigm that transforms a group previously interested merely in the study of nature into a profession or, at least, a discipline. In the sciences (though not in fields like medicine, technology, and law, of which the principal raison d’être is an external social need), the formation of specialized journals, the foundation of specialists’ societies, and the claim for a special place in the curriculum have usually been associated with a group’s first reception of a single paradigm. At least this was the case between the time, a century and a half ago, when the institutional pattern of scientific specialization first developed and the very recent time when the paraphernalia of specialization acquired a prestige of their own.

The more rigid definition of the scientific group has other consequences. When the individual scientist can take a paradigm for granted, he need no longer, in his major works, attempt to build his field anew, starting from first principles and justifying the use of each concept introduced. That can be left to the writer of textbooks. Given a textbook, however, the creative scientist can begin his research where it leaves off and thus concentrate exclusively upon the subtlest and most esoteric aspects of the natural phenomena that concern his group. And as he does this, his research communiqués will begin to change in ways whose evolution has been too little studied but whose modern end products are obvious to all and oppressive to many. No longer will his researches usually be embodied in books addressed, like Franklin’s Experiments . . . on Electricity or Darwin’s Origin of Species, to anyone who might be interested in the subject matter of the field. Instead they will usually appear as brief articles addressed only to professional colleagues, the men whose knowledge of a shared paradigm can be assumed and who prove to be the only ones able to read the papers addressed to them.

Today in the sciences, books are usually either texts or retrospective reflections upon one aspect or another of the scientific life. The scientist who writes one is more likely to find his professional reputation impaired than enhanced. Only in the earlier, pre-paradigm, stages of the development of the various sciences did the book ordinarily possess the same relation to professional achievement that it still retains in other creative fields. And only in those fields that still retain the book, with or without the article, as a vehicle for research communication are the lines of professionalization still so loosely drawn that the layman may hope to follow progress by reading the practitioners’ original reports. Both in mathematics and astronomy, research reports had ceased already in antiquity to be intelligible to a generally educated audience. In dynamics, research became similarly esoteric in the later Middle Ages, and it recaptured general intelligibility only briefly during the early seventeenth century when a new paradigm replaced the one that had guided medieval research. Electrical research began to require translation for the layman before the end of the eighteenth century, and most other fields of physical science ceased to be generally accessible in the nineteenth. During the same two centuries similar transitions can be isolated in the various parts of the biological sciences. In parts of the social sciences they may well be occurring today. Although it has become customary, and is surely proper, to deplore the widening gulf that separates the professional scientist from his colleagues in other fields, too little attention is paid to the essential relationship between that gulf and the mechanisms intrinsic to scientific advance.

As Kuhn says, this tendency has very well known results. Consider the papers constantly being published at arxiv.org, for example. If you are not familiar with the science in question, you will likely not be able to understand even the title, let alone the summary or the content. Many or most of the words will be meaningless to you, and even if they are not, their combinations will be.

It is also not difficult to see why this happens, and why it must happen. Everything we understand, we understand through form, which is a network of relationships. Thus if particular investigators wish to go into something in greater detail, these relationships will become more and more remote from the ordinary knowledge accessible to everyone. “Just say it in simple words” will become literally impossible, in the sense that explaining the “simple” statement will involve explaining a huge number of relationships that by default a person would have no knowledge of. That is the purpose, as Kuhn notes, of textbooks, namely to form connections between everyday knowledge and the more complex relationships studied in particular fields.

In Chapter XIII, Kuhn relates this sort of development with the word “science” and progress:

The preceding pages have carried my schematic description of scientific development as far as it can go in this essay. Nevertheless, they cannot quite provide a conclusion. If this description has at all caught the essential structure of a science’s continuing evolution, it will simultaneously have posed a special problem: Why should the enterprise sketched above move steadily ahead in ways that, say, art, political theory, or philosophy does not? Why is progress a perquisite reserved almost exclusively for the activities we call science? The most usual answers to that question have been denied in the body of this essay. We must conclude it by asking whether substitutes can be found.

Notice immediately that part of the question is entirely semantic. To a very great extent the term ‘science’ is reserved for fields that do progress in obvious ways. Nowhere does this show more clearly than in the recurrent debates about whether one or another of the contemporary social sciences is really a science. These debates have parallels in the pre-paradigm periods of fields that are today unhesitatingly labeled science. Their ostensible issue throughout is a definition of that vexing term. Men argue that psychology, for example, is a science because it possesses such and such characteristics. Others counter that those characteristics are either unnecessary or not sufficient to make a field a science. Often great energy is invested, great passion aroused, and the outsider is at a loss to know why. Can very much depend upon a definition of ‘science’? Can a definition tell a man whether he is a scientist or not? If so, why do not natural scientists or artists worry about the definition of the term? Inevitably one suspects that the issue is more fundamental. Probably questions like the following are really being asked: Why does my field fail to move ahead in the way that, say, physics does? What changes in technique or method or ideology would enable it to do so? These are not, however, questions that could respond to an agreement on definition. Furthermore, if precedent from the natural sciences serves, they will cease to be a source of concern not when a definition is found, but when the groups that now doubt their own status achieve consensus about their past and present accomplishments. It may, for example, be significant that economists argue less about whether their field is a science than do practitioners of some other fields of social science. Is that because economists know what science is? Or is it rather economics about which they agree?

The last point is telling. There is significantly more consensus among economists than among other sorts of social science, and consequently less worry about whether their field is scientific or not. The difference, then, is a difference of how much agreement is found. There is not necessarily any difference with respect to the kind of increasingly detailed thought that results in increasingly technical discussion. Kuhn remarks:

The theologian who articulates dogma or the philosopher who refines the Kantian imperatives contributes to progress, if only to that of the group that shares his premises. No creative school recognizes a category of work that is, on the one hand, a creative success, but is not, on the other, an addition to the collective achievement of the group. If we doubt, as many do, that nonscientific fields make progress, that cannot be because individual schools make none. Rather, it must be because there are always competing schools, each of which constantly questions the very foundations of the others. The man who argues that philosophy, for example, has made no progress emphasizes that there are still Aristotelians, not that Aristotelianism has failed to progress.

In this sense, if a particular school believes they possess the general truth about some matter (here theology or philosophy), they will quite naturally begin to discuss it in greater detail and in ways which are mainly intelligible to students of that school, just as happens in other technical fields. The field is only failing to progress in the sense that there are other large communities making contrasting claims, while we begin to use the term “science” and to speak of progress when one school completely dominates the field, and to a first approximation even people who know nothing about it assume that the particular school has things basically right.

What does this imply about progress in philosophy?

1. There is progress in the knowledge of topics that were once considered “philosophy,” but when we get to this point, we usually begin to use the name of a particular science, and with good reason, since technical specialization arises in the manner discussed above. Tyler Cowen discusses this sort of thing here.

2. Areas in which there doesn’t seem to be such progress, are probably most often areas where human knowledge remains at an early stage of development; it is precisely at such early stages that discussion does not have a technical character and when it can generally be understood by ordinary people without a specialized education. I pointed out that Aristotle was mistaken to assume that the sciences in general were fully developed. We would be equally mistaken to make such an assumption at the present times. As Kuhn notes, astronomy and mathematics achieved a “scientific” stage centuries before geology and biology did the same, and these long before economics and the like. The conclusion that one should draw is that metaphysics is hard, not that it is impossible or meaningless.

3. Even now, particular philosophical schools or individuals can make progress even without such consensus. This is evidently true if their overall position is correct or more correct than that of others, but it remains true even if their overall position is more wrong than that of other schools. Naturally, in the latter situation, they will not advance beyond the better position of other schools, but they will advance.

4. One who wishes to progress philosophically cannot avoid the tendency to technical specialization, even as an individual. This can be rather problematic for bloggers and people engaging in similar projects. John Nerst describes this problem:

The more I think about this issue the more unsolvable it seems to become. Loyal readers of a publication won’t be satisfied by having the same points reiterated again and again. News media get around this by focusing on, well, news. News are events, you can describe them and react to them for a while until they’re no longer news. Publications that aim to be more analytical and focus on discussing ideas, frameworks, slow processes and large-scale narratives instead of events have a more difficult task because their subject matter doesn’t change quickly enough for it to be possible to churn out new material every day without repeating yourself[2].

Unless you start building upwards. Instead of laying out stone after stone on the ground you put one on top of another, and then one on top of two others laying next to each other, and then one on top of all that, making a single three-level structure. In practice this means writing new material that builds on what came before, taking ideas further and further towards greater complexity, nuance and sophistication. This is what academia does when working correctly.

Mass media (including the more analytical outlets) do it very little and it’s obvious why: it’s too demanding[3]. If an article references six other things you need to have read to fully understand it you’re going to have a lot of difficulty attracting new readers.

Some of his conclusions:

I think that’s the real reason I don’t try to pitch more writing to various online publications. In my summary of 2018 I said it was because I thought my writing was to “too idiosyncratic, abstract and personal to fit in anywhere but my own blog”. Now I think the main reason is that I don’t so much want to take part in public debate or make myself a career. I want to explore ideas that lie at the edge of my own thinking. To do that I must assume that a reader knows broadly the same things I know and I’m just not that interested in writing about things where I can’t do that[9]. I want to follow my thoughts to for me new and unknown places — and import whatever packages I need to do it. This style isn’t compatible with the expectation that a piece will be able to stand on its own and deliver a single recognizable (and defensible) point[10].

The downside is of course obscurity. To achieve both relevance in the wider world and to build on other ideas enough to reach for the sky you need extraordinary success — so extraordinary that you’re essentially pulling the rest of the world along with you.

Obscurity is certainly one result. Another (relevant at least from the VP’s point of view) is disrespect. Scientists are generally respected despite the general incomprehensibility of their writing, on account of the absence of opposing schools. This lack leads people to assume that their arguments must be mostly right, even though they cannot understand them themselves. This can actually lead to an “Emperor has No Clothes” situation, where a scientist publishes something basically crazy, but others, even in his field, are reluctant to say so because they might appear to be the ones who are ignorant. As an example, consider Joy Christian’s “Disproof of Bell’s Theorem.” After reading this text, Scott Aaronson comments:

In response to my post criticizing his “disproof” of Bell’s Theorem, Joy Christian taunted me that “all I knew was words.”  By this, he meant that my criticisms were entirely based on circumstantial evidence, for example that (1) Joy clearly didn’t understand what the word “theorem” even meant, (2) every other sentence he uttered contained howling misconceptions, (3) his papers were written in an obscure, “crackpot” way, and (4) several people had written very clear papers pointing out mathematical errors in his work, to which Joy had responded only with bluster.  But I hadn’t actually studied Joy’s “work” at a technical level.  Well, yesterday I finally did, and I confess that I was astonished by what I found.  Before, I’d actually given Joy some tiny benefit of the doubt—possibly misled by the length and semi-respectful tone of the papers refuting his claims.  I had assumed that Joy’s errors, though ultimately trivial (how could they not be, when he’s claiming to contradict such a well-understood fact provable with a few lines of arithmetic?), would nevertheless be artfully concealed, and would require some expertise in geometric algebra to spot.  I’d also assumed that of course Joy would have some well-defined hidden-variable model that reproduced the quantum-mechanical predictions for the Bell/CHSH experiment (how could he not?), and that the “only” problem would be that, due to cleverly-hidden mistakes, his model would be subtly nonlocal.

What I actually found was a thousand times worse: closer to the stuff freshmen scrawl on an exam when they have no clue what they’re talking about but are hoping for a few pity points.  It’s so bad that I don’t understand how even Joy’s fellow crackpots haven’t laughed this off the stage.  Look, Joy has a hidden variable λ, which is either 1 or -1 uniformly at random.  He also has a measurement choice a of Alice, and a measurement choice b of Bob.  He then defines Alice and Bob’s measurement outcomes A and B via the following functions:

A(a,λ) = something complicated = (as Joy correctly observes) λ

B(b,λ) = something complicated = (as Joy correctly observes) -λ

I shit you not.  A(a,λ) = λ, and B(b,λ) = -λ.  Neither A nor B has any dependence on the choices of measurement a and b, and the complicated definitions that he gives for them turn out to be completely superfluous.  No matter what measurements are made, A and B are always perfectly anticorrelated with each other.

You might wonder: what could lead anyone—no matter how deluded—even to think such a thing could violate the Bell/CHSH inequalities?

“Give opposite answers in all cases” is in fact entirely irrelevant to Bell’s inequality. Thus the rest of Joy’s paper has no bearing whatsoever on the issue: it is essentially meaningless nonsense. Aaronson says he was possibly “misled by the length and semi-respectful tone of the papers refuting his claims.” But it is not difficult to see why people would be cautious in this way: the fear that they would turn out to be the ones missing something important.

The individual blogger in philosophy, however, is in a different position. If they wish to develop their thought it must become more technical, and there is no similar community backing that would cause others to assume that the writing basically makes sense. Thus, one’s writing is not only likely to become more and more obscure, but others will become more and more likely to assume that it is more or less meaningless word salad. This will happen even more to the degree that there is cultural opposition to one’s vocabulary, concepts, and topics.

Perfectly Random

entirelyuseless Logic, Mathematics, Metaphysics, Probability, Science, Uncategorized , , , , , , , , ,

Suppose you have a string of random binary digits such as the following:

00111100010101001100011011001100110110010010100111

This string is 50 digits long, and was the result of a single attempt using the linked generator.

However, something seems distinctly non-random about it: there are exactly 25 zeros and exactly 25 ones. Naturally, this will not always happen, but most of the time the proportion of zeros will be fairly close to half. And evidently this is necessary, since if the proportion was usually much different from half, then the selection could not have been random in the first place.

There are other things about this string that are definitely not random. It contains only zeros and ones, and no other digits, much less items like letters from the alphabet, or items like ‘%’ and ‘$’.

Why do we have these apparently non-random characteristics? Both sorts of characteristics, the approximate and typical proportion, and the more rigid characteristics, are necessary consequences of the way we obtained or defined this number.

It is easy to see that such characteristics are inevitable. Suppose someone wants to choose something random without any non-random characteristics. Let’s suppose they want to avoid the first sort of characteristic, which is perhaps the “easier” task. They can certainly make the proportion of zeros approximately 75% or anything else that they please. But this will still be a non-random characteristic.

They try again. Suppose they succeed in preventing the series of digits from converging to any specific probability. If they do, there is one and only one way to do this. Much as in our discussion of the mathematical laws of nature, the only way to accomplish this will be to go back and forth between longer and longer strings of zeros and ones. But this is an extremely non-random characteristic. So they may have succeeded in avoiding one particular type of non-randomness, but only at the cost of adding something else very non-random.

Again, consider the second kind of characteristic. Here things are even clearer: the only way to avoid the second kind of characteristic is not to attempt any task in the first place. The only way to win is not to play. Once we have said “your task is to do such and such,” we have already specified some non-random characteristics of the second kind; to avoid such characteristics is to avoid the task completely.

“Completely random,” in fact, is an incoherent idea. No such thing can exist anywhere, in the same way that “formless matter” cannot actually exist, but all matter is formed in one way or another.

The same thing applies to David Hume’s supposed problem of induction. I ended that post with the remark that for his argument to work, he must be “absolutely certain that the future will resemble the past in no way.” But this of course is impossible in the first place; the past and the future are both defined as periods of time, and so there is some resemblance in their very definition, in the same way that any material thing must have some form in its definition, and any “random” thing must have something non-random in its definition.

 

Truth and Expectation

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Suppose I see a man approaching from a long way off. “That man is pretty tall,” I say to a companion. The man approaches, and we meet him. Now I can see how tall he is. Suppose my companion asks, “Were you right that the man is pretty tall, or were you mistaken?”

“Pretty tall,” of course, is itself “pretty vague,” and there surely is not some specific height in inches that would be needed in order for me to say that I was right. What then determines my answer? Again, I might just respond, “It’s hard to say.” But in some situations I would say, “yes, I was definitely right,” or “no, I was definitely wrong.” What are those situations?

Psychologically, I am likely to determine the answer by how I feel about what I know about the man’s height now, compared to what I knew in advance. If I am surprised at how short he is, I am likely to say that I was wrong. And if I am not surprised at all by his height, or if I am surprised at how tall he is, then I am likely to say that I was right. So my original pretty vague statement ends up being made somewhat more precise by being placed in relationship with my expectations. Saying that he is pretty tall implies that I have certain expectations about his height, and if those expectations are verified, then I will say that I was right, and if those expectations are falsified, at least in a certain direction, then I will say that I was wrong.

This might suggest a theory like logical positivism. The meaning of a statement seems to be defined by the expectations that it implies. But it seems easy to find a decisive refutation of this idea. “There are stars outside my past and future light cones,” for example, is undeniably meaningful, and we know what it means, but it does not seem to imply any particular expectations about what is going to happen to me.

But perhaps we should simply somewhat relax the claim about the relationship between meaning and expectations, rather than entirely retracting it. Consider the original example. Obviously, when I say, “that man is pretty tall,” the statement is a statement about the man. It is not a statement about what is going to happen to me. So it is incorrect to say that the meaning of the statement is the same as my expectations. Nonetheless, the meaning in the example receives something, at the least some of its precision, from my expectations. Different people will be surprised by different heights in such a case, and it will be appropriate to say that they disagree somewhat about the meaning of “pretty tall.” But not because they had some logical definition in their minds which disagreed with the definition in someone’s else’s mind. Instead, the difference of meaning is based on the different expectations themselves.

But does a statement always receive some precision in its meaning from expectation, or are there cases where nothing at all is received from one’s expectations? Consider the general claim that “X is true.” This in fact implies some expectations: I do not expect “someone omniscient will tell me that X is false.” I do not expect that “someone who finds out the truth about X will tell me that X is false.” I do not expect that “I will discover the truth about X and it will turn out that it was false.” Note that these expectations are implied even in cases like the claim about the stars and my future light cone. Now the hopeful logical positivist might jump in at this point and say, “Great. So why can’t we go back to the idea that meaning is entirely defined by expectations?” But returning to that theory would be cheating, so to speak, because these expectations include the abstract idea of X being true, so this must be somehow meaningful apart from these particular expectations.

These expectations do, however, give the vaguest possible framework in which to make a claim at all. And people do, sometimes, make claims with little expectation of anything besides these things, and even with little or no additional understanding of what they are talking about. For example, in the cases that Robin Hanson describes as “babbling,” the person understands little of the implications of what he is saying except the idea that “someone who understood this topic would say something like this.” Thus it seems reasonable to say that expectations do always contribute something to making meaning more precise, even if they do not wholly constitute one’s meaning. And this consequence seems pretty natural if it is true that expectation is itself one of the most fundamental activities of a mind.

Nonetheless, the precision that can be contributed in this way will never be an infinite precision, because one’s expectations themselves cannot be defined with infinite precision. So whether or not I am surprised by the man’s height in the original example, may depend in borderline cases on what exactly happens during the time between my original assessment and the arrival of the man. “I will be surprised” or “I will not be surprised” are in themselves contingent facts which could depend on many factors, not only on the man’s height. Likewise, whether or not my state actually constitutes surprise will itself be something that has borderline cases.

Spinoza’s Geometrical Ethics

entirelyuseless Ethics, Logic, Mathematics, Metaphysics, Uncategorized , , , , , ,

Benedict Spinoza, admiring the certainty of geometry, writes his Ethics Demonstrated in Geometrical Order in a manner imitating that of Euclid’s Elements.

Omitting his definitions and axioms for the moment, we can look at his proofs. Thus we have the first:

1: A substance is prior in nature to its states. This is evident from D3 and D5.

The two definitions are of “substance” and “mode,” which latter he equates with “state of a substance.” However, neither definition explains “prior in nature,” nor is this found in any of the other definitions and axioms.

Thus his argument does not follow. But we can grant that the claim is fairly reasonable in any case, and would follow according to many reasonable definitions of “prior in nature,” and according to reasonable axioms.

He proceeds to his second proof:

2: Two substances having different attributes have nothing in common with one another. This is also evident from D3. For each ·substance· must be in itself and be conceived through itself, which is to say that the concept of the one doesn’t involve the concept of the other.

D3 and D4 (which must be used here although he does not cite it explicitly in the proof) say:

D3: By ‘substance’ I understand: what is in itself and is conceived through itself, i.e. that whose concept doesn’t have to be formed out of the concept of something else. D4: By ‘attribute’ I understand: what the intellect perceives of a substance as constituting its essence.

Thus when he speaks of “substances having different attributes,” he means ones which are intellectually perceived as being different in their essence.

Once again, however, “have nothing in common” is not found in his definitions. However, it occurs once in his axioms, namely in A5:

A5: If two things have nothing in common, they can’t be understood through one another—that is, the concept of one doesn’t involve the concept of the other.

The axiom is pretty reasonable, at least taken in a certain way. If there is no idea common to the ideas of two things, the idea of one won’t be included in the idea of the other. But Spinoza is attempting to draw the conclusion that “if two substances have different attributes, i.e. are different in essence, then they have nothing in common.” But this does not seem to follow from a reasonable understanding of D3 and D4, nor from the definitions together with the axioms. “Dog” and “cat” might be substances, and the idea of dog does not include that of cat, nor cat the idea of dog, but they have “animal” in common. So his conclusion is not evident from the definition, nor does it follow logically from his definitions and axioms, nor does it seem to be true.

And this is only the second supposed proof out of 36 in part 1 of his book.

I would suggest that there are at least two problems with his whole project. First, Spinoza knows where he wants to get, and it is not somewhere good. Among other things, he is aiming for proposition 14:

14: God is the only substance that can exist or be conceived.

This is closely related to proposition 2, since if it is true that two different things can have nothing in common, then it is impossible for more than one thing to exist, since otherwise existence would be something in common to various things.

Proposition 14 is absolutely false taken in any reasonable way. Consequently, since Spinoza is absolutely determined to arrive at a false proposition, he will necessarily employ falsehoods or logical mistakes along the way.

There is a second problem with his project. Geometry speaks about a very limited portion of reality. For this reason it is possible to come to most of its conclusions using a limited variety of definitions and axioms. But ethics and metaphysics, the latter of which is the actual topic of his first book, are much wider in scope. Consequently, if you want to say much that is relevant about them, it is impossible in principle to proceed from a small number of axioms and definitions. A small number of axioms and definitions will necessarily include only a small number of terms, and speaking about ethics and metaphysics requires a large number of terms. For example, suppose I wanted to prove everything on this blog using the method of definitions and axioms. Since I have probably used thousands of terms, hundreds or thousands of definitions and axioms would be required. There would simply be no other way to get the desired conclusions. In a similar way, we saw even in the first few proofs that Spinoza has a similar problem; he wants to speak about a very broad subject, but he wants to start with just a few definitions and axioms.

And if you do employ hundreds of axioms, of course, there is very little chance that anyone is going to grant all of them. They will at least argue that some of them might be mistaken, and thus your proofs will lose the complete certainty that you were looking for from the geometrical method.