Syllogism

Start at the Beginning

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This post will have two kinds of readers:

1) The few who have read the posts on this blog from the beginning, in chronological order, and who are now reading this one simply because it is the only one you have not read yet.

2) The vast majority who did not do the above.

For the first category, I don’t have any particular suggestion at the moment. Well done. That is the right way of reading this blog.

For the second category, you would do much better to stop right here in the middle of this post (without even finishing it), go back to the beginning, and read every post in chronological order.

….

So you are now in the first category? No? Since obviously you did not take my advice, let me explain both why you should, and why you will not.

It is possible to understand something through arguments, even if manipulating symbols may be an even more common result. And since conclusions follow from premises, you can only do this by thinking about the premises first, and the conclusions second. Since my own interest is in understanding things, I intentionally organize the blog in this way. Of course, since the concrete historical process of an individual coming to understand some particular thing is messier and more complicated than a single argument or even than multiple arguments, the order isn’t an exact representation of my own history or someone else’s potential history. But it is certainly closer to that than any other order of reading would be.

You will object that you do not have the time to read 300 blog posts. Fine. But then why do you have time to read this one? Even if you are definitely committed to reading a small number of posts, you would do better to read a small number from the beginning. If you are committed to reading not more than one post a week, you would do better to read the 300 posts over the next six years, rather than reading the posts that are current.

You might think of other similar objections, but they will all fail in similar ways. If you are actually interested in understanding something from your reading, chronological order is the right order.

Of course, other blog authors might well argue in similar ways, but the number of people who actually do this, on any blog, is tiny. Instead, people read a few recent posts, and perhaps a few others if there are a chain of links that lead them there. But they do not, in the vast majority of cases, read from the beginning, whether to read all or only a part.

So let me explain why you will not take this advice, despite the fact that it is irrefutably correct. In The Elephant in the Brain, Robin Hanson and Kevin Simler remark in a chapter on conversation:

This view of talking—as a way of showing off one’s “backpack”—explains the puzzles we encountered earlier, the ones that the reciprocal-exchange theory had trouble with. For example, it explains why we see people jockeying to speak rather than sitting back and “selfishly” listening—because the spoils of conversation don’t lie primarily in the information being exchanged, but rather in the subtextual value of finding good allies and advertising oneself as an ally. And in order to get credit in this game, you have to speak up; you have to show off your “tools.”

…

But why do speakers need to be relevant in conversation? If speakers deliver high-quality information, why should listeners care whether the information is related to the current topic? A plausible answer is that it’s simply too easy to rattle off memorized trivia. You can recite random facts from the encyclopedia until you’re blue in the face, but that does little to advertise your generic facility with information.

Similarly, when you meet someone for the first time, you’re more eager to sniff each other out for this generic skill, rather than to exchange the most important information each of you has gathered to this point in your lives. In other words, listeners generally prefer speakers who can impress them wherever a conversation happens to lead, rather than speakers who steer conversations to specific topics where they already know what to say.

Hanson and Simler are trying to explain various characteristics of conversation, such as the fact that people are typically more interested in speaking than in listening, as well as the requirement that conversational participants “stick to the topic.”

Later, they associate this with people’s interest in news:

Why have humans long been so obsessed with news? When asked to justify our strong interest, we often point to the virtues of staying apprised of the important issues of the day. During a 1945 newspaper strike in New York, for example, when the sociologist Bernard Berelson asked his fellow citizens, “Is it very important that people read the newspaper?” almost everyone answered with a “strong ‘yes,’ ” and most people cited the “ ‘serious’ world of public affairs.”

…

Now, it did make some sense for our ancestors to track news as a way to get practical information, such as we do today for movies, stocks, and the weather. After all, they couldn’t just go easily search for such things on Google like we can. But notice that our access to Google hasn’t made much of a dent in our hunger for news; if anything we read more news now that we have social media feeds, even though we can find a practical use for only a tiny fraction of the news we consume.

There are other clues that we aren’t mainly using the news to be good citizens (despite our high-minded rhetoric). For example, voters tend to show little interest in the kinds of information most useful for voting, including details about specific policies, the arguments for and against them, and the positions each politician has taken on each policy. Instead, voters seem to treat elections more like horse races, rooting for or against different candidates rather than spending much effort to figure out who should win. (See Chapter 16 for a more detailed discussion on politics.)

…

These patterns in behavior may be puzzling when we think of news as a source of useful information. But they make sense if we treat news as a larger “conversation” that extends our small-scale conversation habits. Just as one must talk on the current topic in face-to-face conversation, our larger news conversation also maintains a few “hot” topics—a focus so strong and so narrow that policy wonks say that there’s little point in releasing policy reports on topics not in the news in the last two weeks. (This is the criterion of relevance we saw earlier.)

The argument here suggests that blog readers will tend to prefer reading current posts to old ones because this is to remain more “relevant,” and that such relevance is necessary in order to impress other conversational participants. This, I suggest, is why you will not take my advice, despite its rightness. If you think this is an insulting explanation, just bear in mind that blog authors are even more insulted by Hanson’s and Simler’s explanations, since the reader at least is listening.

Idealized Idealization

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On another occasion, I discussed the Aristotelian idea that the act of the mind does not use an organ. In an essay entitled Immaterial Aspects of Thought, James Ross claims that he can establish the truth of this position definitively. He summarizes the argument:

Some thinking (judgment) is determinate in a way no physical process can be. Consequently, such thinking cannot be (wholly) a physical process. If all thinking, all judgment, is determinate in that way, no physical process can be (the whole of) any judgment at all. Furthermore, “functions” among physical states cannot be determinate enough to be such judgments, either. Hence some judgments can be neither wholly physical processes nor wholly functions among physical processes.

Certain thinking, in a single case, is of a definite abstract form (e.g. N x N = N²), and not indeterminate among incompossible forms (see I below). No physical process can be that definite in its form in a single case. Adding cases even to infinity, unless they are all the possible cases, will not exclude incompossible forms. But supplying all possible cases of any pure function is impossible. So, no physical process can exclude incompossible functions from being equally well (or badly) satisfied (see II below). Thus, no physical process can be a case of such thinking. The same holds for functions among physical states (see IV below).

In essence, the argument is that squaring a number and similar things are infinitely precise processes, and no physical process is infinitely precise. Therefore squaring a number and similar things are not physical processes.

The problem is unfortunately with the major premise here. Squaring a number, and similar things, in the way that we in fact do them, are not infinitely precise processes.

Ross argues that they must be:

Can judgments really be of such definite “pure” forms? They have to be; otherwise, they will fail to have the features we attribute to them and upon which the truth of certain judgments about validity, inconsistency, and truth depend; for instance, they have to exclude incompossible forms or they would lack the very features we take to be definitive of their sorts: e.g., conjunction, disjunction, syllogistic, modus ponens, etc. The single case of thinking has to be of an abstract “form” (a “pure” function) that is not indeterminate among incompossible ones. For instance, if I square a number–not just happen in the course of adding to write down a sum that is a square, but if I actually square the number–I think in the form “N x N = N².”

The same point again. I can reason in the form, modus ponens (“If p then q“; “p“; “therefore, q”). Reasoning by modus ponens requires that no incompossible forms also be “realized” (in the same sense) by what I have done. Reasoning in that form is thinking in a way that is truth-preserving for all cases that realize the form. What is done cannot, therefore, be indeterminate among structures, some of which are not truth preserving. That is why valid reasoning cannot be only an approximation of the form, but must be of the form. Otherwise, it will as much fail to be truth-preserving for all relevant cases as it succeeds; and thus the whole point of validity will be lost. Thus, we already know that the evasion, “We do not really conjoin, add, or do modus ponens but only simulate them,” cannot be correct. Still, I shall consider it fully below.

“It will as much fail to be truth-preserving for all relevant cases as it succeeds” is an exaggeration here. If you perform an operation which approximates modus ponens, then that operation will be approximately truth preserving. It will not be equally truth preserving and not truth preserving.

I have noted many times in the past, as for example here, here, here, and especially here, that following the rules of syllogism does not in practice infallibly guarantee that your conclusions are true, even if your premises are in some way true, because of the vagueness of human thought and language. In essence, Ross is making a contrary argument: we know, he is claiming, that our arguments infallibly succeed; therefore our thoughts cannot be vague. But it is empirically false that our arguments infallibly succeed, so the argument is mistaken right from its starting point.

There is also a strawmanning of the opposing position here insofar as Ross describes those who disagree with him as saying that “we do not really conjoin, add, or do modus ponens but only simulate them.” This assumes that unless you are doing these things perfectly, rather than approximating them, then you are not doing them at all. But this does not follow. Consider a triangle drawn on a blackboard. Consider which of the following statements is true:

  1. There is a triangle drawn on the blackboard.
  2. There is no triangle drawn on the blackboard.

Obviously, the first statement is true, and the second false. But in Ross’s way of thinking, we would have to say, “What is on the blackboard is only approximately triangular, not exactly triangular. Therefore there is no triangle on the blackboard.” This of course is wrong, and his description of the opposing position is wrong in the same way.

Naturally, if we take “triangle” as shorthand for “exact rather than approximate triangle” then (2) will be true. And in a similar way, if take “really conjoin” and so on as shorthand for “really conjoin exactly and not approximately,” then those who disagree will indeed say that we do not do those things. But this is not a problem unless you are assuming from the beginning that our thoughts are infinitely precise, and Ross is attempting to establish that this must be the case, rather than claiming to take it as given. (That is, the summary takes it as given, but Ross attempts throughout the article to establish it.)

One could attempt to defend Ross’s position as follows: we must have infinitely precise thoughts, because we can understand the words “infinitely precise thoughts.” Or in the case of modus ponens, we must have an infinitely precise understanding of it, because we can distinguish between “modus ponens, precisely,” and “approximations of modus ponens“. But the error here is similar to the error of saying that one must have infinite certainty about some things, because otherwise one will not have infinite certainty about the fact that one does not have infinite certainty, as though this were a contradiction. It is no contradiction for all of your thoughts to be fallible, including this one, and it is no contradiction for all of your thoughts to be vague, including your thoughts about precision and approximation.

The title of this post in fact refers to this error, which is probably the fundamental problem in Ross’s argument. Triangles in the real world are not perfectly triangular, but we have an idealized concept of a triangle. In precisely the same way, the process of idealization in the real world is not an infinitely precise process, but we have an idealized concept of idealization. Concluding that our acts of idealization must actually be ideal in themselves, simply because we have an idealized concept of idealization, would be a case of confusing the way of knowing with the way of being. It is a particularly confusing case simply because the way of knowing in this case is also materially the being which is known. But this material identity does not make the mode of knowing into the mode of being.

We should consider also Ross’s minor premise, that a physical process cannot be determinate in the way required:

Whatever the discriminable features of a physical process may be, there will always be a pair of incompatible predicates, each as empirically adequate as the other, to name a function the exhibited data or process “satisfies.” That condition holds for any finite actual “outputs,” no matter how many. That is a feature of physical process itself, of change. There is nothing about a physical process, or any repetitions of it, to block it from being a case of incompossible forms (“functions”), if it could be a case of any pure form at all. That is because the differentiating point, the point where the behavioral outputs diverge to manifest different functions, can lie beyond the actual, even if the actual should be infinite; e.g., it could lie in what the thing would have done, had things been otherwise in certain ways. For instance, if the function is x(*)y = (x + y, if y < 10^40 years, = x + y +1, otherwise), the differentiating output would lie beyond the conjectured life of the universe.

Just as rectangular doors can approximate Euclidean rectangularity, so physical change can simulate pure functions but cannot realize them. For instance, there are no physical features by which an adding machine, whether it is an old mechanical “gear” machine or a hand calculator or a full computer, can exclude its satisfying a function incompatible with addition, say quaddition (cf. Kripke’s definition of the function to show the indeterminacy of the single case: quus, symbolized by the plus sign in a circle, “is defined by: x quus y = x + y, if x, y < 57, =5 otherwise”) modified so that the differentiating outputs (not what constitutes the difference, but what manifests it) lie beyond the lifetime of the machine. The consequence is that a physical process is really indeterminate among incompatible abstract functions.

Extending the list of outputs will not select among incompatible functions whose differentiating “point” lies beyond the lifetime (or performance time) of the machine. That, of course, is not the basis for the indeterminacy; it is just a grue-like illustration. Adding is not a sequence of outputs; it is summing; whereas if the process were quadding, all its outputs would be quadditions, whether or not they differed in quantity from additions (before a differentiating point shows up to make the outputs diverge from sums).

For any outputs to be sums, the machine has to add. But the indeterminacy among incompossible functions is to be found in each single case, and therefore in every case. Thus, the machine never adds.

There is some truth here, and some error here. If we think about a physical process in the particular way that Ross is considering it, it will be true that it will always be able to be interpreted in more than one way. This is why, for example, in my recent discussion with John Nerst, John needed to say that the fundamental cause of things had to be “rules” rather than e.g. fundamental particles. The movement of particles, in itself, could be interpreted in various ways. “Rules,” on the other hand, are presumed to be something which already has a particular interpretation, e.g. adding as opposed to quadding.

On the other hand, there is also an error here. The prima facie sign of this error is the statement that an adding machine “never adds.” Just as according to common sense we can draw triangles on blackboards, so according to common sense the calculator on my desk can certainly add. This is connected with the problem with the entire argument. Since “the calculator can add” is true in some way, there is no particular reason that “we can add” cannot be true in precisely the same way. Ross wishes to argue that we can add in a way that the calculator cannot because, in essence, we do it infallibly; but this is flatly false. We do not do it infallibly.

Considered metaphysically, the problem here is ignorance of the formal cause. If physical processes were entirely formless, they indeed would have no interpretation, just as a formless human (were that possible) would be a philosophical zombie. But in reality there are forms in both cases. In this sense, Ross’s argument comes close to saying “human thought is a form or formed, but physical processes are formless.” Since in fact neither is formless, there is no reason (at least established by this argument) why thought could not be the form of a physical process.