A Subjective Approach to Two Paradoxes

Part 1: The Heap

There is a fairly well-known thought experiment out there that goes more or less like this: You find yourself looking at a heap of something. It doesn’t particularly matter what it is - maybe it is sand, or ash, or chocolate pudding - but it is definitely a big enough quantity of the stuff that we would classify it as a heap. Then, someone else starts removing the substance, little by little - let’s say a cup at a time. Eventually, there will be nothing left because that is how the laws of the universe work. The question is: at what point exactly did the heap cease to be a heap? It clearly was a heap at the beginning of this bizarre ritual, and it is just as clearly not a heap now, so when did the change happen?

(By the way, if the word heap no longer seems to have any meaning to you, welcome to semantic satiation.)

There is, obviously, no answer to this question and there is not supposed to be; any serious answer would sound completely absurd. The only acceptable ways to respond to a thought experiment or paradox like this are: genuine awe (“Whoa, dude! Mind. Blown.”); douchey condescension (“Yeah, yeah, I’ve heard that one before. Is that what philosophy majors do all day while the rest of us are working at our jobs?”); or a slightly-less-douchey elaboration on the point (“Ah, yes, that framework posits the transient and contextual nature of all forms of identity . . .”) Personally, I like to go for a combination of all three. 

Let's not let Bill Cosby ruin chocolate pudding for us, please.

I think the problem with our usual way of understanding this thought experiment (and the many others like it) is that we assume that a heap is an actual thing. Don’t get me wrong. I’m not playing the nothing-is-real card. (Not yet, anyway.) When there’s a massive amount of chocolate pudding on your floor, the pudding definitely does exist (and so, most likely, do some underlying psychological issues.) What doesn’t really exist is a heap. That word heap is just a way that we have of understanding and referring to a large amount of a substance; it is a category that we impose upon the pudding. That’s why it’s even possible to disagree about what to call something. If I called my friend and told him, “There’s a heap of pudding in my apartment,” he could conceivably come over to check it out for himself (and who wouldn’t, honestly?) and then be all like, “Dude, that is not a heap. A heap’s got to be way bigger.” And then we could argue about it for fifteen minutes and post the whole conversation on the Internet and call it a podcast or something, I don’t know.

The point is: the only reason we could have that conversation at all is because "heap" is a term applied by a subject to a given object. (All language kind of works like this, but it’s definitely easiest to visualize with nouns.) And so that brings us back to our thought experiment and the way to resolve it. Instead of focusing our mental energy on the heap itself - taking an objective stance or approach - we should be thinking about the subject, the person who encountered the heap in the first place. Moreover, we should be thinking about the experience that that subject is having as he or she watches cup after cup of pudding being removed. This experience, like all experiences, is happening over time, which is a fact that sort of gets obscured in the usual way of describing the thought experiment.

So, first, the subject sees the pudding (or whatever) and goes, “Yeah, that’s a heap, all right!” Then, one cup of pudding is removed; then, another. This part of the story is pretty repetitive, really. But then: the climax of the narrative occurs when the subject happens to look at the object in front of him or her and says, “That is not a heap anymore.” That can only happen, of course, if the subject remembers that he or she called the thing a heap in the first place. If the subject is daydreaming about something else, the heap remains a heap, because that was the last thing it was described and defined as. But the moment he or she snaps back to reality (oh, there goes gravity), recalls the word "heap," and compares it to the current state of the object, then the heap has ceased to be.

So there is no specific moment we can point to where a heap in general ceases to be a heap - which is the whole point of the thought experiment. But there is a specific moment for each specific heap where it ceases to be a heap, every time that is experiment is performed. And every experience in life is a specific, singular experience.

Are there implications to this? Yes, probably.

Part 2: The Test

There is another thought experiment, or maybe this one is better called a paradox, that I think can be resolved by a similar approach, by taking a subjective rather than an objective stance. This one is probably going to be a bit more difficult to explain, though, so let’s settle in. So there’s this teacher who tells his class one Friday, “You are going to have a test next week. However, because I enjoy the sense of power that it provides me and because I am chained to antiquated notions of what it means to provide a quality education, I am not going to tell you what day the test will be on. In fact, I am going to guarantee and promise that you will not know at any point before the test when the test will be. You will be uncertain right up until the moment that I hand you the test.” He says all of this without thinking about it, because as I already said, he is a teacher and it is Friday.

But later that night, after a couple of beverages (again: teacher, Friday), he starts replaying what he said over and over again in his mind and analyzing the shit out of it. (That’s what everyone does when they drink, right? Guys?) His original plan was to schedule the test for the following Friday, so as to keep his students in suspense for as long as possible and/or to provide them with as much time to study as he could, depending on who was asking. But now he realizes that it won’t work. As soon as the students leave class on Thursday, they will know that the test was going to be the next day, and he had promised them total uncertainty. So Friday was out.

But then, his spiraling brain begins to shout at him, doesn’t that just lead to the exact same problem with Thursday? Since Friday is no longer an option, the last day he can schedule the test is Thursday, which means that the students will all know at the end of class on Wednesday when the test is. So Thursday is no longer an option, which means . . .

“Oh my god,” the teacher says aloud. “What?” responds his husband. (YEAH THE TEACHER WAS GAY THE WHOLE TIME REPRESENTATION BITCHES) “I’ve just realized . . . I’ve got to break a promise I made to my students.”

But does he really? Probably not! And the reason, once again, has to do with the fact that we often tend to ignore the subjective component of puzzles like these. In this case, the subject we need to pay more attention to is not the teacher, but the student. (For the sake of simplicity, I’m going to talk about only one student and then just control-c, control-v everything we’ve said about this one student to all the rest of them.) And again, we need to think about the specific experience that this student is having. If this student is going to have the experience, on Thursday afternoon or evening, of remembering what the teacher said last week and realizing that the test must be on Friday, then the teacher has indeed broken his promise. If she has completely forgotten about the test, though, or wasn’t listening to what the teacher said in the first place because she was thinking about her fidget spinner collection or the newest Snapchat filter (that’s what kids think about, right?), then the teacher can even schedule the test on Friday without breaking his promise.

Pictured: the inside of every young
person's mind, probably

It does seem more likely than not that this student, fidget spinners and all, would remember that there was supposed to be a test at some point during the week. (Of course, it is even more likely when we permit ourselves to remember that, outside of the work of Jean-Jacques Rousseau, there is typically more than one student in a class. And they can’t all have been spinning their fidgets at the same time.) So the teacher is probably right that Friday is not a valid choice - because of a particular experience that would be had by another subject, the experience of certainty.

But let us imagine that the teacher did say “fuck off” to his overactive brain and sense of guilt (lowkey goals) and decided to schedule the test for Thursday. Would the student have experienced certainty regarding the test date at any point? Only if - at some point between the end of Wednesday’s class and the beginning of Thursday’s - she had already thought about the logic that tells us that the test could not be on Friday and therefore must be on Thursday and believed that the teacher had done so as well. It is not enough for the logic to be true; the subject of the student must believe that the subject of the teacher had the experience of understanding it. If the student does not believe that the teacher a) is fully committed to keeping his promise and b) has already had the experience of realizing that the test cannot be on Friday, then she never experiences certainty and the teacher has not broken his promise.

Now here’s where it gets complicated. (Feel free to skip this paragraph if you feel like you already get the point. Actually, I mean, you should feel free to skip any part of it for any reason. But then again, it’s also sort of, like, you should take the initiative to do that yourself if you’re going to do it; I shouldn’t have to give you permission to not have the experience of reading some words just because I had the experience of writing them.) What happens if the teacher decides to set the test for Wednesday? What conditions need to be true in order for the student to have experienced certainty prior to the test? Well, first of all, prior to Wednesday’s class the student will need to have realized that the test cannot be on Friday and believed that the teacher will have thought about that too. However, she also needs to believe that the teacher believed that she would have already experienced that realization. The teacher needs to actually believe that he has a student in his class who has realized already that the test could not be on Friday and would be perceptive enough to think about the fact that the teacher would have already thought of that. (This last point is the greatest barrier to something like this ever happening in real life, as far as I am concerned. My students, at least, would never give me enough credit to consider that I have already considered the logistics of something I said. One of them would surely raise their hand and go, “But doesn’t that mean the test can’t be on Friday? Because you just said . . .” And my inner voice would go, “Yeah, yeah, you’re very smart, we can all see that. But you’re ruining it for everyone else. Now everyone knows it’s not going to be on Friday. Thanks a lot, you little asshole.”) But the point is: in order for this to become an issue beyond Thursday, there need to be two subjects, two human beings, who are extremely in tune with each other, who have a high degree of certainty about the experiences that their counterpart has had or is having.

If you haven't thought about her once while reading this,
then we have nothing in common.

Because that is what is missing from the original version of the paradox, the one that the teacher’s brain confronted him with on Friday night: doubt. Everything proceeds in a logical, orderly manner, but there is no room made for doubt or uncertainty. And doubt and uncertainty are inherent to subjectivity, to the extent that I truly cannot imagine an experience utterly devoid of them, any more than I can imagine an experience with no dimension of space or time. (Kant claimed that space and time were the most fundamental categories of experience, so that nothing recognizable as experience could exist without them. It would have taken a pretty ballsy existentialist to say that doubt was just as fundamental or even more so.)

And so, when you consider things from that perspective, the teacher could very well schedule the test for Friday and know that none of his students could really be absolutely certain about it, since they would always have to contend with the possibilities that he forgot about the test, or changed his mind without telling them, or that the whole conversation on the previous Friday had been only a particularly vivid (and uninteresting) dream or hallucination. But then again, I suppose that’s nothing but conjecture about the experiences of those subjects. If they truly believed what the teacher said last Friday, then they could have the experience of certainty regarding the date of the test even though we could quibble about whether they are justified in being certain or not. What it really comes down to, though, is paying more attention to the specific and actual experiences of subjects rather than just "things in themselves."

Are there implications to this one? Almost certainly not.