Let X be any set and let T be a family of subsets of X. Then T is a topology on X if (and only if):-Any union of arbitrarily many elements of T is an element of T
-Both the empty set and X are elements of T
-Both the empty set and X are elements of T
-Any intersection of finitely many elements of T is an element of T
Now it’s okay if you don’t really understand most of the above. Just know that it makes perfect sense if you have a basic knowledge of set theory. The important thing is that this is the definition of a topology. You will find it day one in nearly any topology course. It will be in the first chapter of any topology textbook you read.
This is the way mathematics works. It’s the way mathematicians work. The first step, the very first step, is to lay out the precise meaning of the thing you’re analyzing. Once everyone knows what a topology is, what the word refers to, then you go about proving that every topology has this that or the other cool property.
Incidentally, a lot of physics also works this way. I started to conduct a simple survey counting the number of times I ran across a definition during some random week of classes, but I decided to stop after a single two-hour lecture. Seven definitions in only two hours. We were starting a new topic, and just like mathematicians, physicists tend to start by laying out their terminology.
This is nothing new to me, nor should anyone find this kind of thing unusual. It is very common not just in math and physics but in academia in general. It’s rare for someone to walk into an economics course and not find definitions of terms like “supply and demand.” It is highly unusual for those studying French culture to disagree on what France is, or for geneticists to endlessly debate what constitutes a gene. Most of the time, when people get together and study something, they start by specifying what exactly they’re studying.
Contrast this to your typical philosophy class, or most any philosophy literature out there. I took three philosophy classes in undergrad, and nowhere in any of those courses did I see any philosophers openly attempting to define their terminology. I saw plenty of discussion that amounted to hashing out definitions, but it was always couched in language that worked to disguise that fact. It seemed that philosophers preferred to think of themselves as investigating the “true nature” of things, instead of just hammering out definitions. I guess it sounds more impressive that way.
But when I step back and examine my philosophy education next to the education I received in math and physics, it seems utterly ridiculous. I spent an entire semester studying the philosophy of mind, and I still have no idea what the word “mind” is supposed to mean in that context. It’s as if the entire philosophical discipline hasn’t gotten as far as the first day of topology class. Ask five topologists for a definition of “topology,” and you’ll get five identical answers. Ask five philosophers of mind what the word “mind” means, and you’re likely to get several different answers. And I don’t just mean the same answer expressed five different ways, with slightly different word choices. Some of those answers will be incompatible with one another.
This is a very strange thing when you stop to think about it. How many fields of study do you know of that haven’t reached an agreement on what precisely they’re studying? And remember that “we don’t yet know all the properties” is very different from “we have no common definition.” The definition of a topology does not immediately tell you that the real numbers are a topology, you have to work that part out for yourself. Pinning down every single detail of a thing is not necessary for creating a working definition. So I’m not complaining that philosophers of mind don’t have the whole mind thing figured out yet. I’m complaining that they don’t even seem to have a common referent for the word “mind.”
Here’s an example where this lack of common referent bites philosophers in the metaphysical butt. There’s a whole wealth of scientific evidence telling us that our thoughts, feelings, and emotions are all a direct consequence of whatever particular state our brain happens to be in. Building on this, some philosophers have suggested that the brain is the mind; the two are identical. After all, the brain is what gives rise to all those phenomena we think of as mental.
One (of several) critiques of this claim points out that while a particular brain state may cause me to feel happy, it is rather ridiculous to go around saying that my brain feels happy. I am the one feeling happy, not my brain. So while the brain may cause all of the mental phenomena, it is not the mind because it is not the one experiencing those phenomena. It is perhaps linked to the mind, but the brain is not itself the mind because it does not experience.
So which one is right? Is your mind simply your brain because that’s what gives rise to all your mental events, or is your mind something other than your brain because your brain does not experience things like happiness or pain?
This question has the exact same problem as another question. If a tree falls in the middle of a forest, and no one’s around to hear it, does it make a sound?
Now I know nobody really takes that question seriously these days, and that’s okay. I’m just using it to demonstrate a point. Suppose that a couple of people did take this question seriously. One person could reasonably answer by saying that of course the tree still makes a sound. After all, the thing we call sound is just a pressure wave traveling through the air. The falling tree still creates a pressure wave, even if that wave doesn’t reach anybody’s ear. So yes, the tree makes a sound.
The second person could critique this position by saying that sound isn’t just a pressure wave. Sure, we all know that pressure waves cause our auditory sensations, but it is the hearing, the sensation we have, that we mean by sound. A pressure wave isn’t sound, it just causes sound when it hits an ear. Since the tree’s pressure wave never hits any ears, it never gets a chance to cause any sound, so no, the tree does not make a sound.
The key thing to notice here is that there is absolutely no disagreement over what happens when the tree falls. Both our hypothetical philosophisters agree that the falling tree creates a pressure wave, and both agree that this pressure wave never gets a chance to generate any auditory response. The only disagreement between the two positions occurs with the use of the word sound. The first person interprets the word sound to mean “pressure wave” while the other interprets it to mean “auditory sensation.” This allows them to disagree over the answer to the question despite the fact that they agree completely on what precisely is going on.
If we defined the word sound ahead of time, none of this ridiculous discourse would take place. If we define the word sound to mean “pressure wave,” then both parties will agree that the tree makes a sound. If we define the word sound to mean “auditory sensation,” then both parties will agree that the tree does not make a sound. So we see that the disagreement is in fact quite shallow. It is nothing more than a disagreement over the meaning of a particular term. Resolving the disagreement amounts to resolving a question of definition. The back and forth between our hypothetical philosophisters does not represent anything profound about the nature of falling trees. It’s just a couple of guys being douchebags.
Compare this to our philosophy of mind example. Both parties are willing to accept the overwhelming scientific evidence and conclude that yes, brains do cause all those mental phenomena. There is no disagreement over what is going on. Both parties are completely capable of recognizing that brains cause thoughts and emotions but do not experience thoughts and emotions. And even while recognizing these things, both parties are perfectly capable of maintaining their position. This disagreement between “brain is mind” and “brain is not mind” does not reflect any disagreement over what is actually going on, over the “nature of things.” The disagreement only arises with the use of the word mind.
If we defined the word mind ahead of time, we would have no need for any of this ridiculous discourse. If we define the word mind to mean “that which produces our mental experiences,” then both parties will agree that this is in fact the brain. If we define the word mind to mean “that which experiences thoughts and emotions,” then both parties will agree that the brain itself is insufficient. This disagreement in the philosophy of mind does not represent anything profound about the nature of minds. It is nothing more than a disagreement over the use of the use of the word mind. It’s just a couple of guys being douchebags, and calling it a profession.
It's a five-part series, so you know the drill. Next week, Word Play Part IV: Words Gone Wild