On Definitions in Philosophy

When trying to define a term, we think generally of providing a set of necessary and sufficient conditions: a recipe for including or excluding a thing in a particular category of existence. For instance, an even number (definitions tend to work best in the mathematical arena, since definitions there can be as precise as possible) is definable as an integer that when divided by 2 does not leave a remainder. It is easy, given this definition, to ascertain whether or not a given number is even. Divide it by two and see if it leaves a remainder. If it does, then it’s not even; if it doesn’t, then it is. We have here a clear test for inclusion or exclusion in the set of even numbers.

Outside of mathematics, things get trickier. (Inside mathematics, things can be tricky as well. Imre Lakatos‘ excellent book Proofs and Refutations details some of the problems here. If you are mathematically and philosophically inclined, this is a must-read book.)

In Ludwig Wittgenstein‘s Philosophical Investigations, he famously talks about the travails of defining the term “game”. Is there a set of necessary and sufficient criteria that will let us neatly split the world into games and non-games? For instance, do all games have pieces? (No, only board games have these.) Winners and losers? (There are no winners in a game of catch.) Strategy? (Ring-around-the-rosie has no strategy.) Players? (Well, since games are a particularly human endeavor, it would be an odd game that had no human participants. But, of course, some games have only one player.) There seems to be no single set of characteristics that spans across everything we’d like to call a game. Wittgenstein’s solution was to say that games share a “family resemblance” — “a complicated network of similarities overlapping and criss-crossing”. A great many games have winners and losers, and so share this family trait; and then there are games that have pieces, and this is another trait that can be shared. Many (but not all) of the games with pieces also have winners and losers, and so there is significant overlap here. Games with strategy span another vast swath of the game landscape, and many of these games have winners and loses, many of which also have pieces. But not all. And so a networks of resemblances between games is found — not a single boundary that separates games from non-games, but a set of sets that is overlapping and more or less tightly connected.

This is a brilliant idea, but one that often leaves analytical philosophers with a bad taste in their mouths. If you try to formalize family resemblances (and analytical philosophers love to formalize things), you run up against the same problems as you had with more straightforward definitions. Where exactly do you draw the line in including or excluding a resemblance? Games are often amusing, for instance. But so are jokes. So jokes share one resemblance with games. But jokes are often mean-spirited. And so are many dictators. And dictators are often ruthless. As are assassins. So now we have a group of overlapping resemblances that bridges games to assassins. And if you want to detail the conditions under which this bridge should not take us from one group of things (games) to the other (assassins), you are back to specifying necessary and sufficient conditions.

Wittgenstein, I imagine, would have laughed at this “problem”, telling us that we just have to live with the vague boundaries of things. Which is all well and good, but is easier said than done.


The defining of knowledge gives us a great example of definitions at work and their problems. For those of you who haven’t been indoctrinated in the workings of epistemology, it turns out that a good working definition for knowledge is that it is justified true belief.

Is Knowledge Justified True Belief
I take it as axiomatic as can be that something has to be believed to be known. If you have a red car but you don’t believe that it’s red, you don’t have knowledge of that fact. But, clearly, belief isn’t sufficient to define something as knowledge. For instance, if I believe that my red car is actually blue, I still don’t have any knowledge of its actual color. So we have to bring truth into the picture. If I believe that my car is red, and it is actually red, I’m certainly closer to having a bit of knowledge. But, again, this isn’t sufficient. What if my wife has bought me a red car that I haven’t seen yet. I believe it’s red because I had a dream about a red car last night. Do I have knowledge of my car’s color? I’d say not. We need a third component: Justification. If I believe that my new red car is indeed red because I’ve seen it with my own eyes (or analyzed it with a spectrometer, if the worry of optical illusions bugs you), then we should be able to say I do indeed have a bit of knowledge here.

In 1963, Edmund Gettier came up with a clever problem for this definition — one that presents a belief that is justified and true, but turns out to not be knowledge. Here is the scenario:

  • Smith and Jones work together at a large corporation and are both up for a big promotion.
  • Smith believes that Jones will get the promotion.
  • Smith has been told by the president of the corporation that Jones will get the promotion.
  • Smith has counted the number of coins in Jones’ pocket, and there are 10.

The following statement is justified:

(A) Jones will get the promotion and Jones has 10 coins in his pocket.

Then this statement follows logically (and is therefore also justified):

(B) The person who will get the promotion has 10 coins in his pocket.

But it turns out that the president is overruled by the board, and Smith, unbeknownst to himself, is actually the one will be promoted. It also turns out that Smith, coincidentally, has 10 coins in his pocket. Thus, (B) is still true, it’s justified, and it is believed by Smith. However, Smith doesn’t have knowledge that he himself is going to get promoted, so clearly something has gone wrong. Justification, truth, and belief, as criteria of knowledge, let an example of non-knowledge slip into the definitional circle, masquerading as knowledge.

More Games

Let’s get back to the problem of defining games, and say that, contrary to Wittgenstein, you’re sure you can come up with a good set of necessary and sufficient conditions. You notice from our previous list of possible necessary traits that games certainly have to have players. Let’s call them participants, since “player” is something of a loaded word here (a player presupposes a game, in a way). And now you also take a stand that all games have pieces. Board games have obvious pieces, but so, you say, do other games. Even a game of tag has objects that you utilize in order to move the game along. (In this case, you’re thinking of the players’ actual hands.) So let’s add that to the list, but let’s call it what it is: not pieces so much as tools or implements. And perhaps you are also convinced that all games, even games of catch, have rules. Some are just more implicit and less well-defined than others. So let’s stop here, and see where we are. We have participants, implements, and rules.

And now we begin to see the problem. If we leave it at that, our definition is so loose as to allow under the game umbrella many things that aren’t actually games. A group of lab technicians analyzing DNA could fall under the conditions of having participants, implements, and rules. But if we tighten up the definition, we run the risk of excluding real cases from being called games. For instance, if we tighten the definition to exclude our lab workers from the fun by saying that games also have to have winners and losers we immediately rule out as games activities like catch and ring-around-the-rosie.

Lakatos coined two brilliant phrases for these definitional tightenings and loosenings: “monster-barring” and “concept-stretching”. Monster-barring is an applicable strategy when your definition allows something repugnant into the category in question. You have two options as a monster-barrer: do your utmost to show how the monster doesn’t really satisfy your necessary and sufficient conditions, or tweak your definition to keep the monster out.

Concept-stretching allows one to take a definition and run wild with it, applying it to all sorts of odd cases one might not have previously thought to. For instance, perhaps we should expand entry into the realm of games to include our intrepid DNA lab workers. What would that mean for our ontologies? And what would it mean for people who analyze games? And for lab technicians?

Philosophers love to define terms; they also love to find examples that render definitions problematic. It’s a trick of the trade and a hazard of the business.


Philosophy Resources on the Web

There is a great wealth of serious philosophy out there on the internet, though you have to dig deep through a great deal of philosophical detritus to get to the good stuff. Here are some of our picks for genuinely good philosophy on the web…


One of our favorite resources out there is Philosophy Bites: a collection of “podcasts of top philosophers interviewed on bite-sized topics”. The hosts, respected philosophers themselves, Nigel Warburton and David Edmonds, have interviewed a lot of renowned philosophers for the show, ranging from Daniel Dennett to Philip Pettit to Frank Jackson to Martha Nussbaum, all in easy-to-digest 15 minute sessions. The website itself is not exactly a treat to navigate, but you can skip the site and go directly to iTunes to download free podcasts. Or you can shell out three bucks for the iPhone app which I can vouch for being well worth it. They also have the MP3s hosted on, if you like to work through these things old school. One of my favorite podcasts is Nick Bostrom on the Simulation Hypothesis — absurdist metaphysics at its finest! — but really there are very few uninteresting interviews on the site.

Another great resource of philosophy audio is Philosophy Talk, a radio program with podcasts by eminent Stanford philosophers John Perry and Ken Taylor.


The next time you’re about to head over to Wikipedia to check out something philosophical, stop yourself and try either the Stanford Encyclopedia of Philosophy or the Internet Encyclopedia of Philosophy. Both sites are peer-reviewed and generally are excellent sources for delving more deeply into philosophy. Check out the Stanford article on thought experiments, for example, or the IEP’s article on Searle’s Chinese Room. Both fine pieces.

Public Domain Texts

If you’re looking for public domain philosophy texts, there are plenty out there, although be prepared to find very little contemporary work. Everybody’s favorite public domain repository, Project Gutenberg, has a respectable collection of philosophy works. The EServer also has a collection of public domain philosophy texts available for download, along with some contemporary pieces that have been appropriately licensed.

If you are looking for more contemporary works online, your best bet is JStor, which scans most of the top philosophy journals and creates PDFs. There are a few journals and articles available for free through JStor to the general public, but if you really want to get the most out of the service, you have to be connected to a university that pays for their best services. If you are so connected, you will have an incredible wealth of philosophy articles at your disposal. If you are a philosophy teacher, or interested in philosophical pedagogy, check out the Philosophy Documentation Center — a subscription service that has all sorts of articles available about teaching philosophy.

Free Online Courses

Universities are starting to beef up their online course offerings, and there are several that offer free courses, consisting of syllabi, lecture notes, slides, audio, and video. Everything short of interaction with and feedback from professors. MIT was one of the first to make freely available such resources. Yale has a couple of courses available as well. As does Notre Dame.

We haven’t gone through any of these courses with a fine-tooth comb, so we can’t say how instructive they really are, but we certainly applaud academia for opening up the ivory tower a bit. If any of you have ever tried any of these courses, let us know what you thought!

The Profession

No list of professional philosophical resources would be complete without a link to the American Philosophical Association — the major professional organization for philosophy professors and students. Their website could use an update from 1999, but there is a good amount of information on the site regarding the profession of philosophy.

If you’re thinking about grad school in philosophy, you should definitely check out the Philosophical Gourmet Report — Brian Leiter’s ranking of graduate programs in philosophy in the English-speaking world.

Let us know if you think of other good web resources for philosophy lovers.


What is Philosophy?

What is philosophy? And why are we bothering to blog about it?

Even people trained in philosophy are often hard-pressed to come up with a pithy definition of it. The first time I taught Introduction to Philosophy, I stammered at the front of the class for a good five minutes trying to explain the sorts of things about which I was going to teach them for the next fifteen weeks. (Later in the semester, I stammered for significantly less time, but with the same significant stammering intensity, over the definition of “ethics”. So it’s not just the general term “philosophy” that’s the issue, I think.)

Of course, if you’re a philosophy aficionado you might well already know the problems attached to the process of defining terms. Wittgenstein, famously, in his Philosophical Investigations, took his readers down the rabbit hole in attempting to define the term “game” — even something so seemingly simple can be difficult to pin down with authority and without counterexamples getting in your way.

But it’s not just the general problem of defining terms that is difficult in the case of “philosophy”. The field to which the term attaches is so broad and so nebulous that it’s no wonder it’s so hard to describe.

It may be fruitful here to think of philosophy as a practice, rather than a field. And you learn about a practice (and how to participate in that practice) more by immersion than by definition. So, while it’s fairly unsatisfying to someone just starting out in the practice of philosophy, I think it’s actually not unfair to say at the beginning of a philosophy course “you’ll see what philosophy is by the end of the semester. For now, crack open your Descartes text and let’s talk…”

That doesn’t help you, our much-appreciated reader, to figure out what it is this blog is about, and whether or not you’ll still be a reader next week. So, despite my trepidation, let me take a stab at saying what philosophy is and why we’ll be blogging about it.

The roots of the word “philosophy” harken back to “lover of wisdom”. Indeed, philosophy is all about the love of knowledge, and unearthing pieces of knowledge wherever you can. And when I say “wherever” I’m not kidding. There are philosophical treatises on such abstruse topics as nonexistent objects, and on subjects as far ranging as everything from humor to subatomic physics.

What, you might ask, makes some bit of knowledge about subatomic physics a piece of philosophy rather than a piece of physics? There have actually been scientists who have argued that philosophy of science is about as useful as astrology; and even the great philosopher Bertrand Russell wrote: “as soon as definite knowledge concerning any subject becomes possible, this subject ceases to be called philosophy, and becomes a separate science.” (Bertrand Russell (1912). The Problems of Philosophy. New York: Henry Holt & Co.) His thought was that the sciences provide definite knowledge, while philosophy provides insightful burrowing into ideas that may someday become science. (Of course, Russell was writing in the heady days when it seemed as if science and mathematics would explain everything, but that’s another story…)

Whether or not that’s true, it is most assuredly true that the philosophy of science has hit upon and explored many important areas of knowledge that scientists, busy doing the important work they’re doing, might never have explored. The importance of exploring these areas remains an open question, but if you have a philosophical disposition, you would seldom if ever doubt the importance of what you were studying. Not because your area of exploration might yield anything, say, scientifically fruitful, but simply because if it’s an avenue of knowledge, whatever lays at the end of it, you want to go down that path. It’s the journey itself that is as important as what you find, along with the fact that whatever you’ve found, it was something that needed discovering.

I remember my first day as a graduate philosophy student, going to the library and just wandering down the aisles. At first, I stuck to the philosophy stacks, marveling at the breadth and depth of the tomes there. But eventually I wandered into the math stacks — a second academic love of mine — and spent some quality time there, once again marveling at the results of humankind’s curiosity. Then it was off to the psychology stacks, and the science stacks, and before I knew it, somehow I was in an aisle of books devoted to 18th Century England. I grabbed a book at random and read a chapter on witchcraft and its relation to the social norms of the times, and marveled at it, even though it was not really something I’d normally be interested in — someone had trodden down this path with great intellectual fervor, and had unearthed theories, knowledge, and connections that no one else had ever thought about in quite the same way. Before putting the book back, I noticed that no one had checked it out of the library for decades. This made me melancholy for a moment, until I realized that if I had written this book, though I’d certainly want people to read it, there would be a big part of me that would be content to have done the work and written it, regardless of my future audience. At least it was in a respected library, filling in a nook in our intellectual history.

If this story resonates with you, you might have a philosophical disposition.

Have I explained what philosophy is yet? Not really, I suppose; though I believe I have explained why we’re bothering to blog about it.

So what is philosophy? The first thing to keep in mind is that it’s always “philosophy of X”, where X can be just about any field. So we have philosophy of existence (generally called metaphysics), philosophy of knowledge (or epistemology), philosophy of morality (ethics), philosophy of art (aesthetics), philosophy of science, philosophy of mathematics, philosophy of language, philosophy of mind, philosophy of humor, philosophy of law, and so many other philosophies-of that it could make your head spin.

I was recently browsing for provocative philosophy paper titles (I thought it would be instructive to look at such titles in order to start to get a sense of what it is that philosophers do), and I came across this essay by Karel Lambert from back in 1974: “Impossible Objects”.

I haven’t read the article (come to think of it, I have to add that to my to-read list!), but I’m guessing that it’s a piece about such “things” as round squares. So now put yourself in a philosopher’s mindset for a moment. Someone says offhandedly to you: “why that’s as likely as a round square,” and you start thinking about that idea. A round square. Well, that’s impossible — such things couldn’t possibly exist. And this gets you thinking… there are things that don’t exist but could if the circumstances were right. Things like a 200-story building in Jamaica or six-legged cows. So there are two classes of things that don’t exist: possible (mammoth buildings in Jamaica) and impossible (round squares). Now you’ve begun carving up reality into interesting categories, and this is a particularly philosophical endeavor.

But wait… “Things” that don’t exist??? How could a thing be nonexistent? Is this really a problem of existence or just a trick of words? This well trod path leads one into the philosophy of language, where we ponder sentences like “The round square doesn’t exist.” Is this sentence true? Does “round square” refer to something in the same way that “George Washington” refers to something in the sentence “George Washington existed.”? These are very philosophical questions as well.

To be interested in why no skyscrapers exist in Jamaica is to be (probably) some sort of historian, sociologist, economist, or architect. To be interested in the difference between non-existent Jamaican skyscrapers and non-existent round squares, well, that’s being a philosopher.

See you next time. (?)