metonymy4u

One of the knottiest philosophical questions of all time is this: do ideas actually exist?

Well, of course they do! If they didn’t, then none of the things we see every day would be real.

I mean think about it: If 2+2 did not really equal 4 then all our buildings, bridges, houses, cars and space ships would just fall apart, wouldn’t they? How could we ever actually accomplish anything in the world if all our ideas didn’t actually correspond to some sort of reality out there independent of our thoughts? So clearly at least some of our ideas, like the ideas of mathematics, or the ideas of space and time, for example, must in fact be “real” in some sense. And this suggests that it is possible, at least in principle, for us to define ideas that are really real, so perhaps all those other ideas that seem less precise, like love or beauty or morality, might also be able to be defined in some real way, if we just had enough time and energy and creativity to figure out the best way to define them that everyone could agree on. In principle. So it seems that in fact ideas actually do exist “out there in the world” and are not just mere “matters of convention.”

Right?

Ok, let’s look at it from another perspective. Take the idea of a circle. A circle has a very precise definition. It is the set of all points in space that are the exact same distance from some central point. That exact distance is called the radius, and is the distance from the circle’s perimeter to the center of the circle. But think about this: even though we can come up with a very precise definition of a circle, we also know that it is very hard to draw a perfect circle. Even with a compass and a very steady hand, if we zoomed in on the drawing on the page there would be little irregularities in the pencil tracing which would cause some parts of the line to be further away from the center than others. So it probably is in fact very hard to draw a perfect circle. Nevertheless, we can distinguish between a drawing of a circle and a drawing of a square, right? So if we think of all the drawings of circles we’ve seen or could see, we still are seeing some type of similarity, even if the particular token examples of circles are all imperfect in some small, even microscopic, way. So there must be something causing this similarity between the particular token instances of circles, call it the “circle-type.” As I said above, there must be some real, actual circle-type out there in the world independent of our thought processes, or all our technology would come crashing down around us.
Of course, this circle-type must itself be circular, since if it wasn’t, how could we recognize it as the cause of all the token instances of circles we see every day? If the circle-type were more square than circular, one would not think that it could be the cause of all the circle patterns we perceive, right? So the circle-type itself must exist and must be circular in some recognizable way.

But hold on: if the circle-type is circular, and circle-tokens are circular, then there must be some third thing causing them to be similar in this way (i.e. they are both circular). So in fact this circle-type is itself just another token example of some other more “essential” type, call it circle-type2. And so circle-type2 must be the cause of the similarity between the first circle-type and all the actual concrete token examples of circles we see around us every day. But of course circle-type2 itself must be circular, so in fact there must be yet another circle type, call it circle-type3. But of course…etc, etc, etc. Right away you can see that to identify any sort of type-token relationship instantly gets us searching for an infinite number of circle-types, and we can never really get to the end of the series. That is, we can never get to the “final circle type” which causes all the other token instances of circles. So it seems that, in fact, there is no one existing ideal type of circle that can be identified, which is the opposite of what we originally concluded when we first asked the question about whether ideas actually exist. Or maybe it does exist, but we can’t actually identify it? But how can we know that something exists if we can’t even come up with a precise way to identify it or locate it? So to say that it exists but we can’t identify it seems ridiculous, so perhaps ideas don’t in fact actually exist?

This objection to our earlier proof that ideas actually exist is called the “third man argument” against the actual existence of ideas.

Where does that leave us?

It seems as if we have proven that ideas both exist and don’t exist. On the one hand we suppose they must exist in order for us to explain the efficacy of our actions in the world, particularly technology which is quite effective at building things and getting things done, and which depends on the absolute truth of ideas like mathematics and geometry. On the other hand, even mathematics it seems can’t lead us to any final discovery of the ultimate causes of these patterns, because as soon as we start looking for the cause of anything in particular, we end up in an infinite search for the ultimate cause.

The way out of this dilemma was proposed by Immanuel Kant in 1781. What he said was very simple: we can define types like circles and the technique of defining such types is very useful to us for accomplishing the things we want to accomplish (like building things, organizing things, or figuring out things). However, we can never completely and absolutely verify the independent truth of these conceptual models, because as soon as we try to do so, we end up in an infinite series of possible candidates for the ultimate truth. So what we learn from this exercise is not that all knowledge is useless illusion, but that knowledge is no more than a useful way of living our lives. It is not a path to any sort of ultimate truths about the universe, our selves, or the nature of freedom or the divine. While we can certainly continue to build houses, write poetry, appreciate beauty or discuss good and evil, these more ultimate truths are best passed over in silence.