I’m blogging my way through Sense and Goodness Without God, Richard Carrier’s handy worldview-in-a-box for atheists. (See the post index for all sections.) In my previous post, I began the discussion of What Everything is Made of: spacetime, matter-energy, and physical laws. Now we move on to something less scientific and more philosophical: III.5.4 Abstract Objects.
There is much confusion about the “existence” of abstract objects, and it is all Plato’s fault.
Plato thought that ideas like “bee” and “rectangle” and “2″ existed as perfect Forms in a special realm of perfect objects, and that particular bees or rectangles we see on earth are only pale imitations of the perfect Forms.
But we need not resort to such silliness. Ideas like “bee” and “rectangle” and “2″ are abstractions – they are “abstracted” from particular things. They are potential patterns of experience. For example, we might see an apple and a Midwestern barn and a Dodge Viper and notice that they all share the pattern of experience of reflecting lightwaves with wavelengths of 625–740 nanometers. We have abstracted from all these things a pattern of experience they have in common, one that we decided, for convenience, to call “red.”
Of course, we do not name or think of many potential patterns of experience. At one time in the distant past there were 4 bacteria, before there were human minds to contemplate the pattern of experience we now call “4.” But this does not require us to suppose that “4″ exists in some kind of magical realm of perfect objects. Nor does it require us to think that “fourness” exists in any sense beyond particular instances of it, or our thoughts about that potential pattern.
All of mathematics is about these patterns. It’s a language of symbols we developed for talking about certain patterns and relations. The same is true of colors (a pattern of lightwaves with a particular wavelength) and other processes. A color is a process of photon oscillation. Likewise, “running” is a pattern of leg movement. There is no object called “running” in some other realm where perfect objects are stored.
And we invent new abstractions all the time. Dan Savage invented an abstraction called “saddlebacking” as a handy shortcut for a pattern of experience that could otherwise be described as “Christian teens engaging in unprotected anal sex in order to preserve their virginities.” (The term is named after fundamentalist Christian megachurch Saddleback Church.)
There is another type of property called a “modal” property, which we can call “possibility” or “ability.”
For instance, Ed Norton can survive a trip to Paris but cannot survive a trip through a meat grinder. Ed Norton’s ability in either case is a modal property: because of what he is, he has certain capabilities and limitations, his pattern contains certain possibilities…
Modal properties are the causal consequences of a particular pattern of matter-energy in space-time… Even if Ed Norton never suffers the horrible fate of falling through a meat grinder, we can say that if he did so, he would be destroyed, and what came out the other side would not be Ed Norton, but a pile of good. We can say this because the pattern of matter and energy instantiated by Ed Norton is such that this is what will result when it collides with the pattern of matter and energy instantiated by a meat grinder. It is a geometric inevitability.
(“Instantiated”, by the way, is a fancy word that means “to represent an abstraction with a concrete example in the real world.” So, the idea of “Ed Norton” is instantiated in the real world by such things as a particular set of arms and legs and water and bacteria and neural connections.)
So, Ed Norton’s modal property of being unable to pass through a meat grinder and remain what we call “Ed Norton” is simply our prediction of what will happen if Ed Norton goes through a meat grinder – namely, that what comes out the other end will lack the arrangement of matter-energy that we refer to as “Ed Norton.” Instead, it will possess the arrangement of matter-energy we might call “pile of goo.”
All modal properties – properties about possibility – are like this. They are all causal predictions about what will happen if one pattern of experience interacts with another pattern of experience in a particular way. So, we need not dream up a special non-natural realm for modal properties, either.
Abstract objects do not “exist” as anything more than potential patterns of experience. For this reason, I prefer not to call them abstract objects, which makes it sound like they are things that might exist somewhere. I prefer to call them abstractions, which is clearer.
Carrier ends section III.5 What There Is with some thoughts on reductionism.
Carrier believes that literally everything can be reduced to matter-energy in spacetime. Why does he believe such an arrogant notion? Well, simply because that fits with everything we have discovered so far, and nothing we have discovered contradicts it.
We’ve discovered that the solar system reduces to masses under gravity in spacetime, which Einstein reduced simply to masses in spacetime, which now look as though they may reduce simply to spacetime geometry. We’ve discovered that genetic “factors” reduce to proteins, which reduce to chemicals, which reduce to atoms, which reduce to subatomic particles. We know that society reduces to humans, which reduce to cells, which reduce to chemical machines, which reduce to atoms, which reduce to subatomic particles. Think of that! Continent-sized societies reduce to subatomic particles! Everything we’ve discovered so far fits this pattern.
But this doesn’t mean that humans “are just” subatomic particles bouncing around randomly. There is obviously a difference between Ed Norton and “pile of goo,” even if both are made of the same subatomic particles. Why? Because the arrangement is different.
A different arrangement can be causally different. Ed Norton interacts with other things in the universe quite differently than a pile of goo does. Likewise, a tree affects things differently than a pile of ash or a stack of boards.
Carrier finishes with two examples: a game of chess and Microsoft Windows.
A game of chess is reducible to binary mathematics, so a computer can play chess. But a pawn is not “just” electrons on a microchip. The arrangement of those electrons makes causal, modal, and other differences.
…it is manifestly false to say that the pawn doesn’t exist. It plainly does – it just took your knight! It is just as absurd to say that the pawn exists in some higher abstract reality. As any… computer engineer can show you, it only and entirely exists as a pattern of electrons in motion on a grid of transistors. Yet that pattern is causally different than any other, distinctly a pawn in its placement and behavior in the game.
Or consider using Microsoft Windows which, in an earlier version, was wholly reducible to DOS, which in turn was wholly reducible to 0s and 1s, which in turn were reducible to electrons on a grid. Windows was composed of nothing else but electrons on a grid, and yet these things called “folders” and “icons” really do exist: they are causally distinct from other arrangements of electrons on a grid.
Next, we are ready for section III.6 The Nature of Mind.