Let’s start with a couple propositions:
The Identity of Indiscernibles
Two objects are identical when they share all the same properties.
The Indiscernibility of Identicles:
If two objects share all the same properties then the two objects are identical.
At a glance, they both seem obvious enough that even mentioning them feels like a waste of time. Things get a little more complicated, however, when you consider the “position” of a property, since it’s also agreed upon by all that no two objects can occupy the same space at the same time. If object x and object y truly share all the same properties, including position, then x and y are truly “identical” in that they are the same object. Even this isn’t terribly controversial (although some have argued against it), but when you apply it to real life something odd can occur, as seen in the following example.
Miami Rick bought a jacket two years ago and wore it often. At some point during those two years common wear and tear caused a button to fall off and disappear down a sewer drain. The Identity of Indiscernibles tells us that the jacket he bought two years ago and the jacket he now wears are identical (they are, in fact, the same object) only if they share all the same properties, but the jacket he bought two years ago had five buttons and the jacket he now wears has only four. Miami Rick knows the Identity of Indiscernibles is pretty hard to argue with, yet it’s clearly an affront to common sense to say that the jacket he now wears isn’t the jacket he bought two years ago. The damned receipt is still in the pocket, after all. But try as he might, he can’t get around ∀F(Fx ↔ Fy) → x=y.
Attempting to resolve this dilemma may seem like a pointless exercise since no rational person would ever really assert that the jacket Miami Rick now wears is not the jacket he bought two years ago. In every sense that matters, it is the same jacket. One jacket didn’t disappear from existence and birth another different jacket simply by the act of losing a button. But the logic behind the Identity of Indiscernibles seemed, at the start, to be so obvious that it was silly even to point it out. It’s around this point that most people decide metaphysics is a waste of time and worse yet one that starts problems where none had previously existed. It’s easy to see why the men and women that study the hard sciences roll their eyes.
When Gottfried Wilhelm Leibniz began his work on metaphysics, he started with a pretty simple idea. For any proposition to be true, the subject must contain the predicate. “The sky is grey,” for instance, can only be considered to have any truth to it if the sky (subject) is indeed grey (predicate). This also seems so natural and obvious that it probably didn’t need to be mentioned, but these sort of propositions contain a reference either implicit or explicit to a set of spacial and temporal coordinates. The statement can only be true if the sky at x location is actually grey at the time the proposition is made. Even so, this appears to add only a tiny bit of complexity to an otherwise boringly simple idea, but when you consider a subject like Miami Rick one may realize that his list of predicates must be extremely large, perhaps infinitely so, because it would contain every thing he’s ever done or will do, has been or will ever be. The full list of predicates — the complete demonstration of Miami Rick, as Leibniz calls it — is large enough that no human could ever see it in its entirety.
Leibniz believed that there must be a reason for things to be the way they are and not otherwise, because if this were not the case then the universe would be completely random and things like science and math would be impossible. As such, each predicate a subject contains must be explained by another predicate, which does indeed seem the case when one observes Miami Rick. In the proposition “Miami Rick is ill,”, the predicate (in this case “is ill”) can be explained by other predicates such as “licked a doorknob at a bus station two days ago,” which itself is explained by predicates such as “wanted to know what a doorknob tastes like” and “has poor impulse control.”
There’s a lot more to be said of Leibniz’s metaphysics, but let’s focus on something relevant to our initial dilemma with Miami Rick’s jacket. Leibniz claims that Miami Rick’s complete demonstration would necessarily include everything he’s ever done or will ever do. From the Internet Encyclopedia of Philosophy:
If the complete concept of the subject (that is, all of its true predicates) together constitutes a complete network of explanation, then these explanations can be followed forward and backward, so to speak, at least in principle. That is, working forward, one could deduce that Caesar will cross the Rubicon from all the predicates that have been true of him; or, working backward, one can deduce from all those predicates true of Caesar at his death the reasons why he won the battle of Pharsalus. The “whole demonstration,” then, is the revelation of the logical structure of the network of explanations that make Caesar who he is.
If any complete subject such as Caesar or Miami Rick is in actuality a network of innumerable predicates stretching through time, then the mystery of Miami Rick’s jacket is easily solved. The collection of predicates that represented the jacket at the time it was bought was by no means “the jacket” in the sense that it wasn’t the complete jacket. The complete jacket is all the true predicates it has, had, or will ever have. What was bought two years ago is merely a piece of the complete jacket, a jacket that stretches through time and is only perceived in three dimensions rather than the four it actually inhabits. Human minds are not able to perceive the complete jacket, we can see only a three dimensional cross-section of a four dimensional object. Thus we arrive at the Doctrine of Temporal Parts.
By this point some readers may insist that, while all of this is certainly very interesting, it is in no way important or useful. Others may argue that the notion of Free Will is actually very important, since our justice system depends on the notion of people having a choice and as such deserve to be held accountable for their crimes, and Leibniz’s model of reality seems to be rather deterministic. If our complete demonstration exists (even if only viewable by God) it would seem our actions are already determined and our poor choices are unavoidable. Leibniz denies this and does a fine job reconciling the notion of Free Will with his model, but I personally think the true importance lies in the conception of time his model illustrates.
Fellow Disinfonaut, Chaos_Dynamics, recently posted an article from Physics Central that references the very same philosopher that made Russell and Whitehead swear off metaphysics forever (an event briefly described in Part 1). The article also states, “Recently, physicists have revisited a topic with modern philosophical origins dating over a century ago: the unreality of time. What if the passage of time were merely an illusion?” This stuck with me for a number of reasons. First, it bears noting that the concept “unreality of time” is a great deal older than a century. McTaggert was merely the first European to address a subject that had been discussed at length in eastern mystic traditions, but because “eww brown people,” McTaggert apparently gets the credit from westerners. We can ignore that slight, however, and focus on this bit:
But McTaggart’s entire argument may help us better understand strange physics at the intersection of quantum mechanics and general relativity. In an attempt to reconcile these two theories, some well-known physicists have developed theories of quantum gravity that imply the world lacks time in a fundamental way.
Leibniz’s metaphysics treats time not as something that flows, but as simply another dimension, another geometric axis requiring coordinates to navigate. When reading about modern particle physics, which I’m sure is something that we all do frequently, one may be confused at the notion of a positron, aka the “antielectron,” which Richard Feynman once famously described as “an electron moving backwards through time.” In general, retrocausality makes a hell of a lot more sense when seen through Leibniz’s perspective. Things like tesseracts and 3-spheres are also a lot easier to conceptualize in this manner too, and Leibniz got there long before Taggert or Feynman.
This may sound like a bragging, like a sort of “metaphysics got there first, dickheads!”, but let’s be real. What we know as “science” today was in its infancy when Leibniz was writing, so it’s not much of a victory for metaphysics that Leibniz was conceptualizing four-dimensional structures three hundred years ago. Sure, physics wasn’t doing that, but only because physics was still being invented by Newton on the other side of Europe at the time.
But surely this is what metaphysics is for, right? Exploring how the world is, rather than how it appears to be? Metaphysics can explore places we haven’t reached yet, can hew a rough path through the wilderness we have yet to navigate. It’s been doing exactly that for the last few thousand years. While the Verificationists probably overstepped their bounds when they declared that a statement only has meaning if it can be proven either true or false, it is right and proper for engineers and chemists and others of their ilk to focus on problems that can be answered with a simple “yes” or “no.” An engineer that, when asked if his bridge can support the weight of heavy automobile traffic, answers “well, yes and no” will have an understandably short career. It’s best for us all if they keep their focus on the material world.
As I see it, the primary problem with metaphysics is that any asshole can do it. It takes no time at all to come up with a theory that is completely ridiculous yet appealing to those with little in the way critical thinking abilities, i.e. the person who thinks that science and religion are both matters of “faith” because they both “come from books written by human beings.” This is why we end up with several books that are fit only for doorstops and something with which to beat suspects in custody so as not to leave any visible bruises. Sure, we can’t all be Leibniz; the man was brilliant in a way that doesn’t come around very often. But when asked if metaphysics really matters, I think history has shown that humanity needs people to look beyond what appears to be.
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