Einstein’s theory of special relativity has been seen as having profound philosophical consequences by some. Persisting objects, for example, including the human person, may be seen as a kind of line (as opposed to a line or point) that stretches from one point to another, as a four-dimensional worm. So Michael Lockwood in his book “Mind, Brain, and the Quantum: the Compound ‘I'”:
“Time has become a fourth dimension; and an individual persisting object, such as a human body, is to be conceived as a four-dimensional ‘worm’, laid out in space-time, each three-dimensional time-slice of which corresponds to the object as it is at a particular moment in its history. (The set of space-time points occupied by this ‘worm’ — if one ignores the fact that it has spatial thickness as well as temporal length — is known as the object’s world-line.) In this conception there is no universal march or flow of time. There cannot be, because there is no universal present; and consequently there is no universal past or future…
This makes trouble, incidentally, for a conception of time that many philosophers from Aristotle to the present day have wished to defend, according to which the future is open, partially undefined, in contrast to the past, which is fixed, closed, a fait accompli. The motivation for such a view lies mainly in a desire to defend free will, to enable us to regard the future (in words I once saw in the Reader’s Digest) as ‘not there waiting for us, but something we make as we go along’. In the context of relativity (as is pointed out by Hilary Putnam), such a view appears not so much false as meaningless.”
As we will come to see, the idea of a human as a four-dimensional “worm” existing as a kind of horizontal, temporal length, begins to look very similar to the theory of monads proposed by Leibniz, articulated within the context of his metaphysics and perspectives on space and time. Leibniz arguably anticipated such a view in his metaphysics (although the human would form a ray rather than a line segment, in light of his Christian belief in the immortality of the human soul). As Lockwood points out, according to this view, the human being is no longer a kind of point that moves into an uncertain future, but a compound substance or object which occupies a certain temporal “length.”
A brief exposition of Leibniz’s metaphysics is in order. Let us begin at his understanding of what constitutes truth, which forms the bedrock of his metaphysics. For Leibniz, a proposition is true if and only if its predicate is contained in its subject. Such a notion is initially not that revolutionary, but Leibniz takes it to an unusual place. The notion of “being contained” is virtually or implicitly the case with other truths.
For example, consider the truth “Felipe is petting a chow chow.” One would think that this is true only if it refers to a real world in which Felipe is actually petting a chow chow. However, for Leibniz, if one knew everything there is to know about Felipe (that is, to use his language, if we had a “complete concept” of Felipe), one would also know that he is petting a chow chow at the moment. Therefore, this proposition si not true not merely because it has a reference to the world, but because someone has a complete concept of Felipe, who is the subject of the proposition, and the subject of the proposition “Felipe” contains, as a predicate, his fact of petting a chow chow at a specific point in space-time.
True, it may be the case that one knows that Felipe is petting a chow chow because someone has witnessed him doing this, but the fact that one discovers this truth in this way doe not make the proposition true, and therefore, a piece of knowledge, because of such observation. Instead, one must distinguish the pragmatic, methodological or epistemological issue of how one finds out about this truth from the metaphysics of the truth itself.
In fact, Leibniz insists that this statement is true for all time. It is true whenever the statement is made at all. So for example, the proposition “Felipe is petting a chow chow” is true, not merely on the date on which he happens to be doing so on January 5th, 2003, but it is also true a thousand years ago before Felipe even existed, and it will remain true a thousand years after he has done so. This is the case even if no one knew about Felipe before he was born, and everyone will have forgotten him a thousand years after he has died.
As we have seen for Leibniz, truth is defined in such a way that the predicate is contained in the subject. Of course, this means that there is an extraordinarily large number of predicates for any individual person. This is because it includes every last thing they will ever do, every state of existence they will have, and the relation they will bear to every single other object or state during every single moment in their existence.
But how do these predicates come to consist in one subject? The predicates are not random. For any subject, each predicate “virtually” or implicitly contains all future predicates, and results from all antecedent predicates. Basically, each object is constituted by one long, propositional definition or explanation. Felipe’s petting a chow chow, for example, is explained by being initially struck by how cute they look at the age of 5. The proposition which explains this moment is explained by the fact that his dad resolved to take him to a kennel one day when Felipe was 3. Likewise, these predicates virtually or implicitly contain the future predicate that Felipe will pet the chow chow.
For Leibniz, the human person is an enduring proposition explanation which persists through its temporal “length” and which explains its relation to every other aspect of existence. This follows from his revolutionary philosophical principle known as the principle of sufficient reason, according to which everything has a sufficient reason by which it can be explained. Predicates that are true of a subject hang together as an explanatory network, in which each predicate is given its sufficient reason by an antecedent explanation, and which virtually or implicitly contains all future predicates. One can speak of a proposition, in the words of Leibniz, laden with the past and pregnant with the future.
This principle of sufficient reason accounts for why Leibniz wants to use the phrase of “completing the whole demonstration” of a subject. This has reference to the notion of having a “complete concept” of a subject like Felipe, in which one has exhaustive knowledge of all of the explanatory predicates of Felipe and the relations which he, as a subject, bears to everything else. A complete concept of a subject consists of a complete network of explanations, such that the principles can be deduced forward and backward, which each predicate being entailed by previous ones, and entailing future ones. The subject can be deduced propositionally forward and backward ad infinitum.
Does this mean that it was logically necessary of the subject “Felipe” that he pet a chow chow? Indeed, some have suggested that Leibniz denies free will, and that Felipe’s petting of a chow chow is simple a domino-like propositional predicate in a series of these which determines everything he has ever done or ever will do. Leibniz certainly did not think that Felipe’s act was necessary in the purely analytic sense that “A = A.” To say that A does not equal A would be to violate the law of non-contradiction, which Leibniz insists, would violate the best of all possible worlds (since God must ordain the maximally perfect world, for Leibniz, and since this world, he argues, contains the law of non-contradiction). History would have been different if Felipe had not petted a chow chow, but it does not entail a logical contradiction the way that A = not-A would; in the strong sense, Felipe’s properties are not logically necessary.
For Leibniz, complete concepts are always concepts of existing substances; that is, they are complete concepts of things which really exist. To be the individual Felipe, therefore, is to be such as to have a notion which includes everything that can be truly predicated of the subject Felipe. Therefore, one can say that “a substance is a complete concept made real, and a complete concept is a real substance expressed or “perceived” in thought.” Indeed, just as for any one predicate, the complete concept contains other predicates which explain that predicate, so also, for any given attribute or property of a substance, the complete individual substance will itself be the explanation for this property or attribute. There are a great many complex reasons for why Felipe decided to pet a chow chow, but they can all be explained by saying that petting a chow chow is the kind of individual that Felipe is.
The “complete concept” of Felipe, however, cannot explain itself exhaustively. From a metaphysical or ontological perspective, Felipe himself cannot provide any explanation of why he should have existed at all. Felipe is a contingent being. It is God alone who is a necessary being. Felipe could have been otherwise if God had created him otherwise. It is conceivable that Felipe could have never existed at all, or at least that he had not decided to pet a chow chow. Indeed, the sum total of the aggregate of all spatiotemporal substances are contingent. They did not have to exist. The totality of contingent things do not explain themselves, but they are explained by God. Why did God decided to create this particular world of contingent beings rather than another?
If the creation of the universe’s particular totality of contingent beings is arbitrary, however, then it does not constitute a sufficient reason for its existence (According to Leibniz). Instead, God created this particular universe because it constitutes the best of all possible world. Some of his critics have argued that such a necessitarian account of the best of all possible worlds rules out the possibility of free will, and issues in a thoroughgoing determinism. Indeed, deterministic philosophers and theologians such as John Piper and Jonathan Edwards have appealed to Leibniz’s principle of the best of all possible world to advocate such a thoroughgoing determinism. In fact, many have argued that Einstein’s theory of special relativity issues in a kind of determinism for reasons closely linked with Leibniz’s own pre-Einsteinian notion of space and time as purely relative.
In the early 18th century, Leibniz and Samuel Clarke exchanged letters, with Newton probably having a hand in the composition of the latter’s letters. Newton and Clarke argued that space and time must be absolute, fixed and constituted by background constants. Newton believed that substances must exist in their own right rather than purely in terms of their spatiotemporal positions. For an object to move, there must be a manner of deciding upon a frame of reference for such a motion. While in the case of linear motion, the frame of reference does not matter, acceleration in a curve (such as, for Newton, the water forced by the sides of a bucket to swirl in a circle and then rising up the sides of the bucket) could only have a single frame of reference. This is because the water rising up the sides of the bucket can be comprehended if the water has its motion in a stationary universe. It makes no sense to think of water as stationary in a spinning universe. Therefore, this curved acceleration requires the notion of absolute space, according to which fixed and distinct frames of reference are possible.
Leibniz rejected the notion that space and time are substances in their own right. Empty space would be a substance lacking properties, and would be one which God would be incapable of destroying or changing. More importantly, however, Leibniz argued that, according to the principles of both sufficient reason and non-contradiction, there was the principle of the identity of indiscernibles. According to this principle, entities which are indiscernible with respect to their properties are identical. Although two substances, such as leaves, may look identical, they are not. For two substances to be alike in every respect means that they are not two distinct substances. According to the principle of sufficient reason, if two objects were distinct, there would be no sufficient reason or possible explanation for why the first is what, where and when it is and the second what, where and when it is rather than the other way around. If one postulates the existence of two objects which differ in number only, then one postulates the existence of an absurd universe in which the principle of sufficient reason is false. This would impugn the wisdom of God, for Leibniz, and therefore, the notion of absolute space-time is absurd.
For Leibniz, space cannot be absolute. If space is absolute, that means that every region of space would be indiscernible for every other and spatial relations would be seen as extrinsic. If this were true, then it would be possible for two substances to be indiscernible yet distinct purely in terms of existing in distinct locations. This would, however, violate the law of the identity of indiscernibles. Space, therefore, cannot be absolute. Absolute space would also violate the principle of sufficient reason. If space is absolute, there would be no sufficient reason for why the entire universe was created “here” rather than such and such a length to the left or the right. In other words, no region of space would be discernible from any other. Therefore, this notion is absurd because it violates the principle of sufficient reason.
Leibniz replaced Newton’s theory of absolute space-time with his own relational theory. The location of an object, for Leibniz, is not a property of an independent space, but is a property of the object itself. Indeed, two objects could be in every other respect identical, but would differ from each other solely by occupying different places in space. This is because space and time are comprehensible purely in terms of their spatio-temporal relations to other objects. This is because space and time are intrinsic or internal, aspects of an object, rather than being extrinsic, as in the case of Newton. To move something in space-time, therefore, involves changing that substance itself rather than changing something about an extrinsic space-time. There is therefore no such thing as absolute space or time. Location necessarily predicates something of an object or event relative to other objects or events. It is an attribute of the object or event itself. Space and time are also illusory.
They are not substances. Instead, they are ideal. Indeed, for Leibniz, space and time are metaphysically illicit ways of perceiving substantial relations. Nevertheless, he argued, they are well-founded illusions of a substance’s internal properties. Such illusion and science are fully compatible. God is capable of grasping the complete concepts of everything at once, which, as we have seen, constitutes the totality of their relations to everything else. Leibniz uses the analogy of using a blueprint to build something in his correspondence with Clarke-Newton. Space and time are not “out there,” for Leibniz. The reality is that the totality of all things look as a kind of static blueprint to God, with space constituting nothing but co-existent objects and time referring simply to a successive order of events.
To speak of spacetime, for Leibniz, is to speak of the hypostatizations of ideal relations. These relations are real insofar as they represent real differences in substances. It is an illusion and a mistake, however, to take space and time as things in themselves or to take spatio-temporal relations as irreducibly exterior to objects.
“Take the analogy of a virtual reality computer program. What one sees on the screen (or in a specially designed virtual reality headset) is the illusion of space and time. Within the computer’s memory are just numbers (and ultimately mere binary information) linked together. These numbers describe in an essentially non-spatial and temporal way a virtual space and time, within which things can “exist,” “move” and “do things.” For example, in the computer’s memory might be stored the number seven, corresponding to a bird. This, in turn, is linked to four further numbers representing three dimensions of space and one of time–that is, the bird’s position. Suppose further the computer contains also the number one, corresponding to the viewer and again linked to four further numbers for the viewer’s position, plus another three giving the direction in which the viewer’s virtual eyes are looking. The bird appears in the viewer’s headset, then, when the fourth number associated with the bird is the same as the viewer’s fourth number (they are together in time), and when the first three numbers of the bird (its position in virtual space) are in a certain algebraic relation to the number representing the viewer’s position and point of view. Space and time are reduced to non-spatial and non-temporal numbers. For Leibniz, God in this analogy apprehends these numbers as numbers, rather than through their translation into space and time.”