Ontology: the Study of Being

An excerpt from the online hypertext Human Knowledge: Foundations and Limits.

Understanding of reality and existence is built up according to experience from elements provided by logic: terms, their properties and relations, and the attributions and inferences that can be made among them.  From these can be derived the ontological notions of causality, existence, time, identity, and space.

circumstance is a set of terms and their fixed properties and relations that as a whole can be distinguished from other such sets and identified with itself. A change is a relation between an ordered pair of distinguishable circumstances and is defined by the two circumstances that it relates. An effect is a change that can be attributed. A cause is that to which an effect can be attributed in whole or in part. An influence is that to which an effect can be only partly attributed.

necessary cause is one which can be inferred from the effect. A sufficient cause is one from which the corresponding effect can be inferred.  To determine is to be the necessary and sufficient cause for. Possibility is the property of not being contradicted by any inference. Logical possibility is the property of not contradicting the laws of logic. Physical possibility is the property of not contradicting the laws of nature.

Is causality an illusion? Does every effect have a cause, or do some effects have no cause? Can there be a cycle of causality, in which an effect both precedes and contributes to its cause? Can one know the answers to these questions?

The universe is the maximal set of circumstances that includes this statement and no subset of which is causally unrelated to the remainder. To exist is to have a causal relationship with the rest of the universe.  An entity is any term that exists. Two circumstances are causally unrelated if neither could ever influence the other.

It is unparsimonious to say other universes exist. One could imagine a set of circumstances causally unrelated to the maximal set that includes this sentence, and could choose to consider it a separate universe. But to say those imagined circumstances "exist" is to cheapen existence from causal reality to mere imaginability. An imagining does not establish the existence of the thing imagined.

Why is there something rather than nothing? Is there an objective purpose for that which exists? How could one recognize an answer to these questions?  Are these questions meaningless?

Humans do not know why there is something rather than nothing, or if the question is even meaningful.   If this question has a parsimonious answer, it must consist in a self-explaining fact or cycle of facts.  A candidate for such a fact would be the concept of God in the Ontological Proof, but that proof is not convincing.  Humans do not know any such fact(s), or even if they could possibly exist. If it is asserted that non-existence is more likely or natural than existence, one could ask why this asserted tendency (toward non-existence) itself exists.

A possibly meaningful (but unparsimonious) answer to the Ultimate Why is that the universe exists (more precisely, is perceived to exist) roughly because it is possible. The reasoning would be as follows. Absolute impossibility -- the state of affairs in which nothing is possible -- is itself not possible, because if nothing truly were possible, then absolute impossibility would not be possible, implying that at least something must be possible. But if at least one thing is possible, then it seems the universe we perceive should be no less possible than anything else. Now, assuming that physicalism is right and that qualia and consciousness are epiphenomena, then the phenomenology of a mind and its perfect simulation are identical. So whether the universe we perceive existed or not, it as a merely possible universe would be perceived by its merely possible inhabitants no differently than our actual universe is perceived by its actual inhabitants. By analogy, the thoughts and perceptions of a particular artificial intelligence in a simulated universe would be the same across identical "runs" of the simulation, regardless of whether we bothered to initiate such a "run" once, twice -- or never.

Thus, the universe might merely be the undreamed possible dream of no particular dreamer.

An event is a change that cannot interestingly be subdivided into constituent changes. Time is the ordering of events according to the potential of some events to causally influence other events. If (as in this universe) causal influence propagates through space only at finite speed, then some events can be far enough apart in space as to be in principle unable to influence each other. In this case time is a partial order on events instead of a total order.

An instant is a point on a linear continuum onto which events have been associated in a particular reference frame according to their order in timeDuration is a measure of the separation between two instants in time determined by counting intervening events of the kind that recur in proportional numbers to each other.  Examples of such events are the swings of a pendulum or the vibrations of an atom.

Eternity is an entire linear continuum of instants. Thus by definition there is between any two instants another instant.  However, it is not necessary that between any two events there is another event.  Nor is it necessary that there be a first event, even if the past is of finite duration.  Just as there is no smallest positive real number, there might be no first event, because there might be no event associated with a first instant (t=0).  Instants are mathematical constructs that do not always have an associated actual event.

The future is, from the perspective of a particular event, the set of all events that the event potentially influences.  The past is, from the perspective of a particular event, the set of all events by which the event is potentially influenced.  The present is, from the perspective of a particular event, the set of all events simultaneous with it.  Simultaneity is a relation enjoyed by two events if and only if they share identical sets of past and future events.

Hypertime. Time is often said to pass or flow or to be moved through. This metaphor of motion is misleading, because motion is spatial displacement over time, measured for example in meters per second. But a 'motion of time' measured in seconds per second is nonsensical, and so temporal displacement 'over time' requires a notion of hypertime, measured in seconds per hyper-second. This is no help, because hypertime too will be said to flow -- through hyper-hypertime. There is no reason to posit an absolute or universal or extra-temporal or distinguished present that flows or passes or marches and continuously turns absolutely future events into absolutely past ones.  Past, present, and future are relations with a particular event and are not absolute properties in themselves.

Changing the future. The present can affect a future event, but it cannot "change" a future event. An event is itself a change and time is no more than an ordering of these changes. If changes themselves can change, these hyper-changes are hyper-events that can be ordered into hypertime. Events cannot change over time because events are defined by their pre- and post-conditions. To talk of different post-conditions for an event is really to talk of a different event, just as to talk of different cardinality for a number is really to talk of a different number. This does not imply determinism, because determinism is a statement about inference and not about inevitability.

Determinism is the thesis that a sufficient knowledge of any particular set of circumstances could be used to completely infer any subsequent circumstance. Some humans take determinism to be the thesis that the future is already decided, that the present was always going to be the way it is, that statements about probability and possibility are merely statements about one's incomplete knowledge, and that only actual possibility is that which is already inevitable.

Such a notion of ontological determinism is different from epistemic determinism only if there is a hypertime in which different points of normal time can "already" coexist.  A notion of ontological determinism that is strictly different from epistemic determinism can have no practical consequences.  As a difference that makes no difference, ontological determinism is a thesis that parsimony demands be rejected.  Adopting the thesis makes as much sense as adopting the thesis that the universe is five minutes old.  It is inconsequential -- and thus meaningless -- to say the future is already decided.

Some humans argue that if determinism is true, then no argument is to be considered valid as it is simply a train of statements following a predestined track.  First, this misconceived argument applies as well to itself as it does to any other argument.  Second, even in a deterministic system there can arise processes that tend to produce certain results. If viable organisms can arise, reproduce, and evolve due to natural selection in a deterministic universe, then surely viable arguments can arise, reproduce, and evolve due to competition in a marketplace of ideas.  The viability of an idea or argument is closely related to its epistemological validity, and so the opposite misconception could occur: an argument might be considered more valid merely because it is at the end of so many predestined tracks.

Time Travel. Time travel would imply the existence of either hypertime or circular causality. Humans have no reason to think either exists.

Temporal Anisotropy. In a short video clip showing two billiard balls bouncing off each other, forward and backward in time are indistinguishable if one ignores friction and inelasticity.  In a longer video of a billiards break, the future is the end in which the balls are no longer in a nicely ordered triangle. If causes can be attributed to effects as easily as effects can be attributed to causes, then causal laws do not distinguish past and future, and the future for an event is the direction of increasing disorder in the system.  Traces and memories of the past are a localized increase in order at the expense of an increase in system-wide disorder. Due to statistical considerations, some systems can cycle between order and disorder.  In such systems the direction locally considered to be future can vary over the timeline of the system.

Temporal anisotropy is not determined by the expansion of the universe, nor by the direction of electromagnetic radiation. For electromagnetism, the attribution of influence works equally well in both time directions. There is no inherent difference between the absorption and emission of a photon. Boundary conditions are logically possible in which photons are set in motion without having been emitted from anything, and which converge in shrinking spheres on an anti-emitter.

Identity is the relation that obtains between two entities (or terms) that are the same instance, i.e., that could never be counted as two.  Leibniz's Principle of the Identity of Indiscernibles states that if there is no possible way to distinguish two entities then they really are the same entity.

A given entity is identified through time with its closest close-enough continuous-enough continuer. A continuer is an entity which is similar to a previous entity and exists because of it. A continuer is close enough if it retains enough of the original entity's properties. A continuer is closest if it retains more of the original entity's properties than any other continuer. A continuer is continuous enough if there is no extraordinary discontinuity in its relationship to the original entity.

Space is the seemingly boundless and continuous three-dimensional extent in which all matter is located and all events occur. It seems logically possible that space could be not only boundless (like the surface of a sphere) but infinite (like an infinite plane). It even seems logically possible that space could be locally discontinuous.

Do space and time have absolute existence independent of their contents? Or are they simply a system of relations among entities and events? Is there a way to answer these questions, or would any answer not make a difference?