A Bayesian Argument for the Existential Inertia Thesis

Why do objects persist in existence instead of ceasing to persist? Consider these two competing theses:

• According to existential inertia theses (EIT), necessarily, temporal objects will continue to exist in the absence of external sustenance and causally destructive factors.
• According to existential expiration theses (EET), necessarily, temporal objects will cease to exist in the absence of external sustenance.

So, which theory best explains why objects persist in existence instead of ceasing to persist? We should favor EIT over EET.

Given a Bayesian characterization of counter evidence, if the probability of q given p is less than the probability of q unconditioned, then q is counter-evidence for p—(∀p)(∀q){[P(q|p)<P(p)] ⊃ Cqp}.

Let us have p stand for ‘EET,’ and let us have q stand for ‘objects persisting in existence instead of ceasing to persist.’ Suppose some object, O, begins to exist at some time, t, and persists in existence at some later time, t’. Furthermore, O exists at all times between the open interval (t, t’). At any time, t_n, within the open interval, the causal sustenance relation that O stands in could fail to hold. Why? Because the relatum standing in the causal sustenance relation with O could cease exercising it’s causally sustaining activity or itself fail to exist. This entails that for any given world, w, in which O persists through the open interval (t, t’) and is then causally destroyed by something, there are worlds in which that object ceases to exist at some point earlier than w due to the withdrawal of sustenance. There is always a non-0 probability that, given the same initial conditions, the relatum standing in the causal sustenance relation with O could fail to stand in that relation to O.

Suppose the relatum standing in the causal sustenance relation with O were God. Given traditional theistic commitments, God is free to sustain O or refrain from doing so. Thus, there is a non-0 probability that O could cease to exist, since God could fail to sustain O in existence. Thus, the probability of q given p is some (arguably low) non-0 value, but it is not 1.

Now, let us have p instead stand for ‘EIT.’ Suppose some object, O’, begins to exist at some time, t, and persists in existence at some later time, t’. Furthermore, O’ exists at all times between the open interval (t, t’). At any time, t_n, within the open interval, O will never fail to persist—apart from the causal activity of some external destructive factors, of course. Why? Because O’ does not stand in any causal sustenance relation, and will only cease to exist given the causal exercise of some external destructive factors upon it. And this is necessarily the case. Thus, the probability of q given p, in this case, is 1. Thus, EET is counter-evidence for q.