Maverick Philosopher

I haven't yet said anything particularly illuminating about the criteria of viciousness, the criteria that would allow us to sort infinite regresses into the vicious and the non-vicious. I should address the problem of criteria.  But in this installment I want to suggest that we may need to make a tripartite distinction among vicious, benign, and virtuous regresses.  If a regress is not vicious, then it is non-vicious. But it may be that non-vicious regresses come in two kinds, the benign and the virtuous.  Here is a crude analogy.  Fearing cancer, I have a certain growth checked out by a medico.  It is determined that the growth is not malignant, but benign. But no one will say that the growth serves a useful purpose.  If something is harmless, it does not follow that it is helpful.  And if something is not vitiating, it does not follow that it is 'empowering.'

Thus I am suggesting that we not refer to non-vicious regresses as virtuous, as some writers do.  For if a regress is merely benign or harmless or innocuous, it does not follow that it is explanatorily useful or helpful.  And it may be that there are some infinite regresses that serve an explanatory purpose.  These would deserve to be called virtuous.  But we need some examples.

I don't endorse the following example, but it is worth thinking about.  Suppose we want to explain why the universe exists, and we want to do so without recourse to anything transcendent of the universe: we seek a satisfactory immanent explanation.  Suppose further, contrary to current cosmology, that the universe always existed.  Let's also assume that to explain the parts of a whole is to explain the whole.  To adapt an example of Paul Edwards, suppose the Three Stooges are hanging out at the corner of Hollywood and Vine on a certain afternoon.  To explain why the boys are there at that time it suffices to explain why Larry is there, why Moe is there, and why Curly Joe is there.  Having explained why each is there, one has explained why the trio is there.  It would be senseless to demand an explanation of why the trio is there after one has been given satisfactory explanations of why each member of the trio is there.  The trio is not something over and above its members.

Applying this Hume-Edwards principle — the principle that to explain the parts of a whole is to explain the whole — to the universe, one could say that to explain why the universe exists it suffices to explain why each phase of the universe exists, so that, if each phase of the universe has an explanation, then eo ipso the universe has an explanation.  Now if the universe is temporally infinite in the past direction, and each phase of the universe is caused by an earlier phase, then every phase of the universe has a causal explanation in terms of an earlier phase.  Since no phase, no temporal part, of the universe lacks an explanation, and since the universe as process just is the whole of these temporal parts, and since to explain the parts of a whole is to explain the parts, it seems to follow that the universe is self-explanatory, that its existence can be accounted for in wholly immanent terms. It looks as if a beginningless universe could be causa sui. Let us assume arguendo that this very bad argument I have just inflicted on you is not bad.

In this argument it appears that the infinite regress of causes does positive explanatory work.  For if there were a temporally first event, or a temporally first phase of the universe, then one could demand an explanation of it, and this demand could not be immanently satisfied.  But if every event or phase has an explanation in terms of an earlier event or phase, then this demand cannot be made.  What we have then is a putative example of an actually infinite regress that is not merely harmless, but positively helpful unto explanation.

Hence my suggestion:  we ought to make a three-fold distinction among vicious, benign (harmless), and virtuous (helpful) infinite regresses.  And thus we ought not conflate benign regresses with virtuous regresses.  Virtuous regresses are a proper subset of benign regresses (since every explanatorily hepful regress is explanatorily harmless), which implies that there are benign regresses that are not virtuous.

Now the example I gave of a virtuous infinite regress is not a very convincing one, or at least it is not convincing to me.  Are there better examples of virtuous infinite regresses, infinite regresses that do positive explanatory work?

What say you, Jan?  Francesco?

What is the difference between a vicious and a benign infinite regress?  We ought to look at a number of examples.  Here is one.  An entailment of a proposition p is any proposition that is a logical consequence of p.  Now consider

1. Every proposition has entailments.

2. To know a proposition one must know its entailments.

(1) gives rise to infinite series.  The entailments of a proposition are themselves propositions, so that if every proposition has entailments, then for every proposition there is an infinite series of propositions.  For example, p entails ~~P, which entails ~~~~P, and so on ad infinitum. There is nothing problematic here.

(2), however, engenders a vicious infinite regress.  For if to know a given proposition I must know its entailments, then to know a given proposition I must know infinitely many propositions.  But I cannot know infinitely many propositions.  So (2) implies that I cannot know any proposition. 

What makes the regress vicious in the second case?  What does viciousness consist in? It has to do with (2)'s being explanatory.  (2) proposes a philosophical explanation: one knows a proposition by knowing its entailments.  (2) proposes a theory as to what knowing a proposition consists in.  But the explanation is faulty.  Suppose p entails q which entails r which entails s, and so on.  The theory proposes that in order to know p, I must know q. But to know q I must know r, and so on.  This implies the impossibility of my knowing p.  Viciousness, then, is the property of being explanatorily unsuccessful.

Perhaps we can hazard the following general formulation. A vicious infinite regress is an infinite regress that arises in the context of an attempted philosophical explanation when the explanation given permits the question that was to be answered to arise at successively higher levels ad infinitum.  In the above example, to know that p one must know p's entailments, but to know them, one must know their entailments, and so on endlessly.

Now consider this pair:

3. Every event has a cause.

4. To explain an event one must explain its causes.

(3) engenders an infinite series: if every event has a cause, and causes are events, then there is an infinite regress of events. But the regress is benign.  (4), however, is the answer to a philosophical question about the nature of explanation: What is it to explain an event?  (4) proposes a philosophical explanation of explanation, namely, that to explain an event one must explain its causes.  But this theory leads to a vicious infinite regress.  Suppose z has y as a cause.  The theory implies that to explain z one must explain y.  But y is an event, so to explain it one must explain its cause x, and so on infinitely.  The regress is vicious because it sets an impossible standard of explanation: if to explain an event one must explain every event in its causal ancestry, then no event can be explained. So (4) is false.

 

The peripatetic (not Peripatetic) Kevin Kim once asked me:

Are all infinite regresses (regressions?) vicious? Why the pejorative label? Of the many things I don’t understand, this must be near the top of my list, and it’s an ignorance that dates back to my undergrad Intro to Philosophy days. When I first read the Thomistic cosmological proofs, I found myself wondering why Aquinas had such trouble countenancing the possibility that, as the lady says, “it’s turtles all the way down.”

Without a first, there can’t be a second… so what? It doesn’t follow that there must be a first element to a series. What makes a temporally infinite series (of moments, causes/effects, etc.) impossible?

Here is the answer I gave him, considerably expanded and updated:

1. No, not all infinite regresses are vicious. Some are, if not ‘virtuous,’ at least benign. The term ‘benign’ is standardly used. The truth regress is an example of a benign infinite regress. Let p be any proposition. And let ‘T’ stand for the operator ‘It is true that ( ).’ Clearly, p entails T(p). The operation is iterable. So T(p) entails T(T(p)). And so on, ad infinitum or ad indefinitum if you prefer. The resulting infinite series is wholly unproblematic. Whether you call this a progression or a regression, it doesn’t cause any conceptual trouble.

Continue reading “Infinite Regresses: Vicious and Benign”