Month: November 2008

Infinite Regresses: Vicious, Benign, Virtuous?

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?

World Philosophy Day

Seldom Seen Slim apprised me of the fact that today is World Philosophy Day.  BBC story here.  I got a kick out of this:

As Princeton philosopher David Lewis once said: "When philosophers follow where argument leads, too often they are led to doctrines indistinguishable from sheer lunacy."

This from a philosopher whose mad dog modal realism is itself hard by the boundary of lunacy.  Talk about the pot calling the kettle black!

 

 

Vicious and Benign Regresses Again

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.

 

Infinite Regresses: Vicious and Benign

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.

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A Protreptic Puzzler

A curious passage from Aristotle's Protrepticus:

. . . the fact that all men feel at ease in philosophy, wishing to dedicate their whole lives to the pursuit of it by leaving behind all other concerns, is in itself weighty evidence that it is a painless pleasure to dedicate oneself wholeheartedly to philosophy. For no one is willing to engage in exhausting work for a long time. (#53, p. 24)

To set the Stagirite straight, I should like to shunt his shade into some Philosophy 101 classroom for a spell.

A Reason to Blog

Chary of embalming in printer’s ink ideas that may be unworthy of such preservation, due perhaps to underdevelopment, or lack of originality, or some more egregious defect, the blogger satisfies his urge to scribble and publish without burdening referees and editors and typesetters, and without contributing to the devastation of forests. He publishes all right, but in a manner midway between the ephemerality of talk and the finality of print.

Is Bradley’s Regress Already in Aristotle?

At Metaphysics Zeta (Book VII, Chapter 17, Bekker 1041b10-30), there is a clear anticipation of Bradley’s Regress and an interesting formulation of what may well count as the fundamental problem of metaphysics, the problem of unity. What follows is the W. D. Ross translation of the passage. It is a mess presumably because the underlying Greek text is a mess. The Montgomery Furth and Richard Hope translations are not much better. But the meaning is to me quite clear, and I will explain it after I cite the passage:

Continue reading “Is Bradley’s Regress Already in Aristotle?”

Francesco Orilia on Facts and Bradley’s Regress Part II

In Part I of this series I provided a preliminary description of the problem that exercises Orilia and me and a partial list of assumptions we share. One of these assumptions is that there are truth-making facts. We also both appreciate that Bradley’s Regress (‘the Regress’) threatens the existence of facts. Why should this be so? Well, the existence of a fact is the unity of its constitutents: when they are unified in the peculiar fact-constituting manner, then the fact exists. But this unity needs an explanation, which cannot be empirical-causal, but must be ontological. The existence of facts cannot be taken as a brute ontological fact. But when we cast about for an explanation, we bang into the Regress. Let me now try to clarify this a bit further. We distinguish between an internal Regress and an external Regress, and in both cases we must investigate whether it is vicious or benign.

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Acting With Others Versus Talking With Others

An excellent insight from Alain’s essay, “The Ills of Others”:

To act with others is always good; to talk with others for the sake of talking, complaining, and recriminating, is one of the greatest scourges on earth . . . . (Alain on Happiness, Frederick Ungar 1973, p. 160)

I once built a small dock with another man. We had little or nothing in common intellectually or spiritually. You could say we lived on different planets. Conversation with him about any matter beyond the sensibly present was pointless or worse. But with tools in hand, confronting the recalcitrance of matter, with a definite physical end in view, engaged in a common project, his words found guidance and anchorage, and our words together served a purpose. Acting together we achieved something. The job done, the handiwork admired, I found myself actually liking the guy. But had we been just talking, I would have found it a moral challenge not to be disgusted with him. Few possess the mental equipment and discipline to engage in fruitful conversation that is not anchored in the mundane.

Again I note, as in an earlier Alain post, the French love of the universal quantifier: “To act with others is always good. . . .” Obviously, acting with others is not always good. for reasons you an easily supply yourself. So why the exaggeration? For literary effect.

Please don’t accuse me of committing a hasty generalization. I am not inferring some such proposition as ‘French writers misuse universal quantifiers for literary effect’ from this one instance, or this instance plus the one cited in the earlier post; what I am doing is illustrating an antecedently established general proposition. This is a distinction one should observe, but is too often not observed, namely, the distinction between generalizing and illustrating. Someone who illustrates a general claim by providing an example is not inferring the general claim from the example.

Why I am Such a Hot Ticket on the Party Circuit

Thomas Cathcart and Daniel Klein, Plato and a Platypus Walk into a Bar . . . Understanding Philosophy Through Jokes, Abrams Image 2007, pp. 183-184:

Contemporary philosopher William Vallicella writes, “Metaphilosophy is the philosophy of philosophy. It is itself a branch of philosophy, unlike the philosophy of science, which is not a branch of science, or the philosophy of religion, which is not a branch of religion.”

It is statements like this that have made Vallicella such a hot ticket on the party circuit.

I haven’t read the book, so I can’t tell you what I think of it. The only reason I know about the above citation is because Dymphna of Gates of Vienna drew it to my attention.

Amiel on Duty

“Duty has the virtue of making us feel the reality of a positive world while at the same time detaching us from it.” (See here.)

This is a penetrating observation, and a nearly perfect specimen of the aphorist’s art. It is terse, true, but not trite. The tip of an iceberg of thought, it invites exfoliation.

If the world were literally a dream, there would be no need to act in it or take it seriously. One could treat it as one who dreams lucidly can treat a dream: one lies back and enjoys the show in the knowledge that it is only a dream. But to the extent that I feel duty-bound to do this or refrain from that, I take the world to be real, to be more than maya or illusion. Feeling duty-bound, I realize the world.

And to the extent that I feel duty-bound to do something, to make real what merely ought to be, I am referred to this positive world as to the locus of realization.

But just how real is the world of our ordinary waking experience? Is it the ne plus ultra of reality? Its manifest deficiency gives the lie to this supposition, which is why great philosophers from Plato to Bradley have denied ultimate reality to the sense world. Things are not the way they ought to be, and things are the way they ought not be, and everyone with moral sense feels this to be true. The Real falls short of the Ideal, and, falling short demonstrates its lack of plenary reality. So while the perception of duty realizes the world, it also and by the same stroke de-realizes it by measuring it against a standard from elsewhere.

The sense of duty detaches us from the world of what is by referring us to what ought to be. What ought to be, however, in many cases is not; hence we are referred back to the world of what is as the scene wherein alone ideals can be realized.

It is a curious dialectic. The Real falls short of the Ideal and is what is is in virtue of this falling short. The Ideal, however, is not but only ought to be. It lacks reality just as the Real lacks ideality. Each is what it is by not being what it is not. And we moral agents are caught in this interplay. We are citizens of two worlds and must play the ambassador between them.

Existence as a Property: A Response to David Brightly

David Brightly commented: “Why bother with existence as a property since everything has it and it does not help distinguish individuals? Is there an argument that convinces you that existence is a property, or is this in some way a matter of ‘philosophical taste’?”

1. Existence can be a property without being a property of individuals. It might be a property of properties or concepts or propositional functions or Tichian offices or some cognate item. But our concern is whether, and in what sense, existence is a property of individuals.

2. If existence is a property of individuals, then one can ask whether it classifies individuals into two groups, the existent and the nonexistent. If existence is classificatory in this way, then the individuals it classifies cannot, in themselves, be existent: they must be nonexistent individuals. But I mention this (Meinongian) theory only to set it aside for the space of this post. I maintain that there are no nonexistent individuals, that all individuals exist. This is not self-evident. Nor is it a logical truth that every individual exists. If it were, then it would be a formal-logical contradiction to say that some individuals do not exist, but it is not. For more on this topic, and a critique of van Inwagen, see here.

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