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An Argument for Necessary Beings

1. A contingent being is one the nonexistence of which is possible, whereas a necessary being is one the nonexistence of which is impossible. (At play in these definitions is broadly logical possibility which is between narrowly logical and nomological possibility.)

2. Framing a definition is one thing, showing that something answers to it is another. Are there any necessary beings? Since a necessary being could be either abstract or concrete, I can show that there are necessary beings by showing that there is at least one abstract necessary being. To convey the senses of 'concrete' and 'abstract' by example one could say that God and Socrates are concrete while the proposition 7 is prime and Socrates' singleton — {Socrates} — are abstract. All and only concreta are causally active/passive whereas abstracta are not. Please avoid the mistake of thinking that x is concrete iff x is physical.

3. Some truths are necessary, others are contingent. 'I am now blogging' is contingently true: it is true, but it might not have been true. I might have been doing something inconsistent with blogging now, sleeping for instance. By contrast, 'If I am blogging, then I am writing' is necessarily true. To see this, negate the sentence in question. The result is a sentence expressing a broadly logical impossibility: 'I am blogging and it is not the case that I am writing.' Consider also, 'If I am blogging, then it is not the case that I am not blogging.' This too is necessarily true, except that the negation expresses a narrowly logical impossibility: 'I am blogging and I am not blogging.'

I don't see how any reasonable person can deny that there are necessary truths. Another example: '7 is a prime number' expresses a necessary truth. This doesn't just happen to be true in the way that it just happens to be true that there are seven cans of Dr. Pepper left in the reefer. It is necessarily true: true in all (BL)-possible worlds.

4. A truth is a true truth-bearer. Now I don't understand how ink on paper, or chalk on a blackboard, or any physical modification of any physical medium, no matter how complex the modification and how complex the medium, could be true or false. I don't understand how anything physical could, qua physical, be a truth-bearer or truth-vehicle, i.e., an item capable of being either true or false. Marks on paper cannot be either true or false. They just exist. But suppose you think they — or complex modifications of the stuff between your ears — can be either true or false. Still, the marked-up paper exists contingently. Consequently, the sentence-token '7 is prime' scratched onto the paper exists contingently. Similarly for anything inscribed in your brain. Your brain and its 'inscriptions' are contingent.

5. But then how could any truth be necessarily true? How could any truth be necessarily true if no truth-bearer is necessarily existent?  There is no possible world in which 7 is not prime, but there are worlds in which there are no material things.  Material things are contingent.  How could the proposition in question be true in those worlds if there is nothing in those worlds to serve as truth-bearer? Let's spell this out.

If an item has a property, then, pace Meinong, the item exists: existence is a necessary condition of property-possession.   So if an item such as a truth-bearer has the property of being necessarily true, then that truth-bearer necessarily exists. For if the truth-bearer is true in every world, then it exists in every world.  Therefore, if there are necessary truths, then there are necessary beings. Now there are necessary truths. Therefore, there are necessary beings. Given that everything physical is contingent, these necessary beings are nonphysical. So they are either mental (accusatives of mental acts) or abstract. For present purposes, it doesn't matter which of these they are. The present point is that there is good reason to believe in (i.e., believe that there are) necessary beings.

6. But I hear an objection coming: An item can have a property essentially without having it necessarily. Thus Socrates is essentially human, but not necessarily human. He is human in every world in which he exists, but he does not exist in every world. So he is essentially but not necessarily human. Why can't the proposition expressed by '7 is prime' be like that? Why can't it be essentially (as opposed to accidentally) true, true in every world in which it exists, but neither true nor false in the worlds in which it does not exist? If this is the way it is, then your argument from necessary truths to necessary beings collapses.

The objector is suggesting that truth-bearers are contingent beings. But this is problematic as Alvin Plantinga argues (Warrant and Proper Function, Oxford UP, 1993, p. 119.) Suppose that truth-bearers are brain inscriptions, and consider the proposition

1. There are brain inscriptions.

(1) is such that it could not have been false. For in a possible world in which there are no brain inscriptions, there are no truth-bearers, which implies that (1) in those words is neither true nor false, hence not false. And in every world in which there are brain inscriptions, (1) is of course true. So (1) is true in every world in which it exists, and not false in every world in which it does not exist. So (1) could not have been false. But this bizarre. Surely there might have been no brains and no brain-inscriptions. It is not necessarily true that there are brains. If it is not necessarily true that there are brains, then it is possibly true that there are no brains. Now what is this possibility of there being no brains? It is plausibly identified with the possibly being true of the proposition, There are no brains. But then this proposition must exist in those possible worlds in which it is not true.

The Existence of Infinite Sets

A reader asked whether one can  prove that there are actually infinite sets.  Well, let's see.

It occurs to me that 'actually infinite set' is a pleonastic expresson. If there are infinite sets, then they are actually infinite, such that a potentially infinite set would be no set at all. For if there are mathematical (as opposed to commonsense) sets at all, then they are quite definite objects whose identity conditions are supplied by the Axiom of Extensionality: two sets are the same if and only they have all the same members. A mathematical set is not exhausted by its membership — it is not a mere plurality — since it is a one to their many; nevertheless, sets are rendered determinate by their members. (Let us for the moment not worry about singletons and the null set which give rise to their own difficulties.) 

It is worth noting that in Georg Cantor's oft-quoted definition, a set (Menge) is a collection of "definite and separate objects." (Contributions to the Founding of the Theory of Tranfinite Numbers, sec. 1) If the members of a set are definite and separate, then the same is true of the set itself. We could say that a math. set inherits its determinacy from the determinacy of its members. 

My point is that, if there are mathematical sets at all, then there is nothing potential, indeterminate, incomplete, or unfinished about them. Each such set is a definite single item distinct from each of its members and from  all of them.  It is a one-over-many. So if there are any infinite sets, then they are actually infinite sets, which is to say that talk of 'actually infinite sets' is redundant.

So our question becomes, Can one prove that there are infinite sets?

I don't know if one can prove it, but one can give an argument. (If a proof is a valid deductive argument the premises of which are self-evident, then damn little can be proven. In particular, the axioms of ZFC are far from self-evident, not that set theorists claim self-evidence for them. Is it self-evident that a null set exists?  Hardly.)

Here is an argument, where 'set' is short for mathematical (as opposed to commonsense) set.

1. There are sets.

2. There are infinitely many natural numbers: no finite cardinal is the number of natural numbers. Therefore,

3. If the natural numbers form a set, then they form an infinite set. (1, 2)

4. The natural numbers form a set.   Therefore,

5. The natural numbers form an infinite set. (3, 4) Therefore,

6. There exists an infinite set. (5)

This is a valid argument, and it renders reasonable its conclusion. But it does not prove its conclusion unless there are proofs for its controversial premises (1) and (4). I argued for (1) in Sets, Pluralities, and the Axiom of Pair.  But what is the argument for (4)?  Why must we think of the natural numbers as forming a set?

Why Mix Philosophy and Politics?

I am sometimes asked why I intersperse political entries with narrowly philosophical ones.  But in every case the question was put to me by someone who tilts leftward.  If my politics were leftist, would anyone complain?  Probably not.  Academe and academic philosophy are dominated by leftists, and to these types it seems entirely natural that one will be a bien-pensant latte-sipping lefty.  Well, I'm here to prove otherwise.  Shocking as it will  seem to some, leftist views are entirely optional, and a bad option at that.

I could of course post my political thoughts to a separate weblog.  But given that philosophy attracts more liberals/leftists than conservatives, it is good for them to be exposed to views  that they do not encounter within the enclaves they inhabit.  Or are contemporary liberals precisely illiberal in their closemindedness to opposing views?  One gets that impression.

Posting the political to a separate weblog would also violate my 'theory' of blogging.  My blog is micro to my life's macro.  It must accordingly mirror my life in all its facets  as a sort of coincidentia oppositorum of this situated thinker's existence.

The Millenials: A Chump Generation?

Robert Samuelson, The Real Generation Gap.  Concluding paragraph:

Millennials could become the chump generation. They could suffer for their elders' economic sins, particularly the failure to confront the predictable costs of baby boomers' retirement. This poses a question. In 2008, millennials voted 2-1 for Barack Obama; in surveys, they say they're more disposed than older Americans to big and activist government. Their ardor for Obama is already cooling. Will higher taxes dim their enthusiasm for government?

Another Look at Anderson’s Trinitarian Mysterianism (Peter Lupu)

(Hauled up from the vasty deeps of the ComBox into the light of day by BV who supplies minor edits and comments in blue.)

I strongly recommend to everyone interested in the subject to read Anderson’s “In defense of mystery: a reply to Dale Tuggy” (2005), Religious Studies, 41, 145-163 in which he replies to Dale Tuggy’s paper “The unfinished business of Trinitarian theorizing”, Religious Studies, 39(2003), 165-183.  I was unable to obtain Dale Tuggy’s original paper.

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Cottingham on the Origin of the Religious Impulse

John Cottingham, On the Meaning of Life (Routledge 2003), p. 52:

. . . the whole of the religious impulse arises from the profound sense we have of a gap between how we are and how we would wish to be . . . .

This is not quite right, as it seems to me. The sense of the gap between 'is' and 'ought' is undoubtedly part of the religious impulse, but there is more to it than this. It must be accompanied by the sense that the gaping chasm between the miserable wretches we are and what we know we ought to be cannot be bridged by human effort, whether individual or collective. Otherwise, the religious sensibility would collapse into the ethical sensibility. There is more to religion than ethics. The irreligious can be aware of the discrepancy between what we are and what we should be. The religious are convinced of the need for moral improvement together with a realization of their impotence in bringing it about by their own efforts.

But now, if I may be permitted to argue against myself:  "Haven't you maintained more than once that Buddhism is a religion?  And isn't Buddhism a religion of self-help?  And haven't you quoted the 'Be ye lamps unto yourselves' verse?  So something has to give.  If Buddhism counts as a religion, then it cannot be essential to a religion that it invoke 'other-power' for moral improvement.  And if the latter invocation is essential to religion, then Buddhism is not a religion."

Well, my man, it looks like we are going to have to think about this some more. 

"And another thing.  You say that there is more to religion than ethics. This implies that ethics is an essential component of religion.  But doesn't Kierkegaard speak of the teleological suspension of the ethical?  Might it not be that one can have religion without ethics?"

A religion worth having cannot be decoupled from ethics.  See Abraham, Isaac, and an Aspect of the Problem of  Revelation and  Kant on Abraham and Isaac.

Simone Weil and the Illusoriness of Worldly Goods

A correspondent, responding to Weil's Wager, has this to say:

[. . .] What worries me when I turn to Weil’s argument is that she seems to be trying to replace Pascal’s serviceable scale of goods with a dichotomy of illusory and absolute goods. I have no idea what it means to say ”health and fitness are illusory goods” or “only God is absolutely good.” The former seems to me just some metaphysically tricked-out term of abuse. I have no idea at all how to unpack “God is the absolute good” (despite your remarks in Part IV ). Pascal at least talks about salvation and an eternal afterlife. Is that what is supposed to be absolutely good for me? And so God as the provider is somehow also valuable or “absolutely good” for me? All of this dark and murky to me in Weil’s argument, while I think I understand what Pascal is proposing.

I agree that the whether-or-not version of (7) is incompatible with (1), but otherwise I remain lost at sea in her attempt to argue that I must pursue the only thing that is “absolutely good” whether or not it really exists. [. . .]

Central to Weil's thought is the notion that the goods of this life are unreal: "Things of the senses are real if they are considered as perceptible things, but unreal if considered as goods." (Gravity and Grace, p. 45) To understand this one must see it in the light of Plato, Weil's beloved master. It has been said with some justice that every philosopher is either a Platonist or an Aristotelian, and there is no doubt that Weil is a Platonist and was hostile to Aristotle. My correspondent, however, is an Aristotelian (to force him into our little schema) and so it comes as no surprise to me that he is at a loss to understand what it could mean to say that such things as health and fitness, food and drink, property and progeny, are illusory goods.

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Ideals

Not only do we fail to live up to the ideals we have, we fail to have the ideals we ought to have. There are two problems here, the first pertaining more to the will, the second more to the intellect, or rather to the faculty of moral discernment.  Let us consider the second problem.

It is not enough to have ideals, one must have the right ideals. This is why being idealistic, contrary to common opinion, is not always good. Idealism ran high among the members of the Sturmabteilung (SA) and the Schuetzstaffel (SS). The same is true of countless millions who became Communists in the 20th century: they sacrificed their 'bourgeois' careers and selfish interests to serve the Party.  (See Whittaker Chambers, Witness, required reading for anyone who would understand Communism.) But it would have been better had the members of these organizations been cynics and slackers. It is arguably better to have no ideals than to have the wrong ones.  Nazism and Communism brought unprecedented amounts of evil into the world on the backs of idealistic motives and good intentions.  Connected with this is the point that wanting to do good is not good enough: one must know what the good is and what one morally may and may not do to attain it.


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