Month: July 2010

But Is It True?

Peter and I were having lunch with a pretty lady yesterday.  While recounting some paranormal experiences, he expressed doubt as to whether they were true.  The lady, quite sympathetic to the experiences and their contents, but having come under the influence of the PoMo crowd, piped up, "There is no truth."  Peter shot back, "So it is true that there is no truth?"

Peter's response was 'knee-jerk,' reflexive, not reflective.  He didn''t need to reflect.  His was a stock response, but none the worse for being stock or easily come by.  It is a prepared line that you should all have at the ready when confronted with  PoMo nonsense.  Not that it will do you much good with the PoMo crowd.

The probative force of Peter's riposte is devastating.  What's amazing, though, is that the Pomo types are not moved by it.  I think this shows that truth is not their concern.  Something else is, power perhaps. It is no surprise that leftism is alive and well within the precincts of PoMo.  I'd have to think about it some more, but 'conservative post-modernist' smacks of being an oxymoron.

Let S be a declarative sentence.  Then surely

E. 'S' is true iff S.

The equivalence schema (E) doesn't say much.  But what it says suffices to refute the claim that there is no truth.  For anyone who asserts 'There is no truth' makes an assertion which is equivalent to "'There is no truth' is true."  And so truth comes back into the picture.  Truth, she's a wily bitch.  Drive her out of the front door, she comes in through the back.  And I don't think it matters how minimalist  is your theory of truth.  My argument does not assume that truth is a metaphysically substantive property.  Even if no property  at all corresponds to the predicate ' is true,' that predicate has a sense.  If it had no sense, then (E) would be gibberish, like

E*. 'S'  is schmue iff S.

I'd have to think about it some more, but it looks as if the equivalence schema by itself suffices to refute the PoMo nonsense that there is no truth.  For even if there is no property of truth, and truth is merely the sense of the predicate 'is true,' that sense cannot be denied.  It's always and necessarily along for the ride.

 

Does Sincere Belief in an Afterlife Entail Religious Zealotry?

Spencer Case e-mails:

Greetings from Afghanistan. I’d very much like to hear your response to a sketch of an argument I’m developing. It goes as follows:

1. Suppose an afterlife is obtainable based on one’s performance in this life. If this afterlife is as I understand it, it must have an infinite value while all the goods in this life have only finite values. In fact, the value of afterlife goods (as I clumsily name them) must be infinite on two planes: quantitative and qualitative; quantitative because the duration of the reward is infinite, qualitative because, I assume—and I think, based on some recent blog posts of yours I’ve read, you would agree—no mortal goods, or accumulation of them, can be qualitatively better than the eternal goods to be found in the afterlife, even when we do not consider duration (this not the case with Islamic fundamentalists, who are promised virgins. But let that pass). Perhaps there is even a punitive afterlife with similar disvalue. 

I agree with this conception of the afterlife.  To put it in a slightly different way, the goods of this life are vanishing quantities axiologically speaking as compared to the goods of the afterlife as portrayed in sophisticated conceptions.  (We agree to set aside crude conceptions such as we find in popular Islam: endless disporting with black-eyed virgins, getting to do there all the sensual things that are forbidden here, etc.)

2.  If this ranking system is correct, it is hard to see how it could ever be rational for one to pursue any set of mortal goods—no matter how well they rank on the finite scale—when one could spend the same time and resources in the pursuit of the afterlife goods or avoiding afterlife evils, which are both endless in duration and of infinitely great quality. If extreme fasts are pleasing to God, and increase my chances of obtaining salvation by a tiny bit, then the rational thing for me to do is to live in such an ascetic state for as long as possible, unless it prevents me from doing other activities that could do even more to promote my own salvation.

Well, Spencer, you have put your finger on a genuine and serious problem, a problem I will rephrase in my own way.  If (i) this world and its finite goods is soon to pass away, and if (ii) one sincerely believes that there is a world to come the value of whose goods infinitely surpasses the values of the goods here below, and if (iii) whether or not one participates in this Higher Life or is excluded from it (either by being sent to the Other Place or by being simply annihilated at death) depends on how one lives in this world, then how can it be rational to pursue mortal goods beyond what is necessary for living in accordance with the precepts of one's religion?  The rational course would be to orient all one's activities to the achievement of the afterlife goal.

For example, if a young person is a Roman Catholic and sincerely believes the teachings of his church, especially as regards what are called the Last Things, and this person is free of such encumbrances as children or aged parents to care for, and has the health and other qualifications necessary to join a monastery, then why doesn't the person do so, and join the most rigorous monastery to be found?  Wouldn't that be the most rational course of action given (i) the end in view, (ii) one's beliefs about this end, and (iii) one's beliefs about the means for securing this end?

Converts often follow this course.  Unlike those who have been brought up in a faith,  they are seldom lukewarm.  They have found the truth with a majuscule 'T' (they think) and their authenticity demands that they act on it.  Thomas Merton, for example, after renouncing his worldly life and joining the RC church was not content to be a good practicing Catholic, or become a parish priest even; no, he had to go all the way and join not just any monastic order but the Trappists!  One can appreciate the  'logic' to it.  And then there is Edith Stein, the brilliant Jewish assistant of Edmund Husserl.  She was not content to convert to Catholicism; she abandoned her academic career and all the usual worldly blandishments (sex, love, children, travel, etc.) to spend the rest of life behind the walls of a strict Carmelite convent until the Nazis murdered her at Auschwitz.

I hope the conversion  'logic' is clear:  if in a few short years we will be pitched head first into Kingdom Come, then pursuing and fretting over the baubles of this life is like re-arranging deck chairs on the Titanic.

Let's note en passant that the same 'logic' is found in the thinking of adherents to nonreligious ideologies.  Thousands of young people, some of them among the best and the brightest, sacrificed their lives to the Communist illusion in the 20th century.  They wasted their lives in pursuit of a fata morgana, while at the same time contributing unintentionally and indirectly to the murder of over 100 million people.

3.  Anyone who pursues only afterlife goods in this way is a paradigm case of a religious zealot.

This formulation needs improvement.  Merton and Stein did not pursue ONLY afterlife goods.  They pursued  this-worldly goods too but only insofar as they were instrumental to the achievement of afterlife goods. (I ignore Merton's lapses.)  A better formulation is as follows:

3*.  Anyone who pursues afterlife goods primarily, and this-worldy goods only insofar as they are instrumental in the achievement of afterlife goods, is a religious zealot.

I can accept (3*), but I would add that being a zealot is not necessarily bad, despite the fact that the word generally carries a pejorative connotation.  Aren't we all legitimately zealous when it comes to the preservation of our lives and the lives of those animals and humans in our care?  Suppose Al Gore is right, and global warming is about to do us all in, then GW zealotry would be justified would it not?

4.  So, accepting these very basic religious propositions makes one rationally committed to religious zealotry and denying our normal reasons for acting.

I don't think your conclusion follows in quite the way you intend it.  For one thing, you seem to be assuming that zealotry as such is bad.  But surely not all zealotry is bad.  To modify a saying of Barry Goldwater: Zealotry in the defense of liberty is no vice!  (He had 'extremism' where I have 'zealotry.')  You may also be assuming that the religious claims are false.  Suppose they are true.  Then one would have a good reason for denying/modifying our normal reasons for acting.  (The same would hold in the case of nonreligious ideologies.)  A 'normal' person, if if he is a practicing adherent of a religion, pursues all sorts of pleasures and diversions which do not advance him toward his spiritual goal, but rather, in many cases, impede his realization of it.  The 'normal' Buddhist, for example, does not carry the precept "Conquer desire and aversion!" to the point where he eats whatever is put on his plate.  (If a fly lands in his soup he does not practice nondiscrimination and eat the fly with the same relish or lack thereof with which he eats the rest of the soup.)  But if our Buddhist really believed Buddhist teachings would it not be rational for him to modify 'normal' behavior and bend every effort towards achieving enlightenment?

What I hope this shows is that religious belief (at least in the religions you and I are most likely to debate about) disallows moderation, which I take it, is a bad thing. What I especially like about this argument is it seems to be an argument that appeals to conservatives, because conservatives are most likely to have strong intuitions against ideologies that tell us to ignore our ordinary reasons for acting.

I think you are right that religious belief, if sincerely professed and lived, disallows moderation of the sort that the average  worldly person displays.  But it is not just religious belief that has this property.  So do many ideologies or action-guiding worldviews.  I gave the example of Communism above.  Other examples readily come to mind. 

You are assuming that moderation of the sort displayed by 'normal' worldly people is a good thing.  But if Communism or Catholicism were true, then moderation of that sort would not be good!  True-blue reds devoted all their energies to their chimerical Revolution  just as true Christians consecrate their lives, without reservation, to Christ.  They don't 'hedge their bets' they way most people do.  Whether that singlemindedness is good or bad depends on whether the underlying beliefs are true or false.  Of course we now know that Communism is a god that failed, but the religious God is safely insulated in a Beyond beyond our ken.

So if your thesis is that sincere belief in an afterlife entails (or maybe only leads to) religious zealotry, and is for that reason  objectionable, then I don't think you have made your case.  Genuine belief in an afterlife will lead to behavior that is 'abnormal' and 'immoderate'  as measured by the standards of the worldly.  But this won''t cut any ice unless worldly standards can be shown to be correct and truly normative, not just statistically 'normal.'

Of course, as you’ve no doubt noticed, this argument does not take into account epistemic uncertainty. Uncertainty about the existence of the afterlife might make it more rational for us to go ahead and pursue other goods. I haven’t yet done the research in probability theory, but I’d be willing to guess our levels of epistemic confidence in religious propositions would have to be very low in order for it to be rational to pursue anything else.

This is another  important side to the problem of balancing the claims of this world with the claims of the next.  People fool themselves into thinking they KNOW all sorts of thinks they merely BELIEVE.  Now it seems to me that no imtellectually honest person can claim to KNOW (using this word strictly) that there is an afterlife: the evidence from parapsychology, though abundant, is not conclusive, and the philosophical arguments, though  some of them impressive, are not compelling.  But I do KNOW the pleasures of good food, and strong coffee, and fine cigars, and chess, and good conversation, and scribbling away as I am now doing, all of them activities which are not necessary for my salvation, and perhaps stand in the way of it.  (Not to mention disporting with ladies of the evening, etc.)

So what is the rational thing to do given my epistemic predicament in which what I KNOW is confined to this ephemeral world which cannot be worth much, and my access to the other is via mere belief and the occasional religious/mystical experience whose veridicality is easily called into question?

A difficult question.  I don't know that there is an afterlife, and I don't know that there isn't.  It strikes me as highly irrational to live for this life alone since it is nasty, brutish, short, miserable, full of natural and moral evil, and of scant value if it doesn't lead to anything beyond it.  It also seems irrational to forego every positive value in this world which is not conducive to otherworldly salvation on the strength of mere belief in that otherworldly possibility.

So my tentative answer is that the rational course is to  inquire ceaselessly into the matter in a critical, exploratory and tentative spirit; avoid being bamboozled by the dogmas of churches and sects which claim to have the Truth; enjoy the limited goods of this life in a measured way while realizing that, in and of themselves, they are of no ultimate value.

In short, be neither a worldling nor a monk.  Be a philosopher! (Not to be confused with being a paid professor of it.)

Sets, Pluralities, and the Axiom of Pair

In a thread from the old blog, resident nominalist gadfly 'Ockham'/'William' made the fascinating double-barreled claim that:

. . . (a) there are such things as sets and (b) the axiom of pairs is false. Briefly, I claim that 'a set of x's' is just another way of saying 'those x's'. The fundamental error of set theory is using a logically singular expression {a, b} to refer to what in ordinary language a plural term refers to, using an expression such as 'a and b' or similar.

I take O to be saying that there are sets, but they are not the sets we read about in standard treatments of axiomatic set theory, and whose properties are all and only the properties ascribed to them in axiomatic set theory, Zermelo-Fraenkel with Choice, to be specific. Suppose we call the latter mathematical sets, and the former ordinary language (commonsense) sets. Then what O is claiming is that there are ordinary language (OL) sets, but there are no mathematical sets. That there are no mathematical sets on O's view follows from O's denial of the Axiom of Pair, a crucial ingredient of ZFC. Here is a formulation of the latter:

PAIR. Given any x and y, there is a set {x, y} the members of which are exactly x and y.

X and y can be either sets or nonsets. So given that Socrates exists and that Plato exists, it follows by PAIR that a third item exists, namely, {Socrates, Plato}. (I use 'there is' and 'there exists' interchangeably.) That a third item exists is what I affirm and what O denies. For O, the plural term 'Socrates and Plato' does not refer to a single third item, the set consisting of Socrates and Plato; and yet it does refer to something, a thing that is an ordinary language set. For O, there are exactly two items in our example, Socrates and Plato, and not three, as I claim.

Let us say that the referent of a plural term such as 'Socrates and Plato' or 'the British Empiricists' or 'the Hatfields' is a plurality. A plurality is an ordinary language set. A gaggle of geese, a pride of lions, a coven of witches, a bunch of grapes, a pack of wolves — these are all pluralities or OL sets. That there are OL sets, or pluralities, is presumably not in dispute. Nor, I think, could anyone rationally dispute their existence. That there is such a thing as a pair of shows cannot be reasonably denied; that the two shoes form a mathematical set can be reasonably denied at least prima facie.

If I understand O, he is saying that all reference to sets is via plural referring expressions such as 'these books,' 'Dick Dale and the Deltones,' 'the barristers of London,' etc. There is no reference to any set via a singular referring device such as the singular definite description, 'the set consisting of these books.'

Now consider the question whether there are sets of sets. I claim that it is a fact that there are sets of sets, and that this fact causes trouble for O's nominalist view that all sets are pluralities. Consider the Hatfields and the McCoys. These are two famous feuding Appalachian families, and therefore two pluralities or OL sets. But there is also the two-membered plurality of these pluralities to which we refer with the phrase 'the Hatfields and the McCoys' in a sentence like 'The Hatfields and the McCoys are feuding families.'

If, however, a plurality of pluralities has exactly two members, as in the case of the Hatfields and the McCoys, then the latter cannot themselves be pluralities, but must be single items, albeit single items that have members. That is to say: In the sentence, 'The Hatfields and the McCoys are two famous feuding Appalachian families,' 'the Hatfields' and 'the McCoys' must each be taken to be referring to a single item, a family, and not to a plurality of persons. For if each is taken to refer to a plurality of items, then the plurality of pluralities could not have exactly two members but would many more than two members, as many members as there are Hatfields and MCoys all together. Compare the following two sentences:

1. The Hatfields and the McCoys number 100 in toto.

2. The Hatfields and the McCoys are two famous feuding Appalachian families.

In (1),'the Hatfields and the McCoys' can be interpreted as referring to a plurality of persons as opposed to a mathematical set of persons. But in (2), 'the Hatfields and the McCoys' cannot be taken to be referring to a plurality of pluralities; it must be taken to be referring to a plurality of two single items.

Or consider the following said to someone who mistakenly thinks that the Hatfields and the McCoys are one and the same family under two names:

3. The Hatfields and the McCoys are two, not one.

Clearly, in (3) 'the Hatfields and the McCoys' refers to a two-membered plurality of single items, each of which has many members, and not to a plurality of pluralities. And so we must introduce mathematical sets into our ontology.

This is connected with the fact that '___ is an element of . . .' in axiomatic set theory does not pick out a transitive relation: If x is an element of y, and y is an element of z, it does not follow that x is an element of z. Socrates, a nonset, is an element of various sets; but he is clearly not a member of any of these set's power sets. (The power set P(S) is the set of all of S's subsets. Clearly, no nonset can be a member of any power set.) But if there are no mathematical sets, and every set is a plurality, then it seems that the elementhood or membership relation would be transitive. A set of sets would be a plurality of pluralities such that if x is an element of S and S an element of S *, then x is an element of S*. My conclusion, contra 'Ockham,' is that we cannot scrape by on OL sets, or pluralities, alone. We need mathematical sets or something like them: entities that are both one and many.

REFERENCES

Max Black, "The Elusiveness of Sets," Review of Metaphysics, vol. XXIV, no. 4 (June 1971), 614-636.

Stephen Pollard, Philosophical Introduction to Set Theory, University of Notre Dame Press, 1990.

Plato

Both his greatness as a thinker and the probity of his quest for truth are revealed in the fact that Plato is not only the father of the Theory of Forms, but also the author of the most penetrating criticisms of them.

(By the way, the above aphorism is crafted in such a way as to demonstrate that the antecedent of a pronoun need not be its antecedent in the order of reading.)

The Vital Imperative: Live Well, Live Now

Wtc1 This is it. This is your life, right here and right now. The present is as real as it gets. If you are not doing with your life right now what you think you ought to be doing with it, then you are doing something wrong.

After the 2001 attack on the World Trade Towers, The New York Times published short pieces on those who had perished. The story of one fellow in particular remains in memory. He was a bond trader whose  office was high up in one of the towers. A man in his late thirties, early forties, his dream was to live in a small town in the Rockies and operate a bait and tackle shop. But first he had to earn his grubstake, or so he thought. So he slaved away in the certain present for an uncertain future. He did what he did not love so that he might do what he did love. He did what he did not love for a present that never came.

His living was not a true living, but a postponing, a placing after. He placed his real life after his present life, forgetting that the present alone is real and that the present,  not the future, is in one's secure possession.

When St Augustine was asked what he would do if he knew he would die in the next hour, he replied, "Nothing other than what I am now doing." He was living as he thought he ought to be living, realizing   rather than postponing his Ideal.

From these lessons we may infer a Vital Imperative: As far as possible, live in the present as if the next hour were to be the hour of your death. How do you want death to find you? Living self-sufficiently in the riches of the moment? Or standing on tip-toe craning your head toward a nonexistent future?

Freud or James? Wish-Fulfillment or Inducement to Strenuous Living?

Sigmund Freud (1856-1939), The Future of an Illusion:

It would indeed be very nice if there were a God, who was both creator of the world and a benevolent providence, if there were a moral world order and a future life. But at the same time it is
very odd that this is all just as we should wish it for ourselves.

William James (1842-1910), "The Moral Philosopher and the Moral Life":

The capacity of the strenuous mood lies so deep down among our natural human possibilities that even if there were no metaphysical or traditional grounds for believing in a God, men would postulate one simply as a pretext for living hard, and getting out of the game of existence its keenest possibilities of zest.

Both of these passages support the view that God is a posit, a postulate, a projection. But there is a striking difference. Freud, seeing the origin of the God-projection in weakness, takes this as
discrediting the God-idea. Having its genesis in our neediness, the God-idea is false or at least unworthy of belief. James, however, viewing the God-idea as an expression of our robustness, takes this fact as a verification of the idea of God.

Of course, there are two different notions of truth in play. I don't know whether Freud ever discussed theories of truth, but I'd guess he is a correspondence-theorist: an idea is true if it corresponds to reality. But James is a pragmatist: an idea is true if it works, if it is something good for us to believe in the long run. For James, we get more out of the game of existence when we believe in God and all that entails: a moral world order that places an ethical demand on us; an ultimate explanation of why anything exists and why we exist; a final guarantor of the veridicality of our ideas; a provider of sense and purpose; a repository of hope; a securer of immortality and adjustor of happiness and virtue.  Believing in God, we live better, richer, fuller lives; we wring from existence its  "keenest possibilities of zest."

To resolve the debate between Freud and James one would have to get clear about the nature of truth and its connection to human flourishing. The problems are deep and perhaps insoluble. But that doesn't stop them from being fascinating and worth pursuing. And we don't know they are insoluble. If we believe that they are soluble, that truth about ultimates is attainable, and we strive for it, then too we will wring from "the game of existence its keenest possibilities of zest."

Companion post:  Freud on Illusion, Delusion, Error, and Religion

The Losertarian Party

Politics is a practical business: it is about the gaining and maintaining of power for the purpose of implementing programs and policies that one believes to be beneficial, and for opposing those whose policies one believes to be deleterious. As the Converse Clausewitz Principle has it, it is war conducted by other means.  For this very reason, I stay clear of it except for voting and blogging: I am by inclination and aptitude a theoretician, a "spectator of all time and existence" to borrow a marvellous phrase from the  Plato's Republic. But part of the theoretician's task is to understand the political. And if I understand it, I understand that the Libertarian Party, though it might be a nice debating society, is a waste of time practically speaking. That's why I approve of and borrow Michael Medved's moniker, 'Losertarian Party.' These adolescents will never get power, so what's the point? It's a party of computer geeks, sci-fi freaks, and adolescents of all ages, the sort that never outgrow Ayn Rand.  Open borders, legal dope, ACLU-type extremism about freedom of expression.  Out of the mainstream and rightly so.

So Ron Paul made a smart move when he joined the Republicans, and his son Rand seems more conservative than libertarian. 

As I said, politics is a practical business. It's about winning, not talking. It's not about ideological purity or having the supposedly best ideas; it's about gaining the power to implement good ideas.  The practical politician understands that quite often  Le mieux est l'ennemi du bien, the best is the enemy of the good.

What is Philosophy?

I found the following on Keith's blog.  It is so good I simply must reproduce it here.

The nearest thing to a safe definition of the word "philosophy", if we wish to include all that has been and will be correctly so called, is that it means the activity of Plato in his dialogues and every activity that has arisen or will arise out of that.

(Richard Robinson, "Is Psychical Research Relevant to Philosophy?" The Aristotelian Society, supplementary volume 24 [1950]: 189-206, at 192.)

This is in line with my masthead motto which alludes to the famous observation of Alfred North Whitehead:

The safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato.  I do not mean the systematic scheme of thought which scholars have doubtfully extracted from his writings.  I allude to the wealth of general ideas scattered through them.  [. . .] Thus in one sense by stating my belief that the train of thought in these lectures is Platonic, I am doing no more than expressing the hope that it falls within the European tradition. (Process and Reality, Corrected Edition, The Free Press, 1978, p. 39)

John Pepples Wants a New Left

During our lazy float down the Rio Salado today, Mike Valle and I had a lot to talk about. He mentioned a new blog he had come across entitled I Want a New Left. The author, John Pepples, aims to develop a self-critical leftism.  Now, having read quickly through most of his posts, I am a bit puzzled by the same thing that puzzles Mike:  why does Pepples hang on to the 'leftism' label?

But labels aren't that important.  What is important are the issues and one's stances on them. On that score, conservatives like me and Mike share common ground with Pepples.  In his biographical statement he says that in college he majored in mathematics and took a lot of physics courses. "But this was during the late 60s and early 70s, when much questioning was occurring, and I ended up as a grad student in philosophy."  Sounds very familiar!  The 'sixties were a heady time, a time of ferment, during which indeed "much questioning was occurring."  I started out in Electrical Engineering but also "ended up as a grad student in philosophy."  I did, however, have a bit more luck career-wise and didn't experience the same difficulties getting into print.

Why did so many of us 60s types end up in philosophy?  Because we were lost in a strange land, traditional understandings and forms of world-orientation having left us without guidance, and we needed to ascend to a vantage point to reconnoiter the terrain, the vantage point that philosophy alone provides.

Political change, a species of the genus doxastic change, is a fascinating topic.  I recently stumbled upon an effort by a distaff blogger who documents her transition from a comfortable enclave of mutually reinforcing Democrats to the more open world of contemporary conservatism, and the hostility with which her turncoat behavior was rewarded.  She calls her blog Neo-Neocon.

Fruitful Conversation

E. M. Cioran, Drawn and Quartered, p. 163:

Conversation is fruitful only between minds given to consolidating their perplexities.

A brilliant aphorism. Philosophy, as Plato remarks (Theaetetus 155) and Aristotle repeats (Metaphysics 982b10),  has its origin in wonder or perplexity.  Fruitful philosophical conversation, rare as it is and must be given the state of humanity, is therefore a consolidation and appreciation of problems and aporiai, much more than an attempt to convince one's interlocutor of something. Herein lies a key difference between philosophy and ideology.

NASA Then and Now

In the '60s, under the leadership of JFK, NASA put a man on the moon.  Forty years later, under the 'leadership' of BHO, 'NASA' has become an acronym for

Nurturing Arab Self Awareness.  (From an e-mailer to the O'Reilly Factor)  Image found here.

On second thought, the e-mailer's suggestion can be improved upon:  Nurturing Arab Self Acceptance.

As for the cartoon below, I needn't point out to my astute readership that the Arabs did not invent mathematics.

NASA

From the Mailbag: Faith and Modality

An astute reader e-mails, 

First, sometime ago I recommended John Bishop's Believing by Faith: An Essay in the Epistemology
and  Ethics of Religious Belief . If you have yet to read the book, I would recommend his new article
on Faith in the Stanford Encyclopedia of Philosophy. You may be particularly interested in
sections 7-10.
 
Second, I do not know a great deal about possible worlds semantics, and am taking a great risk of embarrassing myself in questioning your  argument that "Necessarily, something exists" – but I think
that I will take a stab at it!
 
I am assuming that "Necessarily something exists" = "In at least one possible world, at least one
thing exists." Is this correct?
 
No.  The first sentence is equivalent to 'In every possible world, at least one thing exists.'  In other words, there is no possible world that is empty: every world has at least one item in it.  But this is consistent with there being no one item that exists in every possible world.  Suppose every being is contingent, where a contingent being is one that exists in some but not all possible worlds.  Then there would be no one being that exists in all worlds, and 'Necessarily something exists' would be made true by the fact that each world has something or other in it.  But if there is a necessary being (defined as a being that exists in all worlds), then of course the sentence in question is also true.
 
1. Does not your argument depend upon the assumption of 'modal realism' – that all possible worlds
actually exist, a highly questionable assumption?
 
No, because I am using the 'possible worlds' language only as a façon de parler, a graphic and intuitive way of representing modal relationships which I find helpful.  (Unfortunately, most of my readers are completely 'thrown' by it!) In other words, I could have stated the argument without mentioning possible worlds.  Here is a partial schedule of intertranslation, where 'world' is short for 'broadly logically possible world':
 
X is a necessary being =df X exists in all worlds
X is a contingent being =df X exists in some but not all  worlds
X is an impossible being =df X exists in no world
X is an actual being =df X exists in the actual world
(Note that if x is contingent, it doesn't follow that x is actual, nor conversely)
X is a possible being =df X exists in some world
X is essentially F =df X instantiates F-ness in every world in which X exists.
X is accidentally F =df X instantiates F-ness in some but not all worlds in which X exists
X is necessarily F =df X instantiates F-ness in every world in which X exists, and X exists in every world.
(Example: God is necessarily, not just essentially, omnipotent.)
Proposition p is necessarily true =df p is true in all worlds
P is contingently true =df p is true in some but not all worlds
And so on.
 
Now isn't that neat? The modal notions are explicated in terms of the familiar quantifiers of predicate logic.  The schema facilitates modal reasoning.  For example, if x is necessary, does it follow that x is possible?  Yes, because if x exists in all worlds, then it exists in some worlds. If x is possible, does it follow that x is contingent?  No, because if x exists in some worlds, that leaves it open that it exists in all worlds.  If x is noncontingent, does it follow that x is necessary?  No, because if it is not the case that x exists in some but not all worlds, it does not follow that x exists in all worlds:  x might exist in no world.
 
You characterize modal  realism  as the doctrine that "all possible worlds actually exist."  No philosopher maintains that every world is absolutely actual.  There is only one possible world that is absolutely actual: all the rest are merely possible.  Now there is a philosopher, David K. Lewis, who maintains that there is a plurality of worlds, all on an ontological par, and thus all equally real; but he denies that there is such a property as absolute actuality.  For him each world is actual at itself, but no world is actual simpliciter or absolutely.  I reject Lewis's view which could be called extreme modal realism.  Almost everyone rejects it.  Lewis's idea, which is both brilliant and crazy at the same time, is that modality can be reduced to purely extensional terms via definitions like the ones I gave above.  But few follow him in that.  The above definitions do not allow one to eliminate modality by quantifying over worlds, because the worlds in question are possible, and 'possible' is a modal term.
 
So, to answer what I take to be your question, my argument does not presuppose extreme modal realism.  In fact, it does not require that we take any stand at all on what exactly possible worlds are.  But I do presuppose realism to this extent:  I asssume that modality is not merely epistemic. Thus the possibility that I be sleeping now instead of blogging is a 'real possibility' in that it is subsists independently of what I or anyone know or believe.  It is not possible merely in the epistemic sense of 'possible for all I know,' but possible independently of what I know.
 
2. Does not your use of 'exists' in premises 4 and 5 treat it as, or assume that it can be used as,  a
'real predicate'  rather than merely a 'grammatical predicate' (B. Russell) – again a questionable if
not false assumption?
 
I discuss this is various articles and in my 2002 book A Paradigm Theory of Existence.  I argue, among other things, that Russell's theory of existence, which is closely related to Frege's, is a complete nonstarter, wrong from the ground up.  There is something on Russell's theory in Paul Edwards' Heidegger's Confusions: A Two-Fold Ripoff. 
 
In 'possible worlds' lingo, we say things like this:  There are possible worlds in which Socrates exists but is not the teacher of Plato. Now of course those worlds are all merely possible because we know (or reasonably believe) that in the actual world Socrates is the teacher of Plato.  So what does it mean to say that Socrates exists in those worlds?  Let W be a merely possible world.  To say that x exists in W is to say that, had W been actual, x would have existed.  A merely possible world in which Socrates is not the teacher of Plato is a world which is such that, had it been actual, then Socrates would have existed without being the teacher of Plato.
 
My correspondent continues with several more questions/objections which I don't understand.  In any case the above gives us plenty to discuss.