A self-proclaimed 'neoconservative' explains his philosophy,

Reflections of a Neoconservative: Looking Back, Looking Ahead, by Irving Kristol. New York: Basic Books Inc. 336 pp. $19.95. ''Why not give Lagos a chance?'' It was last year that Irving Kristol suggested moving the United Nations to the capital of Nigeria or some other spot far from the United States. Last month President Reagan and other administration figures cordially invited the UN to leave New York if it chose to do so. Sen. Daniel Patrick Moynihan, a former US ambassador to the UN, did not like this attitude. He came out firmly for keeping the ''diplomatic center of the world'' in ''the principal city of the world's most important democracy,'' even though in his day he was as critical of much of the UN membership as Ambassador Jeane Kirkpatrick is now.

The point at the moment is that Senator Moynihan has been called a neoconservative on the Democratic side almost as often as Professor Kristol on the Republican side. And so neoconservatism must have room for differing views under its tent - unless those who differ with Kristol no longer belong in the family. For he has been named by a supply-side admirer the godfather of neoconservatives.

Yet, from this collection of essays spanning several decades, Kristol seems a more genial than threatening mentor. There is much here of the ''old liberal,'' which is more or less what ''new conservative'' means in his lexicon. But, unlike some in this category, he ungrudgingly accepts his tag: ''I may be the only living and self-confessed neoconservative, at large or in captivity.'' And he is willing to lay his neoconservative hawkish credentials on the line by espousing such a liberal cause as non-first-use of nuclear weapons - for the best of hawkish reasons. He doubts that the US would push the nuclear button anyway; thus the US nuclear umbrella has become ''purely imaginary,'' and it would be better to acknowledge non-first-use while building up ''usable'' conventional weaponry.

Kristol does slip in some neoconservative crowd-pleasers, such as parenthetically defining nonaligned as anti-American and proclaiming that the US is ''blackmailed so successfully by friend and foe alike, that we habitually pay up in advance.'' He sometimes lets his ideas sink or swim by failing to buttress sweeping statements with persuasive evidence. Then he sounds as if preaching to the converted. Or possibly a little like a right-wing version of the lunchroom arguments at the City College of New York when he was a youthful Trotskyist? He warmly evokes that period in an opening essay involving students whose names sound like a roll call of today's social science professors.

Yet, more than most neoconservatives, Kristol preaches to the unconverted, too. And, in three essays from more than 30 years ago, which might be considered padding in a neoconservative volume, he writes of Jewish humor, Freudianism, and Einstein with more cultural sensitivity than political ideology.

In other essays, resolutely unchanged from their time of writing, there is a certain repetitiousness. A feeling emerges that America used to be better, though Kristol says that freedom from nostalgia is what is ''neo'' about neoconservatism. It seeks to grab the future from a left that doesn't know what hit it. In his aiding and abetting, Kristol admits that capitalism has not always had the moral element that Adam Smith may have intended. But he sees a ''predominantly'' market economy as still the best economic hope for the good of all, especially if a tempering community spirit is added. He has no problem with a conservative version of the welfare state. He sees that a nation's moral climate is no less important than its economic climate. He comes up with freshening thoughts apropos democracy, such as that the founding fathers, in what they said and did, ''understand us better than we understand them.''

Sometimes, for all of Kristol's social concern, he doesn't escape the difficulty of sounding compassionate while neoconservatively splitting hairs over who is really poor. Yet here is obviously a man of earnestness and decency, a fluent writer as well as ideologist, striving to maintain, one suspects, the radical idealism of those college-day polemics in the grayer realm of politics when the utmost realism is demanded to preserve freedom and democracy from their foes.

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