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Contemporary Philosophy

The Happiness Paradox by Ziyad Marar (Foci: Reaktion Books) The dream of a happy life has pre-occupied thinkers since Plato, and is the signature tune of our times. In The Happiness Paradox Ziyad Marar shows how our modern obsession with happiness has evolved. In a lively and accessible style, he argues that happiness is a deceptively simple idea that will always be elusive because it is based on a paradox: the conflict of feeling good while simultaneously being good.

The thesis of The Happiness Paradox is that we are destined to seek freedom and justification in life, and that these two endeavors are forever at odds. (This insight is well worked out in Buddhist Madhyamaka philosophy in excruciating detail) It is not that simple, though. Marar addresses the need for all of us to be respected and loved in society and by individuals, and how perceived judgment can influence how we feel about ourselves. We look for worthy audiences, such as family and lovers, to validate us, while also seeking to strip them of their power to do so. For anyone who has ever thought "why am I doing this? Why do I live my life this way?", this book will articulate what one may have suspected all along: we can't get to that place of feeling completely free from judgment and influence and also to a place of feeling justified/respected/validated by others because they are at odds. Such a balance does not exist. It is futile. Yet, we can't help it, we seek both simultaneously

For example the  chapter on romance and love offers up one brutal truth after another that romantic relationships contain inherent contradictions that cannot nor should be resolved, such as freedom and commitment; permanence and dissolution. In fact, according to Marar, the key to a happy relationship is for these opposite qualities, with complete integrity, to exist simultaneously. For example, the constant presence of possible dissolution through death, abandonment, betrayal, etc. should only heighten the joy and love we have together now.

Drawing on a wide and varied range of sources from psychology, philosophy, history, novels, and film, this book will engage those who are looking for meaning in a secular culture. It challenges our conventional search for happiness, while suggesting a bolder way to live with paradox. 

Paradox by Doris Olin (McGill-Queen's University Press) (Hardcover) Paradoxes are more than just intellectual puzzles – they raise substantive philosophical issues and offer the promise of increased philosophical knowledge. In this introduction to paradox and paradoxes, Doris Olin shows how seductive paradoxes can be, why they confuse and confound, and why they continue to fascinate. Olin examines the nature of paradox, outlining a rigorous definition and providing a clear and incisive statement of what does and does not count as a resolution of a paradox. The view that a statement can be both true and false, that contradictions can be true, is seen to provide a challenge to the account of paradox resolution, and is explored. With this framework in place, the book then turns to an in-depth treatment of the Prediction Paradox, versions of the Preface/Fallibility Paradox, the Lottery Paradox, Newcomb's Problem, the Prisoner's Dilemma and the Sorites Paradox. Each of these paradoxes is shown to have considerable philosophical punch. Olin unpacks the central arguments in a clear and systematic fashion, offers original analyses and solutions, and exposes further unsettling implications for some of our most deep-seated principles and convictions.

Doris Olin is associate professor and chair of the Philosophy Department at Glendon College, York University, Toronto.

How quaint the ways of Paradox! At common sense she gaily mocks!
W S. Gilbert, The Pirates of Penzance 

Paradoxes are fascinating: they baffle and haunt. They are among the most gripping of philosophical problems, for as we struggle through the maze of argument and counter-argument, there is the sense that the solution, the crucial insight, lies just beyond the next turn of the path. Still, most of the paradoxes of interest to philosophers are not mere intellectual puzzles. They raise substantive philosophical issues, and their resolution offers the prospect of increased philosophical knowledge.

This book begins by considering what a paradox is, and what the possible avenues are for resolution of a paradox. Chapter 2 examines a challenge to the analysis based on the view that contradictions can be true, and that the conclusion of a paradox may thus be both true and false. In subsequent chapters, the focus is on a detailed study of paradoxes that are particularly riveting and seductive (or, at least, strike me as so), and that appear to have consider-able philosophical depth. The paradoxes studied are also linked by the theme of rationality: they raise difficult issues about the rationality of belief, the rationality of action and the coherence of our language.

We have already seen that paradoxes may be classified as type I or type II. Before going on to consider how a paradox may be resolved, further distinctions will be helpful. First, the notion of a veridical paradox: 

A type I paradox is veridical just in case its conclusion is true (N-true in the case of a narrative-paradox, true simpliciter otherwise). 

A type II paradox is veridical just in case the conclusions of the two arguments are both true.

Of course, the truth of the conclusion(s) does not provide a logical guarantee that the reasoning is impeccable, nor that the premises are true (although one might search in vain for a veridical paradox in which there is a flaw in either). Still, what is deceptive in a veridical paradox, at the very least, is the appearance of falsity in the conclusion (or the appearance that at least one of the conclusions is false).

The notion of a falsidical paradox is understood analogously. A type I paradox is falsidical provided that its conclusion is false; a type II paradox is falsidical if at least one of its conclusions is false. So in a falsidical paradox, the fault lies in the paradox-generating argument (or in at least one of the arguments), either in the premises, or in the reasoning.

Of the paradoxes we have to draw on, only the barber paradox can be considered to be veridical, for it is generally conceded that there is no flaw in the paradoxical argument, either in the premises or in the reasoning. But the conclusion of the barber paradox is:

The barber cuts his own hair if and only if he does not cut his own hair. 

How can we say that this conclusion is true, as required by the definition of "veridical"? After all, any statement of the form "P if and only if —P" is necessarily false.

Here it is essential to remember that in classifying the barber paradox as veridical, we are committed only to saying that the conclusion of the paradoxical argument is N-true, true in the barber story. This is guaranteed if the conclusion is implied by the statements in the description of the paradox. But it is now generally recognized that the story that gives rise to the paradox (there is a village in which there is a barber who cuts the hair of all and only those villagers who do not cut their own hair) is incoherent, that it is impossible for there to be such a village. Hence, there is no problem in granting that the description implies an impossible conclusion, and thus no problem in granting that the conclusion is N-true. A necessarily false premise may imply a necessarily false conclusion.

The same sort of thing may occur in a type II veridical narrative-paradox. Given that the paradox is veridical, the conclusions of both arguments will be N-true. One might naturally assume, in such a case, that the conclusions must be consistent. But if the description of the paradox is itself necessarily false, then the conclusions may both be implied by the description, and yet be inconsistent.

A clear example of a type I falsidical paradox is provided by the Achilles and the tortoise paradox. Of the type II paradoxes already introduced, all seem to be falsidical: the two conclusions, in each case, are unquestionably inconsistent and yet the descriptions seem logically coherent.

The final distinction to be drawn here is between controversial and uncontroversial paradoxes: 

A type I paradox is uncontroversial if either there is general agreement that its conclusion is true or general agreement that its conclusion is false. 

Note that to say that a paradox is uncontroversial does not mean that there is no controversy surrounding it. There may be broad agreement that the conclusion of an argument is false, even though there is no consensus concerning the diagnosis of the flaw in the argument. Both the barber and Achilles and the tortoise provide examples of uncontroversial paradoxes. The corresponding definition for type II paradoxes is: 

A type II paradox is uncontroversial if either there is general agreement that both conclusions are true or there is general agreement that a particular conclusion is false. 

Looking at the type II paradoxes, the Monty Hall paradox can fairly be regarded as uncontroversial, since it is generally recognized that it is rational to switch one's choice of door. But the taxi-cab and the ship of Theseus are both controversial.

To sum up, the distinctions drawn is this section can be illustrated as follows:

Barber  type I,                                      veridical, uncontroversial Achilles and the tortoise                        type I, falsidical, uncontroversial Monty Hall                                           type II, falsidical, uncontroversial Ship of Theseus                                    type II, falsidical, controversial Taxi-cab                                              type II, falsidical, controversial

How to resolve a paradox

At this point, we have an account of what constitutes a paradox, and an understanding of the different types of paradox. What remains to be dealt with is the question of how to respond to a paradox, how to provide a resolution.

Paradoxes present us with apparently impeccable operations of reason that nonetheless lead to apparent absurdity. They are upsetting because, while the illusion persists, we have a challenge to the supposed veracity and reliability of reason. If this is where logic can lead, then why would we recommend logic or respect its dictates? The threat to reason can be overcome only by puncturing the illusion created by the paradox.

To resolve a paradox it is necessary to show that the paradoxical argument does not in fact present us with an impeccable use of reason leading to a patent absurdity. There are thus two principal options in providing a resolution for a type I paradox: (i) we may dispel the illusion that the argument is air-tight by isolating and diagnosing a flaw or fallacy in the argument; or (ii) we may explain away the appearance of falsity in the conclusion. This is accomplished by explaining why the conclusion appears to be false even though it is in fact true. In pursuing alternative (i), attempting to find a flaw in the argument, there are two further options: (a) show that at least one of the premises is not true; or (b) show that the argument is invalid.

Briefly, the options for resolving a type II paradox are as follows. One sort of resolution will consist in finding a flaw in one of the two paradox-generating arguments, either in the premises or in the reasoning. Alternatively, we may explain why it appears that the conclusions cannot both be true even though, in fact, both are.

Later chapters will study instances of the different types of resolutions in detail. For now, let us look at some of the paradoxes already introduced in order to illustrate these distinctions. Of necessity, the discussion will be limited to the uncontroversial paradoxes.

The barber paradox has been cited as an instance of a veridical paradox. This despite that the fact that its conclusion, that the barber cuts his own hair if and only if he does not, is a contradiction. To make sense of this, it is essential to keep in mind, as was pointed out earlier, that it is strictly N-truth and N-falsity that are

relevant to the assessment of the argument of a paradox based on a story. The real issue is whether the conclusion is N-true, that is, whether the description of the village implies the premises of the argument, which, in turn, imply the conclusion. It may at first seem that this could not be, since the description of the village seems perfectly consistent, and a consistent set of statements does not imply a contradiction. But it is not difficult to convince oneself that the description is, in fact, contradictory. After all, it refers to, among others, the barber himself, and says of him that he cuts his own hair if and only if he does not. So there is no problem in granting that the conclusion of the paradoxical argument is N-true, that it is implied by the description of the village. It appears to be N-false only because it is contradictory and the description of the village appears, at first, perfectly consistent. Thus, we can explain the appearance of falsity while granting that the conclusion is true.

This treatment of the barber paradox exemplifies one basic approach to veridical paradox resolution: showing that the description of the paradox is inconsistent. If it is, then there need be no surprise or shock at what the description implies, since anything follows from an inconsistency.

The Monty Hall paradox provides an example of an uncontroversial falsidical paradox, for it is generally agreed that the correct strategy is to switch your choice of door after Monty shows you a goat door. This means that there must be a flaw in the argument that there is no good reason to switch – in the "no switching argument". But what, precisely, is wrong with it? Suppose you pick door A, and then Monty shows you that door C has a goat behind it. A key premise in the no switching argument is that after door C is revealed as a goat door, it is as likely that the car is behind door A as it is that it is behind door B; the two possibilities are equally likely. To find a fallacy in the no switching argument and thereby resolve the paradox, it is this premise, I believe, that must be successfully rebutted.

Consider. If Monty's intent had been simply to open one of the three doors at random, and this intent had resulted in his opening door C, and revealing a goat behind it, then it would be equally likely that the car was behind door A and that it was behind door B. But Monty's choice was in fact restricted to door B or door C, and his intent was to choose a goat door. So you know something about door B that you do not know about door A; there is an asymmetry in your knowledge of the two doors. In a choice between door B and another door, where the intent was to choose a goat door, door B was not chosen. How is this knowledge relevant to the assignment of probabilities? Well, there was a 2/3 chance that Monty's choice was forced – that only one of the two doors was a goat door. Since you knew that Monty's intent was to open a goat door, and that he could do this, his opening door C and revealing it to be a goat door does not change this probability. But if Monty's choice was forced, then the car is behind door B. Thus, there is a likelihood of 2/3 that the car is behind door B; and, accordingly, there is only a 1/3 likelihood that it is behind door A.

If this analysis is correct, then we have dissolved the paradox, dispelled the illusion, by showing that one of the premises in one of the paradox-generating arguments is false. Of course, the reasoning is subtle; the flaw in the no switching argument is not easy to discern. Indeed, some mathematicians and probability theorists have been initially taken in by the no switching argument, although none has persisted in defending it.

Further illustrations of the resolution of a paradox must await the more detailed treatment of individual paradoxes. But, at this point, some words of caution are in order. First, to be satisfactory, the resolution of a paradox should be robust: it should stand up to strengthened versions of the paradox. For instance, the paradox-generating argument may initially be presented with an extremely strong premise, a premise that makes a very broad, sweeping claim. If so, it may take no great acumen to point out counter-examples to the premise. However, before declaring the paradox vanquished, we need to be sure that it cannot simply be reinstated when a suit-ably weakened version of the critical assumption is provided. To be robust, the attack on a paradoxical argument should be focused on the strongest, most impregnable version of the argument available.

A related point concerns different versions of the same paradox. The Achilles and the tortoise paradox, for example, seems to be essentially the same as the racetrack paradox (see the Appendix). If so, then any solution to the one should also be applicable, with the appropriate changes, to the other. An attempted resolution of a paradox that cannot be applied successfully to every version of the paradox must be off the mark in that it focuses on some inessential feature of the paradox. This is not to say that it is always evident whether one paradox is a variant of another. In fact, the criteria for two arguments being versions of the same paradox are far from obvious. One can even imagine cases in which the fact that a solution applies to one argument, but not to the other, would be cited as reason for denying that these are just two versions of the same paradox. Nonetheless, as we shall also see, there are many cases in which it is entirely clear that different scenarios are all versions of the same paradox, and thus require a unified solution.

What does not count as a resolution of a paradox? The negative may be almost as significant as the positive here. One very common and natural response to a stated paradox is to present another argument. More specifically, the response is an attempt to present an even more compelling or persuasive argument for (or against) the conclusion (one of the conclusions) involved in the original paradox. Consider the Monty Hall paradox, for example. Suppose a mathematician friend, having announced that she has a solution to the paradox, proceeds to give a very clear, very explicit, and very powerful argument for the conclusion that one ought to switch doors. Whatever the merits of her argument and the worth of her contribution, they do not constitute a solution to the paradox, for the argument in favour of not switching is left untouched. So there is still an apparent conflict of reasons: two ostensibly strong arguments for inconsistent conclusions. Consequently, there is still a sense of confusion, of being befuddled, which can be cleared up only by an analysis of an error or flaw in one of the arguments. A paradox is not unravelled by attempting, however successfully, to prove that one "side" in the conflict is correct. Later chapters will provide examples of philosophers responding to the challenge of a paradox in this way.

The ideal, in treating a paradox, is to puncture the illusion of letter-perfect reasoning leading to clear absurdity. But short of achieving this ideal, there are still worthwhile contributions one can make. The mathematician's argument alluded to in the previous paragraph may convince us that the rational response in the Monty Hall scenario is indeed to switch, when previously we had been uncertain. While such an argument does not suffice to dissolve the paradox, it may convert a previously controversial paradox to the status of uncontroversial. Assuming the argument to be correct, this constitutes an advance in the understanding of the problem, and progress in the search for a solution. If it is known that the correct strategy is to switch doors in the Monty Hall game, then the focus must be squarely on the no switching argument, and the attempt to locate a flaw in it. The range of possible solutions has been narrowed.

One other way to move a controversial type I paradox into the uncontroversial category is worth mentioning here (and will be illustrated in Chapter 4). Suppose we construct an argument that is strongly analogous to the original paradoxical argument, but that leads to a conclusion even more preposterous or bizarre than that of the paradoxical argument; so bizarre, in fact, that it is completely clear that the conclusion, and therefore the argument, have to be rejected. Since the new argument is strongly analogous to the original paradoxical argument, it is now apparent that the original argument must also be rejected. Again, the set of possible options for a solution has contracted.

There is, finally, one other way to make progress on a paradox, short of resolving it or narrowing the range of possible solutions: progress can be made by clarifying one of the central arguments. This may be achieved in a variety of ways. Among the more significant are: analysing one of the key concepts; setting out, fully, rigorously and explicitly, the premises necessary for the argument; ensuring that the premises are just as strong as needed, but no stronger, so that the argument is as immune to criticism as possible; and making clear exactly what the inferential steps are that take us from the premises to the conclusion, so that any logical gaps in reasoning will be more apparent.

This section has considered how to resolve a paradox, how not to resolve a paradox and how to make progress on a paradox short of resolution. To conclude, let us consider the question of why we feel a pressing need to untangle a paradox, why we care about paradoxes. One answer has already been suggested. An unresolved paradox is a threat to the trustworthiness of reason. How can reason command our respect if it leads to absurdities? But another motivation stems from the fact that the proper resolution of a paradox may give us greater philosophical knowledge. Faulty assumptions concerning, for instance, justified belief, or rational action, may be uncovered in the unravelling of the paradox.

Of course, some paradoxes, of which the barber is one, have little, or no, philosophical punch. The ship of Theseus, on the other hand, may reveal a good deal about the principles governing our concept of the identity of a physical object. The depth of a paradox is generally considered to be a function of the sort of philosophical impact its resolution will have. At one extreme of the spectrum, a paradox may reveal an incoherence that necessitates a fundamental revision of our conceptual scheme; at the other end of the spectrum there is the barber. Unfortunately, a proper appreciation of the depth of a paradox frequently must await its resolution.

A Brief History of the Paradox: Philosophy and the Labyrinths of the Mind
by Roy A. Sorensen (Oxford University press) (Paperback) Can God create a stone too heavy for him to lift? Can time have a beginning? Which came first, the chicken or the egg? Riddles, paradoxes, conundrums--for millennia the human mind has found such knotty logical problems both perplexing and irresistible. Now Roy Sorensen offers the first narrative history of paradoxes, a fascinating and eye-opening account that extends from the ancient Greeks, through the Middle Ages, the Enlightenment, and into the twentieth century. When Augustine asked what God was doing before He made the world, he was told: "Preparing hell for people who ask questions like that." A Brief History of the Paradox takes a close look at "questions like that" and the philosophers who have asked them, beginning with the folk riddles that inspired Anaximander to erect the first metaphysical system and ending with such thinkers as Lewis Carroll, Ludwig Wittgenstein, and W.V. Quine. Organized chronologically, the book is divided into twenty-four chapters, each of which pairs a philosopher with a major paradox, allowing for extended consideration and putting a human face on the strategies that have been taken toward these puzzles. Readers get to follow the minds of Zeno, Socrates, Aquinas, Ockham, Pascal, Kant, Hegel, and many other major philosophers deep inside the tangles of paradox, looking for, and sometimes finding, a way out. Filled with illuminating anecdotes and vividly written, A Brief History of the Paradox will appeal to anyone who finds trying to answer unanswerable questions a paradoxically pleasant endeavor.
Excerpt: Before Quine challenged the analytic-synthetic distinction, there was a tendency to regard philosophy as being qualita­tively different from the sciences. Scientists focus on synthetic statements whereas philosophers focus on analytic state­ments. Scientists explore reality with observations and exper­iments. Philosophers map our conceptual scheme through a logical study of semantics.

Quine agreed that philosophers are more apt to use the strategy of semantic ascent: they love to switch the topic from the things that puzzle us to the words we use in describing those puzzling things. "Don't talk about Truth! Talk about `true'!" This strategy works when the words are better understood than the things. Such will be the case when we lack the standard techniques for solving problems that con­stitute each science. But Quine thinks that the use of semantic ascent is only a rough mark of philosophy. The physicist Albert Einstein engaged in semantic ascent when trying to resolve anomalies about the nature of simultaneity. And metaphysicians sometimes appeal to empirical results to solve philosophical problems.

Quine has fostered this naturalistic turn in philosophy. He maintains that philosophy differs from science in degree rather than kind. Philosophy should heed biology just as biology heeds physics and vice versa. Philosophy takes the further step of trying to organize the results of science into an overall view of the universe. But as we have seen with Brandon Carter's case for human extinction, cosmologists also take a wide perspective.

Lord Kelvin contrasted the unclarity of metaphysics with the rigor of physics by claiming that "In science there are no paradoxes." But if you enter "paradox" in a search engine for scientific journals, you get many references to scientific paradoxes. Many of the scientific paradoxes have been solved. But the same can be said about philosophical paradoxes such as those made famous by Zeno. Philosophical progress tends to be self-effacing because, over time, its solutions are incor­porated as results in other fields. "Philosophy" is an indexical term akin to "here," "yesterday," "news." Its meaning shifts to cover issues that cannot (yet) be profitably delegated to the sciences.

Philosophy is like an expedition to the horizon. Under one interpretation, the venture is hopeless. We cannot reach the destination because what counts as the horizon constantly shifts. But becoming a pessimist on the basis of this tautology is like adopting a here-and-now philosophy on the strength of "Tomorrow never comes."

We can reach the horizon when the meaning of philoso­phy is rooted. Understandably, we look at the history of philosophy from the vantage point of the present. We are impressed by the resiliency of its issues and the broken ambitions of past thinkers. But an accurate measure of progress requires the adoption of an historical perspective. By this, I do not mean simply looking at the past. I mean looking from the past.

The twenty-first-century conception of philosophy will itself become a tonic to the vacuous pessimism of future generations. Given that I have correctly gauged the merits of Carter's doomsday argument, some philosopher in the distant future will find this book aging away in the remote corner of a library. As he browses, he will be amazed by what philoso­phers back in 2003 regarded as philosophy. He will know that many of the "paradoxes" discussed in this book are nowdefinitively answered by physics or mathematics (or by some hitherto unconceived field). This future reader will wonder why philosophers tried to answer those questions. As he reads this final sentence, I remind him that he stands at a new horizon, inaccessible to the author of this book. 

Truth Without Paradox by David A. Johnson (Rowman & Littlefield Publishers) In Truth without Paradox, David Johnson purports to solve several of the traditional problems of metaphysics—those pertaining to truth, logic, similitude, morality, and God.

In the first chapter, Johnson argues against the general acceptability of the schema "if p, then it is true that p," claiming thereby to resolve the paradoxes of the liar and of the sorites. In the second chapter, he clarifies what was settled by Quine about "truth by convention." In the third, he attempts to shed light on the obscure notion of "same­ness" or "uniformity," especially in its application to inductive extrap­olation and to the "grue" paradox. In the fourth chapter, he purports to solve the seemingly insoluble is/ought problem of moral philosophy. And finally, the fifth chapter—which will be of interest to philoso­phers of religion—contains what the author calls a historical proof of the existence of God, based on a resolution of the lottery paradox.

David Johnson is associate professor of philosophy at Yeshiva University in New York.

Excerpt: Metaphysics is the study of fundamental things, of what are sometimes called "first things." Now, the fundamental things are many: among them are truth, logic, similitude, morality, gods, minds, life, free will, causality, material composition, space and time, sets, numbers, and so on. (Almost certainly not to be included here are such things as aardvarks, toothpaste, prostitution, and laughter. And then there are borderline cases, such as holes.)

In practical terms, one might say that the "fundamental things" are the things concerning which there would be rather something wrong with someone who had no interest in them. If you have no interest in aardvarks, then, fine, you have no interest in aardvarks; but if you have no interest in logic, or in morality, then there is something wrong with you.

Some of the fundamental things have been fruitfully studied, so much so that sciences thereof have come into being, such as logic, mathematics, physics, and biology. (One will scarcely find a more beautiful and reward­ing example of metaphysics than Cantor's argument for the Diagonal Theorem, his simple and compelling proof that there is more than one in­finity.) But deep mysteries remain even about these well-studied things; I shall call them the Remaining Mysteries. And then there are all the rest of the fundamental things, whose study has been less marked by useful fe­cundity, and which I shall call the Remaining Things. If you wish to know something important about numbers, or about space and time, you may learn from the mathematician and the physicist. But if you wish to know something important about truth, or similitude, or morality, or the other

Remaining Things, I am afraid that humanly speaking you have no re-course but to consult a philosopher, since there is no other kind of human being who can help you. "Metaphysics," in the narrow sense in which it is peculiarly a branch of academic philosophy, is the study of the Remaining Mysteries and the Remaining Things. I shall call it academic metaphysics.

The Remaining Mysteries and the Remaining Things are too many, and too complex, and too much the subject of recalcitrant myth, to be profitably surveyed in a single book. The reader who is looking merely for a quick (and perforce hazy) overview of the field, and who wishes at all costs to avoid what I suppose the dust jackets would call "burdensome de-tails" (so often consigned to graduate school, or to a future life), must look elsewhere. Academic metaphysics is a complex, subtle, and difficult subject (so is Greek, or Topology, or Quantum Physics), and an introduction to academic metaphysics which goes easy on the details is about as valuable as an introduction to Latin which goes easy on the participles. Every seri­ous subject is a technical subject; on a jot or a `not' do worlds expand or con-tract, and gods come into being.

On the other hand, I have tried to avoid writing, as it were, A Trea­tise of Participles. In any attempt to introduce readers to a large subject which is rife with many important details, one is caught between two ex­tremes. Michio Kaku, in the preface to his Quantum Field Theory: A Modern Introduction, says:

In writing this book, we have tried to avoid two extremes. We have tried to avoid giving an overly tedious treatise of renormalization theory and the obscure intricacies of Feynman graphs. One is reminded of being an apprentice during the Middle Ages, where the emphasis was on master­ing highly specialized, arcane techniques and tricks, rather than getting a comprehensive understanding of the field.

The other extreme is a shallow approach to theoretical physics, where many vital concepts are deleted because they are considered too difficult for the student. Then the student receives a superficial introduction to the field, creating confusion rather than understanding.

Kaku's path to an "intermediate approach" between these two extremes, an approach which is sufficiently comprehensive and yet sufficiently deep and rigorous, is made possible by the fact that his subject is blessed with a wealth of carefully developed theories and well-established results, which may be cited and summarized. Academic metaphysics, I am afraid, is not at all like that. (There is nothing remotely like Noether's theorem, or Wick's theorem, or the Yang-Mills theory, or Feynman's rules, or Fu­jikawa's method.) After more than twenty-three centuries academic meta-physics is still inchoate, still mired in controversy over just about everything, and still trying to get something manifestly right. There are in academic metaphysics no theorems, rules, or methods, and the available theories are rather rough sketches, each an invitation to a nightmare. (It is often unclear even what the claims are: see, for examples, the several mys­terious, perhaps claim-bearing, passages scrutinized in the second and fourth chapters of this book.)

In these circumstances, it seems to me that an introduction to aca­demic metaphysics must risk moving close to the first of Kaku's two ex­tremes. In introducing readers to a problematical discipline (and one which treats of fundamental things!), superficiality and confusion are much more to be feared than are tedium and intricacy. Intellectual virtue, after all, is precluded by the former, but is at least compatible with the lat­ter. H. E. Crampton's three monographs on "the variation, distribution and evolution of the genus Partula" (a kind of land snail), collectively to­taling over 700 pages, are nothing if not intricate; perhaps they are also te­dious; but they have great intellectual virtue, and works of metaphysics could do worse than to emulate their "medieval" qualities.

There is a strange view in the academy that, though in mathematics and in the sciences even an introductory textbook (I don't mean the "_ for Po­ets" kind) must of course go into many forbidding details and demand exact standards of reasoning, the "humanities" should be more easygoing. "Just give students the Big Picture," or (as I have sometimes heard, to my dismay) "just get them to think." Now, I take a dim view of Big Pictures, and I want no one to think who does not think well. (There is a place which is chock-full of those who think, but do not think well; it is called Hell. It was not made for man.) To cajole students in the humanities into thinking, without ensur­ing that their thinking meets at least minimally acceptable standards of rigor; is simply to enslave them to sophistry and illusion; it is to leave them enticed by, but powerless to assess, those many non sequiturs, question-begging ar­guments, pseudo-paradoxes, distortions of evidence (and of history), and other such bits of intellectual badness as are so commonly found of late in the humanities. I do not see why the rigor of thought should be supposed any

less necessary in the things pertaining to humanity than in the things per­taining to, say, supersymmetry.

And what is it to be rigorous? It is to be (so much, we may say, as the flesh allows; but the mathematicians and the physicists should have taught us that the flesh allows a lot more of this sort of thing than the Humani­ties professoriate may suppose): precise, explicit, and meticulously correct about matters of logic; it is to be careful in the stating of propositions and of arguments, and attentive to the formal validity (or invalidity) of argu­ments. (It is remarkable how many famous arguments can be refuted es­sentially just by stating them carefully. How rarely this is done.)

So let us be rigorous, and let us make our students to be rigorous, from the very beginning, and let us care more about the virtue of thought than we do about the avoidance of tedium. (Or about observing foolish restrictions concerning what should be included in a metaphysics book. We shall go into, lovingly and in detail, all that we need to go into—whether it is philosophical, exegetical, historical, linguistic, or other—in order to treat rigorously the issues we discuss. That is a virtue. These are high matters. Let no one carp about the intricacy of an argument or the length of an excursus.)

It is the purpose of this book to introduce the serious reader to rigor­ous academic metaphysics. In order to allow for the necessary carefulness of thought, we restrict our attention to a select few issues pertaining to a select few (though a variegated few) of the Remaining Mysteries and the Remaining Things. But I have chosen such topics as I thought might be of especial interest to the general student of philosophy: truth, logic, simil­itude, morality, and God.

In the first chapter we critique and reject a celebrated claim which Aristotle made about truth. In the second chapter we consider the case against the view that human beings are the very creators of logical truth. (Aside from presenting material of intrinsic interest, this chapter serves as something of a morality tale about the state of the professional literature.) In the third chapter we try to shed light on the very obscure notion of "sameness," or of "uniformity," especially in its application to inductive ex­trapolation. The fourth chapter is twice a morality tale, and conceivably could leave us with one less branch of philosophy. The last chapter contains at least one proof of the existence of God.

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