Peter Suber

From the Editor’s Introduction: THE INTERNAL LIMITATIONS OF HUMAN UNDERSTANDING We carry, unavoidably, the limits of our understanding with us. We are perpetually confined within the horizons of our conceptual structure. When this structure grows or expands, the breadth of our comprehensions enlarges, but we are forever barred from the wished-for glimpse beyond its boundaries, no matter how hard we try, no matter how much credence we invest in the substance of our learning and mist of speculation. The limitations in view here are not due to the mere finitude of our understanding of ourselves and of the world in which we live. They are limitations that come automatically and necessarily with any form of understanding. They are, as we shall see, part and parcel of any organization or ordering of data that we call information. The consequences of these limitations are varied: As a result of them, hermeneutics cannot help but be hermetic; scientific theories of necessity are circumscribed by the boundaries of the ideas that define them; formal systems must choose between consistency and comprehensiveness; philosophical study, because it includes itself within its own proper subject matter, is forced to be reflexive in its self-enclosure. The fundamental dynamic shared by all forms of understanding testifies to an internal limitative keystone.

We human beings do have the power to modify our deep structure, through drugs and surgery. But we cannot yet use this power with enough precision to make deep changes to our neural structure without high risk of death or disability. There are two reasons why we find ourselves in this position. First, our instruments of self-modification are crude. Second, we have very limited knowledge about where and how to apply our instruments to get specific desirable effects. For the same reason, we don't even have good knowledge about what effects are physically possible.

Can we interpret human reason simultaneously as a product of neurochemistry and natural selection and as a transcendental standard? Jeff Mason asks the analogous question of philosophical writing. Can we interpret philosophical discourse as "rhetorical," embodied in language, and designed to persuade historical audiences, and at the same time preserve its traditional intention to disclose truths that transcend language, history, and audiences? Mason argues that these polar attitudes toward philosophical writing are untenable precisely when they exclude each other. This is a significant project with important literary and metaphilosophical consequences.

Kurt Gödel has been called the greatest logician since Aristotle. He was unquestionably the greatest logician of the 20th century, which has been the greatest century for logic since Aristotle's. Despite this stature, his name is little known outside professional circles of logic and mathematics, and astonishingly little is known about his life. His low profile cannot be due to the fact that his major achievements are complex and demanding, unintelligible to the uninitiated, for that is also true of his best friend, Albert Einstein. Nor can it be that Gödel was more conventional than Einstein. He did comb his hair and wear socks, but Gödel's reclusive and reserved personality, thin owlish appearance, forbidding glances, hypochondria, and paranoia are at least as easy to romanticize as Einstein's eccentricities. Part of the cause of his narrower fame must lie in the fact that Einstein's theories were acclaimed as triumphs, while the initial judgment on Gödel's theorems was that they constituted a first-rate calamity for logic and mathematics

A set of routine academic controversies has recently been fanned into a cause célèbre. I call the controversies 'routine' because they concern the design of curricula and syllabi, the regulation of campus life, and the recruitment of faculty and students. These are important but ordinary affairs for a college or university. They call for choices that arise from fundamental convictions on the purpose of education, the nature of knowledge, the firmness of standards, the value of community, and the mission of the institution. So dealing with these routine affairs is routinely attended with controversy. What is new is that the public is watching closely as academics thrash through these controversies nowadays. At least some journalists and politicians are watching closely and talking loudly about what they see. These conflicts would be what they ought to be, occasions for self-examination and growth, if they were not absolutized by observers who have raised the stakes by raising their voices and simplifying the issues.

Dyson's book is an argument disguised as an intellectual history. The argument is that all intelligence is collective, in the way that human intelligence emerges from the collection of unintelligent neurons, and that a global collective intelligence is now emerging from the growing interconnections among human beings and their machines. The history traces the rise of computation and thinking about machine intelligence from Hobbes to the present. The history is fascinating and detailed. The thesis about collective intelligence is fascinating but lacking the detail which would make it more than merely suggestive.

I call these six hitches "exploding" knots because they untie easily and completely with one tug of the ripcord. Unlike slipped knots that untie with a ripcord, these knots leave absolutely no tangle. Yet they give up nothing in strength or ease of tying. To learn to tie them, jump to the illustrations and skip the commentary. In each illustration, the line labelled "R" is the ripcord ("running part"). The line labelled "S" is to be attached to the load ("standing part"). Tighten the knot with the "S" line. To decide which of these knots is best for which application, see the table at the end, which presupposes some of the text you might have skipped. After learning to tie the knots from the illustrations, read the text if only for safety issues. These knots are "probably original" in Clifford Ashley's sense of this phrase.

The Problem Background Some Political History, Pre-1790 Federalist and Republican Principles Some Demographic History, 1790-1980 To What Extent Have the Possible Dangers Become Actual? The Discriminatory Impact and Prospects for Future Amendments Remedies Conclusion Appendix Table 1. The Possibility of Federalist Minority Amendment: Decade by Decade Table 2. The Possibility of Federalist Minority Amendment: Amendment by Amendment Table 3. Discriminatory Impact of Population Changes Table 4. Relative Strength of Voice of Citizens of the Various States Notes Second Thoughts..

We know from more than two millenia of experience that self-referential statements, such as the liar's ("This very statement is false"), can be debated by philosophers and logicians for millenia without producing consensus on their solutions. We should not be surprised, then, if self-referential laws produce paradoxes which puzzle lawyers. What is surprising, though, is that some of these paradoxes bother only the logicians and philosophers who study law from outside, and do not bother lawyers at all. This fact should interest philosophers of law even more than the paradoxes themselves.

I find (as others have found) that question-begging is formally valid but rationally unpersuasive. More precisely, it ought to be unpersuasive, although it can often persuade. Despite its formal validity, question-begging fails to establish its conclusion; in this sense it fails under a classical or foundationalist model of argument. But it does link its conclusion to its premises by means of acceptable rules of inference; in this sense it succeeds under a non-classical, non-foundationalist model of argument which is spelled out in the essay. However, even for the latter model question-begging fails to link the conclusion to premises that the unconvinced would find more acceptable than the conclusion. The essay includes reflections on the conditions under which the circularity of mutually supporting claims can avoid question-begging and legitimately be persuasive.

_The Case of the Speluncean Explorers, _written in 1949 by Lon Fuller, is the most famous fictitious legal case of all time. Describing a case of trapped travellers who are forcd to cannibalize one of their team, it is used on courses in philosophy of law and Jurisprudence to show how their trial upon rescue touches on key concepts in philosophy and legal theory such as utilitarianism and naturalism. _The Case of the Speluncean Explorers: Nine New opinions_ includes a reprint of Fuller's classic article and a much-needed revision of and addition to the five openings originally expressed in the case by the five Supreme Court Judges. Peter Suber carefully and clearly introduces students to the main themes of Fuller's article before introducing nine new opinions. These opinions include perspectives from communitarian, feminist, multicultural, postmodern and economic theories of law, updating Fuller's original case and bringing contemporary theories of law to bear on the five original opinions. Why read this book? One reason is to get beyond sloganeering about "judicial activism" and "activist judges". The book is an enjoyable and even-handed way to understand what the debate is about. It doesn't tell you what to think, but illustrates the contending positions and lets you think for yourself. It will show you how judges with different moral and political beliefs interpret written law, how they use precedents, how they conceive the proper role of judges, how they conceive the relationship between law and morality, and how they defend their judicial practices against criticism. It anchors all of this in a Supreme Court hearing of a gripping, concrete case on which real people disagree. The book uses no jargon and assumes no prior knowledge of law or legal philosophy.