Recent Responses

What, if anything, do philosophers make of the fact that after centuries of philosophy, there is little consensus on the anwers to most philosophical questions?

The chief lesson I have drawn is that reaching consensus is not an important criterion for progress in philosophy. This is true in several areas of my own professional life, including in my discussions with colleagues, in my own study of philosophical texts, and in my own philosophical research.

First, there is much be learned by exploring diverse perspectives to complex philosophical issues. My best discussions with colleagues are ones where we understand and explore the differences between our philosophical views; when this occurs, I rarely end up agreeing with others but I frequently gain new insight nonetheless.

Second, this lack of agreement among philosophers—which occurs at so many levels--is itself a fascinating intellectual phenomenon. As an historian of philosophy, I am often enthralled by the ways that philosophers' thoughts about a single issue or idea have changed over time.

Finally that philosophical questions and issues are not amenable to simple answers is exciting to me as a scholar: the same intellectual characteristics that lead to a lack of consensus mean that I and other philosophers have a wealth of opportunities to contribute to the discipline in diverse, creative ways.

One of my pet peeves has been that Critical Thinking is not a requirement at the high school level. If high school is supposed to prepare kids to make important life decisions, it would seem to be one of the most important disciplines. I rarely hear any discussion about the issue, however. Do you think an introduction to critical thinking (or for that matter, an introduction to philosophy) should be required at the high school level or before? Why isn't it?

I agree that critical thinkingskills are vital. Taking a course in critical thinking is not the onlyway to gain these skills, however, and so I think the most importantquestion is whether high school students have plentiful opportunitiesto do this.

Inpart, this is a matter of curriculum. I suspect that required coursesin critical thinking or introduction to philosophy are not the bestways to inspire high school students to work hard on developingcritical thinking skills. Instead, I agree with the idea that criticalthinking should be taught “across the curriculum,” which is to sayshould be taught in diverse ways in nearly every course. The trick, ofcourse, is designing excellent curriculum that does this well.

Thatsaid, I suspect that quality of teaching matters more than curriculardesign: it is our relationships with individual teachers that caninspire us to work hard and learn the most, and the most importanteducational reforms may be those that help our teachers to learn how toinspire as many of their students as possible.

Why is there no "happiness"ology? It seems that throughout history philosophy has strived to legitimize and analyze most basic human questions except that of what happiness is and how it is achieved. Is this accurate or am I mistaken?

A few, but only a few, words on two 19th-century philosophers: Jeremy Bentham and his disciple, who went off in his own, individual direction, John Stuart Mill. Both were utilitarians, and believed in the moral principle: "the greatest happiness for the greatest number." But they understood "happiness" differently. Bentham took it hedonistically: happiness (the good, the summum bonum) is pleasure. Sexual pleasure is a paradigm of the good in this sense: exquisite and exhilarating sensations. There are others: eating, sleeping, playing sports--all fun things. Mill thought that there were lower and higher pleasures: bodily, sensual pleasures, and the pleasures of the mind. These include, for example, reading a poem and enjoying its beauty. For Bentham, "pushpin is as good as poetry," that poetry was good only when and because it could produce sensations similar in kind to the bodily. Not so for Mill, who thought that these pleasures were qualitatively different (and only those who experienced both kinds could pronounce on their relative value). Mill thought that a full human life, one that exhibited what flourishing is for a human, would include both kinds of happinesses. He also thought: it is better to be a philosopher [Socrates] dissatisfied [grouchy, in part] than a pig satisfied. I still haven't decided whether Mill was right about that. Philosophers would tend to say such a thing, wouldn't they?

What's the best definition of Nature and its contrast to the supernatural?

In the early modern period, there was considerable debate about the metaphysical status of miracles. Philosophers as different as Hobbes and Malebranche seem to agree, however, that some event is a miracle if and only if it caused by God's willing that that event take place.

On this account, even an event that normally takes place according to natural laws could occur miraculously, if and only if it were a direct effect of God's will. This would be a metaphysical characterization of a miracle. Even granting this definition, of course, there remains a question as to how one could know that some event were a direct effect of God's will. This would be an epistemological question.

An alternative definition of miracle, advanced by Leibniz, is that some event is a miracle just in case it cannot be understood by a created mind. According to Leibniz, all natural events can in principle be understood by created minds, provided one has access to the information necessary to understand that event; a miracle cannot be understood by any created mind, because comprehension of a miralces requires access to knowledge that goes beyond the order of nature.

Although the preceding definition is akin to that proposed by Jyl, it differs from hers insofar as it postulates that natural events are in principle comprehensible and supernatural events are in principle incomprehensible. According to Leibniz, the reason that all natural events are comprehensible is that we can at least know the laws that govern those events, even if we lack access to the information necessary required to instantiate those laws, whereas supernatural events are subject to laws that we cannot know. In this respect, Leibniz's proposal is akin both to Alex's, and to the first definition I presented above. Leibniz has an argument why there must be laws in principle inaccessible to us, which turns ultimately on his belief that there is a divine providential order, distinct from the natural order.

This commitment is, of course, shared by proponents of the first definition presented above. It may turn out that whether one is willing to countenance the miraculous depends on whether one believes that God exists.

It seems that most of my thoughts are expressed as reflections of familiar stimuli received through the agreed-upon 'five senses' (this includes spoken and written language). Is there any appropriate way to speculate on what form the thoughts of a hypothetical person born without access to sight, sound, smell, touch, or taste might take? I guess what I mean is: "please speculate!"

There was a real life case of a girl named Genie (a pseudonym) who was deprived of any real sensory stimuli for much of her young life because of the abuse of her father. Her story is told in a book called Genie by Russ Rymer. Her case suggests, in line with what Alex says above, that the absence of early senory stimuli prevents a human being from developing a normal mental life.

Is Russell's Paradox a problem for our confidence that 2+2=4 is true? I've never understood how big a problem it represents in math. Does it throw everything into doubt, or just some things? The <i>Stanford Encyclopedia</i> entry is a bit technical.

Russell's Paradox is a problem for set theory--or at least it was when Russell discovered it. The most popular modern approach to set theory is based on the axioms developed by Zermelo and Frankel, and the Zermelo-Frankel (ZF) axioms are formulated to avoid the paradox. So Russell's Paradox is not a problem for modern set theory.

The reason paradoxes in set theory are considered to be such a serious matter is that most mathematicians regard set theory as the foundation of all of mathematics. Virtually all mathematical statements can be formulated in the language of set theory, and all mathematical theorems--including your example 2+2=4--can be proven from the ZF axioms.

But you ask about our "confidence" that 2+2=4 is true. I don't think anyone's confidence in 2+2=4 is based on the fact that it is provable in ZF set theory, even though ZF is regarded as the foundation of mathematics. It's hard to imagine anyone having serious doubts about whether or not 2+2=4, and having those doubts relieved by seeing the proof in ZF. So if a new paradox were discovered that showed that the ZF axioms were flawed, I don't think anyone's confidence in 2+2=4 would be shaken. We'd just try to fix the flaw in the axioms in a way that would allow us to still develop mathematics.

How do we resolve the fact that our finite brains can conceive of mental spaces far more vast than the known physical universe and more numerous than all of the atoms? For example, the total possible state-space of a game of chess is well defined, finite, but much larger than the number of atoms in the universe ( Obviously, all of these states "exist" in some nebulous sense insofar as the rules of chess describe the boundaries of the possible space, and any particular instance within that space we conceive of is instantly manifest as soon as we think of it. But what is the nature of this existence, since it is equally obvious that the entire state-space can never actually be manifest simultaneously in our universe, as even the idea of a board position requires more than one atom to manifest that mental event? Yet through abstraction, we can casually refer to many such hyper-huge spaces. We can talk of infinite number ranges like the integers, and "bigger" infinite ranges like rational numbers, and yet still "bigger" infinite ranges like the irrationals. In what sense can we say all of these potential huge spaces exist (and they must, since we can so easily instantiate well-formed members of them, at will) yet we don't have even the slightest fraction of sufficent space for them in our known universe?

To add a word or two to Dan's great response: there is no questionthatmathematics deals with infinite collections, but what those are, whatwe mean when we make claims about them, which claims are correct —these have been hotly disputed issues for thousands of years. (Inthe history of mathematics, concern for these foundational questionshas waxed and waned. There have been times, for instance in theearly part of the twentieth century, when disputes over these issues,were very heated and split the mathematical community. There have beenother times, for instance now, when mathematicians have been lessinterested in these issues — although of course there are alwaysexceptions, like Dan.) The basic question — what does it mean to call aset "infinite"? — is so fundamental that it's simply astounding that wedon't know how to answer it.

Onone way of looking at the matter, what Dan called "platonism", to saythat a set is infinite is simply to have given a measure of its size.To say that a set is infinite is much like saying that it's got 17elements in it: if you counted up the elements in the second set you'dfind there were 17 of them, and if you counted up the elements of aninfinite set you'd find there were infinitely many of them.

But on another of way looking at the matter, this is insane. How can one finishcounting up the elements in an infinite set? Isn't that what "infinite"means, that the process of counting never stops? On this way of lookingat things, to call a set "infinite" is not to describe the size of someactual collection, but rather to mark it off from all finitecollections: finite collections are ones for which the process ofcounting their members eventually stops, while infinite ones arecollections whose elements we can keep on generating without end.

The first conception accepts the existence of the actual infinite:a collection that actually contains infinitely many objects. The secondconception rejects this as unintelligible and talks instead of the potential infinite:to say that a set is infinite is not to make a claim about the size ofan actually existing object but rather to say that each of its elementscan potentially be brought into existence. (The two conceptions will beconfused if you think that an entity that can potentially be broughtinto existence really exists after all — and has the property ofpotential existence attached to it. See here for some comments on a comparable error.)

Should education be a means to an end?

I don't see anything wrong with using education as a means to an end, as when I suffer through a dreary course on car mechanics so that I can learn how to fix my own engine. Having said this, I don't think education is always merely a means to an end: not only can it be fulfilling to learn certain things even if this knowledge is put to no practical use, but the very process of educating oneself can be fulfilling independently of any value practical or otherwise in the things learned.