I haven't posted on here in a long while... anyhow, I'll start things off again by posting something that rather amused me.
In Newsweek (yeah, I get it -- apparently they offered my mom one of those "get a free subscription for a friend" things, so she signed me up) today I saw a short article on a new book. Written by "a journalist who specializes in evolutionary psychology" (I'm still trying to wrap my head around how this is any sort of qualification), it has the title The Evolution of God. Those of you who have read Chesterton's The Everlasting Man should know why this was so amusing to me. From Chapter 1 of Chesterton's book:
"[...] concerned a comment on Grant Allen, who had written a book about the Evolution of the Idea of God. I happened to remark that it would be much more interesting if God wrote a book about the evolution of the idea of Grant Allen. And I remember that the editor objected to my remark on the ground that it was blasphemous, which naturally amused me not a little. For the joke of it was, of course, that it never occurred to him to notice the title of the book itself, which really was blasphemous; for it was, when translated into English, 'I will show you how this nonsensical notion that there is a God grew up among men.' "
The Newsweek article implies that the forthcoming book is not quite so uncharitable as that. But the point remains that people seem to think that this kind of approach to religion somehow does it more justice than the acerbic treatment of the 'new atheists'. Yes, the history of religion has its place (though in this and similar cases I am skeptical about how much of the 'history' is history and how much is simply speculation), but its place is not where people want to put it. If you don't care that Christianity is making claims about what sort of universe we live in, I don't care how sanguine you are about it: you aren't taking it seriously. Musings on the potential evolutionary adaptivity (etc.) of religion are not relevant to the problem. Yes, the 'faith debate' (poor description from the Newsweek article) can be pretty nasty and unproductive, even actively destructive, with vocal people on either 'side' calling each other deluded fools. But it's not any more productive to just ignore the fact that people are actually making truth claims when they claim a religious creed, no matter how many warm fuzzies you provide about how maybe it's not so bad to believe in God after all.
I'm actually quite often struck by how many of the conventional thought patterns Chesterton attacks in the society of his day are still (or maybe it's again?) present now. I wonder, where is our 21st century GKC?
Tuesday, June 2, 2009
Thursday, February 26, 2009
Work and Value
What do we pay people to do, and why?
There are, somewhat loosely, three kinds of jobs. There are those worth doing in themselves; they would be worth doing whether or not they were necessary, and worth doing whether or not one was paid to do them. In this category fall many scholarly or intellectual activities, including science and other pursuits of knowledge, art, writing literature, etc. . There are those with no inherent value, but which are valuable as means to an end, and ought to be done even if nobody was paid to do them. Most skilled and unskilled labor falls into this category: farming, road work, etc. -- but also (arguably) things like entertainment production (it is good to have some produced entertainment -- games, movies, the like -- available, though obviously quality matters here and far more is produced than is really optimal), medicine, and many sorts of engineering. Finally, there are those which are worth doing only if, and only because, one is paid to do them. The production and (especially) sale of useless gadgets, and many facets of advertising (is anyone prepared to maintain that telemarketers or the producers of obnoxious internet pop-up ads are doing something worthwhile or that needs doing?) fall into this category.
It seems to be nearly tautological that it is desirable to have as many people as possible doing the first sort of activity (things good in themselves), and that labor ought to be directed toward the second (instrumental goods) just insofar as is necessary to uphold society and improve the general human condition -- and whenever such an activity can be done with less effort, it ought to be done so, to free up time and energy for enjoyment and for pursuit of activities good in themselves.
Now originally the vast majority -- nearly all -- of human effort was devoted to the second kind of activity. Absent large-scale organization, industry, advanced technology, and automation, it takes much of the general effort of society to feed, clothe, shelter, and defend itself. The people who pursued philosophy (and later science), for instance, were generally those who were lucky enough to be wealthy enough not to have to do ordinary work.
Well, we now have large-scale organization. We have massive industrial capability. We have quite a lot of labor-saving and labor-easing technology, and an increasing amount of automation capable of doing our labor for us. Especially in the West, we have the capacity for an unprecedented amount of our society to simply not need to work on those necessary, but in themselves valueless, tasks that have so long occupied our efforts, and with every advance in technology this becomes more and more true.
What have we done with this capability? Now that we are so much more efficient, do we now have so much more free time to think about things which are valuable in themselves? Are we a society of scholars, devoted to knowledge? Or, at least, do we have more and more free time to associate with one another and develop friendships?
You need only turn on the television, or browse the internet, or walk through a store, or be rudely interrupted at dinner (provided that you are one of those people with enough free time to have a regular dinner with family, of course) by yet another telephone call insisting that you need to refinance your mortgage, to see that this is, of course, not the case. More and more people are doing that third kind of job -- the kind you only do because you are paid to do it. Do not mistake me: I have no ill-will towards those who can get no other job than to sit at a phone bank and call perfect strangers in order to get them to buy something. Those of us lucky enough to have a more meaningful occupation should pity, not despise, them.
But it is a particularly damning commentary on our society that we have used our enormous efficiency and technological capability, not to give ourselves more free time for relationships and contemplation, not to make ourselves a society of scholars in pursuit of knowledge, but instead to create make-work. Such an enormous portion of our vast resources are devoted to the "manufacture of silly luxuries and then of sillier advertisements to persuade us to buy them". What evil have we done, that the fruits of our efforts should not be contemplation or leisure but a suffocating deluge of pointless products and irritating advertisements for them? What evil have those poor folks in the telemarketing call centers done, that we should refuse to pay them except to provide a worthless "service", at best useless and at worst actively harmful to themselves and their fellow human beings? What kind of a society are we, that we should allow and even encourage all of this, valuing sales above knowledge, make-work above rest, and money above everything?
May God have mercy on us all.
There are, somewhat loosely, three kinds of jobs. There are those worth doing in themselves; they would be worth doing whether or not they were necessary, and worth doing whether or not one was paid to do them. In this category fall many scholarly or intellectual activities, including science and other pursuits of knowledge, art, writing literature, etc. . There are those with no inherent value, but which are valuable as means to an end, and ought to be done even if nobody was paid to do them. Most skilled and unskilled labor falls into this category: farming, road work, etc. -- but also (arguably) things like entertainment production (it is good to have some produced entertainment -- games, movies, the like -- available, though obviously quality matters here and far more is produced than is really optimal), medicine, and many sorts of engineering. Finally, there are those which are worth doing only if, and only because, one is paid to do them. The production and (especially) sale of useless gadgets, and many facets of advertising (is anyone prepared to maintain that telemarketers or the producers of obnoxious internet pop-up ads are doing something worthwhile or that needs doing?) fall into this category.
It seems to be nearly tautological that it is desirable to have as many people as possible doing the first sort of activity (things good in themselves), and that labor ought to be directed toward the second (instrumental goods) just insofar as is necessary to uphold society and improve the general human condition -- and whenever such an activity can be done with less effort, it ought to be done so, to free up time and energy for enjoyment and for pursuit of activities good in themselves.
Now originally the vast majority -- nearly all -- of human effort was devoted to the second kind of activity. Absent large-scale organization, industry, advanced technology, and automation, it takes much of the general effort of society to feed, clothe, shelter, and defend itself. The people who pursued philosophy (and later science), for instance, were generally those who were lucky enough to be wealthy enough not to have to do ordinary work.
Well, we now have large-scale organization. We have massive industrial capability. We have quite a lot of labor-saving and labor-easing technology, and an increasing amount of automation capable of doing our labor for us. Especially in the West, we have the capacity for an unprecedented amount of our society to simply not need to work on those necessary, but in themselves valueless, tasks that have so long occupied our efforts, and with every advance in technology this becomes more and more true.
What have we done with this capability? Now that we are so much more efficient, do we now have so much more free time to think about things which are valuable in themselves? Are we a society of scholars, devoted to knowledge? Or, at least, do we have more and more free time to associate with one another and develop friendships?
You need only turn on the television, or browse the internet, or walk through a store, or be rudely interrupted at dinner (provided that you are one of those people with enough free time to have a regular dinner with family, of course) by yet another telephone call insisting that you need to refinance your mortgage, to see that this is, of course, not the case. More and more people are doing that third kind of job -- the kind you only do because you are paid to do it. Do not mistake me: I have no ill-will towards those who can get no other job than to sit at a phone bank and call perfect strangers in order to get them to buy something. Those of us lucky enough to have a more meaningful occupation should pity, not despise, them.
But it is a particularly damning commentary on our society that we have used our enormous efficiency and technological capability, not to give ourselves more free time for relationships and contemplation, not to make ourselves a society of scholars in pursuit of knowledge, but instead to create make-work. Such an enormous portion of our vast resources are devoted to the "manufacture of silly luxuries and then of sillier advertisements to persuade us to buy them". What evil have we done, that the fruits of our efforts should not be contemplation or leisure but a suffocating deluge of pointless products and irritating advertisements for them? What evil have those poor folks in the telemarketing call centers done, that we should refuse to pay them except to provide a worthless "service", at best useless and at worst actively harmful to themselves and their fellow human beings? What kind of a society are we, that we should allow and even encourage all of this, valuing sales above knowledge, make-work above rest, and money above everything?
May God have mercy on us all.
Sunday, February 15, 2009
Musing on Memories and the Past
Apparently "tomorrow" means "in a week". I keep meaning to write, but then I get distracted and lose the inspiration. I apologize in advance for the somewhat stream-of-consciousness style of the below; I am rather tired and wanted to dump out some of my thoughts that I had been meaning to write about, and that is how it happened.
Last week there were several days of warm weather -- it was above 50 degrees (F) one day -- and this led to my thinking about the past. There is something about a fresh breeze, moist and cool-but-not-cold air blowing in my face, that brings up memories and vivid emotions. There is something powerful about the past. I remember things I did, places I have been, thoughts I have though, and (perhaps most poignantly) emotions I have felt, and there is something otherworldly about them. Sometimes I can almost feel myself back in the past situation; on other occasions, it is as if I am remembering not my own life but the life of some past self who, somehow, is not the 'I' that I am now.
Of course I know that I am the 'I' of those memories, occasional feelings to the contrary aside; my ontological theory of myself is not so muddled as all that. But there is the fact that the past often seems so arbitrary; I remember what did happen (or I do at least insofar as my memory is correct), but it seems like it might just as well have happened otherwise. I went, for example, to Mathcamp in the summer of 2004; might I have not? What if I had done differently? The past is strange; it is immutable, but it is hazy. My memories are my view of my past, but they are as through a glass, darkly; at times I hardly recognize myself. The past is so fuzzy to me, it almost seems as though it should not be so set in stone. Surely I could go back and fix those mistakes I remember making; make different choices. But no, the past is fixed; there is no going back; there is only going forward. Exiles cannot return home; none of us can return to the past. It seems strange that there should be something so irrevocable about a contingent thing, but that, I suppose, is part of the grand miracle of the universe.
The past is irrevocable. It cannot be changed. But of course that is also to say that all actions are, in a sense, irrevocable. When I choose to do one thing rather than another, I make not a momentary but a permanent choice. For all eternity I have done what I have done, and there is no possibility of later erasing it. Lewis talks about the mistaken conception people have that the mere passage of time wipes away sins and mistakes. Of course it does not; it cannot. No matter how distant I feel from that young fool who cheated, or lusted, or did some other evil, no matter how many years ago it was, it is nevertheless true that I did it. "What has been done cannot be undone." (How grateful I am -- at least in my lucid moments -- for God's forgiveness! There certainly can be no other way out.)
And another thought. There is something almost mystical about memory, especially memory of emotion. I stand and let the breeze wash over me, and I remember that summer of 2004, where I recall -- it was in Maine -- standing in the cool moist breeze and feeling those same emotions which I feel now in remembering it. Lewis talked of a certain poignant feeling which he remembered and longed for, but when he honestly examined his memories, he found that the emotion he remembered was this kind of longing itself. This must be akin, if not the same. It is certainly with some fondness that I see myself standing as I remember doing some four and a half years ago, though some of the things I remember thinking about that summer were rather foolish. (I like to think that I have learned better. I remember thinking, soon after, as I realized my foolishness, that I was learning something. I am not certain how sure I am that I have, indeed, learned anything meaningful.)
I get the same sort of experience remembering such things as I get from thinking about certain literature (the good kind, that has deep ideas and makes one think). The memories have the advantage that they are trying, at least, to tell a story that is very close to me, though the storyteller is generally rather inferior. (I wonder how I should tell the story of my life... Would it be any good? Would anyone -- even myself -- think it interesting or profound?) I think I can learn from literature; I think I can learn from my memories, though quite often it is difficult to say exactly what I have learned. Quite often it is even more difficult because I do not try to say it until I have begun to forget. I emphatically maintain that this does not mean I have not learned anything. But what, exactly, is it that I have learned just now?
I couldn't say.
Last week there were several days of warm weather -- it was above 50 degrees (F) one day -- and this led to my thinking about the past. There is something about a fresh breeze, moist and cool-but-not-cold air blowing in my face, that brings up memories and vivid emotions. There is something powerful about the past. I remember things I did, places I have been, thoughts I have though, and (perhaps most poignantly) emotions I have felt, and there is something otherworldly about them. Sometimes I can almost feel myself back in the past situation; on other occasions, it is as if I am remembering not my own life but the life of some past self who, somehow, is not the 'I' that I am now.
Of course I know that I am the 'I' of those memories, occasional feelings to the contrary aside; my ontological theory of myself is not so muddled as all that. But there is the fact that the past often seems so arbitrary; I remember what did happen (or I do at least insofar as my memory is correct), but it seems like it might just as well have happened otherwise. I went, for example, to Mathcamp in the summer of 2004; might I have not? What if I had done differently? The past is strange; it is immutable, but it is hazy. My memories are my view of my past, but they are as through a glass, darkly; at times I hardly recognize myself. The past is so fuzzy to me, it almost seems as though it should not be so set in stone. Surely I could go back and fix those mistakes I remember making; make different choices. But no, the past is fixed; there is no going back; there is only going forward. Exiles cannot return home; none of us can return to the past. It seems strange that there should be something so irrevocable about a contingent thing, but that, I suppose, is part of the grand miracle of the universe.
The past is irrevocable. It cannot be changed. But of course that is also to say that all actions are, in a sense, irrevocable. When I choose to do one thing rather than another, I make not a momentary but a permanent choice. For all eternity I have done what I have done, and there is no possibility of later erasing it. Lewis talks about the mistaken conception people have that the mere passage of time wipes away sins and mistakes. Of course it does not; it cannot. No matter how distant I feel from that young fool who cheated, or lusted, or did some other evil, no matter how many years ago it was, it is nevertheless true that I did it. "What has been done cannot be undone." (How grateful I am -- at least in my lucid moments -- for God's forgiveness! There certainly can be no other way out.)
And another thought. There is something almost mystical about memory, especially memory of emotion. I stand and let the breeze wash over me, and I remember that summer of 2004, where I recall -- it was in Maine -- standing in the cool moist breeze and feeling those same emotions which I feel now in remembering it. Lewis talked of a certain poignant feeling which he remembered and longed for, but when he honestly examined his memories, he found that the emotion he remembered was this kind of longing itself. This must be akin, if not the same. It is certainly with some fondness that I see myself standing as I remember doing some four and a half years ago, though some of the things I remember thinking about that summer were rather foolish. (I like to think that I have learned better. I remember thinking, soon after, as I realized my foolishness, that I was learning something. I am not certain how sure I am that I have, indeed, learned anything meaningful.)
I get the same sort of experience remembering such things as I get from thinking about certain literature (the good kind, that has deep ideas and makes one think). The memories have the advantage that they are trying, at least, to tell a story that is very close to me, though the storyteller is generally rather inferior. (I wonder how I should tell the story of my life... Would it be any good? Would anyone -- even myself -- think it interesting or profound?) I think I can learn from literature; I think I can learn from my memories, though quite often it is difficult to say exactly what I have learned. Quite often it is even more difficult because I do not try to say it until I have begun to forget. I emphatically maintain that this does not mean I have not learned anything. But what, exactly, is it that I have learned just now?
I couldn't say.
Sunday, February 8, 2009
Let's try this again
So it's been almost a year since I last posted here. I keep wanting to write things and then not doing it, because I don't have a vehicle for it... except I do. Silly me.
So I'll give this another shot; maybe I can actually post with some regularity this time. Right now I am slightly tired and should get to bed soon, so perhaps an interesting post will come tomorrow.
For now, I will tie up a little bit of a loose end from before by giving an indication of the solution to the problem I mentioned in my previous post. The following describes how to compute the function f(x) from just the k-subset x of [n] (no reference to other values of f). First, view x as a binary string of length n, with 1's in positions corresponding to elements of x and 0's elsewhere. Then, count along this string, beginning at the end (at the imaginary position n+1) with a cumulative count of 0, subtracting 1 every time you reach a 0 and adding 1 every time you reach a 1. So, for instance, the subset {1, 3, 4, 7} of [7] yields the binary string 1011001. Starting at the right end of this with 0, we get in the 7th position a running total of 1, then 0, then -1, then 0, then 1, then 0, then 1. This gives us the new string (1)(0)(1)(0)(-1)(0)(1) (from left to right). Now, to obtain f(x), find the leftmost position in this last string generated where the value is both minimal and at most 0. (If all the values are greater than 0 f(x) is not defined.) Notice that x does not contain the number corresponding to that position (this is easy to see by minimality) -- in the case above, we find that the leftmost minimal value occurs in position 5, and 5 is not in x. Add to x that number (in this case insert 5 into x) to obtain f(x).
It is not terribly difficult to show by induction that this actually gives us the correct function f(x). In particular, this means that f is defined on all k-subsets of [n] whenever k
Okay, bedtime now.
So I'll give this another shot; maybe I can actually post with some regularity this time. Right now I am slightly tired and should get to bed soon, so perhaps an interesting post will come tomorrow.
For now, I will tie up a little bit of a loose end from before by giving an indication of the solution to the problem I mentioned in my previous post. The following describes how to compute the function f(x) from just the k-subset x of [n] (no reference to other values of f). First, view x as a binary string of length n, with 1's in positions corresponding to elements of x and 0's elsewhere. Then, count along this string, beginning at the end (at the imaginary position n+1) with a cumulative count of 0, subtracting 1 every time you reach a 0 and adding 1 every time you reach a 1. So, for instance, the subset {1, 3, 4, 7} of [7] yields the binary string 1011001. Starting at the right end of this with 0, we get in the 7th position a running total of 1, then 0, then -1, then 0, then 1, then 0, then 1. This gives us the new string (1)(0)(1)(0)(-1)(0)(1) (from left to right). Now, to obtain f(x), find the leftmost position in this last string generated where the value is both minimal and at most 0. (If all the values are greater than 0 f(x) is not defined.) Notice that x does not contain the number corresponding to that position (this is easy to see by minimality) -- in the case above, we find that the leftmost minimal value occurs in position 5, and 5 is not in x. Add to x that number (in this case insert 5 into x) to obtain f(x).
It is not terribly difficult to show by induction that this actually gives us the correct function f(x). In particular, this means that f is defined on all k-subsets of [n] whenever k
Okay, bedtime now.
Thursday, February 14, 2008
A Combinatorics Problem
A bit over four years ago I was given what remains one of my favorite combinatorics problems. It goes like this:
Define An,k to be the set consisting of all k-element subsets of the set [n] (the integers 1 to n). For instance, we have A4,2 = {{1,2}, {1,3}, {1,4}, {2,3}, {2,4}, {3,4}}. (Thus, |An,k| is equal to the binomial coefficient.) For each n > k ≥ 0, we define a (possibly partial) function f : An,k → An,k+1 by the following "greedy inclusion algorithm".
First, order the sets in both An,k and An,k+1 in lexicographic order (in increasing order of smallest element, then, in increasing order of second-smallest element, etc., so that they are in an order as in the example of A4,2 above). Initially mark each element of An,k+1 as unused. For each set x ∈ An,k, in lexicographic order, do the following. Find out if there is some y ∈ An,k+1 such that x ⊆ y and y is marked as unused. If there is not, f(x) is undefined. If there is, take the earliest such y (in lexicographic order), define f(x) = y, and then mark that y as used. In either case, continue on to the next element of An,k.
This algorithm gives a partial function f which is defined on some (possibly all) elements of An,k. The question is this:
(a) Find the pairs (n, k) where f is defined on all of An,k.
(b) Find a simple, fast (linear time in n is good; if you are pedantic about integer comparisons not actually taking constant time this might be instead O(n log n)) method for taking an element x of An,k and determining whether f(x) is defined and, if so, its value.
As it's been four years since I solved the problem, I don't remember the details of the solution. Thus, I'll put the solution in a later post when I figure them out again.
Define An,k to be the set consisting of all k-element subsets of the set [n] (the integers 1 to n). For instance, we have A4,2 = {{1,2}, {1,3}, {1,4}, {2,3}, {2,4}, {3,4}}. (Thus, |An,k| is equal to the binomial coefficient.) For each n > k ≥ 0, we define a (possibly partial) function f : An,k → An,k+1 by the following "greedy inclusion algorithm".
First, order the sets in both An,k and An,k+1 in lexicographic order (in increasing order of smallest element, then, in increasing order of second-smallest element, etc., so that they are in an order as in the example of A4,2 above). Initially mark each element of An,k+1 as unused. For each set x ∈ An,k, in lexicographic order, do the following. Find out if there is some y ∈ An,k+1 such that x ⊆ y and y is marked as unused. If there is not, f(x) is undefined. If there is, take the earliest such y (in lexicographic order), define f(x) = y, and then mark that y as used. In either case, continue on to the next element of An,k.
This algorithm gives a partial function f which is defined on some (possibly all) elements of An,k. The question is this:
(a) Find the pairs (n, k) where f is defined on all of An,k.
(b) Find a simple, fast (linear time in n is good; if you are pedantic about integer comparisons not actually taking constant time this might be instead O(n log n)) method for taking an element x of An,k and determining whether f(x) is defined and, if so, its value.
As it's been four years since I solved the problem, I don't remember the details of the solution. Thus, I'll put the solution in a later post when I figure them out again.
Sunday, January 13, 2008
A little on education
Prompted by a blog post elsewhere I've been thinking a bit about education. Pretty much everybody agrees that education is a good thing, and that it's important to educate people, but not so clear is what we want to accomplish with that education. What should people be taught, and why should they be taught it?
Here are a few popular (?) theories on why people should be educated:
1. We need an educated workforce to operate our economy, so people need to be educated in order to be productive workers.
2. Since we're a democracy, we need people to be well-informed in order to make wise decisions in their voting; people should be educated in order that they can be good citizens.
3. People need to understand the world in which they live, including how it works physically (science), its culture and history, etc. So they should be educated so they can understand how the world works.
4. People should be educated so that they have the appropriate knowledge and reactions for society to run smoothly.
5. People should be educated so that they can have opportunities to do those things that require an education if they want; since, e.g., mathematics is a prerequisite for certain vocations, so we should teach it to give people an opportunity to pursue those vocations.
6. Education is the path to power and prosperity and Good Jobs, so people should be educated in order to have a fair chance at those things.
7. It is just good, simpliciter, for people to know Certain Things which are being taught.
8. People should be educated because it leads them to some sort of spiritual-cum-philosophical growth.
There are more, of course, and most people (if they think about it at all) probably hold to several of these in mixture. Certainly most of these (except perhaps 7 and 8) are fairly uncontroversially true about education: that is, they are correct assessments of some role or outcome of education in our society. But none of them fully captures what the goal of education is.
A certain kind of cynic might say that whatever our professed goals, (4) serves as education's primary directive. Education is a tool for conformism. Well, it certainly does do that (often, anyway) -- but with someone who is certain that that is all it can ever be or that that ought to be one of its main goals I can have no further conversation.
Similarly I think that (1), (2), (5), and (6) (and to an extent (3) depending on its sense) are too much practical considerations to really capture what we want education to be. We are bound by charity and justice to at least try to give people what they need to do well, so I suppose these do form sufficient reasons for education, but they don't encompass everything. Yes, we want people to be able to do well at their job, to make good civic decisions, to have opportunities to do what they want, to not be shut off from advancement. But surely even if none of these were at stake we should still, all else equal, want people to be educated? Surely we should prefer people to understand arithmetic or read philosophy or what have you, even if (in some strange and faraway society) they would not need to?
I think that (7) gets a little closer, but begs the question a bit. Why, is it good for people to know those things, and why those things in particular and not others? (8), too, has some trouble -- at least it does not at all correspond to what we really do in modern education, close as it is to Plato's ideal. And at any rate (7) and (8) (and (3)) can easily become a sort of self-justification for high-brow "culture" and its perpetuation, especially if we just assume without justification what sorts of education really accomplish the goals.
Like any mathematician or philosopher, I think that in order to talk seriously about something, we should try to outline our assumptions (axioms, perhaps). If the theories above are unsatisfactory, that seems the only way to do better.
A. Knowledge, simply and in itself, is a good thing. It is not the greatest or highest good, and may be outweighed in some cases by the negative consequences of knowledge, but it is a simple good: that is, it is good in itself for people to know things, not just good because of some result that that state of affairs may bring about.
Of course knowledge is also instrumentally good:
B. Physical well-being is a good thing. Insofar as education provides for it, it is good.
C. Spiritual well-being is a good thing. Insofar as education leads to it, it is good.
D. Beauty is a good thing; so is exposure to and understanding of it. Insofar as education exposes people to it, it is good.
That is, education exists for the same reason as any other human institution ought to exist: for meeting people's physical needs, and so that people can have "the True, the Good, and the Beautiful". That is its purpose; this is why we ought to educate people.
So, what should we teach?
This is difficult, but the first thing to throw out is the notion that our guiding principle in education ought to be the purely practical use of the knowledge and skills imparted to the student. That would be focusing on the physical needs to the exclusion of the others. To be sure, we ought to teach people practical knowledge and skills, but we ought not to stop there. (My Latin professor remarked to me, tongue-in-cheek, that my decision to take a classics class was a decision to "finally get an education along with your training" at HMC. I'd like to think that my time at HMC, even in my mathematics classes, which relate to my future career, gave me some education as well as training, but the point is well made: there is a difference, and having the education in addition to the training is worthwhile.) Insofar as we think of education as practical training we perpetuate the notion that ordinary people shouldn't study "higher" mathematics, or literature, or philosophy, or art: it might be training for the intellectual elites, but it is superfluous for the average worker. This is no good, because there is a good reason for everyone to have exposure to and understanding of at least some of these topics, and it has nothing to do with the job they plan to hold.
Still, there is a lot to be said for teaching practical skills, not the least of which that those practical skills which one learns in school can be practical both for those jobs and for learning those things which give better access to "the true, the good, and the beautiful". We teach arithmetic, basic reading and writing, basic outlines of history, basic science -- and we used to teach languages, especially classical languages -- for these reasons. It is hard (understatement of the day) to appreciate the truth and beauty of the theories and theorems in mathematics without understanding arithmetic, besides the fact that most people are practically better off if they can add and subtract and multiply; you cannot read and appreciate literature without being able to read, besides the enormous practical importance of reading in our society.
But at some point we should actually teach those other things; those things which are not really practical for most people's jobs; those things which are good because they give access to the true, the good, and the beautiful. And we have to realize when we teach it that that is what we are doing. When we teach even calculus (which does have practical applications for many more ordinary people), we should be clear that it won't be practical for everyone, but that it can be good for those people who will never use it to know, because there is elegant truth and beauty in it: and so a primary goal should be to help people see that. When we teach literature, the focus should not be on that faux-practical aspect of knowing facts about the "greats" and understanding allusions, but we should focus on using the literature to bring out truths and moral thought and beauty. This might be hard. So much of our culture is against this sort of thing: it thinks that the practical is what is important, the rest is a waste of time (fun, or boring, but a waste of time). We have to have the courage to counter that assumption, because it is so very wrong.
I cannot stop without making some comment on religious education; specifically, Christian education. It is in some sense even more important. For of course from the Christian point of view, no matter how good your secular education is, no matter how much you give to people tastes of truth and goodness and beauty, it cannot be sufficient. The most secularly-enlightened soul is still damned if it rejects God. But I think that a good Christian education can be thought of in similar terms to a good secular education. There are practical matters (such as particulars of habit and behavior) which of course cannot be ignored, but it is important to remember that there is more good to be had than that. For in the Christian view, God Himself is the epitome of Truth and Goodness and Beauty, and contains them all within Him -- and I think that a good Christian education, in addition to the many practical matters, should really teach us how to see that. Not that many of us are truly in a position to be good teachers of that (I certainly am not). But after all it is God who provides most of the education; we can at least do our best.
Here are a few popular (?) theories on why people should be educated:
1. We need an educated workforce to operate our economy, so people need to be educated in order to be productive workers.
2. Since we're a democracy, we need people to be well-informed in order to make wise decisions in their voting; people should be educated in order that they can be good citizens.
3. People need to understand the world in which they live, including how it works physically (science), its culture and history, etc. So they should be educated so they can understand how the world works.
4. People should be educated so that they have the appropriate knowledge and reactions for society to run smoothly.
5. People should be educated so that they can have opportunities to do those things that require an education if they want; since, e.g., mathematics is a prerequisite for certain vocations, so we should teach it to give people an opportunity to pursue those vocations.
6. Education is the path to power and prosperity and Good Jobs, so people should be educated in order to have a fair chance at those things.
7. It is just good, simpliciter, for people to know Certain Things which are being taught.
8. People should be educated because it leads them to some sort of spiritual-cum-philosophical growth.
There are more, of course, and most people (if they think about it at all) probably hold to several of these in mixture. Certainly most of these (except perhaps 7 and 8) are fairly uncontroversially true about education: that is, they are correct assessments of some role or outcome of education in our society. But none of them fully captures what the goal of education is.
A certain kind of cynic might say that whatever our professed goals, (4) serves as education's primary directive. Education is a tool for conformism. Well, it certainly does do that (often, anyway) -- but with someone who is certain that that is all it can ever be or that that ought to be one of its main goals I can have no further conversation.
Similarly I think that (1), (2), (5), and (6) (and to an extent (3) depending on its sense) are too much practical considerations to really capture what we want education to be. We are bound by charity and justice to at least try to give people what they need to do well, so I suppose these do form sufficient reasons for education, but they don't encompass everything. Yes, we want people to be able to do well at their job, to make good civic decisions, to have opportunities to do what they want, to not be shut off from advancement. But surely even if none of these were at stake we should still, all else equal, want people to be educated? Surely we should prefer people to understand arithmetic or read philosophy or what have you, even if (in some strange and faraway society) they would not need to?
I think that (7) gets a little closer, but begs the question a bit. Why, is it good for people to know those things, and why those things in particular and not others? (8), too, has some trouble -- at least it does not at all correspond to what we really do in modern education, close as it is to Plato's ideal. And at any rate (7) and (8) (and (3)) can easily become a sort of self-justification for high-brow "culture" and its perpetuation, especially if we just assume without justification what sorts of education really accomplish the goals.
Like any mathematician or philosopher, I think that in order to talk seriously about something, we should try to outline our assumptions (axioms, perhaps). If the theories above are unsatisfactory, that seems the only way to do better.
A. Knowledge, simply and in itself, is a good thing. It is not the greatest or highest good, and may be outweighed in some cases by the negative consequences of knowledge, but it is a simple good: that is, it is good in itself for people to know things, not just good because of some result that that state of affairs may bring about.
Of course knowledge is also instrumentally good:
B. Physical well-being is a good thing. Insofar as education provides for it, it is good.
C. Spiritual well-being is a good thing. Insofar as education leads to it, it is good.
D. Beauty is a good thing; so is exposure to and understanding of it. Insofar as education exposes people to it, it is good.
That is, education exists for the same reason as any other human institution ought to exist: for meeting people's physical needs, and so that people can have "the True, the Good, and the Beautiful". That is its purpose; this is why we ought to educate people.
So, what should we teach?
This is difficult, but the first thing to throw out is the notion that our guiding principle in education ought to be the purely practical use of the knowledge and skills imparted to the student. That would be focusing on the physical needs to the exclusion of the others. To be sure, we ought to teach people practical knowledge and skills, but we ought not to stop there. (My Latin professor remarked to me, tongue-in-cheek, that my decision to take a classics class was a decision to "finally get an education along with your training" at HMC. I'd like to think that my time at HMC, even in my mathematics classes, which relate to my future career, gave me some education as well as training, but the point is well made: there is a difference, and having the education in addition to the training is worthwhile.) Insofar as we think of education as practical training we perpetuate the notion that ordinary people shouldn't study "higher" mathematics, or literature, or philosophy, or art: it might be training for the intellectual elites, but it is superfluous for the average worker. This is no good, because there is a good reason for everyone to have exposure to and understanding of at least some of these topics, and it has nothing to do with the job they plan to hold.
Still, there is a lot to be said for teaching practical skills, not the least of which that those practical skills which one learns in school can be practical both for those jobs and for learning those things which give better access to "the true, the good, and the beautiful". We teach arithmetic, basic reading and writing, basic outlines of history, basic science -- and we used to teach languages, especially classical languages -- for these reasons. It is hard (understatement of the day) to appreciate the truth and beauty of the theories and theorems in mathematics without understanding arithmetic, besides the fact that most people are practically better off if they can add and subtract and multiply; you cannot read and appreciate literature without being able to read, besides the enormous practical importance of reading in our society.
But at some point we should actually teach those other things; those things which are not really practical for most people's jobs; those things which are good because they give access to the true, the good, and the beautiful. And we have to realize when we teach it that that is what we are doing. When we teach even calculus (which does have practical applications for many more ordinary people), we should be clear that it won't be practical for everyone, but that it can be good for those people who will never use it to know, because there is elegant truth and beauty in it: and so a primary goal should be to help people see that. When we teach literature, the focus should not be on that faux-practical aspect of knowing facts about the "greats" and understanding allusions, but we should focus on using the literature to bring out truths and moral thought and beauty. This might be hard. So much of our culture is against this sort of thing: it thinks that the practical is what is important, the rest is a waste of time (fun, or boring, but a waste of time). We have to have the courage to counter that assumption, because it is so very wrong.
I cannot stop without making some comment on religious education; specifically, Christian education. It is in some sense even more important. For of course from the Christian point of view, no matter how good your secular education is, no matter how much you give to people tastes of truth and goodness and beauty, it cannot be sufficient. The most secularly-enlightened soul is still damned if it rejects God. But I think that a good Christian education can be thought of in similar terms to a good secular education. There are practical matters (such as particulars of habit and behavior) which of course cannot be ignored, but it is important to remember that there is more good to be had than that. For in the Christian view, God Himself is the epitome of Truth and Goodness and Beauty, and contains them all within Him -- and I think that a good Christian education, in addition to the many practical matters, should really teach us how to see that. Not that many of us are truly in a position to be good teachers of that (I certainly am not). But after all it is God who provides most of the education; we can at least do our best.
Thursday, January 3, 2008
Some thoughts on some Lewis arguments
I was reading a thread over at TheologyWeb, in which several people were impugning some of C.S. Lewis’s arguments with some nonsense about their being pure rhetoric with no (or highly flawed) logic behind them, and so forth. Now being a bit of a Lewis fanboy and pretty familiar with the arguments, I thought that I ought to say something in response; and since I now have this page to put my comments on where I won’t have to deal with people making inane and insulting comments in response instead of thinking. Thus, this goes here.
I’d like to start with a few comments on what is probably Lewis’s most popular and most unpopular apologetic argument, the argument known as the trilemma. For those who might not remember, it goes about like this:
“Consider the things that Jesus said and did. Things like claiming Messianic titles like Son of Man, like applying the name ‘I am’ to himself, like claiming to forgive sins against God. There are three ways in which a person can say these things. Either he does not believe them, or he believes them and they are false, or he believes them and they are true. Thus a person who says these sorts of things can reasonably only be one of three things: in the first case, he’s a blasphemous liar and malus homo (as many Jewish leaders came to think); in the second case, he’s completely insane, being an ordinary person who thinks he’s God; in the third case, he actually is who he says he is. Now if we’re convinced by his other actions that he’s not a lunatic (and we should be), and that he’s not Satanically evil (and we should be), that leaves the last option. If we think that Jesus was a good, sane man, we ought to think that he was God.”
Of course as you’ll recognize by the Latin above this argument is much older than Lewis: aut Deus aut malus homo is a very old argument, and all Lewis has done is fill in the third option (that of insanity). Now the first thing to notice about the argument is that it’s valid. Given that Jesus said such things, there are really only those three options. And it’s pretty hard to make a good case for Jesus’s being an evil man or a nutcase, so we’re left (shockers!) with the last as the most reasonable case. And since we have a valid argument, there’s only one way to get out of the conclusion...
Which is to deny the premise. Now, the funny thing about most of the people who object to the trilemma argument is that they think that the premise is part of the argument itself. So they respond with some obvious comment like, “Well, what if Jesus didn’t say those things, and other people later made it up? Then what? No trilemma now, huh? That’s another option!” Well, duh. That’s another option indeed, but it doesn’t mean that Lewis’s argument is obviously fallacious and that he was just a rhetoric-slinging illogical blowhard. It just means that they’ve denied the premise. It’s not that hard to get out of an argument’s conclusion by denying the premise. Thus we have lesson #1. Arguments have premises. Just because you think the premise is false doesn’t mean the argument is stupid.
Of course this leaves us in the position now of defending the premise. And its denial does have rather a lot of prima facie plausibility. So why should we accept that premise? And what is Lewis doing making an argument with this kind of premise?
There can be many cases made for accepting the premise. Lewis makes a number of them in other places, and hordes of other people tackle the topic also. I won’t go into them now. What I’m more interested in is the fact that Lewis doesn’t need to defend the premise here because the argument is directed at people who already (mostly) accept it. If you are convinced that the Jesus presented in the Gospels is a product of rapid mythmaking and that the things he says there are not reasonably accurate preservations of things he actually said, then the argument is not directed at you. The argument is for those people who think that the things that Jesus says (if not the miracles that he does) in the Gospels are pretty close to the things he actually said. After all, if the Gospels don’t preserve what he said pretty well, then why would you say Jesus was a great moral teacher (those that say this are the audience of Lewis’s argument here)? You’d have nothing to base the assessment on.
Now I’d like to write a little about another much-maligned argument that Lewis makes: the argument from reason (for supernaturalism). This one appears in a lot of places -- Mere Christianity, Miracles, and a number of essays -- and it has a number of variants. The basic gist of the argument is that naturalism (the claim that only physical things exist) leaves us with no grounds for trusting in our reasoning capacity. Since reasoning leads to truth, we should reject naturalism.
One form of the argument can be summarized by the statement that Naturalism is self-defeating. It runs like this. Suppose that naturalism is true. Then, all of our thoughts are nothing more than physical interactions, with purely physical causes. Thus when we believe in some logical deduction, we don’t believe it because it is true (as we think), but because of some physical interactions which have no particular propensity to lead to what we call a true belief. So we have no reason to think that our reasoning is true. But why should we believe naturalism? Well, because of some chain of reasoning. Now if we can trust our reason we might debate whether that chain is sound or not, but if we can’t, then it doesn’t matter: there’s no particular reason to think that our reasoning has led us to anything true; thus, there’s no reason to believe that naturalism is true.
There is an obvious objection to this which in my experience people never fail to bring up. They don’t want to give up reason, so they dispute that the physically-caused nature of our thoughts means that we have no reason to think them true. They say that true beliefs and accurate reasoning are survival characteristics, so evolution has produced them in us: thus we can trust our reason. This takes a little force out of the argument. Though it’s a bit question-begging to assume that correct reasoning is a survival characteristic and favored by evolution, at least with that assumption a naturalist thesis can survive this form of the argument.
But there’s still something fishy going on here. Under Lewis’s supernaturalist thesis, Reason is a given -- it’s something which God bestows on us, and we begin by assuming that our reason is reliable. Under a naturalist thesis, however, it can’t be: but this objection tries to make it so.
Consider that a metaphysical theory has to provide an answer to the question: “Why should we believe our reason?” Validity of reason is so fundamental that there is no question of accepting a theory which can’t tell why we should believe it. Now note that the answer to the question need not be derived from outside the metaphysic. Indeed it cannot be, because you can’t offer a proof that reasoning is valid (for the very obvious reason that such a proof would need to use reasoning, whose validity is the problem in question!). But there must be an answer to the question.
Now, Lewis’s Christian supernaturalism gives this answer to the question: we believe that our reason can be accurate as a premise. Because it’s a supernaturalist system it can do this; obviously the correctness of reason isn’t a physical premise, but it might as well be a supernatural one. Then, once it’s taken as a starting point, we can talk more about its source (in God, in Lewis’s case). What answer can naturalism give?
It can’t give any supernatural or mysterious source of reason, because we’re dealing with a naturalist thesis, which automatically precludes such things. So it can’t take the correctness of reason as a premise. Well, then, how will we be convinced to trust our reason, if its correctness is not a premise? By reasoning from premises, obviously... and we see the problem. We’re going to need to assume the correctness of reason – namely, the reasoning we use in our argument -- to show that reason is correct, and that is the one thing that a naturalist account cannot assume. It is stuck. There is no possible way out.
This may sound rather strange, that we’ve so thoroughly eliminated naturalism... without even considering its arguments. Isn’t there something funny going on here? Well, sort of. We’ve certainly not shown that naturalism is false. That’s not something you can do without appealing to certain supernaturalist intuitions (about, e.g., notions of self, soul, etc.), and of course the naturalist isn’t going to let us do that (how come is a topic for another time). Instead, what this shows is that we cannot rationally believe a naturalist metaphysic. Still a pretty strong statement. And (as every argument has premises) what were our premises? That our reason is reliable, and that our metaphysics should be able to tell us why we should believe our reason, given the metaphysical premises. I think that’s a pretty good criterion for rational belief in a metaphysical system.
Of course there are even more forms to the argument from reason than the ones I’ve mentioned here. (I mentioned that Lewis gives several, and the second form I have given here is one he does not give, but is my adaptation.) Still, I think this shows that there’s a lot more to the argument than its detractors give credit for. I’ll probably come back to the argument later.
But this is getting long already and I am tired, so I think I’ll stop here.
Tuesday, January 1, 2008
In Principio
I decided that I wanted to start a blog. Having some free time around the new year, I decided that this was a good time to do it. So I did.
I plan the contents of this blog to be mostly essays and musings on various topics, not personal journaling. (I tried that; I can't do it.)
I called this blog The Think Turtle because I felt it to be amusing and oddly appropriate; plus, the other things I thought of were already taken.
In any case there's not much else to say in an introductory post.
I plan the contents of this blog to be mostly essays and musings on various topics, not personal journaling. (I tried that; I can't do it.)
I called this blog The Think Turtle because I felt it to be amusing and oddly appropriate; plus, the other things I thought of were already taken.
In any case there's not much else to say in an introductory post.
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