Blog Moved

Saturday, December 19, 2015

Monday, December 14, 2015

Amazing Photo Essay on Consent

"Face Value is a series of photographs, taken by staff photographer Aubrey Schuring, that showcase the emotions of various human beings as they discuss moments of consent, assault, and their feelings of worth with Project Consent."

See it on Project Consent.

Thursday, November 12, 2015

Do Welders Make More Than Philosophers?

Early in the Fox Business Network debate, Marco Rubio took a strong stand in favor of vocational education. "For the life of me I don't know why we stigmatize vocational education," he said. "Welders make more money than philosophers. We need more welders than philosophers."
So begins a complete debunking of this claim by Matthew Yglesias, who just happens to have been a student of mine at Harvard. Read the rest here. It's a corrective that's especially welcome to those of us who have to have the same conversation, over and over, with budding philosophy concentrators: How do you tell your parents?

Of course, as Yglesias says, that doesn't mean we should stigmatize vocational education. For many people, it's clearly the right choice. And, to be honest, I'm not sure many people do stigmatize vocational education. I happen to live very close to Blue Hills Regional Technical School, a vocational high school that serves several of the surrounding towns. (Avon, Braintree, Canton, Dedham, Holbrook, Milton, Norwood, Randolph and Westwood.) My understanding is that there are almost always more applicants than there are slots. And the school is widely respected in the area. Indeed, Blue Hills students scored higher than the state average on all three recent MCAS examinations.

Sunday, September 20, 2015

Roasted Eggplant with Artichoke Hearts and Salsa Verde

I keep printing out this recipe and then losing it, and then I've got to search for it and find it again. So I'm tired of that and am posting it here.

Last summer, we had this probably ten times. This year, we haven't had as many eggplant, due to the lack of rain, but we've had it a few times, and it is always, always wonderful, if you have the right kind of eggplant. You absolutely must have really fresh eggplant, about as thin as you can get them, and with really soft, thin skin. The original recipe calls for Japanese eggplant, but we've found that really long, thin ones work best. Don't bother with the big purple ones you can usually get, unless you peel them, and it isn't as good even then. So this is really a late summer recipe, when the eggplants come in.

The recipe originally comes from Food 52.

  • About a pound of long, skinny eggplants, cut into ½ inch rounds
  • 1 small red onion, halved and sliced
    The original recipe says "quartered", but I like them bigger.
  • 6 ounces artichoke hearts
    The original recipe calls for marinated artichoke hearts, which you can also try, but I've used the straight variety successfully
  • 1 tbsp capers
  • 1 tbsp fresh parsley, chopped
  • 1 tbsp chives, chopped
    Juice from half a lemon
  • 2 tbsp olive oil
  • 1/4 tsp salt
  1. Preheat the oven to 450F.
  2. Combine the first three ingredients in a baking dish, with enough olive oil to coat. You want to brown everything a bit, so spread them out as best you can. Bake for 20 minutes, then turn it all over and bake another 15-20.
  3. Combine the other ingredients to make a dressing. I've sometimes lightly chopped the capers, which seems to work pretty well. 
  4. Add the dressing to the eggplant mixture and serve.
The original recipe suggests using this as a topping for some kind of fish. If you do that, then I've found that a flaky whitefish (cod, scrod, haddock) is best. We've also just had it over rice, as a main course, with a side vegetable.

Sunday, August 2, 2015

Reading Frege's Grundgesetze: Now in Paperback

My book Reading Frege's Grundgesetze has just been published in paperback in Europe. It is due out in paper in the US around 1 October. (Links are to OUP websites.)

My other book, Frege's Theorem, has been out in paper for some time now. These were never terribly expensive (as such things go), but they are cheaper now.

Reviews of Reading Frege's Grundgesetze

With the publication of Philip Ebert's review in Phlosophia Mathematica, there are now four reviews out of my last book, Reading Frege's Grundgesetze:
Thanks to Philip, Gregory, Oran, and Marcus for doing these.

If anyone knows of one I have missed, please do let me know.

Thursday, July 23, 2015

Encoding a Passphrase in a Bash Script

There's an ftp server I need to access from time to time, and the password is one that was assigned to me, and so not one that is very memorable. Like 87sa!9s8op12mn or something. One solution is to put the password in a script and use that, but there are some obvious reasons that is a bad idea. A better idea is to adapt the encryption and decryption methods mentioned in this post.

First, we need to get an encrypted version of the old password:
echo  '87sa!9s8op12mn' | openssl enc -des -a -e -pass pass:MyMemorablePassword
That returns:
So now, in our script, we can simply do this:
PASSWORD=$(echo U2FsdGVkX1/ewCk0xYTJF33NCLpJ6eULDqQC60Hh3oY=  | openssl enc -des -a -d);
When that runs, it will ask us for OUR password, which it will then use to decrypt the actual password.

My First Cat Video!!

I caught our cat Lily playing with one of her favorite toys the other day: a piece of carpet fuzz. Since I happened to have my phone with me, I recorded her. I'm biased, obviously, but I think she is hilarious.

Tuesday, July 7, 2015

Frank Bruni on the "Gay Marriage" Decision

For anyone who can't understand what Justice Kennedy was going on about when he talked about the dignity denied to gay people, read Frank Bruni's piece in the New York Times.

Wednesday, July 1, 2015

Racism and the Confederate Battle Flag

Speaking as someone who grew up in the South, and who saw the Confederate battle flag damn near everywhere back then, I have to say it's damn near time it was removed, at least, from public places. But, in truth, I wonder if this isn't a distraction: Take down the flag, and then you don't have to do anything to deal with the actual problems the popularity of that flag indicate.

Having lived in the South, I can say with some certainty that a lot of people with whom the flag is popular really don't understand its true meaning. They really do think of it as a symbol of heritage and rebellion, kind of like a pirate flag. Of course, as Tim Wise argues at AlterNet, that's no excuse:
Those who defend the flag consider the black experience irrelevant, a trifle, hardly worthy of their concern. Who cares if the flag represented a government that sought to consign them to permanent servitude? Who cares if segregationists used that flag as a blatant symbol of racist defiance during the civil rights movement? Remembering the courageous heroics of one’s great-great-great-grandpappy Cooter by waving that flag or seeing it on public property is more important than black people's lived experience of it.
But if that is the real problem, then we need Southern politicians to do more than object to a symbol of racism. We need them to start objecting to racism itself and to stop their cynical exploitation of it for political gain. We need them to start understanding, as Wise says again, that "Sometimes racism isn't about vicious bigotry and hatred...". Though, of course, that may be difficult, since that might mean looking honestly at their own prejudices.

Maybe the best thing about the article, though, it is the way it mocks American exceptionalism, and ties it to American racism:
For Gohmert to claim that [after the gay marriage decision] God's protection will be withdrawn is to suggest that prior to this time we were the active recipients of that protection, that to this point God had shined his light upon America, blessing us with all good things, happy at the sight of our superior morality. And yet, for that to be true, one would have to believe that God saw nothing wrong with the enslavement of African peoples for over two hundred years, the slaughter and forced removal of indigenous peoples from their land, the invasion and theft of half of Mexico, the abuse of Chinese labor on railroads, the internment of Japanese Americans—nothing wrong with lynching or segregation. You would have to accept that God is more offended by marriage equality than any of those things, that God was essentially sanguine about formal white supremacy, and willing to extend his protective blanket over us even in the face of that, but somehow so-called "gay marriage" is a bridge too far.
I'll stop quoting there. Read the article.

Wednesday, June 24, 2015

Amazing Vegetarian (Mostly Vegan) Thanksgiving Food

OK, it's way early for Thanksgiving, and given the heat around here I'm not even thinking about turning on the oven. But it's nonetheless worth reminding Isobel about these dishes, which we made for Thanksgiving last year. They're due to Bryant Terry, who seems to have made it his life's work to create incredible vegan food.
  • Holiday Seitan Roast
    It's possible to make this with store-bought seitan, and if your local store carries seitan from The Bridge that might even be acceptable. (Their tofu is the best I have ever had. I basically don't buy anyone else's tofu.) But Terry's recipe for Homemade Seitan is really easy, and it is really, really good, too. So make it.
  • Honeyed Sweet Potatoes
    OMG! These are so yummy!
Here's Terry's wonderful version of the southern classic Smothered Pork Chops.
That recipe, and many other amazing ones, can be found in Terry's book Vegan Soul Kitchen. I heartily recommend it, as well as his other books.

While we're at it, let me throw out this vegetarian version of shepherd's pie, which we also made last winter. It's really, really good. I found the recipe at the Vegetarian Times website, but it seems as if it may originally have been due to Annie Somerville, the chef at the famous Greens Restaurant in San Francisco There's a companion recipe for Parmesan Mashed Potatoes that I haven't tried yet, but will.

Tuesday, June 23, 2015

Linguine with Crudaiola (Uncooked Tomato Sauce)

This recipe came from Bon Appetit, but it never seems to have made it to Epicurious. The sauce needs to marinate at least half an hour, and longer if you have the time. So make that ahead. There's almost nothing to be done after that, so this is a good dish for serving to friends, with salad and crusty bread, as a simple but yummy supper.

  • 1 3/4 pounds ripe tomatoes, chopped
    Since these are not going to be cooked, try to get them as fresh and firm as you can.
  • 1 cup coarsely chopped fresh basil
    This seems to be about 2 ounces of basil, which is a lot. Buy a four ounce container, if you can find one, instead of two one-ounce ones (which may well cost more), and use the rest for something else.
  • 1/2 cup pine nuts, toasted
    The right way to do this is to heat a small, heavy skillet until it's good and hot and then put in the pine nuts and stir them until they're browned a bit. (Test it by flicking water off your fingers. When the water jumps and spits, it's ready.) The nuts will toast very quickly this way, and you won't be as likely to burn them.
  • 1/2 cup olive oil
  • 6 garlic cloves, finely chopped (or pressed)
  • 1 teaspoon salt
  • 1 teaspoon black pepper
  • 1 pound linguine
    The original recipe called for taglierini, but I've never seen it
  • 1/2 cup freshly grated Parmesan cheese (about 1 1/2 ounces)
Combine the first seven ingredients in a bowl and marinate in the fridge for at least half an hour and as long as three hours.
Cook the pasta until it's almost done and definitely still firm. (It will cook a bit more later.) Reserving a cup of the liquid, drain the pasta, but don't shake it dry. Put the pasta back in the pot, add the sauce, and turn the heat back up to medium-high. Toss until the sauce is heated through and it coats the pasta, adding water as needed, in small amounts, to keep everything moist. Remove from the heat and add the cheese, tossing to blend, and add a little more water, if need be. Check the seasoning and serve with additional cheese.

Lasagnas for Isobel

Two 'fancy' lasagnas.
  • Mixed Mushroom Lasagna with Parmesan Sauce
    A really good lasagna that's fairly easy to make. Most of the work goes into slicing a pound and a half of mushrooms, and then cleaning up the pan that you made the parmesan sauce in.
    I usually use some shiitakes in this, and I've used some wood-ears, too, when I can get them, which gives a really nice flavor.
  • Artichoke and Mushroom Lasagna
    A holiday staple for us, and always a crowd-pleaser. Just very different from your typical lasagna.
    I often use grated mozarella, purchased just that way, instead of the sliced stuff. Slicing mozarella is a PITA. And I usually use crimini mushrooms, though baby bellas also work, and you can get even more adventurous if you want.
Both these recipes call for no-boil lasagna noodles, and they can be made that way, but I have decided in recent years not to use those ever. They never come out right. So I just use regular lasagna noodles or, better yet, fresh ones.

More Recipes for Isobel

Non-pasta recipes now, most but not all from Epicurious, again.
  • Risotto with Peas and Porcini
    We got this one from Whole Foods a while ago. It's apparently also been published in Fine Cooking. We make it with vegetable stock. You can also use almost any kind of dried mushroom, obviously.
  • Vegetable Moussaka
    A vegetarian version of the Greek classic. It takes a long time to make it, and it generally leaves a huge mess in its wake, but it is very delicious, and you can eat it for days.
  • Scallops with Mashed Potatos and Tarragon Sauce
    This has an almost perfect rating on Epicurious, and that is not surprising. This is one of the best things I've ever made, and it's easy and fast, as well. I've used half and half a couple times, just to lighten the sauce a bit, but it's not that heavy, anyway.
  • Scallops with Melted Leeks and Tarragon-Caper Butter
    Not quite as good as the other one, but almost. The fresh thyme sprigs are not crucial, if you don't have them.
  • Sole Meuniere
    Classic French dish. There are a lot of recipes for this online. They're all minor variations on each other. Be warned it makes a huge mess, but it's great.
  • Sole with Orange Brown Butter
    A variant on Sole Meuniere, with a bit of orange as well as lemon.
  • Yukon Gold Potato and Chive Soup
    We have a ton of chives in our yard so are always looking for something to do with them. This simple, fast soup is one of our favorite choices.
  • Grilled Tuna Burgers with Homemade Remoulade
    The remoulade here is the crucial thing. The recipe calls just for tuna steaks grilled and put on a bun. Frozen tuna steaks are just fine for this purpose, and a lot cheaper than the fresh stuff. But you can really use it with any sort of fish burger. 
  • Grilled Three Potato Salad
    This goes with the previous recipe, but can of course be made on its own, as well. It's a really great potato salad that looks impressive, too, with sweet potatos, golden potatos, and purple potatos. You can use whatever mix of potatos you want, really—it's often hard to find purple potatos that aren't expensive—but the key is to get them cooked way ahead of time so they have plenty of time to cool. As with any potato salad, you have to get them cooked just right, too, so they don't disintegrate. Better a little bit underdone than overdone.
  • Bulgur Salad with Feta and Mint
    Very simple salad that lets us use some of our mint.

Bulgur Salad with Avocado, Cucumber, and Mint

We have a lot of mint that grows in our yard, so I try to use at least some of it in something other than tea. There are all sorts of variations on tabouleh that work. This one came from the Top of the Apple blog. I'm re-posting it here, in case that should disappear.

  • 2 cups veggie stock
    We generally make this with the Better than Bullion mix
  • 1 cup bulgur wheat
  • 1+3 teaspoons olive oil
  • 1 cup minced red onion
  • 1 pinch sugar
  • 1 cucumber, seeded and diced into 1/4-inch cubes
  • 1 large avocado, halved, pitted, peeled and diced
  • 1 cup chopped mint
  • 3/4 cup golden raisins
  • 1/2 cup chopped roasted almonds
  • 1 tablespoon lemon zest
  • 1/3 cup lemon juice (Meyer if you’ve got ’em)
  • Salt and pepper

In a small sauce pot, bring stock to a boil. Add bulgur and simmer until water is absorbed, about 8 minutes. Put in large bowl and fluff with fork. In same pot over medium-high heat, heat 1 teaspoon of the oil. Add onions and sugar; cook until fragrant and glossy, about 2 minutes. Add to bulgur. Add all the remaining ingredients, including the 3 teaspoons of oil, to the bowl and toss gently to combine. Season to taste.

More Pata Recipes for Isobel

A bunch of pasta recipes from Bon Appetit that we've made over the years.
  • Penne with Roasted Tomato Sauce, Orange, and Olives
    One of those things that sounds like a weird combination, but works. It's not the best thing I've had, but it's pretty good, and a nice change of pace from more typical summer pastas. I often make it on the grill.
  • Pasta with Tomatos, Artichokes, and Feta
    One of Isobel's favorite recipes when she was little. Very simple, and delicious.
  • Pasta with Spicy Sun-dried Tomato Cream Sauce
    Fairly rich cream sauce: It uses a cup of heavy cream. You can make it a little more special by roasting the red peppers instead of using jarred ones.
  • Pasta with Arugula and Plum Tomatos
    Not a high rating on Epicurious, but maybe you have to love arugula to get into this dish. If you do, as I do, it's fantastic, and really fast. Of course we use vegetarian stock.
    The trick here is to get the timing right. You want the pasta to be ready at more or less the very moment it's time for it to go into the pan with the sauce. If you start it right when you start the sauce, you should be close. If it's done too early, drain it, and put just a little bit of olive oil on it to keep it from sticking. If it's not quite done when the sauce is, then turn the sauce off until the pasta is ready. You don't want to overcook the arugula.
  • Linguine with Sausage, Mushroom, and Cream Sauce
    Another rich one. We usually make it with vegetarian Italian sausages from Field Roast, which are incredibly good and have the right sort of texture for this dish.
  • Fettucine with Porcini Mushroom Sauce
    Another simple cream sauce. Very fast, and very good. (Again, we make it with vegetarian stock.)
  • Farfalle with Forest Mushrooms, Peas, and Parsley
    Another cream sauce. The peas add a really nice texture, and a different sort of flavor than you get in most such dishes. The recipe calls for 12 ounces each of shiitake, crimini, and chanterelle mushrooms, but it's often hard to get the latter, and they're really expensive when you can get them. I often make it with a pound of shiitakes and a pound of criminis (or baby bellas, if you can't get those). But you can really use almost any mix of wild-ish mushrooms you want.
  • Angel Hair Pasta with Peas, Prosciutto, and Lemon
    A cream sauce, again. (Hmm, I see a pattern.) I actually can't remember what I used in place of the prosciutto. Probably some vegetarian lunch meat. You'll want something substantial.
  • Linguine with Shrimp and Plum Tomatos
    This is really good, but be warned that it makes a ton. You may well want to halve the recipe. (I personally find that shrimp doesn't keep that well, so leftovers of this need to be eaten fast.) You also need a lot of basil for it. The typical one ounce container probably isn't enough, even for half the recipe. So, if you have the option, get a four ounce container (which they usually have at Whole Foods.)

Monday, June 8, 2015

Recipes for Isobel

Our daughter Isobel is living in an apartment this summer in Providence, and so is cooking for herself. When she was home a couple weekends ago, she was looking through some of our recipes, and I told her I'd post some of them here so she didn't have to take pictures of them. So here's the first batch: A bunch of recipes from Bon Appetit.

Greek-Style Noodles

This is a recipe that we adapted from one in the Vegetarian Express Lane Cookbook, by Sara Fritschner. It's a fast and easy summery pasta.


  • 12 ounces pasta
    We prefer capellini (angel hair), but you can use any long, thin pasta
  • 5 tbsp olive oil
  • 1 clove garlic, minced
  • Small red onion, sliced
  • 1/2 cup parsley, chopped
  • 1/2 cup greens of scallions, chopped
  • Zest and juice of half a lemon
  • 2 tbsp white wine
  • 1 tbsp chopped fresh oregano (or 1 tsp dried)
  • 8 oz feta cheese, crumbled


Heat the oil in a good-sized skillet. (The pasta will be added later.) Add the garlic and onion and cook until starting to soften. Then add the parsley, scallion greens, oregano, lemon, and wine, and cook about two minutes, just to wilt the parsley a bit. Lower the heat to keep this stuff warm, if need be.
Meanwhile, cook the pasta until not quite al dente. (It's best to try to time this so the noodles are done just when the sauce is.) Save about half a cup of the cooking liquid and drain the noodles.
Add the noodles to the sauce. Increase the heat a little bit, and mix the whole thing together. Add half the feta and cook until the sauce becomes just a bit creamy.
Serve the remaining feta alongside the noodles.

Thursday, February 12, 2015

Creating, Modifying, Etc, SSH Keys

Another "remind myself how to do things" post.

To create a new ssh key:
ssh-keygen -t rsa -b 2048 -C "COMMENT"
 To change the passphrase on a key:
ssh-keygen -p -f KEYFILE [-P OLDPASS] [-N NEWPASS]
 There's a nice guide to this sort of thing here.

Simple Encryption With OpenSSL

Every once in a while, I need to transfer something from one computer to another, and emailing it to myself is an easy way to do it. But sometimes what I want to transfer isn't something I want out in the open. So the obvious thing to do is encrypt it, and the obvious tool to use to do this is openssl.

Here, so I remember it, is the command for doing this:
openssl enc -des -a -e -pass pass:PASSWORD -in INFILE -out OUTFILE
If you leave out INFILE or OUTFILE, it defaults to stdin and stdout. So you can do:
echo "This is  a secret" | openssl enc -des -a -e -pass pass:PASSWORD
and the encrypted version will be written to the terminal.

To decrypt:
openssl enc -des -a -d -pass pass:PASSWORD -in ENCRYPTED -out DECRTYPED
Or, again:
echo "U2FsdGVkX1+Kqcs+25e+6MiQBr4NT8ykx3POhv9yAf9gnvSn4D2L0A==" | openssl enc -des -a -d -pass pass:PASSWORD
And again you'll get the decrypted version written to the terminal.

Sunday, February 8, 2015

Two Excellent Articles By Veterans About "American Sniper"

Both on Alternet:
And let me emphasize something at the end of the first one: This isn't about Chris Kyle.
Let’s talk about [Bradley] Cooper and [screenwriter Jason] Hall, and the culture industry that recycles propagandistic fiction under the guise of a “true story.” And let’s focus our anger and our organizing against the authorities and the institutions that craft the lies that the Chris Kyles of the world believe, that have created a trail of blowback leading from dumb war to dumb war, and that have sent 2.5 million veterans to fight a “war on terror” that persists in Iraq, Afghanistan, Yemen, Syria and Pakistan.

Saturday, February 7, 2015

Thought Wins PROSE Award for Best New Journal in the Humanities and Social Sciences

The journal Thought, which was founded a few years ago by Crispin Wright, and for which I am the Associate Editor for Philosophy of Language and Philosophy of Mathematics, has been recognized as the Best New Journal in the Humanities and Social Sciences at the PROSE Awards.

I had not previously heard of these awards, but apparently they are the American Publishers Awards for Professional and Scholarly Excellence. They describe themselves this way:
The PROSE Awards annually recognize the very best in professional and scholarly publishing by bringing attention to distinguished books, journals, and electronic content in over 40 categories. Judged by peer publishers, librarians, and medical professionals since 1976, the PROSE Awards are extraordinary for their breadth and depth.
This is a wonderful recognition for what has quickly become, IMHO, an excellent journal. Congratulations are due especially to Crispin and to the other to editors: Carrie Jenkins and John Divers.

For those who have not previously heard of Thought, we specialize in publishing shorter pieces (under 4000 words), kind of like Analysis. We try our best to have a fast turn-around time, though it doesn't always work out that way.

Wednesday, February 4, 2015

Sam Killermann's TEDx Talk on Gender

I'm a big fan of Sam Killermann, who is the human behind the website It's Pronounced Metrosexual, the Genderbread Person, a wonderful and very commonsensical book on gender (which can be downloaded for free or for a donation, if you wish), the world's best sign for gender neutral bathrooms, and much else that is wonderful. He's also a very funny guy, who first made his name doing a sort of stand-up routine about gender. So I was thrilled the other day to discover his TEDx talk, "Understanding the Complexities of Gender", on You Tube. Even if you already know all the basics, it's worth watching, if only for how compassionate Sam is towards those he is trying to help understand.

There's a wonderful bit at the end (it starts at about 15:35) where Sam articulates his hopes for the future:
Now, in my dreams, I don't foresee a society that is gender-blind, but I do foresee one that is gender-creative. Where people can figure out who they are and be themselves, exploring what that means, and in that they'll be supported. Where questioning one's gender won't be shunned, but an expectation. And where realizing that you don't fit into this gender mold won't lead to isolation and depression, but will be a source of celebration. And above all a society where people, regardless of their gender formation, are safe. 
It's sad one even has to mention that last bit, but Amen to all of it.

Thursday, January 29, 2015

Emphasis in HTML and CSS

This is really a very simple matter, but perhaps one that will be helpful to other people. In working on reading notes for one of my classes, I have wanted to insert questions for the students to think about. The questions are indented and in italics, so that they stand out:
P.question {
 margin-left: 1em;
 margin-right: 1em;
 font-style: italic;
The downside to this is that emphasis doesn't work right. So if I write:
<p class="question">In Russell's reply (which you do not <em>have</em> to read)...</p>
the emphasis has no effect. A kludge would be to use bold, instead, which is what I want there, but then what if I copy it elsewhere? Then I have to change it again. A better solution is to use CSS to style it appropriately:
P.question em {
 font-weight: bold;
I am guessing that one could use similar techniques to make emphasis inside emphasis work properly.

Wonderful Piece on Queer Theology

If we don’t abundantly love each other, we can’t have an abundant relationship with God. I must embrace an interpretation of my faith that requires unconditional love for queer people because any less would be to deny my own humanity and that of my community.
Preach it, sister!

More at Autostraddle.

Tuesday, January 27, 2015

Trans Woman Nominated as Pennsylvania's Next Physician General

Her name is Rachel Levine. Harvard undergrad, did her MD at Tulane.

Seriously: Even five years ago, could you have imagined such a thing? Of course, as noted in the story, it is still legal in Pennsylvania to fire someone for being trans, though there is a bill pending to correct that injustice.

Coverage from and the Washington Blade.

Wednesday, January 14, 2015

PDF of "From a Logical Point of View"

More and more cool stuff appears in electronic form, this time a PDF of Quine's From a Logical Point of View, free on

While we're at it, how about Russell's Inquiry Into Meaning and Truth?

Thursday, January 1, 2015

The Squeezing Argument in "Is Frege's Definition of the Ancestral Correct?"

I mentioned in an earlier post my paper "Is Frege's Definition of the Ancestral Correct?" It has now been refereed at Philosophia Mathematica and officially accepted for publication. One of the two reports was unusually helpful and led to some significant improvements in the final version, which is now available online.

The most helpful comment caught a nasty thinko in one of the proofs. But the most interesting observation this referee made was that perhaps the central argument of the paper is a so-called "squeezing argument". (See Robbie Williams's discussion of such arguments here, and Peter Smith's here, a version of which was eventually published in Analysis.)

The rough structure of such arguments is as follows. Suppose there is some intuitive notion I and you want to show that some rigorous notion R is co-extensive with I. Then one way to do so is as follows. Suppose that it is uncontroversial that R gives a necessary condition for I. And suppose further that we can find a different rigorous notion Q that uncontroversially gives a sufficient condition for I. So, to put it set-theoretically, we have:
Then if we can show rigorously that R is sufficient for Q, i.e., that R ⊆ Q, then it will follow that both Q and R are co-extensive with I. As it's put, I has been "squeezed" between  Q and R.

The way this works in the paper is that I is the intutive notion of the ancestral; R is Frege's definition; and Q is an alternative definition that I give and claim, in fact, is intensionally correct. In response to an objection to the intensional correctness of that definition, however, I fall back on this squeezing argument.

This makes at least three instances of this sort of argument: The original, in Kreisel, which is meant to show that the model-theoretic account of validity is extensionally correct; Smith's, which is supposed to show that Turing's analysis of computability is extensionally correct; and now this one. Are there others? I'm guessing maybe there are?