A Critical Look at Goodman’s “The New Riddle of Induction”
November 30, 2007
My computer got stolen and I’ve had a ton of work, so I haven’t been able to post much. I just wrote this essay in American Philosophy, and I figured why not post it up so some people can learn about the modern problems with induction (that is, if I pull ten marbles from a bag, and they are all black, I would seem to be justified in inductively inferring that all of the marbles in the bag are black, in other words, drawing general conclusions from finite samples).
Here it is
A Critical Look at Goodman’s
“New Riddle of Induction”
In a series of lectures in which Nelson Goodman laid out some of the problems and solutions with the practice of induction, Goodman found considerable fame and acclaim for his account of the “new riddle of induction” in which he created the predicate “grue” in order to prove that, using grue, it is possible to present two choices and make the one which is entrenched to a much lesser degree equally likely. This leads one to wonder if the results of an instance of induction, such as all of modern science, are ever justifiably believed. It is important to note that Goodman is not concerned with the reasoning for which we do use induction in our every day lives, but why we should use it. Goodman want’s to know if we are, in fact, correct in assuming that because the sun rose yesterday and it rose today, it will rise tomorrow. To do this, Goodman tells us, we should forget about what we are justified in doing, and instead attempt to define what makes an instance of induction good or bad. In this paper, I will discuss Goodman’s New Riddle showing the problems it brings about when ever one tries to define good induction, and present some reasons that it may not be as large of a problem as he originally thought.
Goodman opens his work by searching for the definition of good induction. On this question, he takes a holistic point of view. According to Goodman, good induction is based upon positive instances of our hypothesis, and our positive instances are informed by the already accepted inductive inferences which we have. Unfortunately, this leads to a whole new series of problems, chiefly the logical conclusion that, by this thinking, any proposition inductively supports any other proposition. This is because, according to induction, anything that confirms a hypothesis also confirms whatever follows from that hypothesis. For example, “8497 is a prime number and the other side of the moon is flat and Elizabeth the First was crowned on a Tuesday” (69) are all statements which could be proven, but proving and one has no bearing on the others. If we prove that 8497 is, in fact, a prime number, that has no bearing on the dark side of the moon or the day on which Elizabeth the First was crowned, but according to our present definition of induction, it does. Goodman fixes this by amending his definition and adding that a good instance of induction will be one in which the conclusion is of the same general kind as the premises. After solving this dilemma, Goodman turns to what he believes it the “new” and truly pressing issue facing induction, his “New Riddle of Induction”.
To open the discussion of the New Riddle, Goodman tells the reader about lawlike hypotheses and accidental ones. For example, Goodman writes “that a given piece of copper conducts electricity increases the credibility of statements asserting that other pieces of copper conduct electricity…but the fact that a given man now in this room is a third son does not increase the credibility of statements asserting that other men now in this room are third sons” (73). For Goodman, the problem is distinguishing between lawlike cases, such as when the conductivity of one piece of copper increases the probability that all copper is conductive, and cases which are purely accidental, such as the fact that one man in a room full of people being a third son inductively supporting the claim that all men in that room are third sons.
Defining lawlikeness at first seems easily solvable, involving only a few small cases of accidental hypotheses sneaking in amongst the lawlike ones. However, Goodman changes this when he introduces the predicates “grue” and “bleen” in relation to emeralds. An emerald is grue if it is green and inspected before future time t, and if not, it is blue. According to this predicate, every emerald that has ever been found is equally likely to be grue as it is to be simply green, because it is green before future time t, and it has been inspected; therefore it meets the requirements of grue equally well as it does green. This leads Goodman to assert that “If we simply choose an appropriate predicate, then on the basis of these same observations we shall have equal confirmation, by our definition, for any prediction whatever about other emeralds or indeed about anything else. We are left once again with the intolerable result that anything confirms anything” (75). Because we are able to find two equally likely scenarios from the existence of the predicate grue, induction basically tells us nothing, since we are now never sure if we are correct in assuming anything based on previous experience.
From this, Goodman tries to answer on how we could possibly pick one predicate, namely the more established green, over another, grue. What many would do, according to Goodman, is to rely on the more natural and time worn phrase because “Plainly ‘green’ as a veteran of earlier and many more projections than ‘grue’, has the more impressive biography” (76). Because green is more commonly used it is thus, more “correct”. Sadly for the user of induction, this is not the case, because, as Goodman states “if we start with ‘grue’ and ‘bleen’, then ‘blue’ and ‘green’ will be explained in terms of ‘grue’ and ‘bleen’” (79-80). In other words, the only reason green is more entrenched than grue is because of the order in which they were discovered or became common in usage, having nothing to do with the quality or correctness of the predicate. Finally on this subject, Goodman has an answer for the critic who brings up the point that the predicate grue is based partially on time and is, therefore, invalidated for some reason. Goodman answers, first of all, that there is nothing wrong with grue’s dependence on time. Also, the author offers that if green were being explained in terms of grue, as previously, time would be essential in its explanation.
Next, Goodman offers a response to the critic who wonders why we need worry about “such unfamiliar predicates as ‘grue’ or about accidental hypotheses in general” because, after all, if we are never going to encounter them in daily life, why should we worry about them in our thought experiments. To this question, Goodman answers that if we were conducting regular science that would be sufficient. However, in the case of philosophy if we “seek a theory at all we cannot excuse gross anomalies” because they show the symptoms of a “widespread and destructive malady”. In other words, it may be enough to have these errors in our conception of the world for daily life, but when looking for a precise theory of induction, these seemingly small mistakes, in the end, add up to a great deal.
Goodman’s work “The New Riddle of Induction” leaves the reader wondering how he will be able to solve the problems which the new predicate grue brings to the table. However, there are several errors within Goodman’s conception of grue that, upon closer examination, allow us to escape from the paradox. First, we must understand the nature of Goodman’s statement that there is no qualitative difference between grue and green, and that the only difference lies in their use in our language. For Goodman, these two things have completely compatible results in practical use; their only difference is how they are used in language. If, for our entire lives, we had been using grue and bleen, green and blue would have equally confounding results for us as grue and bleen presently do. But the clear problem with this is that to be able to tell grue and to be able to tell green when one sees them involves two completely different skill sets. For the viewer to see green in a picture, he must see a pigment which reflects light of a certain wavelength and then meets his eye. For a viewer to see grue (call him Mr. Grue), he must first see the light of that same wavelength, and then be able to instantly discern the date associated with this picture, in order to know if it takes place before or after time t. Baker and Achinstein use the example of two exactly similar black and white pictures of grass, superimposed upon the same scene, for example the Harvard commencement or any other pastoral scene, but with each scene taking place 50 years apart. The first scene takes place before time t, and the second, after. If we were able to somehow cover all of the background features that make it obvious which is the later picture, such as the Boston skyline at the Harvard commencement, and ask Mr. Grue to paint the correct color on the grass, how could he possibly perform this task? According to Goodman, Mr. Grue has the ability to look at the grass and tell just what color it should be, just like I could look at a pastoral scene and instantly paint green upon it. Mr. Grue simply could not perform the task and still be a person of the same powers as our speaker of the green-blue language. Thus, strangely, a large problem for Goodman is that his belief in the similarity between grue and green leads Mr. Grue to have “a faculty of extrasensory perception not possessed by people such as ourselves who are speakers of the green-blue language” (Baker/Achinstein 6). Unfortunately for Goodman, it would seem that his New Riddle needs some tightening or re wording, because, thought it may be useful to those of us with extrasensory perception, it is useless for speakers of the green-blue language here on Earth. However, Baker and Achinstein may run into criticism as well. Their formulation is dependent upon pictures of future or past events, which are not real things, but are, in fact, representations of real things. Furthermore, how are we ever to know that the pigment on the painting is, in fact, green. We are in our every day lives trained to see “that pigment on the painting” as green, but with things such as colors, which have a nearly infinite amount of permutations of shades, how are we to know which is the one being spoken of. Therefore, it would be easy for one to wonder whether it is enough to use a representation of grue or green to disprove the existence of the other
Nort Korea vs. Pirates
November 8, 2007
North Korea is really psyched that the U.S. helped them fend off pirates.
“The North’s Korean Central News Agency hailed the rare maritime collaboration as a ’symbol of cooperation” between the two countries “in the struggle against terrorism,’ and pledged to work with the international community to fight terrorism.”
When the North can’t get any money out of terrorism, but stands to lose commerce (who knew they traded?) they’re so against terrorism. Buying nuclear secrets from Pakistani scientists and then selling them to terrorist supporting states like Iran…NO PROBLEM. This is an irrational regime which can’t be worked with, I will believe that until the day Kim Jong-il is gone.
Don Shula Pops Off
November 8, 2007
Well, we’ve come to that special time which only comes around every few years. It’s that magical season when someone from the ‘72 Dolphins says something asinine, and everything laughs at all of those old fogies who have nothing to live for but their record. It happens every time a team starts to have a serious shot at going undefeated. We all know that the ‘72 ‘Fins were a great team, they went 17-0, and nobody can take that away from them. Furthermore, they had a great, Hall of Fame coach to lead them. There, now that that’s out of the way, let me get to it.
As a Patriots fan, this year is an almost surreal feeling. I spend half of the year caring what Yankee fans are doing and saying, caring what people think of the Celtics and Bruins, and until now, caring how the Patriots are perceived. For years, New England fans reveled in our “underdog”, complete team aura. We were everything that was good in the NFL, and that was a great feeling. That was nice, but you know what feels better? Not caring what anyone thinks, because no matter what they think, your team is better than theirs. The Pats are better than the ‘72 Dolphins. They’re better than any Steelers team during the steel curtain years. They are better than the Colts (it would have been even more obvious if not for possibly the most one-sided officiating I have ever seen, was there one good pass interference call?). Bottom line is, unless you have watched a team like this, you don’t know how it feels. I hear the constant criticism that they are classless (because of the “eff-you TD, as Bill Simmons would put it), that they cheat, that Bellechick is a bad guy, whatever; we just don’t care about any of these things because we know, when push comes to shove, you envy us. Say it all you want, “I want to win with class, I want to win the right way” point is, that’s just not how it works in the real world. Did Raiders fans hate rooting for their team? No! As a fan, the ultimate goal is to win, and the Patriots do that better than anyone else.
Put an asterisk on the Patriots for this season. Hell, put it on there for the last six seasons. Nobody around here will give a damn. We are watching the best team of a generation (or two?) play football, and nobody, no asterisk, no commissioner, can take that away from us. Keep talking Don Shula, but I won’t be able to listen, I’ll be too busy enjoying this team.
* Shula backed down from these comments minutes after this was posted. Nice.
Last Night’s Debate
October 31, 2007
Good summation of last night’s debate over at ABC. The most important exchange came when Hillary was asked about New York Governor Elliot Spitzer’s plan to give licenses to illegal immigrants:
“I did not say that it should be done, but I certainly recognize why Gov. Spitzer is trying to do it,” Clinton said.
Her rivals pounced.
“Sen. Clinton said two different things in the course of about two minutes just a few minutes ago, and I think this is a real issue for the country,” Edwards said.
Said Obama: “I was confused on Sen. Clinton’s answer. I can’t tell whether she was for it or against it, and I do think that is important.”
Taliban Resurgence in Afghanistan
October 31, 2007
The Taliban is having success like it hasn’t had since 2001. They’ve moved into southern Afghanistan, drawing close to one of the largest cities in the “nation” Kandahar.
Running Diary- Philadelphia Democratic Debate
October 31, 2007
Tonight is a big night for the Democrats. With Hillary’s recent surges, look for the next tier candidates to really go after her tonight. It’s still early, but you can be sure that any one of these guys is getting to the point of desperation where they know they have to either make a big move, or they will be out of this race before it really gets going.
9:04- The debate kicked off with a question to Senator Obama regarding Senator Clinton, basically giving Obama the opportunity to bash the frontrunner. Obama delivered a measured response, telling the viewers that she has flip flopped, and that she is leaning Republican.
9:05- Question number two is directed at John Edwards, asking him what the “double talk” that he earlier referred to was. He proceeds to speak against Hillary’s hawkish voting record and her flip-flopping position on Social Security, which, according to Edwards, she said she does not want to change but “privately has said otherwise”.
9:09- Russert steers the questioning back to Hillary’s vote to name the Iranian Revolutionary Guard as a terrorist organization, thus theoretically giving the president the pretense for military action in Iran. Clinton answers that she is not in favor of rush to war in Iran, but she is not in favor of doing nothing. She “prefers vigorous diplomacy” such as that used in Libya and North Korea.
9:10- Seems like Senator Clinton is really flexing her foreign policy muscle here, this is an issue that Obama and Edwards can’t win because of their lack of real foreign policy experience and expertise. She finished by stating that she is”prepared to pass legislation…to make it abundantly clear that sanctions and diplomacy are the way to go in Iran.”
9:13- Senator Biden says that the Iranian resolution is tantamount to a war compact. He also blames the resolution for the rise of the price of a barrel of oil to over $90, said Bush has been emboldened and is now issuing “world War III” rhetoric, and extols the problems we have created for Pakistan and Afghanistan by furthering the “myth” that America is anti-Islamic.
9:15- Senator Obama refused to say at what point he would attack Iran. We should be “reaching out aggressively but also talking directly to our enemies,” we should be talking to Iran about the carrots that we can use to convince them not to create a nuclear weapon, such as joining the WTO. No mention of sticks, though.
9:18- Clinton again notes that we should “not be rushing to war, but we should not be doing nothing”.
9:20- Strong, factual rebuttal by Edwards, saying that the Iranian bill “looks like it was written literally by the neocons” and believing that the way to put pressure on the Bush administration is not to appease them but to stand up and say no to them.
9:25- The Iran issue really has legs here. 25 minutes of nearly uninterrupted talk on Iran… When asked if he would pledge to do everything he can to avoid war in Iran, Obama quickly changes the subject, saying that we cannot be run by “politics of fear”.
9:30- Richardson is really hitting on his area of expertise, diplomacy, mentioning twice in the first half hour that he has more credentials and he is the only one to have done “any real negotiating” (amid much grumbling from the other candidates).
9:31- Kucinich is almost insufferable. He is the most dangerously idealistic man I have ever seen. How does he keep getting re elected in his home district? I hope it’s not just because they love to see him bow out early in a presidential election every 4 years. I will waste no more space on this man.
9:34- Obama wants to “convene a meeting of Muslim leaders” upon taking office, so as to “send a message that we are willing to listen”. Sounds great Barack, I can’t wait to see the PLO, Hamas, Khamenei, Ahmedinijad, al-Maliki, Musharaff, and Karzai hanging out in the same room, just getting along swimmingly.
9:38- Clinton says she wants troops to stay in Iraq to guard diplomats and fight terrorism there. This answer seems a little disengenuine, considering there are reports that she would keep upwards of a hundred thousand troops there.
9:43- After a short commercial break, the topic switches to electability, asking Clinton for her response to some harsh words from Major Giuliani regarding her electablility. Clinton again tells us her experience, as a senator, in Arkansas, as an advocate, and as a senator. She then gave a brief overview of her vague goals as a candidate in order to change the subject.
9:48- Senator Edwards says that Republicans may keep bringing Senator Clinton up because they want to run against her. ummm… what John? He then calls her into question for raising the most money. How does one win in politics if having the opposing party dislike you (because they fear you) and raising the most money are bad things. Senator Edwards seems to be hurting himself tonight, at least in my eyes.
9:54- Richardson’s egocentrism all of the “I, I, I” BS is starting to sound awkward. You don’t win as a candidate by telling everyone how great you are. You show it by making sense on this issues that people are about. I don’t care that you’re the only CEO, that 7 of 8 of the last presidents are been governors, or that you have more foreign policy experience. If these things are all true SHOW me, don’t TELL me.
10:00- Biden, known for his loose lips, has let them slip again. Calling Giuliani the most under prepared candidate since George Bush (there haven’t been that many since then, but that’s beside the point) and then saying that all he says in a sentence is “a verb, a noun, and 9/11″. Seems like a little too much, Giuliani was the top executive in some little city on the eastern seabord of America in probably its greatest time of crisis. He knows how to lead.
10:05- Clinton is met with a direct contradiction on what she is saying (that social security isn’t in as dire of straits as we may think) and what her Husband said 9 years ago. She handles the question beautifully, saying that her husband moved us towards fiscal responsibility, and the economic numbers show that it worked. She seems to be answering strongly and factually tonight, leaving little doubt in the viewers mind because of the forcefulness behind her words.
10:10- Brian Williams just in all seriousness asked if Obamba was afraid of confusion between his name and that of Osama bin Laden. His response “no, because I have faith in the American people”. It’s amazing that this needs to even be an issue because Republicans are so dirty these days.
10:16- After another commercial break, the new topic is energy and its costs in relation to the newly skyrocketing price of a barrel of oil.
10:17- Biden blames it on us, saying we cause it by being bellicose towards Iran. Edwards says he will investigate Oil companies because they are “vertically integrated” and thus casts the blame on them, since they presumably control production.
10:18- Clinton suggests looking at the strategic petroleum reserve in the short term and a move toward energy efficiency and conservation. Obama expounds on Biden’s point, telling us that 30% of the cost of a barrel of oil is in “risk” caused by our actions in the middle east.
10:25- “We didn’t need a surge in Baghdad, we needed a surge in New Orleans”. John Edwards’ stab at creating the “quote of the night”. To me, he’s the example of the problem with modern Democrats. The electorate wants a social progressive who has a backbone on foreign policy issues, get this through your head! If we bury our head in the sand, our problems will not go away, John, we must project force.
10:30- Obama hopes to offset payroll taxes, giving a break to low income families and the elderly, while at the same time rolling back tax cuts to the top 1% and closing corporate loopholes. All to be expected, but he’s still the only one to say it. Good for Obama. It seems like this is the type of thing Hillary would have said 10 years ago before she became a political automatron.
10:33- Edwards tells us that our troops are serving honorably, while thousands of mercenaries are running around and giving hundreds of thousands to Bush… so when a paid “mercenary” takes a bullet to protect an L. Paul Bremer or maybe even Condi, he’s not a patriot, because he isn’t part of the military?
10:35- Subject is switched to education, would you, as President, extend the school day or the school year? Each candidate will have 30 seconds to answer.
10:36- Richardson- yes, more money for teachers, science, and math.
10:37- Obama- more time in classroom, increase grants in math in science to make jobs here more attractive to foreigners.
10:38- Clinton- Help for families, family is a child’s first teacher. Patriotism through education
10:39- Edwards- Universal Pre-K, start a national teaching university, incentives for teachers willing to work in under-funded communities
10:39- Biden- Longer schoolday, minimum 16 years of education, focus on socioeconomic divide between school systems
10:40- Dodd- Education shouldn’t depend on where you are born.
10:47- Edwards takes a 30 second question on “how to ensure we have enough doctors in the future” and answers that we need universal healthcare, and then tells us about a nursing shortage… for some reason.
10:48- Almost all of the cadidates have answered the previous question by blaming “the insurance companies” saying that doctors must constantly be looking over their shoulders as they make the stressful decisions that they make.
10:53- Only Chris Dodd is willing to say that he believes Illegal immigrants should not have a driver’s license, believing that a license is “a priviledge, not a right” and causing a retort from Clinton, asking him “what are you supposed to do if an immigrant runs into you today without a license”?
10:56- Edwards is asked a question on internet censorship, and quickly responds that he is confused by Clinton’s answer about immigrants’ drivers license. Barack quickly piles on that he is also confused, and they both think this is a real issue, that she cannot give strait answers. One has to wonder how much of a real issue it is that they cannot answer a direct question when asked. On the other hand, Clinton pretty much made the previous point about her “double speak” for her.
11:00- As someone who is steadfastly for decriminalization of Marijuana, I’m deeply disappointed that almost all of the major candidates raised hands in opposition to decriminalization.
11:02- I actually laughed out loud when Obama told the nation that for Halloween he would be wearing a Mitt Romney mask which “goes both ways”. Nice.
Well, that was fun. I think nobody really stood out as head and shoulders above everyone else. Clinton had a major screw up at the end when she refused to answer the question on drivers licenses for illegal immigrants, but she didn’t seem to lose her cool to the point as to create that “kodack moment” that is necessary to make the mess up really punitive. I Liked a lot of the things that Chris Dodd said as well. Despite his egocentrism, Richardson came off pretty well, and well informed on many of the key issues.
The 07-08 Boston Celtics
October 30, 2007
With the Celtics tipping off on Friday, it’s time for me to throw together some sort of preview. Admittedly, Baseball and Football are my 1 and 1a as far as knowledge goes, but I do sit down and watch a good 90% of Celts games. Unlike with Baseball and Football, though, I never played beyond the 8th grade in Basketball, so my advanced knowledge is little. Hell, maybe that gives me more of a “fan’s perspective” than in Baseball and Football, who knows.
Basically I just want to commend Danny Ainge for not sucking quite so much this off season. For years and years, he’s told us that he has a plan, that he’s stockpiling draftpicks, that the young players are getting better and they just have to mature. He traded one of our top players of the last several decades, Antwan Walker, because he didn’t like his game, all in the name of “his plan”.
I’ll be the first to admit, I believed him that he had a plan, and that the plan would work. I saw a lot of young talent, I saw a team that was fun to watch, and I thought I saw a team that was getting better right before my eyes. Then I stopped listening and started thinking. I quickly realized that this team was getting WORSE not better. Right when they should have been coming into their own, they actually mangaed to run out a team with the second worst record in the NBA last season. Yes , the young guns were exciting to watch, but let there be no doubt that they were not a good basketball team last year.
Then, we turned our collective eyes to the college rands and saw our savior. We saw Kevin Durant chucking up three’s, penetrating the lane, and hitting clutch shot after clutch shot to win games for Texas. We saw Greg Oden simply dominate with pure physicality, athleticism, and coordination that many had not seen since Patrick Ewing’s days at Georgetown. In short, we saw the future of the Celtics franchise, and we saw that we could get there through losing.
We began rooting for the losses, we tolerated the tanking, we chose to ignore the fact that the NBA has a lottery specifically to avoid this type of tanking, and we lost our soul as sports fans, because we needed to have one of those top two picks. All of this was fine, because who needs a soul when you’ve got Kevin Durant hitting bombs from deep or Greg Oden dominating the paint for the next 15 years.
And then, the lottery happened. With hopes of landing at worst the number two pick and presumably taking Durant there (I thought he should have unequivocally been first, but that’s another article completely), the ping pong balls did not roll well for the Irish that day, and the Celtics were given the fifth pick in the draft. We all went from dreaming that Oden or Durant would wear Celtic green, to hoping that a guy who’s name is pronounced like the letter “E” would still be around at number 5.
And that’s when Danny said “you know what, screw my plan”. The Celtics were never going to win a championship without an absolute star player, one who can carry a franchise, and they seemed to have lost their chance at getting one. Paul Pierce is a nice player, but he has shown time and time again that not only does he lack the leadership qualities off the court, but he lacks them on it; he would not be the one to carry the Boston Celtics to another title. So Danny Ainge did the expedient thing and he mortgaged the future of the franchise for a bright next several years.
He sent basically the entire population of Waltham to the Minnesota Timberwolves for Kevin Garnett, a legitimate star who will take the Celtics to heights they haven’t seen in 20 years. He parlayed the number five draft pick into Ray Allen, another solid scorer and veteran presence who will do nothing but help. He signed James Posey, a great defender and a solid/clutch shooter from deep.
All of these additions have one thing in common: they are veterans. Danny Ainge finally got the balls to admit he was wrong and took a chance. He’s attempting to grab a championship by the throat and take it. And for that audacity, I’m finally withdrawing my hat from the “fire Danny Ainge” crew that had gained so much momentum.
(Until all of the old guys are gone in a couple years, and we’re left with Kendrick Perkins, Rajon Rondo, Leon Powe, and a few more scrubs)
