Guest post by Landon from the Churchland on morality and science thread.
@alqpr: I share the concerns of those who object to the weight you seem to attach to the authority of so-called “experts” in moral philosophy rather than just looking at the quality of the arguments.
To quote Ophelia, “Those? Who?”
In any case, I cannot find a single instance of Ophelia (or myself, for that matter) leaning on the expertise of an individual as a surety that the conclusions are good, rather than as a heuristic device for finding better arguments. In short, do not mistake “Experts are more likely to have good arguments” for “this is a good argument (solely) because it was forwarded by an expert.” Ophelia and I have both said something like the former, but neither of us have said anything like the latter.
But wrt the training issue, I have to add that in my opinion Harris appears even more naive than Shermer, and Harris does at least have a BA in philosophy and according to Wikipedia he IS a “philosopher”
A BA doesn’t make you a philosopher. It indicates that you might be qualified to train as one. See my post at #11 – this has been dealt with already.
If I am proposing a “new” solution for an old problem I would be well advised to ask a philosopher to assess its novelty and point out any weaknesses. But If I see an error in someone else’s argument I don’t need an expert to tell me whether it’s really an error.
I am glad, at least, that you see the value in philosophical training. Likewise, I don’t dispute that you NEED not be a philosopher to see an obvious error in an argument. However, many arguments offered by philosophers have been cleansed of OBVIOUS errors, so if the argument is at all competently formed, it’s going to take someone who has a good degree of philosophical competence to spot what errors persist. And, in my experience in teaching, undergrads frequently misunderstand the force of certain objections and misconstrue the consequences of various errors they detect. They also, usually due to lack of understanding of the nuances of certain terms of art, believe they see objections where none actually exist, which they would know if they had a greater familiarity with the supporting literature and thus a better understanding of the significance of the author’s use of THIS term or THAT term, rather than some other, in the context of the argument. So it’s not always true that you don’t need an expert to tell you if the error you (think you) see is really an error.
Finally,
I would be most grateful if either Ophelia or Landon (or anyone else!) could point me to even one example of an interesting (philosophical) problem that has been solved by an “expert” and explained in terms that Richard Feynman would find simple enough to justify a claim of real “expert” understanding.
I won’t address Feynman’s criteria except to note that Feynman, while a brilliant scientist, had a only very shaky grasp of what philosophy was about and repeatedly displayed ignorance regarding the methods, aims, and value of philosophy. In any case, the question is poorly formed. Philosophy does not “solve” problems in the scientific sense because philosophical problems are, by definition, beyond the realm of empirical investigation – that is, we can never “point to” some set of evidence that “proves” some particular answer is the correct one. Indeed, to the extent that a problem is amenable to such solutions, it migrates OUT of philosophy’s domain.
Philosophy problems are only ever more or less “settled,” because, lacking the ability to investigate the issues empirically, we (philosophers) try to define terms very clearly and then make the best arguments we can for various possible answers to the problems. We critique these arguments, and take the most plausible, least ontologically-promiscuous valid argument to be the best one. As “most plausible” is somewhat subjective, there will never be perfect agreement on any proposed solution, but that’s to be expected when we cannot appeal to the stern, austere realm of physical evidence for a final ruling. That said, there is a large degree of consensus on a number of issues, all of which are philosophical problems that have been at various points throughout history hotly contested by professional philosophers, and all of which were largely settled through the work of people who were essentially, for their respective eras, professional philosophers. A small sampling of these issues includes:
1) Materialism is the proper paradigm for understanding the operation of the mind (a refutation of dualism).
2) Religious belief is not rationally required (and there is only a rear-guard action maintaining that it is rationally permissible).
3) The correct paradigm for analyzing ethical problems is some variant of consequentialism that includes a concept of rights.
4) Democracy with universal adult suffrage is not only rational and ethically justifiable, it is probably the only rational and ethically justifiable form of government.
This doesn’t even mention the important work in logic that has made modern computer science possible.
The problem you may be running into, which trips up a lot of people, is that by the time a non-philosopher runs into a philosophical issue that has reached consensus, it has already seeped into the culture and looks a lot like “common sense.” It can be hard to remember that there was a time that universal suffrage was not taken for granted as the “right” way to do things, when democracy itself was a mad, experimental proposal. Non-philosophers tend to point to the people who campaigned to bring those ideas to realization in the social and political systems, but those people were almost always persuaded of the rightness of their cause by reading the philosophers who championed those ideas in the first place. The founders of the United States brought forth constitutional democracy into this world, but they did so after becoming convinced by Locke and Rousseau of the correctness of such an enterprise. If you’re having trouble figuring out what effect philosophy has had on the world, look at a map depicting the number of governments founded on the principle of constitutional democracy throughout history.
If the idea of democracy is just common sense then why has the party of the man who said “government of the people, by the people, for the people, shall not perish from the earth.” is doing its best to make that extinction happen?
@kevinalexander:
It is clear that democratized power is best for a nation and/or people as a whole on rational and ethical grounds. That doesn’t mean it’s the best on economic grounds or theological grounds or on the grounds of effective population control.
Not only that, it’s the best on rational/ethical grounds for a nation/people: Obviously some people who are good at acquiring and wielding power will note that they themselves would make out better with more power even if the nation as a whole might make out worse.
Since the people good at acquiring and wielding power are also much more likely to actually *have* power, you end up with a society in which quite a few of the powerful are advocating against democratic rule for their own *self interest* – not for the national interest.
If they then attempt to create arguments framing their position as in the national interest (the people who have all the money are the ones that hire other people – you don’t hire a butler, do you? – and therefore we should take more money away from those without it and give it to the people with it so that they can hire more people!!! Logic! QED!!!) that’s hardly surprising when democratic power isn’t dead, merely undermined to greater or lesser extents in various of society’s enterprises.
———-
Plus, he said that by the time the non-philosophers among us encounter an argument like this,
Note he didn’t say such arguments are merely common sense. He’s showing you how things that appear on the surface to be common sense are actually not: they are carefully crafted argument built upon years of observation, definition building, logic, and rigorous debate.
So your question was wrong in its premise *and* quite easily answerable when you read what Landon actually said.
Is it silly that I’m all giddy that something I wrote is featured as a guest post here? 🙂
Oh, and Crip Dyke, I LITERALLY could not have said that better myself!
Oh, pshaw. Now you’re making me blush. :blush:
It’s too bad that only a few trained philosophers are capable of understanding the much better arguments that philosophers have. If only everyone were as smart as a philosopher things would be so much better and most folks wouldn’t dismiss philosophy as pure wankery. But that ain’t how it is!
As for Feynman, he may not have known much about philosophy (I don’t know if he did or not – he knew a lot about a lot of things) but he solved a lot of major problems in the real world and was, to boot, an eminently sensible person.
I am really puzzled by this. The “logic that has made modern computer science possible” is a branch of mathematics, not philosophy, as far as I can tell. Though in a sense mathematics is like philosophy in that it cannot depend on empirical evidence, but it is also unlike philosophy in that its conclusions are even more certain than those of the sciences.
Hmm. I’m not entirely sure that 3 actually is a consensus view, Landon: Deontological and virtue theoretic ethical theories still have a very broad base of committed defenders, and consequentialism still has many, many critics and criticisms (some of which seem very difficult to answer convincingly). At the very least, it would be clearly incorrect to describe non-consequentialist ethics as no more than a rear-guard action, like those desperately defending the rational defensibility of faith. In fact, most applied ethicists use a mix of concepts and approaches from all three of those theoretic foundations, with different emphases for different categories of ethical problem.
That said, I’m still delighted to see your broader point so clearly articulated. Yes, there is progress in philosophy. Yes, there is such a thing as philosophical expertise, and it does matter. No, Western philosophy is not just a 25+ century intellectual circle jerk (no matter how bad things got in the Middle Ages when the church dominated intellectual life). Kudos!
[And silly or not, I recall being rather giddy myself when Ophelia first turned one of my comments into a post, lo these many years gone. 🙂 ]
Crip Dyke,
Thanks for setting me straight.
@Harald: This is a common misconception. Mathematics is posterior to logic. Turing was a mathematician who did good work in logic, to be sure, but his work was based on Goedel’s, who was a logician and who was working in response to Russell and Whitehead, also philosophers. Frege, a philosopher, developed quantified logic, which is important to modern work in artificial intelligence, as is modal logic, which is also a hot topic in philosophy.
Logic is also much, much less “tidy” than non-philosophers imagine. What most people outside the profession take for granted as the “rules” of logic are themselves subject to debate. Some call into question whether the Law of Non-Contradiction (that there can be no true sentences asserting both A and not-A) is true, attempting to develop what are called para-consistent logics, while matters in modal logic are far from settled, with numerous systems of modal logic still considered “going concerns.”
We let the mathematicians play with our toys, but logic is still philosophy. 😉
Harald Hanche-Olsen
Logic is used by mathematics, and is the ‘base-class’ of mathematics. Philosophers did a lot of work on symbolic logic since the mid 1800. I’m thinking of Frege, Russell, et al.
thephilosophicalprimate
Those who left Omelas type problems?
Landon beat me to it. 🙂
@philosophicalprimate:
You may have me on the consequentialism issue, but while I think there are powerful objections to both deontic and virtue theoretic approaches that have never been successfully answered, I was most persuaded by the fact that even those who take something of a deontological or virtue-driven approach feel compelled to incorporate SOME consequentialist insights, while many consequentialists feel unbeholden to reciprocate. Nonetheless, I admit, I may have overstated the case a bit on that one. 😉
[And thanks!]
@7: The foundation of computer science. at least in its digital forms is Boolean algebra which is, as you point out, a branch of mathematics first published by Boole in the 1850s. It has nothing to do with philosophy. It is the basis of the basic digital circuits in computers – and gate, or gate, nand gate, nor gate, inversion. Were philosophy to be applied to computer science we might at last create the long-awaited “maybe gate”. Then again “maybe not”.
according to Wikipedia he IS a “philosopher”
According to the quality of his arguments, he’s NOT.
BTW – The scientific method is an epistemological method. It is philosophy. Philosophy pwns!
Joking aside, Feynman displayed the traditional hard scientists’ disdain for philosophy, and was not very familiar with it. I have some old audio stuff (some of the tapes Leighton later turned into “Surely you’re joking…”) of Feynman telling stories, and there are a couple times he’s pretty dismissive – he appears to have discovered the epistemological trap that skepticism forced philosophy into and rejected the usefulness of philosophy thereafter. That’s actually not a very unreasonable position – if Feynman had spent his brain and life trying to refute pyrrhonism he’d probably have wasted his time, given up, and made a living repairing radios or playing bongos instead.
Already done. 😉
http://www.anselm.edu/homepage/dbanach/dnr.htm
So, the problem with the “common sense” argument is that we’ve observed that it may change over time. Thus we can’t really call it common or sense. That’s one of the big problems with consequential arguments: something may seem perfectly right and common sensical to us right now, but in 20 years it may turn out to be incredibly evil. For example: selling tobacco. Or, perhaps some day: eating meat. Or using fossil fuels. Or giving the Irish the potato.
Here’s an example: it’s obvious common sense that saving lives is a good thing if you can do it. So Norman Borlaug did a good thing when he released high yield wheat, corn, and rice and triggered the green revolution. Or will we find out 75 years from now that what he did was set humanity up for a malthusian collapse in which billions die instead of mere tens of millions?
Common sense may only be sensible at a particular point in time, based on our knowledge at that time (which may vary, like in the instance of tobacco) So what if there are other political systems that are vastly superior to liberal democracy, but which are not going to enter the marketplace of ideas for decades or centuries because of our misplaced common sensical idea that democracy is good? (This is the same reasoning that might apply to religion, btw)
Of course we can accept moral relativism and say that our ideas of right and wrong depend entirely on our knowledge and the consensus of the time. Which is another way of saying there’s not really any such thing as right and wrong other than the consensus of the crowd – a crowd which we now look back and see has been wrong over and over and over.
Hume cheated. Sextus Empiricus wouldn’t have missed a beat:
Hume: Whether your scepticism be as absolute and sincere as you pretend, we shall learn by and by, when the company breaks up: we shall then see, whether you go out at the door or the window; and whether you really doubt if your body has gravity, or can be injured by its fall; according to popular opinion, derived from our fallacious senses, and more fallacious experience
Sextus: How would you know if I did?
Landon @ 3 – not the least bit silly! 😀
Touché!
But since we are not rationalists, but empiricists, that is how we’d know, by the evidence we’ve observed. If you want certainty, there’s Descartes Cogito Island for you, plenty of time alone in solipsistic paradise.
Speaking of common-sense and rationalism:
In my opinion the truest thing that Descartes said. 🙂
Have philosophers actually established that there is such a thing as a mind and that it somehow operates- actual widely accepted agreement as to just what a mind is and what it does- though?
No, Marcus Ranum, the distance between Bortaug’s act and the- hypothetical but becoming more frighteningly likely- consequences is too great to say that he “set humanity up” for it. Bortaug and others gave the human race time to solve the problems of Malthusian logic without widespread starvation; if we failed to use that time, it is our fault, not theirs.
No, Marcus Ranum, the distance between Bortaug’s act and the- hypothetical but becoming more frighteningly likely- consequences is too great to say that he “set humanity up” for it. Bortaug and others gave the human race time to solve the problems of Malthusian logic without widespread starvation; if we failed to use that time, it is our fault, not theirs.
Who are you to say what is the appropriate distance in time for something to lose moral significance? Cause and effect is what it is; many people are willing to grant that he saved millions of lives. Does that same reasoning not apply if his actions later in whole or part cause the death of millions? By the same token, if you wish to excuse his long-term effects in favor of his near-term effects, then why credit him at all, since he is not the guy who actually grew the grain.
Besides, it was just an example. If you prefer, you could consider the question of Hitler’s grandmother and whether or not she was acting morally to ride her horse in a drunken state. You’re welcome to quibble with my examples but perhaps you understand the point I’m trying to make: causality is beyond our ken since it is incomprehensibly complex backward and forward, and our tendency is to only consider the short-term. Both of those seem to be problems with our ability to assess the consequences of anyone’s actions including our own.
It may be worth noting that Landon’s post here was prompted by my response to a parenthetical comment in the first paragraph of Ophelia’s post pointing out the vast superiority of Patricia Churchland’s book on science and morality over the corresponding works of Sam Harris and Michael Shermer.
Ophelia qualified her accusation of amateurism (directed at Shermer) with “I am an amateur, and that’s why I want to get moral philosophy from philosophers rather than non-philosophers, and why I wouldn’t myself try to set everyone straight about morality.” Commenter ‘jose’ responded with “you shouldn’t go out of your way saying that someone who isn’t an expert on something can’t do a good job on the subject”. After Ophelia and Landon responded to jose, I just had to stick my own oar in to “share the concerns of those who object to the weight you seem to attach to the authority of so-called ‘experts’ in moral philosophy rather than just looking at the quality of the arguments” and to ask for “even one example of an interesting (philosophical) problem that has been solved by an ‘expert’ “.
(Now of course I probably wouldn’t want to read anything that wasn’t, in some sense, expertly thought out and presented, so here I think that jose’s and Ophelia’s use of the word “expert” probably meant to refer to someone with specific training and credentials in academic moral philosophy – and that appears to be what Landon is saying also.)
Commenter ‘Eamon Knight’ pointed out the usefulness of a knowledge of philosophical history as providing some protection from falling into known traps, and I want to emphasize that I readily agreed that “If I am proposing a ‘new’ solution for an old problem I would be well advised to ask a philosopher to assess its novelty and point out any weaknesses.” But I also insisted that “if I see an error in someone else’s argument I don’t need an expert to tell me whether it’s really an error.”
Landon’s extensive reply to my comments, posted above, is very useful, and it may even be true that my discomfort with the emphasis on philosophical expertise is unfounded. But I seem to often hear philosophers complaining about lack of respect from their non-peers these days, and so even some of them may be interested in finding out whether there is anything they could do to change that.
So I am going to read Landon’s reply quite carefully to see both where it hits home for me and where I remain unconvinced.
He explains that he sees the value of experts as mainly “a heuristic device for finding better arguments”.
It is certainly true that Landon’s original comment only claimed progress rather than results, and so I was wrong to respond by demanding results. But it may be that hearing “results” for “progress” is a tendency that is fairly widespread and that philosophers who want to protect themselves from misinterpretation need to be more proactive in making that distinction.
While not claiming that you NEED to be a philosopher to see an obvious error in an argument, Landon adds some thoughts on why it might be helpful when the errors are less obvious.
I’m sorry, but I still find that condescending. With regard to the detection of subtle errors, I think there is a certain arrogance in the assumption that others are not equally qualified. And with regard to the use of technical “terms of art”, it is the responsibility of an author to keep the language appropriate to the intended audience. I would not claim to have found an error in a philosophical journal article without checking my understanding of the terms, but if one in the ‘New Yorker’ or ‘Scientific American’ doesn’t mean what it says in plain language then it’s just plain wrong. A kind of converse to this is that if I see what looks like a triviality in a popular account, perhaps I should look at a more “professional” source to see whether there is something deeper going on, but in at least two cases – Chinese Room and Gettier Problems – I have been unimpressed. (My objections may not have been undiscovered by others but they had to be pointed out to the proponents and their efforts at resuscitation reminded me more of Monty Python’s parrot seller than anything else.)
Finally, in response to my question regarding an admittedly overstated version of his claim about progress toward solutions, Landon says the following:
OK let’s look at that list:
I strongly suspect that this position has come into favour more as a result of success of the scientific programme than from philosophical argument. In fact I see no logical reason why failure of the scientific approach would not bring dualism back into favour; and in any case, just as in the more trivial case of statistical mechanics, the appropriate paradigm for understanding a phenomenon depends on the aspects of interest; it may be that referring to emergent mental phenomena as if they were fundamental is often the best way to deal with them. A possibly related issue is that the “non-overlapping magisteria” viewpoint may suggest that a language for pressing normative arguments – expressed in terms of such emergent phenomena – might be for all intents and purposes almost indistinguishable from a revival of dualism.
I doubt that many of the classical pagans believed their religious belief was rationally required. It was socially required, but that is quite another matter. When arguments were made for the rationality of religion, the context was that there was a substantial social reward for making them – while for opposing them the consequences were markedly less attractive.
All I can say is that that sounds like a pretty big bucket. Does pleasing God (or not) count as a “consequence”?
Except perhaps for absolute dictatorship by an essentially random person chosen at birth as in classical Tibet?
Tell me about it! (and are you going to claim all the rest of mathematics as well?)
In fact, it seems to me that with regard to who leads whom (the philosophical elite vs the common culture) it’s very much a chicken&egg issue. Ideas circulate without getting much traction until society is ready for them. Those who give the first expression that gets noticed and widely circulated do make a useful contribution, but if they hadn’t done so someone else would probably get there not much later. I think many people realize (or if you prefer, they just “think”) this, and so are offended by the claims of Philosophers to being the leaders of popular thought rather than perhaps more appropriately the recorders and reviewers of its development.
Not to put too fine a point on it, I suspect that Philosophers don’t always get the respect they think they deserve because they are perceived as overstating the uniqueness of their capacities and as condescending in their approach to non-peers. I think it may be useful for Philosophers to consider whether there is some truth in that, but if it is a misperception, any effort to correct it needs to be very careful not to reinforce it.
And, getting back to Churchland. On p2 we have this. “a lot of contemporary moral philosophy, though venerated in academic halls, was completely untethered to the ‘hard and fast’; that is, it had no strong connection to evolution or to the brain, and hence was in peril of floating on a sea of mere, albeit confident, opinion. And no doubt the medieval clerics were every bit as confident.” Hear! Hear!
What does who I am- or who you are- a different philosophical queston- have to do with the distance between an action and its possible future consequences?
Cause and effect is not an absolute and unalterable sequence. Between the work of Bortaug and others and the possible Malthusian disaster so many other people will have acted with consequences which inspired more actions with consequences which…that there is no traceable route by which to ascribe blame to Bortaug.
We can easily assess the immediate consequences of anyone’s actions, including our own. What we can’t do is predict the long-term future. This isn’t just a matter of our ability. Too many possiblilities- including other actions and their consequences- intervene.
There’s the Awful Warning of Admiral Collingwood as an example of long-term planning and its consequences. When Britain had the largest navy in the world it was completely dependent on imported wood to build ships for the navy. To ease this dependency in the future, Collingwood planted acorns to grow oak trees, which were used to make ships’ hulls. As a result of his foresight, the oak trees he planted were ready for felling to build ships in time for the Battle of Jutland in 1916.
alqpr – and wouldn’t you rather hear that last bit from a philosopher? Simply because she knows whereof she speaks?
What does who I am- or who you are- a different philosophical queston- have to do with the distance between an action and its possible future consequences?
You’re the one who raised it as if it means something. I suppose I could have phrased my question better: why do you think that matters? And what’s your rule by which you determine that something is too far apart in time (is that what you mean by distance?) to still matter? Since you’re willing to say that Borlaug’s actions are too far in the past for their consequences in the unforseen future to matter, how do you make that determination?
that there is no traceable route by which to ascribe blame to Bortaug.
But would you ascribe credit to him? Or are you taking the position that cause and effect are too complex and the notion of blame, responsibilty, and credit are meaningless?
We can easily assess the immediate consequences of anyone’s actions, including our own.
Yes, but can we do it accurately? Really? Or is it simply that we choose what’s convenient for us to believe in because we can’t make sense of all the complexity?
It’s very easy to take a particular set of events in time and portray them as a linear set of causes and effects but that denies the reality of how causation works: every effect has an incomprehensibly complex set of causes and every cause has an incomprehensibly complex set of effects. What about Borlaug’s 9th grade biology teacher who instilled in him a love of science (I just made that up for the sake of example) do they get partial credit for the good things Borlaug did 40 years ago and no blame for the potential downside consequences of his actions 40 years from now? Does the sandwich Borlaug ate on the day he discovered high yield wheat have anything to do with it? What about the sandwich-maker who provided the necessary carbs to inspire the great man’s great idea? What about the pig that became the ham in the sandwich?
When someone points at a simple interpretation of causality regarding a particular event, what they are doing is editing the totality of everything happened down into their own interpretation of what was or was not relevant. But, in fact, what was or was not relevant is vastly more complex than that – incomprehensibly so. As were the consequences.
What we can’t do is predict the long-term future.
I agree with this statement.
We can’t even predict the immediate future. Yet the idea of making a moral decision appears to depend on that.
the oak trees he planted were ready for felling to build ships in time for the Battle of Jutland in 1916.
I’m skeptical about that story. What was distinctive about Jutland was it was the first massive engagement between coal-fired dreadnoughts made of iron and steel. I guess they may have had wooden decks and some components but the age of wooden fighting sail ended for all intents and purposes after the battle of Hampton Roads.
@Kevinalexander –
There are two things that I find more valuable than anything else:
1) a person’s ability to recognize when they are mistaken
2) a person’s ability to show me how I am mistaken
You make a great case that #1 can be easily found on in the internet, despite persistent rumors to the contrary.
I am all-too-acquainted (for worse *and* better) with plenty examples of #2.
All my life I have preferred the company of people who are smarter than me. That’s why I come here. I usually just shut up and listen but now and then I do open my mouth.
If only to put my foot in it.
@alqpr:
There’s a great deal going on here, so I’m going to be careful to address as much of it as I can, or at least as much as I think will be productive.
With regard to my point about the necessity of expertise to detect subtle errors, you said, “I’m sorry, but I still find that condescending. With regard to the detection of subtle errors, I think there is a certain arrogance in the assumption that others are not equally qualified.”
I’m not really sure how to reply to this. I’m sorry you feel condescended to, but that feeling is immaterial to whether or not expertise IS in fact required to spot subtle errors. Certainly you would agree that mathematical expertise is required to spot subtle mathematical errors (which are, by hypothesis, hard to detect, on account of being “subtle”). Even though you can do math, you nonetheless recognize a significant difference in ability between expert mathematicians and yourself. Conversely, though you do not say so directly, you seem to think that there is no comparable expertise available to trained philosophers. In short, you seem to think that argumentation and the critique of arguments is not something that one can gain substantial expertise at – at least, your comments indicate this as a background, if perhaps unconscious, assumption. It is, in any case, incorrect. Laypeople are not equally well-equipped to detect subtle errors in extended and/or highly technical arguments, as has been demonstrated to me time and again – your own discomfort at the suggestion notwithstanding.
You go on to assert that you should not have to check terms to be sure you understand an article in “New Yorker” or “Scientific American.” I have no idea about the extensiveness of your vocabularly or the editorial aims of those publications, so I can’t say anything in particular about this, except that the sophistication of an argument is not always directly related to the obscurity of the terms it uses. Some philosophical arguments are quite involved yet explained in very simple language, while others might be quite simple in terms of complexity while expressed in challenging language. Oh, and you’re unlikely in the extreme to find anything philosophically “cutting-edge” in any popular publication, book or magazine. So I don’t know what the point of this particular comment was meant to be.
The next bit is quite revealing to me, and the conclusion I draw is only supported by what follows after it. You mention that neither Searle’s Chinese Room puzzle nor the matter of Gettier Problems have “impressed” you. I’m not sure what you mean by the fact that you were not impressed, nor have I any idea what “more professional” sources you looked to for explication of these topics, but I can assure you, both were (and to some extent, still are) philosophically “meaty” issues that have generated productive discussion. The fact that neither “impressed” you is more indicative of a lack of understanding on your part than any lack of merit to the problems themselves. I know many of the people involved in work on those issues, and they are for the most part highly intelligent, very incisive individuals. With no disrespect intended, if these people think the problem is significant and you do not, I’m siding with them.
Your assessment of my list of more-or-less settled issues confirms my initial impression that you lack a sufficient grasp of philosophy to really understand what you’re talking about here. As to #1, arguments for materialism about the mind predated any significant success in the scientific program and, indeed, served to convince a number of very smart people that the scientfic program was worthwhile. Likewise, for #2, while I cannot speak to the pagans as such, for centuries it was precisely the position of most prominent philosophers that religious belief was the only rationally defensible position. The irrelevant non-sequiturs offered for #3 and #4, as well as the flippant closing comment which reveals your misunderstanding of the relative roles of logic and mathematics (logic is a branch of philosophy and prior to math, as has been discussed upthread), also show that you’re in a bit over your head. Likewise, your impression that philosophers are “more appropriately the recorders and reviewers” popular thought than (generally) intellectual pioneers reveals a profound lack of familiarity with the history of ideas.
As for Churchland, while you might find her quote inspiring, I must conclude that you’re in no position to evaluate the accuracy of her assessment. I’m glad you like it, but that’s immaterial.
Incidentally, the Churchlands have offered a number of important arguments, of which “Neurophilosophy” is a part, but their program has been largely refuted. Patricia Churchland is entitled to her views about moral philosophy, but many of her arguments have been shown to be flawed. Take that for what you will.
Marcus Ranum
The question you actually asked: ‘Who are you to say what is the appropriate distance in time for something to lose moral significance?’ was completely different. What I actually said is that distance in time puts so many intervening decisions and consequences between two events that we can’t say one caused the other, so- obviously-the amount of responsibility diminshes over time too. For example, Bortaug- like you, I use him as a representative example- has a lot of moral credit for the people who lived immediately after him and didn’t starve to death, but much less for people living now- someone else would have made similar discoveries in the years between anyway- and still less for people in the future: the decisions many people made in the time since Bortaug and now have had more effect on how things are now.
Well,no. For example, the fact that many fewer people starved to death immediately after the green revolution can be ascribrd to Bortaug. The fact that we may face many more deaths from starvation in the immediate future is far more the result of the decisions we- the human species- made since then. As you say, ‘every cause has an incomprehensibly complex set of effects’. Too many decisions and their consequences have interevened.
We can predict the immediate future pretty accurately in fact. More important, whatever we decide there will be a future anyway, so we don’t have much choice about making desisions..
Actually, I cited that story to show the futility of trying to see the distant future and believing present actions have foreseeable consequences. Collingwood assumed that the future would be similar to his own time and planned accordingly and mistakenly.
Crip Dyke:
Just to bring this up again, something occurred to me just now, which probably was all to obvious for you guys to even bring up….
Under Deontological ethics, within which I think the church’s natural law is comprehened, not allowing Savitha to abort the fetus that was dead anyway was correct, because thems the rules, and the rules are what’s moral. Under virtue Ethics, if the bishops, doctors, etc were acting in accord with good internal virtues their acts were moral in letting her die. Only under consequentialism, which we’re all steeped with since Machiavelli can we look at the result of the act and say “that’s fucking evil!”. Say what you will against consequentialism, and this only because it’s probably today’s common sense that I feel this, but not taking the consequences into account at best if robotic and as Hume said, ‘reason is and always will be the slave of the passions’, and so being robotic is just being inhuman, but really, it’s just fucking evil when taken to it’s logical conclusion. It’s why we look at the catholic church in horror as it says condoms are against nature – and add a bit of mendacity by saying they cause the spread of aids, when the consequence of their correct us is exactly the opposite – as if something being natural overrides the consequences of blindly doing it, or not.
But as has been said, consequentialism, isn’t everything in ethics.
@Landon: The main purpose of my comment was identified in the fifth and penultimate paragraphs. I take it that either you don’t share the concern that some Philosophers have expressed regarding lack of due respect for their discipline, or that you don’t agree with my suggestions on the matter. That’s fine with me.
@Ophelia(re#27) Indeed! I would like to be able to say that I always trust the expertise of Philosophers as to the merits of those other Philosophers they disagree with 🙂 But actually the reverse is true. One of my frustrations with reading about Philosophy was the extent to which each trend appeared to be built on an almost wilfuly over-literal misinterpretation of its predecessor. Unproductive pedantry “untethered” from reality. Always concerned with winning points as to how the other guys got it wrong when there’s no precisely wordable “it” to get.
Actually, I cited that story to show the futility of trying to see the distant future and believing present actions have foreseeable consequences.
Oh! I see! I totally missed your point ( /facepalm ) sorry about that.
Otherwise, I think your argument that the direct obvious consequences of an action erode over time is a good one. Assuming I buy that, then all that remains is the question of conditions before the action. Would you say the same thing? (since at the macro-scale the universe appears to be deterministic, I withhold judgement about whether we can really talk usefully about decisions and responsibility – that seems to presuppose free will, which is apparently absent other than as an illusion we cherish) Indeed as you say, we can predict the immediate future fairly well – because our choices and other people’s choices are more circumscribed and predictable than we’d probably like to think they are.
I’m still uncomfortable with the idea that we can adequately understand cause/effect enough to assign blame or credit, but I do like your argument that it becomes murkier over time. That lets Hitler’s grandmother off the hook, too.
@alqpr (re: #34 and #35):
In fact, I am concerned about the lack of respect for philosophy, but it’s not so much that I disagree with your suggestions as that I find them to lack cogency. As I indicated in my reply at #31, you seem to lack an understanding of the philosophical enterprise. This phrase in particular, taken from your reply to Ophelia:
“One of my frustrations with reading about Philosophy was the extent to which each trend appeared to be built on an almost wilfuly over-literal misinterpretation of its predecessor. Unproductive pedantry “untethered” from reality. Always concerned with winning points as to how the other guys got it wrong when there’s no precisely wordable “it” to get.”
is – in a word – baffling. I cannot parse what you mean by, specifically: “trend” (style of argument? interest in particular topics? something else?), “wilfuly (sic) over-literal misinterpretation of its predecessor” (an indictment against the principle of charity, or perhaps of the lack of its use? are arguments meant to be interpreted non-literally?), the scare-quotes are “untethered” (are the arguments in fact tethered, but only appear not to be? what is it to be “tethered” to reality or not in this sense?), and “…when there’s no precisely wordable “it” to get.” (what would it be to have a precisely-wordable “it” to “get”? how does philosophy fail to do this? what is “it”? why is “getting it” desirable?).
Not to be rude, but you don’t seem to have any clearly stated criticisms of philosophy, just vague unease and dissatisfaction. A worthwhile critique ought to be specific – one must state what is wrong in clearly specified terms. You are concerned that philosophy is “untethered,” whatever that means exactly, which you seem to think because Patricia Churchland said so. Noting that Churchland is only one voice and is occasionally prone to flights rhetoric, this is far from enough to convince us that your criticism has any substance to it. What – in your own terms – does Churchland mean, in the criticism you quote? What specific examples of such “untethered”-ness can you give, explaining how each meets the criteria for being so-called?
It is not that I disagree with your critique – that is too generous an assessment. You have offered no critique worthy of the name. You have, at best, informed us that you don’t like philosophy very much, while trying to recruit a single sentence from a professional philosopher to show that philosophy is not a worthwhile enterprise. This does not move me. You have given us little reason to believe you have even read much philosophy, aside from (at least one sentence of) Churchland’s book, and have given us every reason to believe that what philosophy you have read, you did not understand. You’ve typed a great many words to make no discernible points whatsoever in an attempt to criticize a field the aims, method, and substance of you show no mastery of or even substantial familiarity with. In short, your disappointments with philosophy are not evidence of any shortcomings in the discipline itself, and I am unmoved by your opinion.
*scare-quotes around
@Landon (#10): I really don’t want to hijack Ophelia’s blog in what could be seen as a senseless turf battle between philosophy and mathematics, but I can’t leave it alone either.
Sure, but then so is philosophy, for sure? Without at least a rudimentary form of logical thought, philosophy and mathematics would both be impossible. Logic does indeed lie at the foundation of both our disciplines, but I do take exception to your declaration of logic as belonging to the philosophers, as if mathematicians had nothing to offer.
Gödel, Russell, Whitehead and Frege were indeed all philosophers, but they were also mathematicians. Much of their work may be hard to classify as either philosophy or mathematics – the boundaries are sure rather fuzzy down there in the foundations of mathematics – but to take one example, I think there can be no doubt that Gödel’s incompleteness theorem is a work of mathematics, not of philosophy. However, some of its consequences are indeed in the philosophers’ domain, as it does say something about the inherent limitations of mathematical thought, and therefore of thought more generally. But if that theorem is not a theorem of mathematics, then it seems that the word “mathematics” has lost its meaning.
But actually, in my first response I was thinking more of Church and his lambda calculus than the other people you mentioned. Another philosopher/mathematician, for sure.
I admit I find that rather condescending, smiley notwithstanding.
@Harald (#39):
It’s not really a turf battle, as logic IS a branch of philosophy. This is not in dispute by either mathematicians or philosophers. Mathematicians STUDY logic and USE logic and have contributed to its development, to be sure, but when they do so, they are doing philosophy, the same as when a biologist USES mathematics it does not suddenly become biology. The math may be in the service of a project that could be more properly classified in the realm of biology, but that does not make the math into something it is not. It remains math, recruited in the service of another science, just as logic remains philosophy, recruited in the service of math.
You are right to point out that philosophy requires at least some informal logic, but this only muddies the issue, as we were clearly talking about formal logic. The development and expansion of systems of formal logic is a branch of philosophy. Now, we must given mathematicians and mathematics its due – it was with an eye toward articulating a foundation for mathematics that formal logic saw its most impressive advances, not very long ago, as these things are considered. But that in itself is a clue – when any practitioners of [x] are attempting to unearth/articulate a FOUNDATION for [x], they are (by definition) not doing [x] so much as they are doing philosophy of [x]. And logic, it should surprise no one, is a significant part of the philosophy of mathematics.
As for mathematics losing its meaning, this is not a worry once the distinction is properly understood. Mathematics is the study of a special kind of abstract entity known as “numbers.” Because numbers are abstract, its methods (though not assumptions – this is crucial) are entirely constrained by formal logic. However, as Goedel proved, some axioms must be assumed. Evidence for which axioms are correct (or most correct) is gathered, quite simply, through experiment, as befits a science: in the case of mathematics, the “experiments” are attempts to accurately describe certain phenomena. Those methods founded on inadequately formulated axioms will inevitably fail to accurately describe.
(Full disclosure – my views on this are more in line with Goedel’s, but are not universally held by all philosophers of mathematics. Some, for instance, would assert that mathematics is the study of formal systems, not a special class of abstract entities. Regardless, all would agree that its methods are entirely contained by formal logic and that some of its axioms must be assumed. This alone is enough to distinguish logic from math and to show the priority of the former over the latter.)
Because the methods of mathematics are entirely constrained by formal logic (though, again, the substance of mathematics is not so constrained), it is not surprising that many mathematicians would engage in research in logic, especially those working at the highest levels. Much of this work will have implications for mathematics, again quite unsurprisingly. That does not make it math, any more than a discovery in biology which has implications for medicine is a discovery in medicine as such, or a discovery in linguistics which has implications for theology is a discovery in theology as such.
Goedel’s incompleteness theorems are works of logic, not math, because they deal with no mathematics specifically. They are not about any particular mathematical system. They rely on no assumptions native to any particular mathematical paradigm. They are ABOUT math and have CONSEQUENCES for math, but they are not math as such. They are works of pure logic, and two of the best proofs one can have of this are that (a) you need have no background in math whatsoever to understand them (which would not be true, ex hypothesi, of any proof in math, especially a complicated one) and (b) their results are directly applicable, without interpretation, to any and all non-mathematical formal systems (which would not be true, ex hypothesi, of any result in math).
As for my last statement, it was not meant to condescend, but then I suppose you did not mean for me to become irritated at the repeated insistence of those who are neither mathematicians or philosophers to insist they know the proper boundaries of each discipline – yet I am irritated nonetheless. Let us each grant each other some charity, then, and assume that neither one of us out to annoy or offend the other. Because regardless of how it is phrased and regardless of whether you take my own word for it or not, logic remains a branch of philosophy.
Reminds me of Saul Kripke’s brilliant little quip, “ There is no mathematical substitute for good philosophy”
In any event Harald, I think the boundaries between various academic disciplines is superficial and just a mechanism to help sort departments and literature. I think Landon is just trying to point out that and isn’t trying to be condescending. A lot of pure mathematics goes beyond the purview of the logician, topology and what have you.
…no. no. it doesn’t work like that. people don’t just read Locke or Mill or Rousseau and then magically wake up and realize “hey, I must be suffering”. people suffer. when they suffer, they look for why. and yes, some of them turn to amazing philosophers like the aforementioned, or Hume, or Russell, or others.
on the other hand, some turn to feminist writers such as bell hooks. some turn to Marx, some to Malcolm X.
and some turn to Rand. some turn to the ravings of Ron and Rand Paul. some turn to Glenn Beck and Rush Limbaugh and Alex Jones.
and in those writings and speeches they find words that appear to explain the root cause of their suffering (regardless of whether they actually do). they find “philosophy” that they agree with and push as the solution to problems (regardless of whether the solutions actually work).
but the words are not why they’re searching and fighting. they search and fight not because of the words of some long-dead philosopher, but because they are suffering in the real world due to the effects of what they fight against. and it was the very institutions they fought against that granted most of these dusty old philosophers the privilege to have their words made immortal, with a yawning silence (to us) coming from those who weren’t as privileged as the Lockes and Humes and Rousseaus of the world.
it is that privileged detachment that has caused our problems. it is that detachment we seek to avoid. we should not be venerating the words of those who overcame their privilege blindness over the struggle of those who suffered because of said blindness; especially considering that there’s no reason why the strugglers could not have come to these conclusions on their own — they just weren’t privileged enough to be heard above the rich white faces.
In one sense everything is a branch of philosophy. But if Logic is to be considered as a subordinate to anything else rather than a subject in its own right, then I’d put it as subordinate to psychology, as it is really just about using the limits to what a sane human mind can conceive of in order to produce arguments that a sane human mind cannot resist. But Boolean Algebra is certainly a branch of Mathematics, even though it also provides a mathematical model of the logic on which mathematics is based.
As for Godel’s famous theorems, they certainly do refer to specific mathematical systems- in particular only to systems in terms of which it is possible to construct a model for the natural numbers. (It is NOT true that all of mathematics is about things called “numbers”!). And although the assertion of consistency for arithmetic does translate (via Godel’s clever trick) to a numerical proposition which is not provable without recourse to the assumption of consistency, the fact that the axioms are not “complete” does not mean that Godel proved “some axioms must be assumed” (Of course if we really don’t assume anything then we get no conclusions but that’s not due to Godel.) Indeed Godel’s proof extends to showing that even if we did assume an arbitrary number of additional axioms, that would still not be sufficient for completeness of the resulting extended system, so Godel provides us with no incentive to assume axioms that we haven’t chosen already.
And I should also add that only a vanishingly small fraction of mathematicians would ever talk of axioms being “correct”. The value of an axiomatic system is in some combination of whether it amuses by yielding surprising results and/or is useful for modelling or abstracting something else, but a boring and useless system would not be called “incorrect”.
@alpqr (#42):
All I can say on this is that it is evident you do not actually understand Goedel’s proofs. I’m not a specialist in logic and would not claim such expertise, but in graduate school my understanding of Goedel was rigorously examined by people who were, and they were satisfied my comprehension was adequate. Your idiosyncratic take on both Goedel and logic generally convince me that there’s nothing to gain in paying heed to your take on either.
@Setar (#41):
Of course I would never suggest that people don’t recognize their suffering without philosophy – you are quite right to call that laughable. But as I said in a different thread, philosophy serves as both backdrop and instrument for turning translating suffering into social action. When we unpack the word “fight” that you keep invoking, most commonly, we find a great deal of philosophy.
The great activists use philosophical arguments to persuade, justify their calls to arms with appeals to moral precepts. History is littered with stark examples of the difference between campaigners for social change who can frame their program within a coherent intellectual framework – the sort of thing that can reach those who do NOT suffer similarly – and those who simply act out their inchoate rage. As I have stated elsewhere, a great deal of the success of the feminist program has come about in just this way: through inroads that feminist philosophy has made in the academy, allowing the eminent truth of feminism to be put in front of young men and women thirsty for knowledge.
The sad fact is, if letting those who are in power know you are suffering were enough to bring about change, the world would be a better place, because the great failing of so many of the privileged is not that they do not KNOW about the suffering of the less fortunate, but that they are able to rationalize not taking action to ameliorate the suffering. No program of social change can succeed – short of simply seizing the mechanisms of power – without convincing those who control the institutions of power that NOT acting is irrational. That’s the use of philosophy in effecting social change.
One of the problems with relying on experts is that “it takes one to know one”, and it is only too easy to be bamboozled by a pretentious windbag who, to quote Elizabeth Anscombe “sounds rather edifying…”(but I am sure you can Google the rest of that quote!)
Fortunately, Landon has now exposed himself. Anyone who has taken an undergrad course on “Introduction to Analysis” or “Proof in Mathematics” will be able to asses his most recent responses to me, and anyone who can read will soon be able to do so after reading the Wikipedia page on Godel’s theorems (which is really not too bad) or the lovely little book by Nagel and Newman whose expertise, while well documented, stands on its own two feet as once you have read the book you will understand the main ideas of the proof as well as a good part of what it implies.
Patrick:
I don’t quite agree that the boundaries between academic disciplines are superficial. But they are somewhat arbitrary and fuzzy, and they shift with time. The case under discussion here is a good example: It used to be that logic was a branch of philosophy, nothing else. But I contend that the moment formalized logic appeared on the scene, with stricty defined syntax, axioms, and rules of inference, it became mathematized. I am not saying it became one hundred percent mathematics and ceased to be philosophy at that moment, but it did become more like mathematics, and at least in part it became mathematics, thus both blurring and moving the boundaries between the disciplines. But in spite of the blurring, the distinct flavours of philosophy and mathematics are still present.
Landon:
We can certainly agree that there is much philosophy to be found at the foundations of mathematics. I know many mathematicians who will insist that philosophy has nothing to offer to mathematics. I don’t agree with them. But rather than your view that mathematics builds on philosophy, I would say it has become intertwined with philosophy at the foundational level. In fact, I will go so far as to say that the philosopher who is investigating a certain formal logic is doing mathematics, even if doing it for philosophical ends.
Your views of mathematics as being the study of numbers seems utterly bizarre to me. People might have viewed it that way in the past, but you’d be hard pressed to find a modern mathematician believing that, as it would exclude abstract algebra, graph theory, and topology from the field.
Your claim that Gödel’s incompleteness theorems deal with no mathematics specifically is factually wrong. In fact, his proofs concentrated on Russell and Whitehead’s Principia Mathematica – or more precisely, on a combination of that system with the Peano axioms. However, that was only done in order to keep the proof manageable, and Gödel did indeed remark that the proof could be easily adapted to many similar systems.
I would also point out that mathematics thrives on abstraction and generality, and to state that something is not mathematics because it is general and not specific is to get things exactly backwards.
Furthermore, your point (a) that you need have no background in mathematics to understand the proofs is true, but that does not make them not mathematics. It just means that the proofs are elementary. I hasten to add that this does not mean they are easy, only that they do not require a lot of deep theory. There are some incredibly difficult but elementary proofs in mathematics. I notice that you are making a very similar point regarding philosphy in a response to alqpr, so I am sure you can see this point. I can understand quite a bit of logic without an extensive knowledge of philosophy. That does not make logic not-philosophy!
Your point (b) does not make any sense to me, so I will refrain from commenting on it, other than to point out that not all formal systems are subject to Gödel’s incompleteness theorems. An admittedly simple example is predicate calculus, for which a complete axiomatization exists. But then predicate caclulus is not sufficiently powerful to model arithmetic, and therein lies the rub. That is an essential property of the systems to which you can apply Gödel’s theorems, as is quite clear from the proof: One encodes the whole system using numbers, so that “X is provable” can be written as a statement in arithmetic; then one expresses such statements as formulas in the language; and finally, one constructs a formula R which can be interpreted via the preceding encoding as saying “R is not provable”, and the result follows. If you cannot represent arithmetic in the system, the proof fails. And so, it seems to me that you were a bit rash in dismissing alqpr’s comment (currently at #43).
Quick followup: I did not see alqpr’s post (just in front of mine) until after I had posted mine. Just saying.
@Harald:
You raise some good points and, indeed, I was perhaps hasty (on account of testiness) in some of my answers. Let me see if I can address some of your points.
Math is, among the sciences, a strange case – non-empirical in some sense yet legitimately a science, you might say. Perhaps it is difficult – more difficult than I have thus far been willing to acknowledge – to pull them apart at the higher levels. Perhaps. I still maintain that because the methods of mathematics are completely enclosed by logic it is more appropriate to consider mathematics a particular kind of applied logic. Likewise, logic strikes me as more basic than mathematics – formulating a correct logic is fundamentally about how to arrive at correct conclusions. This seems clearly an element of philosophy to me, and I’ve yet been offered no specific rebuttals to these points. However, it is probably the case that nothing much of importance turns on this and my persnicketiness on this account has been somewhat self-defeating. I’ll concede at least, then, that at a certain level of mathematics, it doesn’t matter what you call it – philosophy or math – it looks very much the same.
Re: my view on mathematics – I did say my views were essentially Goedel’s. I am not a specialist in philosophy of math (though I claim competence in philosophy of science more generally), so I’ll refer you to their debates about what the nature of mathematics really is. They prosecute the arguments more eloquently and knowledgeably than I can. I don’t take it that such fields as abstract algebra are a problem for Goedel’s “Platonist” view, as an understanding of these fields is cognate to or perhaps parasitic upon the study of numbers (I believe that’s how the argument goes, anyway – it’s been awhile since I’ve plumbed these particular areas). However, as I said, I have no interest in trying to defend Goedel’s views on this and don’t think they affect my overall case anyway.
You are quite right to point out that the phrasing of my claim that the proofs “deal with no mathematics specifically” could not have been more infelicitous. I meant to convey by that poorly-chosen phrase that the substance of Goedel’s argument was not particularly about Peano arithmetic but rather only used it as an example on which to demonstrate the results. This was the force of the “without interpretation” remark – if the results generalize directly to non-mathematical formal systems, it’s hard for me to accept that the proofs are indeed works of math rather than logic, as math, by definition, does no include non-mathematical formal systems, while logic does.
You mention that I claim one needs to have “no background in math” to understand Goedel’s proofs, but I think perhaps you read that less strongly than I intended. I meant it to communicate that you can be utterly ignorant of even the most elementary arithmetic and still understand the proofs so long as you know enough logic, which, to my mind, obviously indicates that they are logic and not math. However, to the extent that we established earlier that we may be in an area of crucial disagreement about what constitutes logic and what constitutes math, there may be no way for us to settle this point. I do, however, see your point about elementary but difficult proofs, and it is well-taken.
You are also correct in noting that in my haste I slightly overstated the applicability of Goedel’s results. I maintain that the results are not “about” math in particular, but I concede the specific point you raise here. By the time I reached alpqr’s comment at #42, I had given up on reading him carefully, which was in error and for which I apologize, as it led me to do him an injustice in this case. I stand by my responses to many, if not most, of the things I said in response to his other comments.
I don’t think we’re going to settle between us whether logic is math or philosophy simply because it seems that we differ somewhat in where we draw the (admittedly, unavoidably fuzzy) boundaries on these systems – and it seems further that logic is in some way the locus point of these disagreements. That is, sorting out whether logic is math or philosophy would require us to come to agreement on issues that we appear to differ over for, at least in part, the very reason that we already consider logic to be either math or philosophy (respectively!). Many of the points you raise are good ones; I flatter myself to think you believe likewise about mine. But I think we need to lay the issue aside, as further discussion of it is unlikely to be productive.
@Harald (or anyone else who might actually know): I am curious. Is there a version of Godel’s proof that does not explicitly depend on the arithmetic of factorization to implement the mapping from meta-theory into statements within the theory itself, and so which applies to theories which do not include arithmetic as an essential feature and not just as a convenience or example? If so, then maybe I owe Landon a partial apology, but given the tone he has taken with me so far, I’m in no rush to provide it. O heck, what the hell! I will at least trade an apology for my #45 in exchange for his rather grudging one for #44 – and then, who knows, we may actually work our way further back up the ladder!
Just to clarify something – and perhaps to make Landon less angry, I should emphasize that my initial point was not intended to dismiss the value of Philosophy per se but to decry the emphasis on experts. I have the same attitude to any subject that involves thinking more than memorization, and mathematics is no exception.
Here’s a story which may help illustrate that:
In order to point out the importance of restricting to systems which include the natural numbers when talking about Godel’s theorems it is of course necessary to identify a mathematical system which does not include them. Simple Boolean Algebra is one – whose consistency is in fact provable. But given Landon’s position, that might not be an effective example. Other algebraic structures naturally come to mind – except for the awkwardness that they are often (though probably not essentially so) set up in terms of a “set” of objects and so it might look at least superficially as if the axioms therefore presuppose those of ZF set theory – which does include a model of the natural numbers (and on to just about everything else). Then I thought “aha the existence of Finite Geometries must show that the Euclidean axioms don’t imply the ability to construct a full model of the Natural numbers”. But fortunately I checked before posting and noted that only the incidence axioms were listed – which is fine for my purposes but raises the question of whether the standard Euclidean geometry could have been used as an example. If I had thrown out my first thought there, it would not have taken an expert to see that I was wrong (or at least hadn’t thought carefully enough about which of the often not clearly itemized axioms I was referring to). Anyone with even the slightest familiarity with high school Euclidean Geometry could have said “But Euclidean geometry allows you to construct the mid-point between any two points, and if you then construct the mid-point between that and one of the first two, and so on then don’t you get an infinite sequence of distinct points which could be identified with the ordinal numbers?” and I would have had to stop and think about what goes into that mid-point construction which has been left out of the axioms in terms of which finite models do exist.
In mathematics, and actually I suspect in other disciplines as well, it is often newcomers who make the major advances – perhaps because those new to the field are less encumbered by either repeatedly reinforced preconceptions or masses of irrelevant detail. If I can be excused a bit of a play on words: they may be expert but they are not yet experts.
If you are unsure of something then by all means consult an expert, but if you are really clear about what you think, and why, then you are as likely to be right as any expert and the expert who denies you without really understanding what you are saying is the one to be censured (even if you do turn out to be wrong!)
PS@Landon, I don’t want the previous comment to be taken as weaseling out of having said some “rude” things about Philosophy but until #45 I don’t think I was rude to you personally. Actually, pending correction, I still stand by the comments I have not already withdrawn. But my (declared and real) intent was less to denigrate the discipline than to try and explain/understand what underlies the disrespect that many philosophers claim to experience (especially from some in the sciences). If you read what I said less clouded by anger you may see it differently, and if you express your responses with less personal dismissive rudeness you might even change my mind on some issues.
@Landon: Thank you for clarifying. I agree that this is a good place to end our mini debate, for all the reasons you mention. But since I have your attention: Can you recommend a decent introduction to modal logic? My grasp of that subject is tenuous indeed, and I really don’t know what to think of it.
@alqpr: I have seen proofs of the incompleteness theorems relying on strings of symbols and manipulation of strings, such as concatenation. This sits better with a modern audience, which – thanks to computers and programming – is not at all surprised that a lot of structure can be expressed that way. But of course, arithmetic can also be encoded as string manipulation – it is what we learned in elementary school after all – so this does not weaken the assumptions required to make the proof work. I could also mention a short article by George Boolos in the Notices of the American Mathematical Society in 1989, in which he gives a different proof of Gödel’s first incompleteness proof. He proves that there is no algorithm that will output all truths on arithmetic and no falsehoods on same. The incompleteness theorem follows from that.
@Harald, Thanks. I’m not surprised at the existence of a proof directly in terms of a system of strings (since the arithmetic version was based on encoding string relationships as statements about numbers); but, as you say, any mathematical theory capable of modelling arbitrarily long strings also contains a model of the natural numbers. It’s interesting to hear of the Boolos proof of the explicitly arithmetic case, but I suspect that its brevity is based on drawing heavily on other work about algorithmic computability that I am unfamiliar with and so I’ll probably give it a pass in this lifetime.
P.S. All I know about modal logic is that allegedly according to Godel, in the spirit of the way he expressed things in his 1951 Gibbs lecture: Either Modal Logic is Fatally Flawed OR God Exists!