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November 16, 2006

MacIntyre on Rational Judgment

Posted by David Corfield

Let us continue to develop the MacIntyrean theme of belonging to a tradition of enquiry. The central practice with which MacIntyre has been concerned is the life of a moral-political community. But for any community to operate rationally, it must do so in terms of a common good, internal to the practice of that community, which in turn must engage itself in a quest to better understand this good which constitutes its end. Something I have worked on over previous months has been whether we can see the mathematical community in similar terms. So where your typical Anglo-American political philosopher or ethicist and their philosopher of mathematics colleague will have very little to talk about, this is not the case with MacIntyre and myself, hence the number of posts, both here and at the old blog, which I have devoted to him.

Now, what is it to perform well in a community?

Since what discriminates one kind of character from another is how goods are rank ordered by the agent, and since each rank ordering of goods embodies some conception of what the good life for human beings is, we will be unable to justify our choices until and unless we can justify some conception of the human good. And to do this we will have to resort to theory as the justification of practice.

Rationality however does not necessarily, nor even generally, require that we move to this point. I may on many types of occasion judge rightly and rationally that it is here and now desirable and choiceworthy that I do so and so, without having to enquire whether this type of action is genuinely desirable and choiceworthy for someone such as myself. I may on many types of occasion judge rightly and rationally that this type of action is desirable and choiceworthy for someone such as myself, without having to enquire whether the type of character that it exemplifies is genuinely good character. And I may judge rightly and rationally on many types of occasion that this type of character is indeed better than that, without having to enquire about the nature of the human good. Yet insofar as my judgment and action are right and rational they will be such as would have been endorsed by someone who had followed out this chain of enquiry to the end (in two senses of “end”). It is always as if the rational agent’s judgment and action were the conclusion of a chain of reasoning whose first premise was “Since the good and the best is such and such…” But it is only in retrospect that our actions can be understood in this way. Deduction can never take the place of the exercise of phronesis. (Ethics and Politics, CUP 2006: 36-37)

On many posts back at the old blog I noted similarities between moral thinking and mathematical thinking. As I have indicated this is unsurprising from the Thomistic Aristotelianism of Alasdair MacIntyre. Elsewhere I sketched out some mathematical reasoning modelled on Aristotelian practical reasoning:

Since perfected understanding of its objects is the goal of mathematics, and since 3-manifolds are and plausibly will remain central objects of mathematics, with deep connections to other central objects, and since seeking sufficient theoretical resources to prove the Geometrization Conjecture will in all likelihood require us to achieve an improved understanding of 3-manifolds, and indeed yield us reasoning approximating to that of a perfected understanding, it is right for us to try to prove the Geometrization Conjecture. (p. 13)

This is highly schematic. For a fuller account we would want to hear what makes 3-manifolds so important, what it means for the Geometrization Conjecture to point us in the right direction, etc.

Now, if we continue the analogy, we can conclude that a mathematician may ‘judge rightly and rationally’ without having a full understanding of what he or she is doing. And doesn’t this accord well with our views of the great mathematicians? We may know more now, and be able to recast what our predecessors just began to glimpse, but still feel they were tuning in to the way things are.

I think this reflects on what I said in my Berlin talk. How does the historian tell us what, say, Poincaré was thinking in 1890 using the public language available at the time? Even if we had access to his private language, isn’t a part of the truth of what he was thinking only expressible in a language unavailable to him, i.e., in retrospect when understanding has improved? Hence, intellectual history must have something of the future perfect to it. At the same time one must beware the pitfall of incorrectly forcing older ways of thinking into a modern conceptual apparatus for fear of shielding off reasoning which could act to challenge our current conceptions.

Posted at November 16, 2006 10:17 AM UTC

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Re: MacIntyre on Rational Judgment

To discuss the social structure of the Mathematics community, and its evolution, and the evolution of its evolution as interpreted in philosophy, do we not need a n-Category theory of the Erdos graph, and its morphisms?

When Molière poked fun at the pretensions of grand Paris ladies, his main target was the fashion for Descartes’s astronomy: “I adore his vortexes,” Armande coos in “The Learned Ladies,” which was first produced in Paris in 1672. “And I his falling worlds,” Philamente sighs.

THINK AGAIN
by ANTHONY GOTTLIEB
What did Descartes really know?

– Jonathan Vos Post

Posted by: Jonathan Vos Post on November 16, 2006 5:54 PM | Permalink | Reply to this

Re: MacIntyre on Rational Judgment

To discuss the social structure of the Mathematics community, and its evolution, and the evolution of its evolution as interpreted in philosophy, do we not need a n-Catgeory theory of the Erdos graph, and its morphisms?

If we had n-categorical tools for handling the Erdos graph, I’m sure we could adapt them to the theory of scale-free networks. We would therefore be one step closer to the elusive goal of Buzzword Unification. The next step would be to incorporate supersymmetry, or at least supersymmetric quantum mechanics.

Posted by: Blake Stacey on November 16, 2006 6:14 PM | Permalink | Reply to this

Re: MacIntyre on Rational Judgment

David wrote:

How does the historian tell us what, say, Poincaré was thinking in 1890 using the public language available at the time? Even if we had access to his private language, isn’t a part of the truth of what he was thinking only expressible in a language unavailable to him, i.e., in retrospect when understanding has improved? Hence, intellectual history must have something of the future perfect to it.

Right! Since Poincaré was struggling to develop a new language, we misrepresent his thoughts if we phrase them in the language of his day. But our account of how he was thinking will also be distorted if we phrase it in modern language. Historians of science are very sensitive to the latter sort of anachronism - acting as if Poincaré lived, not in his present, but in ours. I see your point as this: it’s also anachronistic to treat Poincaré as if he lived solely in his present. In fact, he had one leg in his present and one leg in ours - since he helped create ours.

Now, if we continue the analogy, we can conclude that a mathematician may ‘judge rightly and rationally’ without having a full understanding of what he or she is doing.

This is true not just for the above reasons, but because (I believe) any attempt to judge rightly and rationally rests on unexamined layers of implicit assumptions. The chain of “why?” questions has no end, but we have to stop somewhere or risk paralysis.

Posted by: John Baez on November 17, 2006 4:24 PM | Permalink | Reply to this

Re: MacIntyre on Rational Judgment

it’s also anachronistic to treat Poincaré as if he lived solely in his present

That’s a great way of putting it. It raises the question of whether there’s a best balance to strike to minimise both kinds of anachronism while keeping both more or less equally small.

any attempt to judge rightly and rationally rests on unexamined layers of implicit assumptions.

We’re on the verge of running into our ‘perfected understanding’ disagreement, though it’s not completely clear to me where the disagreement lies, as I never suggest that we must, or even can, become aware of all the layers of implicit assumptions you mention. Let me worry you though by mentioning footnote 8 of my MacIntyre paper which says:

Aquinas in Disputed Questions on Truth, I, 2 draws a distinction between the adequacy of the divine intellect and of the human intellect. Also, against Aristotle he argues that we only know essences through their effects, i.e., through the quidditas of the existent particular, Disputed Questions on Spiritual Creatures II, replies to objections 3 and 7. Might this account for the Gelfand Principle, expounded at the conference by Gowers: give the simplest non-trivial example of any concept you are explaining?

I haven’t had a chance to chase up these references.

Posted by: David Corfield on November 17, 2006 5:12 PM | Permalink | Reply to this

Re: MacIntyre on Rational Judgment

It may not be a big deal, but I just don’t believe this thing you said about “perfected understanding”:

We and our descendents may never achieve this, or may achieve it but not know we have achieved it, but still a notion of rational enquiry presupposes its possibility.

I don’t think I’ve ever had a perfected understanding of anything - my understanding always seems to have room for growth. So, not suffering from excessive modesty, I’m willing to extrapolate and guess that nobody has ever had a perfected understanding of anything. It seems more likely that any understanding can always be improved.

Suppose so. Suppose it’s impossible to ever attain a perfected understanding. Why does this stop us from talking about rational enquiry? Rational enquiry could just about moving towards better and better understandings.

Posted by: John Baez on November 18, 2006 4:38 AM | Permalink | Reply to this

Re: MacIntyre on Rational Judgment

Nothing hangs on this for the way we go about research. This was my best attempt to respond to you. The nub of the matter is that when you say:

Rational enquiry could just be about moving towards better and better understandings.

I want to know better according to whom? According to you now? You could be wrong. But wrong according to whom? According to our successors? But they could be wrong? Mustn’t we hope that what we take to be better understanding really is better understanding? And what does this ‘really’ mean? Doesn’t it mean from the perspective of an understanding which cannot be bettered, at least on the point in question?

Posted by: David Corfield on November 18, 2006 11:16 AM | Permalink | Reply to this

Re: MacIntyre on Rational Judgment

John wrote:

Rational enquiry could just be about moving towards better and better understandings.

David wrote:

I want to know better according to whom?

Your answer amounts to “according to God”. But, I don’t see how this helps us.

According to you now? You could be wrong. But wrong according to whom? According to our successors? But they could be wrong? Mustn’t we hope that what we take to be better understanding really is better understanding?

Yes, we must hope we’re at least roughly on the right track - if not, our sense of what counts as “better” could be wrong.

I am willing to live with this, since I consider it to be an inescapable aspect of our situation. We could always be wrong; okay, fine - let’s get on with business.

But somehow that’s not good enough for you - you want to posit a perspective that could never be wrong.

And what does this ‘really’ mean? Doesn’t it mean from the perspective of an understanding which cannot be bettered, at least on the point in question?

This is close to saying “better is what the best thinks is better”. At worst, this is completely circular. At best, it leads us into theology - which is why, right around here, you wind up quoting Aquinas’ discussion of the adequacy of the human intellect versus the divine intellect.

But theology is, if anything, even trickier than what we were talking about before. We don’t know that this divine perspective exists. And even if it does, how does it help us actually do anything? Our access to this perspective is at best imperfect.

Posted by: John Baez on November 18, 2006 10:33 PM | Permalink | Reply to this

Re: MacIntyre on Rational Judgment

I haven’t yet taken the step to God. I’m just trying to see what lies behind the idea of ‘better understanding’ that we both seem to agree is a key notion in a philosophical treatment of an intellectual enquiry such as mathematics.

Just to remind ourselves, this is quite a break with much contemporary epistemology which wants to analyse what it means to say ‘X knows p’. My philosophical enquiries began with Lakatos who converted the question to ‘How does our knowledge grow?’ But this knowledge is still read purely in terms of propositions. Indeed, he criticised Polanyi for trying to introduce know-how into the philosophy of science. I think many of the problems with Lakatos stem from this attitude.

So over the past few years I discover a philosopher reviving Aristotelian ideas and making a great many points about enquiry in general that have resolved problems I have had in rectifying Lakatos’s position. Naturally, I’m tempted to see where these ideas lead me. Essential to this position is the notion of ‘improved understanding’. MacIntyre warns us, however, the adoption of this notion necessarily entails, along with a theory of the virtues of a tradition of enquiry, something along the lines of Aristotle’s teleological metaphysics, and that clear-sighted opponents of such a metaphysics, such as Nietzsche, in standing out against it are driven to relativism. As someone who wants to lean on the notion of ‘improved understanding’, I am duty bound to see whether MacIntyre is right or not when he claims that ‘better understanding presupposes perfected understanding’.

Now to return to your comment. Your first step takes ‘perfected understanding’ to require God (something I haven’t committed myself to, despite that reference to the footnote about Aquinas, as I haven’t looked at it yet). Let’s put off this further entailment for now and keep with ‘perfected understanding’.

Now, you seem to agree that when we say we have a better understanding of an area of mathematics, that there’s a rightness or wrongness to this belief which transcends our parochial view of the matter. I would like to know what this might mean.

You paraphrase this thought with “we must hope we’re at least roughly on the right track”. But how does this help? Again, I ask you what you mean by the ‘right track’. Towards what?

We both agree that we can’t know that we’re on the right track (taken either in the sense I am examining of towards perfected understanding, or taken in the sense you have yet to explain to us), an Aristotelian idea again, by the way, and one which goes against a large amount of modern epistemology which holds that knowledge of p implies knowledge of knowledge of p. But this is not what’s at stake between us, we agree that it’s “an inescapable aspect of our situation”.

So, now “let’s get on with business”. I never suggested it would make a difference to business. It’s just a question of consistency. Does our use of the notion ‘better/improved understanding’ presuppose that of ‘perfected understanding’?

As an aside, I would say that holding, as we do, that the goal of mathematics is improved understanding does imply that mathematical business should carry on differently. For one thing, expository efforts such as your own should be recognised, rewarded and emulated. As you’ll know from the end of my MacIntyre paper, Thurston also believes something along these lines.

Now, “better is what the best thinks is better”. Right, this is the implication we’re examining. But, you say, either it’s circular or it leads to theology. This is what MacIntyre thinks. Let’s go along with it. So what’s wrong with theology?

We don’t know that this divine perspective exists. And even if it does, how does it help us actually do anything? Our access to this perspective is at best imperfect.

It’s not its helpfulness that’s in question. It’s whether our choice is between theology or abandonment of a non-relativist notion of improved understanding. If A presupposes B, you can’t say I want A but I don’t want B because I can’t know about B, don’t like what else it entails, etc.

To have improved understanding without theology, you need to challenge the claim itself that the former presupposes the latter. So we’d need to know what the ‘right track’ means. There’s the Peircian long run to consider, but I doubt it works.

Posted by: David Corfield on November 19, 2006 4:24 PM | Permalink | Reply to this

Re: MacIntyre on Rational Judgment

David wrote:

I haven’t yet taken the step to God. I’m just trying to see what lies behind the idea of ‘better understanding’ that we both seem to agree is a key notion in a philosophical treatment of an intellectual enquiry such as mathematics.

I’m all in favor of seeing what lies behind the idea of ‘better understanding’. I just don’t like how you seem to want to tackle the problem using some concept of ‘perfected understanding’:

You can believe that what has been taken to be of central importance in mathematics has changed greatly over the centuries and will continue to do so, while still believing there is a something towards which mathematics is moving. For Aristotle, this something is a perfected understanding. We and our descendents may never achieve this, or may achieve it but not know we have achieved it, but still a notion of rational enquiry presupposes its possibility.

Maybe you weren’t really espousing Aristotle here, just paraphrasing him, or playing some sort of `devil’s advocate’ game where you try to defend him. I’m still hoping.

To me, defining the concept of ‘better’ in terms of the concept of ‘perfect’ is completely backwards. I define the concept of ‘perfect’ in terms of ‘better’. Something is perfect if there’s nothing better than it - or, if you prefer a stronger definition, it’s better than everything else. It’s clear from our chat about partial orderings that there are many situations where ‘better’ makes sense, yet nothing is ‘perfect’. I think understanding of math is a bit like this!

Mind you, I don’t really think understandings of math are modeled by a partial ordering except in a very rough-and-ready, approximate, whoops-I-guess-I-was-wrong sort of way. I don’t think there’s any clear-cut way to stare at two ‘understandings’ and always be sure which one is better. My point in bringing up partial orderings was not to make things seem more precise than they actually are. It’s just that:

  • I don’t want to foreclose the possibility of ever better understandings!
  • And, I don’t want to base my notion of ‘better understanding’ on the less robust, possibly mythical ideal case of a ‘perfect understanding’!

David wrote:

Now, you seem to agree that when we say we have a better understanding of an area of mathematics, that there’s a rightness or wrongness to this belief which transcends our parochial view of the matter. I would like to know what this might mean.

Me too. I don’t think this is an easy question.

You paraphrase this thought with “we must hope we’re at least roughly on the right track”. But how does this help? Again, I ask you what you mean by the ‘right track’. Towards what?

I don’t know. Since I’m not a philosopher, I don’t need to know the answers to all such questions. But, I somehow I doubt it’s “towards some point at infinity that we call `perfected understanding’.” That’s too global and idealized a concept to play much of a role in my actual practice of mathematics. In my life, there are things that confuse me, puzzles I can’t solve - and when I start doing things that seem to make the confusion lessen, or let me solve those puzzles, I feel I’m “on the right track”. In other words: I seem to be a bit better off than yesterday, with hopes of being even better off tomorrow and the next day.

And, I can look back at the history of math and see how confusions diminished, and people could do more and more things… so I feel I’m part of a tradition that’s “on the right track”.

By the way, nothing about this is supposed to imply there’s only one “right track”. There are obviously lots. They tend to merge as people’s trains of thought roll along, and that’s part of why they seem “right”. But, I’m not claiming they all merge at one Grand Central Station called PERFECTED UNDERSTANDING.

Does our use of the notion ‘better/improved understanding’ presuppose that of ‘perfected understanding’?

To repeat, I claim it doesn’t. The concept ‘perfect’ is not a prerequisite for understanding what ‘better’ means. On the contrary, ‘better’ is a logical prerequisite for understanding ‘perfect’: “that which cannot be bettered”, or perhaps “that which is better than everything else”.

Now, “better is what the best thinks is better”. Right, this is the implication we’re examining. But, you say, either it’s circular or it leads to theology. This is what MacIntyre thinks. Let’s go along with it. So what’s wrong with theology?

Wow, so you actually want to talk about theology here! The main thing wrong about theology is that it’s a quaqmire. In mathematics, you can very often get almost everyone to agree about something. In philosophy, you can sometimes get a lot of people to agree about something (usually that some position is wrong). In theology, you can hardly ever get anyone to agree about anything.

So, if understanding the concept of ‘better understanding’ in mathematics required that I understand theology, I’d pretty much just give up. Theology is fun for its own sake, but using it as a tool to clarify something else is like using mud to clean your windshield.

John wrote:

We don’t know that this divine perspective exists. And even if it does, how does it help us actually do anything? Our access to this perspective is at best imperfect.

It’s not its helpfulness that’s in question.

It is for me. I avoid concepts when you can’t actually tell when they apply in a given case. I find them unhelpful. So, I’d like a concept of “better understanding” that would actually help me guess when I’m understanding something better. If the concept amounts to “just ask God”, I’m skeptical as to whether it will help.

Whew. I find this stuff rather enervating. I’m not getting that satisifying “crunch” that happens when we figure something out.

Posted by: John Baez on November 20, 2006 7:39 PM | Permalink | Reply to this

Re: MacIntyre on Rational Judgment

Whew. I find this stuff rather enervating. I’m not getting that satisifying “crunch” that happens when we figure something out.

Perhaps we should take a break. For one thing I have a conference coming up in Vancouver in a fortnight I’ll post about soon. I have to get my talk into shape. And I know you have a 101 things to do. Of course, this could be a sneaky plan to drive you back to the sure and steady progess of klein 2-geometry.

But you’ve been very helpful. So thanks. I’m sure the shift to ‘understanding’ from ‘knowledge that’ is a good one, and leads to the consideration of points we both appreciate, such as the one about the writing of history which occurred early in the thread. I’ll let its further implications about the nature of the mind doing the understanding tick over in the back of my mind.

Posted by: David Corfield on November 20, 2006 8:19 PM | Permalink | Reply to this

Re: MacIntyre on Rational Judgment

David Corfield:

Of course, this could be a sneaky plan to drive you back to the sure and steady progess of Klein 2-geometry.

You’ve certainly got me yearning to talk about that - a topic I actually know something about. But to really get your plan to work, don’t keep posting articles about the philosophy of mathematics that are basically brilliant, but with annoying little technical flaws - do it for Klein 2-geometry!

Posted by: John Baez on November 21, 2006 12:02 AM | Permalink | Reply to this

Re: MacIntyre on Rational Judgment

Before I begin this comment, on word on the poset of understandings: I agree that we should not think of this as merely a poset but as a much richer structure. (Certainly we are not simply talking about sets of true propositions, ordered by inclusion.) But if it is at least a poset (that is, if we know what it means to say that one understanding is better than another), then we can at least get some good out of that, even though we might get more good out of a richer structure. So for the moment, I’ll speak of it as a poset; I’ll return to the ‘if’ later.

John wrote:

By the way, nothing about this is supposed to imply there’s only one “right track”. There are obviously lots. They tend to merge as people’s trains of thought roll along, and that’s part of why they seem “right”. But, I’m not claiming they all merge at one Grand Central Station called PERFECTED UNDERSTANDING.

You seem to be suggesting (although not claiming) that the poset of understandings is directed: any two elements have a common upper bound (not necessarily a least upper bound, that’s another matter). People usually throw in —and I would insist upon it— that a directed poset must be occupied; that’s obviously true in this case. It then follows (by induction) that any finite set of understandings has a common upper bound. We might consider whether an infinite sequence of understandings has a common upper bound, or even larger cardinalities, but perhaps this is pushing the applicability of this mathematical model. On the other hand, if we go so far as to claim that every set of understandings has a common upper bound —including the set of all understandings— then the existence of perfected understanding (PU) will follow. (The converse also holds, of course.) Thus, while you might claim (and I might agree with this) that the set of understandings is directed, or even ω-directed (although I would doubt this myself), you must not believe that it has all upper bounds (and I agree with you).

Now, I don’t think that this is David’s argument for PU. Rather, if I understand him, then his argument is much more subtle, and hinges on the ‘if’ that I mentioned above: Do we know what it means to say that one understanding is better than another? To talk about whether one understanding is better than another seems to commit us to such a poset (although as I said before, it doubtless has richer structure as well). But David’s point (again, if I understand him correctly) is that comparing two understandings also requires understanding. What is the perspective of the person that draws the poset? That perspective (external to the poset) is PU; only in the next step of the argument does one point out that PU is also an element of the poset (internal to the poset).

Now, as I mentioned, I agree with you [John]; I am (at best) agnostic about the existence of PU. So in the end, I don’t believe that understandings form (even at least) a poset; that is, I don’t believe that, given any two understandings, I know what it means to say that one is better than the other. Rather, I believe only in small portions of (what would be) the poset of understandings, and these are themselves tentative knowledge. Normally, I’ll happily talk about whether one understanding is better than another —whether in the context of a single debate or over the course of millennia of history—, but it’s all done from the perspective of now, not generations into the future. Naturally, I care about what future generations will think of these matters, but I have no access to that knowledge; I can only go by my current understanding.

We can analyse this further. There are meta-understandings (MUs); a MU consists of (at least) a partial order on some set of understandings (not necessarily on the set of all understandings, and I’ll happily remain agnostic about the existence even of that). Now, a MU relies on an understanding, so each MU is in fact a pointed poset of understandings, arguably in fact a poset of understadings with a maximum. (In this, I think that I’m agreeing with David to some extent; a MU must rely on an understanding which is in some sense perfect, but perfect only relatively to the understandings ordered by that MU.) We can also argue the converse: Every understanding gives rise to a MU comprising all the understandings that it understands more than (or at least understands itself to).

What about the idea that the poset of understandings is directed? It seems to me that this is the central idea to the optimism that we want to have about knowledge: Given any two people, whatever their current understandings may be, there is some perspective (an understanding better than both of theirs) through which they may be reconciled; thus, they may be part of a community of scholars, with at least the potential to learn from one another. I don’t care if there is no PU, as long as I can improve my understanding by learning from you. (There is also the matter of whether I can come up with anything new on my own; that’s a separate sort of optimism, also desirable.) I would like to think about this in terms of MUs, but I don’t have an answer.

Posted by: Toby Bartels on November 20, 2006 11:24 PM | Permalink | Reply to this

Re: MacIntyre on Rational Judgment

Thank you for formulating this so clearly. The optimism of your final paragraph is very much to the point. I like the idea that it comes in shades. I hope that, through my own thinking and encounters with others, my understanding changes in such a way that I can see what was partial about my understanding from earlier stages of my career. I might also hope that others will learn from me, including my descendants. And I might hope that my meta-undestanding (MU) will be ‘preserved’ in future MUs, at least approximately. (In the simplistic language of posets, this preservation could be phrased as an order preserving map.) But I care about this preservation only to the extent that the community continues to operate ‘rationally’, while of course caring that it does continue to operate rationally. But then maybe I don’t mind so much that my MU fails to be preserved at some point in the future, but that in ‘the long run’ it is preserved (all MUs after a certain point preserve it), so long as it is preserved for the right kinds of reason. But what could I know of these if convergence happens far into the future, when new forms of mind (natural or artificial) may have arisen?

You can see the temptation to postulate a straightforward perfected understanding.

One last point, perhaps we should be amazed that this discussion set out from someone’s discussions of how a community should go about working out how to lead the good life.

Posted by: David Corfield on November 21, 2006 12:01 PM | Permalink | Reply to this

Re: MacIntyre on Rational Judgment

John Baez wrote:
“Rational enquiry could just be about moving towards better and better understandings.”

That is a natural assumption of convergence of iterated scientific revolution. However, it makes unproven assumptions about the toplogy of the Ideocosm (to use Fritz Zwicky’s terms for the space of all possible ideas) and about the nature of scientific (or philosophical) revolutions.

Revolutions are not, naively, progress. Thomas Kuhn made the meta-revolution in the study of revolutions.

You also assume (default metaphysics for scientists) that there is just one real world being studied. You assume that there can, at a given level, be only one valid theory of that world. Hard to exclude ad hoc that there could be two incommeasurable valid theories – think QM and GR!

Posted by: Jonathan Vos Post on November 19, 2006 5:42 AM | Permalink | Reply to this

Re: MacIntyre on Rational Judgment

Vos Post wrote:

You also assume (default metaphysics for scientists) that there is just one real world being studied.

I do? Just because I said rational enquiry be just about moving towards better and better understandings?

I’d have to know exactly what you meant to agree or disagree with you. For example: what alternatives do you claim I’m ruling out?

But frankly, I don’t even want to talk about this stuff! The sense in which the world does and does not depend on our experience of it is one of those famously tricky questions of philosophy. I don’t have a straightforward “realist” position on this question. I’m not even sure what I think. All I know is that this blog is not where I want to ponder it… a cave in the hills of Hangzhou would be better.

Posted by: John Baez on November 20, 2006 6:22 PM | Permalink | Reply to this

Re: MacIntyre on Rational Judgment

Dear John Baez,

I apologize for attributing beliefs to you that I could not know you have.

I taught several hundred students, aged 50 to 90, courses including “The Frontiers of Ignorance” from Kuhn’s “Structure of Scientific Revolution.” I’ve taught epistemology, psychology, anthropology, oceanography, sociology, and many other subjects outside my adjunct professorships in Mathematics and in Astronomy. My musings above were sparked by that, and my fascination with the topological and categorical questions raised by Zwicky’s Idocosm and your suggestion of convergence. I am not formally equipped to answer those questions. Nor, I agree, is this the right venue.

There is that old Chinese parable.

Two monks were walking across a bridge.

Monk 1: “See how they fish leap and splash in the stream below! They must be happy.”

Monk 2: “How do you know? You are not a fish.”

Monk 1: “How do you know? You are not me!”

Posted by: Jonathan Vos Post on November 20, 2006 9:36 PM | Permalink | Reply to this

Re: MacIntyre on Rational Judgment

Thanks. That’s one of my favorite Taoist parables. The oldest version comes from a text called the Chuang Tse. Monk 1 is the famous Taoist Chuang Tse (= Zhuangzi), while Monk 2 is the famous logician Hui Tse (= Huizi).

The Chuang Tse version includes an extra round:

Zhuangzi and Huizi were strolling along the dam of the Hao Waterfall when Zhuangzi said, “See how the minnows come out and dart around where they please! That’s what fish really enjoy!”

Huizi said, “You’re not a fish — how do you know what fish enjoy?”

Zhuangzi said, “You’re not I, so how do you know I don’t know what fish enjoy?”

Huizi said, “I’m not you, so I certainly don’t know what you know. On the other hand, you’re certainly not a fish — so that still proves you don’t know what fish enjoy!”

Zhuangzi said, “Let’s go back to your original question, please. You asked me how I know what fish enjoy — so you already knew I knew it when you asked the question. I know it by standing here beside the Hao.”

Here Chuang Tse’s last move seems a bit weak - I’d say the logician is winning. But as you can see, they enjoyed arguing with each other. There’s also a story that later, when passing by Hui Tse’s grave, Chuang Tse said he had no more material to work on, since there was no one he could really talk to anymore.

Posted by: John Baez on November 20, 2006 11:20 PM | Permalink | Reply to this

Re: MacIntyre on Rational Judgment

Note to self. MacIntyre writes

It is always as if the rational agent’s judgment and action were the conclusion of a chain of reasoning whose first premise was “Since the good and the best is such and such…” But it is only in retrospect that our actions can be understood in this way. Deduction can never take the place of the exercise of phronesis.

This puts Lakatos’s rational reconstructions in a better light. Rather than merely rewriting history to make scientists appear more rational, it is the extraction of the “as if”.

Posted by: David Corfield on March 15, 2011 10:07 AM | Permalink | Reply to this

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