[FOM] methodological thesis

Studtmann, Paul pastudtmann at davidson.edu
Fri May 2 12:50:22 EDT 2008

Let us suppose, then, that 'philosophical' is replaced with 'intellectual' in the two questions that I posed.  Although you did not answer the second question explicitly, I assume that your answer is 'yes'.  Because your thesis is a P paper, by your own thesis unless it has a corresponding Q paper it does not represent intellectual progress.  But, as you said, there is a corresponding Q paper to your thesis that formally captures the concept of intellectual progress, even though that paper has not yet been written.  Hence, your thesis represents intellectual progress.

It seems to me that unless you elaborate more fully on the way in which the concept of intellectual progress is to be formalized it is hard to know what to make of your thesis.  Merely saying that the Q paper that corresponds to your thesis would contain many examples of P papers and their corresponding Q papers does not help all that much.  In the first instance, although you have asserted your thesis and claimed that various philosophical works do not represent counterexamples to it, you have not presented your own examples of philosophical papers that are widely thought to represent intellectual progress for which there are corresponding Q papers.  Hence, it is hard to know exactly what you have in mind when you say that the Q paper that corresponds to your thesis would have many such examples.  Second, to the extent that you would characterize intellectual progress via examples of P papers and their corresponding Q papers, you are in danger of begging the question against someone who thinks that intellectual progress need not result from a P paper that has a corresponding Q paper.  Of course, whether you would have begged the question would depend to some extent on the range and number of examples that you use in order to characterize intellectual progress.

In this context, therefore, answers to the following two questions would be very helpful.  (1) Can you present examples of P papers and their corresponding Q papers.  Because you claim that your own work consists of Q papers that have in your own mind corresponding P papers, perhaps you could point us to one of your mathematical papers and then briefly characterize the P paper to which it would correspond were you ever to write it down.  Alternatively, you could give examples of philosophical works that the majority of philosophers would agree represent intellectual progress and then cite their corresponding Q papers?  (2) Can you alleviate the worry that characterizing intellectual progress in terms of P papers and their corresponding Q papers threatens to beg the question against opponents of your thesis?

Paul Studtmann
From: fom-bounces at cs.nyu.edu [fom-bounces at cs.nyu.edu] On Behalf Of Harvey Friedman [friedman at math.ohio-state.edu]
Sent: Thursday, May 01, 2008 3:58 AM
To: Foundations of Mathematics
Subject: Re: [FOM] methodological thesis

Here are replies to Studtmann, Heck, and Chow, whom I thank for

On Apr 30, 2008, at 10:11 AM, Studtmann, Paul wrote:

> Just two quick questions about this thesis.  How would you formalize
> the concept of philosophical progress?  If the concept of
> philosophical progress cannot be properly formalized, does it not
> follow by your thesis that your thesis does not represent
> philosophical progress?

In the THESIS, I wrote "intellectual progress". I wrote "philosophical
progress" later in the posting, in error.

Intellectual progress is a basic concept that transcends
"philosophical progress" and "mathematical progress" and "scientific
progress", etcetera.

The putting forward of that THESIS in my posting does represent
intellectual progress. Of course, it is an extremely short P rather
than any kind of Q. Obviously if it is elaborated properly by my
standards - something I certainly haven't done - then it would become
a Q. It would have, among other things, lots of examples of mine and
others, where Q's supplant P's.

On Apr 30, 2008, at 11:08 AM, Richard Heck wrote:

> The only difference seems to be the restriction "represents
> intellectual
> progress" in the Thesis. So it looks as if the stronger thesis is that
> formal methods are applicable where there is no intellectual progress.
> So the weaker thesis is just that formal methods are applicable to
> every
> philosophical problem where there is a possibility of intellectual
> progress. Or am I missing something?

I am not fully comfortable with the phrase "formal methods" but don't
have a good short substitute. I prefer to use "systemizations". Formal
methods have already gotten an unfair reputation. It is incredibly
more varied, deeper, and more powerful, than what is normally done
under its banner.

With that caveat about the phrase "formal methods", I would
reformulate your restatement replacing "there is a possibility of"
with "there has been".

> Counterexample 1: John Rawls, /Theories of Justice/
> Counterexample 2: Peter Strawson, /Individuals/
> Counterexample 3: Willard Van Orman Quine, /Word and Object
> /Counterexample 4: Thomas Kuhn, /The Structure of Scientific
> Revolutions/
> Counterexample 5: Saul Kripke, /Wittgenstein on Rules and Private
> Language/
> Counterexample 6: Saul Kripke, /Naming and Necessity/
> Counterexample 7: David Hume, /A Treatise of Human Nature/
> Counterexample 8: Immanuel Kant, /A Critique of Pure Reason/
> I can't think of any formal systematization of the insights in these
> books that would "fully subsume" them. That is absolutely not to say
> that formal work can't be inspired by them, or important to the
> assimilation and development of the insights contained in those books.
> But it is asking far too much of formal methods to ask them to do all
> the work.
I haven't the slightest idea why you would think that any of these
works are counterexamples. Can you give us just some sample insights
from some of these that constitute intellectual progress, but which
you think are not subsumable with appropriate systematizations
combined with a relatively small amount of prose? I don't mean "no

On Apr 30, 2008, at 1:56 PM, Timothy Y. Chow wrote:
> This looks to me like a proposed *definition* of "intellectual
> progress"
> rather than a "thesis."

As I said earlier, in my response to Studtmann, "intellectual
progress" is a basic prior concept.

It is of course an interesting challenge to go deeply into its meaning
- both theoretically and in practice.
> The Declaration of Independence could be considered a "philosophical
> paper" that "represents intellectual progress," but its significance
> has
> to do with the time and place of its formulation and its impact on
> human
> history, so I do not think it makes sense to "subsume" it by a text
> that
> exists in platonic eternity, dissociated from the particular social
> context of its composition.

This is quite different. This document is not a paper in the sense
that I am talking about. It is primarily an event. As a piece of
political philosophy only, I believe that it is not a counterexample.
> In other cases, a paper may represent progress because it is written
> especially clearly or compellingly, even though the ideas that it
> elucidates are, in some sense, contained in previous documents.  The
> formal nature of Q would necessarily mean that its expository value
> could
> not supplant the expository value of P.

Again, quite different. I could reformulate the THESIS so that I am
using only a careful notion of paper. But I don't think we need to do
this in order to join the serious methodological issue.
> The above "counterexamples" can be eliminated by saying that this
> kind of
> "progress" is not what was intended by the phrase "intellectual
> progress."
> That is why I see the "THESIS" as really a definition of that term.

I do not agree that the THESIS is a definition of intellectual
progress. I think that the THESIS is formulated decently enough
(obviously it can be improved) to join the serious methodological

Harvey Friedman
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