[FOM] methodological/rigorous systemization

Harvey Friedman friedman at math.ohio-state.edu
Fri May 2 01:45:37 EDT 2008

I don't think that the phrase "formal methods" is a good one for what  
I mean. What I have in mind is far broader than the current narrow -  
and incorrect - image that "formal methods" has among philosophers.

Philosophers have a narrow image of "formal methods" largely because  
so many attempts to employ formal methods lack sufficient imagination  
and technical skill. This has given the phrase "formal methods" a bad  
name, and caused it to be grossly undervalued - and misunderstood.

So I now prefer to use the phrase "rigorous systemization".

THESIS. Suppose that a philosophical paper P, in any part of  
philosophy, consisting of informal prose, without rigorous  
systemization, represents intellectual progress. Then there exists a  
paper Q with the following properties.
1. Q focuses on rigorous systemization.
2. Q has a relatively small amount of informal prose.
3. Q can be written using the current level of practice in rigorous  
systemization and foundational thinking.
4. P is fully subsumed by Q.

Now obviously any important paper Q is going to leave a large number  
of issues unresolved. In fact, it may raise more issues than it  
resolves. So what is to be done with these remaining issues?

Here is what I do, under the methodology I have in mind. I don't  
publish a paper P on the remaining issues. Instead I wait until I can  
publish a paper Q on the remaining issues. And then the process  

HOWEVER, there is a place in the methodology that I have in mind for  
informal communications IC of type P. They take the form "here are  
some issues and here are some approaches that have not yet  
materialized". Under this methodology, the main effort is NOT spent on  
publishing polished versions of IC. INSTEAD, the serious effort is  
spent on (doing the research needed for, and) publishing the  
associated Q.

An example of such an IC of type P is this posting. It will be  
subsumed by an appropriate Q, which, as expected, will take some  
serious effort to research and write. As a special case of what I have  
just said, a determined effort to publish a polished form of this  
posting would NOT be in keeping with the general methodology.

In particular, SOME of the objections that have appeared here on the  
FOM to this THESIS certainly have some merit - but only rhetorically -  
and nothing of intellectual value would be attained in reformulating  
the THESIS to meet those objections. At least, nothing compared to the  
effort involved. Surely the THESIS could be modified appropriately -  
with real effort - to meet these particular kinds of objection, but  
this is not going to be of high value.

HOWEVER, SOME of the objections that have appeared - though rather  
unspecifically - do go to the heart of the matter. And these, of  
course, I do want to draw out and comment on.

Harvey Friedman

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