[FOM] Formalization Thesis

[Neil Tennant]

Harvey Friedman has advanced the following
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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.
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A great deal of indignation might be caused by the use of the phrase
'there exists'. But what Harvey means is that there there could, or
ought to, exist a paper Q such that ... . Read this way, the Thesis
becomes a statement of a *regulative ideal* for foundational research,
not a naive claim about the dispensability (let alone: a denigration
of the value) of the prior works P.

There is a long historical tradition of seeking to Q-ify prosaic Ps.
Think of Aristotle's syllogistic, Leibniz's characteristica universalis,
Frege's Begriffschrift, and Carnapian explications.

Harvey's Thesis (HT) is not to be compared with Church's Thesis. CT states
that the preformal, intuitive concept of computable function (on the
naturals) is exactly captured by any one of various mathematically
equivalent and precise notions [function computable by a Turing
Machine/recursive function/...]. It is the provable coextensiveness of
the mathematical notions that lends support to CT. But CT is regarded
as not susceptible of formal proof, since it contains the informal
notion of computable function.

HT, by contrast, contains informal notions at point P *and at point
Q*. HT's description of the sought paper Q is as informal as is the
description of a function as computable. So one cannot look for
sources of support for HT analogous to the ones we have for
CT. Moreover, any argument for HT would have to be expressed in
informal terms.

Philosophers like to play the reflexive trick on any thesis in the
theory of meaning or epistemology. They ask whether the thesis is
meaningful or knowable by its own lights. Are we to take HT as some
kind of P to which HT itself should apply? If HT, as stated above,
were to appear in a philosophical journal, it would not rank as the
shortest paper ever published (in prose) in a philosophy journal. The
reader of fom might find this surprising, but there have been shorter
philosophical papers published. The only way to embarrass HT
reflexively would be to grant that it (HT) represents intellectual
progress. Then the challenge could be issued to Harvey to produce a
paper Q that would subsume HT. But this is quite easy. For Q, take HT.
Now observe:

1. HT focuses on rigorous systemization.
2. HT has a relatively small amount of informal prose.
3. HT has been written using the current level of practice in
rigorous systemization and foundational thinking.
4. HT is fully subsumed by HT.

Since HT, to repeat, is being offered as a *regulative ideal*, it does
not have to be provable, even if only in informal terms. But of course
there are those who would still cavil at adopting any regulative ideal
without some assurance that the ideal that one is being urged to aim
at is accessible in at least some cases. And the best proof of
accessibility is actual access. So, HT provoked requests from some
(e.g., Richard Heck) for examples of past Ps and their corresponding
Qs.

In debating proffered examples, and whether they are confirming or
disconfirming examples (for the claim that HT is a feasible regulative
ideal), a great deal will turn on what one regards as intellectual
progress. It is also pointless for one refusing to adopt HT as a
regulative ideal to foist on the proposer of HT the burden of actually
producing the appropriate Q for any P chosen from a list like

	Leibniz: Monadology
	Descartes: Meditations on First Philosophy
	Spinoza: Ethics
	Hume: A Treatise of Human Nature
	Locke: An Essay concerning Human Understanding
	Kant: Critique of Pure Reason
	Hegel: The Phenomenology of Spirit
	Heidegger: Being and Time
	Wittgenstein: Tractatus Logico-Philosophicus
	Carnap: Logical Syntax of Language
	Quine: Word and Object
	Rawls: A theory of Justice
	Kripke: Wittgenstein on Rules and Private Language

This would be to have the productive work that could result from
adopting HT as a regulative ideal frittered away in unnecessary debate
over the extent to which the chosen work P really represented
intellectual progress. It would also be to ignore the limitation of HT
to *papers*, not treatises. Well, the order-of-magnitude problem might
be overcome by stating HT so as to apply to all philosophical works P,
huge tomes included, and claiming only that one should seek an
appropriately 'scaled down' Q version, such that

	length(Q) = k . length(P)

where k is a suitable factor << 1.

I know one very distinguished philosopher of science who, when at
graduate school with me, read Wittgenstein's Tractatus and reported
"It's just truth-tables!". And I know many an analytical philosopher
who would be quite prepared to Q-ify Heidegger's 'Being and Time' as
follows:

	$\bot$.

Those extreme examples aside, there are some points to be made,
concerning items in the foregoing list, that offer some support for HT
as a regulative ideal. Ed Zalta has made a serious attempt to
axiomatize Leibniz's ontology; that's one Q that readers of fom might
look at. One might also argue that Hume on the passions and
instrumental rationality finds its Q in the work of Frank Ramsey and
his followers in rational decision theory. Note too that Hume on
causation finds its Q in the work of David Lewis. Bob Brandom's work
on Hegel might produce something like a quasi-Q for the Phenomenology.
Carnap himself was already trying to make his P a Q---it was the very
Leitmotif of the Syntax.  Quine (RIP) would be the first to delight in
seeing the whole of his work condensed into 'grade-A idiom', i.e., to
be Q-ified. And it might just be that Kripke, the last example above,
was moved to write his monograph P because he was already apprised of
the relevant Q in recursive function theory, but knew that his
philosophical readers would need to have the material in P-form.

Indeed, much of what is judged as constituting intellectual progress
in contemporary analytical philosophy can fairly be described as
Q-ifying erstwhile influential Ps.

It is also worth noting how great an impact a short, P-work can have
when it is well on it way to being a Q. One thinks here of the 91-page
'Social Choice and Individual Values' by Kenneth Arrow (1951).

Sadly, the great Q-seeking tastes and tendencies of analytical and
post-positivist philosophy in the mid-twentieth century were thwarted
by a combination of factors: the sheer depth and difficulty of
Q-production itself; the limited numbers of qualified and appreciative
readers for Q-type work; the greater political effectiveness, within
the academy, of the anti-Q factions; the mind-boggling stupidity of
postmodernism, ironically brought to light by the brilliantly
deceptive Q-ifications of Alan Sokal; and the failure of the
(American) high school system to produce college-bound minds possessed
of enough literacy and numeracy to be drawn to Q-type work.

Those who denigrate the search for Q-versions of existing Ps do
foundations a disservice. HT is worth having out there, clearly
stated, even if only as an epitaph to better days.

Neil Tennant