# [OPE-L:3079] RE: assumptions, assumptions, assumptions

Gerald Lev (glevy@pratt.edu)
Sat, 21 Sep 1996 20:01:28 -0700 (PDT)

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Andrew wrote in [OPE-L:3075]:

> Now we seem to be clear: you object to all discussion of the maximum
> profit rate "except in the special case where v=0 is employed to critique a
> theory that likewise uses that assumption" or "to simplify the
> equations." In the latter case, you contend, "the 'results' are
> formally dependent on the assumptions made." (Actually, I'm not
> entirely clear; I understand "dependent," but not "formally dependent.")

To clarify:

(1) My objection did not specifically mention the concept of the maximum
profit rate.

(2) I *do* object to the v = 0 assumption where the *only* purpose is to
simplify the equations.

(3) "formally dependent" is perhaps redundant. It was intended to convey
the idea that the results are dependent on both the assumptions
and the formal logic embodied within the math selected.

> I do not agree. v = 0 is a limiting case, and I think it is often helpful to
> clarify the implications of certain propositions and concepts by considering
> limiting cases.
> In the present context, we are considering a theory proposed by a certain
> individual who Jerry prefers I not mention, a theory which contends that the
> magnitude of the capital advanced to production (the denominator of the
> profit rate) is potentially unbounded, while the magnitude of profit
> (the numerator of the profit rate) is bounded from above by the amount
> of living labor extracted.

Freeze frame. What is the basis for saying that the denominator of the
profit rate (c + v) is "potentially unbounded"? Unless one is going to
make the case that the profit rate = s/c, then the lower boundary *must*
be such that v > 0. [NB: no mention is made *at this point* on my part
regarding what the "certain individual" did or did not write].

> One way of gaining
> an understanding of these propositions, and testing their consistency, is to
> examine the limiting case, i.e., the magnitude of the profit rate when profit
> is at its maximum level. One does so by setting v = 0.

As noted above, *this* idea of the maximum level of the profit rate
assumes (absurdly) that a positive level of v does not set a lower
boundary.

Let's consider the non-mathematical implications of v = 0. If v = 0 then
either workers are working for capital for free or they are also "living
on air." Is there *any* reason to make this supposition? In either case,
the categories of both capital and wage-labor are no longer required to
analyze capitalist social relations.

Furthermore, if we are to assume that v = 0, this requires us to move
analytically from the more complex and concrete to the more simple and
abstract since the v = 0 assumption essentially requires us to *negate*
the capital form. Yet how can the capital form be negated without
*transcending* the capital form?

Moreover, Andrew (Paul Z take note): what is your definition of the
accumulation of capital? Is accumulation possible or even conceivable if v
= 0?

> One finds that when v = 0, s/v is infinite, but the profit rate
> is finite, and can fall is the above-mentioned ratio rises.

When v = 0, s/v becomes reduced to the simple identity of s/0.
How is this a meaningful statement (or "instructive", to use Allin's
phrase in #3077)?

> I also think there are at least two other valid uses of v = 0 that Jerry's
> strictures exclude. One is that the assumption may be used to test claims
> when v = 0 is among the cases which the claim covers. This is not the
> same as critiquing a theory that uses v = 0.

I will accept this point.

> The other valid use is this. When one is studying a question or
> questions the
> answer(s) to which one *knows ahead of time* do not depend on whether the
> magnitude of v, or whether it is rising, falling, or constant, I think it is
> quite legitimate to abstract from changes in v by setting v = 0.

that was a rhetorical question.

Why don't you in this case hold v *constant* and then verify that the
results are not fundamentally altered if v increases and decreases?

> One may be doing so because one is thereby able to study the
> question(s) at hand in their "pure" form, without the intrusion of
> extraneous
> factors, and not because one cares about the numerical results.

This is *too* pure for my tastes. How can v be an "extraneous factor" for
the profit rate when v is included in the formula for the profit rate?

> Again, I don't agree. Why should I have to accept either the purpose or the
> assumptions of your model before you write it down? All development of
> models would be paralyzed forever if anyone waited for the agreement of
> his/her audience.

I think that it is somewhat exaggerated to say that "all development of
models would be paralyzed forever."

> Jerry: "it is entirely legitimate to scrutinize and critique a model
> based on the assumptions made."
> It depends on the purpose of the model. If the purpose is to predict,
> and the model predicts well, then why criticize the assumptions.

Well ... we're not talking about predictive models here. However, if we
were, then it is not legitimate to assume that if a predictive model makes
accurate predictions that verifies the model. If a model accurately makes
predictions, it could be an accident. Or, even where the predictions are
shown to be accurate ex post, there could be mistaken causation or the
fallacy of association as causation. So, in order to evaluate a predictive
model as well, the assumptions need to be scrutinized. Another problem
common to many predictive models is essentially assuming that certain
trends from the past will continue into the future. On the basis of such
models, huge amounts of money were lost by certain investors in recent
years on the stock market and real estate market (to give only two
examples).

> If it does not
> predict well, then it is legitimate to point to the assumptions as a reason
> for this failure, but then one is critiquing the model for failure to
> meet its objective, not the assumptions per se.

Well, if a predictive model turns out to be in error ex post, that does
not necessarily invalidate the model since, for example, "external shocks"
(like hurricanes) could develop and some of these exogenous forces by
their very nature can not be accurately predicted ex ante.

> Why simple reproduction?-that's
> not realistic. Why a uniform profit rate?--that's not realistic. Why no
> fixed capital?, why are workers paid in kind?, why is there no technical
> change? why only two departments, why?, why?, why?, why?, why?

Since I stated clearly in the last post that my objections were not based
on whether an assumption was "unrealistic" per se, why? why? why? are you
asking me all of the above questions?

Simple reproduction and a uniform profit rate, for example, are *abstract
formal possibilities*. That is quite separate from the v = 0 assumption
which is *theoretically* inconceivable if we are discussing capitalism.

> Jerry: "if we are to agree that the subject of _Capital_ is capitalism, this
> [assumption] is illegitimate."
> I don't know how I can respond to this. A little earlier in his post, Jerry
> had just rejected my proposal on how to continue the v = 0 discussion,
> "Let's first discuss the meaning of the v=0 assumption *independently of the
> question of whether Marx utilized that assumption, when, where, and for what
> purpose*. Let's then discuss under what conditions and as part of the analysis
> of what subjects this assumption is legitimate and/or illegitimate. *After
> that*, we can discuss the questions of whether Marx employed that assumption
> and whether it was legitimate for the subject and purpose at hand." Now I am
> supposed to agree with a statement concerning the relationship between v = 0
> and the subject of _Capital_, which he supposedly doesn't want to discuss
> except at the end.
> Which is it, Jerry?

I refine my statement to read: If we agree that the object of study is
capitalism, this assumption is illegitimate.

> Jerry: "to vacate wages and v from the analysis entirely requires us to
> *fundamentally* depart from both Marx's analysis and the analysis of
> capitalism itself."
> Again, you're violating the order of discussion you yourself proposed.

OK, delete the reference to Marx.

> Jerry: "let me note that neither Alan, John, Ted, or yourself have attempted
> to answer my question posed in the 'Developing Marx' thread concerning the
> ways in which each of you believe one can 'develop' Marx from a TSS
> perspective."
> John has since done so. I agree fully that the issues John raises are
> unresolved and extremely important. I'm not sure, however, that this
> qualifies as "developing Marx" (a phrase I don't really understand anyway).

First: thank you John for offering an answer to my question. I eagerly
await answers from the other TSSers.

Second: *You* [Andrew] were the one who first mentioned the expression
"developing Marx" on this list. Now you say it is a phrase you don't
understand. Which is it?

> By refuting these allegations, the TSS
> interpretation challenges the non-existence of Marx's Marxism and enables it
> to be reclaimed, concretized, and developed.

"developed"? You use the term again. What does "developed" mean in this
context -- especially since you say you don't understand what the
expression "developing Marx" means?

> I'll also add that the TSS interpretation is far too particular for it to be
> the basis of a return to or development of Marx's Marxism.

Then what is?

Finally (on a lighter note) re Andrew's mess-up earlier today: I am
reminded of the headline on the back page of yesterday's _New York Post_
that concerned the Yankees loss to the O's in the second game of a
doubleheader where the Yanks won the 1st game and lost the second game
after having a big lead: "Split Happens".

In OPE-L Solidarity,

Jerry