Re: Attempt at a Schema

[Ted Winslow <winslow@xxxxxxxx>]

Goncalo wrote:

> (2) On Keynes:
>
> I agree that his attitude may be hard to pin down.  But I don't think he was
> ambivalent.  He did write a Treatise on this stuff in 1921, so he must have
> had some strong views.
>
> I am not quite persuaded by your claim that he allowed objective randomness.
> The magic of the die ("risk") versus calculating "interest rates twenty
> years hence" ("uncertainty") lies in the kind of information you have.  The
> die provides clear and simple information that permits you to calculate
> probabilities with precision.  But to conclude that the probability of a
> particlar face on a die is 1/6 does not imply "objectivity". It simply means
> that one has not bothered to calculate how the strength of your hand, the
> position of the die, the angle of the throw, the friction in the air, etc.
> will affect the outcome.  But still, on the basis of the information that
> you DO have, you can calculate that probability is 1/6.

The objectivity of probability to which the Treatise points derives from the
foundational assumption made there that there are directly perceivable
objective "logical probability relations".  The Treatise, therefore, does
allow for objective probabilities though not for "objective randomness".
Keynes, however, subsequently explicitly abandoned the foundations of his
Treatise argument.

In his 1931 review of Ramsey's *Foundations of Mathematics* he explicitly
abandons the idea of logical probability relations.  He substitutes for it
the idea that rational degrees of belief are "useful mental habits" having
their basis in something analogous to perception and memory rather than in
formal logic and adopts Ramsey's term - "human logic" - to designate the
field of study concerned with the analysis of these habits.  He rejects,
however, Ramsey's attempt to elaborate the idea in terms of Charles Peirce's
pragmatism.

"Thus he [Ramsey] was led to consider 'human logic' as distinguished from
'formal logic'.  Formal logic is concerned with nothing but the rules of
consistent thought.  But in addition to this we have certain 'useful mental
habits' for handling the material with which we are supplied by our
perceptions and by our memory and perhaps in other ways, and so arriving at
or towards truth; and the analysis of such habits is also a sort of logic.
The application of these ideas to the logic of probability is very fruitful.
Ramsey argues, as against the view that I had put forward, that probability
is concerned not with objective relations between propositions but (in some
sense) with degrees of belief, and he succeeds in showing that the calculus
of probabilities simply amounts to a set of rules for ensuring that the
system of degrees of belief which we hold shall be a consistent system.
Thus the calculus of probabilities belongs to formal logic.  But the basis
of our degrees of belief - or the a priori probabilities, as they used to be
called - is part of our human outfit, perhaps given us merely by natural
selection, analogous to our perceptions and our memories rather than to
formal logic.  So far I yield to Ramsey - I think he is right.  But in
attempting to distinguish 'rational' degrees of belief from belief in
general he was not yet, I think, quite successful.  It is not getting to the
bottom of the principle of induction merely to say that it is a useful
mental habit." (X, pp. 338-9)

This change left much of the rest of the Treatise's treatment of probability
intact.  In particular, in locating the basis of degrees of belief in human
rather than formal logic, Keynes retained the view that objective rational
grounds were available for such beliefs.   As his account of the idea in the
passage just quoted demonstrates (he describes human logic as "a sort of
logic" concerned with the analysis of certain "useful mental habits"  we
have "for handling the material with which we are supplied by our
perceptions and by our memory and perhaps in other ways, and *so arriving at
or towards truth*"), Ramsey, by making human logic part of "logic", meant to
indicate that it was concerned with determining "what we ought to believe",
"what it would be reasonable to believe".

"Let us therefore try to get an idea of a human logic which shall not
attempt to be reducible to formal logic.  Logic, we may agree, is concerned
not with what men actually believe, but what they ought to believe, or what
it would be reasonable to believe." (Ramsey, *Foundations of Mathematics*,
p. 193).

The description of "what men actually believe" differed from this; it was
"descriptive psychology" rather than human logic. Ramsey proposed a system
based on betting for doing this.  The interpretive literature on Keynes (and
Ramsey) frequently ignores the fact that this system is a method of
"descriptive psychology" rather than of human logic.  The mistaken
implication is then drawn that human logic designates a subjective rather
than an objective approach to probability.

Keynes himself points to this distinction between descriptive psychology and
human logic and to the fact that by "human logic" Ramsey meant a field of
study able to provide objective rational grounds for degrees of belief.

"in attempting to distinguish a 'human' logic from formal logic on the one
hand and descriptive psychology on the other, Ramsey may have been pointing
the way to the next field of study when formal logic has been put into good
order and its highly limited scope properly defined." (X, p. 339)

>
> On the "interest rate twenty years hence", you have none of the necessary
> information to mathematically derive a single probability estimate.  You
> might be able, in some circumstances, to derive upper and lower bounds
> within which the
> probability should lie.  This is how I am reading the quote you provide:
>
>> "...it [the market valuation] cannot be uniquely correct, since
>> our existing knowledge does not provide a sufficient basis for
>> a calculated mathematical expectation."
>
> Notice how carefully he uses his words.  He always does this.  Whenever he
> talks about the "impossibility" of deriving a precise probability, he always
> precedes that remark with "on the basis of existing knowledge" or something
> to that effect.  He never simply comes out and says simply "it is unknown".

The quoted passage is part of a claim that an "assumption" underpinning the
"conventional" approach to forecasting is *mistaken*.

"We are assuming, in effect, that the existing market valuation, however
arrived at, is uniquely *correct* in relation to our existing knowledge of
the facts which will influence the yield of the investment, and that it will
only change in proportion to changes in this knowledge; though,
philosophically speaking, it cannot be uniquely correct, since our existing
knowledge does not provide a sufficient basis for a calculated mathematical
expectation.  In point of fact, all sorts of considerations enter into the
market valuation which are in no way relevant to the prospective yield."
(VII, p. 152)

The second and third conventions have the result that those dominated by
"mass psychology" tend (unreasonably) to hold the same beliefs about the
future and to be  "much more similar than they are dissimilar in their
reaction to news." (VII, 199)

Best,

Ted Winslow

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