[lit-ideas] Re: Hartiana
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- Date: Fri, 27 Mar 2015 06:20:23 -0400
My last post today!
P. H. Nowell-Smith was a genial member of J. L. Austin's Saturday Mornings'
Play Group. In his "The Logical Basis of Ethics" he is using ethics so
genially that he was bound to interest Hart, who was into jurisprudence,
rather, but which Nowell-Smith read as "legal philosophy". Nowell-Smith KNEW
of
Hart's separability thesis ('morality and legality are separable, which
does not mean they are separated), and he invited Hart to consider the
'logical basis'. The trend became a fashion, and soon R. M. Hare got an
interest
too. With the advent of Grice and his conversational implicature talk, the
scenarios became more sophisticated, and the Play Group had J. O. Urmson to
provide the extra alleged counter-example. That was fun!
Once McEvoy dismissed epistemic logic from a Popperian point of view, and I
would think Popper would dismiss deontic logic. It fascinated R. M. Hare,
if not especially H. L. A. Hart. Recall that Hare was Hart's junior, and
that may have something to do with it. "O" is sometimes rendered by "ought",
but it's best to render it by "obligation" (if you're feeling Roman). And
deontic logic allows us to FORMALISE what, say, Hart's conceptual analysis
yields about oblige-obligate.
The five normative statuses of the Traditional Scheme are:
it is [legally] obligatory that (OB)
it is permissible that (PE)
it is impermissible that (IM)
it is omissible that (OM)
it is optional that (OP)
The first three are familiar.
But the fourth is widely ignored.
The fifth has regularly been conflated with “it is a matter of indifference
that p” (by being defined in terms of one of the first three), which is
not really part of the traditional scheme.
Typically, one of the first two is taken as basic, and the others defined
in terms of it, but any of the first four can play the same sort of
purported defining role.
The most prevalent approach is to take the first as basic, and define the
rest as follows:
PEp ↔ ~OB~p
IMp ↔ OB~p
OMp ↔ ~OBp
OPp ↔ (~OBp &~OB~p).
These assert that something is legally permissible iff (if and only if)
its negation is not legally obligatory.
This is held as analytically true, but not thereby 'vacuous' and 'circular'
(McEvoy's qualifications in a different context, vide Hart's rule of
recognition). something is impermissible iff its negation is obligatory,
omissible iff it is not obligatory, and optional iff neither it nor its
negation
is obligatory.
Call this “The Traditional Definitional Scheme (TDS)”.
If one began with OB alone and considered the formulas on the right of the
equivalences above, one could easily be led to consider them as at least
candidate defining conditions for those on the left.
Although not uncontestable, they are natural, and this scheme is still
widely employed by anyone following Hart.
Now consider:
If OBp then p (if it is obligatory that p, then p is true).
If p then PEp (if p is true, then it is permissible).
These propositions are transparently false, for obligations can be violated
(as Hart well knew -- hence his need to instruct his Oxonian undergraduate
students on that with his "The concept of law") and impermissible things
do hold.
Hart and Hartians are only interested in deontic logics that contain
classical propositional calculus (PC).
So let's assume we add THAT as the FIRST ingredient in specifying any
deontic logic, so that, for example,
OBp → ~~OBp
can be derived in any system to be considered.
it is obviously desirable to have
OBp → ~PE~p
as a THEOREM.
After all, this well-formed formula merely expresses one half of the
equivalence between what would have been definiens and definiendum had we
chosen
the alternate scheme of definition in which “PE” was taken as basic
instead of “OB”.
However,
OBp → ~PE~p
is not thus far derivable.
For
OBp → ~PE~p
is definitionally equivalent to
OBp → ~~OB~~p
which reduces by PC to
OBp → OB~~p
but the latter formula is not tautological. So we cannot complete the
proof.
So tautology or analyticity becomes the STANDARD for the construction of
the system, rather than a term of abuse!
What we need what is perhaps the most fundamental and least controversial
rule of inference in deontic logic, and the one characteristic of “classical
modal logics”:
OB-RE:
If p ↔ q is a theorem, so is OBp ↔ OBq.
It is now easy to prove the equivalences corresponding to the alternative
definitional schemes.
For example, since
⊢ p ↔ ~~p
by OB-RE, we get
⊢ OBp ↔ OB~~p
i.e.,
⊢ OBp ↔ ~~OB~~p
which generates
⊢ OBp ↔ ~PE~p
A deontic system, such as Hart's must contain a thesis asserting that a
logical contradiction (conventionally denoted by “⊥”) is always omissible:
OD: ~OB⊥
So, for example, OD implies that it is a logical truth that it is not
obligatory that my taxes are paid and not paid.
A principle of a legal system like Hart's is that obligations cannot
conflict:
NC:
~(OBp & OB~p).
One paradox of deontic logic that has cross-references with Hart, Hare, and
Grice is Ross's Paradox (Ross 1941) -- Ross being a member of what Hart
calls Scandinavian realism (O. K. may reflect on this -ism).
Consider:
(1) It is obligatory that the letter is mailed.
(2) It is obligatory that the letter is mailed or the letter is burned.
In "Practical Inferences", R. M. Hare (recall he was White's professor of
Moral Philosophy, while Hart chaired the Oxford chair of Jurisprudence)
quotes H. P. Grice to the effect that the use of 'or' in (2) triggers the wrong
conversational implicature -- and so Ross's paradox dissolves once this
type of cancellable implication is brought to play a role.
One good thing that J. L. Austin's Saturday Morning Play Group that Hart
(being albeit Austin's senior) would occasionally attend, was J. O. Urmson.
He was there to provide the right counter-example.
When Grice provided his analysis of 'mean', Urmson brought in the example
of a torture (Grice turned that into bribery): the recognition of the
intention on the utterer, by the addressee, cannot be 'obliged', it has to be
based on a reason, not merely CAUSED or forced otherwise.
It is not surprising that Urmson also provided counterexamples to Hart's
and Hare's legal and moral systems.
One of Urmson's puzzles concerns Indifference versus Optionality:
Consider:
1) It is optional that you attend the meeting, but not a matter of
indifference that you do so.
This seems to describe something quite familiar: optional matters that are
nonetheless not matters of indifference.
But when deontic logicians and ethicists gave an operator label for the
condition
~OBp & ~OB~p
it was almost invariably “It is indifferent that p”, “INp”. But then it
would seem to follow from the theorem
OBp ∨ (~OBp & ~OB~p) ∨ IMp
that
(~OBp & ~IMp) → INp
that is, everything that is neither obligatory nor prohibited is a matter
of indifference. But many actions, including some heroic actions, are
neither obligatory nor prohibited, yet they are hardly matters of
indifference.
We might put this by saying that SDL can represent optionality, but not
indifference, despite the fact that the latter concept has been a purported
target for representation since nearly its beginning.
Not satisfied with offering that to Hare and Hart, Urmson felt there was
another problem: supererogation.
Some things are beyond the call of duty or supererogatory (e.g.,
volunteering for a costly or risky good endeavor where others are equally
qualified
and no one person is obligated). Some deontic systems have no capacity to
represent this concept, which calls for a substantial increase in expressive
and logical resources. Hare and Hart were forever grateful to Urmson, as
was Grice.
Cheers,
Speranza
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