Reuben Post Halleck Professor of Philosophy

Yale University, New Haven, USA

**A**

I
had a pre-formal interest in the modal concepts of* *
necessity and possibility which can be traced back to Aristotle.
This led me to study, with the encouragement of my undergraduate
tutor JC. McKinsey, the work of* *
C.I. Lewis who had developed modal systems of* *
propositional logic. As a graduate student at Yale this
interest was pursued with the support of* *F.B.
Fitch. At that time, and through the early forties,
a prevailing view about interest in modal logic was that of*
*W.V. Quine who claimed that its source was in a misguided
confusion between use and mention. It was also claimed that any attempt
to develop a system of* *quantified modal logic
would lead to deep problems of* *interpretation, including
incoherence.

I set
about extending some of* *the Lewis systems to
first and then second order (*JSL,
11, *1946 and *JSL*, 12, 1947) under Ruth C.
Barcan included is an attribute forming
abstraction operator and the "Barcan formula" taken as an axiom:

◊($*x*)*Fx*
Þ
($*x*)◊*Fx*

On the
given formalizations the converse is provable. The “Barcan Formula” and
its converse remains a subject for debate.

The
system Quantified Modal Logic (QML) had some outcomes which answered to
some nonformal speculation and debate about modalities such as.

a. A formal proof of the necessity of
identity.

b. Despite Lewis’ claim that strict
implication was supposed to 'capture the relation of deducibility or
logical consequence the strict analogue of the deduction theorem in
unmodalized predicate logic was *not *provable. A weaker more
plausible deduction theorem is provable in some of the Lewis systems. *
JSL *1946. (See also *JSL *18, 1953 for a more extended
account.)

c. A substitution theorem which *
proscribes* the substitution of non-necessary equivalences in the
scope of the necessity operator.

**B.
Interpretation of QML**

a. I defend Smullyan’s claim that Quine’s examples of substitution
failures in modal contexts are mistaken, Russell’s formal theory of
descriptions is adopted as well as a linguistic theory of direct
reference for proper names, (Proper names are not taken to be disguised
descriptions.) *JSL, 13, *1948.

*
b. *Modalites and Intensional
Languages, *Synthese, *1961.
Several issues are addressed using formal methods.

i.
A direct reference view for genuine proper names is defended. I
called them *tags *since they are unmediated. On such a direct
reference view of proper names in conjunction with the theory of
descriptions, the much advertised; "failures" of substitution for
identity in modal contexts are dispelled within interpreted QML.

ii. The necessity of identity is
defended. (The "=" in identity formulae is flanked by individual
variables or constants. Only proper names are individual constants.)

iii. A substitutional alternative to objectual quantification is
proposed for consideration in some contexts. It is seen as of
interest but not urged. See also "Quantification and Ontology" *
Nous, *VI, no. 3, 1972 where Quine’s claim that the
substitu1ional account leads to a contradiction is formally shown to
be fallacious.

iv.
A non-formal account of essentialism challenges the claim that
essentialism is "invidious". Formal accounts within QML are given in
*Nous *l, 1967, some versions of which have been adopted,
often without attribution.

v.
A sample model theoretic semantics with fixed domain is given in
which the Barcan formula is provable. Metaphysically understood,
domains of interpretation contain only actual objects. Possibility
concerns properties actual objects might have. My arguments against
*possibilia *are linguistic and empirical and discussed in *
The Proceedings of The American Philosophical Association, *1975,
*Grazer Philosophicshe Studien, vol. 25, *1985/86, *Revue
lnternationle de Philosophie, *1997.

vi.
The paper here considered was delivered in 1962 and was followed by
comments from Quine and a discussion with Quine, Kripke , Follesdaal
et al which were published in *Synthese, *1962. There Quine
says that "the distinction between names and descriptions is a red
herring." That distinction (the red herring) was later adopted by
Kripke (1971) and others. The historical chain account of the name
transmission was first proposed by Peter Geach in "The Perils of
Pauline", *Revue of Metaphysics, *1969.

**C.
Moral dilemmas and consistency **

An analogue of the formal model
theoretic definition of consistency is used to dispel the received claim
that when a moral code can mandate incompatible actions in a particular
case, it must be inconsistent. But, what is formally required for
consistency is that there is a *possible *world which is dilemma
free, e.g. where keeping promises does not conflict with saving lives as
in Plato' s example. There are ethical conclusions to be drawn; we ought
to arrange our lives and institutions to minimize occasions of conflict.
*Journal of Philosophy, LXXVIT, *no 3, 1980 and in Homer Mason
editor, *Moral Dilemmas and Moral Theory, *OUP, 1996. This account
runs counter to many formalizations of deontic logic where conflicts of
obligations in a particular case entails inconsistency.

**D.
Set theory in a Modal Framework**

The syntax and semantics of QML
can be enriched to accommodate a theory of collections described by
inventory and sets described as satisfying some attribute not given by
inventory e.g.

*^x*(*x*
is a planet)

from

*^x(x=N *
Ú *x=V
*Ú *
x=M *
Ú *x=P *
Ú *
x=Ma *Ú *
x=U *
Ú *x=S *
Ú *x=E
*Ú *
x=J)*

where
the upper case letters are names of the actual planets.

Any two attributes given by inventory, if
they describe the same collection then they are necessarily equivalent.
No axiom of extensionality is required. This is just an extension of the
necessity of identity for the singular case. That does not hold for
attributes which may be satisfied by the 8ame things where the
equivalence is not necessary but analogous to a material equivalence.

This
paper was written in two versions; there was a problem of making the *
vocabulary *and symbolism perspicuous. *Acta Philosoophica Fennica,
*XVI, 1963, *American Philosophical Quarterly, *1974.

**CODA**

The list above is partial account of the way that formal methods have
been essential to my philosophical work. In recent years I have been
writing on epistemological issues such as belief and rationality. Here
I have rejected most received accounts of propositional attitudes and
attempts to systematize epistemic logic. The entire project is in a
formative stage so it has been omitted from the discussion