## 1. Work on Tense Logic




Prior's most significant achievement was the invention and
development of tense logic. Tense logic involves two new modal
operators, 'It will be the case that' and 'It has
been the case that'.




During the 1940s, the logic of time was in its infancy. In 1941
Findlay briefly suggested a 'calculus of tenses', as
explained below, and in 1947 both Los, in Poland, and
Reichenbach, in the United States, published limited proposals
concerning the logic of time (Los 1947, Reichenbach 1947;
Los's paper was reviewed in English by Hiz 1951;
see also Prior 1967a: 12-15, 212-213, and Tkaczyk and Jarmuzek
2018). However, neither Los nor Reichenbach anticipated the
crucial idea of using modal operators to create a formal calculus of
time.




Prior catalysed the field with his detailed proposals for a modal
logic of time-distinctions. His tense logic was nothing less than a new
paradigm for the study of time (Hasle and Ohrstrom 2016).
Prior went on to use his tense logic to articulate theories about the
structure and metaphysics of time and to mount a robust defence of
freewill and indeterminism. Tense logic is now also employed for the
manipulation of time-dependent data and has numerous applications in
computing, including database management, program verification, and
commonsense reasoning in artificial intelligence.


### 1.1 Origins of Tense Logic




Prior's earliest mention of a logic of time-distinctions is to
be found in the penultimate chapter of his unpublished manuscript
*The Craft of Formal Logic*. *The Craft*, completed in
1951 (Prior 1951), was intended to be his first book on formal logic.
Following von Wright in 'Deontic Logic' (von Wright 1951b),
Prior remarked that there are other groups of modal predicates to be
set alongside the ordinary or 'alethic' modes of necessity
and possibility. He referred to these non-alethic modalities as
'quasi-modals'. After noting that Peter of Spain classified
adverbial distinctions of time as modes, he said:



> 
> 
> 
> That there should be a modal logic of time-distinctions has been
> suggested in our own day by Professor Findlay. (1951: 750)
> 
> 
> 




Findlay's paper 'Time: A Treatment of Some
Puzzles' had appeared in the *Australasian Journal of
Psychology and Philosophy* in 1941. Prior became aware of it as a
result of its appearance in Flew's 1951 collection *Essays on
Logic and Language*, which arrived in New Zealand just as Prior was
writing the final chapters of *The Craft.* The suggestion Prior
referred to is barely more than a passing comment: '[O]ur
conventions with regard to tenses are so well worked out that we have
practically the materials in them for a formal calculus', wrote
Findlay. He continued in a footnote:



> 
> 
> 
> The calculus of tenses should have been included in the modern
> development of modal logics. It includes such obvious propositions as
> that
> 
> 
> 
> > 
> > 
> > 
> > \(x\) present \(\leftrightarrow(x\) present) present;
> > 
> > 
> > 
> > 
> > \(x\) future \(\leftrightarrow(x\) future) present \(\leftrightarrow 
> > (x\) present) future;
> > 
> > 
> > 
> 
> 
> 
> 
> also such comparatively recondite propositions as that
> 
> 
> 
> > 
> > 
> > 
> > \((x).(x\) past) future; i.e., all events, past,
> > present and future, *will* be past.
> > 
> > 
> > 
> 
> 
> 




Prior's discovery of Findlay's footnote followed hard on
the heels of another discovery. In 1949 he learned (from Geach's
review of Julius Weinberg's *Nicolaus of Autricourt: A Study
in 14th Century Thought*) that, for the scholastics, an expression
like 'Socrates is sitting down'--an example discussed
by Aristotle--is complete, in the sense of being assertible as it
is, and is true at certain times, false at others. Prior was more
familiar with the view (still widespread today) that such an expression
is *incomplete* until a time-reference is supplied, and hence
that--despite the seeming naturalness of doing so--one cannot
regard the expression as changing its truth-value with the passage of
time. The ancient view, that this change in value can and does occur,
was a crucial discovery for Prior. He wrote about it in *The
Craft*, contrasting it with the modern view that 'Socrates is
sitting down' is not a 'complete proposition' but
rather a 'movable part' that occurs in many different
complete propositions: '"Socrates is sitting down" is
thought of, we might say, as a diary entry, with a date, hour, minute
and second beside it, and this date, etc. is part of the
"proposition"' (1951: 98). (For more about
Prior's discussion of temporality in *The Craft* see
Markoska-Cubrinovska 2017.)




This idea that tensed propositions are liable to be true at one time
and false at another became central to Prior's philosophy. In a
summary of his views, composed nearly two decades later, he wrote:



> 
> 
> 
> Certainly there are unchanging truths, but there are changing truths
> also, and it is a pity if logic ignores these, and leaves it ...
> to comparatively informal 'dialecticians' to study the more
> 'dynamic' aspects of reality. (Prior 1996a: 46)
> 
> 
> 


#### 1.1.1 Tense, indeterminism and freewill




Geach's review sent Prior back to the ancient sources, and he
found Aristotle saying that some propositions about the future, namely
propositions concerning events that are not determined at the time of
utterance, are neither true nor false when they are uttered, since
there is, at that time, as yet no definite fact with which they accord
or conflict. Prior quoted Aristotle's argument (in ch. 9 of
*De Interpretatione*) for believing in such events: if the
future were determined, 'there would be no need to deliberate or
take trouble, on the supposition that if we should adopt a certain
course, a certain result would follow, while, if we did not, the result
would not follow' (Prior 1953: 322-323).




For many years Prior had been a Barthian Calvinist, and, as Prior
put it, the theologian Karl Barth 'attacked freewill in the name
of religion' (Prior n.d.b: 1). In his mature work, however, Prior
was on the side of freewill and indeterminism. He developed profound
technical analyses of the idea that the future is open, a branching
tree of possibilities. The mature Prior said:



> 
> 
> 
> One of the big differences between the past and the future is that
> once something has become past, it is, as it were, out of our
> reach--once a thing has happened, nothing we can do can make it
> not to have happened. But the future is to some extent, even though it
> is only to a very small extent, something we can make for ourselves.
> And this is a distinction which a tenseless logic is unable to express.
> (Prior 1996b: 48)
> 
> 
> 




There can be no doubt that the origin of Prior's tense logic
was bound up with his change of mind about freewill. Landmark papers on
his path from determinism to indeterminism and the rejection of
Calvinism were:


* (Prior n.d.a), in which a transitional soft determinism is
propounded. This early typescript--which cites William James on
freewill and determinism--probably dates from around 1941.
According to determinism, the 'causal chain' is
'all-embracing', Prior said, but even though we are
'part of the causal chain', we are not 'pure
effect'. The 'chain of causation' runs
'within' us 'as well as outside': we ourselves
are causes. He continued: 'The only kind of universe in which
general freedom is conceivable is one which we might call
"loosely packed"', and he emphasized that determinism
'is compatible with a relatively loose packing of the things in
the world'. In a loosely packed universe, 'Causes and
effects may not form a single chain; events may run in a number of
chains which are partly independent of one another'. He
explained:



> 
> 
> 
> In a box of powder which is ground infinitely small and packed
> infinitely tightly, the slightest disturbance in one area will affect
> the most distant grains. If, however, the grains are relatively large
> and packed relatively loosely, one can imagine, for example, a circular
> motion of the grains in one area which does not affect even quite
> closely adjacent grains at all ... Common notions of freewill and
> partial responsibility seem to involve a picture of the world rather
> like this.... The common notion assumes a 'moderately'
> loose packing in which there is elbow-room for a measure of free
> action, but in which we are sufficiently bound together by
> 'necessity' for us to have a measure of influence on one
> another and responsibility for one another.
> 
> 
> 




(In another typescript from the same period (Prior n.d.b) he wrote
that 'our choices are pre-determined' but that 'it is
in our power to find out what the forces are which determine our
choices, and even to exercise some control over them (while, of course,
being in this very exercise "controlled" by other forces
which do not worry us). Prior's (n.d.b) is discussed in detail in
Hasle (1999) and (2012).)
* (Prior 1947), in which he firmly distances himself from Barth.
* (Prior 1953), in which (following the Polish logician Jan
Lukasiewicz) he uses a 3-valued logic to formalize the
Aristotelian view that 'propositions about such future events as
are not already predetermined' are neither true nor false (1953:
322).
* (Prior 1955b), his first publication on tense logic.


#### 1.1.2 The first tense logic




Prior wished to formalise the ancient insight that propositions can
change in truth value with the passage of time. He soon realised that
off-the-shelf modal syntax could be adapted to do this. It was simply a
matter of taking seriously the idea he had discussed in *The Craft
of Formal Logic*: tense is a species of modality, to be set
alongside the ordinary ('alethic') modes of necessity and
possibility. When he discovered the '*Master
Argument*' of Megarian logician Diodorus Chronos (in Benson
Mates' 1953 book *Stoic Logic*), Prior's exegesis of
Diodorus's argument became the backdrop to his first publication
on tense logic, 'Diodoran Modalities' (1955b).




Diodorus defined the possible as what is or will be true: according
to Diodorus, what actually happens is all that *can* happen.
Diodorus, Prior later said, 'seems to have been an ancient Greek
W.V. Quine, who regarded the Aristotelian logic of possibility and
necessity with some scepticism, but offered nevertheless some
"harmless" senses that might be attached to modal
words' (1967a: 16). Prior found this deterministic definition of
the possible uncongenial and set about locating a fallacy in the
argument that Diodorus had used to support it, the so-called Master
Argument:



> 
> 
> 
> The aim of the Master Argument, as I conceive it, was to refute the
> Aristotelian view that while it is now beyond the power of men or gods
> to affect the past, there are alternative futures between which choice
> is possible. Against this, Diodorus held that the possible is simply
> what either is or will be true. (Prior 1962a: 138; see also 1967a:
> 33.)
> 
> 
> 




Consideration of the Master Argument brought together three of
Prior's great interests: indeterminism, modal logic, and the
logic of time. In the course of his reflections on the argument,
Findlay's footnote pushed its way to the front of his mind. His
wife Mary remembered 'his waking me one night, coming and sitting
on my bed, and reading a footnote from John Findlay's article on
time, and saying he thought one could make a formalised tense
logic' (Kenny 1970: 336).




'Diodoran Modalities', completed by early 1954, set out
Prior's initial exploration of his calculus of tenses. On the
first page he wrote:



> 
> 
> 
> I here propose to do something a little different, namely to employ
> the ordinary propositional variables '\(p\)',
> '\(q\)', '\(r\)' etc., for
> 'propositions' in the Diodoran sense [i.e. propositions
> which 'may be true at one time and false at another'] and
> to use certain operators which take such propositions as arguments, and
> which form functions taking such propositions as values. I shall use
> '\(Fp\)' for 'It will be the case that
> \(p\)'. (1955b: 205.)
> 
> 
> 




The calculus of tenses presented in 'Diodoran
Modalities' is the system produced by adding the following
axioms, rules, and definition, to the ordinary propositional calculus.
\((1)\ F(p \vee q) \equiv(Fp) \vee 
(Fq)\). \((2)\ FFp \rightarrow Fp\). (3) If \(p \equiv q\) is provable in the calculus (or is an axiom) then
\(Fp \equiv Fq\) follows. (4) If \(p\) is provable
in the calculus (or is an axiom) then \(Gp\) follows; where
\(Gp\), the future perpetual form 'It will always be the
case that \(p\)', is defined as
\(\neg F\neg p\).


#### 1.1.3 Prior's 1954 Wellington Address




There was clearly more work to be done on this calculus--for
one thing there was no mention of the past--and Prior duly set
about extending his creation. He worked fast, and in August 1954
unveiled a system of far greater sophistication, in his Presidential
Address to the second New Zealand Congress of Philosophy, held in
Wellington.




Prior's expanded calculus contained two additional axioms
concerning futurity, \(Gp \rightarrow Fp\) and \(Fp \rightarrow FFp.\)
There was also a simplification: instead of following his previous
practice and defining \(G\) as \(\neg F\neg\), Prior took \(G\) as
undefined and defined \(F\) as \(\neg G\neg\); this enabled him to
replace the somewhat unwieldy axiom (1) by the more elegant \(G(p
\rightarrow q) \rightarrow(Gp \rightarrow Gq)\). Moreover, he
transformed this calculus of 'pure futurity' into a
calculus of 'pure pastness' by replacing \(F\) throughout
the axioms, rules, and definition, by the past tense operator \(P\)
('It has been the case that'), and replacing \(G\) by the
past perpetual operator \(H\) ('It has always been the case
that').




Like ordinary modal logic, both these 'pure' calculi are
*mono*modal; that is, each contains only one undefined modal
operator. Prior wanted a 'full tense calculus', containing
the two undefined operators \(G\) and \(H\), together with
the operators \(F\) and \(P\) defined in terms of them (such
a calculus is known as a \(bi\)modal logic). To obtain the full
calculus it was not enough simply to bundle together the two
'pure' systems, because the two tense operators would
remain independent of one another. Some *interactive* axioms,
'laws which relate to the interaction of pastness and
futurity', were also required. Prior chose \(p \rightarrow\)
\(GPp\) and \(p \rightarrow HFp.\)




What are the justifications for his axioms and rules? In
'Diodoran Modalities', Prior was content to describe
\(FFp \rightarrow Fp\) as 'obvious enough', but by
the time of the Wellington Congress his thinking had moved forward
considerably. He there set out what he called the
'\(l\)-calculus' (he was later to prefer the term
'\(U\)-calculus'). '\(l\)' is the
relation 'is later than' (relating dates). In the
\(l\)-calculus, the propositions of the tense calculus are treated
as expressing properties of dates. '*lxz* &
\(px\)' (where \(p\) might be 'Socrates is
sitting down', for example) is read '\(x\) is later
than \(z\) and \(p\) at \(x\)' \((x\) and
\(z\) are dates). Using the (arbitrary) date \(z\) to
represent the time of utterance, \(Fp\) is equated with
\(\exists x(lxz \amp px)\) ('\(p\) at
some time later than \(z\)'), and \(Pp\) with
\(\exists x(lzx \amp px)\) ('\(p\) at
some time earlier than \(z\)'). \(Gp\) and \(Hp\)
are equated with the universal quantifications
\(\forall x(lxz \rightarrow px)\) and
\(\forall x(lzx \rightarrow px)\) respectively. (Much
later, Prior recast the date-terms of his \(U\)-calculi as
'instant propositions'--propositions true at one and
only one instant--so introducing what is now called 
 hybrid logic.)




Prior showed that if various assumptions are made concerning the
relation \(l\), the axioms of the tense calculus can be proved in the
\(l\)-calculus. (Two years later, he and Meredith used essentially the
same strategy in creating the possible worlds semantics for ordinary
modal logic.) He discovered that \(FFp \rightarrow Fp\) and its image
\(PPp\rightarrow Pp\) follow from the assumption \(lxy \rightarrow
(lyz \rightarrow lxz),\) stating that the relation \(l\) is
transitive. \(Fp \rightarrow FFp\) and its image \(Pp \rightarrow
PPp\) follow given the assumption *lxz* \(\rightarrow \exists
y(lxy \amp lyz),\) stating that 'between any two dates there is
another date' (a condition sometimes said to express
time's *density*). \(Gp \rightarrow Fp\) follows given
\(\exists xlxz,\) stating that 'there is a date later than any
given date', i.e., that there is no last moment of time. \(Hp
\rightarrow Pp\) requires \(\exists xlzx,\) stating that there is no
first moment of time.




Prior showed, furthermore, that no assumptions at all are needed for
the derivation of the two interactive axioms \(p \rightarrow GPp\) and
\(p \rightarrow HFp,\) nor for the axioms \(G(p \rightarrow q)
\rightarrow(Gp \rightarrow Gq)\) and \(H(p \rightarrow q) \rightarrow
(Hp \rightarrow Hq)\). In the case of these formulae, the ordinary
machinery of truth-functional and quantifier logic suffices for their
proof. The same is true, he showed, of the four rules of the tense
calculus ((3) and (4) above, together with the \(P\) form of (3) and
the \(H\) form of (4)). This part, therefore, of Prior's
calculus of tenses is purely logical, whereas others of the
axioms--those stating that \(l\) is transitive, that time is
dense, and that there is no first or last moment of
time--express *physical* properties of time. In later
work, Prior considered further calculi, in which these particular
'physical' axioms are replaced by others, for example
axioms stating that time has a first moment, or is linear (a
'straight line'), or is non-linear, with the present
always standing at the junction of a number of branches, any of which
might become the actual future.




Which is metaphysically basic, the tense calculus or the
\(l\)-calculus? Prior issued a warning against regarding the above
interpretation of the tense calculus within the \(l\)-calculus as
'a metaphysical explanation of what we mean by is, has been and
will be': the \(l\)-calculus, he said, is not
'metaphysically fundamental'. His reason is that
'\(F\)(Socrates is sitting down)' means 'It is
*now* the case that it will be the case that Socrates is sitting
down', whereas there is no genuine way of representing the
indexical 'now' in the \(l\)-calculus (the date
variable \(z\) is not an indexical, any more than '21
January 1954' is an indexical). Prior continued: 'If there
is to be any "interpretation" of our calculi in the
metaphysical sense, it will probably need to be the other way round;
that is, the \(l\)-calculus should be exhibited as a logical
construction out of the \(PF\)-calculus rather than *vice
versa*.' This idea of the primacy of the tense calculus over
the \(l\)-calculus (or, as he later put it, of McTaggart's
\(A\)-series over the \(B\)-series) became a central and
distinctive tenet of his philosophy. Prior took a similar metaphysical
position with respect to ordinary modal logic, arguing that the
language of possible worlds is to be interpreted in terms of a language
with modal operators and not, as is popularly held, *vice
versa*. These issues form the theme of his final book *Worlds,
Times and Selves*. (For more about the world-time parallel, see Rini and Cresswell 2012.)


#### 1.1.4 The Master Argument and three-valued logic




In a matchless piece of philosophical reconstruction--in
'Diodoran Modalities'--Prior expresses the conclusion
of the Master Argument, that what neither is nor will be true is not
possible, as \((\neg p \amp \neg Fp) \rightarrow \neg \Diamond p\),
and derives this in his calculus from Diodorus' premisses, \(Pp
\rightarrow \neg \Diamond \neg Pp\) and \(\neg\Diamond q \rightarrow
(\Box(p \rightarrow q) \rightarrow \neg\Diamond p),\) together with
two 'broad assumptions about time, likely to have been taken for
granted both by Diodorus and by his main opponents', viz. \(p
\rightarrow HFp\) and \((\neg p \amp \neg Fp)
\rightarrow P\neg Fp.\)




So the Master Argument is indeed valid. The fallacy, Prior tells us,
lies with the second 'broad assumption' \((\neg p \amp
\neg Fp) \rightarrow P\neg Fp\) (which says: when anything
neither is nor will be the case, it has been the case that it will not
be the case). This, Prior tells us, is not true if \(p\) refers to a
future contingency, and thus has the truth value 1/2 or
'indeterminate'. Where \(p\) is indeterminate, both \(Fp\)
and \(\neg Fp\) are indeterminate, so the consequent of the disputed
formula, \(P \neg Fp\), is false. \(\neg p\) must also be
indeterminate (for if the negation of \(p\) were determinate, \(p\)
could not be indeterminate). Thus the antecedent of the 'broad
assumption', \(\neg p \amp \neg Fp\), is indeterminate, since
both its conjuncts are indeterminate.




The next step of Prior's argument was to appeal to
Lukasiewicz's 3-valued truth-table for \(\rightarrow\). According to
the table, an indicative conditional with a false consequent and an
indeterminate antecedent is not true but indeterminate:




|  |  |  |  |
| --- | --- | --- | --- |
| \(\rightarrow\) | 1 | 1/2 | 0 |
| 1 | 1 | 1/2 | 0 |
| 1/2 | 1 | 1 | 1/2 |
| 0 | 1 | 1 | 1 |




Thus Prior was able to 'deny that propositions of the form [\((
\neg p \amp \neg Fp) \rightarrow\) *P\(\neg\)Fp*] are in all cases
true', so faulting the Master Argument.




The Master Argument for determinism continued to exercise Prior for
the rest of his life, and some of the most useful and mathematically
most interesting parts of his work were inspired by his thoughts on it.
To pick just one example, from computer science, tense calculi that
Prior developed--leading on from the idea that the Master Argument
is defeated if time is conceived as branching into the
future--have become useful for describing and verifying the
behaviour of distributed and concurrent processing systems (see e.g.
Ben-Ari, Pnueli, and Manna 1983).


### 1.2 Tense Logic Comes of Age




The text of Prior's Wellington address was not published until
1958 (in the journal *Franciscan Studies*, under the title
'The Syntax of Time-Distinctions'). It was Prior's
1956 John Locke lectures at Oxford and the ensuing book *Time and
Modality* (published in 1957) that brought Prior's
discoveries in tense and modal logic before a wider audience. A number
of logicians--notably Thomas, Geach, Lemmon, Meredith and
Kripke--took an immediate interest in Priorean modal logic, in
particular his Diodoran system and his system \(Q\), a multivalued
logic admitting the existence of contingent beings. Less immediate
attention was paid to his tense logic. The bibliography of the subject
in Prior's 1968 volume *Papers on Time and Tense* reveals
that up until 1965 the only publications in the field were either by
Prior himself or were reviews of his work (chiefly of *Time and
Modality*). Yet a momentum was slowly gathering.




At a colloquium on modal and many-valued logics held in Helsinki, in
1962, Hintikka proposed a tense-logical construal of his possible
worlds semantics, maintaining that 'if we do not want to tie our
logic to old-fashioned physics, we are undoubtedly wiser if we ...
no longer require that the alternativeness relation (in this case it
could perhaps be more appropriately termed "futurity
relation") effect a linear ordering' (1963: 76). Prior had
happily tied his 1954 \(l\)-relation to 'old-fashioned
physics': he later made it clear that he did not think much of
the view of time embodied in twentieth century physics (1996b:
49-51).




A pupil of von Wright, Hintikka had been stimulated by the
latter's proposals for the wide application of modal logic (see
the next Section) and had come to appreciate the possibility of
applying modal notions to the study of the logic of time before he
learned of Prior's sophisticated work (through reading *Time
and Modality*, which he reviewed in 1958). Hintikka was perhaps the
first to stress the importance of a semantical approach to the tenses.
During the early 1960s, he travelled regularly between Helsinki and
California and his ideas on tense influenced a number of logicians
working in California, in particular Dana Scott.




1962 was a significant year for tense logic. As well as
Hintikka's talk in Helsinki, Scott gave a lecture on tense logic
in Amsterdam (Hans Kamp, then an undergraduate, was among his
audience). Scott's work on tense logic was one aspect of his
study of the semantics of natural language, which he pursued in close
collaboration with Richard Montague. Scott was aware of Prior's
work, and was also influenced in his understanding of tense by
Reichenbach's 1947 analysis (the latter was a powerful figure at
UCLA until his death in 1953). Prior himself was critical of
Reichenbach's analysis of the tenses, describing it as having
been 'in some ways a hindrance rather than a help to the
construction of a logic of tenses' (Prior 1967a: 13).
Scott's work in tense logic was different in style from
Prior's. He established the completeness and decidability of
various axiomatic tense logics, and also showed that the temporal
predicate logic of the reals is non-axiomatisable. His work in tense
logic is widely cited but remains unpublished. Prior learned of
Scott's work in January 1964, in a letter from Lemmon (who the
previous year had left Oxford for Claremont, near Los Angeles).




In 1965 Prior visited California for several months, as Flint
Professor of Philosophy at UCLA. For the first time he found himself
among a group of enthusiasts for tense logic. Shortly after the visit
ended he was to write: 'I suppose that California is the most
logically mature place in the world, and now that the logic of tenses
is pursued so widely and so vigorously there, its raw pioneering days
can be considered over' (1967a: vi). When Prior arrived at UCLA,
Nino Cocchiarella was just completing a Ph.D. thesis on quantified
modal and tense logic, under Montague's supervision ('Tense
and Modal Logic: A Study in the Topology of Temporal Reference').
Cocchiarella's interest in the philosophy of time had initially
been aroused by Reichenbach's work on space and time, but it was
his acquaintance with Prior's *Time and Modality* that
swept him into tense-logical research. (Only later did he learn of
Scott's work.) Prior's visit also coincided with Hans
Kamp's arrival at UCLA as a graduate student. Kamp attended
Prior's lectures on tense logic in his first semester and became
deeply interested in the subject. The lectures led more or less
directly to the topic of Kamp's Ph.D. thesis, written under
Montague's supervision and entitled 'On Tense Logic and the
Theory of Order' (1968). In Kamp's work the development of
tense logic achieved a new level of formal sophistication. Segerberg,
too, had just arrived in California, to study under Scott at Stanford.
Segerberg had become interested in tense logic in Finland in 1964, at a
series of summer seminars given by von Wright, who was independently
pursuing a tense logic arising from his study of the logic of action,
and later shown to be equivalent to a system Prior had discussed in
*Time and Modality* (Prior 1957: 23-4; see von Wright 1965 and
Segerberg 1967, 1989).




In December 1965 Scott delivered his famous talk to the Hume Society
at Stanford entitled 'The Logic of Tenses'. A multilith of
Scott's handwritten notes for this talk has been circulating ever
since among tense logicians. Four days later Prior himself addressed
the Society, again on tense logic. It was in this fecund atmosphere
that Prior completed the manuscript of his book *Past, Present and
Future*, which remains to this day one of the most important
references in the field.




The years 1965-7 saw the publication of work in tense logic by
Aqvist, Bull, Clifford, Cocchiarella, Garson, Geach, Hamblin,
Luce, Makinson, Rescher, Segerberg, von Wright--and, of course,
Prior. In a little over a decade Prior's invention had become an
internationally pursued branch of logic.




Prior always had a firm belief that his tense logic would one day find
useful applications in other disciplines (possibly in mathematical
physics, he thought). When the outside demand for tense logic did
come, it was from linguistics (via Montague's papers, especially
his 1970) and from computer science. An early and influential computer
science application was by Pnueli, who employed tense logic in formal
reasoning about the behaviour of concurrent programs (Pnueli 1977).
Pnueli is sometimes mistakenly credited with having originated tense
logic, but in fact he first learned of it from the classic 1971 volume
*Temporal Logic* by Rescher and Urquhart
(Ohrstrom and Hasle 1995: 344)--a book dedicated to
Prior and which is an elegant introduction to his work. The citation
for Pnueli's 1996 A. M. Turing Award begins 'For seminal
work introducing temporal logic into computing
science'. (Goldblatt 1987 surveys the connections between
temporal logic and computer science that were emerging during the
decade following Pnueli 1997.)




Prior would not have been completely surprised to learn how useful
tense logic has proved to be in computer science. He himself took
little interest in computing, beyond including material on elementary
boolean circuit theory in his undergraduate lectures, but a number of
the logicians with whom he was in touch were more deeply involved (Dov
Gabbay and Dana Scott, for instance). Through others Prior knew
something of the potential. He wrote 'There are practical gains
to be had from this study too, for example in the representation of
time-delay in computer circuits' (1996a: 46). In *Past,
Present and Future* he remarked concerning logics of discrete time
that their usefulness 'does not depend on any serious
metaphysical assumption that time *is* discrete; they are
applicable in limited fields of discourse in which we are concerned
only with what happens next in a sequence of discrete states, e.g. in
the workings of a digital computer' (1967a: 67). Other logics
from a wide group that Prior and von Wright pioneered are also finding
computational applications, for example epistemic logic in artificial
intelligence and knowledge-base engineering, and the logic of action in
programming theory. It is pleasant to reflect that two major forces in
the genesis of these software technologies were Prior's love of
ancient and medieval logic and his concern to make conceptual room for
freedom of the human will.


## 2. Work on Modal Logic




Of the four technical papers that marked the explosive beginning of
Prior's career as a formal logician in 1952 (1952a-d), two concerned modal
logic. 'Modality De Dicto and Modality De Re' is a
discussion of this distinction as it appears in Aristotle, Ockham, and
Peter of Spain, together with a comparison of these earlier views with
those of von Wright in his 1951 book *An Essay on Modal Logic*. 'In What
Sense is Modal Logic Many-Valued?' concerns
Lukasiewicz's four-valued matrices for modal logic. In this
paper Prior took issue with the view 'that the logic of modality
cannot be satisfactorily studied unless we use a many-valued calculus
for its formal expression', and he proposed a subversive
interpretation of the four-valued matrices according to which modal
propositions remain bivalent. This paper was the curtain raiser to
Prior's extensive study of Lukasiewicz's work on
modality, and thereafter he read Lukasiewicz widely--even
material in Polish, saying 'the symbols are so illuminating that
the fact that the text is incomprehensible doesn't much
matter'.


### 2.1 *The Craft of Formal Logic*




Prior's entry into modal logic was bound up with his passion for
ancient and early logic. His first essay on the subject, the
penultimate chapter--'Modality'--of his
ill-fated manuscript *The Craft of Formal Logic*, is largely
historical in nature, with discussions of Aristotle, Peter of Spain,
John Wallis, the *Port Royal Logic*, Isaac Watts'
*Logick*, Whately, Aldrich, de Morgan, and Hume and Mill on
natural necessity. To judge by his references in *The Craft*,
his first encounters with modern symbolic modal logic must have been
the pioneering explorations by Lewis in his and Langford's
*Symbolic Logic*, Bochenski's chapter 'La Logique
de la Modalite' in his *La Logique de
Theophraste*, and Feys' article 'Les
Systemes Formalises des Modalites
Aristoteliciennes' (Lewis and Langford 1932, Bochenski
1947, Feys 1950). Other important early influences were von
Wright's 'Deontic Logic' and *An Essay in Modal
Logic*, both published in 1951. Probably through Bochenski's
writings, Prior had discovered Lukasiewicz's work in
symbolic modal logic by the time of 'In What Sense is Modal
Logic Many-Valued?'. In that paper Prior focussed on
Lukasiewicz's 'On Variable Functors of Propositional
Arguments' (Lukasiewicz 1951b), which he described in a
1952 review of Lukasiewicz's symbolic logic as 'quite
the most exciting contribution that has been made to symbolic logic in
English for a very long time'. Lukasiewicz's work on
modality was a major influence on Prior, who wrote in the Preface to
*Time and Modality*: '[W]hile I differed radically from
the late Professor Lukasiewicz on the subject of modal logic, my
debt to him will be obvious on almost every page'.)


One of Prior's conclusions in 'Modality',
significant for his later work, is that '[t]here is everything to
be said ... for the ... view that we may not only use devices
developed in the study of quantity to throw light on modality, but also
*vice versa*' (1951: 747). One of the most distinctive
features of his mature philosophy was the view that quantification over
possible worlds and instants is to be interpreted in terms of modality
and tense, which constitute primitive notions--a view he held in
tandem with the belief that the study of such quantifications could
usefully illuminate the study of modality and tense (as in his own
\(U\)-calculi, described below).




Prior arrived at another important insight in the penultimate
chapter of *The Craft*. Early in 1951 he read von Wright's
article 'Deontic Logic' and in 'Modality' he gave a
cameo discussion of this area. His reading of von Wright reinforced in
his mind an idea that he had come across in Peter of Spain, Isaac
Watts, and the *Port Royal Logic*, an idea that was to be of
considerable significance for his own future work. What von Wright
called the 'alethic' modes--necessity, possibility,
impossibility and contingency--are members of an extended group of
concepts that includes the epistemic modes ('it is known
that', 'it is not known to be false that', etc.), the
doxastic modes (such as 'it is believed that'), and the
deontic modes (which include 'it is permitted that' and
'it is obligatory that'). In *The Craft* Prior also
listed Watts' 'it is written that' and 'it is
said that', noting that 'one could think of innumerable
others' (1951: 749). Later, von Wright was to draw attention to
what may be called the agentive modes: 'the agent brings it about
that', 'the agent makes it true that', and the like
(von Wright 1963).




Prior introduced the collective term 'quasi-modals' for
the non-alethic modes (1951: 749) and remarked, accurately, that
'there is a hint of a large field here' (1951: 752). He was
later to refer to his own tense operators as quasi-modal operators
(1968: 138). By the time he wrote *Formal Logic* he was
advocating the study of 'the general modal form "It is
-- that \(p\)" ... as a distinct propositional
form', observing that 'this field has not been much
cultivated' (1955a: 218).


### 2.2 General Intensional Logic




Between them Prior and von Wright pioneered the now much
investigated field of general intensional logic, in which the syntax,
and latterly the semantics, developed for the study of the alethic
modalities is used in the analysis of a wide range of quasi-modal
concepts. Von Wright's deontic logic and Prior's tense
logic were the first major successes in this field.




Prior was convinced that no satisfactory *metalinguistic*
analysis can be given of sentences having the general modal form
'It is -- that \(p\)'. In *Formal Logic*
he wrote: 'It is quite plain, for example, that I am not talking
about the sentence "Socrates is dead" when I say "I
wish that Socrates were dead"' (1955a: 219). In *Time
and Modality* he reiterated the point, now in connection with the
tenses: '"Professor Carnap will be flying to the
moon" ... is quite obviously a statement about Professor
Carnap, and quite obviously not a statement about the statement
"Professor Carnap is flying to the moon"' (1957:
8).




What, then, is the semantic value of an expression replacing
\(p\) in a sentence of the general modal form 'It is --
that \(p\)'? Certainly not a truth value, as is the case
with the standard extensional propositional calculus, for substituting
a different expression with the same truth value into the sentence of
the form 'It is -- that \(p\)' may alter the
truth value of the latter sentence. Prior's answer--and in a
sense it amounts to a rejection of the question--is that modal
functions take propositions as arguments, but propositions are logical
constructions. All sentences containing the word
'proposition'--including such sentences as 'A
modal operator expresses a function from propositions to truth
values'--mean no more and no less than sentences which
contain neither the word 'proposition' nor an equivalent.
In essence, Prior's view is that there are intensional contexts
but no intensions. For the last six years of his life he worked on a
book that was to give systematic expression to his views on
propositions. The incomplete manuscript, which Prior had entitled
*Objects of Thought*, was published posthumously in 1971.


### 2.3 Prior and Possible Worlds Semantics




Prior's detailed contributions to the development of modal
logic are legion. At least one aspect of his work has not received the
recognition it deserves. Several years ahead of Kripke, Prior and his
collaborator Carew Meredith invented crucial elements of the possible
worlds semantics for propositional modal logic, including the
all-important binary relation, which opens the way to modelling systems
of different strengths. Meredith was a lecturer in mathematics at
Trinity College, Dublin; his interest in logic had been stimulated by
the arrival of Lukasiewicz in Dublin shortly after the second
world war.




Prior foreshadowed his later work on possible worlds semantics in
*The Craft*. Discussing work by Boole, he wrote:



> 
> 
> 
> What Boole was after might perhaps have been plainer if he had said
> something like this: There is one 'hypothetical Universe',
> which contains the totality of what we might call possibilities, or if
> you like, 'possible worlds'. (1951: 462.)
> 
> 
> 




Then in the penultimate chapter of *The Craft* he said:



> 
> 
> 
> For the similarity in behaviour between signs of modality and signs
> of quantity, various explanations may be offered. It may be, for
> example, that signs of modality are just ordinary quantifiers operating
> upon a peculiar subject-matter, namely possible states of affairs
> ... It would not be quite accurate to describe theories of this
> sort as 'reducing modality to quantity'. They do reduce
> modal *distinctions* to distinctions of quantity, but the
> variables to which the quantifiers are attached retain something modal
> in their signification -- they signify
> 'possibilities', 'chances', 'possible
> states of affairs', 'possible combinations of
> truth-values', or the like. (1951: 736-7.)
> 
> 
> 




As sources for these ideas Prior cited John Wallis (a seventeenth
century mathematician) and the account of logically necessary and
logically impossible propositions given by Wittgenstein in the
*Tractatus* (1951: 737). Interestingly, he mentioned Carnap only
in a footnote: 'Professor Carnap has a similar definition of
logical necessity in terms of what he calls
"state-descriptions"' (ibid). Prior did not refer to,
and presumably had not at that time read, Carnap's 1946 paper
'Modalities and Quantification', which attempted a
semantics for quantified S5 in terms of state-descriptions. (A
state-description is a class of sentences satisfying certain
conditions; each state-description represents a possible state of
affairs.) Carnap too cited the *Tractatus* account of modal
propositions as his inspiration (1946: 47).




Prior goes on in *The Craft* to defend his account of
modality as quantification over possible states of affairs against
various alternatives, for example the Andersonian account, according to
which 'Every table here is necessarily brown' means
'There is a property which every table here in fact possesses,
and of which it is true that everything that possesses it is in fact
brown'. John Anderson, Professor at the University of Sydney, was
a leading figure in the development of philosophy in Australasia.




In 1956 Prior wrote up (and circulated in mimeograph form) his and
Meredith's formal work on what he later described (1962a: 140) as
the 'logic of world-accessibility', in a paper entitled
'Interpretations of Different Modal Logics in the "Property
Calculus"' (Meredith and Prior 1956, first published in
Copeland 1996). It carried the attribution 'C.A.M., August 1956;
recorded and expanded A.N.P.'. Prior mentioned this paper in
*Past, Present and Future* (1967: 42-5) and in his 1962 articles
'Possible Worlds' and 'Tense-Logic and the Continuity
of Time'. The paper seems to have been the earliest to employ a
binary relation between points in order to discriminate between S5 and
weaker systems, the points being regarded as possible states of
affairs. Carnap's pioneering 1946 paper concerned only S5 and
contained no such relation.




The property calculus is essentially a variation of Prior's
1954 \(l\)-calculus described above. In the \(l\)-calculus,
tense-modal propositions are treated as predicates expressing
properties of dates, and quantification theory is supplemented with
various special axioms for a binary relation '\(l\)'
taking dates as arguments. In the modal version of the calculus,
sentences of modal logic are treated as if they express properties of
certain objects \(a, b, c\), etc. Objects are
related by a binary relation \(U\). In their 1956 paper Prior and
Meredith supplied no account of what a formula of form
'\(Uab\)' might express. They gave the following
definitions of necessity \(\Box\) and possibility \(\Diamond\), where
'\(pa\)' indicates that object \(a\) has the
property expressed by the sentence \(p\).




\[\begin{align}
(\Box p)a &= \forall x(Uax \rightarrow px) \\
(\Diamond p)a &= \exists x(Uax \amp px).
\end{align}\]



(Following Lukasiewicz, Prior and Meredith themselves used
'L' in place of '\(\Box\)' and 'M'
in place of '\(\Diamond\)'.) Their calculus consisted of ordinary
quantification theory supplemented by these definitions, together with
certain axioms governing the relation \(U\)--see
below--and the following clauses:



\[\begin{align}
(\neg p)a &= \neg (pa) \\
(p \rightarrow q)a &= (pa) \rightarrow (qa). 
\end{align}\]



It is implied in the 1956 paper that a proposition \(p\) is to
be called a theorem of the calculus if and only if \(pa\) is
provable for an arbitrarily chosen object \(a\).




Axioms for \(U\) are selected from a list containing (among
others):





1. \(Uaa\) \((U\) is reflexive)




2. \(Uab \rightarrow (Ubc \rightarrow Uac)\)
(\(U\) is transitive)




3. \(Uab \rightarrow Uba\) (\(U\) is symmetrical).





Axiom 2 was also present in the 1954 \(l\)-calculus.




Prior and Meredith stated in their 1956 paper that the distribution
principle \(\Box(p \rightarrow q) \rightarrow 
(\Box p \rightarrow \Box q)\) is a theorem in the
absence of any special axioms for \(U\); that \(\Box p \rightarrow p\) is a theorem if axiom 1 is imposed; that axiom 2
gives the S4 principle \(\Box p \rightarrow \Box \Box p\); and that 2 together with 3 give the S5
principle \(\Diamond \Box p \rightarrow \Box p\). Their
approach was proof-theoretic in its basic orientation and they offered
no completeness results. In (1962a) and (1962b) Prior extended this
approach to systems between S4 and S5, and to systems independent of S4
between T and S5.




What of the meaning of the binary relation \(U\)? As previously
remarked, the idea that the variables of quantification of the calculus
should range over possible states of affairs or possible worlds is
present in *The Craft*. In 1960, following a suggestion by
Geach, Prior began thinking of \(U\) as a relation of
*accessibility* between worlds. Prior tells us that Geach cashed
out the notion of 'reaching' one world from another in
terms of 'some dimension-jumping vehicle dreamed up by science
fiction' (1962b: 36; see also 1962a: 140). (Geach referred to the
whole business as 'Trans World Airlines'.) With this
interpretation of \(U\) to hand, the property calculus can be
viewed as treating \((\Box p)a\) -- or
'Necessarily\(-p\) in world \(a\)' -- as
short for '\(p\) is true in all worlds accessible from
\(a\)'.




Lemmon, in a draft of material intended for his and Dana
Scott's projected book 'Intensional Logic',
mistakenly credited Geach with the idea that the binary relation
'may be intuitively thought of as a relation between possible
worlds'. In a letter to Scott, written after Lemmon's death
in 1966, Prior remarked: 'What Geach contributed was not the
interpretation of \([U]\) as a relation between worlds (God knows
when *that* started), but the interpretation of \([U]\) as
a relation of accessibility'. When Prior said 'God knows
when *that* started' he was presumably referring to the
idea that the 'objects' of the calculus be regarded as
possible worlds. He was right to think that the history of this idea is
a tangled one. Priority is often assigned to Leibniz, but scholars have
traced the idea back to Duns Scotus and William of Ockham (Knuuttila
1993).




It seems that the binary relation first made its appearance in a
1951 article by Jonsson and Tarski, 'Boolean Algebras with
Operators'. In their Theorem 3.14 they established that every
closure algebra is isomorphic to an algebraic system formed by a set
and a reflexive and transitive relation between its elements; their
Theorem 3.5 considered also a symmetry condition. In hindsight, these
theorems (which explicitly concerned boolean algebras) can be viewed as
in effect a treatment of all the basic modal axioms and corresponding
properties of the accessibility relation. Concerning this article, Saul
Kripke remarked (in Copeland 1996: 13):



> 
> 
> 
> Had they known they were doing modal logic, they would have had the
> completeness problem for many of the modal propositional systems
> wrapped up, and some powerful theorems. Mathematically they did this,
> but it was presented as algebra with no mention of semantics, modal
> logic, or possible worlds, let alone quantifiers. When I presented my
> paper at the conference in Finland in 1962, I emphasized the importance
> of this paper. Tarski was present, and said that he was unable to see
> any connection with what I was doing!
> 
> 
> 




During the next eight years the binary relation was reinvented by a
number of logicians. Prior, in his address to a conference in
Wellington in 1954, seems to have been the first to use the binary
relation in an explicitly tense-modal context. Other landmarks were an
address by Montague to a conference held at UCLA in 1955
(Montague's binary relation held between models rather than
points or indices interpretable as worlds, and the notion of a possible
world was absent), Prior and Meredith's property calculus of
1956, lectures by Smiley in Cambridge in 1957 (Smiley pursued an
algebraic approach), Kanger (1957), Hintikka (1957, 1961) and Kripke
(1959a, 1959b, 1963). Kripke was familiar with Kanger's work
involving the binary relation at the time he obtained his own results.
Kanger himself had read the 1951 paper by Jonsson and Tarski and he
described his results as similar to theirs (Kanger 1957: 39). (Copeland
(2002) gives a detailed history of possible worlds semantics.)




To the modern eye, Prior's 1956 possible worlds semantics looks
familiar yet also strange. There is no semantic ascent, and there are
no frames, models, valuations, satisfaction clauses or truth
conditions. Prior's modal semantics belongs to a pre-modern era,
the era of 'translational' semantics, a type of semantics
that pre-dated the meteoric rise of Tarski-style truth-conditional
semantics in the 1960s and 1970s (Copeland 2016). A translational
semantics translates the targeted sentences into a more illuminating
language, such as Prior's enriched predicate calculus. For
anyone who understands Prior's augmented predicate calculus, his
translational clauses, such as \((\Diamond p)a = \exists x(Uax \amp
px),\) offer both an explanation of the meanings of the modal
operators and an account of how the meanings of complex sentences
(e.g. the S4 and S5 axioms) arise recursively from the meanings of
their parts.


### 2.4 Prior and Kripke




Kripke first became interested in modal logic in 1956, as a result
of reading Prior's paper 'Modality and Quantification in
S5' (Prior 1956a). Kripke was at this time still at high school,
working on logic in almost complete isolation in Omaha, Nebraska. In
1958, he read *Time and Modality* and was impressed by the
parallel Prior drew between tense and the alethic modalities.




At almost exactly the same time, Prior was reading Kripke's
first paper, 'A Completeness Theorem in Modal Logic'
(Kripke 1959a), in his capacity as referee for the *Journal of
Symbolic Logic*. In this paper Kripke stated and proved a
completeness theorem for an extension of S5 with quantifiers and
identity; the binary relation made no appearance. His first publication
to mention the binary relation--which he interpreted as a relation
of relative possibility between worlds--was written in 1962 and
appeared in 1963 (Kripke 1963); the paper contained completeness proofs
for propositional \(M\), S4, \(B\), and S5. Kripke reported
(in correspondence with Copeland) that the idea of the binary relation
occurred to him much earlier than 1962, in fact shortly after his paper
on S5 was first submitted in the spring of 1958.




By the late summer of 1958, Kripke had a completeness result for S4.
On 3 September 1958 he wrote to Prior, mentioning his work on
semantical completeness theorems for quantified extensions of S4 with
and without the Barcan formula (Marcus 1946, 1962). (Prior himself had
already given an early counterexample to the Barcan formula in a
tense-modal context (Prior 1957: 26, Copeland 2016).) In his September
letter, Kripke gave a branching-time matrix, characteristic for S4.
This is essentially a tense-logical interpretation of the reflexivity +
transitivity semantics for S4. He wrote:



> 
> 
> 
> in an indetermined system, we perhaps should not regard time as a
> linear series, as you have done. Given the present moment, there are
> several possibilities for what the next moment may be like--and
> for each possible next moment, there are several possibilities for the
> moment after that. Thus the situation takes the form, not of a linear
> sequence, but of a 'tree'.
> 
> 
> 




(Some of the Kripke-Prior correspondence is now published in
Ploug and Ohrstrom 2012.)




There was a two-way traffic of ideas. A constant domain was assumed
in Kripke's 1959 'A Completeness Theorem in Modal
Logic', and Kripke suspects that *Time and Modality* first
interested him in the problem of treating variable domains. He worked
on Prior's suggestion--formalised in Prior's system
\(Q\)--that variable domains might lead to truth-value gaps
even at the level of propositional logic, although Kripke did not
pursue this approach in his published material. Further, Kripke thinks
it probable that Prior's work on many-valued matrices in *Time
and Modality* gave him the idea of converting possible worlds
models into many-valued matrices, an approach he followed in his 1963
paper 'Semantical Analysis of Modal Logic I: Normal Modal
Propositional Calculi'.


## 3. Life and Philosophical Development


### 3.1 Launching Out




In 1932, at the age of 17, Prior left his home town, sleepy
Masterton in the North Island of New Zealand, to become a student at
the University of Otago in the South Island city of Dunedin. He seemed
to prefer the South Island, saying the North Island gave him 'the
willies'. The son of a doctor, he initially planned a career as a
biologist, but was soon beckoned away by theology and philosophy,
graduating from Otago in 1935 with a B.A. in philosophy. At Otago he
had thoughts of entering the ministry of the Presbyterian Church, and
he was accepted into the required program of study. 'Who',
he had asked himself in a 1931 manuscript, 'are the greatest
thinkers the world has known?'--answering 'I have no
hesitation in placing JESUS OF NAZARETH at the top of this list'
(Prior 1931: 107). In 1936, he abandoned the idea of entering the
ministry, although he did subsequently work for a time as a locum
minister in Birmingham, England, during his 'bohemian
period' at the end of the 1930s.




It was John Findlay, Professor of Philosophy at Otago, who
introduced Prior to logic. Findlay, a contemporary of Gilbert Ryle and
William Kneale, had studied at Oxford and at Graz; his influential book
*Meinong's Theory of Objects and Values* was published
during Prior's second year at Otago. Under Findlay's
direction, Prior studied the 18th century British moralists
and cut his teeth on W.E. Johnson's classic text *Logic*.
It was Findlay who first aroused his interest in the history of logic.
In correspondence, Prior described Findlay's Otago lectures as
'thrilling', and remarked that his offprint of
Findlay's 1936 article 'Relational Properties' was
one of his 'most valued literary possessions'. In 1949 he
wrote of Findlay, 'I owe to his teaching, directly or indirectly,
almost all that I know of either Logic or Ethics' (1949: xi), and
he was later generously to describe Findlay as 'the founding
father of modern tense-logic' (1967a: 1).




In 1936, the year following his graduation, Prior married. It was a
whirlwind romance. In a letter written at the beginning of June 1936,
he said he was 'taking an interest in a rather desperate & in
some ways rather dangerous little friend', adding that he had
been solemnly advised 'not to fall in love' with her. The
rather dangerous Clare Hunter, an up-and-coming freelance reporter for
the *Otago Daily Times*, was a feminist and free thinker. She
encouraged Prior in what he called his 'innate
Bohemianism'. Before July was out, the two were planning to
'get quietly married at the end of the year', wrote Prior.
This must soon have seemed too long a wait, for they wed the very next
month. (There is a thumbnail biography of Hunter in Grimshaw
(2018).)




Prior gained his M.A. in philosophy in 1937. His thesis, criticizing
various philosophical approaches to logic, involved him in reading
'a lot about Wittgenstein & certain kindred writers',
including Karl Popper. But the thesis was awarded only a second by the
external examiner. Fortunately, Findlay knew a budding logician when he
saw one, and secured Prior a one-year assistant lectureship at Otago.
During the 1937 academic year Prior gave courses on logic, ethics, and
probability theory. Findlay pressed him to contribute to the
*Australasian Journal of Psychology and Philosophy*, and
Prior's 'The Nation and the Individual' (influenced
by John Wisdom) became his first published paper in philosophy, in
December 1937. (Prior's earlier theological writings are
discussed in Hasle (1999) and (2012), Grimshaw (2002), and Jakobsen
(2012) and (2016).) Prior mentioned 'The Nation and the
Individual' and its origins in a 1937 letter:



> 
> 
> 
> The view of Philosophy as 'analysis' (to which
> Wittgenstein & co. have made important contributions) has proved
> remarkably fruitful in the fields of Logic, Ethics, Physics, Psychology
> & Metaphysics; but I would like to see it applied--& I
> think it is capable of very fruitful application--in Theology,
> Sociology, Economics & Political Ethics. ... I'm
> ... trying a little work along those lines at present
> myself--figuring out the consequences of treating a Nation as what
> these champions of 'Analysis' call a 'logical
> construction'.
> 
> 
> 


### 3.2 Religious Journalist




At the end of 1937 Prior set aside thoughts of an academic career

and travelled to Europe with Clare, spending three bohemian years

there. They planned to earn a living from freelance writing; Arthur

wanted to gain 'a footing in the English literary world'
(as he wrote to the New Zealand poet Ursula Bethell), and said he had
'hopes of ending up eventually as the editor of a religious
periodical'. This interlude in Europe, and its aftermath in New
Zealand, was a critical period in Prior's development--the
crucible in which the mature thinker was formed. His social and
political philosophy settled firmly to the far left, but ultimately
fell short of Marxism; his pacifism escalated, only to be overturned by
world events; and his theism began to wane into unbelief.




January 1938 saw the couple boarding the Orient Line's S.S.
*Ormonde* in Sydney, carrying large rucksacks. The
*Ormonde* was bound for London via Colombo, Suez, Naples and
Toulon. In Colombo, Prior took the opportunity to visit 'a Hindoo
temple, a Buddhist one, a Mahommedan mosque, a Roman Catholic church
& an Anglican church'. He was, at this stage of his life,
obsessed with religion. He believed in the virgin birth and the voice
of the devil, and was a devout Presbyterian (Prior 1940). His
impressions after his first encounter with extreme religious diversity
were, he said, 'very vivid, but very confused'. He
described the Anglican church as 'a foreign growth', and
what he called 'the R. C. place' was, he said, not
'sufficiently distinguishable from the idolatries around
it'. He decided that 'Buddhism was a much saner sort of
religion than either Hinduism or Mohammedanism', and that
'the Mahommedans are a particularly arrogant crowd, &
obviously think they're the lords of creation'.




Prior mused in a letter, 'Ought I not to be trying to do a bit
of "witnessing" to these crowds of heathen?' Several
of his early publications were given over to propounding the Christian
message: the Christian God, he wrote, is 'the Lord God
Omnipotent, the High and Holy One who inhabiteth ETERNITY, absolutely
independent of all being other than himself, and Creator, Lord and
Judge of all' (Prior 1934).




In later life, however, he described himself as having 'no
religious beliefs' (Prior c.1967). In 1961, when Max
Cresswell--then a logic student aged 21--met him for the
first time, in Manchester, Prior announced: 'Mr Cresswell,
isn't it a pity that God does not exist'.


### 3.3 First Taste of Europe




The Priors disembarked from the *Ormonde* in France. They
planned to sleep out, but with winter fading into spring they soon
tired of it, and moved into a small apartment in the village of
Roquebrune, on the south coast. They ended up staying several months.
Arthur liked France, saying 'It's the Reddest country
we've been in so far'. Clare worked as a baker in a cake
shop while Arthur translated essays by the French philosopher Georges
Sorel. They swelled their meagre income by gambling at nearby Monte
Carlo. '[W]e play very cautiously', Arthur
said--'we're a few hundred francs up'.




A short visit across the border to Hitler's Germany left Prior
aghast. 'We got out of the place as fast as we could', he
said: 'the general mental atmosphere is just one big Hell'.
At Roquebrune he met a young German backpacker, a Lutheran, pleasant
and mild of manner, according to Prior, but pro-Hitler and virulently
anti-Jewish--the German responded with 'a queer look'
when Prior 'told him that if I was in Germany I would be a member
of the Bekenntniskirche', the anti-Hitler, Barth-inclined German
Confessional Church. The Priors also visited Austria, not long after
the March 1938 *Anschluss* (union) with Germany. Horrified by
the rampant anti-semitism they found there, they wrote an article about
the plight of the Austrian Jews for the *Otago Daily Times*,
under Clare's nom de plume 'John Everdean'. They
reported that posters bearing slogans like 'You will never get
clean milk if you get it from Jews' were ruining Jewish
businesses, and Jewish shops had a 'dirty yellow placard pasted
across the door', warning customers away (Everdean 1938).




Prior anticipated his arrival in England with mixed feelings. He had
experienced the English at close quarters aboard the *Ormonde*:
they 'stink with Race Prejudice', he wrote. His experiences
on the boat had he said taught him that he liked 'Americans
better than Englishmen'--and 'Australians better than
New Zealanders'. It was in the early summer of 1938 that the
couple crossed the English Channel and settled in London. Whether the
reality was better or worse than Prior's expectations is hard to
say. He certainly found 'abominable race-prejudice', and
politically there was also 'plenty to disgust us'--as
well as 'the extraordinary backwardness of England as compared
with N.Z.'.




'England's a country that fills one with a kind of
impotent and maddening despair', he said. But he also emphasized
that 'London *is* the place to meet worth-while
people', saying not very long after he arrived, 'We have so
far been much more "successful" in London than we ever
expected'. There was also a disappointment awaiting him: the SCM
Press had declined a book manuscript on theologian Karl Barth he had
sent to them just before leaving New Zealand. Next he tried T. & T.
Clark, but the book never did see the light of day.




Prior was soon contributing reviews to a handful of magazines,
including *The Student Movement* and the left-wing feminist
weekly *Time and Tide*. The snag was that his work was usually
unpaid--but he was allowed to keep the books he reviewed and he
sold them at half-price. Things looked up when T. S. Eliot gave him a
'decent payment' for two reviews in the literary magazine
*The Criterion*. (Prior found Eliot 'decidedly on the old
side' and 'very shy & quiet'.) But money was
always tight. Eventually Clare started taking in typing and Arthur
found temporary clerical work in the Examinations Department of London
University (Prior 1941).


### 3.4 Politics




At first, the Priors lived in a handsome Georgian hotel close to the
famous libraries of the British Museum and University College, but they
quickly moved into cheaper accommodation in Lambeth. They were a short
stroll from the bustling working-class street market of Lambeth Walk,
and not far from overcrowded and insanitary slums. No doubt Lambeth
reinforced the views Arthur had expressed the year before in the
*Otago Daily Times*, under the pseudonym 'Independent
Labour': 'We must all fight either with the wage-earners
for a society of wage-earners or with the profit-seekers for a society
of profit-seekers'. For Arthur the 'fundamental
question' was: 'Are the workers going to group together to
organise and undertake their own enterprise, or are they going to be at
the beck and call of a privileged class' (Prior 1937a).




He saw London through socialist eyes. The streets 'are full of
beggars', he wrote to his cousin Hugh Teague: 'blind men,
paralytics, pavement artists, organ grinders, Welsh miners'. He
gave the Red salute to the miners (who were fleeing in their thousands
from devastating unemployment in Wales) and found they returned it
'with great gusto'. The previous year he described his
'thinking on social questions' as owing 'a great
deal' to the Trotskyist writings of Auckland philosopher William
Anderson and also to the writings of the Marxist-Leninist thinker
Sorel, whose essays he translated at Roquebrune. He said he learned
more from Sorel 'than from any other Marxist
theoreticians'. Like Sorel, he saw the importance of 'the
substitution of a "producer-mentality" for an
"employee-mentality" among the workers':
England's problems, Prior said, included the 'servility of
the English masses' and 'their almost unbounded willingness
to "keep their place"'.




He told Hugh: 'I personally get much the same kind of
"kick" out of reading Lenin at his best, as I do out of
reading some of the tough & argumentative old Scottish
Calvinists--John Knox and the rest'. Prior remained strongly
left-wing for the rest of his life, but his flirtation with communism
was over by 1946. In that year he wrote to his friend Lex Miller,
saying he had been 'released' from 'a sort of complex
that I have had about Marxism right up till now, a kind of inward
bondage to it despite all my points of difference from it, based on the
feeling that though its philosophy might be abominable its economics
were unanswerable.'




As Prior explained to Miller, he now saw that 'the Marxists
were guilty of an economic fallacy':



> 
> 
> 
> all this business about capitalism involving a
> 'contradiction' seems to be just hooey ... I write, of
> course, with the zeal of a convert; or more accurately with the
> indignation of a man who has just discovered that he has been
> hoodwinked for years.
> 
> 
> 




In February 1939, Arthur summed up his and Clare's situation
in London: 'I'm afraid we haven't acclimatised
ourselves to the ways of England', he wrote: 'We've
no desire to be back in N.Z., but there's a lot over here that
it's hard to stomach'. Worse, war was approaching. During
the Munich crisis, in the autumn of the previous year, Clare had
watched sandbag air-raid shelters being constructed across London, and
she saw long queues everywhere as people waited to get gas masks
fitted. She was (she wrote) 'half-expecting to hear any moment
the noise of thunder as planes filled the air' (Everdean
1938a).




Hitler invaded Czechoslovakia in March 1939, and in July Arthur
wrote about the plight of Czech refugees in the weekly newspaper
*The Christian World* (Prior 1939). The Priors had been involved
for some time in aiding refugees, and they applied for a job that
Arthur called 'tutor-&-mother-superior' at a small
hostel in the East End, caring for Jewish children fleeing Austria. It
was, he said, 'a very bitter disappointment' when they did
not get the job.




As Europe sank into war, the Priors were ardent pacifists. Not long
after their visits to Germany and Austria, and as the Spanish Civil War
raged, they joined the pacifist organisation Pax. New Zealand writer
Dan Davin--who described the prewar Prior as resembling Welsh poet
Dylan Thomas--spent some time with him in Oxford during the weeks
before Britain's declaration of war on Germany, saying that Prior
would argue for long hours about pacifism in Oxford's 'Lamb
& Flag' pub (Kenny 1971).




When Britain finally lurched onto a war footing in September 1939,
Prior found doubts about his pacifism creeping in: 'I must
confess my pacifism was a little shaky round about that time', he
wrote in December. 'I was sure enough of my own duty not to join
up, but was hesitant to condemn the whole business'.


### 3.5 Personal Courage, Bleak Times




During the first months of 1940 Prior worked on what he described as
'a large book, on "The Theology of the Church of
Scotland"'. Life in London went on almost normally during
this time of Phoney War, but the situation worsened dramatically after
the fall of France in June. A German invasion of Britain seemed
imminent. Chillingly, Winston Churchill warned of the coming fighting
'in the fields and in the streets' (Churchill 1940/2007).
For the Priors, it was time to go home.




Once back on New Zealand soil, Prior met with criticism and
hostility for failing to stay and play his part in the war. But the
journey home was certainly no cowardly retreat: more than 12,000 miles
of unfriendly ocean lay between the Priors and New Zealand. At the
beginning of August 1940, in Glasgow, they boarded an armed New Zealand
liner, the MV *Rangitiki*, bound for Wellington via the Panama
Canal. Their route lay across the North Atlantic, where German
submarines and aircraft had sunk a total of 81 civilian vessels during
the preceding two months, with a further 144 civilian vessels going
down in British coastal waters in the same period (Roskill 1954). There
were also armed German surface vessels preying on shipping in the
waters around New Zealand, even laying minefields in the approaches
(Waters 1956). During June-August these armed raiders sank
several defenceless ships close to New Zealand--news that, like
news of the Atlantic sinkings, could hardly have failed to reach the
Priors. All in all, it must have been a nerve-racking journey.




Luckily the voyage passed without incident, and in September the
Priors disembarked from the *Rangitiki* in Wellington. The ship
was not so fortunate on her return journey to England, when she was
attacked by a German battleship in the North Atlantic--in the same
month that her sister liner the *Rangitane* was sunk while also
en route from New Zealand to the UK. It had been a narrow escape for
the Priors. As they started to pick up the threads of life in
Wellington, the Luftwaffe's bombs devastated their previous home
of Lambeth.




The couple took an apartment in central Wellington, and in October
Arthur started teaching French, English and History at a secondary
school in the suburb of Rongotai. He gave this up in March 1941 and the
Priors returned to Dunedin, joining the household of fellow pacifists
Jack Brailsford and his wife Ruth--Arthur's 'Aunty
Ruth', who had cared for him when his mother died not long after
his birth. Jack, a conscientious objector in the first world war, had
been imprisoned for his pacifism in 1916 and was not released until
just before the end of the fighting in 1918 (Brodie 1999).




It was while the Priors were living with the Brailsfords that Clare
fell for their adopted Russian son Victor Roussin--at that time
known as Norman Brailsford--and her marriage to Arthur
disintegrated. Arthur, who did not want the relationship to end,
eventually fled to Christchurch. The divorce became final in March
1943. What might have been a lengthy period of sadness for him was cut
short in January of that year. He met Mary Wilkinson, the daughter of a
Presbyterian minister, while attending a Student Christian Movement
conference in Christchurch. They said afterwards that it was love at
first sight. 'We got engaged after meeting four times',
Mary remembered. The marriage began in October 1943 and lasted for the
rest of Arthur's life.




During 1941 Arthur had come to view his pacifism as untenable,
though in December he wrote two letters to the *Otago Daily
Times* defending 'liberty of conscience' and the right
to be a conscientious objector. In January 1942, while he and Clare
were still living with the Brailsfords in Dunedin, Arthur was called
up, and instead of appealing for conscientious objector status himself,
he applied to enlist in the Royal New Zealand Air Force (perhaps
because, under the regulations in force at that time, such an appeal
would have required him to say 'that it is wrong to engage in
warfare in any circumstances'). There is no evidence that
Clare's pacifism had also weakened, and Arthur's thinking
was manifestly undergoing other fundamental changes at this time. His
enlistment papers contained the brief but telling entry
'Religion: Atheist'. It seems that a philosophical and
spiritual chasm had opened up between him and Clare.




The Air Force finally embraced him in November 1942 and he became a
wireless mechanic, servicing aircraft radio equipment in New Zealand
until January 1945, when he was posted to the New Hebrides islands (now
Vanuatu), some 2000 miles to the north of New Zealand. There he
remained until the Pacific war ended, returning to New Zealand in
October 1945.


### 3.6 New Man




With his second marriage, Prior changed. He became 'secure and
serene' (Kenny 1971). The rather priggish young man disappears
from his letters and a more mature, more lovable Prior emerges. In
November 1945, he applied for a temporary lectureship at Canterbury
University College, in Christchurch, a vacancy created by
Popper's departure. By now he had a further three articles in the
*Australasian Journal of Psychology and
Philosophy*--'Can Religion be Discussed?' (1942),
'The Meaning of Good' (1944), and 'The Subject of
Ethics' (1945)--and with a strong recommendation from
Findlay, he got the job. Prior started work in February 1946, on a
salary of PS600 a year. It was a new beginning.




At Canterbury he was thrown entirely on his own resources, being as
he put it 'the only philosopher about the place'. Prior
bore the responsibility for providing a broad and balanced philosophy
curriculum, yet his own formal education in philosophy had stopped
short nine years previously. His one recourse in the face of isolation
was to read, and read he did. In logic he began by returning to W.E.
Johnson. Next came J.N. Keynes's *Studies and Exercises in
Formal Logic* and then (in his own phrase) he got stuck into
*Principia Mathematica*. He learned a lot about the history of
the subject from Peirce, whom he found 'unexpectedly
magnificent'. An important discovery, in 1950, was
Bochenski's *Precis de Logique Mathematique*
(Bochenski 1949). Prior was fascinated by the 'very neat symbolic
notation' due to Lukasiewicz, and before long he turned his
back completely on the more usual Peano-Russell notation. In
Lukasiewicz's parenthesis-free notation, C\(pq\) is
written for 'If \(p\) then \(q\)', and Bochenski
was later to describe Prior as even more of a
'CCCC-logician' than he was himself.
Lukasiewicz's own *Aristotle's Syllogistic* and
Tarski's *Introduction to Logic* soon followed. By now the
logic bug had well and truly bitten. Prior saw from the work of the
Poles that formal precision is possible in philosophy and this
delighted him. The upshot of Prior's reading for the curriculum
was that his students learned Aristotelian and medieval logic, using
Polish notation and with Bochenski's *Precis de Logique
Mathematique* as a text. 'Despite the language difficulty, I
have found this a first-class textbook to accompany lectures to New
Zealand students', Prior declared (1952c: 35).




An exuberant, playful man of seemingly inexhaustible vitality, Prior
made an excellent teacher. He had no trace of pomposity or pretension.
His students appreciated the friendly welcome they would receive at his
home, not to mention his relaxed attitude toward the administrative
paraphernalia of roll-taking and the like. In those days Canterbury
University College was a formal, stuffy place and Prior was a breath of
fresh air. Formality made him impatient; and he despised people he
called 'bullshit artists' and 'dicky-lickers'.
In a milieu where jacket and tie were the norm--even in a
sweltering New Zealand summer--Prior would lecture in baggy khaki
shorts and roman sandals. His student Jim Wilson recalls the friendly
informality of Prior's first-year classes:



> 
> 
> 
> The strained precision of clock time was alien to him, so he was
> usually late for his own lectures (or anyone else's for that
> matter--he was very egalitarian about it). But he almost always
> turned up eventually, thinning hair blown vertical by his dash on his
> bike when he remembered the time. He would pull cycle clips off his
> trousers and plonk an ancient shopping bag on the desk in front of him.
> Out of this bag would come ... a cabbage, a bunch of carrots, a
> loaf of bread, a bottle of milk ... until, always at the bottom,
> he would find the book he was looking for. Back into the bag went the
> rest of the goodies, then he would look up at us, apologise for being
> late if he was more than usually so, and ask: 'Now where were we
> last time?' Someone in the front row would consult her or his
> notes--Arthur couldn't as he never had any--and would say
> 'You were just dealing with such and such'. 'Ah yes,
> thank you' Arthur would respond, and forthwith launch into an
> extempore exposition which followed on perfectly from the previous
> session and was beautifully structured and clear even though he was
> just thinking along with us. And of course we could stop him and ask
> for clarification or elaboration at any time, without in the slightest
> affecting the overall structure and direction of his thoughts.
> 
> 
> 




Soon after his discovery of *Precis de Logique
Mathematique*, Prior wrote to Bochenski in Fribourg and then, a
little later, to Lukasiewicz in Dublin. He was excited to receive
replies. 'We are, all of us, very isolated, being few and
scattered', wrote Bochenski. 'It is a real pleasure to
hear that a Colleague so far away is interested in the same problems
you are working at and that he finds one's little writings may
be of some use.' Thus began Prior's voluminous
correspondence with logicians the world over. There were other ways,
too, in which his isolation lessened. In 1951 he met and became
friends with John Mackie and Jack Smart, at a conference in
Sydney. This was Prior's first experience of being among a large
gathering of philosophers; Mary Prior described the conference as his
'entry into a wider world'. In the same year George
Hughes was appointed to the Victoria University of Wellington. Prior
and Hughes had to make the most of their all-too-infrequent meetings,
sometimes talking until the birds woke. Prior soon imparted his
enthusiasm for logic to Hughes.


 

Prior was also fortunate in having a number of excellent students
during these early years, among them Jonathan Bennett and Ronald
Butler: for Prior they were oases in the desert. In 1952, he gained an
assistant lecturer, Sandy Anderson, son of the Sydney philosopher John
Anderson, and following Prior's promotion to Professor later
that year, Philosophy became a department in its own right. Prior
argued successfully for a new permanent member of staff, and in 1954
J.M. (Michael) Shorter was appointed to a lectureship. The young,
Oxford-educated Shorter worked previously at Aberdeen University,
where Prior happened to be in touch with Polish logician
Wladyslaw Bednarowski.




Prior worked intensely, often all through the night. 1949 saw the
publication of his first book, a slim but potent volume titled
*Logic and the Basis of Ethics*. It was published by the
Clarendon Press and soon became prominent in Oxford. Austin liked it
and Ryle approved of 'Prior's complete lack of
mugwumpery'. In the Introduction Prior explained that by the
'logic of ethics' he meant 'not a special kind of
logic, nor a special branch of logic, but an application of it',
and the book is a vigorous examination of the arguments of each side in
the naturalism/anti-naturalism debate.



*Logic and the Basis of Ethics* contained no symbolism, and
Prior's phrase 'the logic of ethics' was little more
than a battle cry. The few technical concepts that he used all related
to syllogistic logic. It was not until 1952 that Prior began publishing
papers in symbolic logic--four of them, suddenly, in the same
year. At the unusually late age of 38 Prior had become a formal
logician. He wrote these papers while completing the manuscript of what
was intended to be his second postwar book, *The Craft of Formal
Logic*. This began life in 1949 as a Dictionary of Formal Logic,
but, at the advice of the Clarendon Press, Prior soon switched to a
more orthodox format.




His logical interests veered sharply while he was writing *The
Craft*. To sixteen chapters on the logic of categoricals,
hypotheticals, terms and relations, he added, almost as an
afterthought, one on modal logic and one on the axiomatic method. Prior
finished the manuscript in December 1951 and sent it to the Clarendon
Press; fourteen months later they wrote agreeing to publish the book if
Prior would both shorten it and give greater emphasis to modern logic.
He undertook to make the changes, but ended up writing a completely
different book. This was finally published in 1955 with the title
*Formal Logic*; it ran into a second edition in 1962.



*The Craft* was Prior's third book-length manuscript
that failed to make it into print. His manuscript on Barth had died the
death before the war, and his *The Theology of the Church of
Scotland* was a casualty when the Priors' Christchurch house
caught fire in 1949--the book's remains, 163 charred pages
of his handwriting, are in the Bodleian Library. (Scottish theology
nevertheless remained 'part of the mulch that nourished his
work', Mary Prior said.) *The Craft* survives intact in
the Bodleian, except for a few missing pages. Some parts of it were
published posthumously, under the title *The Doctrine of
Propositions and Terms*, but much of this fascinating manuscript
remains unpublished.



*Formal Logic* is steeped in Polish notation and the
axiomatic method, and typifies Prior's mature work. It teaches,
enthusiastically yet without fuss, that there was
life--fascinating life--before the here and now of logic.
What Prior once wrote admiringly of Lukasiewicz is no less true of
Prior himself: 'having done very distinguished work as a
mathematical logician in the modern style, [he] is at the same time
interested in the history of his subject ... and contrives both to
use modern techniques to bring out more clearly what the ancients were
driving at, and to learn from the ancients useful logical devices which
the moderns have in general forgotten' (1952c: 37).




After Findlay, Lukasiewicz was the greatest single influence on
Prior's development as a logician. Prior's 1952 review
article 'Lukasiewicz's Symbolic Logic' was one
of his first papers to make extensive use of symbolism. He there
discussed Lukasiewicz's book *Aristotle's
Syllogistic From the Standpoint of Modern Formal Logic* (published
in 1951) and two articles, 'The Shortest Axiom of the
Implicational Calculus of Propositions' and 'On Variable
Functions of Propositional Arguments'. The first of these
articles stimulated Prior's interest in economical bases for
propositional and pure implicational logics (initially aroused by his
study of Peirce) and the opening chapters of *Formal Logic* drew
heavily on Lukasiewicz's work in this area.




Prior seems first to have learned of Lukasiewicz through the
writings of his pupil Bochenski. Lukasiewicz had devised an
axiomatic treatment of Aristotle's reduction of the imperfect
syllogistic moods to those of the first figure, which Prior encountered
in Bochenski's *Precis*. This enchanted Prior. He
was taking his students through the derivations as early as 1951, and
summarized Lukasiewicz's system in the final chapter of
*The Craft*. Throughout the chapter he made extensive use of
Lukasiewicz's symbolic notation. 
It was Lukasiewicz's axiomatic treatment of traditional
logic that fully brought home to Prior the power of modern symbolic
methods. Moreover, it was probably his reading of Lukasiewicz that
made clear to him the fundamental importance of propositional logic.
'It seems that Aristotle did not suspect the existence of another
system of logic besides his theory of the syllogism',
Lukasiewicz had written, '[y]et he uses intuitively the laws
of propositional logic ...' (1951a: 49).
(Lukasiewicz's axiomatisation of the syllogistic
incorporated his own three-axiom formalization of propositional logic
(1951a: 80).)



In his review, Prior approvingly quoted
Lukasiewicz's assertion that 'the logic of the Stoics,
the inventors of the ancient form of the propositional calculus, was
much more important than all the syllogisms of Aristotle'
(Lukasiewicz 1951a: 131). In *The Craft*, propositional
logic is barely mentioned until the final chapter, whereas *Formal
Logic* begins with a thorough introduction to the subject. On page
3 of *Formal Logic* Prior stated that the logic of propositions
is 'basic, and the rest of logic built upon it'.


His interest in economical bases for propositional and pure implicational logics, initially aroused by his study of Peirce, was stimulated by Lukasiewicz's article 'The Shortest Axiom of the Implicational Calculus of Propositions', and the opening chapters of *Formal Logic* draw heavily on Lukasiewicz's work in this area.


### 3.7 Back to England




In 1954, Gilbert Ryle visited New Zealand. He brought Prior an
invitation to visit Oxford and deliver the John Locke lectures. Prior
arranged a twelve month leave of absence from Canterbury and arrived in
Oxford at the beginning of 1956. Rather quickly a small group began to
form around him: Ivo Thomas, John Lemmon, Peter Geach. (His meetings
with Prior were Lemmon's first introduction to modal logic.)
Hughes summarized the news arriving back home: 'this wild
colonial boy just hit Oxford and started to gather around him the main
people [interested in] logic, and he started to organise a lot of
parties, almost, for the serious doing of logic'. Prior kitted
out his tiny rented apartment with a toyshop blackboard and held open
house. On Mondays during Hilary and Trinity terms he lectured on modal
logic, his great passion, and on tense logic, his great invention. The
lectures were published the following year, under the title *Time
and Modality*.




In the summer break following the John Locke lectures, Prior
organised a Logic Colloquium in Oxford. Logic was deeply out of fashion
in 1950s Britain, and its practitioners were isolated and somewhat
demoralized. As Prior wrote shortly after the Colloquium, 'There
*are* logicians in England and Ireland; but it must be admitted
that they are somewhat scattered, and so far as I could gather they had
never had any general get-together' (1956b: 186). Prior's
Colloquium brought together Lemmon, Thomas, Geach, M. Kneale, W.C.
Kneale, M.W. Dick, Lewy, Smiley, Bennett, Lejewski, Faris, Nidditch,
Carew Meredith, David Meredith, and others. It was all a huge success,
and the Colloquium became a regular fixture. Through his John Locke
lectures, the Colloquium, and his numerous visits around the country,
Prior helped to revitalise British logic. The group he left behind saw
similarities between themselves and the close-knit group of researchers
that existed in Warsaw before 1939.




It was no doubt with mixed feelings that he returned to New Zealand.
After twelve months of logical companionship on a grand scale, life at
Canterbury was a lonely prospect. Seething with enthusiasm for logic,
he threw himself once more into a massive correspondence, but it could
no longer satisfy him. Prior pined. When the offer arrived of a newly
established second chair at the University of Manchester, he snatched
it up. The Priors left New Zealand again in December 1958.


### 3.8 Religion




As well as Prior's journeyings between the hemispheres, there
was his seemingly complicated inner journey from religious believer to
non-believer. The inner journey, which is not easy to chart, was
complete by the time he arrived in Manchester, and seems to have taken
many years. It may have begun in 1941, with Prior's developing
interest in psychoanalytic explanations of the origin of religious
beliefs (a topic first alluded to in Prior (1935)). In his September
1942 publication 'Can Religion Be Discussed?'--a
dialogue between five characters named Barthian Protestant, Modernist
Protestant, Catholic, Logician, and Psychoanalyst--Prior gave the
closing speech to Psychoanalyst, who explains that circumstances may
'push' a believer into



> 
> 
> 
> an emotional crisis in which they will go mad unless they do
> something about it, and then in the painful process of their own
> analysis they will see for themselves the roots of their urge to
> believe. Only in this way are genuine atheists made. (Prior 1942a:
> 150)
> 
> 
> 




If these remarks were autobiographical there is no hint of it within
the article. But Prior was more forthcoming in an unpublished
seven-page manuscript dated 25 March 1942 (Prior 1942b, Jakobsen 2016).
There he made it clear that he no longer considered himself a
Christian, speaking of his 'Christian days' in the past
tense, and denying that his ongoing interest in theology was a
'relapse into Christianity'.




In 'Can Religion Be Discussed?' Prior made Psychoanalyst
say 'it's the religious illusion that's
irresistible', and in the 1942 manuscript he stated bluntly that
'Theology is an illusion', adding 'but it is an
illusion that is somehow "close to life"'. In this
manuscript he mentioned Freud by name several times; and in a
typescript concerning the application of Freudian theory to religion,
possibly also written in 1941 or 1942 (Prior n.d.c., Hasle 1999, 2012),
Prior explored 'the hidden non-religious basis and source of all
religious worship'. He spoke of 'breaking the religious
spell' and of 'the subconscious roots of religion'
being 'laid bare'. The 'Being' that the
religious 'refer to as the real object of worship' is,
Prior suggested, 'all the time a fiction'.




Prior's position at this point, then, was seemingly that
religious discourse is a form of fictional discourse--although the
fiction is 'close to life'. He also appears to have thought
that believers utilize what Psychoanalyst calls 'tricks' in
order to prevent knowledge of the subconscious origins of this fiction
from reaching their consciousness, and so breaking the religious spell
(Prior 1942a: 146-7).




Prior soon retreated from this leap toward unbelief. According to
his military record, he was a 'Presby' (Presbyterian) again
by about 1944. But although his scepticism born of psychoanalysis had
weakened, it seems this was eventually replaced by philosophical
scepticism of a more ordinary sort. The New Zealand philosopher Jim
Thornton, who was Prior's student during the period
1949-1953, recollected that 'at the time when I was one of
his senior students I got the impression that he thought Hume's
scepticism on religious belief was impressive'. Thornton
continued 'He enjoyed drawing our attention to Hume's irony
in various passages in the *Dialogues Concerning Natural
Religion*, and also in the closing paragraph of the essay *Of
Miracles*':



> 
> 
> 
> Mere reason is insufficient to convince us of its veracity: And
> whoever is moved by Faith to assent to it, is conscious of a continued
> miracle in his own person, which subverts all the principles of his
> understanding, and gives him a determination to believe... (Hume
> 1777, 10.101)
> 
> 
> 




Despite his liking for Hume's scepticism, Prior took the
serious step in 1951 of becoming an elder of St Martin's
Presbyterian Church in Christchurch. Elders are responsible for the
spiritual oversight of the congregation, and he was assigned a
'district' of perhaps 15-20 households drawn from the
congregation, and was expected to visit each of them regularly.
Whatever his philosophical doubts may have been, Prior was now a pillar
of the Presbyterian community. 'Lord, I believe; help thou mine
unbelief!' he had made his Barthian Protestant character say in
1942.




1956, the year of Arthur's sabbatical in Oxford, seems to have
been a turning point. Perhaps sheer distance helped to loosen
religion's tug, not only on him but also on Mary. Once back in
New Zealand, the family's churchgoing was much less regular.
Speaking of this time, their son Martin said 'I think Mary and
Arthur were starting to lapse in their beliefs'. Arthur continued
as an elder at St Martin's, officially until he left the country
for Manchester in December 1958, but ceased attending the monthly
meetings of elders from April 1958--and contrary to custom, did
not even bother to send in his apologies for the meetings that he
missed.




Robert Bull, who was Arthur's student from 1957, remembered him taking
his church duties flippantly. On one occasion Arthur broke off a
conversation about logic with a puckish 'I've got to go and
deliver the fucking communion cards'. Mary laughed, exclaiming
'Arthur!'. The cards were invitations to the communion
service and, as an elder, he was obliged to deliver one to each person
in his district. By this time, the Priors' religious observance
was probably just a matter of not wanting to upset the boat--and
perhaps especially not the Reverend Frank Wilkinson, Mary's
father.




Once the Priors were in Manchester, churchgoing became a thing of
the past.


### 3.9 Last Years




Prior was at Manchester for seven years. In 1966, Anthony Kenny
recommended him for a fellowship at Balliol. The move would mean a drop
in both status and salary, not to mention an increase in teaching, but
Prior did not hesitate. His sabbatical in Oxford had been one of his
happiest years. 'This is the good life', he told George
Hughes once he was settled in at Balliol. He felt he simply belonged.
Prior soon built up a reputation for being one of the best teachers in
Oxford--though his students were sometimes surprised to be given
eighteenth century moralists to read instead of books by the currently
fashionable.




Just before his departure from Manchester, Prior told Tom Richards,
a visiting New Zealander, that he was going to Oxford with a mission.
Prior's own work was an exemplary fusion of philosophy and logic,
and he went to Oxford with the intention of interesting the
mathematical logicians in philosophy and the philosophers in
mathematical logic. The time was right; and Prior spared no energy in
preaching his message:



> 
> 
> 
> [F]ormal logic and general philosophy have more to bring to one
> another than is sometimes supposed. I do not mean by saying this to
> underrate the work of those who have explored the properties of
> symbolic calculi without any concern as to what they might be used to
> mean ... Nor do I mean to underrate what recent philosophers have
> done in the way of exploring the obstinate and intricate
> 'logic' embedded in common discourse, even when they have
> not derived or sought to derive anything like a calculus from it
> ... But these activities are, or can be, related to one another
> very much as theory and observation are in the physical sciences; and I
> must confess to a hankering after well-constructed theories which much
> contemporary philosophy fails to satisfy. (1957: vii.)
> 
> 
> 




Prior did not live to enjoy the *entente cordiale* between
philosophy and logic that he helped usher in. His health began to let
him down during his second year at Balliol. He was found to have both
angina pectoris and polymyalgic rheumatism. During the autumn of 1969
the rheumatism grew steadily worse. He was at this time on sabbatical
at the University of Oslo. The pain left him with no zest for work. He
dutifully gave his weekly seminars and spent the remainder of his time
brooding savagely on how painful it was to do such elementary things as
put on a coat. His hosts made him an appointment with a rheumatologist,
who prescribed cortisone. In a letter written a few days later, and a
few days before his heart failed, Prior described himself as one of the
miracles of modern medicine. 'I've been sleeping well ...
running up and down stairs ... I can stand on one leg and put a
sock on the other (first time for months) ... they've got me
cured now and I'm fine.'


### 3.10 Legacy in New Zealand



Long after he departed for England in December 1958, Prior and his
ideas remained a strong influence on the development of logic in New
Zealand--beginning with his arranging for Robert Bull and
Jonathan Bennett to share the teaching of his Advanced Logic course at
Canterbury in 1959. Bull had recently found a completeness proof for a
Diodorean logic of pure implication and taught this to the class
('heaven help me--and them', he says now).



Hugh Montgomery was among Bull's audience. Montgomery had been a
mathematics student at Canterbury during the 1940s, while Prior was
single-handedly booting undergraduate logic into existence. Now
resuming his studies after a career as a furniture manufacturer in
Christchurch, Montgomery fell heavily for logic. He found himself
'becoming more and more interested in tenses', after
reading Prior's 'Diodoran Modalities'. 1962 saw him
joining the Canterbury philosophy department as an assistant lecturer
(by then Shorter had succeeded Prior as professor and two lecturers
had been appointed, Jim Thornton and Rudi Ziedens).



Montgomery was soon publishing a brisk flow of papers on modal
logic. Many were co-authored with Richard Routley, who graduated from
the Victoria University of Wellington--known to all as
'Vic'--not long before Montgomery enrolled in
Bull's course. 'I grew up in the shadow of Prior',
Routley said: 'He was, I suppose, the dominant figure in New
Zealand philosophy in the late 1950s'. There were other
important philosophers working there, Routley conceded, 'but
they did not have the panache of Prior, or the larger-than-life
stature, or the doctrine' (Sylvan 1996: 126). Routley moved to
Australia and went on to pioneer relevant and dialethic logics, as
well as environmental philosophy, changing his name to Sylvan in the
1980s (he loved trees, especially the New Zealand
kauri). Montgomery--with Prior's forceful backing--was
appointed associate professor at Auckland University in 1969, and then
to Auckland's chair of philosophy in 1970.



Bull, meanwhile, had followed Prior to England in 1960. He was
supposed to be going to Cambridge, but Prior's suggestion that
he divert to Manchester won the day. Max Cresswell joined them in
Manchester a year later. A student of George Hughes and David Londey
at Vic, Cresswell had accidentally come across Prior's *Formal
Logic* in the university library in 1957, at the end of his first
undergraduate year. Excited by this discovery he also devoured *Time
and Modality*. When he won a Commonwealth Scholarship for
postgraduate study in the United Kingdom, Cresswell seized the
opportunity to work with Prior. In 1963, he turned in his Ph.D., on
propositional logics, and--with a strong reference from
Prior--arrived back at Vic to step into Londey's
shoes. (Londey, an Australian, was returning home.) Cresswell went on
to dominate New Zealand logic for the next three decades. Bull
completed a Ph.D. on modal logic under Prior, in 1962, and then enrolled
at Oxford to study for a DPhil under Michael Dummett. At Oxford, Bull
began publishing an important series of papers developing Priorean
tense and modal logics (including his 1964, 1965 and 1970--his
and Krister Segerberg's 1984 handbook entry 'Basic Modal
Logic' is still valuable today). With two doctorates in hand,
Bull worked at Birmingham and then Leeds before returning to a senior
lectureship at Canterbury, at the end of 1968. From afar, Prior was
stationing his men to fight for logic in his native land.



When Cresswell arrived back, Wellington was becoming the focal point
of logic in New Zealand. Hughes and Londey had a strong group of
graduate students, including Dorothy Grover and Tom Richards. Londey
liked to use the English translation of Hilbert and Ackermann's
pre-war *Grundzuge der Theoretischen Logik* as a text for his
advanced course, and in 1965 he and Hughes published their own *The
Elements of Formal Logic*, aimed at undergraduates--Prior
reviewed it in the *Australasian Journal of Philosophy*,
describing it as 'a very good buy' and 'broadly in
the style of Hilbert and Ackermann, and even more that of von
Wright' (Prior 1966). Also in 1965, Hughes and Cresswell
trialled the idea of an undergraduate course in modal logic. *The
Elements* contained no modal logic, and the lack of any suitable
textbook for the new course was a problem. 'We'll have to
write our own', Hughes said jokingly to Cresswell. Their
famous *An Introduction to Modal Logic* appeared in 1968,
overnight turning modal logic from a subject accessible only to
experts into one that almost everybody with a bit of logic could
understand.



Logical mass was building. Malcolm Rennie, a young Australian, joined
Auckland University in 1965 as a lecturer (snatched it is said from
under the nose of Jack Smart, who wanted him for the University of
Adelaide). Rennie was strongly influenced by Prior's work, and
began publishing a stream of papers on tense and modal logic. His 1971
article on Prior's tense system \(QK\_t\) included a
eulogy: 'This paper is dedicated to the memory of the late
Arthur Prior: it was never my good fortune to meet him, but I am very
grateful for his personal encouragement in correspondence, and for the
interest generated by his many fertile and imaginative writings'
(Rennie 1971: 107). In 1968, Rennie taught a graduate course on Prior
to his Auckland students, covering Priorean tense logic in Polish
notation.



On the other side of the world, at the 1968 Joint Session of the
Aristotelian Society and Mind Association at Liverpool University,
Prior attended a symposium on 'What Actually Exists?',
given by Peter Geach and Robert Stoothoff. He was impressed by
Stoothoff, saying approvingly in a letter to Montgomery that the young
American had 'done a lot of fighting for logic'. Stoothoff
was unexpectedly contacted by Canterbury and offered
Shorter's--Prior's--chair. He accepted, arriving
in Christchurch in 1970. (Shorter was moving on to a fellowship at
Lincoln College, Oxford.) Also in 1970, the Czech logician Pavel
Tichy accepted a senior lectureship in philosophy at the University
of Otago. Tichy had fled his native Prague soon after Soviet tanks
took command of the streets in 1968. (His escape from East to West
was ably assisted by Geoffrey Keene, a logician from Exeter University
in the UK (Svoboda et al. 2004: 26).) Once settled in New Zealand
Tichy wrote a paper on quantified S5, taking Hughes and Cresswell to
task for mis-formalizing a modal principle stated by Prior and von
Wright (Tichy 1973, Prior 1955a: 211). Soon he was indulging in the
national logical pastime of exploring Priorean temporal logics.



1970 saw Cresswell visiting Segerberg in Finland (on the shores of the
Baltic at Villa Wolax, the gracious 19th century summerhouse that the
Segerbergs were renting from the von Wright family). Cresswell and
Segerberg gathered mushrooms in the forest and spoke of logic in New
Zealand. It was an auspicious meeting. When Montgomery died, at the
tragically early age of 53, Cresswell proposed Segerberg for the
Auckland chair. The Segerbergs remember getting a call from New
Zealand 'in the middle of the night'. The job came
'on a silver platter', Segerberg said. After a brief visit
in 1979, Segerberg moved to Auckland in 1980. He found that New
Zealand logic was 'in a vibrant state'.



By about 1970 a new generation of home-grown logicians had begun to
enter the post-Prior landscape. In 1971, Rob Goldblatt took up a
junior lectureship in mathematics at Vic. Wellington born and bred,
Goldblatt learned modal logic from lectures by Cresswell and Hughes
during his second undergraduate year, and he completed his Ph.D. thesis
'Metamathematics of Modal Logic' under Cresswell in
1974. 'That remarkable thesis established modal logic as a
mature mathematical discipline', Bull said. Soon Goldblatt was
publishing a deluge of papers on modal logic. Also in 1974 Fred Kroon,
previously one of the students in Rennie's Prior course at
Auckland, was appointed to a lectureship in the Auckland philosophy
department. John Bigelow, who, as a Canterbury undergraduate, had been
taught 'terrific logic' by Montgomery, took up a
lectureship in philosophy at Vic in 1973. Another admirer of Prior,
Bigelow was deeply immersed in tense and modal logic (working with
Hughes on tense logic), and he later staunchly defended Prior's
presentism. When Bigelow arrived home in 1973 from his Ph.D. studies at
Cambridge, he found that New Zealand had become 'a powerhouse in
logic'.



An interdisciplinary logic group formed around Hughes and Cresswell in
1968, meeting at first fortnightly, and then weekly from about
1970. The Wellington logic group 'was a deliberate attempt to
marry interests in mathematics and philosophy', said Wilf
Malcolm, who worked on the foundations of mathematics (Malcolm 1975)
and later became Professor of Pure Mathematics at Vic. Apart from the
sheer logical talent of those involved in the Wellington group,
Cresswell put the group's stellar success down to the fact
that--unlike much in today's universities--it was not
a managed creation: it had 'just grown and wasn't
planned'.



The Wellington group, and New Zealand logic more generally, were a
magnet for visitors. Angelika Kratzer first visited the group in 1974,
initiating an association with the University of Konstanz and
logicians in Germany. Others from Germany soon arrived, including
Arnim von Stechow and Rainer Bauerle. Stanislaw Surma
visited, also in 1974, kick-starting the group's association
with Polish logicians (later, Segerberg hired Surma at Auckland). Dick
Epstein visited the group from the United States in 1974, and then
returned in 1975 for a two-year stay at Vic; while there he worked on
computability and also on what he called 'relatedness
logic', a form of relevance logic. Other visitors from North
America included Doug Walton, who spent the year 1975-76 at Vic
working on the logic of action. Steve Thomason visited the group in
1973 while spending a year with Bull at Canterbury, where he worked on
embedding second-order logic in modal logic and on applying category
theory to modal logic.



Mike Dunn and Nuel Belnap visited the Wellington group during
1975-76, Donald Davidson in 1977, Leszek Szczerba (a colleague
of Tarski) in 1977, and Segerberg briefly in 1979 (in 1971 the group
worked through his recent Ph.D. thesis 'An Essay in Classical
Modal Logic' (Segerberg 1971)). Many others spent time with the
group. David Lewis first visited in 1971, and then for several months
in 1976, thereafter becoming a regular visitor to New Zealand. Lewis
and Ken Pledger, another member of the group, shared an enthusiasm for
train timetables, which they exchanged eagerly. Pledger was a geometer
from the Vic mathematics department who--like many--first
encountered modal logic in Hughes' and Cresswell's 1968
book. Pledger worked on extensions of S3 and on a modal system lying
somewhere between B and S5, and later spent a sabbatical at Warsaw
University with Szczerba--another geometer--where he
finished a Ph.D. on 'Some Interrelations between Geometry and
Modal Logic'.



In 1976 the Wellington group ran a week-long logic school, coinciding
with Lewis's stay. Epstein did much of the organizing. Hughes
lectured on modal logic and Cresswell on the formal semantics of
natural languages--his groundbreaking book *Logics and
Languages* had appeared in 1973. Numerous other group members and
visitors lectured on their research. The school 'brought out
into the open ... a wide variety of quite exciting work ...
that had in fact been building up over quite a period of time',
Malcolm said. The Vic logicians were surprised by the large number of
enrolments in the school--academics and students from New
Zealand, Australia, and beyond. It was a spectacular shop-window,
heaped with New Zealand logic. Malcolm later described the school as
the Wellington group's 'coming-of-age'.



By then, the compliment that the founding father of logic in New
Zealand had once paid to California was true also of his own
country. New Zealand had become one of the most logically mature
places in the world for the study of modality and tense.