Issue #02. July 1995. Pp. 76-94.
Critical Notice of R. Orayen's Logica, significado y ontologia
Copyright © by SORITES and Lorenzo Peña
Raul Orayen's Views on Philosophy of Logic
Lorenzo Peña
Raul Orayen's book Logica, significado y ontologiaFoot note 119 is a profound book, a thorough inquiry into several important issues in the philosophy of logic. Raul Orayen is one of the outstanding analytical philosophers in the Spanish speaking world. As in his other publications, he displays a masterly reasoning power. No patched-up solutions in this book. Orayen is not going to let what he takes to be unsatisfactory treatments off the hook with vague considerations of their being able to cope «somehow or other» with such difficulties as beset them.
The book's general line may be taken to be the defence of some kind of intensional approach in philosophy of logic, with meanings playing a central role in implementing the notion of logical truth.
Orayen regards Quine as his main interlocutor. He is keen on keeping set theory as the general framework of our worldview, and cleaves to classical logic. Yet, precisely because Quine's thought has challenged the intensional notions he considers indispensable, several chapters are given over to discussing Quinean arguments. All in all it is fair to say that the book is further proof that Quine's contributions are at the very core of contemporary philosophy of language and philosophy of logic.
There is a major topic gone into through the book, which is logical form, validity and logical truth. As an outgrowth, Quine's operationalist view of language receives an extensive coverage and discussion. Then, the investigation into the notion of logical truth and validity leads to a critical assessment of the relevantist challenge to the classical conception. And finally -- if perhaps a little cursorily -- acknowledging the ontological assumptions of the classical first-order calculus raises the issue of how to deal with Meinongian approaches, especially Castañeda's. This last chapter, although short, is quite important and will be duly gone into in this review. On the other hand, I will not dwell on Orayen's discussion of the indeterminacy of translation thesis -- a subject on which I broadly agree with him, if for partly different reasons.
Section 1.-- Truth-bearerss, Logical Truth and Validity
Orayen's approach is dual. In natural language the primary truth-bearers are sentence-tokens. In formal or artificial languages they are sentence-types. Such a cleavage is so strong and even startling that the reader may straight away demand a sufficiently strong justification thereof. Orayen provides it.
In any natural language there are plenty of sentences (types) which cannot be given a general meaning once and for all, i.e. which are such that only their respective tokens can be ascribed meanings depending on the particular utterance context. If we are keen on ascribing truth to types, then we need to regard truth not as a property but as a relation, and one with a large number of places. So the sentence type `John will be ready by tomorrow morning' will be true for a particular entity (probably a man) being in that case denoted by `John', a particular task intended for which he is supposed to be ready, a particular day on which the sentence is uttered, and so on. If it is uttered on the sun, it cannot apparently be true since on stars there is no to-morrow and no morning -- unless our planet's standards apply everywhere, or anything like that. Moreover, a sentence exactly like that one both in spelling and pronunciation may belong to a different language, wherein it may mean that cheese is a healthy food, e.g., which may be true or false according to the context. Not only is the number of arguments or places for the relation high, but moreover it seems variable. Well, perhaps that could be dealt with by letting a number of them feature in every sentence, even if trivially or vacuously so. Or they can all be packed into «the context». But all such solutions have difficulties of their own. At the same time, a number of sentence tokens lack definite truth value. Think of the just written sentence when no task is intended, or no entity with which the utterer or the listener are acquainted is named `John' etc.
Thus, Orayen chooses to ascribe truth mainly or primarily to some sentence tokens (which have been or will be actually uttered), individuated by their respective utterance context, and which he calls `enunciations'. The individuation conditions ensure that each sentence token belongs to a definite language, has a definite meaning and so definite truth conditions. Iff it has a truth value, it is an enunciation.
A context is taken to be a spatio-temporal zone. In order to avoid complications about a sentence token changing its truth value as it is being uttered, a durationless instant is taken to constitute the precise temporal component of the context, and it is the final instant of the utterance. Odd cases of the speaker's mastering two (or more) languages with identical sentence types belonging to both are solved by resorting to the speaker's «intention», and in case he himself is at a loss about it, by resorting to a disjunction of the separate meanings -- and so of the different truth-values. No unuttered sentence is ascribed a truth value, as such an ascription would trigger a regress -- we would thus be compelled to take truth to be a relation and go on and on with multiplying the number of places of that relation.
Now, is such a modest attribution of truth-values sufficient for a logical treatment of sentences of natural language? Orayen thinks so. For one thing, logical truth is primarily attributed to sentences in logical languages, that is in formal, artificial languages -- and, as we are going to see, Orayen thinks that for such languages truth-bearers are types, not tokens. For another, in so far as logical truth applies to natural language sentences, it does so through translation, and translation requires identity of meaning. So what can be said is that a natural-language pattern or sequence of sentences (of sentence tokens) is a valid reasoning iff it is a correct translation of a valid inference of a formal language. The synonymy link is decisive here. What about valid but unused inferences which could be uttered in a natural language? No worry! No need for them. We have our formalized languages to provide us with all our wherewithal. All we need to say is that, should there be a sequence of utterances in a natural language with the same meaning as a given valid inference of a formalized language, it would be a correct (valid) reasoning. Nothing else is required.
Thus Orayen has chosen the most economical solution as far as truth-bearers in natural language are concerned. Only a finite number of truth-bearers in fact. But obviously such a solution does not apply to formal languages. The simplest well-formedness rule, that to the effect that, if p is a sentence, so is not p would break down -- a maximal length, whatever it may be, doubtlessly constraining our utterances past or future. Orayen's solution is to regard types as truth-bearers in formal languages.
Why not statements, propositions or the like? Orayen does not deny that there may be such entities, but he claims that resorting to them is not necessary. Moreover, while the existence of such entities is not only controversial but also fraught with obscurities, sentence types are entities whose existence is admittedly not obvious but whose structural features are clear, since they are isomorphic to their respective tokens, which are material entities whose constituent structure can be studied. Hence, such metaphysical conundrums as surround propositions and the like do not arise concerning sentence types.
Validity, as Orayen is concerned with, is mainly a matter of reasoning or inference. We need to ascribe validity to inference patterns in formalized languages, for they can be infinite in number. As for natural languages, an inference worded in one of them is indirectly ascribed validity in so much as it is synonymous with one of a formalized language which is so.
Orayen distinguishes formal validity form intuitive validity. The former is defined in terms of interpretation in the usual, Tarskian way. (The relationship between such a definition and that, much simpler, in terms of truth-preservation is gone into, the conditions under which both notions of formal validity coincide for a number of formal languages being carefully spelled out.) Intuitive validity is different. It consists in the impossibility of the premises being true and the conclusion false, in virtue of meaning-relations between the terms involved in those sentences. Orayen claims that neither concept of validity implies the other. An inference pattern can be formally valid without being intuitively valid, and the other way round. How is that possible?
That a reasoning can be intuitively valid without being formally valid is brought about by the existence of analytic truths which are not logical truths, namely such as involve meaning links -- as e.g. the link between `being a bachelor' and `being unmarried' and so on. It is impossible for a man to be both a bachelor and married, so a reasoning from `Kevin is a bachelor' to `Kevin is not married' is intuitively valid. Not formally valid, needless to say: no such inference is countenanced by any logical system whatsoever.
On the other hand, an inference can be formally and yet not intuitively valid. Such is the case when ontological implications of the classical first order quantificational calculus are involved. From `There is no entity such and so' it can be classically concluded that there is some entity which is not such and so. Yet -- according to Orayen -- the former could be true and the latter false, if nothing existed at all (he assumes such a case to be possible).
Validity of sentences ensues on validity of inference patterns of either
kind, through the connection provided by modus ponens and the deduction
meta-theorem. Within the framework of a wide range of logical approaches the
validity of an inference p
Such is Orayen's account. The reader can appreciate to what extent it
depends on an intensional approach, with meaning relations carrying an enormous
weight not just in connecting natural and formal languages but also providing
the link for intuitively valid inference patterns among different sentences of
one and the same language.
Such an approach seems to me to be committed to an intensionalism which
is enshrouded in obscurities and which in the end does not seem to yield even
what it was expected to provide. Orayen himself admits as much, and then he
patches up the approach with some minor corrections.
The most apparent source of dissatisfaction is the gulf Orayen digs
between natural and formal languages. On that issue almost everybody will agree.
Orayen himself does not espouse such a cleavage with a light heart, but as a
price to pay in order to avoid enormous complications and uncertainties. Yet,
the complications and uncertainties do not vanish with such an account. What is
a context? We know that it is a uniquely determined spatial zone at an instant.
But no criterion for uniquely determining the extension and length of the zone
is offered. If I say `It is cold here', what is the spatial zone to which my
sentence is to apply? The room? A small cranny of the room? The building? The
whole city? The country? (As I am writing in Canberra, the whole of Australia?)
The Earth? The solar system? The galaxy? Well, perhaps other components of the
context give us the clue. Yet, it is not possible then to have the elegant,
simple concept of «context» Orayen puts forward, just a spatial zone at an
instant. Contexts become more complex entities, perhaps sets or bunches of
facts, or situations, or whatever. We cannot rest content with a general
consideration that something like that is a context, of course. We need
something more specific and enlightening.
Furthermore, instants are very problematic entities, and even if they
exist, nothing happens at them. What is said to be true at an instant is best
construed as an abbreviated way of saying what happens at all intervals around
the instant. If sentence tokens can change their truth value along any of those
intervals, taking an instant as the temporal component of the context does not
solve the difficulty.
I am not happy either with Orayen's approach to validity. First and
foremost, formal validity defined in terms of Tarskian satisfaction applies to
some sorts of languages only. How is such an account to apply to combinatory
logic for instance? Well, Orayen himself allows for the more appealing idea of
truth-preservation to be equalled with Tarskian validity -- under some
particular circumstances -- and with that I have no quarrel. Yet truth
preservation is clearly not enough. The pattern «Tweety is a bird; hence Tweety
is an animal» is truth-preserving. It is not Tarski-valid because under some
interpretation of `bird' or of `animal' it is not truth preserving. And anyway
it is no logically correct inference. It is a zoologically correct inference.
Which brings us to the issue of logical truth -- the subject which
features most centrally in Orayen's book. Orayen would want to find a nice,
direct account of logical form, but he thinks none is available. Nothing is in
fact to be found as regards what logical constants are, except that they are the
ones logicians are interested in. We cannot say that a sentence's logical form
is something like its underlying or deep structure. Views of that kind were for
some time fashionable but whether or not they are correct is an empirical
matter, and probably they are wrong. Nor can we say that logical constants are
topic-neutral, since there are doxastic, deontic and temporal logics, and the
logical vocabulary can be further expanded. Nor can we claim that, should there
be no logical system, or no logicians, there would be logical forms and logical
truth all the same, except in the sense that, since there are logicians, we, in
our world with them and with logical systems, can say that even in worlds
lacking both logicians and logical systems there are -- relatively to us, so to
speak -- logical truths. Logical form and logical truth are constrained by
logical vocabulary. And logical vocabulary is just a matter of what logicians
do. Perhaps some particles are such that logicians had better include them in
their vocabulary, but until and unless they do so, such particles don't belong
to the logical vocabulary, and such truths as involve them essentially are not
logical truths.
What about logical truths in natural language? In the same way as for
validity, logical truth is extended from formal to natural languages trough
meaning links: a sentence of natural language is a logical truth iff it has the
same meaning as a logical truth of a formalized language.
No one is going to deny that such an approach is careful and prudent. Too
prudent, to my mind. A new problem arises straight away: whom are we to call
`logicians'? This is no trivial issue, and in fact a generation ago such people
as were professional academics dignified with the title of professors of logic
for the most part taught a very different thing from what nowadays goes by the
name of `logic'. And the reign of classical logic may be short-lived, since new
alternative systems are propounded with increasing vigour. Well, perhaps they
all constitute logic. No denying that they share many features with classical
logic. And what debars new, more daring deviant logicians, from constructing and
proposing systems which, from the viewpoint of a classically minded logician,
are not logics at all? So, e.g., formal systems which have been proposed as
logics of comparatives, and essentially involve phrases like `very', `somewhat',
`more ... than', `less ... than', `to that extent that', `fairly', `rather',
`completely' and so on. Are they logics? Are those who work or them logicians?
Some conservatively oriented professionals say no, since such systems last the
simple proof procedures of more conventional logics. Should the dispute be
solved on the basis of «profession consensus» or something of that ilk,
doubtless the conservatives would win -- for the time being. But are such
procedures acceptable, rationally admissible? Don't they beg the question in
favour of the more conservative, whatever the issue, whether in logic or in
astronomy or in any other discipline whatever?
Most of all, a partly true, partly illuminating answer is better than no
answer at all. The idea of topic-neutrality, or generality, is not free from
defects, but is it as hopeless as Orayen thinks? Well, perhaps that is so if
there are no degrees. But if generality admits of degrees, we can claim that
everything the logicians is interested in is general, and very often more
general than that in which he is not interested. Doxastic operators are perhaps
less obviously general (and I know that in some vacuous, trivial sense,
everything is totally general, namely any entity is such that p, for a true
sentence p whatever it may be). Despite all difficulties, such relations as are
denoted by `and', `or', `less ... that', `to the same extent that' etc. are
clearly general while such as are denoted by `brother', `gravitate', `increasing
the price' etc. are particular. It seems to me that failure to realize such a
point is ensuant upon an implicit all or nothing approach, which in turn
is a sequel of classical two-valued logic.
So, I put an end to the digression on logical truth and come back to the
subject of validity. I have contended that the Tarskian concept of validity is
parochial. (Well, yes, via translation it can be extended to systems which do
not lend themselves to Tarskian interpretation in a direct way; yet the very
notion of translation is fraught with further difficulties as Orayen is
perfectly aware.) The obvious connection between formal validity and logical
truth which -- despite problems surrounding rules such as necessitation -- is,
needless to say, indispensable entails that such problems as beset the notion
and extension of logical truth also bear upon the notion and extension of formal
validity.
Now, if we accept -- with whatever provisos, qualifications and
restrictions -- the idea that logical constants are general -- all in all the
most general ones --, then a winsome notion of «formal» validity emerges: an
inference pattern is «formally valid», or logically correct, iff the result
of linking the premises with conjunction (`and') and then linking such a
conjunction with the conclusion through are `only if' is a logical truth. (Some
qualifications are needed in order to accommodate U.G. and the G”del rule.) The
source of the logical correction (or «formal validity» in Orayen's words) is
generality. As Ferdinand Gonseth viewed it, logic is the physics of any object
whatever. The difference between logically correct and zoologically correct
inferences is not that the former alone are truth preserving. Perhaps the former
alone are necessarily so, but I do not think we need the concept of necessity
here. If we can grasp a useful notion of logical correction without resorting
to the contentious (and not very clear) notion of necessity, all the better.
However, Orayen does not want to embark on such a metaphysical or
ontological approach. It seems to me that his thought is closer to a view of
logic and validity like that of the logical positivists. Other parts of his
book, which defend analyticity -- vs Quine -- confirm that impression.
Orayen's view of formal validity and logical truths in natural language
through translation functions subject to meaning-preservation constraints seems
to me unattractive. Meanings are so muddy! Moreover, as we are going to see
later on -- apropos Orayen's criticism of Quine's extensionalism --
meaning-preservation, whatever it may be, turns out to be neither a necessary
nor a sufficient condition of an adequate paraphrase.
I think there is a more appealing approach, and one Quine has developed
and emphasized. Logic is not implemented in an artificial language. Nor are
mathematics. We are to view mathematical and logical scripts as schematic
representations of some delimited fragments of natural language.
Writing systems fall into several kinds. One of them is that of
iconographic systems, which don't represent language but things or situations.
Some people take mathematics to be written in an iconographic system. Yet there
are cogent arguments to the contrary. Non-iconographic, or glottographic,
systems represent language in a written form, but they can be of several kinds.
Some of them are holistic, taking either sentences, or words, or other
meaningful units as a whole. Some are not so -- especially phonetically oriented
scripts. Some are schematic: they do not represent sentences unit by unit, but
in a sketchy way, which can be read in a variety of alternative ways. It seems
very clear to me that mathematical scripts are of this latter kind. All those
distinctions are of course a matter of degree. Yet, there are powerful reasons
why mathematics (and set theory and logic) are best regarded as being written
in such a way. The passage from pre-theoretical mathematical thought (as was
obviously practised by our ancestors for hundreds of thousands of years --
people also counted in the palaeolithic era, of course -- and as is practiced
by illiterate people worldwide) to formalized mathematics ceases to be a
mysterious jump. (If mathematics was written in an iconographic system, there
would be no passage, one thing would have nothing to do with the other.)
Moreover, what about the reading of mathematical formulae in stilted
mathematical-school English? Whether stilted or not, it is English. Orayen seems
to view such utterances as not belonging to natural language. More generally,
he regards utterances of regimented English as not-English. Well, they may have
an «un-natural» ring in some sense, but they are part of that natural
language, English. Orayen conceives of natural language as what is spoken
«naturally» by ... whom? Is parliamentary talk also unnatural -- a different
sort of artificial language? And talk by broadcasting professionals? And thiefs'
jargon? And children's speech? Well, it seems to me that with such strictures
our view of natural language would be most unnaturally constrained and narrow.
On the other hand, logic does not concern itself with language. Logic is
not a theory about language at all. The logician is not speaking about
linguistic entities in particular. This is obscured because, when put in a
first-order framework -- which is reasonable, since higher-order calculus raises
untractable philosophical difficulties --, the logician uses schemata, and in
order carefully to specify his schemata he must describe sentences. Yet that is
unessential. The logician's description is neutral towards different views of
linguistic structures and linguistic entities. Any careful wording of medical
science, sociology or biology would have to resort to similar procedures. Still
nobody is going to claim that medical science or biology are concerned with
sentences.
It seems to me unsafe to bridge formal-language types with
natural-language enunciations (as truth bearers in general and as bearers of
logical truth in particular) through meaning equalities. Again, such meaning
relations are so obscure and problematic that we had better do without them.
Do we need them? I do not think so. In fact we needn't say what entities
the primary truth-bearers are. What is true (or a truth) is that Rome is in
Italy. What is logically true is that, if Rome is in Italy, it is in Italy or
the Earth is flat. A sentence is logically true to the extent that it says that
p, and it is logically true that p. This is a schema, not a sentence. By
«asserting» the schema we are in fact committing ourselves to asserting every
substitution instance thereof which can be formulated with symbols we use and
understand.
This, by the way, disposes of the so-called `Strawson effect' which Orayen
discusses at length. For one thing, as Orayen acknowledges, Quine's reply to
Strawson -- which resorts to reference only, with no appeal to meanings --
suffices to avoid drawing false conclusions from true premises in virtue of
logically correct rules. (The remaining difficulty about necessity being solved
through an extensionalized treatment of modality, i.e. modal realism.) For
another, usage of the syntactic «meta-language», so-called, is not part of
what logic puts forward, but only of the logician's way of specifying what he
has to say. The logician speaks about things, not words.
Since a sentence is true to the extent that (not just if), for some
p, it says that p, and p, we need some account of «saying that». I think that
a satisfactory account of that semantical relation involves positing facts, and
that facts' existence is what really truth consists in. Yet I do not want to say
that, short of a metaphysics of facts, no account of truth is available.
Everything depends on the price to pay. If you are content with positing the
semantical relation of saying-that as a primitive and with leaving its
second relatum unaccounted for, then fine! (In fact I am -- for our concerns at
hand -- propounding a minimalistic or deflationary concept of truth; such a
concept is not sufficient for all purposes -- witness Tarski's point about the
third sentence in the leftmost book on the third shelf in my library being true;
for our current purposes we needn't speak about sentences. Alternatively we
could turn to something like Davidson's account of `saying that'.)
Facts may be contentious, but I do not see that Orayen is right when he
says that they are more obscure than sentence types.
On the other hand, facts can be treated in an extensional way: the fact
that Abraham is a father can be taken to be the set of people he begets; and the
fact that he begets Isaac can be taken to be a set that only comprises itself
-- the same being the case for all «intransient actions» and states. Begetting
can be taken to be a function which maps Abraham into the function which maps
Isaac into the state (or fact) of Isaac's being a son of Abraham. `And' can
denote a function which maps the fact that p into a function which maps the fact
that q into the fact that p-and-q. (Rather than functions we could speak about
quasi-functions, which may fail to map and which in some cases may yield a value
even when no argument is provided.) Are facts in that sense unpalatable for the
Quinean?
We can speak of types as a mere fa‡on de parler, but if we are bent
on taking type-talk literally, what are we supposed to countenance?
Sentence-types have parts, constituent structure, don't they? So they are
spatial objects, or temporal objects. Where and when are they? At every location
where one of the tokens exists? No, not so, for obvious reasons. How large is
a type? For instance, a token of `It is very hot' (in spoken English) lasts for,
let us say, several seconds; very slowly said perhaps an hour. There is a
minimal duration, not a maximal one -- although more an more slowness impairs
intelligibility to that point of rendering the utterance un-English. No such
thing applies to types. Types are Platonic Forms. The Form of Bed is a perfect
Bed, with a perfect Mattress, perfect Sheets and so on; and the perfect Length
of a Bed. It is in the perfect Location. No need to dwell on the difficulties
besetting such Things. Those surrounding types are exactly parallel.
Of course we can think of types as classes of tokens. But what about
uninstantiated types?
I think Orayen had better resort to possible tokens. After all he
countenances possibles -- else his introduction of necessity into the notion of
intuitive validity would amount to little. Possible utterances, possible tokens
are concrete. A full account of them may lead us into something like David
Lewis's modal realism. (I for one would be glad to embrace such a view, which
after all extensionalizes the purportedly intensional modal contexts, and so
regains for extensionalism the treasures and explanation power claimed for the
notions of necessity and possibility.)
To sum up, I think there are alternatives to Orayen's views which are more
congenial to the Quinean and which employ nothing to which Orayen seems to be
necessarily averse. Those alternatives turn out to be much less dependent on
intensional talk than Orayen wants to concede -- modal talk being
extensionalized through modal realism.
Section 2.-- Orayen's Criticism of Quine's Extensionalism
Orayen subjects Quine's approach to two main objections, one dealing with
the thesis of indeterminacy of translation, IT for short, the other with Quine's
extensionalism. I agree -- with some reservations -- with Orayen's views on IT,
so my comments will only focus on the other subject.
Orayen's main argument is that Quine's extensionalism threatens logical
truth as applied to natural language. No need here to say why, since as much is
obvious for the preceding section. Quine in his reply (pp. 293-7) concedes a lot
to Orayen. But in fact a part of what he grants results not from extensionalism
but from IT (and of reference). (Orayen seems to me to be so deeply concerned
with meaning and intensionality that he regards IT mainly as a threat to
meaning-links, as if reference links would be more secure, were IT right.)
Orayen's point is simple and clear. Logic is useless if it applies only
to sentences in formalized languages, if therefore nobody can be claimed in
ordinary or scientific talk to reason rightly or wrongly according to logical
standards. What is directly a logical truth is, e.g., what is said in a formal
language with the formula p or q if p. That Marion is 46 or 47 if she is 46 is
a logical truth only because such an English sentence is translated into one of
a formal language with the same meaning. Failure to admit meaning relations --
in particular, synonymy -- ensues upon a breakdown of logical truth for natural
language.
No logical teaching is interesting nor perhaps even possible if no
paraphrase in natural language is available for formulae written in formal
languages. But more seriously, it is not just teaching but the very purpose of
the logical enterprise what is at stake.
Yet, Orayen acknowledges a difficulty for his account. Not all
meaning-preserving paraphrases do. If a logic teacher tries to illustrate p or
q if p with examples, he cannot use e.g. p or q if: p or q and p (for some
particular p and q) even though such a paraphrase would be truth preserving (in
fact linking both through a biconditional is a logical truth).
Orayen's solution is to resort to a restricted notion of economic
paraphrase. Roughly speaking, the adequate paraphrase has both to preserve
meaning and to do so through what we can call the most literal translation
available -- or something like that.
Orayen has shown us that there is a way of modelling the general procedure
of the logic teacher. He does not act arbitrarily. He does not choose his
paraphrases in a random way. Something like the principle of economic
meaning-preservation is doubtless employed. But what is really enacted here?
Not merely meaning. Orayen concedes that. Meaning and something else.
What? Well, of course economic wording, or a maximal degree of literality, or
something like that. Yet such a further constraint does not ensue upon meaning
preservation. Its rationale is not meaning at all. In fact it seems very clear
to me that its ground can only be of a pragmatic sort. But then why not say that
all the linkage needed is just of a pragmatic sort?
Orayen's qualms could apply exactly in the same way to any other domain.
They have nothing to do with logic in particular. You can say that medical
truth, or architectural truth, is also threatened by extensionalism. Medical
science would be useless if the physician could not put (some of) his
considerations and advice in words other people can understand. Yet, are such
words synonymous with those of a medical science treatise? Well, with so murky
«entities» as meanings are, any claim on such an issue would be most dubious.
What is certain is that without some both-ways transfer between ordinary talk
and learned speech among professional physicians medical science would not have
existed and would not be possible or helpful.
But do we need meanings? The physician uses his paraphrases in a very free
way, as does the logic teacher or logic manual author. Yet there are some
constraints. Those constraints seem to me pragmatic. What is implicitly required
is that, to the extent that a sentence says that p, and it is medically (or
architecturally, or logically) true that p, and putting such a fact in the words
forming the sentence is -- given the circumstances -- adequate, the professional
can convey his advice or his teaching by uttering that sentence.
In his reply to Orayen, Quine mentions the research currently developing
which aims to implement mechanical translation from English to «logicalese»
and conversely with no use of «meanings». Orayen's main objection to such a
solution is that it is no good for the extensionalist, in so far as the very
same project can be formulated only through intensional concepts.
I am by no means convinced that Orayen is right in this connection. Why
is reference not enough? We define a logical vocabulary as the set {`and', `or',
`to-the-extent-that', `less', `not', `completely', `some', `exists',
`comprises', `before-than', ...}. Our underlying idea is generality. Then we
pick up expressions of usual talk which we take as equal in reference with those
ones, and we implement a recursive procedure for much more complicated cases
wherein such splitting into units is not easy or is not feasible. (E.g., Orayen
stresses that there is no mechanical way of knowing that `Sam and Jim are
Australians' is to be paraphrased as `Sam is an Australian and Jim is an
Australian', since no such paraphrase is feasible for `Sam and Jim are
friends'.) Meaning -- Orayen claims -- has to be resorted to. Is that so? Well,
it depends on what meanings are, but it seems to me clear that meanings «as
such» are of little help. What we need is a recursive procedure which is built
up on purely syntactic grounds, and which aims at reference. After all, what if
the paraphrase preserves reference only, not meaning, whatever that may be?
Logic would be none the worse for it, would it?)
Orayen concedes that meaning preservation is not a sufficient condition
for a paraphrase to be adequate on two accounts. One is that a further
requirement is needed -- the one we have referred to as literality or economy,
which is pragmatically constrained. The other is that such paraphrases as depend
on non-logical synonymies (`unmarried' and `bachelor' and the like) are of
course inadequate in this context. Again, why are we then supposed to need
meanings? Why not just reference?
At some point, Orayen clearly says that meanings are necessary for what
we can call epistemic reasons. A paraphrase of a logical truth is to count as
a logical truth, too, iff we are entitled to be absolutely certain they have the
same truth value, and our certainty is grounded on purely linguistic
considerations. Yet later on he somehow retracts from such strong claims, taking
a less optimistic view of certainty on such matters.
What is important for me here is to discern epistemic necessity, alethic
necessity and logical truth. Not all necessary truths are logical truths (in
virtue of G”del's theorem, if for no other reason). Not all necessary, not even
all logical truths are epistemically obvious (otherwise no controversy would
exist on such matters and no logical mistakes would be committed). Not
everything that is obvious is either logically true or necessary, not even if
its truth is learnt along with the acquisition of language, as is the case with
«My name is So-and-So» or «Mum is my matter and Dad is my father». (The
latter sentence is necessarily true or Kripke's view of the essentiality of
origins is wrong. But many other sentences which are «analytical» -- in the
modest sense of being learnt with the acquisition of language -- are not even
necessarily true.)
Yet I cannot deny that Orayen has a strong point here, even though, after
Kripke's arguments, many people now agree that obviousness, logicality and
necessity are not coextensive. Logic seems to be somehow «special». After all,
Frege and Husserl claimed that, logic being «apodeictic», no inductive and
fallible approach to logical truth would be acceptable. We somehow feel that we
need security in our logic. If logic itself is not that certain, what certainty
is left?
Well, none. Or no complete and absolute certainty. If we ignore degrees,
we are apt to reason in terms of all or nothing, and then we hanker after
[unblemished] certainty. We harbour security illusions. Gradualism cures us from
such anxieties.
To sum up, we again have alternatives to Orayen's intuitionalism which
seem to me simple and free of any commitment to meanings, which are the mistiest
and obscurest [pseudo] things in the philosophical marketplace. We can think of
logic as developed directly in natural language schematically represented
through symbolic notations, which do not constitute a separate language of their
own. We can posit infinite unuttered sentence tokens which exist in possible
worlds, each of them being some «part» of Reality. We can base the program of
paraphrase on reference, syntax and pragmatics, with no appeal to meanings. And
-- more contentiously -- we can fill in the gaps in our treatment by resorting
to facts, which can be accounted in a combinatory way (following F. Fitch's
steps, if not necessarily on the details), which is close to a set-theoretical
approach in spirit, if not in its articulation.
It would be silly to claim that such alternatives as I am embracing are
free from difficulties or that their superiority over Orayen's intensionalism
is plain and uncontroversial. Far from it. After all probably more analytical
philosophers would agree with Orayen thank with the reviewer on such issues. If
Orayen's views command such a widespread acceptance, something speaks for them.
If the «apriorist» defense of analyticity, necessity, intimate connection
between meaning and logical truth and validity, and so on, holds its ground
despite Quine on the one hand, Kripke on the other hand, some deep source is
bound to exist from which such attitudes re-emerge. All that I reluctantly
concede. Yet such considerations must not be allowed to cloud the central point
of the foregoing arguments, that we can do without «meanings» by resorting to
other conceptual tools which seem to be, all in all, less problematic, less
difficulty ridden.
Section 3.-- Relevant Logic and disjunctive syllogism
There is perhaps a deep reason why Orayen is interested in relevant logic
-- RL for short. RL arises from a qualm concerning the classical relation of
deducibility, namely, that such a relation depends on what exists, and so is not
a priori. The ontological (or perhaps alethic) commitments are clear in the case
of the quantificational calculus, but there is an implicit alethic commitment
in the case of the sentential calculus. CL enforces rules such as VEQ (Verum
e quolibet: p |- qCp) in virtue of which, from the fact that it is true that
p, it follows that, if q, p; and hence it follows that p can be drawn as a
conclusion from q, for any q. Admittedly such an inferability of p from q is
contingent upon a previous assertion of p. All the same, CL countenances such
a conditional inferability. Yes, we do not need it, but that is beside the
point.
RL takes exception at such commitments. Nothing can be inferred from other
things (assertions) in any way which depends on what happen to be true, whether
necessarily or not. Inferability is a matter or meaning-connections which can
be grasped entirely a priori, analytically, without resorting to
knowledge of the empirical world or even of necessary truths. Logic, as the pure
study of inferability, must be previous to the knowledge of truths. Valid
inferences must not be just truth-preserving -- not even just necessarily
truth-preserving. They must also preserve something else: meaning. The sense of
the conclusion has to be included in that of the premises. (Or something like
that.)
After the preceding sections of this critical notice, the reader can
appreciate why Orayen is prone to find relevantist qualms congenial. After all,
his own views of logic's nature are not far away from relevantist
considerations. So, he canvasses the arguments of the «founding fathers» of
relevantism, Anderson and Belnap -- A&B for short -- very carefully.
(Perhaps he takes them too seriously.) In fact, such arguments do not carry us
very far, except as witty illustrations of the general relevantist standard,
namely that what happens to be true, whether contingently or necessarily, must
not bear on what can be inferred from what, conditionally or not -- the purely
analytic, or meaning-grounded, link between premises and conclusion being
destroyed by such dependence on truth. Yet, unlike the relevantists, Orayen
keeps a lingering attachment to some sort of close connection between
analyticity and necessity. That connection may remain short of full identity but
anyway Orayen tends to think that only all necessary truths are analytical and
a priori. No such belief is apparently shared by the relevantists,
although A&B were not entirely clear on that issue -- deep relevantism as
developed by Richard Sylvan is far more consequential, claiming that relevance
is an intensional but ultra-modal relation. The issue of the relation between
necessity and analyticity in the original work of A&B is obscured by their
adherence to S4 rather than S5.
Now, Orayen's attitude towards relevantist concerns is -- as can be
gathered from the above considerations -- initially very sympathetic. The
relevantists' central idea -- that deducibility arises from an intimate,
analytical meaning- or sense-relationship -- is quite congenial to Orayen's own
views. Thus, Orayen goes about discussing relevantist considerations very
carefully. The relevantists' appeal to intuitions is to his liking. Yet, he
finds a strong reason for not acquiescing to the relevantist rejection of all
nonrelevant deductions, i.e. of such inferences as fail to comply with the
standards of variable sharing ad use-in-proof. The reason concerns Disjunctive
Syllogism -- DS for short --, which has to be rejected if no non-relevant
inference is to be maintained -- unless of course some other, commonly accepted,
principle or rule is dropped, e.g. addition, or simplification; Orayen rightly
rejects such moves, as do the relevantists themselves.
Let me summarize the way DS lends to nonrelevant deductions -- following
a much discussed argument of C.I. Lewis, which Orayen scrutinizes in length.
From p and not-p to infer p and not-p. From not-p and p or q to infer q (in
virtue of DS). Hence, form p and not-p to infer q. The last is the rule of
Cornubia, usually called Pseudo-Scotus.
Orayen's recommendation amounts to weighing such claim on our intuitions
as is possessed both by each step involved in Lewis's argument and by the
rejection of those steps. He thinks that D.S. is so intuitively appealing that
doing away with it would run against logic's vocation to capture intuitive
deducibility connections.
Besides such a general appeal to its intuitive nature, i.e. to its direct
obviousness -- an appeal which only needs to be confirmed by some sort of
statistical account if people's reactions, in particular of how logic students
respond to what they are taught -- Orayen also musteres a different
consideration in support of DS, namely that to accept p or q commits one to
accept, in some sense, that, if not-p, then q. In some sense. What conditional
is involved is a different matter. In general Orayen does not believe that
classical horseshoe captures the conditional of everyday language -- whether
subjunctive or even indicative. So, I take it that the conditional which he
thinks is implicitly involved in justifying DS is some special conditional, like
the one he thinks is used in mathematics. Yet, if it is a technical connective,
belonging to a professional jargon, how is it that every natural language
speaker is so committed each time he utters a disjunction? I suppose the answer
is that we commit ourselves to claims which cannot be put into adequate words
except on the basis of theory-implementation. (Perhaps we all commit ourselves
in our use of numerals to very sophisticated, far-reaching and hard-to-prove
theorems of number theory.)
Anyway, that separate argument -- the invocation of an implicit
conditional where the first disjunct, upon being negated, becomes the protasis,
the second disjunct becoming the apodosis -- is not necessary for Orayen's
purposes. If DS is intuitively correct, that is enough.
But is it correct? Well, Orayen -- unlike most writers on these issues --
is extremely careful, and he hedges his sentences. He claims only that for some
negation DS is valid, and hence so is Cornubia. And this I wholeheartedly
concede. But what negation?
Orayen admits that there may be other negations, but he thinks that the
usual negation in science and everyday speech is classical, and that DS and
Cornubia are applicable to that negation. Well, my comment is that it depends
on what the usual negation is assumed to be. If it is what is most frequently
conveyed by a mere `not', I disagree. If, however, it is what is meant by
phrases like `not ... at all', `by no means' or `It completely fails to be the
case that', then I am sure Orayen is right. As for when it expresses a negation
weaker than the classical one, that is a difficult matter. I take it that in our
spoken language we can use prosodic means unavailable in written English, some
of which may be [part of] strong-negation markers -- in addition to contextual
factors.
The problem is whether such an exclusion as is admittedly converged by
negation is always a strong or total exclusion, or if it can admit of degrees.
If the former in the case, each utterance of `Yes and no', `I did and I didn't',
`He was and he wasn't', and so on, are either utterly illogical or else bad ways
of putting a logically unobjectionable message. If, however, exclusion admits
of degrees, what is espoused by `not' may be non-total exclusion. Thus, not-p
may denote a state of affairs which does not bear to the state of affairs that
p a relation of utter incompatibility, but instead one of
not-necessarily-complete exclusion -- partial exclusion. To the extent that
not-p is true, p is not true, and the other way round.
Should such a suggestion be acceptable, we would have a clue to why and
when DS is warranted. Only whenever negation is strong -- whether a
strengthening `at all' or the like is explicit or only implicit -- is DS
applicable.
Such a motivation for discarding [unqualified] DS is of course entirely
different from the relevantist qualms on this issue. Yet, some odd similarity
emerges. If we espouse degrees of truth, we need a connective expressing
something like «to the extent that», and a careful study of such a connective
shows that it is bound to have at least all the properties of `->' in A&B's
relevant system E of entailment -- and in fact some further properties,
too, since E's arrow is too weak. Likewise, upon such an approach we need
some inference relation -- not necessarily the only one -- in virtue of which
the conclusion is not less true than the falsest premise. Again, implementing
such a relation bears a close similarity to A&B's natural-deduction account
of entailment (again with some important strengthenings).
So my provisional conclusion on this debate is that Orayen is right
against the relevantist scruples, but only conditionally and qualifiedly so. DS
obtains for some negation -- strong negation -- but not for every negation --
Orayen concedes as much. I surmise that the most common use of negation is not
that strong. And if a gradualistic approach to truth has real merit, the
relevantist (or more exactly «entailmentalist») enterprise, duly strengthened,
is not as ill-advised as that, after all.
I'll bring this discussion to a close by touching on a minor point. On p.
233 Orayen considers A&B's claim that DS is applicable only whenever p or
q contains an «intensional» `or' in virtue of which the disjunction in
question can be paraphrased as «Were it not the case that p [it would be the
case that] q». Orayen elaborates on an illustration by E. Adams. From `Either
Oswald killed Kennedy or somebody else did' and `Oswald didn't kill Kennedy',
we should conclude that someone else killed him. Yet -- Orayen claims -- we
would'n draw from the premise the conclusion that, if Oswald had not killed
Kennedy, somebody else would have done so -- unless we think there was a
conspiracy, or that Kennedy was fated to be killed by Destiny, or something like
that. But is the appropriate subjunctive conditional rightly stated? Why not
this other way: `Were it not the case that Oswald killed Kennedy, it would be
the case that somebody else did it'?
Anyway, this comment is of quite secondary importance for my main purpose
in this section, which was that of showing that, even if Orayen is right against
the relevantist arguments, yet DS may need to be hedged.
Section 4.-- Castañeda's Guises
Orayen's book's last chapter (chp. VI, pp. 263ff) deals with problems of
logic and existence. Orayen discusses Meinong's original approach, Russell's
objection and one among the several neo-Meinongian approaches currently
available, namely Castañeda's guise theory.
Orayen's main objection to Castañeda's theory is that it leads to a wrong
counting. One of the principles of Castañeda's theory is that the expression
«the entity that p» is the only entity which has only one characteristic,
namely that of being such that p.
Indeed Castañeda distinguished several ways of having a property (several
predication relations) and several [quasi]identity relations -- identity proper,
consubstantiation and consociation, the last one being left aside in the present
discussion. A guise, something denoted by a definite description,
internally has only such properties as are ascribed to it in (or by) the
description, but externally has all properties of any guises with which it is
consubstantiated. Now, only existent entities are consubstantiated (with
themselves and with other entities). (In order to overcome certain infelicities
which stem from such an approach concerning non-existent entities -- such as,
e.g., that nothing could be ascribed to a nonexistent entity except what, word
for word, served to characterize it in the first place -- Castañeda resorts to
consociation; as announced, that side of his approach lies beyond the scope of
our present comments.)
There are serious problems about Castañeda's guise theory e.g. whether
the entity that is a horse, that flies, that eats rabbit-meat, that never
sleeps is the same (exactly the same entity) as the horse that flies and
eats rabbit-meat and never sleeps. Also such problems -- already discussed
by a number of critics of guise theory -- as arise concerning descriptions
(«second-order descriptions» perhaps) which contain the technical terms which
are used in the theory. Castañeda seems to be led to something like Frege's
plight about the concept [of being a] horse. An ordinary entity, like the
Eiffel Tower, is a system of guises (Castañeda sometimes calls it a set
of guises and Orayen comments on that unfortunate application of the word; in
fact, `system' is, if vague, more appropriate here than `set', although of
course an axiomatic treatment has then to be propounded for «system theory»,
in order for us to be able to assess what one is committed to when he regards
an ordinary individual as a system of guises). One of those guises is the
tower built by Eiffel; another one the highest building in Paris (or
was it?), etc. Now, what about the system of guises which has only all
properties had by at least one of the guises consubstantiated with the Eiffel
Tower? Let us abbreviate that phrase as `ë'. If ë is one of the guises
making up the [ordinary entity] Tour Eiffel, then a number of odd results ensue:
ë internally has the property of being the ordinary entity Tour Eiffel, a system
of guises; one of that system's components is the system itself, which badly
calls for a treatment allowing non-well-founded systems; furthermore, ë
internally has all the properties externally had by the Tour Eiffel. With more
convoluted descriptions, worse would follow. A way out is to say that such
descriptions do not describe what they seem to; but then what about the initial
point, namely that each guise internally has the property which characterizes
it?
Orayen's main objection to Castañeda's theory is closely related to the
foregoing comment. Orayen's point is that guise theory leads to counting
trouble. Thus if we know that at this tomb are the remains of the English writer
who made methodism world-wide famous, the woman whose pen-name was `George
Eliott' and the author of Silas Marner, we say that only one entity is
buried there, Mary Ann Evans. Yet Castañeda is bound to agree that there are
three, an English writer, a woman and the author of Silas Marner -- and
infinitely many others of course.
Castañeda's initial reply to that problem was the converse to our just
considered way-out to the problem of «the system of guises such that...», viz.
that sometimes an ordinary definite description does not denote the guise it
would normally denote, but the system the guise is a member (or a «part») of,
i.e. the system of all the guises consubstantiated with the guise in question.
Orayen (p. 282) points to two difficulties with such a solution. First its
ad-hoc-ness. Second, and more seriously, what about the descriptions `the
system of guises consubstantial with the woman whose pen-name was `George
Eliott» and `the system of guises consubstantiated with the author of Silas
Marner'? According to guise theory they denote different guises. Which
brings us back to our previous concern over descriptions which use the very same
technical terms the theory avails itself of. But, if it is true that those
descriptions denote different entities (guises -- in fact none of them denotes
a system of guises!), then the very same clarification sentence `Sometimes the
description `the author of Silas Marner' denotes the system of guises
consubstantiated with the author of Silas Marner' is a sentence that says
something different from what it was meant to, and in fact sometimes surely
false according to Castañeda's lights. Thus the clarification cannot be uttered
within guise theory with the intended meaning -- as Frege could not say within
his own framework that the concept of being a horse is what is denoted by the
verbal phrase `is a horse'.
Castañeda, in his reply, contained in Orayen's book (pp. 303-5), devises
a procedure through which he ensures that for any property P there is an
equivalence class, A, of guises which picks up just one guise out of a system
of mutually consubstantiated guises with [externally] property P.
Incidentally, it seems to me there is a slip in Castañeda's formulation
of condition (ii): if what he wanted -- as Orayen says, in footnote, 23, p. 285
-- was to ensure that A comprises only one guise of each system of mutually
consubstantiated guises which are P, then a protasis is missing to the effect
that the guises are different; namely, Castañeda's condition (ii) is
`(Ag¹,g2)(g¹[epsilon]A&g2[epsilon]AC~C*(g
¹,g2)'; I think that either he was using Hintikka-like exclusive
quantifiers, or he meant
`(Ag¹,g2)(g¹=/=g2&g¹[epsilon]A&g
2[epsilon]AC~C*(g¹,g2))', i.e. no two different
consubstantiated guises are members of A -- in other words
`~(Eg¹,g2)(g¹=/=g2&g¹[epsilon]A&
g2[epsilon]A&C*(g¹,g2))'. A different problem is
that there is an implicit appeal to something like the axiom of choice here. A
detailed axiomatization of system theory is needed in order for us to see what
is afield.
Through such a device, we may ask how many entities belong to such a class
A and [externally] have a separate property Q. By so doing we'll solve the
counting problem in an obvious way. The answer will obviously be: one.
Orayen's objection (pp. 285-6) is that such a device yields the correct
and expected counting result, but paying the price of debarring us from naming
what is thus counted. We know that there is only one entity which is the entity
belonging to the class A of guises meeting Castañeda's three requirements and
externally having the property of writing Felix Holt. But such an entity
is a guise, which internally has the property of belonging to the class A of
guises meeting Castañeda's three requirements and externally having the
property of writing Felix Holt. Now, by counting guises we wanted to
count guise systems -- that was the very purpose of devising the A classes in
the first place. Can we name those systems? No, we cannot. Each phrase we may
happen to coin for the purpose turns out to denote a guise.
There is a coda to Castañeda's reply that Orayen refrains from
going into. Castañeda points to an enrichment of the formal language in which
guise theory is formulated, consisting in the addition of a new sort of
variables ranging over guise systems. A categorial predicate `M' can also be
added, which -- although Castañeda does not dwell on specifics here -- would
be such that for any new variable, `m', `m[epsilon]M' (or `Mm') would be
«analytic» -- or something like that --, whereas apparently -- since predicate
`M' is categorial -- for any variable of a different sort, `x', `x[epsilon]M'
(or `Mx') would be ill-formed.
Again, such a solution shares all the ineffability problems known to
afflict type-theory and many-sorted languages. Nothing really new. The
concept-horse trouble is still with us. Pluricategorial ontologies are
ineffable, all of them. So simple a sentence as `guises are not systems of
guises', which Castañeda's reshuffled theory obviously intends to espouse,
cannot be said within the theory. Any new reshuffling will entail similar
problems one stage up.
Section 5.-- Conclusion
The are of course lots of extremely interesting discussions in Orayen's
book which I have abstained from commenting on, out of a sense of space
limitations. The reader has realized that my line is not Orayen's. Yet I have
read only a few books as thought-provoking as this one. If you are not
indifferent to the problems of philosophy of logic, read it. Apparently, an
English translation is in prospect. Meanwhile, that may be a good opportunity
to study Spanish.
The main merit in a book is the author's. Nevertheless, let me also praise
the publisher, the National University of Mexico, which deservedly has acquired
a high reputation for the excellent work in analytical philosophy which is done
there -- of which this book is a telling example.Foot note
120
Lorenzo Peña
CSIC [Spanish Institute for Advanced Studies]