Absolute Truth in a Changing World

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Absolute Truth in a Changing World

Peter Simons

University of Leeds

The fundamental things apply

As time goes by

Herman Hupfeld

1 Philosophical Method and the History of Philosophy, Especially in Poland

With Jan Woleński I share a great admiration for the achievements of Polish philosophers

and logicians from Twardowski onwards, and we likewise share a fascination for their

personalities, foibles and vicissitudes. More importantly, we both agree that Polish logic and

analytical philosophy got the balance about right between philosophy and its history. Other

things being equal, it is better – for philosophy – to be a good philosopher who is ignorant of

the subject’s history than a good historian with no good sense of what is philosophically

important. But other things are not equal, and it is possible to both have a good nose for

philosophical importance and plausibility, as well as being sensibly informed of relevant

portions of the subject’s history. The reason is not simply that by knowing the history one is

able to avoid tumbling into the pitfalls of the past or wasting time reinventing theories that

have already been invented. It is also that the historical dimension lends depth to one’s

appreciation of the problems themselves, and gives one a sense of the historical element in

any current discussion. No one philosophizes in a vacuum and it is folly to suppose

otherwise. When the history is relatively recent, as with the history of Polish philosophy from

1895 to 1939, some of the issues are likely still to be with us. One such issue is the

philosophy of truth, about which Jan and I collaborated some years ago in a long historical

essay.i An aspect of it is the subject of this essay.

Knowledge of the past should not imply slavish adherence to past views. Which ones

would they be? Philosophers were as divided then on doctrine as they are now. Even

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philosophy makes progress, albeit somewhat crabwise, so mere repetition is a waste of time.ii

That is why it is better to have a good new idea in ignorance of its novelty than to simply

bang on about what X said then, as if that solved a problem. There are outstanding examples

of historically-informed philosophers and logicians among the Lvov–Warsaw School:

Łukasiewicz among the logicians, Ajdukiewicz and Kotarbiński among the philosophers. Yet

all three were considerable and innovative thinkers. Indeed the history of logic as a modern

subject started with Łukasiewicz. And here is the historical part of the explanation. The

founder of the School, Kazimierz Twardowski, was himself historically aware. His teacher

Brentano was both a philosophical innovator and a knowledgeable historian who derived

inspiration from the past. Twardowski also – rare for his time, rare even today– appreciated

Bolzano, whose own great Wissenschaftslehre of 1837 was subtitled “Attempt at a

comprehensive and mainly new exposition of logic with constant attention to its previous

authors”.iii

Perhaps Twardowski’s most important and influential paper was one which he

published in 1900, called “O tzw. prawdach względnych”, “On so-called relative truths”.iv In

it, Twardowski takes issue with those who claim that truth should be considered a property

relative to time, or place, or speaker, or anything else. His argument is that since ordinary

language is mainly a practical tool, it is replete with ellipsis. If someone says “It’s raining”,

the words of which alone fail to determine a unique place and time, and thus fail to determine

a unique truth-value, this may mean in a particular context what is more adequately expressed

by the words “On 1 March 1900 by the Gregorian Calendar at 12 noon Central European

Time it is raining in Lvov on Castle Hill and its surroundings.” Twardowski practises what

has been called the “decontextualization” of thought.v The problem with decontextualization,

which has been a common move in logical semantics from Bolzano and Frege through

Leśniewski to Tarski, Carnap and beyond, is that it most naturally suggests and goes together

with semantic platonism, the view that the proper or primary bearers of truth are timeless

propositions and that their constituents are themselves timeless abstract ideas.vi The only

person among those cited who disagreed with this view is Leśniewski , and his way of doing

things has been widely sidelined, most influentially by Tarski himself. In any case

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Leśniewski’s very narrow interest in an artificial logical language meant that he did not

address at length the contextuality problem of Twardowski.vii

In this paper I shall first show how Tarski, for mathematical reasons, deviated in the

direction of platonism in his theory of truth, against the views of his teacher Leśniewski. I

shall suggest that platonism about truth-bearers and their parts makes no essential

contribution to our understanding of the real phenomena of language and truth. I shall then

outline the magnitude of variety of potential truth-bearers needing to be accounted for in a

realistic but non-platonist account of truth. Finally I shall show how in principle such a

plethora of different truth-bearers, all participants in the hurly-burly of the real world, may be

true or false, and yet truth and falsity remain absolute in the spirit of Twardowski.

2 Tarski’s Heresy and Modern Semantic Platonism

Standard formal theories of truth of the sort pioneered by Alfred Tarski are designed for the

languages of deductive sciences. Tarski explicitly rejected the possibility of producing an

adequate and consistent theory of truth for vernacular languages because their semantic

closure means that it is possible to formulate semantic antinomies. More recent theories of

truth have extended Tarski’s methods to larger and more ambitious languages more closely

akin to the vernacular. I suggest that one may and should modify the theory of truth in a

different direction, one which is more closely related to Tarski’s own background and the

logical heritage in which he grew up.

Tarski’s doctoral supervisor was Stanisław Leśniewski. Jan Woleński and I share the

opinion that Leśniewski was one of the finest as well as one of the most remarkable in a

century not short of great logicians, and in our private conversations we habitually refer to

him as ‘Big Stan’. The reason I mention Leśniewski is that his way of conceiving of

languages for everyday as well as for logic was quite different from the way adopted by

Tarski in his 1933 work O pojęcie prawdy w językach nauk dedukcyjnych (hereafter PP),viii

and which came to be the standard for later theories of truth and for model theory. In standard

semantics it is usual to assume that the language is a fixed structure of abstract or eternal

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entities, in an abundant, countably infinite, supply. There is never any shortage of expressions

in such a language. In such ‘platonic languages’ the linguistic expressions of which they are

composed, whether modelled on natural or on formal languages, are construed as platonic

entities existing independently of space and time and irrespective of whether there are

actually any physical embodiments or tokenings of any particular expression. Anyone who

accepts at face value the statements of such a semantics is a platonist about expressions, if

about nothing else. To utilize Peirce’s terminology, in such a semantics linguistic expressions

are conceived one and all as types, and the question whether this or that expression is as a

matter of fact tokened in the history of the physical universe is an incidental and empirical

one of little or no concern to semantics as such.

Leśniewski was a nominalist, or as near a nominalist as makes no difference,ix and

for this reason he was unable to accept philosophically the way in which Tarski treated

expressions as abstract entities. In his own metalogical work, Leśniewski was scrupulous

about treating linguistic expressions as individual tokens rather than platonic types.x Tarski

was of course acutely aware of Leśniewski’s views. In a footnote of PPxi he excuses himself

for formulating his theory so as to “give the appearance of a widespread error which consists

in identifying expressions of like shape” and using his metalinguistic terms to denote not

individual expression-tokens but whole classes of such tokens, by saying that this “is

convenient” and is “to avoid…the introduction of superfluous complications into the

discussion, which would be connected among other things with the necessity of using the

concept of likeness of shape”.xii In this footnote Tarski appears to endorse Leśniewski’s

view and to apologise for not following it, but for pragmatic reasons only. One gets the

impression that if he had chosen to do so, Tarski could have recast his theory of truth – with

considerable complications no doubt – in a nominalistically acceptable form which would

have placated his teacher, who did not welcome the methodological innovations of the truth

paper.

However Tarski could not in fact have recast his theory in such a way without

significantly weakening its results. Tarski’s metalogic includes the assumption that the set of

consequences of a set of sentences may be denumerably infinite, an assumption used in the

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truth paperxiii but explicitly stated earlier in the 1930 paper ‘Fundamental Consequences of

the Methodology of the Deductive Sciences’,xiv where Tarski states that he regards the

assumption that there are denumerably infinitely many sentences as “quite sensible…and …

even … useful from a metamathematical standpoint”.xv Tarski’s misgivings about the

mathematically cramping restriction imposed by an assumption that sentences are tokens

emerges in the somewhat tortured discussion between Definitions 17 and 18 of PP.xvi There

he admits that without the assumption that sentences exist such as those needed in the middle

of proofs of often simpler sentences than themselves, using the definition of ‘provable

sentence’ that he gives (Definition 17), statements to the effect that all sentences of a given

kind are provable become impossible to interpret without introducing existential assumptions

which are intuitively weaker than those already eliminated from the axioms. Further, such

concepts as consistency and completeness require similarly strong existential assumptions.

The furthest that Tarski is prepared to go in weakening his existential assumptions is to

consider interpreting his metatheory within the natural numbers, but even here he would need

to rely on a strong existential assumption, namely the Whitehead–Russell axiom of

infinity.xvii

Having somewhat salved his Leśniewskian conscience with this writhing, Tarski

thereupon elects to largely ignore such worries and proceed with his platonistic theory. There

can be no doubt that he was caught on the horns of a dilemma: either to make his metalogic

ontologically unproblematic by assuming only the existence of expression tokens, but then be

unable to derive the mathematical results he wanted, or to embrace a limited platonism for

the sake of the mathematical results and risk Leśniewski’s ire. As it was, the lure of the

mathematics was greater than his desire to placate his teacher, and despite his own no doubt

deeply harboured misgivings about the methodological platonism,xviii he continued in that

vein. In due course the expected rejection came from Leśniewski , but Tarski was by this

time able to withstand the severe disapproval.

The rest is history – the history of modern logical semantics. In the early part of the

twentieth century the mathematical approach to logic was in the ascendant, and there was a

kind of scramble for the major metalogical and metamathematical results. This scramble in

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metalogic was largely completed, barring details, by Church’s and Turing’s proofs of the

undecidability of first-order predicate logic in the 1930s. Nowadays, mathematical logic is a

branch of mathematics, and its relevance to the traditional philosophical concerns which gave

it birth, except for a few issues such as the semantics of possible worlds or the significance of

relevance logic, has receded. Meanwhile, Leśniewski’s nominalistic alternative and his

honest if inconvenient scruples have been largely sacrificed on the altar of mathematical

advance. No one – myself not least – will deny the significance and beauty of the

metamathematical results achieved within the platonist framework. But – I shall suggest in

the next section – it is largely irrelevant to understanding how language works and how we

have truth in the real world. So the question then is how the shortfall in a real theory of truth

should be remedied.

3 The Irrelevance of Platonism

Even if it were true that there are timeless, spaceless, abstract entities which are the senses of

expressions of actual languages, and of which a subset (the propositions) are the primary

bearers of truth and falsity, of what would this avail us? We should be guaranteed that truth,

falsity, logical validity, consistency, compatibility, and other semantic concepts, defined

platonistically, are well-defined and furthermore defined in the simplest and most language-

invariant possible way. This will guarantee the objectivity of logic, as indeed was the

principal aim of those who invoked such platonic meanings - Bolzano, Frege, Husserl.

Now let us turn our attention groundwards to ourselves and our endeavours. Is the

assurance of a platonic heaven of meanings any help to understanding what we do when we

talk, refer, judge, and reason? I suggest it is an extravagant irrelevance. Every human being

learns to speak in space and time from other human beings in space and time via causal

signals in space and time and with reference to their enveloping spatio-temporal environment.

That the spatio-temporally produced words they utter and hear and understand have to

express things, say things, be right or wrong, needs to be appreciated and understood in terms

of what resources are at their evident disposal. These are all spatio-temporal. Miracles – or

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surd and incomprehensible grasping or intuiting – aside, we have no way of communing with

the extra-causal realm of meanings. We need a theory of how we can speak, understand,

infer, be right or wrong, which makes use just of those things which a naive observer can

observe. This is bound to be messy, untidy, mathematically inconvenient and unlovely, with

holes and gaps, anything but fit to ground the elegant results of mathematical logic. So what?

Are we interested in mathematical beauty or in explaining the real facts? If someone wishes

to idealize and simplify, or to come along afterwards and give a nice elegant mathematically

invariant theory of what is going on, they are heartily welcome. Let them not imagine they

are explaining. They are merely summarizing that for which another explanation is required.

This is no knock-down argument against platonism. There is none. Like all good

metaphysical theories (and I mean ‘good’ literally, not ironically), platonism is not to be

refuted by gut feelings or gauche incomprehension. The best way to look at it is associated

with the name of Brother William. If we can give a reasonable account of what is going on

when people refer, predicate, tell the truth or not, infer validly or otherwise, which both

covers the plethora of things to be explained and does not drag in any supernatural entities,

then even if platonic entities exist that explanation is to be preferred as the more parsimonious

over the platonic. Platonism may be true. In the absence of a convincing account of the

relationship between us and the platonic objects, we cannot afford to rest content with a

platonistic explanation of logical notions such as truth. There is real work to be done.

4 The Variety of Truth-Bearers

In the history of semantics from Plato to the present, several kinds of entities have been put

forward as candidates for having the properties of being true and being false, and standing in

logical relations such as consequence or incompatibility. Most frequently – in terms both of

the length of time over which such views have been held and the variety of champions – have

been mental occurrences and dispositions such as judgements, assumptions, and beliefs.

From the twentieth century – and here the Lvov–Warsaw School played a leading part in the

shift; one observes it when progressing from Twardowski to Łukasiewicz – it has been

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linguistic entities such as sentences or statements or assertions which have played the part.

From Bolzano onwards, notably with Frege, Husserl, and Church, the truth-bearers have been

abstract propositions, construed as the meanings of sentences and the contents or objects of

judgements and beliefs. With the disagreements about what should be regarded as truth-

bearers have gone disagreements as to whether truth is absolute or relative, or indeed whether

it can properly be defined for anything so unruly as a vernacular language.

The problem of the plethora of truth-bearers is much worse than is dreamt of in

Plato’s worst nightmares. Practically anything can be a truth-bearer, and very many diverse

kinds of things in fact are.

Mental events may be true or false: occurrent judgements, assumptions, and the

propositional acts which are part of others. One need not believe or judge something to

entertain that thing mentally. Someone who judges a disjunction entertains both disjuncts

even if she judges neither. Even someone who expressly denies or doubts something that is

true entertains the true proposition non-believingly.

Mental states such as beliefs, whether they are dispositions or not, likewise admit of

evaluation as true or false. We are all familiar with people who live all their lives subjectively

convinced of falsehoods, as well as truths. But a belief may also be short-lived. I may judge

on the basis of a reported aeroplane accident that a loved one has met a tragic death, only to

be reassured seconds after acquiring the belief by a telephone call that she was fortuitously

delayed and missed the fatal flight. The belief may last a shorter or a longer time.

The vast majority of our mental convictions, the thousands per minute arising

continuously during our waking life by perception, having to do with the humdrum properties

and configurations of things in our immediate environment, rarely rise to the dignity of being

expressed in words or of forming themselves into salient thoughts. For all that they may be

true or, less frequently, false, and prove their existence on those occasions when need for

witness drags them from previously mute memory.xix

Some of our thoughts and beliefs are unconscious. Eliciting them or finding this out is

clearly a more indirect process than simply asking the subject, but they do exist just the same.

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Let us move on to linguistic items. Primarily of course there is spoken language,

which consists in events of production of intelligible sounds with a meaning. There are in

general three phases to such events: production, propagation of the sound from the speaker,

and reception by the audience, who hear and in normal circumstances understand what is

said. Then there is writing, in which language is fixed graphically in some way as relatively

stable signs, whether written by hand or printed. Finally there are now manifold other ways

of recording and presenting linguistic items: sound recording, video recording and film, and

other relatively stable media such as computer disks. Also many people now read much of

their language on a computer screen, which is a more evanescent medium than the printed

page but less fleeting than spoken language. In the case of all the media which store spoken

or written language, such as tape, disk, CD and so on, the actual form of the stored

information is not immediately intelligible to people, being in such forms as magnetized

domains or the pits and bumps of a CD surface, and which require equipment and often

software to translate into a form intelligible to human beings. Similar remarks apply to the

modes of propagation of language from place to place, whether via the electric pulses of

landlines, radio waves carrying (by amplitude or frequency modulation) mobile and satellite

telephone conversations, radio and television channels, or the encoded bytes of internet

communication. There is no obvious barrier short of physical impossibility to the ingenuity of

scientists and engineers in discovering new ways to encode and transmit linguistic

information from one place to another. In the past other ingenious propagation systems such

as smoke signals, drums, semaphore, maritime flag signals, heliographs and Aldis lamps

using morse code were used to overcome the problems of sending linguistic messages long

distances.

We are indeed very familiar with the many methods by which linguistic

communication takes place: I am simply recalling their unbridled variety. Without for one

moment denying the ontological primacy of spoken language in all this, and the secondary

but still important position of written language, all the carriers of linguistic messages in

whatever form may in a more or less derivative sense be called true or false whenever what

they carry is interpretable at either end propositionally. A string of bits on a computer disk

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may be true or false as can a series of frequency modulations carrying part of a mobile

telephone conversation. They may not be immediately intelligible to us, but they carry or

bear a truth-value.

In all this variety a general ontological duality is present, that between persisting

things and events, or continuants and occurrents. This duality entered perceptible language

with writing and pervades all aspects of the communicative process. Writing a sentence in a

letter is an event, but the resulting written sentence is a thing which may persist long after the

event of writing it has ceased. That of course is the main point of writing: to record

permanently or at least for a longer time what otherwise dies away. But the duality is actually

present from the beginning in a less obvious way, since the memory traces of what someone

has said persist within us. People can still remember years afterwards what they heard on

some special occasion such when they proposed marriage, or a dramatic public event such as

President Kennedy’s utterance of “Ich bin ein Berliner”. Less dramatically, we may

remember more everyday spoken sentences for some seconds, minutes or hours after they are

spoken, and may remember their “gist” rather than the actual words for much longer.

This brings me to what may be the most numerous class of truth-bearers directly

concerning human beings, which are events of hearing or reading (and understanding). A

single production event may propagate and cause reception events in many thousands or even

millions of people, as when one person addresses a crowd or makes a broadcast. An author

may write a sentence only once but once it is printed and published, many millions of people

may read and understand it. Each of these events is truth-evaluable. When a TV newsreader

says “Concorde has crashed” and millions of viewers hear it then each of these events of

understanding has the same truth-value as the original statement, and the number of tokens of

this truth increases by millions in a second.

5 Primary Truth-Bearers

In all this multiplicity, it would be surprising if there were not some candidate truth-bearers

which play the role more centrally and more fundamentally than others. Proposition theorists

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have always assigned this role to propositions: thoughts or utterances are true or false in so

far as the propositions they express or have as their content are true or false. The rationale for

this is twofold. Firstly, propositions are objective and mind-independent and guarantee the

same truth or falsity for all. Secondly, their truth or falsity is not subject to the vicissitudes of

circumstance: since they are eternal objects, truths are true and falsehoods false without

qualification or variation. Truth is absolute. Without propositions, these desirable qualities

have to be underwritten in another way.

There are some general principles which can guide us to a reasoned decision as to

what are the primary truth-bearers. If one item is meant as a record of another item, whether

written or audio or video recording or some other way, then clearly the item which is

recorded has priority over the recording. Thus diaries are posterior to the thoughts the diarist

has which are set down, and recordings of conversations posterior to the conversations

recorded. A second principle is that an item whose truth-value can be uniquely recovered

from the situation and the facts is preferable to an item whose truth-value cannot be so

recovered. A scribbled note on a locked office door saying “Not in this afternoon” does not

allow the casual reader to assess whether it is true or false because the note leaves no trace of

when it was posted. There are several ways to “disambiguate” such a note: one is to replace

the relative time expression by an absolute one: “Not in on the afternoon of 21 July”, or

indeed to leave the relative time but note the date of posting: “21 July – Not in this

afternoon”. But with the message as it stands we would be able to determine its truth-value if

we knew on what day it was posted. So the physical act of posting the written message, rather

than the written words themselves, should be considered the primary truth-bearing item. But

it is not the only prior truth-bearer connected with this notice. Anyone coming by and reading

the message will probably think to themselves something like “The occupant of this office is

not in this afternoon”. They are thereby assuming it was posted on the day they see it, which

may be false: perhaps the note has been there for one or more days. So those reading the

notice on subsequent “wrong” days think a thought not intended. the friend of propositions

would say that the note’s text does not determine a unique unambiguous proposition. Without

propositions, I say: the note itself conveys one thing when posted and that act as well as any

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act of understanding on the same day share their truth-value, whereas any act on subsequent

days might have a different truth-value. Here the items whose truth and falsity are up for

consideration are acts of “uttering” (in this case, the physical act of posting the notice on the

door), and any number of acts of understanding the notice.

When a speaker addresses a large audience, whether in one place or via the mass

media, and says for example “I shall bring forward legislation in this parliamentary session to

improve our schools”, whereas the friend of propositions would say the speaker and the

audience all understand the same proposition, I say the speaker commits one truth-bearing

act, the act of uttering those words assertively with understanding, while each (linguistically

suitably competent) hearer experiences another truth-bearing act, that of understanding them.

There are as at least as many acts as there are participants, active or passive, in the

communication. Even if the speaker is lying, or if some in the audience do not believe what it

said, these acts have the same truth-value (true or false as the case may be). If the speaker

indeed is lying, he or she is “saying in his or her heart” the opposite, and those who

disbelieve the speaker are thinking to themselves “I don’t believe this”. These are acts whose

truth-value may vary (and in the speaker’s case must) differ from that of the acts of asserting

and understanding.

So it will be seen from these examples that brief, occurrent acts of thinking, uttering

or asserting, and understanding are what I am putting forward as primary truth-bearers. Many

of these are mental acts not marked by immediate outward activity, and in that respect I

return to the views of Twardowski, who held, following Brentano, that it is individual

judgements which are truth-bearers, rather than sentences, as in later Polish philosophy.

However sentences, in the sense of occurrent, spoken sentence-tokens, may be considered to

have their truth-values coevally with the acts of asserting or propounding them: there is little

point in forcing a priority on the act of uttering a token over the token itself, or vice versa,

since the two are so intimately interdependent. These public items (aural linguistic events)

may thus be considered primary truth-bearers. Sentence-token-understandings by contrast are

not public linguistic events but private, mental linguistic events. Other linguistic items may

have truth-values, but they have them derivatively. A written or recorded sentence token, one

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which perdures as a continuant after the event of producing it has ceased, may by virtue of its

persistence come to be systematically misleading, as in our note on the door example. We

have a choice of ways of regarding its derived truth-value. We could say it inherits it from the

act of production, and so remains true or false despite the fact that due to its linguistic

meaning it becomes misleading as time goes by. Or we could say its meaning forces a

different truth-value on it as circumstances change around it. Both of these ways of assigning

it a truth-value are consistent, and by carefully labelling them differently they are consistent

with one another. Each form of derivation has its drawbacks: the first leaves truth-value

invariant but decouples it from the token’s meaning, while the second keeps the link between

meaning and truth-value at the cost of relativizing truth. But in either case the truth-value is

derivative so the absoluteness and transparency of primary truth is unaffected.

A continuant linguistic token may vary with other factors than time. Imagine a

travelling circus which takes around with it portable notices saying “Our circus here tonight”.

At each town they visit they put up the notices, but the place referred to on each occasion is

different, as well as the time. One could imagine the circus going bankrupt and the signs

being sold to a different circus, so the signs refer to a different circus from then on.

Obviously when we move from sentence-tokens to sentence-types the scope for

variation is much greater and more apparent. One can well understand the attractiveness of

“eternal” or “standing” sentences, whose truth-value, given their linguistic meaning together

with the way the world is, is invariant across the type. Such sentences share with propositions

their absoluteness without suffering the same ontological obscurity. Even if one admits

abstract types in addition to concrete tokens, their relationship to the tokens is more

transparent than that of propositions to – what? Sentences? Acts of uttering and

understanding? Sadly though, eternal sentences are a tiny minority of those actually

produced. Nearly all sentences have a meaning which makes their truth-value dependent on

the circumstances of their utterance. Far from being central, they are a sideline, a welcome

exception to the hard work which needs to be put in to guarantee the absoluteness of truth.

Beliefs, considered as standing or continuant dispositions to assent, share similar

vagaries of truth-value variation to sentence-tokens, though being private states they are not

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obvious to others for inspection except as the person whose beliefs they are manifests them

through utterance or other linguistic act.

These central examples may stand as representatives for the whole variety of truth-

bearers. Primacy is accorded to occurrent events of production or understanding or concrete

linguistic tokens, and other things that are ascribed a truth-value derive theirs from these

primary truth-bearers. The question whether truth is absolute or not should therefore

concentrate on the primary truth-bearers.

6 Terminological Repossession

It is convenient to have a word for primary truth-bearers. I shall for the remainder of this

essay re-appropriate the word ‘proposition’ for this purpose. The reasons are threefold.

Firstly, it is short and suggestive. Secondly, the sense of a proposition as an abstract Satz an

sich or Gedanke — a use going back no further than to Moore and Russell in the early 20th

century — is not being employed constructively for the duration of this essay. In future I

shall use the expression ‘abstract proposition’ for such things. Thirdly, and most importantly,

this is by far the oldest of uses of the term ‘proposition’ in English, dating from the time (and

pen) of Wyclif in the 14th century and used in the first logic book in English, Thomas

Wilson’s Rule of Reason of 1551: “A Proposition is, a perfecte sentence spoken by the

Indicatiue mode, signifying either a true thyng, or a false.”xx Sense 4. a. (a), dating originally

from around 1340, of the noun ‘proposition’ in the Oxford English Dictionary is given as

“The making of a statement about something; a sentence or form of words in which this is

done; a statement, an assertion”. This definition corresponds closely with our analysis to the

effect that primary truth-bearers include both acts of proponing (I shall use this word, dating

back to c. 1375, for the act) and the (token) utterance produced. The only slight discordance

with our findings of the previous section is that acts of understanding would not typically

have been called ‘propositions’.

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7 Context-Dependency of Truth-Value, What

The obvious threat to the absoluteness of truth comes from the apparent context-dependency

of truth-value for propositions. But we need to be clear what this context-dependency

amounts to. Propositions, as we are now using the term, are concretely situated events. They

are indeed typically associated with forms of words or sentence-types (which means they are

associated with particular languages), and these types tell us which linguistic competence a

speaker or hearer has to bring to the understanding of a particular utterance. However the

assessment of the truth-value of what someone says depends in most cases on more than the

meaning associated with the expression token uttered. It is the dependence of truth-value of

linguistic expressions of this type on their context which is what context-dependency is, not

dependence of the particular proposition on its context. The context is in general richer in its

descriptive content than is exhausted by the relevant linguistic type. When my friend John

says at five on a Friday afternoon “I need a drink” then my knowledge of English does not

suffice for me to know who needs a drink when, but knowing who says it when is sufficient,

and my knowledge of the meaning of the English first-person singular nominative pronoun

and the present tense do enable me, in conjunction with the knowledge of who speaks when,

to compute the likely proposition (and its truth-value). Were my friend Anne to say the same

thing the next day at lunchtime then similar linguistic competence would come into play in

conjunction with my particular knowledge of the situation of her utterance to enable me to

pull off a similar feat. But the propositions themselves, their proponings and my

understandings, are not context-dependent, since they are already embedded as the acts they

are in their contexts. Propositions as such are not context-dependent: what is context-

dependent are the relevant sentence or expression types. Context-dependence affects

expression-types in respect to reference, truth-value, and other dimensions of disambiguation

such as the use of multivocal words or proper nouns naming more than one object –

Manchester (England) vs. Manchester (New Hampshire), or my friend Ewa Kowalska vs.

Maria’s cousin Ewa Kowalska. When a proposition (of whatever ontological type, whether

mental or linguistic) suitably matches the type of its associated sentence-token (produced or

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understood), i.e. is in context about what the sentence would be properly taken to be about,

and means what the sentence would properly be taken to mean, then I shall call the

proposition appropriate to the sentence.

8 How To be Absolutely True — In Context

Let us consider how a proposition (in our sense) can be absolutely true, and yet how the

meaning of any associated type-expression may contribute towards determining the truth-

value. What we are looking for is a generalisation of Tarski’s T-schema which takes account

of context. Here is a typical case. I say to Jan ‘Maria’s cousin Ewa is getting married in St.

Mark’s tomorrow’. Many tokens of such a sentence type could and some most probably have

been uttered in proponing different propositions. Consider then such a proponing act. Assume

for a start that it is a genuine assertion. Then provided the speaker and the addressee both

know who is being spoken about and which church is in question, they understand one

another and their proponings match in truth-value. The link to the linguistic meaning is

regular and can be captured in a quantified conditioned biconditional as follows:

(1) For all P, D, E and C:

if P is a proposition appropriate to the utterance on day D of a token of the English

sentence ‘Maria’s cousin Ewa is getting married in St.Mark’s tomorrow’ such that

‘Maria’s cousin Ewa’ refers to the person E and ‘St.Mark’s’ refers to the location C

then:

P is true if and only if E gets married in C on the day after D.

There are one or two perhaps surprising aspects of this analytical suggestion but let us first

consider a few more examples.

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(2) For all P, S, H and T:

if P is a proposition appropriate to the utterance by S to H at time T of a token of the

Polish sentence ‘Kocham ciebie’ then:

P is true if and only if S loves H at T.

(3) For all P, L and T:

if P is a proposition appropriate to the utterance at T by a speaker indicating location

L of a token of the German sentence ‘Ist dieser Platz frei?’ then:

P is true if and only if the location L is unoccupied (free) at T

(4) For all P, H and T:

if P is a proposition appropriate to the utterance to H at time T of a token of the

French sentence ‘Asseyez-vous!’ then:

P is true if and only if the H sits down immediately after T.

Here is a case of a standing sentence:

(5) For all P:

if P is a proposition appropriately connected to a token of the English sentence type

‘17 is a prime number’ then:

P is true if and only if 17 is a prime number.

Finally, here is a surprising example:

(6) For all P, L and T:

if P is a proposition appropriate to the utterance at time T in external surroundings L

of the Polish sentence ‘Śnieg pada’ then:

P is true if and only if it is snowing at T in L.

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These and similar analyses are meant to stand in for an open array of examples, simpler and

more complex. Let me now draw attention to the most salient features of the examples.

(A) Within the context of the universally quantified implicational sentence, the embedded

biconditional is a T-sentence schema.

(B) The predicate ‘is true’ in this schema does not contain any bound variable within it and

is accordingly absolute, and in particular untensed.

(C) The dependence of truth-conditions for the proposition on factors of context is carried

by the universally quantified variables affecting the T-schema and by the conditions in

the antecedent.

(D) These variable factors and conditions affect different aspects of context of utterance

and the form of dependence, common but by no means invariable factors including

speaker, addressee, time and place of utterance.

(E) There is no uniform recipe for all cases: how the dependence works depends on

features specific to the language and expression type in question.

(F) The common denominators to all cases are the biconditional form, the variable for the

proposition P, the absoluteness of the truth predicate, and therefore of the right-hand

side of the biconditional once the variables are replaced in any actual case by

constants, and the need to specify the language to which the sentence token belongs.

(G) It is not always necessary to know who the speaker is or the time of utterance. In some

cases, as in (5), knowledge of the utterance act itself is unnecessary beyond minimally

knowing to what language the token is intended to belong.

(H) The proposition need not be directly connected to an assertion. It may be involved in

uttering or understanding a question (Example (3)) or a command (Example (4)). A

competent German speaker will propone to herself a proposition to the effect that the

indicated place is free when hearing the question – whether she accepts that the place

is free or not. If she knows it is not, she will almost certainly immediately afterwards

propone to herself a proposition negating this – ‘(No,) This place isn’t free’. A

competent French speaker will propone to herself in case (4) a proposition to the effect

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that the addressee will sit down – whether or not she expects it. Such a proponing is

not necessarily assertive, it comes with simply understanding what is said and so

makes clear the general dependence of propositions like those considered on specific

linguistic competences (which may involve much less than a good grasp of the

language in question).

(I) It is not assumed that the speaker must be speaking in good faith or in full knowledge

or that speaker and addressee or speaker and hearer (if hearer is a third party) share all

the relevant knowledge. For instance in (2), the speaker may be lying, or self-deluded,

or making a linguistic mistake (e.g. thinking that ‘kochać’ means ‘to like’), or have

mistaken the addressee in the indifferent lighting of a discotheque. These are all forms

of what Austin would call “infelicity” which do not affect the embedded truth-

conditions. In some cases it will not be the speaker who is proponing P. If I, under the

mistaken impression that ‘kochać’ means ‘like’, say to Ewa ‘Kocham ciebie’ then my

proponing is to the effect that I like her whereas hers and that of competent Polish

speakers who might chance to overhear is to the effect that I love her. We make

symmetrical mistakes: due to my linguistic incompetence they do not understand my

proposition and I invoke inappropriate propositions in them (especially in Ewa!) But

their propositions are appropriately connected to my misleading utterance, mine is not.

They misunderstand me because they correctly understand my utterance.

(J) It is in general possible for certain kinds of mistake to be unimportant for the truth-

conditions of a proposition: for example both speaker and hearers in Example (1) may

wrongly think that the church C is called ‘St. Mark’s’ when it is in fact called ‘St.

Matthew’s’. But in the context, our parallel mistakes do not matter: ‘St. Mark’s’ does

refer in such a case (inappropriately) to St. Matthew’s. Someone who knew that C is

called ‘St. Matthew’s’ would therefore misunderstand the speaker’s utterance or could

be even more knowledgeable and know the speaker was wrongly referring to St.

Matthew’s church as ‘St. Mark’s’. There is no obvious upper bound to the kinds of

infelicity that may occur. For example perhaps speaker and listeners know that St.

Matthew’s is meant but have made a prior arrangement to use the wrong name because

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they fear the bride’s revengeful ex-boyfriend may turn up and cause trouble, and

suspect he or a friend of his may be lurking around to find out when and where the

wedding is to take place. All it takes is a lively imagination or a surfeit of reading spy

novels to come up with still more devious cases.

(K) Standing sentences (Example (5)) are particularly straightforward and yield – modulo

the fact that ‘P’ varies over tokens rather than types – Tarski’s T-schema.

(L) Speaking of Tarski, Example (6) is his and is meant by him to illustrate the basic

(absolute and context-free) T-schema. It cannot be both absolute and context-free: I

say to preserve absoluteness of truth it is doubly context-dependent: on time and

location.

(M) Because the analysis always brings in tokens of sentences of a particular language, it

will not work for cases of mental propositions not connected to utterances or

occurrences of sentence-tokens. Nor should there be any expectation that it should.

How such mental propositions work and get their truth-conditions and therefore get to

be true or false is a difficult and delicate matter and I shall simply duck the issue here

for reasons of lack of space, but it will clearly entail delving into the mental

equivalents of reference, predication and other overtly linguistic manifestations of

thought.

(N) The analysis provides only partial relief from Liar-type paradoxes. Suppose we lay

down the obvious valuation principle that a sentence-token be deemed true iff all

propositions appropriate to the token are true and false if all propositions appropriate

to the token are false. Then if T is the token sentence ‘This sentence is not true’ and P

is any proposition appropriate to it, then P is true iff T is not true, and the assumption

that T is true leads to its opposite and vice versa. However we could simply deny that

just because appropriate propositions are true, the sentence T is true. That would allow

us to consistently allow that T is not true and so any appropriate proposition P is true,

without inferring on the rebound that therefore T is true. In this case, as in the

analogous truth-teller case of a sentence-token saying of itself that it is true, there is no

way out of the circle of assumptions if we accept the obvious valuation principle, but

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we do not need to accept it. More tricky would be a sentence-token U of ‘no

proposition appropriate to this sentence-token is true’. If there were such an

appropriate proposition then if it were true it would not be true and since this would

apply to all such propositions by the obvious valuation principle U would be not true.

Here though the buck stops as something’s not being true does not entail its being

false: cats, cups and computers are neither true nor false. Hence there can be no

proposition appropriate for U. However Liar-type self-reference can be more devious:

there appears to be nothing to stop a proposition being about itself, expressible in

words tantamount to ‘This very proposition is not true’, so by the expected T-sentence

it would be true if and only if it were not true. Hence although certain kinds of

linguistically-mediated paradoxes may be disarmed, at rather little cost to our

intuitions, the possibility of paradoxical propositions cannot be ruled out, provided

only propositions can refer to or quantify over propositions. Thus the switch from

abstract to concrete propositions as primary truth-bearers only avoids some paradoxes

and not others. The switch to concrete propositions may safeguard the absoluteness of

truth where truth is well-defined, but it is not a panacea against paradox.

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References

Leśniewski , Stanisław: 1992, Collected Works. Dordrecht: Kluwer.

Pearce, David and Woleński, Jan, eds.: 1988, Logischer Rationalismus. Philosophische

Schriften der Lemberger–Warschauer Schule. Frankfurt/Main; Athenäum.

Simons, Peter: 1997, Linearity and Structure: The Discrepancy between Speaking and

Thinking. In Alex Burri ed., Sprache und Denken/Language and Thought, Berlin: de

Gruyter, 30–41.

Suppes, Patrick: 1988, Philosophical Implications of Tarski’s Work, Journal of Symbolic

Logic 53, 80–91.

Tarski, Alfred: 1933. Pojęcie prawdy w językach nauk dedukcyjnych. “Prace Towarzystwa

Naukowego Warszawskiego, Wydział III. Nauk Matematyczno-Fizycznych”, nr. 34.

Warszawa. Reprinted in Tarski, Pisma logiczno-filozoficzne Tom 1 “Prawda”,

Warszawa: Wydawnictwo Naukowe PWN, 1995, 13–172. English translation: The

Concept of Truth in Formalized Languages, in Tarski, Logic, Semantics,

Metamathematics. Oxford: Clarendon Press, 1956, 152–278. Reprinted Philadelphia:

Hackett, 1983.

Twardowski, Kazimierz: 1900, O tzw. prawdach względnych, in: Księga Pamiàtkowa

Uniwersytetu Lwowskiego ku uczczeniu pięćsetnu rocznicy fundacji jagiellońskiej

Uniwersytetu Krakowskiego. Lwów. German translation by M. Wartenburg, ‘Über

sogenannte relative Wahrheiten’, Archiv for systematische Philosophie 8 (1902), 415–

447. Reprinted in Pearce and Woleński, eds., 1988, 38–58.

Wilson, Thomas: 1551, The rule of Reason, conteinyng the Arte of Logique set forth in

Englishe. London: Grafton, 1551. Reprinted London: Kyngston, 1580.

Woleński, Jan and Simons, Peter: 1989, De Veritate: Austro–Polish Contributions to the

Theory of Truth from Brentano to Tarski. In: K. Szaniawski, ed., The Vienna Circle

and the Lvov–Warsaw School. Dordrecht: Kluwer, 391–442.

Yourgrau, Palle: 1991, The Disappearance of Time. Cambridge. Cambridge University Press.

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i Woleński and Simons 1989. ii I stress, for philosophy. History of philosophy has to be brought to each new generation anew. iii The fact that the historical passages refer mainly to figures now wholly forgotten serves only to highlight the magnitude of Bolzano’s leap forward. iv Twardowski 1900. v Cf. Yourgrau 1991, pp. 104 ff. vi The first and still perhaps the greatest proponent of semantic platonism is Bolzano, ably seconded by Frege. vii An exception is tense, which Leśniewski treats – like Bolzano and Carnap – by invoking time-slices of objects. See Leśniewski 1992, 379–82. viii Cited according to the English translation of 1956 and the Polish reprint of 1995. ix Leśniewski did not describe himself as a nominalist because he believed in phenomena such as after-images, but after-images and any other mental qualia are not necessarily universal entities though they might not be physical. There is no reason why a physical/phenomenal dualist may not believe that all entities are particular, and hence be a nominalist. x Cf. Leśniewski 1992, 471: “Two expressions equiform to each other written in two different places are never the same expression.” xi Tarski 1995, 19n.5; 1956, 156n. xii Ibid. xiii Cf. Definition 18, Tarski 1995, 57;1956, 185. xiv Cf. Tarski 1956, 63. xv Tarski 1956, 64. xvi Tarski 1995, 55–7; 1956, 183–5. xvii Tarski 1995, 57; 1956, 185. xviii Tarski’s anti-platonism even to the end of his days is tellingly described in Suppes 1988. xix See Simons 1997. xx Wilson 1551, cited after the Oxford English Dictionary from the edition of 1580, p. 18.