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.....SIX KINDS OF PROPOSITION - Sections 2-5


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2. PROPOSITIONS

Most philosophers understand "propositions" to be the meanings conveyed by sentences such as The traffic lights have just changed to red, "Red" means "stop", Red is a colour, Nothing is both blue and red all over, Either you are at home or you are not at home, All fish have gills, Some fish live in holes, Sabrina avait un crayon jaune, There are about 20 million people living in Australia, 400 x 50,000 = 20,000,000, The shortest distance between two points is a straight line, If Harry plays the Socceroos will win, It will rain in Timbuctu on 31st March 2066, Had it rained the cabbages would have grown, If it rains 2+2=4, I have a terrible headache, Lucy has a terrible headache, I believe what she said, Jack will consider marrying Jill, Allah is the one true god, Frodo is a Hobbit, The King of Australia has a green beard, Smokeless aeroplanes don't exist, The only thing people have in common is that they are different. Most philosophers also regard propositions as the bearers of truth: they are said to be true if what they say is factual or correct (though, as we shall discover mainly in §9.3.2, the assignment of a truth value to a proposition radically changes its nature). The above examples may be elementary, but they will suffice to show that there are different kinds of proposition, apparently requiring different techniques for deciding whether they are true or false (if, indeed, any such technique can be found).

Not all theories of verbal communication, meaning and truth call for propositions. Although of course there are sentences and utterances, according to these theories there are no universals corresponding to "the meanings" (see Endnote 1) of verbal expressions. This viewpoint appears to have its origins in the belief that if propositions fall short of the eternal ideal - if a given sentence-form is not associated more or less unchangingly with a certain meaning - there's nothing useful left for them to do. It seems to me, on the contrary, that most propositions are short-lived, dynamic creatures whose being derives from the interaction of people with their environment, and which are generally well served by whatever ingenious turn of phrase kindles the pleasure of the moment. If it makes sense to speak of (at most) the same sentence communicating the same information on more than one occasion, then it makes sense to speak of meaning and of propositions. And to abandon propositions in this sense is to deny the possibility of language.

Accordingly I consider a proposition (or loosely a statement*) to be a declarative sentence which (i) acquires a sufficient meaning to perform a particular communicative function, (ii) conserves this meaning throughout the performance of that function and (iii) is capable of attaining a truth value. But, in taking it for granted that any number of sentences (forms or tokens, including sentences in different languages) may represent the same proposition, I intend the term "proposition" to refer primarily to its functional meaning, content or utility, and only passively to whatever apparatus conveys this meaning. (*And conversely, of course, the same sentence can have different meanings in different circumstances, which seems reason enough for denying sentences all of the logical properties of propositions. "Sentence" will therefore be used only when it is necessary to refer to the means of expressing propositions, for example in discussing equivalence and semantic theories of truth. Statements have a broader usage than propositions, and include various pseudo-propositions, which for one reason or another cannot attain a truth value, or whose truth value seems ambiguous depending on the circumstances or the person making the statement. My basic approach throughout this article, therefore, conforms to the conventional model, including the assumption that propositions depict or reflect "facts" of one kind or another - a view which I no longer hold. Language does not passively mirror facts; it plays an active role in designing them by imposing its inherent structural properties upon our interpretation of reality.)

The notion of performance of a function involves two distinct ideas. In the first place it implies that propositions take part in active, purpose-oriented processes, including extended language processes such as "arguments", a term which I employ loosely to refer to collections of propositions (only) linked by connectives which may be open to a logical interpretation. Traditionally, a valid argument is one that exhibits (as a minimum requirement) the structure of a tautology, and it might be considered a primary purpose of arguments, in a stricter sense, to approach this type of structure. In the second place the notion of performance of a function is associated with that of assertion - the idea that the work of a proposition consists in advancing a specific fact or connection of meanings, regardless of tacit background assumptions or "presuppositions". Often the brunt of this work is borne by a discrete component of the sentence, typically the predicate. In what follows I shall lean on the view that there is a limited, indeed a proper, sense of falsification which consists in denying only what is asserted and never what is merely presupposed (though the difference is not always clear). On this account, a "genuine" proposition purports to be true, in just one of the several senses of truth, and if not true it is either false - implying that there is a true proposition which contradicts what is asserted - or else incompetent - implying that the underlying conditions required for truth or falsity are somehow flawed, by reason of which the assertion relinquishes its argumentive potential. (This is the underlying form of each of the "hexagonal" schemes outlined in §9.1.)

Purportment is not a psychological notion: a proposition purports to be true even when an utterance of it is a deliberate lie: indeed we should not call an expression a lie if it did not purport to be true - for how, then, could it mislead us? While of course negated propositions also purport to be true, a proposition cannot purport to be false: the purportment of truth (of some type) is, so to speak, an intrinsic or necessary default condition of every proposition (of that type) - an observation whose chief importance is that it apparently establishes an inviolable link between truth and meaningfulness. For if every (declarative) proposition contains the possibility of being true, then there's a lot going for the claim that expressions which lack that possibility are meaningless, and therefore not genuine propositions at all. Furthermore one might contend that the purportment of truth and the meaning of a proposition are identical. (Amongst the possible repurcussions of this view are that it puts verificationism on a firmer footing than falsificationism.) Now it may be accepted (usually by definition) that every genuine proposition is either true or false. But clearly the assertion or "positing" of a proposition does not establish its truth value, unless, perhaps, the proposition is a formal tautology or inconsistency. (This is not to be confused with the assumption of the truth of premises in a formal argument.) The mere occurrence of a proposition, whether it be an utterance, an inscription or other representation of it, does not spontaneously make it a true proposition, an observation which receives further attention in §9.3.2 in relation to deflationary theories of truth. Finally let us be quite clear: it makes no sense whatsoever to assert "p purports to be true" or to question whether, or deny that, p purports to be true. The purportment of truth is a basic inherent property of all propositions. How this changes the way we should handle propositions is discussed in §9.3.2, but in what follows it is assumed to have negligible effect. (This para was extended Dec 2014 and Dec 2015.)

The purportment of a simple proposition is therefore associated with its type (the kind of truth engaged to evaluate it), though there are invariably non-assertoric elements present whose "type" differs from that assumed by the proposition as a whole. I include all such inactive elements under the "presupposition" label*, and in §9.1 I submit a classification of basic propositions which broaches the idea that certain of their presuppositional aspects conform to a hierarchy of types, which may be invoked to examine the propositional integrity of any expression. (* A proposition is said to be incompetent if any of its presuppositions don't hold up. I have also used the term ungrounded, both here and in other articles, especially in relation to the environment or context which a statement presupposes. Note that Kripke's idea of groundedness is quite different.)

Whether or not this concept of purportment is sustainable, it's clear that most propositions are each endowed with just one way of being true (one kind of meaning), and that although they might fail to be true for any of a wide variety of reasons nevertheless they generally carry expectations as to how they might legitimately be falsified: that is, expectations as to the kind of meaning conveyed by the negation of the proposition. And since this kind of meaning is typically the same as that required for verifiability, there exist classes of typical propositions whose evaluation depends on only a single species of criterion and which, therefore, are logically unrelated to any of the typical propositions evaluated by other species of criterion. Such propositions conserve their type both under negation and (where applicable) under quantificational manipulation. These represent the basic classes which I contend number at least six. In respect of every basic proposition, therefore, its being held true in the characteristic sense does not imply that it is true in any other sense, nor can the proposition be "reduced" to any other kind.

In any natural language (such as conversational English) the most common propositions belong in a category which I call "material" (see §6). "The cat is on the mat" is a simple example of a material proposition, and it will also serve to illustrate an additional point about the nature of propositions, pertaining to their correspondence with the real world (or our experience of the real world). "The cat is on the mat" describes a state of affairs (it is what I have elsewhere referred to as a situation statement). It does not represent a relation (either logical or of some other sort) between two objects, or between two terms that stand for objects. How language relates to mental imressions and thence to real states of affairs is a question for the philosophy and science of the mind, a field which is doubtless still in its infancy, but this line of enquiry I believe will gain no momentum from the idea that a proposition is a kind of framed reflection of a discrete bit of the world with atomic parts. A more holistic approach is required.

Of putatively non-basic propositions, there appear to be some of mixed type and arguably some which can only be tested for truth in one way and for falsehood in another, or which may change type under quantification. Moreover some assertoric sentences in ordinary language situations appear to discharge two or more functions concurrently (or one or another of them indistinctly). While these mongrel types of expression are quite acceptable in ordinary discourse (for examples see §s 6 and 9), philosophically they are the result and the cause of intolerable confusion, and, were it not for the fact that they often deploy the various types of concepts in a pragmatically coordinated manner, I'd be tempted to dismiss them at once. It must also be acknowledged, however, that many apparently unobjectionable arguments combine different types of proposition, and since any argument can be represented as a complex proposition it might seem that there must exist viable mongrel propositions. This matter receives further consideration in §s 7 and 9, where I suggest that many such arguments are underpinned by a single, type-determining orientation which permits an unequivocal evaluation; otherwise the components of the argument are irrelevant to one another and the argument as a whole is effectively vacuous.

In spite of this setting, it cannot be presumed that all meaningful assertions have determinable truth values. But in keeping with the conventional idea that to assert a proposition, from a position of integrity, is to make a statement with some claim to truth of some kind, this discussion will be more or less confined to the range of expressions that seem to me to possess acceptable and clear criteria of truth determinability. Nonetheless these same criteria find application in a variety of expressions - including probability statements and counterfactual and subjunctive conditionals - which I think properly belong in the class of propositions even though they are commonly supposed to be neither true nor false but only inductively strong or weak. In practice the test of truth for most conditionals is similar to that for most direct statements. The fact is, many conditional statements (including subjunctives and counterfactuals) are supported by much more evidence than many direct statements, and this suggests that any distinctions as to truth status formulated on logical or grammatical grounds are almost certainly trivial. Much the same applies to probability statements. Our present concern, however, is with certainties rather than probabilities.

A proposition might be considered certain or necessary if it seems absurd to deny that it correctly depicts a particular process or state of affairs; or if a process or state of affairs that it depicts cannot be conceived to be other than it is; or if the proposition couches a well established regularity of nature or an instance of such regularity; or if its symbolic or semantic relationships reiterate established conventions of usage; or if regardless of symbology or meaning its structure appears to reflect unchallengeable canons of reason; or if its structural elements are arranged in a prescribed pattern or comply with an agreed rule of calculation; or perhaps for less credible reasons, such as that it expounds a self-evident duty or voices the will of an absolute authority. While there may be some who consider such reasons respectable enough to explain the necessity of the propositions, it seems to me that, on the contrary, none of these cases supplies an intrinsic answer to the question why we feel certain in just this case while in a variety of others we remain doubtful. Nor shall I directly address that question here. My aim in this regard is only to suggest (where necessary) that, although the categories I shall describe may be distinguished by the unique quality and durability of their limits, in fact they embrace no indubitable concepts and therefore provide no foundation for the common assumption that human enterprise is constrained by rigid built-in principles.


3. CONSTITUTIVE PROPOSITIONS

Propositions, then, may be classified according to the kinds of criteria used for deciding their truth values. A commonly held belief, derived from Leibniz and Hume and championed by the logical positivists, is that every proposition belongs to one of only two such classes: analytic or synthetic. The evaluation of analytic propositions is said to depend only on their logical structure (overt or implicit) while that of synthetic propositions appeals to the results of empirical investigation. It is commonly held further that true (tautological) analytic propositions are necessarily true, or true of all possible situations, while true synthetic propositions are only contingently or probably true. All formal tautologies, mathematical propositions and linguistic conventions are contained in the former class while all, if not only, empirically true propositions belong in the latter.

Critics of this view, rather than attempting to undermine its foundations, have tended only to blur the analytic/synthetic distinction by contending that (a) propositions may function ambiguously in one mode or the other or change their allegiance with the passage of time; or (b) especially in scientific contexts, the two kinds depend inextricably upon each other for meaningfulness. Thus although they question the stability of propositional roles, they do not, I think, altogether succeed in escaping from the conceptual environment delineated by the analytic/synthetic dichotomy: they quietly suffer the two kinds, while remaining reluctant to point to a statement that epitomises either one of them. The prevailing attitude has sometimes been represented in the following way: provided that the meaning postulates of a language are specified, then we know what's analytic and what's synthetic; however, meaning postulates incline towards arbitrariness and are open to revision. In a sense this is so gross an understatement as to be worthless, since the meaning postulates in my language, anyhow, are apt to change whenever I walk from one room to another.

If we accept this dualism, however, we are compelled also to admit that any two empirical propositions are logically independent. For each proposition is separately capable of verification or falsification, and there could never be any logical necessity that the outcome of an experiment to evaluate either one would affect the outcome of an experiment to evaluate the other. What could be plainer, therefore, than the logical independence of the statements in each of the following pairs?

(a) Joe hit the ball. Share prices collapsed in Tokyo.
(b) Joe hit the ball. Flo missed the catch.
(c) Joe hit the ball. The ball didn't move.
(d) The ball is moving upwards. The ball is moving sideways.
(e) The ball is red. The ball is blue.
(f) The door is open. The door is closed.
(g) The switch is on. The switch is off.
(h) The electron took this route from A to B. The electron took another route from A to B.
But while almost everyone would agree that the propositions in the couplets (a) and (b) are logically independent, and many would say the same of (c) and (d), I've little doubt that most would find increasing difficulty with (e)-(g), ), even though they might hold the opinion that the propositions in the analogous example (h) are, at least, not plainly contradictory. And although the logical independence of empirical propositions appears to be an inescapable consequence of the analytic/synthetic dichotomy which is the cornerstone of logical positivism, astonishingly it is just the proponents of this creed who have contended most strongly that propositions like those in the couplets (e), (f) and (g) are logically incompatible (which is to say that the proposition which expresses the negation of their conjunction is tautological).

Hahn (1933), for example, asserts: "Like the statements 'every snow rose is a helleborus niger': and 'nothing is both red and not red', the statement 'nothing is both blue and red' says nothing at all about the nature of things; it likewise refers only to our proposed manner of speaking about objects, of applying designations to them". But although it's possible to give academic credence to this aloofness of language from the world of facts, the practical absurdities inherent in this approach are all too obvious: a language with no points of contact with reality can never speak about anything. There appears to be a lamentable confusion between matters of nomenclature, such as the definition of the snow rose as helleborus niger, and possible states of affairs, such as that the door cannot be open and closed at the same time.

Rationalists of a certain breed are inclined to demand the best of both worlds by insisting that any two apparently substantial but incompatible propositions such as (g) are at once factual and logically (hence "necessarily") contradictory. But their standpoint leads, in my view inevitably, to the unacceptable extravagances of a kind of "global essentialism" (wherein any attribute or state assumed by an object is "necessarily" tied to it): since they would, I think, be obliged to turn our list of examples on its head and thus finally to admit that not only (g) but all the pairs of propositions with the possible exception of (h) are logically connected, while doubtless they would feel compelled to translate (h) into more subtle language. Yet there's a corollary to this outlook, namely that physically unrelated propositions cannot consort in a single cohesive argument, which I shall support in §7.

Such radical essentialism is untenable. The hallmark of these seemingly incompatible physical states is precisely their lack of logical sharpness. For example, between the door being fully open and fully closed there is an infinite number of possible intermediate conditions. Is the door open or closed if there is a 5 mm gap between it and the door jamb? The switch might be "off" when there is a 2 volt difference in electric potential across it, but when the difference is 200 volts a series of electrostatic discharges might occur, causing a current to flow. Is the cat in the basket or not in the basket if its tail is hanging overboard?

I am not now too sure about all of this. For example, it's arguable that exactly the same observations would be relied on to verify that the switch is on as to verify that it is off. In other words it's arguable that there are not really two empirical propositions to consider, since their content (meaning and reference) is the same. Example (e) is also questionable, while (c) and (d) seem fair enough (see below). But by the same token how could one ever be certain that the propositions in (a) are not logically contradictory? Nevertheless, I continue to maintain below that "'The cat is in the cupboard' and 'The cat is not in the cupboard'" violate the general constitutive (intrinsic) proposition "No organic individual can be in two places at once".

My view, then, is that "The ball is red" and "the ball is blue" are logically independent empirical propositions; so "The ball is not both red and blue" expresses an empirical relationship and not a tautology or a linguistic convention. For the reality appears to be such whether or not we possess the language to express it: language conforms with the facts and not vice-versa. Still, it can hardly be doubted that this proposition depicts a fact of a strikingly different kind from the mere fact that the ball is red. It is different for just those reasons which the positivists customarily offer: it contains what looks like a logical relation and it's not the sort of fact that one would ordinarily verify by physical examination. And these are just the qualities that imbue propositions representing facts of this sort with a distinctive air of necessity.

An air of necessity the likes of which can be found nowhere else. In comparison, the definitions of language are mere artefacts that can blow away in the wind, while many scientific laws seem fragile alongside these megaliths. In the ideal gas laws, for example, one can imagine the constants having different values; one can even imagine that gases might contract in volume when heated at constant pressure. But one cannot imagine a surface that's red and blue all over at once, or a cat that exists in two places at once. The laws in this category, one might say, are indispensable and inescapable, and in that sense "more certain" than many scientific laws. However, there are no sharp boundaries between the two kinds, and one can discern a gradation of necessity through both kinds. (Consider, e.g. "No person can survive without oxygen" and "No person can survive unprotected at the centre of the Sun".) And this admission of degrees of certainty must create doubts about the inescapability of any physical laws. Many fundamental concepts must have appeared inescapable to one generation or another - Newton's Laws, for example - but the progress of science has pushed them aside (see §3.1). This is further evidence that the apparent indubitability of the most obdurate of these concepts is not logical in character; so what is its origin?

An answer given by J.S. Mill (1884) was that such laws are inferred from large numbers of observations of supporting instances together with a total absence of conflicting observations. The surface of every object we have ever seen has been of just one colour in the same part at the same time; so if this ball is red all over the chances are extremely high that no part of it is also blue. The weakness of this answer is its failure to distinguish this type of case from the more ordinary: "Every sheep we have ever seen eats grass; so there's a good chance that this sheep eats grass". For while we might not be all that surprised to learn that a particular sheep doesn't eat grass, we should be incredulous of any suggestion that the ball is red and blue all over at the same time. The difference is that we can imagine sheep that don't eat grass but we cannot imagine surfaces that are coloured in more than one way in the same part at the same time. Nor can we imagine a cat that is both in the cupboard and out of the cupboard, or an electron that went through two holes at once, or a person who lives and moves in a 5-dimensional space*, or parallel lines that meet, or a straight line that is not the shortest distance between two points, or.... Regardless of the practical utility of any of these "concepts", the truth is that we cannot conceive of them at all, because the world of our immediate experience accommodates no such phenomena. The weird monsters of modern science and the contortions of pure geometry provide no grounds for censure of the Kantian notion of a priori synthetic propositions. For the illusion of necessity inherent in propositions of this type derives entirely from our inability to form a picture of any state of affairs that doesn't comply with them. Whether this is due to our mental constitution or to the structure of objective reality or to some other cause is not now at issue (and perhaps it isn't a genuine issue anyway). What is clear, however, is that the relationships expressed by these propositions are not purely formal. (* Note: Considering the example of space, one can imagine that there may be more than three dimensions in which some kind of entity exists and moves, but one cannot imagine that space in itself, any more than one can imagine colours that are outside the observable colour spectrum. There's a vast difference between conjecture and experience.)

Particular statements that express impossibilities in the real world, such as "The ball is red all over and blue all over" and "The cat is in the cupboard and out of the cupboard" and "The ball is not moving up or down, left or right, back or forth, nor is it motionless", all exemplify general propositions representing the way things in the real world are not. These propositions can be re-stated (essentially by negating them) as natural laws setting out the way things are, and can only be in the world in which we live, thus: "No discrete surface can be covered all over with more than one visible colour at once"; "No organic individual can be in two places at the same time"; "No macroscopic object can move in more than three dimensions". All such expressions, as well as all specific cases that exemplify them, may be called constitutive propositions - intrinsic if positive (seemingly tautologous) and inconceivable if negative (seemingly inconsistent) (see Endnote 2). Constitutive propositions, it could be said, frame the conditions for observation or, more correctly, for exploration, for dynamic interaction between persons and their surroundings. Or you might say they are propositions which declare the pre-conditions for thought and experience, or which depict instances of such. In §7 we will consider these propositions further, along with the (trite) question whether we should call them "logical" or not. Although it must be admitted the boundaries of this class of propositions are quite vague, there are, I think, many unambiguous examples that can be clearly distinguished from other kinds of proposition which one might also be tempted to call "logical". And despite the inherent weakness of the constitutive category, I believe much philosophical dialogue to this day labours uncompromisingly within its walls, a situation which is to some extent exemplified by recent discussion of the status of scientific unobservables.

3.1 Unobservables

The constitutive concept might appear to some to be open to broader and narrower interpretations. Thinkers in many fields and in every age have recognised in their own ways, implicitly or explicitly, the existence of fundamental principles governing our universe: Euclid with his axioms, in particular the infamous parallel postulate; Locke with his primary qualities; Newton his laws of dynamics; Kant his forms of intuition and the somewhat over-zealous list of categories; and more recently philosophers of science in their discussions of unobservables. But philosophers of science often construe the concept of unobservability so widely as to deprive many quite ordinary entities of their passports to the domain where ordinary rules hold sway. Among scientific unobservables they might well include, for example, microwave radiation and magnetic fields, just because we do not possess the sensory apparatus for directly detecting these phenomena. On this account they would also be compelled to admit that, for a person blind since birth, light (or what it reveals or seems to reveal to a sighted person) is a scientific unobservable. And I do not think they could then escape from the primitive doctrine that nothing is observable apart from "pure sensations"; whales and queens would be banished to the underworld of wormholes and quarks.

Clearly this will not do: the class of observables includes at least whales and queens, and issues arising out of consideration of the roles of specific sensory mechanisms are philosophically rather uninteresting. Thus the inclination of some philosophers to apply the "unobservable" and "theoretical entity" tags so much more readily than do scientists themselves is apt to lead to absurdities. The great majority of today's physicists will continue to pursue their investigations using instrumentation and methodologies that comply with the same conditions of exploration as those that have constrained adventurers throughout time, from Archimedes and the Argonauts to Avogadro and Apollo 11; and they will continue to interpret their results in ways that relate them intelligibly, if not intrusively, to the world of common experience. For scientists can only do what they do and find what they find - their discoveries only have scientific meaning in so far as they are useful in the real world. Which is to say, at least, that no descriptions of experimental methods or of observable effects conflict with any constitutive proposition.

This still appears, to most of us, to leave science with a formidable exotic zoo; and, even though the gates may one-day swing open, one wonders whether there will ever be customers able to pay the entry fee. But if takers there are none, Kant should feel no duty to revise his treatise. The onus falls, rather, on the shoulders of the new generation of philosophers of science to test the locks on these gates. I believe the best opportunity for rapid progress in this direction lies in acquiring a deeper understanding of the interaction between mathematics and empirical reality (§s 8 and 11).


4. DIAGNOSTIC PROPOSITIONS

Their acceptance of the analytic/synthetic dichotomy has led many philosophers (e.g. Ayer, 1973) to sanction a quite extraordinary jumble of concepts under the "analytic" umbrella. I've called attention to one of the most pernicious of these confusions - that between constitutive and verbal propositions. But what is a "verbal" proposition? Traditionally it is one which, though employing words whose meanings more often than not relate to the real world, lacks any reportive intent: its truth depends only on the supposed logical relationships of the concepts expressed, and not on the correspondence of these concepts with observable facts. Others might put it differently: "the truth of analytic propositions depends only on the meanings of the words composing them, and furthermore they remain true for all situations and all time". But this, of course, depends on those words retaining a constant meaning over time and place. This "semantical" notion of analyticity has of late come increasingly under fire - and not without cause, for it is a mixed concept and logically too much has been expected of it. I shall argue that "verbal" statements fall into two distinct categories: diagnostic, which delimit the meanings of terms, and generative, which expand or contract linguistic frameworks by providing alternative terminology. This section deals with the first category.

There are two common, but mistaken, ways in which a proposition might be thought to be "analytic in virtue of meaning". One way falsely ascribes an underlying analytic meaning to a statement, whose proper meaning is thereby suppressed or corrupted. The other way correctly ascribes a certain meaning to (for example) the subject of a statement - that is, it verbally defines or characterises the subject - but falsely charges that ascription with redundancy, tautologousness and necessity. The first of these is a ploy frequently adopted by positivists and their heirs in respect of propositions such as

(h) The internal angles of a triangle sum to two right angles
in which, according to them, the only admissible sense of truth is the logico-mathematical sense: the sentence yields a true proposition only by virtue of the axioms of Euclidean geometry (or some other geometry in which (h) is a theorem). Moreover, they say, we do not even need to invoke the concept of what we should ordinarily call a triangle - that is, a three-sided planar figure - in order to establish its truth: we can use pure algebra to guide our thoughts instead. (Notice, here, the preference for algebraic formulae over geometrical figures and the unquestioned assumption that our thoughts - whatever they may be - are better guided by that picture than by the latter.)

But now how can it be maintained that a collection of algebraic expressions (or whatever it is that makes them tick) is in any sense a triangle? In what sense is the general concept of the one equatable to the general concept of the other? One might as well ask how a receipt for ten bails of wool is to be identified with the consignment of wool itself. Clearly those who use this argument to persuade us of the analyticity of (h) are not talking about the same class of objects that we normally have in mind when we speak of triangles. They mean a certain species of abstract mathematical entity; we mean a three-sided two dimensional figure such as we might imagine to exist in real space; much as by a sheep we mean a four-legged woolly herbivorous creature. And although there exist computer models describing the nutrition and wool production of sheep, there appears to be no more and no less merit in preferring the model to the real animal than there is in preferring the algebraic formula to the genuine triangle. The difference is that we should not dream of substituting the model for the sheep (though science fiction writers might). And for the vast majority of our everyday concepts we do not entertain mathematical parallels at all. Nonetheless there are expressions, like (h), which can be construed as propositions of pure mathematics or logic, and which are usually held to be analytic. These receive consideration in §s 7 and 8.

Although perhaps reluctant to describe sheep in terms of some underlying mathematical structure, as they seem all too willing to do for triangles, still most philosophers of the analytic school would say that characterising descriptions such as:

(i) A ewe-lamb is a young female sheep
(j) A sheep is a herbivorous mammal
(k) Sheep are herbivorous
are really tautologous and consequently that they express necessary truths. While the routes taken to justify this extraordinary belief vary among its devotees, they all lead us through essentially the same Carrollian terrain, dotted with the spectral landmarks of redundancy, semantic analyticity, logical reducibility and logical necessity.

By a diagnostic or characterising (see Endnote 2) proposition, in its simplest form, I mean one that expounds the meaning of a term, either determinately (i) or indeterminately (j, k); which is to say that it presents, in one way or another, one or several or all of the salient features of whatever objects fall under a given name. Even when determinate, characterisation is not a symmetrical relation: if an expression B characterises a term A, A does not characterise B. Nor is it a property of the verb "to mean" that if B means A, A and B have the same meaning.

Although no diagnostic proposition claims to depict any contingent association of observable facts, it would be absurd to conclude that none has any experiential content. For we normally come to understand the connotational limits of a word just because the properties connoted do, in the real world, occur in some sort of more or less regular association. By defining the boundaries of organic processes, or what have come to be known as "natural kinds", most diagnostic propositions reflect the organisation of reality, as we perceive it and in so far as it has any practical importance for us. Their utility consists in assembling and preserving associations of ideas which tend to optimise the ways in which we interact with our environment - and this explains the tendency for definitions to become increasingly scientific. Nevertheless, while these complexes of attributes (relations etc) are in themselves of an evidential nature, the establishment of the boundary of a set of characteristics which is to be included under a given name must always be to some extent a matter of convention. Here I intend to convey no more than what is implied by the following example: I cannot tell, equipped with a certain limited knowledge of language and context, whether the statement "Sheep are herbivorous" delimits the use of the word "sheep" or hypothesises that sheep (defined somehow else) are in fact universally herbivorous. The second alternative, however, strikes me as being decidedly incoherent (§9).

On the other hand, it isn't a diagnostic property of diagnostic propositions that the classes to which they relate are organic processes: they may describe quite arbitrary collections. The crucial feature of diagnostic propositions is just that they set limits on the meanings of words, as employed in particular contexts. And it is clear that language, as we know it, would be of no service if words failed to acquire specific meanings pertinent to given contexts, no matter what the kind. As a basic ingredient of language in all its applications, therefore, characterisation is entirely independent of any particular theory of practical utility or kinds.

4.1 Analyticity

Like other descriptive propositions, diagnostic descriptions may be general or particular, and both forms are subject to a similar degree of woolliness. Thus while today both

(l) Sugar is sweet, and
(m) The Sydney Harbour Bridge is in Sydney
might well purport to be characterising, it's conceivable that tomorrow either could become material but false ("misrepresentative" is the term I employ - see chart). The possibility of a term changing its sense, however, is of no relevance to the question whether the proposition that communicates the sense of a term is analytic. Our language contract terminates with the clause that states that this is what the term means in the present context, any speculative extensions of the contract being liable to render it useless. If meaning were not both context relative and stable within a given context, everyday conversation could not exist and it's hard to imagine how we should succeed in communicating at all. Linguistic symbols, whether words or sentences, adapt themselves to particular tasks just as do the p's and q's of formal logic. It is the concept of analyticity within an agreed context which we now question.

If "analyticity" be considered a logical property, then this label is inappropriately applied to diagnostic propositions, which make no appeal whatever to logic: they are entirely independent of formal rules or axioms and devoid of any calculative means of expanding or contracting them. Nor can I begin to understand why anyone should hold them to be "reducible" to propositions of the latter kind, any more than they would think this of ordinary reportive or adventitious propositions (§6). I can only surmise that their belief has its origins in the same everglade that spawns the phantom of redundancy, which we shall now examine.

A proposition is redundant, I presume, if it is uninformative, superfluous, useless. Since it is immediately clear that this notion is accountable to the states of knowledge of the recipients of propositions, perhaps some of us would feel more comfortable if we said that statements or utterances can be redundant. But why should anyone suppose that a characterising statement, uttered with the best of intentions as a characterisation, is more prone to redundancy than any other kind? "Sheep are herbivorous mammals" is redundant if it conveys information that we already possess, but by the same token so is "Cook landed in Australia in 1770" and for someone somewhere doubtless so is "Grandma just swallowed a blowfly". Well, maybe redundancy is seen by some as a pre-requisite for semantic analyticity, if the latter concept is understood as implying that the meaning of the predicate of a proposition is contained in the meaning of its subject. For if a diagnostic proposition is not redundant (that is, if it does usefully characterise) it is simply false that the meaning of the predicate is contained in the subject, since the function of the proposition is precisely to attribute meaning to the subject term. But if it is redundant, it might be thought, this meaning relationship is already understood and the notion of semantic analyticity is seemingly saved.

The problem with this suggestion is that, so far as it goes, it is no less valid for adventitious than for diagnostic propositions. For the argument hinges, not on the distinction between characterisations and factual reports, but on the role of "containment". I do not believe we can ascribe a deeper meaning to this term than can be wrested from the notion of redundancy, namely that we are already familiar with what the proposition says about its subject. If an adventitious description of subject/predicate form is redundant, its subject too "contains" the predicate, in just this limited sense.

It might be protested, however, that the redundancy of "Sheep are herbivorous mammals" has little to do with anyone's state of knowledge, but consists only in the fact that nothing incidental or extrinsic is said about sheep - nothing, that is, beyond what is implied by the meaning of the word "sheep". Although I believe this claim is confused, even if it were true it would not be pertinent, since the statement never purported to convey this sort of information, but only to amplify the meaning of a term; and in this regard it is not redundant. Of course, if anyone mistakenly believed its purportment to be adventitious, he would also hold the statement redundant. I don't know what might persuade him to think this way, unless it be that language contains overtly existential propositions such as "These sheep are herbivorous mammals", whose predicate appears to be characterising despite the expectations of contingency attending the subject term. But if "These sheep are herbivorous mammals" is a fair statement (and assuming it doesn't refer to a subclass) it is indeed adventitious: it asserts that certain members of the class "sheep", which has been characterised by criteria other than that its members are mammalian and herbivorous, are now observed to possess in addition mammalian and herbivorous attributes. That there might exist other characterisations of sheep which do include these criteria is of no relevance.

One might imagine, therefore, that the proponents of the "necessity" of characterising propositions engage in some such train of thought as the following:

1. A characterising proposition is redundant because it makes no contingent report.

2. If a characterising proposition is to be held "analytic" (simplistically, the predicate is contained in the subject), then it must be redundant.

3. If we substitute an adequate definition of the subject for the subject itself, any characterisation of the subject will result in a tautology. So a characterisation is "reducible" to a tautology.

4. A tautology is a logically necessary proposition, so characterising propositions express necessary truths.

But we have seen that characterising propositions do not pretend to report adventitious facts and that, with respect to the kind of information which they do convey, there are no grounds for supposing them to be any more liable to redundancy than other propositions. Moreover it could be said of any redundant proposition of subject/predicate form, whether characterising or adventitious, that the subject contains the predicate, and to this degree one could maintain, somewhat pointlessly, that either kind of proposition is potentially "semantically analytic". And while both kinds are equally amenable to processing by formal logic, there's no reason to suppose them ever to be inherently reducible to tautologies. Not that I find this conclusion noteworthy since, if a tautology is taken to be a logically necessary proposition, I believe there exists no such species (§7).


5. GENERATIVE PROPOSITIONS - TRANSLATIVE SYNONYMY

5.1 Synonymy

It has sometimes been supposed that the concept of synonymy is pivotal to that of semantic analyticity. If it were correct to say that any two expressions are synonymous only if they have the same "meaning", this supposition might deserve attention, even though the prospects for headway in this direction appear dismal. It seems to me, however, that there are just as many basic kinds of "synonymy" as there are basic kinds of proposition: two sentences may be said to be type-x synonymous if they convey the same type-x information. But it seems to me also that none of these kinds of synonymy either expresses a genuine (let alone "necessary") equivalence or identity or plays a crucial part in explaining any other semantical or logical function. If there's a noteworthy feature of synonymy, it is just that different word-forms/sentences may represent a single meaning/ proposition, of whatever type: because success in communicating the same information in different circumstances often depends as much on idiom and perspective as on "saying what you mean". The reason why problems of synonymy, and of translation in general, arise at all has very little to do with the meanings of words and propositions, but everything to do with the who, when and where of their production. If "I'm counting on you" expresses the same proposition as "You were counting on me", then the second sentence is a correct translation of the first. And if "Ich zähle auf Sie" doesn't look like an accurate rendition of "You were counting on me", it may only be because of an initial unwillingness to untangle the confusion that results from the switch of person and tense compounded by the need to be understood by members of a different community. (We too easily assume that the German sentence must always be a correct translation of the English.) Again, if "I'm counting on you" seems not to mean the same as "You were counting on me", this may only be due to an inherent tendency to think of meaning in terms of the most general uses of the words composing each sentence. As in bygone centuries, philosophers of the twentieth have found it hard to kick the dictionary habit.

So far my own use of the word "meaning" also displays the lexicographer's stamp, and suggests an affinity, if not identity, with characterisation. The predicate of a typical determinately characterising proposition supplies the meaning of the subject; often this is achieved by means of a verbally diverse predicate and it is assumed that there is a recipient who knows how to apply the predicate but not the subject. "Meaning", in this sense, could perhaps be construed essentially as a synthesis of words, and we might have managed to grasp the concept of characterisation without ever alluding to the psychological notion of meaning. This approach would doubtless be appealing if it were possible to understand verbal diversity without reference to conceptual diversity, and if it were not the case that (as I think) archetypal characterising propositions do not have verbal predicates at all, but teach meaning ostensively. Thus although the meaning of "meaning" may remain vague, it is not so vague as to prevent us from seeing that characterisation involves more than mere verbal juggling, and depends for its success on some relationship (whatever it may be) between words and objects or ideas.

The concept of translation, on the other hand, pertains to a class of propositions which have no concern with meanings but speak only about the interchangeability of linguistic symbols between occasions on which they may be usefully produced. For the sake of economy and clarity I shall consider only word-for-word synonymy. In "Every snow rose is a helleborus niger" we have already encountered an example of what might well be taken to be, in a suitably bland context, a statement of unblemished synonymy - that is, an identity of verbal function in which neither term expounds the meaning of the other but, rather, both terms are tokens of the same word. To say that the proposition expresses only sameness of word is to suggest that the form "snow rose" = "helleborus niger" is an appropriate representation; while (for example) the inappropriateness of "open" = "not closed" reflects the fact that "If and only if anything is open it is not closed" is not about word usage but about experience. The first proposition differs from the second in that the question whether we can imagine a state of affairs that doesn't comply with the proposition does not arise. It also differs from characterising propositions such as "Ewe-lambs are young female sheep" because the predicate does not elucidate the meaning of the subject. In fact it's possible to invent translative synonymies in which neither subject nor predicate has any assigned meaning: which is to say that the only "meaning" (utility) possessed by the synonymous terms is that which ensues from their interchangeability in some context.

Now if synonymy could be explained entirely in terms of syntax, irrespective of the objective meanings of words, the perception that there's a special problem of synonymy would surely be less prevalent. For to my knowledge most theorists in this field ride quite happily with the general notion of sameness and recognition which underlies not only the possibility of communication and argument but the whole gamut of interactions with our environment. They do not question, for example, that in the formula logic hook (plogic hookq) the second occurrence of q represents the same object as the first occurrence of q, or that various auditory renditions of the formula, such as "Kue entails pee entails kue" (which may well be how it automatically registers with them), function in precisely the same way as a variety of printed and hand written versions, which in turn function in the same way as one another.

But the concept of translative synonymy appears to be exactly of this kind. The analogue of conversational synonymy in formal logic is a so-called "defining" expression (actually a prescriptive translation) such as Q =def q, which decrees that the symbols q and Q are to function equivalently. One might re-phrase this: Q =def q merely instructs us to broaden our field of recognition so as to include capital as well as small q's among the symbols that are to count as q. The formula could as well have been written "Q" = "q". There seemed to be no need, however, to provide the instruction "q" = "q", as it was taken for granted that our early education furnished us with at least the capacity to recognise all occurrences of signs of that sort sufficiently well to appreciate their sameness and to distinguish them from signs of other sorts. And "q" = "q" is clearly absurd if it's meant to inform us that successive uses of q are uses of the same sign, since the defining expression itself contains successive uses of q. Likewise in botanical parlance we have no need of "snow rose" = "snow rose", nor of "SNOW ROSE" = "snow rose", but we might well need "snow rose" = "helleborus niger". For unless Linnaeus was our father we did not learn that when we were four years old. But we could have done. After all we did make the far more remarkable discovery that the graphical symbols C-A-T represent the same word as the sound kat. Until then words were just sounds. Yet for most of us now, any attempt to formally capture that identity would seem hardly less absurd than it was in the case of "q" = "q".

The fact that translative and characterising propositions have traditionally been grouped together in the analytic category partly explains the persistent tendency to confuse them. A more basic reason for the confusion is that most translative propositions express equivalences, a peculiarity which hides the logical properties of translation in general and may lead one to commit the error of thinking that simple translations are really determinate characterisations, or vice-versa. This common mistake can often be avoided by considering the effects of syntactical devices such as quotes and quantifiers. (For example, to say that all sheep are animals is not at all the same as saying that whenever we use the word "sheep" we could use "animal", since, going by dictionary meanings, not all statements of fact about sheep are also true of every animal. Yet there may be circumstances in which "animal" is a perfectly adequate translation of "sheep".) In classical (but, I think, woefully regressive) terms the difference between the two types could be summarised thus: while characterising propositions range over the objects of language (the things we talk about), translative propositions range over linguistic contexts and statement situations.

Though permeating every fibre of language, the concept of translative synonymy rarely finds overt expression in propositions. One reason for this sparsity is the exceedingly casual nature of everyday conversation. We have seen how the repetitive use of "identical" signs, whether in formal or natural languages, is taken for granted, and how the attempt to crystallise this usage in definitions would be unfeasible. Similar considerations apply to signs which are less obviously alike but which are used in parallel ways in different linguistic environments. We just do use them one for the other without fuss as occasion demands, and that is what constitutes their synonymity. To formalise this usage seems impossible because in the act of formalisation we make a deliberate attempt to alter the nature of the beast: we imagine ourselves to be exhorting the signs to behave to order, so to speak, even though they may not, and even though there can be no guarantee that our directive will be heeded in future. Synonymy is a relation we can understand and use but cannot dictate. And where else, in all this, can we detect any evidence of structural perfection, of necessity? The informality and logical weakness of the concept is epitomised in the thought that translation consists in nothing more than this: we use a spade to dig the garden, but on occasion we may use a cultivator because it's more efficient, more appropriate or just more fun.

To use words, phrases or sentences synonymously, then, is to count them as being the same verbal sign, and if there are clouds veiling this notion they are no darker than those surrounding the mystery of how we come to use any expression repetitively. Why, then, do I consider translative synonymy to be of fundamental significance? The reason is that it holds not only the keys to the doors of language synthesis and enrichment but the pestle to crush a popular view in the theory of meaning and truth, namely that propositions necessarily possesses distinct extensional and intensional aspects.

Since translative synonymy implies verbal correspondence without consideration of existing meanings, its effect is not to relate word meanings within the current language frame but to modify the language frame itself. Aside from obligatory applications such as change of tense, there are essentially three directions which translation can take: (1) it can convert an expression in the language we are using to an analogous one in a substantially different ethnic language (which, presumably, we propose to use); (2) it can expand the language we are using by enlarging its vocabulary; or (3) it can restrict the use of an expression to specific contexts, thereby helping to define the boundaries of a sub-language or "language game". In each case we find ourselves using a language that is new and different from the original, even if only in a small way; so this type of activity, if successful, is innovative and generative - not of ideas but of uses of words. Thus translation, like characterisation, is not a strictly reflexive relation, and we cannot properly claim that two words are synonymous, in this sense, just because either one can be freely substituted for the other. We might say, rather, that translative synonymy consists in the fact that a word in a home idiom has its analogue in a target idiom. However, the target idiom may comprise no more than the home idiom plus the analogue.

5.2 Intension and extension

Because synonymy is not only language-relative but language-game-relative, the verbal economy and expressive richness of language both owe much to that concept. Translative synonymy ranges between more or less universal (I should rather say encyclopaedic) and extremely domestic contexts, providing language with an additional, exceedingly fertile dimension. For nothing could be more stifling of progress in linguistic philosophy than the belief that words and propositions stand for completely fixed concepts, or uniquely represent fixed atoms and molecules of reality. (Beliefs of this kind have led to much redundant philosophy even by those who have tried to overthrow them, for example Wittgenstein (1953) on "language-games" and, in more popular vein, Pirsig (1974) on "Quality"). No language is a single, static entity with defined boundaries. Language comprises an indefinitely large, continuously evolving array of overlapping idioms, almost every situation requiring a different one, and of which different ethnic languages are just the extreme cases with least overlap. Through the creative process of translation, we discover new uses for old words and new words to fit old uses. But while the latter aspect may be of greater interest to linguists, it is the former that is philosophically the more important.

The elementary observation that one and the same word can have extremely narrow, as well as broad, applications supplies the principal means to eradicate one of the most persistent myths of philosophy, ancient and modern, namely that we necessarily comprehend the world in terms of two distinct kinds of entity corresponding to two distinct logical parameters: on the one hand universals or attributes (the sense or intension of an expression) represented by logical predicates or relational functions, and on the other particulars or individuals (the reference or extension of an expression) represented by individual terms or variables ranging over the elements of a domain. For it seems to me only that we use words sometimes in a more encyclopaedic and sometimes in a more domestic fashion and that this largely explains (but certainly does not simulate) the intension/extension dualism. Consequently, though undoubtedly convenient, this division is entirely relative and of limited metaphysical and logical significance.

This same viewpoint can be reached from another angle. What has been said about word-for-word translation applies equally to propositions. While compound propositions that relate other propositions to one another translatively are extremely rare, two simple propositions such as "In Australia the sky's the limit" and "Australien ist das Land der unbegrenzten Möglichkeiten" may stand to one another in the relationship of translative synonymy. A complication appears to arise, however, in the case of propositions which, though essentially translative, include overt or tacit reference to the circumstances of their production: for example, "I have a headache" and (said by you to me) "You have a headache", or "It will rain" and (said later) "It's raining". Although in each example both utterances may in fact be making the same statement, one might think that they have different meanings. From the perspective of someone outside these situations, of course, they do have different meanings, different uses (as a consequence of which they translate differently into German, for example). But philosophers have tended to place too much importance on matters of this kind (for more examples see near end of §9.5), even to the extent of regarding context-dependent language as logically untidy and replacing it by "eternal sentences". To my mind, both eternal sentences and uniquely referring sentences are mythical entities; the progression from narrower to broader perspectives is a gradual one, any profit realised by distinguishing between sense and reference deriving only from this process of linguistic re-orientation. Add to this the weak status of reference (see §9.6) and we can see that it is redundant. (Essentially my argument is that the "face-value" referential capability of genuine propositions and expressions is no greater than that of the pseudo-propositions and expressions in fairy tales and novels, save for the circumstances of their creation and evaluation and their lodgement in a general background of shared experience. This set of conditions, however, is an immensely significant aspect of truth and meaning, for I believe that propositions, or perhaps more correctly statements and utterances, are themselves members of the same objective world of which they speak. Also see Endnote 1)

(In short I flatly reject the distinction between sense and reference along with the classical logic that cradles this distinction.)

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