Philosophy of Science

A DNA Account of Propositions as Events: Dummett, Nāgārjuna, Aristotle (1)

Khristos Nizamis
Independent philosopher, scholar, meditator

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ABSTRACT: Michael Dummett has argued that antirealism requires a rejection of bivalence. However, his version of antirealism is not the only available one. In fact, it is arguable that his antirealism is not sufficiently antirealist and falls short of his intentions. On the basis of a study of the Indian Buddhist philosopher, Nāgārjuna, I think that a more complete and coherent kind of antirealism is possible, one that respects the phenomena of conventional ontology and retains the principles of classical logic, but reinterprets both in a radical way.

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sarvaṃ ca yujyate tasya śūnyatā yasya yujyate
sarvaṃ na yujyate tasya śūnyaṃ yasya na yujyate (2)

Nāgārjuna, Mūlamadhyamakakārikā, XXIV.14

anairōn gar logon hupomenei logon (3)
Aristotle, Metaphysics, Γ.4, 1006a 26

Michael Dummett (4) has argued that anti-realism requires a rejection of bivalence. However, his version of anti-realism is not the only available one. In fact, it is arguable that his anti-realism is not sufficiently anti-realist and falls short of his intentions. On the basis of a study of the Indian Buddhist philosopher Nāgārjuna, I think that a more complete and coherent kind of anti-realism is possible, one that respects the phenomena of conventional ontology and retains the principles of classical logic, but reinterprets both in a radical way.

The set of questions I would have liked to tease out and consider here goes something like this:

Does anti-realism require a rejection of bivalence, as Dummett argues? Does Nāgārjuna's methodology provide us with a parallel alternative to Dummett's solution to his problem; or perhaps even with a superior and more desirable alternative in that it retains the classical principles of logic, and it retains the conventional 'realist' world, but, at the same time, radically re-interprets both within an alternative epistemological paradigm (the 'highest truth' or 'meta-truth' (paramārtha-satya) of Madhyamaka philosophy), thereby demonstrating that we can have a kind of 'conventional realism' and we can have 'conventional logic' not only without essence, but only without essence. And isn't Dummett's critique of realism ultimately grounded in epistemological concerns, not metaphysical ones, given also that the relevant metaphysical problems are generated, on his account, by the classical logic itself?

To explore fully the issues indicated by these questions, one would have to examine in detail the nature and function of negation in Nāgārjuna's methodology and in representative sites of twentieth century Western philosophy. This question of negation discloses further underpinning questions concerned with the relations between logic on the one hand, and ontology, metaphysics, and epistemology on the other. But the topic of negation, radically interesting though it is, must be omitted from the present paper.

Instead, I shall limit this account to a problematic and erotetic that might conveniently be gathered under the following question: what can we critically determine concerning the relations that might be supposed to hold between propositions, on the one hand, and, on the other hand, events in a spacetime-causal continuum. But, it should be kept in mind that, necessarily, a proposition is itself also an event in a spacetime-causal continuum. On this matter, it should be noted, I shall not subscribe to any modern form of surreptitious metaphysical Platonism, of which, for example, any 'type/token' schema is arguably one kind of representative.

From the perspective of Dummett's critical challenge to realism, what this leads us to is the question of whether or not it makes sense to be realist about time and space, and various orders of events that cannot be conceived in terms other than those of time, space, and causation-even if those concepts were to be defined in unfamiliar ways and according to unfamiliar laws (e.g., as in the case of theories explaining subatomic events). Such a discussion is, of course, far too broad for a short paper; so I shall gather attention to a single representative problem.

At this point, then, I shall very briefly summarise just what Dummett intends by 'metaphysical realism' and just what he thinks the implications of such a view must be, since it is against these implications that Dummett takes his stand.

[For the metaphysical realist,] statements about physical reality do not owe their truth-value to our observing that they hold, nor mathematical statements their truth-value to our disproving them, but in both cases the statements' truth-value is owed to a reality that exists independently of our knowledge of it, [and] these statements are true or false according as they agree or not with that reality.(5)

For the anti-realist, in Dummett's understanding, the notion that a statement could have a truth-value independently of any means of recognising that value is incoherent. There are, for Dummett, two significant and problematic implications following from the realist position:

(1) To adopt the realist view is to accept the logical principal of bivalence that every statement is determinately either true or false; and from this it follows that there will be statements which, even if we cannot prove or find evidence that they are either true or false, must still be either true or false.

(2) To adopt the realist view is to adopt a 'truth conditional theory of meaning': that is, a theory for which to know the meaning of a sentence requires only that we know the conditions under which it is true or false, but not that we should be able to determine whether or not these conditions actually hold.

Dummett believes that both of these implications are intolerable, and that the only way to eliminate them, and the realist view from which they stem and which they support, is to amend the principles of classical logic (most notably, the principles of bivalence and double negation). In contrast, this paper shall propose that it is possible for a thorough anti-realism to retain the second implication stated above - and hence, too, the basic principles of classical logic - while definitely rejecting the metaphysical tenor of the first implication of realism stated above by re-interpreting the nature of the relations between the logic of language and extra-linguistic events. Having briefly spelled out these points, I shall return to the main line of this paper.

If one were to take an anti-realist line about events at other times, such as future times, or even past times, such a stance could understandably seem counter-intuitive; especially when, as Dummett argues, it is supposed to require the abandonment of the principle of bivalence (PB). (6)So the statement 'Tomorrow there will be a sea-battle' will, on one kind of anti-realist line, be neither true nor false. Again, either it just has no truth-value (a 'truth-value gap' account), or it has some other truth-value, such as 'indeterminate' (a 'multivalent' or 'many-valued' account).

On the other hand, at least according to some (notably, Łukasiewicz), if one were committed to upholding PB one would also be committed to strict determinism concerning future events. That is, our proposition will already at this moment be determinately true or false in relation to a determinate future event. A determinist may be very happy with this alternative; others will probably not be too happy with it. Furthermore: the future event may be considered determinate either because it will be a necessary consequence of present causal conditions, or because it actually already exists (in the sense that spacetime exists as a complete entity, in toto, a notion that some interpreters and popularisers of general relativity theory have promoted), and this latter view is, if one thinks about it, a non-causal view. So in retaining PB in relation to future (or past) events, one could appeal either to a causal determinist account, or to a non-causal (and metaphysical) determinist account. Both accounts would be species of realism, however, on Dummett's reading, precisely because of their respective commitments to PB.

Are these the only alternatives we have to work with? If we turn to the source of the sea-battle example, the ninth chapter of Aristotle's On Interpretation, so infamously difficult to interpret, we find Aristotle's 'solution' to the problem of future contingent propositions:

So, since statements are true according to how the actual things are, it is clear that whenever these are such as to allow of contraries as chance has it, the same necessarily holds for the contradictories also. This happens with things that are not always so or not always not so. With these it is necessary for one or the other of the contradictories to be true or false - not, however, this one or that one but as chance has it; for one to be true rather than the other, yet not already true or false. (7)

The vote of the commentators seems to go in favour of the interpretation that Aristotle is here recommending some kind of modification to PB in the case of contingent propositions. However, probably by a mere stroke of chance, the particular alternative that I shall be proposing in this paper happens to map onto Aristotle's text quite nicely; and it does not in fact require either a modification or a rejection of PB at all, although it does require a profound, and perhaps for some even a disturbing, reinterpretation of the entire problem.

Dummett does touch upon the most radical form of anti-realism that seems possible in relation to these questions: namely, anti-realism not only about future and past but also present events. Would this line require abandoning PB in all possible instances? Would all propositions consequently be neither true nor false? Or are propositions not necessarily true or false except under certain conditions, or with certain qualifications? What could these be, and what could they entail? Whatever such conditions might be, I think that what they would entail is that truth and falsity can only be defined conventionally. But if that were the case, would we still be committed to abandoning PB? I think not; in fact, on the contrary, the conventionalist account may well require PB within the context of the special conditions or qualifications according to which propositions and the assigning of truth values to them must operate, by definition.

The claim that the semantics of propositions is in some sense conditionally defined, and the additional claim that, for that same reason, it is ultimately conventional, is in fact the line that I want to pursue here. I also want to test the idea that such an account preserves PB unproblematically, yet without committing us to an excessive realist metaphysics, at least of a certain substantialist or essentialist kind (thus perhaps providing one kind of solution to Dummett's concerns).

Subjunctive conditional propositions, as deployed by linguistic phenomenalists, share some of the problems of future contingent propositions. An account of the semantics of future contingent propositions might shed some light on that of subjunctive conditionals in the phenomenalist context; it might also end up being an account of any type of proposition just as a proposition per se.

If A were to be at place x at time y, then A would experience perception w.

Whether time y is taken to be a future, past, or present time, the form of the proposition makes it a temporally contingent one (or, more exactly, of course, a spatiotemporally contingent one). Dummett argues that (linguistic) phenomenalists should have rejected PB as a step towards defeating realism; but they didn't, and, in consequence, they fell prey to the like of Isaiah Berlin's critique of phenomenalism, to the effect that subjunctive conditional propositions can only make sense and be assigned a determinate truth value in dependence upon indicative propositions which in turn immediately commit phenomenalists to realism. The alternative account of the semantics of propositions pursued here may well provide a new interpretation of the kind of view for which the phenomenalists were inappropriately groping.

Aristotle's qualms about the semantics of propositions referring to perceptual phenomena-specifically, his deeply felt belief in the necessity of defining and positing substance and essence as guarantors of the truth value of any such proposition-led him to formulate a definition of such propositions that depends heavily upon spatiotemporal qualifications. Similarly, his complete definition of the principle of contradiction (PC) is also bound by spatiotemporal qualifications. In rather different ways, this significant fact provides to him-and to us-a nice way out of the epistemological and metaphysical consequences feared, respectively, by Aristotle on the one hand and by Dummett on the other.

The way out, essentially, is to be found along these lines: the metaphysical posits of substance and essence end up obstructing and defeating Aristotle's intended solution to the problem of phenomenal flux (or ontological flux-it is the same thing) rather than facilitating it in the name of semantics. The lesson to be learned from Nāgārjuna's project is that only by excising the metaphysical axiom of substance or essence from logic and ontology can these make any real sense, either pragmatically or conceptually. The absolute absence of any such substance or essence is what Nāgārjuna intends with the term 'emptiness' (śūnyatā). Substance and essence, on the other hand, are ultimately what Aristotle intends by the notion of 'being per se' (to on kat' hauto), which is the metaphysical equivalent of the Indian concept of 'own-being' (svabhāva). It is against the reified metaphysical posit of svabhāva that Nāgārjuna's arguments are directed for the sake of establishing the epistemological result of emptiness.

Rather than set out on a comparative examination of the arguments of Aristotle and Nāgārjuna, which is what I had initially attempted to do before deciding it was simply not possible to achieve within the scope of a very brief paper intended for oral presentation, I will attempt, instead, to exemplify some key features of what I have referred to as an alternative anti-realism by framing them within the context of future contingent propositions. So let's consider Aristotle's famous proposition:

Tomorrow there will be a sea-battle.

To arrive at the conclusion that, in the case of a proposition such as this one, if we hold on to PB we are thereby committed to some form of strict determinism about real future events, requires both of the following presuppositions:

(a) Concerning entities and events: that, in one sense or another, extra-linguistic entities exist and are inherently characterised by their unique essences (understood in terms either of essential substance or of essential properties or both). (8) (9)This presupposition could be characterised by the term 'ontic realism' (which, in the present context, is equivalent to 'ontic essentialism').

(b) Concerning propositions (that is, concerning language and logic): that propositions, in one sense or another, possess essential meanings and essential truth-values. This presupposition might be characterised by the term 'semantic realism' (which, in the present context, is equivalent to 'semantic essentialism'). (10)

The claim that PB entails determinism definitely requires the second of these presuppositions. At first glance, however, it might not seem as obvious that it requires the first of them; but on closer consideration, it becomes apparent that it does. If semantic essentialism only were to be adopted, to the exclusion of ontic essentialism, then it ought to follow that there would be no difficulty concerning tomorrow's extra-linguistic sea-battle because anything extra-linguistic would be without essence (that is, not definitively 'real') and hence irrelevant to our system of logic and language. We ought to be able to predict (that is, to infer) today which truth value must be assigned to the proposition on purely intra-linguistic, intra-logical grounds. But of course we cannot do so. (11)The best we can do today is to 'predict' that either one or the other truth value will indeed be properly assignable tomorrow; and this is not much of a prediction, of course, given that it is simply the statement of that principle of our logic (and language) that is in question. The Delphic Oracle of ancient Greece seems to have had a sophisticated grasp of this principle, and, at least on certain occasions, was able to formulate future contingent propositions (i.e., prophecies) whose grammatical construction was very precisely ambivalent between two mutually exclusive possibilities. In other words, the Oracle's predictions, when formulated in this particular manner, were inevitably proven to be 'true'!

On the other hand, we cannot omit semantic realism and adopt only ontic realism and remain consistent: if one of these aspects of essentialism is adopted, the other is also required. As Aristotle realised, if there were to be no essential correspondence between the essences of entities and the meanings of propositions, neither logic, language, nor scientific discourse would be possible: it is precisely for this reason that he was led to propose that the essence of a thing must correspond to its unique definition. (12)A 'complete' substantialist metaphysics - that is, one that is to have any hope of being consistent with itself - requires the presuppositions both of ontic and of semantic essentialism.

Let us say, then, that ontic essentialism plus semantic essentialism equals metaphysical realism. We are now at the nub of all our difficulties. By accepting metaphysical realism we have committed ourselves to the validity of the following argument: that if a future contingent proposition is determinately either true or false prior to the event to which it refers, then strict determinism must be the case in the world to which that proposition refers.

From this conclusion it has then been inferred that if strict determinism in the world to which the future contingent proposition refers is not the case, then the proposition cannot be determinately either true or false prior to the event to which it refers; consequently, the principle of bivalence cannot be valid.

These arguments appear to be logically coherent only because they are infused with a kind of metaphysical glue. Dissolve the glue, and the arguments would quickly become incoherent. An alternative interpretation of the situation would be required in order to reformulate valid arguments about what it does and does not entail. Even if one happened to be a formal logician working on this problem in a purely notational medium, as long as one comprehended the future tense in dependence upon an essentialist presupposition concerning the nature of time in relation to semantics, one would still be painfully struggling to detach one's symbols from this glue. The 'glue' in this metaphor, of course, is the sticky and pernicious presupposition of the existence of both ontic and semantic essence.

If one exorcises that presupposition, one is no longer burdened with a problematic commitment to the notion that a future contingent proposition just must - and I emphasise the profound emotional tone of this deep-rooted 'must' - now, at this moment, somehow and somewhere be either true or false if there is no value other than 'true' and 'false' for it to be! But let us continue to maintain that, like any other form of proposition, a future contingent proposition can in principle only be assigned the values 'true' or 'false'; and that this principle holds good even 'now', at this 'present moment', for our proposition concerning tomorrow's sea-battle. There really ought to be no problem with the principle itself: it is an integral and efficient convention woven into the fabric of our logic and semantics.

What has worried most of us, of course, is the corresponding idea that if the proposition can only be either 'true' or 'false', then it must necessarily be one or the other right now, at the 'present moment'. Why do we assume this? I think it is because we presume that the proposition, right now, at this moment, already possesses an objective, essential 'meaning'; and that this essential 'meaning' is 'truth-conditional'; and that it can only properly be 'truth-conditional' inasmuch as it refers to an 'extra-linguistic reality'. One could add a further clause here: that this 'extra-linguistic reality' is to be defined as 'real' just because the entities that it comprises 'exist' in virtue of the essential properties and / or substances that constitute them.

Contrary to this nice set of assumptions, I am arguing that the proposition does not in fact possess an essential 'meaning'. I do not deny that it has a functional and transient 'meaning'; but what 'meaning' it has is entirely dependent upon a complex set of necessary conditions, amongst which we would conventionally distinguish between those that we might call cognitive or conceptual (i.e., epistemological) and those that we might call extra-cognitive or empirical (i.e., ontological). As long as the necessary and sufficient conditions are effective, the 'meaning' of the proposition is effective for us. But one of the necessary conditions for the arising of that 'meaning' is precisely the principle of bivalence.

The proposition, as a present spatiotemporal event, has, for us (not just for me or for you, but for us), the conditionally specific 'meaning' that it does have just because one of the conventional (but formal) conditions supporting that 'meaning' is that the proposition means just what it means because it can only be either true or false; and, at least in a basic and general way, in an everyday and conventional way, we all understand and agree upon what it means for a proposition to be either true or false.

But now we confront the fact that, even if the argument thus far is granted, we still cannot determinately assign either value to the proposition in relation to the extra-linguistic event to which we take it to refer. What does this fact mean? It means that there is a certain specific condition absent from the current set of conditions by which we presently comprehend the meaning of the proposition. This condition could perhaps be termed a 'truth-making' condition. In the case of the future contingent proposition that we are using as an example, the truth-making condition would be the occurrence or the non-occurrence of a certain sea-battle at a relevant moment in time.

But what happens when, to a set of necessary and sufficient effective conditions that support a certain result, a further effective condition is added? The result is altered: it is no longer just the same result. In the present case, the proposition is altered: it is no longer just the same proposition.(13) Today, we comprehend the 'meaning' of our future contingent proposition, and one of the conditions for our comprehension is that we understand the function of bivalence. Tomorrow, at the moment that the sea-battle commences, the 'meaning' of our proposition changes because one further condition, the truth-making condition, is added to the set of conditions upon which that 'meaning' depends.

However, by this very same token, the future contingent proposition, strictly speaking, is no longer a future contingent proposition. We could say that its 'truth' depends upon, or is defined by, the possibility of its transformation into a present indicative proposition (which is similar to the form of the argument used by Berlin against the phenomenalists, but, in the present context, leading to a very different conclusion). The addition of the truth-making condition, then, alters our proposition in at least two interesting ways: it alters its 'meaning' in the semantic dimension because it adds a further effective condition to the generation of that 'meaning'; and it entails (or at least permits) an alternative grammatical form or transformation of the proposition, the present indicative form, such that it is temporally brought into referential 'correspondence' with the 'extra-linguistic' event of our sea-battle.

Of course, tomorrow we could still be talking about yesterday's future contingent proposition, 'Tomorrow there will be a sea-battle'; and, if we forget ourselves, we might even make the mistake of thinking that, in hindsight, yesterday's proposition was in fact true (or false). But in reality (that is, in logical and empirical terms), when tomorrow we speak of yesterday's future contingent proposition, we will definitely not be speaking of today's future contingent proposition; and the 'meaning' that arises for us tomorrow when we comprehend the proposition 'Tomorrow there will be a sea-battle' is just not the same 'meaning' that arises for us today when we comprehend the proposition 'Tomorrow there will be a sea-battle'.

Just at this point, it might be useful to clarify the argument a little, and to recapitulate some of the preceding points, by making use of a small illustration. Suppose that there is a room somewhere in this city, call it Room Z, which has been completely closed off: it has no windows, and the door is also locked and sealed. In this room there are no sentient creatures whatsoever. There is, however, a light-bulb connected to a live electric circuit that, to begin with, is not closed; an operational computer; and a device that connects the computer to a switch in the light-bulb's electric circuit. The computer has been programmed to run some kind of randomising procedure at 12:00 midnight: at the end of this procedure, the computer will register one of only two possible results: either 0 or 1. If it registers 1, this result will trigger the intermediate device to close the electric circuit and turn the light bulb on. If it registers 0, this result will have no effect on the intermediate device, and the light will remain off.

Let's leave future contingent propositions aside for a moment. Let's consider a simple present indicative proposition, and imagine that it is now one minute past midnight. The proposition in question is:

The light bulb in Room Z is now on. (p)

We all readily comprehend the meaning of this proposition, and of its simple (narrow-scope) negation or contradictory form:

The light bulb in Room Z is now off. (-p)

So far so good. Now, the first claim is that we comprehend the meaning of these propositions at least in part because we comprehend the distinction between 'on' and 'off'; and I don't mean that we comprehend it only in virtue of our memory of relevant perceptual experiences, but also because we 'comprehend' in accordance with the principle of contradiction ('the light bulb cannot be both on and off at the same time'), the principle of excluded middle ('the light bulb can only be either on or off at any one time'), and the combination of these two principles in the principle of bivalence ('the light bulb is determinately either on or off at any one time').

A metaphysical realist will claim that, at 12:01 am, the light bulb in Room Z is determinately either on or off; and, in correspondence with this empirical fact, proposition p is determinately either true or false. For the metaphysical realist, both of these facts, the one concerning the light bulb and the one concerning the truth value of p, are now determined, even if no sentient being in the universe knows the determination of either fact. Precisely this claim is one of the major reasons why Dummett proposes anti-realism and the rejection of bivalence (and also of the principles of excluded middle and of double negation); and it is significant that this reason is at basis an epistemological one. Dummett finds fundamentally incoherent the realist notion that a statement should be determinately either true or false independently of any observation or proof that it is either one or the other. I strongly empathise with his intuition in this matter, and with its epistemological basis; but I comprehend the nature of the problem differently.

For completeness, let me briefly sketch out what a 'pure semantic realist' and a 'pure ontic realist' would probably claim about the light bulb in Room Z at 12:01 am and about proposition p.

The semantic realist, who, as you will recall, believes only in essential meanings and their truth values, might claim that if it cannot be determined whether proposition p is true or false, then the light bulb in Room Z must be neither on nor off, or again, both on and off. If this sounds absurd to you, then just think back to the interpretation of quantum mechanics which led to the peculiar story of 'Schrödinger's cat'. It may well be arguable that such an interpretation of quantum mechanics constitutes a type of semantic realism. Or again, think back to Aristotle's attempt to defuse the problem of indeterminable contradictories, as in the case of future contingent propositions, by an appeal to the distinction between 'actuality' and 'potentiality'.

The ontic realist, on the other hand, who believes only in essential entities, might claim that if it cannot be determined whether the light bulb in Room Z is on or off, then proposition p is neither true nor false, or again, both true and false. Curiously, this second characterisation appears prima facie to be roughly similar to Dummett's statement of his own position.

There are two reasons for this apparent similarity. First: Dummett is primarily and quite deliberately concerned with logic and propositions, not with ontology and metaphysics. Second: quite in spite of his anti-realist intentions, Dummett inadvertently retains the presupposition that the principles of bivalence and excluded middle have essentialist ramifications for any semantics of propositions. I would like cautiously to suggest that, had Dummett rejected this presupposition, his anti-realism could have been better defined as anti- what I have termed metaphysical realism: that is, the combination of what I have termed semantic realism and ontic realism; and, furthermore, he would no longer have found a need to reject the logical conventions of bivalence, excluded middle, and double negation, nor a certain form of nominalist-conventionalist realism corresponding to these conventions, given that the conventions are precisely conventions because they are defined and determined conditionally, not essentially.

Finally, on this present account, the thoroughly anti-metaphysical anti-realist would claim that the proposition p has a determinate signification for us precisely because we comprehend it, among other necessary conditions for the arising of that signification in our experience, according to all of the conventional rules of (classical) logic; and even in the absence of that further condition, the 'truth-making' condition, which would add to this signification, and thereby alter it with, the specific information (the truth value) 'true' or 'false'. We comprehend p, then, at least in part because we comprehend that p is either true or false, even if we cannot assign either value determinately to p at some, or any, given time. Furthermore, we comprehend that p is either true or false because we comprehend (in accordance with) the mutually exclusive yet mutually dependent relation between all 'absolute terms' such as (true, false), (on, off), or (1, 0).

Given the preceding arguments and illustration, I have to confess that I can discern no logical problem about the principle of bivalence in relation to future contingent propositions, or, indeed, in relation to most, if not even perhaps all, kinds of propositions.(14)The problem, inasmuch as there is one, lies elsewhere: namely, in the commitment to metaphysical realism. Without that commitment, Dummett attains the kind of anti-realism that I think he is really after, yet retains bivalence; Nāgārjuna smiles and nods his head in approval; and Aristotle finally achieves a logically coherent semantics and ontology, and thereby the driving obsession of his never-quite-satisfactory philosophising attains a 'thorough peacefulness' (prapañca-upaśama, as Nāgārjuna terms it).

In conclusion, it should be noted that Aristotle clearly recognised the fact that bivalence is necessary to the process of 'meaning' when he claimed, in Metaphysics, that if his opponents wished to dispute the validity of the principle of contradiction, sooner or later they would have to open their mouths and speak an intelligible sentence. As soon as they did so, Aristotle was quick to point out, they would have defeated themselves. On this score, Aristotle was perfectly correct. Unfortunately, he wandered on to construct a logically unsatisfactory metaphysical theory because of his initial commitment to an inappropriate presupposition: 'inappropriate', that is, in a logical sense because, just like the immediately self-defeating first sentence of his opponent's counter-argument, Aristotle's obstinate clinging to this unnecessary presupposition spelled the internal defeat of his entire project. If he had set out without it - if, perhaps, he had more fully grasped the kindred challenges of his predecessors Herakleitos and Parmenides - I am of the opinion that he might well have turned out to be a kind of Greek Nāgārjuna, almost half a millennium prior to the writing of the Indian Buddhist philosopher's brilliant treatise, Root Stanzas of the Middlemost Way (Mūlamadhyamakakārikā). Unfortunately for Western philosophy, and for Western culture in general, Aristotle was not able to release his tight grip upon the mirage of essence; and yet, in almost every argument that he elaborates, he runs parallel to the arguments of Nāgārjuna.

One could imagine a path-think of it as the path of logic and philosophy: Aristotle is walking along this path in one direction, trying to find his way to essence. Quite unexpectedly, he meets with Någårjuna, who is walking along the same path, but in the opposite direction.

"Where are you going, friend?" inquires Aristotle. "For the path truly leads this way, to the essence of being."

"No, my friend," says Någårjuna, "the path truly leads this way, to the emptiness of being; that is, to the complete absence of essence."

For a moment Aristotle is taken aback; but then, with typical acuity, he asks: "Why, then, are you walking this path at all?"

Någårjuna smiles. "Only because you are walking it."

I then like to imagine these two truly great philosophers (15) becoming the very best of friends: as though, so to speak, they complemented one another perfectly.

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(1) This paper is dedicated to the great Indian Buddhist philosopher Ācārya Nāgārjuna,who probably lived in the latter half of the 2nd century AD. Even though his work is neither directly quoted nor overtly discussed in this paper, it nevertheless provides the basis and inspiration for everything that appears here. However, every misinterpretation and error that may be found here is necessarily my own. I wish gratefully to acknowledge the generous help of my PhD supervisor (from May 1997 to December 1998), Professor Jay L. Garfield, who patiently, and ever insightfully, read most of what I wrote as background to this paper (there was a lot to read!) and provided to me much astute criticism, guidance, and discussion.

(2) Translation: "All of that is valid (appropriate) of which emptiness is valid. / All of that is not valid of which emptiness is not valid."

(3) Translation: "In annulling reason, one submits to (stands under) reason."

(4) M. Dummett, The Logical Basis of Metaphysics, Harvard University Press, Cambridge, Massachusetts 1994.

(5) M. Dummett, ibid., p. 9.

(6) The principle of bivalence can be defined as the conjunction of the principle of contradiction (PC) and the principle of excluded middle (PEM). Given that PB is a principle in a two-valued semantics, it could be most literally defined as the principle that a proposition cannot be both true and false ("at the same time and in the same respect", if we add the qualifications of conditionality that Aristotle rightly considered to be necessary) and must be either true or false (what conditions might be necessary for the second statement in the conjunction I shall consider in a moment).

Dummett defines PB as "the principle that every proposition is determinately either true or false." I do not necessarily disagree with this definition: it could be read as synonymous with the compound proposition (PC · PEM) set out above. But it could also be read differently, and problematically, when it comes to the consideration of future contingent propositions. The problem lies in just how to understand the qualification 'determinately either true or false'. Dummett does not include a temporal qualification in this definition: and this is just where an apparently self-evident and commonly assumed semantic essentialism enters the picture, I think. Dummett seems to accept the conventional wisdom, in order to reject it, that a proposition must be determinately true or false at any moment in time whatsoever.

However, he does not directly address the question of the ontology of propositions, saying only that he will not commit himself to admitting propositions into our ontology. So one must ask, what could it mean for a proposition necessarily to be determinately true or false, even if contingently so, at any given moment in time whatsoever? I do not think it is possible to provide any kind of answer to this question without making clear just how its interpretation is to be supported by presuppositions about how the notion of a 'proposition' is supposed to be understood and how the notion of 'time' is supposed to be understood, and what determining relations hold between them. The point is that the relations between propositions and their various kinds of temporal contexts cannot be ignored: the concept of a 'proposition' is dependent upon and defined by the concept of 'time', at more than one level.

More completely, I think we would have to say that the concept of a 'proposition' is dependent upon and defined by some presuppositional 'theory' or 'ideology' concerning a spatiotemporal-causal continuum (or, to put it in a different vocabulary, the structural phenomenology of our sensory and ideational experience). But it will suffice to consider 'time' here; in any case, the concept of 'time' implicates and requires that of 'space', and implicates that of 'causation', in numerous ways.

It is significant, even if an obvious point, that Aristotle added the qualification "at the same time and in the same respect" to his definition of PC (and he also added a similar qualification to his explanation of propositions referring to sensory experience in order to annul relativist claims about contradiction): I shall refer to this, in general, as a spatiotemporal qualification; and I shall claim that it is necessary (and that Aristotle rightly intuited this necessity) because propositions are fundamentally spatiotemporal events (and this is to make no claims about their ontological status, of course, because nothing has been said nor will be said in this paper about a metaphysical definition of spatiotemporal events). It is a fundamental and unavoidable principle, as far as I can see, that propositions are events 'inscribed' into spacetime fabrics, and the spacetime fabrics into which they are inscribed, it is clear, need not be the spacetime fabrics to which their 'meanings' purport to refer.

Now, two crucial distinctions need to be delineated here if my argument in this paper (and it is only formative at this stage) is to make some sense. But first, I shall also claim that a proposition cannot be something other than the event of its 'meaning' at any given time (and this requires cognising subjects, of course). On this view, a presumed 'sentence' written in an indecipharable Martian script could not possibly be defined as a 'proposition'. It is a spatiotemporal event, to be sure, a 'material' event; but it is not an 'internal' semantic event of the cognitive kind about which we are thinking here. Now, the two distinctions:

(1) Already a distinction has just been suggested between the spacetime conditions in which a proposition is inscribed (stated and comprehended), and which support its actual occurrence, and the spacetime conditions to which the proposition, according to the logic of its sense, is understood to refer. In a future contingent proposition, for example, the proposition may be stated and comprehended at t(now), while it is comprehended as referring to t(tomorrow). This is a fairly obvious distinction, to be sure.

(2) The second distinction is the more difficult, more subtle, and probably much more controversial one. It depends upon an argument against any metaphysical definition of 'time'. 'Time', similarly to 'space' in a Leibnizian or Einsteinian view, is understood as a variable system of relations; however, these (spatiotemporal) relations are also understood to be 'conventional' in nature, and not 'metaphysical entities'. To be 'conventional', of course, implies that they are functions of some sentient creature's mode of cognition, and not empirically determinate features of an extra-cognitive reality (but one is advised to restrain oneself from making hasty inferences about Kantian views at this stage). On this understanding, then, the supporting spatiotemporal conditions (the context or fabric) within which a proposition arises (is inscribed) are ultimately conventional, in a manner that is cognate to the manner in which the proposition's 'sense' (the proposition as an event of 'meaning') is 'internally' conventional; that is, the manner in which the conventional logic and semantics that support the proposition as a 'present' event of meaning (at 't(now)') permit the proposition to refer to an 'event' at a 'future time' (at 't(tomorrow)'). On this account, the 'present moment' within which the proposition is inscribed, and the 'present meaning' of the proposition, are conventional cognitive constructs, just as much as is the semantic definition of the 'future event' to which the proposition purportedly refers. To put it another way: there is nothing metaphysically essential and given about the 'present moment' of the proposition's empirical context nor the 'present moment' of the proposition's 'meaning': both are, in every possible respect and detail, events that arise absolutely dependent upon complexes of conditions. That is why Aristotle, although of course he was far from seeing it in this manner, was quite right to define the principles of the logic of propositions such that they are, at the very first level, spatiotemporally bound. It is incoherent to do otherwise (Aristotle's empirical nose led him in the right direction on this count).

All this is not to deny that 'reality' is real; it is to argue that 'reality' may be real in a way very different to the way we conventionally think it to be real. That the nature of this situation may be indicated, tracked down, and fruitfully analysed precisely where we seem to encounter a logical aporia (such as in the case of future contingent propositions, non-referring propositions, and paradoxes) is one of the key assumptions with which I am working in an experimental paper such as the present one. The pragmatic-philosophical distinction elucidated by Mādhyamikas between 'conventional truth/reality' (saṃvṛti-satya) and the 'truth/reality of the highest meaning' (paramārtha-satya) is the real gist of the anti-metaphysical anti-realism that I have tried to sketch out in this paper; and I shall try to continue improving upon its formulation, because I am quite aware of its present lack of clarity and of various points of logical confusion and even error that need to be more carefully thought through.

(7) For the present, I have made use of J. Ackrill's translation, as quoted in D. Frede, 'The Sea-Battle Reconsidered', Oxford Studies in Ancient Philosophy Volume III, Clarendon Press, Oxford 1985, p. 75. The passage is from Aristotle, De Interpretatione 19a 32-39. I am not entirely comfortable with Ackrill's translation of Aristotle's unusually synoptic Greek, and I shall provide an alternative translation for comparison in the next draft of this paper. Nevertheless, I think that the point I wish to make can still be made on the basis of Ackrill's version. Frede's essay, by the way, is to be recommended.

(8) Just where such an essence is to be located is problematic for metaphysicians of this inclination. Is it to be found in a fundamental substance? Could it be found in 'matter', for example, however that may be defined? But the definition of matter is going to have to be the definition of its essence, isn't it? Let's say that a definition of 'matter' is proposed that is a set of mathematical formulae, and that the formulae are taken to constitute the definition of material essence. Will these formulae depend upon terms that are not defined as 'material essence' per se-such as various types of forces, and space and time? Quite probably. Then the definition of 'matter' is not definitionally essential.

Very well. Perhaps it is the complete mathematical description, inclusive of all its necessary terms, their interdependent definitions, and their functional relations, that constitutes the proper definition of real essence, or essential reality. In that case, the definition of essence comprises a set of axioms, rules of inference and transformation, and sets of arguments: in essence, then, it is a logic. But a logic is a tautological system; therefore it is a formal system empty of content. It does not refer outside of itself; it does not 'bring into itself' that which is extraneous to the system. We are back to the 'original' problem of grounding or relating the logic to the world of our experience: precisely the challenge to which Aristotle rises so admirably in Metaphysics, by indicating - not demonstrating, for as he admits, it is not possible to provide a demonstration of every axiomatic principle of a logic, for this would continue in a regressus ad infinitum - but indicating what he takes to be the surest and most self-evident first principles (arkhai) of 'classical' logic. The problem of the definition of essence, then, has not been resolved or explained, but merely deferred.

One can only presume that there is some kind of formal (= natural) correspondence between the logic and the reality; or, one could push the case to its limit and propose that the logic and the reality are, in some sense or at some level of description, one and the same thing (and there are a few contemporary physicists who are indeed thinking along these lines). Alternatively, of course, one could adopt a pragmatic or instrumental view of the logic: it works very well for certain human purposes, and that is all that there is to the matter, and all that really matters. From this viewpoint, it could be argued that the metaphysical questions and their attendant difficulties are not prior to the logic, but posterior to it. That is, they arise out of the semantic possibilities of the logical system, but the system does not require them or depend upon them for its internal consistency and operations.

This latter view might lead one to ask whether the logic, then, ought to be considered as 'conventional' or 'natural' (e.g., as an evolutionary development of the cognitive mode of a certain species). But already it is clear that this particular question is not very well formed because it does not demarcate a significant distinction between the notions 'conventional' and 'natural'. If the logic were indeed an evolutionary development in the cognitive mode of a certain species, then it could quite legitimately be described either as 'natural' or as 'conventional'. The question underlying the concern about whether the logic is 'natural' or 'conventional', however, is really the question about just what the relationship might be between the logic and the extra-logical reality (of which the logic is certainly a component feature), and, following from this, whether the logic can in any way be validated in relation to that extra-logical reality. This is a very interesting and problematic question. I would like to explore it much further in another paper.

(9) As we note in Metaphysics, Aristotle's reasoning led him along the line that undifferentiated matter (hulē) could not provide the essential substance of individual entities; he reasons that it is more likely to be their forms (eidē) that provide their essences (ousiai), their being per se. But how are their forms to be defined? The 'matter/form' dichotomy, as he recognises, is highly problematic, particularly for an empirically-inclined philosopher who desires to effect a deep philosophical break with the system of his teacher and predecessor. If one wishes to constrain one's metaphysics to the empirical domain, one has to find a coherent explanation for these empirical 'forms' that does not appeal to extra-empirical devices (such as platonic genera).

This, I think, is Aristotle's greatest challenge and the deepest problem of his theory. How can each of many entities also be one in itself? The answer must be, I think, that each entity just cannot be one in itself. There just is no such thing. The problem of the dichotomy between universals and particulars is to imagine that universals and particulars must in some sense really 'exist'; but there cannot be any sense in which universals and particulars really 'exist'. (Similarly, one of the logical difficulties of Plato's theory of forms (the 'third man' argument) arises from the presupposition that the forms must in some sense 'exist' and that in some way they are connected with empirical entities.) Problems with this conceptual dichotomy can only arise if we permit ourselves to assume that certain kinds of 'axiomatic' cognitive differentiations (such as the differentiations 'one/many' and 'identity/difference') have some kind of fundamental ('realist' and 'essentialist') ontological basis.

(10) I need to make a careful distinction here, however. Dummett uses the term 'semantic realism' in a sense that is specific for his argument: he uses the term to sum up his claim that to hold to PB is to commit oneself to a truth-conditional theory of meaning (TCTM), and that to commit oneself to a TCTM is to commit oneself to an untenable form of realism about the extra-linguistic universe. Hence, 'semantic realism'. I do not agree with this argument: with a very specific modification to the infrastructure of one's presuppositions (namely, the omission of the 'axiom' of essence or substance), it becomes quite coherent to hold to PB and yet not to commit oneself to an untenable form of realism. It may still be the case that PB commits one to a TCTM; but a TCTM can now be understood to operate not 'realistically' (such that 'truth' is somehow linked to (a real 'fact' marking) an existing state of affairs in an extra-linguistic domain) but just conventionally (such that the definition and function of 'truth' remains entirely within the linguistic-logical system and serves to generate, to discriminate, and to evaluate meanings within that system).

(11) The following paragraphs from Wittgenstein's Tractatus provide a thoughtful if not exactly precise consonance with the present line of argument:

5.135 There is no possible way of making an inference from the existence of one situation to the existence of another, entirely different situation.

5.136 There is no causal nexus to justify such an inference.

5.1361 We cannot infer the events of the future from those of the present. Superstition is nothing but belief in the causal nexus.

5.1362 The freedom of the will consists in the impossibility of knowing actions that still lie in the future. We could know them only if causality were an inner necessity like that of logical inference.-The connexion between knowledge and what is known is that of logical necessity.

('A knows that p is the case', has no sense if p is a tautology.)

L. Wittgenstein, Tractatus Logico-Philosophicus (German text with translation by D. F. Pears and B. F. McGuinness), Routledge & Kegan Paul, London, 1974, pp. 77-79. Unfortunately, I do not now have the opportunity to provide a commentary here that would explain in detail just why I find these statements of relevance to the argument of this present paper, and in just what ways I think them to differ from that argument.

(12) The following observation of Quine's (of which I am particularly fond) is very pertinent in this context: "Things had essences, for Aristotle, but only linguistic forms have meanings. Meaning is what essence becomes when it is divorced from the object of reference and wedded to the word." Willard van Orman Quine, 'Two Dogmas of Empiricism', in From a Logical Point of View, Harvard University Press, Cambridge, Massachusetts 1953, p. 22. Conversely, and in precise complementarity, I would propose that in the context of the present analysis the following formula requires to be conjoined with Quine's: 'Essence is what meaning becomes when it is divorced from the word and wedded to the object of reference.'

(13) The implication here would be that this further semantic condition, the 'truth-making' condition, is not a necessary condition for the generation of the 'meaning' of a proposition. As I develop this argument at a later opportunity, I shall attempt to discuss this interesting implication in more detail.

(14) I am working on two other separate papers which, along with this present paper, constitute a kind of triad on the topic of language and reality. One of these papers examines major accounts of negation in twentieth-century Western philosophy and compares these with two forms of negation operating in the logic of Nāgārjuna's texts and in later Madhyamaka philosophy. In that second paper I also explore the question of apparently logically-anomalous cases such as non-referring and paradoxical propositions. The final paper makes explicit the theoretical underpinnings of the other two papers, particularly my implementation of Nāgārjuna's methodology and its motivation.

(15) This is not to leave Michael Dummett out of the picture, of course. There can be no doubt that he too is a truly great philosopher, and, like Aristotle and Nāgārjuna, not always an easy one to understand!

First posted 2-9-1999, reformatted 4-6-2012

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